Used Car Price Predictions
Daniel Chang, Vo Nguyen, & Akib Hossain
2023-01-30
Link to Presentation Video: https://www.youtube.com/watch?v=KSOq29tFUoQ&ab_channel=DannyChang
#Needed Packages
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.3.6 ✔ purrr 0.3.4
## ✔ tibble 3.1.8 ✔ dplyr 1.0.9
## ✔ tidyr 1.2.0 ✔ stringr 1.4.0
## ✔ readr 2.1.2 ✔ forcats 0.5.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
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## ✖ dplyr::lag() masks stats::lag()library(caret)## Loading required package: lattice
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## Attaching package: 'caret'
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## The following object is masked from 'package:purrr':
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## liftlibrary(naniar)
library(stringr)
library(ggplot2)
library(dplyr)
library(reshape2)##
## Attaching package: 'reshape2'
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## The following object is masked from 'package:tidyr':
##
## smiths#Load Data
car_details = read.csv("Car details v3.csv", header = T, stringsAsFactors = T)Exploratory Data Analysis 1
Viewing Dataset
We first take a look at our dataset. There are a total 221 nulls in current dataset that we are going to omit. There are a total of 8128 rows and 13 columns.
During our data wrangling process, we are going to be seperating the
name column to create a brand column. We will
also clean up the engine, max_power, and
mileage columns to extract the numbers and make the them
numeric variables. Lastly, we only want the first word in the
owner column.
## name year selling_price km_driven fuel seller_type
## 1 Maruti Swift Dzire VDI 2014 450000 145500 Diesel Individual
## 2 Skoda Rapid 1.5 TDI Ambition 2014 370000 120000 Diesel Individual
## 3 Honda City 2017-2020 EXi 2006 158000 140000 Petrol Individual
## 4 Hyundai i20 Sportz Diesel 2010 225000 127000 Diesel Individual
## 5 Maruti Swift VXI BSIII 2007 130000 120000 Petrol Individual
## 6 Hyundai Xcent 1.2 VTVT E Plus 2017 440000 45000 Petrol Individual
## transmission owner mileage engine max_power
## 1 Manual First Owner 23.4 kmpl 1248 CC 74 bhp
## 2 Manual Second Owner 21.14 kmpl 1498 CC 103.52 bhp
## 3 Manual Third Owner 17.7 kmpl 1497 CC 78 bhp
## 4 Manual First Owner 23.0 kmpl 1396 CC 90 bhp
## 5 Manual First Owner 16.1 kmpl 1298 CC 88.2 bhp
## 6 Manual First Owner 20.14 kmpl 1197 CC 81.86 bhp
## torque seats
## 1 190Nm@ 2000rpm 5
## 2 250Nm@ 1500-2500rpm 5
## 3 12.7@ 2,700(kgm@ rpm) 5
## 4 22.4 kgm at 1750-2750rpm 5
## 5 11.5@ 4,500(kgm@ rpm) 5
## 6 113.75nm@ 4000rpm 5## [1] 8128 13## Warning: `gather_()` was deprecated in tidyr 1.2.0.
## Please use `gather()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.
## [1] 221## name year selling_price km_driven fuel seller_type
## 1 Maruti Swift Dzire VDI 2014 450000 145500 Diesel Individual
## 2 Skoda Rapid 1.5 TDI Ambition 2014 370000 120000 Diesel Individual
## 3 Honda City 2017-2020 EXi 2006 158000 140000 Petrol Individual
## 4 Hyundai i20 Sportz Diesel 2010 225000 127000 Diesel Individual
## 5 Maruti Swift VXI BSIII 2007 130000 120000 Petrol Individual
## 6 Hyundai Xcent 1.2 VTVT E Plus 2017 440000 45000 Petrol Individual
## transmission owner mileage engine max_power
## 1 Manual First Owner 23.4 kmpl 1248 CC 74 bhp
## 2 Manual Second Owner 21.14 kmpl 1498 CC 103.52 bhp
## 3 Manual Third Owner 17.7 kmpl 1497 CC 78 bhp
## 4 Manual First Owner 23.0 kmpl 1396 CC 90 bhp
## 5 Manual First Owner 16.1 kmpl 1298 CC 88.2 bhp
## 6 Manual First Owner 20.14 kmpl 1197 CC 81.86 bhp
## torque seats
## 1 190Nm@ 2000rpm 5
## 2 250Nm@ 1500-2500rpm 5
## 3 12.7@ 2,700(kgm@ rpm) 5
## 4 22.4 kgm at 1750-2750rpm 5
## 5 11.5@ 4,500(kgm@ rpm) 5
## 6 113.75nm@ 4000rpm 5## [1] 0Visualizations
Looking through our visualizations, we find that our mean selling price increases year after year and our graph seems to resemble an exponential curve, if we do not take into account our last year(2020). This can also be seen in our boxplot where the median price per year gets higher and higher. There are many outliers every year as well.
When do a fuel count, we find that petrol and diesel have the highest count. After that we want to do a brand count, Maruti, Hyuandai, Mahindra, Tata and Honda are the brands that appear the most.
When we create a histogram of mileage, we find that the distribution is normal. For our engine plot, we find that the engine around 1100 has the highest count. Next, we find that the distribution of kilometers driven is heavily right-skewed. When we look for the top 5 names/makes, we find that Swift Dzire VDI(highest count), Alto 800 LXI, Alto LXi, Swift VDI and X4 M Sport X have the highest count of all.
Creating a scatterplot with a logged selling price and max power, we find that there is a positive relationship between the two. When we take a look at our boxplot, we find that those with one owner commands the highest selling price with those cars that have been owned. However, if we factor in the test(no previous owners), that would be the highest.
When we take a look at the different types of sellers, we find that there are dealers have the widest range and median out of all, but we see that for individual sellers there are quite a number of outliers.
When looking at the correlation map for the numeric variables, we find that max power, year and engine are strongly or moderately correlated(positive) with selling price.
## Objective 1 Problem Statement: We are through a process of comparing
multiple models using linear regressio. One model does not consists of
any logged variables and the other model, we log the response variable.
The goal is to see if altering the variable is necessary or produce a
better model and address the assumptions correctly.
Model 1: No Transformation : We will not log anything in this model and see if it meets the necessary assumptions.
Model 2: Log-Linear Transformation with Interactions: We log the response variable(selling price) to see if the assumptions have been met. If the assumptions are met, we will use this model as our base which we will improve on.
##
## Call:
## lm(formula = selling_price ~ year + km_driven + fuel + seller_type +
## transmission + owner + mileage + engine + max_power + seats +
## brand, data = car_details)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3301768 -103494 -10999 84871 5589889
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.897e+07 2.714e+06 -32.775 < 2e-16 ***
## year 4.439e+04 1.357e+03 32.714 < 2e-16 ***
## km_driven -6.272e-01 7.495e-02 -8.368 < 2e-16 ***
## fuelDiesel 1.363e+05 4.425e+04 3.080 0.00207 **
## fuelLPG 1.536e+05 6.898e+04 2.227 0.02599 *
## fuelPetrol 4.369e+04 4.447e+04 0.982 0.32592
## seller_typeIndividual -5.582e+04 1.167e+04 -4.784 1.75e-06 ***
## seller_typeTrustmark Dealer -7.401e+04 2.433e+04 -3.042 0.00236 **
## transmissionManual -9.658e+04 1.460e+04 -6.616 3.93e-11 ***
## ownerFourth -2.156e+04 2.627e+04 -0.821 0.41180
## ownerSecond -5.874e+04 9.150e+03 -6.419 1.45e-10 ***
## ownerTest 2.465e+06 1.435e+05 17.181 < 2e-16 ***
## ownerThird -3.504e+04 1.572e+04 -2.229 0.02582 *
## mileage -3.576e+03 1.626e+03 -2.200 0.02785 *
## engine 4.968e+01 1.856e+01 2.676 0.00746 **
## max_power 6.261e+03 2.066e+02 30.308 < 2e-16 ***
## seats -5.189e+03 6.057e+03 -0.857 0.39161
## brandAshok -3.194e+05 3.507e+05 -0.911 0.36251
## brandAudi 6.639e+05 1.666e+05 3.985 6.80e-05 ***
## brandBMW 2.257e+06 1.616e+05 13.965 < 2e-16 ***
## brandChevrolet -4.409e+05 1.587e+05 -2.778 0.00548 **
## brandDaewoo 1.292e+05 2.399e+05 0.538 0.59034
## brandDatsun -4.761e+05 1.626e+05 -2.928 0.00342 **
## brandFiat -4.403e+05 1.647e+05 -2.673 0.00753 **
## brandForce -3.574e+05 2.027e+05 -1.764 0.07784 .
## brandFord -3.698e+05 1.581e+05 -2.339 0.01934 *
## brandHonda -3.712e+05 1.583e+05 -2.345 0.01907 *
## brandHyundai -3.636e+05 1.577e+05 -2.305 0.02117 *
## brandIsuzu 2.384e+05 2.109e+05 1.130 0.25833
## brandJaguar 1.086e+06 1.630e+05 6.660 2.92e-11 ***
## brandJeep 3.761e+05 1.683e+05 2.234 0.02551 *
## brandKia 5.562e+04 2.222e+05 0.250 0.80233
## brandLand 1.977e+06 2.034e+05 9.718 < 2e-16 ***
## brandLexus 3.101e+06 1.697e+05 18.270 < 2e-16 ***
## brandMahindra -3.541e+05 1.577e+05 -2.245 0.02481 *
## brandMaruti -2.767e+05 1.577e+05 -1.755 0.07931 .
## brandMercedes-Benz 7.917e+05 1.640e+05 4.827 1.41e-06 ***
## brandMG 1.966e+05 2.405e+05 0.817 0.41377
## brandMitsubishi -8.852e+04 1.780e+05 -0.497 0.61890
## brandNissan -3.938e+05 1.611e+05 -2.445 0.01449 *
## brandOpel 6.738e+04 3.500e+05 0.192 0.84737
## brandRenault -3.877e+05 1.590e+05 -2.438 0.01478 *
## brandSkoda -4.038e+05 1.603e+05 -2.520 0.01177 *
## brandTata -4.726e+05 1.577e+05 -2.998 0.00273 **
## brandToyota -5.227e+04 1.581e+05 -0.331 0.74086
## brandVolkswagen -4.581e+05 1.590e+05 -2.881 0.00397 **
## brandVolvo 1.442e+06 1.631e+05 8.838 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 312600 on 7859 degrees of freedom
## Multiple R-squared: 0.8532, Adjusted R-squared: 0.8524
## F-statistic: 993.2 on 46 and 7859 DF, p-value: < 2.2e-16## Warning: not plotting observations with leverage one:
## 4246## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
##
## Call:
## lm(formula = log(selling_price) ~ year + km_driven + fuel + seller_type +
## transmission + owner + mileage + engine + max_power + seats +
## brand, data = car_details)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.31555 -0.14306 0.01039 0.15886 2.05831
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.205e+02 2.123e+00 -103.860 < 2e-16 ***
## year 1.154e-01 1.061e-03 108.734 < 2e-16 ***
## km_driven -3.122e-07 5.861e-08 -5.327 1.03e-07 ***
## fuelDiesel 3.507e-01 3.460e-02 10.137 < 2e-16 ***
## fuelLPG 2.027e-01 5.394e-02 3.757 0.000173 ***
## fuelPetrol 1.203e-01 3.478e-02 3.459 0.000544 ***
## seller_typeIndividual -3.715e-02 9.123e-03 -4.073 4.69e-05 ***
## seller_typeTrustmark Dealer -1.594e-02 1.902e-02 -0.838 0.402090
## transmissionManual -6.717e-02 1.142e-02 -5.885 4.15e-09 ***
## ownerFourth -1.485e-01 2.054e-02 -7.229 5.33e-13 ***
## ownerSecond -8.387e-02 7.155e-03 -11.722 < 2e-16 ***
## ownerTest 6.578e-01 1.122e-01 5.863 4.72e-09 ***
## ownerThird -1.172e-01 1.229e-02 -9.536 < 2e-16 ***
## mileage 8.736e-05 1.271e-03 0.069 0.945213
## engine 2.021e-04 1.452e-05 13.921 < 2e-16 ***
## max_power 8.239e-03 1.615e-04 51.007 < 2e-16 ***
## seats 3.594e-02 4.736e-03 7.590 3.57e-14 ***
## brandAshok -4.826e-01 2.742e-01 -1.760 0.078475 .
## brandAudi 7.894e-02 1.303e-01 0.606 0.544493
## brandBMW 3.173e-01 1.264e-01 2.511 0.012071 *
## brandChevrolet -5.955e-01 1.241e-01 -4.799 1.62e-06 ***
## brandDaewoo 9.681e-02 1.876e-01 0.516 0.605883
## brandDatsun -5.784e-01 1.271e-01 -4.549 5.47e-06 ***
## brandFiat -4.383e-01 1.288e-01 -3.403 0.000670 ***
## brandForce -4.509e-01 1.585e-01 -2.845 0.004454 **
## brandFord -3.300e-01 1.236e-01 -2.670 0.007592 **
## brandHonda -1.731e-01 1.238e-01 -1.398 0.162160
## brandHyundai -2.324e-01 1.233e-01 -1.884 0.059593 .
## brandIsuzu -3.205e-01 1.649e-01 -1.944 0.051948 .
## brandJaguar 2.165e-01 1.275e-01 1.698 0.089458 .
## brandJeep -1.804e-01 1.316e-01 -1.370 0.170582
## brandKia -1.315e-01 1.737e-01 -0.757 0.449281
## brandLand 5.761e-01 1.590e-01 3.622 0.000294 ***
## brandLexus 4.052e-01 1.327e-01 3.053 0.002276 **
## brandMahindra -3.672e-01 1.233e-01 -2.977 0.002919 **
## brandMaruti -1.859e-01 1.233e-01 -1.508 0.131677
## brandMercedes-Benz 2.041e-01 1.283e-01 1.591 0.111570
## brandMG 1.183e-01 1.880e-01 0.629 0.529187
## brandMitsubishi -6.320e-02 1.392e-01 -0.454 0.649744
## brandNissan -2.724e-01 1.259e-01 -2.163 0.030580 *
## brandOpel 6.364e-02 2.737e-01 0.233 0.816148
## brandRenault -3.214e-01 1.243e-01 -2.585 0.009765 **
## brandSkoda -2.678e-01 1.253e-01 -2.137 0.032611 *
## brandTata -6.580e-01 1.233e-01 -5.337 9.71e-08 ***
## brandToyota -1.346e-02 1.236e-01 -0.109 0.913289
## brandVolkswagen -3.052e-01 1.243e-01 -2.455 0.014125 *
## brandVolvo 2.033e-01 1.276e-01 1.594 0.111038
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2444 on 7859 degrees of freedom
## Multiple R-squared: 0.9133, Adjusted R-squared: 0.9128
## F-statistic: 1799 on 46 and 7859 DF, p-value: < 2.2e-16## Warning: not plotting observations with leverage one:
## 4246
## Warning: NaNs produced
## Warning: NaNs produced
#Check for Multicollinearity
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recode## The following object is masked from 'package:purrr':
##
## somevif(model2)## GVIF Df GVIF^(1/(2*Df))
## year 2.223523 1 1.491148
## km_driven 1.465653 1 1.210641
## fuel 2.763542 3 1.184616
## seller_type 1.588551 2 1.122665
## transmission 1.971307 1 1.404032
## owner 1.512754 4 1.053103
## mileage 3.480106 1 1.865504
## engine 7.077703 1 2.660395
## max_power 4.410666 1 2.100159
## seats 2.730299 1 1.652362
## brand 13.966946 30 1.044925#OLSRR
set.seed(1234)
library(olsrr)##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riversforward = ols_step_forward_p(model2,prem = .05,details=TRUE)## Forward Selection Method
## ---------------------------
##
## Candidate Terms:
##
## 1. year
## 2. km_driven
## 3. fuel
## 4. seller_type
## 5. transmission
## 6. owner
## 7. mileage
## 8. engine
## 9. max_power
## 10. seats
## 11. brand
##
## We are selecting variables based on p value...
##
##
## Forward Selection: Step 1
##
## - brand
##
## Model Summary
## -------------------------------------------------------------
## R 0.948 RMSE 0.265
## R-Squared 0.898 Coef. Var 2.035
## Adj. R-Squared 0.898 MSE 0.070
## Pred R-Squared 0.897 MAE 0.203
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4863.728 34 143.051 2044.083 0.0000
## Residual 550.835 7871 0.070
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -244.074 1.697 -143.845 0.000 -247.400 -240.748
## year 0.127 0.001 0.594 150.962 0.000 0.126 0.129
## transmissionManual 0.004 0.012 0.002 0.353 0.724 -0.019 0.027
## engine 0.000 0.000 0.227 30.510 0.000 0.000 0.000
## max_power 0.008 0.000 0.345 46.463 0.000 0.008 0.008
## brandAshok -0.449 0.296 -0.006 -1.519 0.129 -1.030 0.131
## brandAudi 0.117 0.141 0.010 0.832 0.405 -0.159 0.392
## brandBMW 0.334 0.137 0.049 2.448 0.014 0.067 0.602
## brandChevrolet -0.643 0.134 -0.131 -4.802 0.000 -0.906 -0.381
## brandDaewoo 0.170 0.203 0.004 0.841 0.400 -0.227 0.567
## brandDatsun -0.724 0.137 -0.079 -5.279 0.000 -0.992 -0.455
## brandFiat -0.434 0.139 -0.038 -3.114 0.002 -0.706 -0.161
## brandForce -0.569 0.171 -0.019 -3.320 0.001 -0.905 -0.233
## brandFord -0.371 0.134 -0.097 -2.781 0.005 -0.633 -0.110
## brandHonda -0.285 0.134 -0.081 -2.130 0.033 -0.547 -0.023
## brandHyundai -0.323 0.133 -0.147 -2.425 0.015 -0.584 -0.062
## brandIsuzu -0.406 0.178 -0.012 -2.277 0.023 -0.756 -0.056
## brandJaguar 0.263 0.138 0.030 1.910 0.056 -0.007 0.533
## brandJeep -0.325 0.142 -0.025 -2.286 0.022 -0.604 -0.046
## brandKia -0.063 0.188 -0.002 -0.337 0.736 -0.432 0.305
## brandLand 0.635 0.172 0.021 3.698 0.000 0.298 0.972
## brandLexus 0.138 0.142 0.011 0.971 0.331 -0.140 0.416
## brandMahindra -0.403 0.133 -0.143 -3.028 0.002 -0.664 -0.142
## brandMaruti -0.249 0.133 -0.138 -1.871 0.061 -0.510 0.012
## brandMercedes-Benz 0.133 0.139 0.013 0.962 0.336 -0.138 0.405
## brandMG 0.008 0.203 0.000 0.038 0.970 -0.391 0.406
## brandMitsubishi -0.128 0.150 -0.007 -0.852 0.394 -0.423 0.167
## brandNissan -0.340 0.136 -0.041 -2.499 0.012 -0.607 -0.073
## brandOpel -0.093 0.296 -0.001 -0.316 0.752 -0.673 0.487
## brandRenault -0.374 0.134 -0.076 -2.790 0.005 -0.638 -0.111
## brandSkoda -0.327 0.135 -0.045 -2.417 0.016 -0.593 -0.062
## brandTata -0.692 0.133 -0.240 -5.197 0.000 -0.953 -0.431
## brandToyota -0.125 0.133 -0.035 -0.935 0.350 -0.386 0.137
## brandVolkswagen -0.348 0.134 -0.063 -2.587 0.010 -0.611 -0.084
## brandVolvo 0.229 0.138 0.025 1.662 0.096 -0.041 0.500
## -------------------------------------------------------------------------------------------------------
##
##
##
## Forward Selection: Step 2
##
## - fuel
##
## Model Summary
## -------------------------------------------------------------
## R 0.954 RMSE 0.250
## R-Squared 0.909 Coef. Var 1.923
## Adj. R-Squared 0.909 MSE 0.062
## Pred R-Squared 0.908 MAE 0.190
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4922.980 37 133.054 2129.579 0.0000
## Residual 491.583 7868 0.062
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -239.173 1.621 -147.515 0.000 -242.351 -235.994
## year 0.125 0.001 0.582 155.186 0.000 0.123 0.126
## transmissionManual -0.071 0.011 -0.029 -6.224 0.000 -0.093 -0.049
## engine 0.000 0.000 0.148 19.541 0.000 0.000 0.000
## max_power 0.008 0.000 0.350 49.835 0.000 0.008 0.008
## brandAshok -0.480 0.280 -0.007 -1.718 0.086 -1.029 0.068
## brandAudi 0.122 0.133 0.010 0.918 0.359 -0.138 0.382
## brandBMW 0.313 0.129 0.046 2.425 0.015 0.060 0.566
## brandChevrolet -0.595 0.127 -0.121 -4.700 0.000 -0.843 -0.347
## brandDaewoo 0.239 0.191 0.006 1.251 0.211 -0.136 0.615
## brandDatsun -0.578 0.130 -0.063 -4.462 0.000 -0.832 -0.324
## brandFiat -0.452 0.132 -0.039 -3.433 0.001 -0.709 -0.194
## brandForce -0.469 0.162 -0.016 -2.898 0.004 -0.787 -0.152
## brandFord -0.346 0.126 -0.090 -2.739 0.006 -0.593 -0.098
## brandHonda -0.181 0.126 -0.051 -1.430 0.153 -0.428 0.067
## brandHyundai -0.251 0.126 -0.115 -1.995 0.046 -0.498 -0.004
## brandIsuzu -0.333 0.169 -0.010 -1.974 0.048 -0.663 -0.002
## brandJaguar 0.232 0.130 0.026 1.780 0.075 -0.024 0.487
## brandJeep -0.213 0.135 -0.016 -1.580 0.114 -0.476 0.051
## brandKia -0.135 0.178 -0.004 -0.761 0.447 -0.483 0.213
## brandLand 0.608 0.162 0.020 3.747 0.000 0.290 0.926
## brandLexus 0.380 0.134 0.030 2.824 0.005 0.116 0.643
## brandMahindra -0.345 0.126 -0.123 -2.747 0.006 -0.592 -0.099
## brandMaruti -0.190 0.126 -0.105 -1.512 0.131 -0.437 0.056
## brandMercedes-Benz 0.185 0.131 0.018 1.409 0.159 -0.072 0.442
## brandMG 0.123 0.192 0.003 0.643 0.520 -0.253 0.500
## brandMitsubishi -0.065 0.142 -0.003 -0.461 0.645 -0.344 0.213
## brandNissan -0.296 0.129 -0.036 -2.306 0.021 -0.549 -0.044
## brandOpel 0.072 0.280 0.001 0.258 0.796 -0.476 0.620
## brandRenault -0.328 0.127 -0.066 -2.586 0.010 -0.577 -0.079
## brandSkoda -0.280 0.128 -0.039 -2.190 0.029 -0.531 -0.029
## brandTata -0.663 0.126 -0.230 -5.268 0.000 -0.910 -0.416
## brandToyota -0.016 0.126 -0.004 -0.124 0.901 -0.263 0.231
## brandVolkswagen -0.328 0.127 -0.060 -2.584 0.010 -0.577 -0.079
## brandVolvo 0.195 0.130 0.022 1.492 0.136 -0.061 0.450
## fuelDiesel 0.368 0.035 0.222 10.422 0.000 0.299 0.437
## fuelLPG 0.232 0.055 0.019 4.234 0.000 0.125 0.340
## fuelPetrol 0.152 0.035 0.091 4.324 0.000 0.083 0.221
## -------------------------------------------------------------------------------------------------------
##
##
##
## Forward Selection: Step 3
##
## - owner
##
## Model Summary
## -------------------------------------------------------------
## R 0.955 RMSE 0.246
## R-Squared 0.912 Coef. Var 1.892
## Adj. R-Squared 0.912 MSE 0.061
## Pred R-Squared 0.911 MAE 0.187
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4938.715 41 120.456 1990.699 0.0000
## Residual 475.848 7864 0.061
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -225.836 1.822 -123.926 0.000 -229.408 -222.264
## year 0.118 0.001 0.551 130.738 0.000 0.116 0.120
## transmissionManual -0.068 0.011 -0.028 -6.044 0.000 -0.090 -0.046
## engine 0.000 0.000 0.149 20.042 0.000 0.000 0.000
## max_power 0.008 0.000 0.350 50.571 0.000 0.008 0.008
## brandAshok -0.418 0.275 -0.006 -1.520 0.128 -0.958 0.121
## brandAudi 0.084 0.131 0.007 0.640 0.522 -0.173 0.340
## brandBMW 0.326 0.127 0.048 2.570 0.010 0.077 0.575
## brandChevrolet -0.573 0.125 -0.116 -4.597 0.000 -0.817 -0.328
## brandDaewoo 0.136 0.188 0.003 0.721 0.471 -0.234 0.505
## brandDatsun -0.561 0.128 -0.061 -4.394 0.000 -0.811 -0.311
## brandFiat -0.439 0.129 -0.038 -3.388 0.001 -0.692 -0.185
## brandForce -0.441 0.159 -0.015 -2.765 0.006 -0.753 -0.128
## brandFord -0.330 0.124 -0.086 -2.660 0.008 -0.574 -0.087
## brandHonda -0.168 0.124 -0.048 -1.351 0.177 -0.412 0.076
## brandHyundai -0.231 0.124 -0.105 -1.866 0.062 -0.474 0.012
## brandIsuzu -0.327 0.166 -0.010 -1.974 0.048 -0.653 -0.002
## brandJaguar 0.232 0.128 0.026 1.812 0.070 -0.019 0.483
## brandJeep -0.205 0.132 -0.015 -1.546 0.122 -0.464 0.055
## brandKia -0.118 0.175 -0.003 -0.673 0.501 -0.460 0.225
## brandLand 0.630 0.160 0.021 3.941 0.000 0.316 0.943
## brandLexus 0.400 0.132 0.032 3.024 0.003 0.141 0.660
## brandMahindra -0.332 0.124 -0.118 -2.684 0.007 -0.575 -0.090
## brandMaruti -0.173 0.124 -0.096 -1.399 0.162 -0.416 0.070
## brandMercedes-Benz 0.197 0.129 0.020 1.528 0.127 -0.056 0.450
## brandMG 0.148 0.189 0.003 0.782 0.434 -0.223 0.518
## brandMitsubishi -0.065 0.140 -0.003 -0.466 0.641 -0.339 0.209
## brandNissan -0.279 0.127 -0.034 -2.208 0.027 -0.527 -0.031
## brandOpel 0.076 0.275 0.001 0.278 0.781 -0.463 0.616
## brandRenault -0.313 0.125 -0.063 -2.504 0.012 -0.557 -0.068
## brandSkoda -0.266 0.126 -0.037 -2.111 0.035 -0.513 -0.019
## brandTata -0.652 0.124 -0.227 -5.264 0.000 -0.895 -0.409
## brandToyota 0.000 0.124 0.000 0.001 0.999 -0.243 0.243
## brandVolkswagen -0.308 0.125 -0.056 -2.467 0.014 -0.553 -0.063
## brandVolvo 0.206 0.128 0.023 1.602 0.109 -0.046 0.457
## fuelDiesel 0.362 0.035 0.218 10.400 0.000 0.293 0.430
## fuelLPG 0.217 0.054 0.017 4.010 0.000 0.111 0.323
## fuelPetrol 0.139 0.035 0.083 4.004 0.000 0.071 0.207
## ownerFourth -0.152 0.021 -0.026 -7.368 0.000 -0.193 -0.112
## ownerSecond -0.090 0.007 -0.047 -12.619 0.000 -0.104 -0.076
## ownerTest 0.677 0.113 0.021 6.002 0.000 0.456 0.898
## ownerThird -0.125 0.012 -0.037 -10.154 0.000 -0.149 -0.101
## -------------------------------------------------------------------------------------------------------
##
##
##
## Forward Selection: Step 4
##
## - seats
##
## Model Summary
## -------------------------------------------------------------
## R 0.955 RMSE 0.245
## R-Squared 0.913 Coef. Var 1.886
## Adj. R-Squared 0.912 MSE 0.060
## Pred R-Squared 0.911 MAE 0.186
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4942.068 42 117.668 1958.171 0.0000
## Residual 472.495 7863 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -224.513 1.825 -123.044 0.000 -228.090 -220.936
## year 0.117 0.001 0.548 129.721 0.000 0.116 0.119
## transmissionManual -0.076 0.011 -0.031 -6.754 0.000 -0.098 -0.054
## engine 0.000 0.000 0.120 14.463 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.284 0.000 0.008 0.009
## brandAshok -0.536 0.275 -0.007 -1.951 0.051 -1.075 0.002
## brandAudi 0.066 0.131 0.006 0.509 0.611 -0.189 0.322
## brandBMW 0.319 0.127 0.047 2.518 0.012 0.071 0.567
## brandChevrolet -0.620 0.124 -0.126 -4.985 0.000 -0.863 -0.376
## brandDaewoo 0.083 0.188 0.002 0.443 0.658 -0.285 0.452
## brandDatsun -0.605 0.127 -0.066 -4.750 0.000 -0.854 -0.355
## brandFiat -0.466 0.129 -0.040 -3.610 0.000 -0.719 -0.213
## brandForce -0.460 0.159 -0.015 -2.896 0.004 -0.771 -0.149
## brandFord -0.351 0.124 -0.092 -2.833 0.005 -0.594 -0.108
## brandHonda -0.193 0.124 -0.055 -1.561 0.118 -0.436 0.049
## brandHyundai -0.258 0.124 -0.118 -2.088 0.037 -0.500 -0.016
## brandIsuzu -0.342 0.165 -0.010 -2.069 0.039 -0.666 -0.018
## brandJaguar 0.222 0.128 0.025 1.740 0.082 -0.028 0.472
## brandJeep -0.204 0.132 -0.015 -1.547 0.122 -0.463 0.054
## brandKia -0.140 0.174 -0.004 -0.803 0.422 -0.481 0.202
## brandLand 0.580 0.159 0.019 3.638 0.000 0.267 0.892
## brandLexus 0.407 0.132 0.032 3.085 0.002 0.148 0.665
## brandMahindra -0.391 0.124 -0.139 -3.164 0.002 -0.633 -0.149
## brandMaruti -0.210 0.123 -0.116 -1.700 0.089 -0.452 0.032
## brandMercedes-Benz 0.193 0.129 0.019 1.505 0.132 -0.059 0.445
## brandMG 0.118 0.188 0.003 0.624 0.532 -0.252 0.487
## brandMitsubishi -0.089 0.139 -0.005 -0.637 0.524 -0.362 0.184
## brandNissan -0.299 0.126 -0.036 -2.371 0.018 -0.546 -0.052
## brandOpel 0.057 0.274 0.001 0.207 0.836 -0.481 0.595
## brandRenault -0.349 0.124 -0.070 -2.800 0.005 -0.593 -0.105
## brandSkoda -0.284 0.126 -0.039 -2.260 0.024 -0.530 -0.038
## brandTata -0.684 0.124 -0.238 -5.542 0.000 -0.927 -0.442
## brandToyota -0.036 0.124 -0.010 -0.293 0.770 -0.279 0.206
## brandVolkswagen -0.329 0.125 -0.060 -2.638 0.008 -0.573 -0.084
## brandVolvo 0.194 0.128 0.022 1.518 0.129 -0.057 0.445
## fuelDiesel 0.354 0.035 0.213 10.218 0.000 0.286 0.422
## fuelLPG 0.207 0.054 0.017 3.846 0.000 0.102 0.313
## fuelPetrol 0.131 0.035 0.079 3.796 0.000 0.063 0.199
## ownerFourth -0.155 0.021 -0.026 -7.524 0.000 -0.195 -0.114
## ownerSecond -0.090 0.007 -0.047 -12.692 0.000 -0.104 -0.076
## ownerTest 0.678 0.112 0.021 6.031 0.000 0.457 0.898
## ownerThird -0.126 0.012 -0.037 -10.250 0.000 -0.150 -0.102
## seats 0.034 0.005 0.039 7.470 0.000 0.025 0.043
## -------------------------------------------------------------------------------------------------------
##
##
##
## Forward Selection: Step 5
##
## - km_driven
##
## Model Summary
## -------------------------------------------------------------
## R 0.956 RMSE 0.245
## R-Squared 0.913 Coef. Var 1.882
## Adj. R-Squared 0.913 MSE 0.060
## Pred R-Squared 0.911 MAE 0.186
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4943.970 43 114.976 1920.856 0.0000
## Residual 470.593 7862 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -220.928 1.929 -114.534 0.000 -224.710 -217.147
## year 0.116 0.001 0.540 120.770 0.000 0.114 0.117
## transmissionManual -0.073 0.011 -0.030 -6.519 0.000 -0.095 -0.051
## engine 0.000 0.000 0.123 14.757 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.319 0.000 0.008 0.009
## brandAshok -0.481 0.274 -0.007 -1.752 0.080 -1.018 0.057
## brandAudi 0.086 0.130 0.007 0.660 0.509 -0.169 0.341
## brandBMW 0.333 0.126 0.049 2.638 0.008 0.086 0.581
## brandChevrolet -0.597 0.124 -0.121 -4.806 0.000 -0.840 -0.353
## brandDaewoo 0.095 0.188 0.002 0.508 0.611 -0.272 0.463
## brandDatsun -0.579 0.127 -0.063 -4.558 0.000 -0.829 -0.330
## brandFiat -0.441 0.129 -0.038 -3.423 0.001 -0.694 -0.188
## brandForce -0.443 0.159 -0.015 -2.797 0.005 -0.754 -0.133
## brandFord -0.327 0.124 -0.085 -2.645 0.008 -0.569 -0.085
## brandHonda -0.168 0.124 -0.048 -1.360 0.174 -0.411 0.074
## brandHyundai -0.233 0.123 -0.106 -1.887 0.059 -0.475 0.009
## brandIsuzu -0.325 0.165 -0.010 -1.969 0.049 -0.648 -0.001
## brandJaguar 0.237 0.127 0.027 1.858 0.063 -0.013 0.487
## brandJeep -0.185 0.132 -0.014 -1.403 0.161 -0.443 0.073
## brandKia -0.126 0.174 -0.003 -0.724 0.469 -0.467 0.215
## brandLand 0.595 0.159 0.020 3.738 0.000 0.283 0.906
## brandLexus 0.430 0.132 0.034 3.265 0.001 0.172 0.688
## brandMahindra -0.368 0.123 -0.131 -2.985 0.003 -0.610 -0.127
## brandMaruti -0.186 0.123 -0.103 -1.505 0.132 -0.427 0.056
## brandMercedes-Benz 0.211 0.128 0.021 1.643 0.101 -0.041 0.462
## brandMG 0.142 0.188 0.003 0.755 0.450 -0.227 0.511
## brandMitsubishi -0.059 0.139 -0.003 -0.425 0.671 -0.332 0.214
## brandNissan -0.273 0.126 -0.033 -2.170 0.030 -0.520 -0.026
## brandOpel 0.067 0.274 0.001 0.245 0.806 -0.470 0.604
## brandRenault -0.322 0.124 -0.065 -2.592 0.010 -0.566 -0.079
## brandSkoda -0.259 0.125 -0.036 -2.063 0.039 -0.504 -0.013
## brandTata -0.660 0.123 -0.229 -5.352 0.000 -0.902 -0.418
## brandToyota -0.008 0.124 -0.002 -0.065 0.948 -0.250 0.234
## brandVolkswagen -0.304 0.124 -0.056 -2.446 0.014 -0.548 -0.060
## brandVolvo 0.207 0.128 0.023 1.620 0.105 -0.043 0.457
## fuelDiesel 0.356 0.035 0.214 10.286 0.000 0.288 0.424
## fuelLPG 0.206 0.054 0.016 3.825 0.000 0.100 0.311
## fuelPetrol 0.124 0.035 0.074 3.589 0.000 0.056 0.191
## ownerFourth -0.152 0.021 -0.026 -7.415 0.000 -0.193 -0.112
## ownerSecond -0.087 0.007 -0.046 -12.270 0.000 -0.101 -0.073
## ownerTest 0.677 0.112 0.021 6.040 0.000 0.458 0.897
## ownerThird -0.121 0.012 -0.036 -9.913 0.000 -0.145 -0.097
## seats 0.035 0.005 0.041 7.781 0.000 0.026 0.044
## km_driven 0.000 0.000 -0.023 -5.637 0.000 0.000 0.000
## -------------------------------------------------------------------------------------------------------
##
##
##
## Forward Selection: Step 6
##
## - seller_type
##
## Model Summary
## -------------------------------------------------------------
## R 0.956 RMSE 0.244
## R-Squared 0.913 Coef. Var 1.880
## Adj. R-Squared 0.913 MSE 0.060
## Pred R-Squared 0.911 MAE 0.185
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4944.989 45 109.889 1839.379 0.0000
## Residual 469.574 7860 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## ----------------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ----------------------------------------------------------------------------------------------------------------
## (Intercept) -220.511 1.933 -114.049 0.000 -224.302 -216.721
## year 0.115 0.001 0.539 120.285 0.000 0.114 0.117
## transmissionManual -0.067 0.011 -0.027 -5.888 0.000 -0.089 -0.045
## engine 0.000 0.000 0.123 14.756 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.294 0.000 0.008 0.009
## brandAshok -0.482 0.274 -0.007 -1.759 0.079 -1.020 0.055
## brandAudi 0.079 0.130 0.007 0.608 0.543 -0.176 0.334
## brandBMW 0.318 0.126 0.047 2.513 0.012 0.070 0.565
## brandChevrolet -0.595 0.124 -0.121 -4.800 0.000 -0.838 -0.352
## brandDaewoo 0.097 0.187 0.002 0.519 0.603 -0.270 0.465
## brandDatsun -0.578 0.127 -0.063 -4.551 0.000 -0.827 -0.329
## brandFiat -0.438 0.129 -0.038 -3.402 0.001 -0.691 -0.186
## brandForce -0.451 0.158 -0.015 -2.844 0.004 -0.761 -0.140
## brandFord -0.330 0.124 -0.086 -2.670 0.008 -0.572 -0.088
## brandHonda -0.173 0.124 -0.049 -1.396 0.163 -0.415 0.070
## brandHyundai -0.232 0.123 -0.106 -1.883 0.060 -0.474 0.010
## brandIsuzu -0.320 0.165 -0.010 -1.944 0.052 -0.644 0.003
## brandJaguar 0.217 0.127 0.025 1.700 0.089 -0.033 0.467
## brandJeep -0.180 0.132 -0.014 -1.370 0.171 -0.438 0.078
## brandKia -0.132 0.174 -0.004 -0.757 0.449 -0.472 0.209
## brandLand 0.576 0.159 0.019 3.622 0.000 0.264 0.887
## brandLexus 0.406 0.132 0.032 3.084 0.002 0.148 0.665
## brandMahindra -0.367 0.123 -0.131 -2.977 0.003 -0.609 -0.125
## brandMaruti -0.185 0.123 -0.103 -1.506 0.132 -0.427 0.056
## brandMercedes-Benz 0.204 0.128 0.020 1.593 0.111 -0.047 0.456
## brandMG 0.118 0.188 0.003 0.629 0.529 -0.250 0.487
## brandMitsubishi -0.063 0.139 -0.003 -0.453 0.651 -0.336 0.210
## brandNissan -0.272 0.126 -0.033 -2.162 0.031 -0.519 -0.025
## brandOpel 0.064 0.274 0.001 0.234 0.815 -0.472 0.600
## brandRenault -0.321 0.124 -0.065 -2.584 0.010 -0.565 -0.078
## brandSkoda -0.268 0.125 -0.037 -2.136 0.033 -0.513 -0.022
## brandTata -0.658 0.123 -0.229 -5.338 0.000 -0.899 -0.416
## brandToyota -0.013 0.124 -0.004 -0.107 0.915 -0.255 0.229
## brandVolkswagen -0.305 0.124 -0.056 -2.454 0.014 -0.549 -0.061
## brandVolvo 0.203 0.128 0.023 1.595 0.111 -0.047 0.453
## fuelDiesel 0.351 0.035 0.211 10.144 0.000 0.283 0.419
## fuelLPG 0.202 0.054 0.016 3.766 0.000 0.097 0.308
## fuelPetrol 0.120 0.034 0.072 3.479 0.001 0.052 0.188
## ownerFourth -0.149 0.021 -0.025 -7.231 0.000 -0.189 -0.108
## ownerSecond -0.084 0.007 -0.044 -11.729 0.000 -0.098 -0.070
## ownerTest 0.658 0.112 0.020 5.864 0.000 0.438 0.878
## ownerThird -0.117 0.012 -0.035 -9.543 0.000 -0.141 -0.093
## seats 0.036 0.005 0.042 7.895 0.000 0.027 0.045
## km_driven 0.000 0.000 -0.021 -5.327 0.000 0.000 0.000
## seller_typeIndividual -0.037 0.009 -0.017 -4.072 0.000 -0.055 -0.019
## seller_typeTrustmark Dealer -0.016 0.019 -0.003 -0.837 0.403 -0.053 0.021
## ----------------------------------------------------------------------------------------------------------------
##
##
##
## No more variables to be added.
##
## Variables Entered:
##
## + year
## + transmission
## + engine
## + max_power
## + brand
## + fuel
## + owner
## + seats
## + km_driven
## + seller_type
##
##
## Final Model Output
## ------------------
##
## Model Summary
## -------------------------------------------------------------
## R 0.956 RMSE 0.244
## R-Squared 0.913 Coef. Var 1.880
## Adj. R-Squared 0.913 MSE 0.060
## Pred R-Squared 0.911 MAE 0.185
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4944.989 45 109.889 1839.379 0.0000
## Residual 469.574 7860 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## ----------------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ----------------------------------------------------------------------------------------------------------------
## (Intercept) -220.511 1.933 -114.049 0.000 -224.302 -216.721
## year 0.115 0.001 0.539 120.285 0.000 0.114 0.117
## transmissionManual -0.067 0.011 -0.027 -5.888 0.000 -0.089 -0.045
## engine 0.000 0.000 0.123 14.756 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.294 0.000 0.008 0.009
## brandAshok -0.482 0.274 -0.007 -1.759 0.079 -1.020 0.055
## brandAudi 0.079 0.130 0.007 0.608 0.543 -0.176 0.334
## brandBMW 0.318 0.126 0.047 2.513 0.012 0.070 0.565
## brandChevrolet -0.595 0.124 -0.121 -4.800 0.000 -0.838 -0.352
## brandDaewoo 0.097 0.187 0.002 0.519 0.603 -0.270 0.465
## brandDatsun -0.578 0.127 -0.063 -4.551 0.000 -0.827 -0.329
## brandFiat -0.438 0.129 -0.038 -3.402 0.001 -0.691 -0.186
## brandForce -0.451 0.158 -0.015 -2.844 0.004 -0.761 -0.140
## brandFord -0.330 0.124 -0.086 -2.670 0.008 -0.572 -0.088
## brandHonda -0.173 0.124 -0.049 -1.396 0.163 -0.415 0.070
## brandHyundai -0.232 0.123 -0.106 -1.883 0.060 -0.474 0.010
## brandIsuzu -0.320 0.165 -0.010 -1.944 0.052 -0.644 0.003
## brandJaguar 0.217 0.127 0.025 1.700 0.089 -0.033 0.467
## brandJeep -0.180 0.132 -0.014 -1.370 0.171 -0.438 0.078
## brandKia -0.132 0.174 -0.004 -0.757 0.449 -0.472 0.209
## brandLand 0.576 0.159 0.019 3.622 0.000 0.264 0.887
## brandLexus 0.406 0.132 0.032 3.084 0.002 0.148 0.665
## brandMahindra -0.367 0.123 -0.131 -2.977 0.003 -0.609 -0.125
## brandMaruti -0.185 0.123 -0.103 -1.506 0.132 -0.427 0.056
## brandMercedes-Benz 0.204 0.128 0.020 1.593 0.111 -0.047 0.456
## brandMG 0.118 0.188 0.003 0.629 0.529 -0.250 0.487
## brandMitsubishi -0.063 0.139 -0.003 -0.453 0.651 -0.336 0.210
## brandNissan -0.272 0.126 -0.033 -2.162 0.031 -0.519 -0.025
## brandOpel 0.064 0.274 0.001 0.234 0.815 -0.472 0.600
## brandRenault -0.321 0.124 -0.065 -2.584 0.010 -0.565 -0.078
## brandSkoda -0.268 0.125 -0.037 -2.136 0.033 -0.513 -0.022
## brandTata -0.658 0.123 -0.229 -5.338 0.000 -0.899 -0.416
## brandToyota -0.013 0.124 -0.004 -0.107 0.915 -0.255 0.229
## brandVolkswagen -0.305 0.124 -0.056 -2.454 0.014 -0.549 -0.061
## brandVolvo 0.203 0.128 0.023 1.595 0.111 -0.047 0.453
## fuelDiesel 0.351 0.035 0.211 10.144 0.000 0.283 0.419
## fuelLPG 0.202 0.054 0.016 3.766 0.000 0.097 0.308
## fuelPetrol 0.120 0.034 0.072 3.479 0.001 0.052 0.188
## ownerFourth -0.149 0.021 -0.025 -7.231 0.000 -0.189 -0.108
## ownerSecond -0.084 0.007 -0.044 -11.729 0.000 -0.098 -0.070
## ownerTest 0.658 0.112 0.020 5.864 0.000 0.438 0.878
## ownerThird -0.117 0.012 -0.035 -9.543 0.000 -0.141 -0.093
## seats 0.036 0.005 0.042 7.895 0.000 0.027 0.045
## km_driven 0.000 0.000 -0.021 -5.327 0.000 0.000 0.000
## seller_typeIndividual -0.037 0.009 -0.017 -4.072 0.000 -0.055 -0.019
## seller_typeTrustmark Dealer -0.016 0.019 -0.003 -0.837 0.403 -0.053 0.021
## ----------------------------------------------------------------------------------------------------------------backward = ols_step_backward_p(model2,prem = .05,details=TRUE)## Backward Elimination Method
## ---------------------------
##
## Candidate Terms:
##
## 1 . year
## 2 . km_driven
## 3 . fuel
## 4 . seller_type
## 5 . transmission
## 6 . owner
## 7 . mileage
## 8 . engine
## 9 . max_power
## 10 . seats
## 11 . brand
##
## We are eliminating variables based on p value...
##
## - mileage
##
## Backward Elimination: Step 1
##
## Variable mileage Removed
##
## Model Summary
## -------------------------------------------------------------
## R 0.956 RMSE 0.244
## R-Squared 0.913 Coef. Var 1.880
## Adj. R-Squared 0.913 MSE 0.060
## Pred R-Squared 0.911 MAE 0.185
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4944.989 45 109.889 1839.379 0.0000
## Residual 469.574 7860 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## ----------------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ----------------------------------------------------------------------------------------------------------------
## (Intercept) -220.511 1.933 -114.049 0.000 -224.302 -216.721
## year 0.115 0.001 0.539 120.285 0.000 0.114 0.117
## km_driven 0.000 0.000 -0.021 -5.327 0.000 0.000 0.000
## fuelDiesel 0.351 0.035 0.211 10.144 0.000 0.283 0.419
## fuelLPG 0.202 0.054 0.016 3.766 0.000 0.097 0.308
## fuelPetrol 0.120 0.034 0.072 3.479 0.001 0.052 0.188
## seller_typeIndividual -0.037 0.009 -0.017 -4.072 0.000 -0.055 -0.019
## seller_typeTrustmark Dealer -0.016 0.019 -0.003 -0.837 0.403 -0.053 0.021
## transmissionManual -0.067 0.011 -0.027 -5.888 0.000 -0.089 -0.045
## ownerFourth -0.149 0.021 -0.025 -7.231 0.000 -0.189 -0.108
## ownerSecond -0.084 0.007 -0.044 -11.729 0.000 -0.098 -0.070
## ownerTest 0.658 0.112 0.020 5.864 0.000 0.438 0.878
## ownerThird -0.117 0.012 -0.035 -9.543 0.000 -0.141 -0.093
## engine 0.000 0.000 0.123 14.756 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.294 0.000 0.008 0.009
## seats 0.036 0.005 0.042 7.895 0.000 0.027 0.045
## brandAshok -0.482 0.274 -0.007 -1.759 0.079 -1.020 0.055
## brandAudi 0.079 0.130 0.007 0.608 0.543 -0.176 0.334
## brandBMW 0.318 0.126 0.047 2.513 0.012 0.070 0.565
## brandChevrolet -0.595 0.124 -0.121 -4.800 0.000 -0.838 -0.352
## brandDaewoo 0.097 0.187 0.002 0.519 0.603 -0.270 0.465
## brandDatsun -0.578 0.127 -0.063 -4.551 0.000 -0.827 -0.329
## brandFiat -0.438 0.129 -0.038 -3.402 0.001 -0.691 -0.186
## brandForce -0.451 0.158 -0.015 -2.844 0.004 -0.761 -0.140
## brandFord -0.330 0.124 -0.086 -2.670 0.008 -0.572 -0.088
## brandHonda -0.173 0.124 -0.049 -1.396 0.163 -0.415 0.070
## brandHyundai -0.232 0.123 -0.106 -1.883 0.060 -0.474 0.010
## brandIsuzu -0.320 0.165 -0.010 -1.944 0.052 -0.644 0.003
## brandJaguar 0.217 0.127 0.025 1.700 0.089 -0.033 0.467
## brandJeep -0.180 0.132 -0.014 -1.370 0.171 -0.438 0.078
## brandKia -0.132 0.174 -0.004 -0.757 0.449 -0.472 0.209
## brandLand 0.576 0.159 0.019 3.622 0.000 0.264 0.887
## brandLexus 0.406 0.132 0.032 3.084 0.002 0.148 0.665
## brandMahindra -0.367 0.123 -0.131 -2.977 0.003 -0.609 -0.125
## brandMaruti -0.185 0.123 -0.103 -1.506 0.132 -0.427 0.056
## brandMercedes-Benz 0.204 0.128 0.020 1.593 0.111 -0.047 0.456
## brandMG 0.118 0.188 0.003 0.629 0.529 -0.250 0.487
## brandMitsubishi -0.063 0.139 -0.003 -0.453 0.651 -0.336 0.210
## brandNissan -0.272 0.126 -0.033 -2.162 0.031 -0.519 -0.025
## brandOpel 0.064 0.274 0.001 0.234 0.815 -0.472 0.600
## brandRenault -0.321 0.124 -0.065 -2.584 0.010 -0.565 -0.078
## brandSkoda -0.268 0.125 -0.037 -2.136 0.033 -0.513 -0.022
## brandTata -0.658 0.123 -0.229 -5.338 0.000 -0.899 -0.416
## brandToyota -0.013 0.124 -0.004 -0.107 0.915 -0.255 0.229
## brandVolkswagen -0.305 0.124 -0.056 -2.454 0.014 -0.549 -0.061
## brandVolvo 0.203 0.128 0.023 1.595 0.111 -0.047 0.453
## ----------------------------------------------------------------------------------------------------------------
##
##
##
## No more variables satisfy the condition of p value = 0.05
##
##
## Variables Removed:
##
## - mileage
##
##
## Final Model Output
## ------------------
##
## Model Summary
## -------------------------------------------------------------
## R 0.956 RMSE 0.244
## R-Squared 0.913 Coef. Var 1.880
## Adj. R-Squared 0.913 MSE 0.060
## Pred R-Squared 0.911 MAE 0.185
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4944.989 45 109.889 1839.379 0.0000
## Residual 469.574 7860 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## ----------------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ----------------------------------------------------------------------------------------------------------------
## (Intercept) -220.511 1.933 -114.049 0.000 -224.302 -216.721
## year 0.115 0.001 0.539 120.285 0.000 0.114 0.117
## km_driven 0.000 0.000 -0.021 -5.327 0.000 0.000 0.000
## fuelDiesel 0.351 0.035 0.211 10.144 0.000 0.283 0.419
## fuelLPG 0.202 0.054 0.016 3.766 0.000 0.097 0.308
## fuelPetrol 0.120 0.034 0.072 3.479 0.001 0.052 0.188
## seller_typeIndividual -0.037 0.009 -0.017 -4.072 0.000 -0.055 -0.019
## seller_typeTrustmark Dealer -0.016 0.019 -0.003 -0.837 0.403 -0.053 0.021
## transmissionManual -0.067 0.011 -0.027 -5.888 0.000 -0.089 -0.045
## ownerFourth -0.149 0.021 -0.025 -7.231 0.000 -0.189 -0.108
## ownerSecond -0.084 0.007 -0.044 -11.729 0.000 -0.098 -0.070
## ownerTest 0.658 0.112 0.020 5.864 0.000 0.438 0.878
## ownerThird -0.117 0.012 -0.035 -9.543 0.000 -0.141 -0.093
## engine 0.000 0.000 0.123 14.756 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.294 0.000 0.008 0.009
## seats 0.036 0.005 0.042 7.895 0.000 0.027 0.045
## brandAshok -0.482 0.274 -0.007 -1.759 0.079 -1.020 0.055
## brandAudi 0.079 0.130 0.007 0.608 0.543 -0.176 0.334
## brandBMW 0.318 0.126 0.047 2.513 0.012 0.070 0.565
## brandChevrolet -0.595 0.124 -0.121 -4.800 0.000 -0.838 -0.352
## brandDaewoo 0.097 0.187 0.002 0.519 0.603 -0.270 0.465
## brandDatsun -0.578 0.127 -0.063 -4.551 0.000 -0.827 -0.329
## brandFiat -0.438 0.129 -0.038 -3.402 0.001 -0.691 -0.186
## brandForce -0.451 0.158 -0.015 -2.844 0.004 -0.761 -0.140
## brandFord -0.330 0.124 -0.086 -2.670 0.008 -0.572 -0.088
## brandHonda -0.173 0.124 -0.049 -1.396 0.163 -0.415 0.070
## brandHyundai -0.232 0.123 -0.106 -1.883 0.060 -0.474 0.010
## brandIsuzu -0.320 0.165 -0.010 -1.944 0.052 -0.644 0.003
## brandJaguar 0.217 0.127 0.025 1.700 0.089 -0.033 0.467
## brandJeep -0.180 0.132 -0.014 -1.370 0.171 -0.438 0.078
## brandKia -0.132 0.174 -0.004 -0.757 0.449 -0.472 0.209
## brandLand 0.576 0.159 0.019 3.622 0.000 0.264 0.887
## brandLexus 0.406 0.132 0.032 3.084 0.002 0.148 0.665
## brandMahindra -0.367 0.123 -0.131 -2.977 0.003 -0.609 -0.125
## brandMaruti -0.185 0.123 -0.103 -1.506 0.132 -0.427 0.056
## brandMercedes-Benz 0.204 0.128 0.020 1.593 0.111 -0.047 0.456
## brandMG 0.118 0.188 0.003 0.629 0.529 -0.250 0.487
## brandMitsubishi -0.063 0.139 -0.003 -0.453 0.651 -0.336 0.210
## brandNissan -0.272 0.126 -0.033 -2.162 0.031 -0.519 -0.025
## brandOpel 0.064 0.274 0.001 0.234 0.815 -0.472 0.600
## brandRenault -0.321 0.124 -0.065 -2.584 0.010 -0.565 -0.078
## brandSkoda -0.268 0.125 -0.037 -2.136 0.033 -0.513 -0.022
## brandTata -0.658 0.123 -0.229 -5.338 0.000 -0.899 -0.416
## brandToyota -0.013 0.124 -0.004 -0.107 0.915 -0.255 0.229
## brandVolkswagen -0.305 0.124 -0.056 -2.454 0.014 -0.549 -0.061
## brandVolvo 0.203 0.128 0.023 1.595 0.111 -0.047 0.453
## ----------------------------------------------------------------------------------------------------------------stepwise = ols_step_both_p(model2,prem=0.05,details=TRUE)## Stepwise Selection Method
## ---------------------------
##
## Candidate Terms:
##
## 1. year
## 2. km_driven
## 3. fuel
## 4. seller_type
## 5. transmission
## 6. owner
## 7. mileage
## 8. engine
## 9. max_power
## 10. seats
## 11. brand
##
## We are selecting variables based on p value...
##
##
## Stepwise Selection: Step 1
##
## - brand added
##
## Model Summary
## -------------------------------------------------------------
## R 0.948 RMSE 0.265
## R-Squared 0.898 Coef. Var 2.035
## Adj. R-Squared 0.898 MSE 0.070
## Pred R-Squared 0.897 MAE 0.203
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4863.728 34 143.051 2044.083 0.0000
## Residual 550.835 7871 0.070
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -244.074 1.697 -143.845 0.000 -247.400 -240.748
## year 0.127 0.001 0.594 150.962 0.000 0.126 0.129
## transmissionManual 0.004 0.012 0.002 0.353 0.724 -0.019 0.027
## engine 0.000 0.000 0.227 30.510 0.000 0.000 0.000
## max_power 0.008 0.000 0.345 46.463 0.000 0.008 0.008
## brandAshok -0.449 0.296 -0.006 -1.519 0.129 -1.030 0.131
## brandAudi 0.117 0.141 0.010 0.832 0.405 -0.159 0.392
## brandBMW 0.334 0.137 0.049 2.448 0.014 0.067 0.602
## brandChevrolet -0.643 0.134 -0.131 -4.802 0.000 -0.906 -0.381
## brandDaewoo 0.170 0.203 0.004 0.841 0.400 -0.227 0.567
## brandDatsun -0.724 0.137 -0.079 -5.279 0.000 -0.992 -0.455
## brandFiat -0.434 0.139 -0.038 -3.114 0.002 -0.706 -0.161
## brandForce -0.569 0.171 -0.019 -3.320 0.001 -0.905 -0.233
## brandFord -0.371 0.134 -0.097 -2.781 0.005 -0.633 -0.110
## brandHonda -0.285 0.134 -0.081 -2.130 0.033 -0.547 -0.023
## brandHyundai -0.323 0.133 -0.147 -2.425 0.015 -0.584 -0.062
## brandIsuzu -0.406 0.178 -0.012 -2.277 0.023 -0.756 -0.056
## brandJaguar 0.263 0.138 0.030 1.910 0.056 -0.007 0.533
## brandJeep -0.325 0.142 -0.025 -2.286 0.022 -0.604 -0.046
## brandKia -0.063 0.188 -0.002 -0.337 0.736 -0.432 0.305
## brandLand 0.635 0.172 0.021 3.698 0.000 0.298 0.972
## brandLexus 0.138 0.142 0.011 0.971 0.331 -0.140 0.416
## brandMahindra -0.403 0.133 -0.143 -3.028 0.002 -0.664 -0.142
## brandMaruti -0.249 0.133 -0.138 -1.871 0.061 -0.510 0.012
## brandMercedes-Benz 0.133 0.139 0.013 0.962 0.336 -0.138 0.405
## brandMG 0.008 0.203 0.000 0.038 0.970 -0.391 0.406
## brandMitsubishi -0.128 0.150 -0.007 -0.852 0.394 -0.423 0.167
## brandNissan -0.340 0.136 -0.041 -2.499 0.012 -0.607 -0.073
## brandOpel -0.093 0.296 -0.001 -0.316 0.752 -0.673 0.487
## brandRenault -0.374 0.134 -0.076 -2.790 0.005 -0.638 -0.111
## brandSkoda -0.327 0.135 -0.045 -2.417 0.016 -0.593 -0.062
## brandTata -0.692 0.133 -0.240 -5.197 0.000 -0.953 -0.431
## brandToyota -0.125 0.133 -0.035 -0.935 0.350 -0.386 0.137
## brandVolkswagen -0.348 0.134 -0.063 -2.587 0.010 -0.611 -0.084
## brandVolvo 0.229 0.138 0.025 1.662 0.096 -0.041 0.500
## -------------------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 2
##
## - fuel added
##
## Model Summary
## -------------------------------------------------------------
## R 0.954 RMSE 0.250
## R-Squared 0.909 Coef. Var 1.923
## Adj. R-Squared 0.909 MSE 0.062
## Pred R-Squared 0.908 MAE 0.190
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4922.980 37 133.054 2129.579 0.0000
## Residual 491.583 7868 0.062
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -239.173 1.621 -147.515 0.000 -242.351 -235.994
## year 0.125 0.001 0.582 155.186 0.000 0.123 0.126
## transmissionManual -0.071 0.011 -0.029 -6.224 0.000 -0.093 -0.049
## engine 0.000 0.000 0.148 19.541 0.000 0.000 0.000
## max_power 0.008 0.000 0.350 49.835 0.000 0.008 0.008
## brandAshok -0.480 0.280 -0.007 -1.718 0.086 -1.029 0.068
## brandAudi 0.122 0.133 0.010 0.918 0.359 -0.138 0.382
## brandBMW 0.313 0.129 0.046 2.425 0.015 0.060 0.566
## brandChevrolet -0.595 0.127 -0.121 -4.700 0.000 -0.843 -0.347
## brandDaewoo 0.239 0.191 0.006 1.251 0.211 -0.136 0.615
## brandDatsun -0.578 0.130 -0.063 -4.462 0.000 -0.832 -0.324
## brandFiat -0.452 0.132 -0.039 -3.433 0.001 -0.709 -0.194
## brandForce -0.469 0.162 -0.016 -2.898 0.004 -0.787 -0.152
## brandFord -0.346 0.126 -0.090 -2.739 0.006 -0.593 -0.098
## brandHonda -0.181 0.126 -0.051 -1.430 0.153 -0.428 0.067
## brandHyundai -0.251 0.126 -0.115 -1.995 0.046 -0.498 -0.004
## brandIsuzu -0.333 0.169 -0.010 -1.974 0.048 -0.663 -0.002
## brandJaguar 0.232 0.130 0.026 1.780 0.075 -0.024 0.487
## brandJeep -0.213 0.135 -0.016 -1.580 0.114 -0.476 0.051
## brandKia -0.135 0.178 -0.004 -0.761 0.447 -0.483 0.213
## brandLand 0.608 0.162 0.020 3.747 0.000 0.290 0.926
## brandLexus 0.380 0.134 0.030 2.824 0.005 0.116 0.643
## brandMahindra -0.345 0.126 -0.123 -2.747 0.006 -0.592 -0.099
## brandMaruti -0.190 0.126 -0.105 -1.512 0.131 -0.437 0.056
## brandMercedes-Benz 0.185 0.131 0.018 1.409 0.159 -0.072 0.442
## brandMG 0.123 0.192 0.003 0.643 0.520 -0.253 0.500
## brandMitsubishi -0.065 0.142 -0.003 -0.461 0.645 -0.344 0.213
## brandNissan -0.296 0.129 -0.036 -2.306 0.021 -0.549 -0.044
## brandOpel 0.072 0.280 0.001 0.258 0.796 -0.476 0.620
## brandRenault -0.328 0.127 -0.066 -2.586 0.010 -0.577 -0.079
## brandSkoda -0.280 0.128 -0.039 -2.190 0.029 -0.531 -0.029
## brandTata -0.663 0.126 -0.230 -5.268 0.000 -0.910 -0.416
## brandToyota -0.016 0.126 -0.004 -0.124 0.901 -0.263 0.231
## brandVolkswagen -0.328 0.127 -0.060 -2.584 0.010 -0.577 -0.079
## brandVolvo 0.195 0.130 0.022 1.492 0.136 -0.061 0.450
## fuelDiesel 0.368 0.035 0.222 10.422 0.000 0.299 0.437
## fuelLPG 0.232 0.055 0.019 4.234 0.000 0.125 0.340
## fuelPetrol 0.152 0.035 0.091 4.324 0.000 0.083 0.221
## -------------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.954 RMSE 0.250
## R-Squared 0.909 Coef. Var 1.923
## Adj. R-Squared 0.909 MSE 0.062
## Pred R-Squared 0.908 MAE 0.190
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4922.980 37 133.054 2129.579 0.0000
## Residual 491.583 7868 0.062
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -239.173 1.621 -147.515 0.000 -242.351 -235.994
## year 0.125 0.001 0.582 155.186 0.000 0.123 0.126
## transmissionManual -0.071 0.011 -0.029 -6.224 0.000 -0.093 -0.049
## engine 0.000 0.000 0.148 19.541 0.000 0.000 0.000
## max_power 0.008 0.000 0.350 49.835 0.000 0.008 0.008
## brandAshok -0.480 0.280 -0.007 -1.718 0.086 -1.029 0.068
## brandAudi 0.122 0.133 0.010 0.918 0.359 -0.138 0.382
## brandBMW 0.313 0.129 0.046 2.425 0.015 0.060 0.566
## brandChevrolet -0.595 0.127 -0.121 -4.700 0.000 -0.843 -0.347
## brandDaewoo 0.239 0.191 0.006 1.251 0.211 -0.136 0.615
## brandDatsun -0.578 0.130 -0.063 -4.462 0.000 -0.832 -0.324
## brandFiat -0.452 0.132 -0.039 -3.433 0.001 -0.709 -0.194
## brandForce -0.469 0.162 -0.016 -2.898 0.004 -0.787 -0.152
## brandFord -0.346 0.126 -0.090 -2.739 0.006 -0.593 -0.098
## brandHonda -0.181 0.126 -0.051 -1.430 0.153 -0.428 0.067
## brandHyundai -0.251 0.126 -0.115 -1.995 0.046 -0.498 -0.004
## brandIsuzu -0.333 0.169 -0.010 -1.974 0.048 -0.663 -0.002
## brandJaguar 0.232 0.130 0.026 1.780 0.075 -0.024 0.487
## brandJeep -0.213 0.135 -0.016 -1.580 0.114 -0.476 0.051
## brandKia -0.135 0.178 -0.004 -0.761 0.447 -0.483 0.213
## brandLand 0.608 0.162 0.020 3.747 0.000 0.290 0.926
## brandLexus 0.380 0.134 0.030 2.824 0.005 0.116 0.643
## brandMahindra -0.345 0.126 -0.123 -2.747 0.006 -0.592 -0.099
## brandMaruti -0.190 0.126 -0.105 -1.512 0.131 -0.437 0.056
## brandMercedes-Benz 0.185 0.131 0.018 1.409 0.159 -0.072 0.442
## brandMG 0.123 0.192 0.003 0.643 0.520 -0.253 0.500
## brandMitsubishi -0.065 0.142 -0.003 -0.461 0.645 -0.344 0.213
## brandNissan -0.296 0.129 -0.036 -2.306 0.021 -0.549 -0.044
## brandOpel 0.072 0.280 0.001 0.258 0.796 -0.476 0.620
## brandRenault -0.328 0.127 -0.066 -2.586 0.010 -0.577 -0.079
## brandSkoda -0.280 0.128 -0.039 -2.190 0.029 -0.531 -0.029
## brandTata -0.663 0.126 -0.230 -5.268 0.000 -0.910 -0.416
## brandToyota -0.016 0.126 -0.004 -0.124 0.901 -0.263 0.231
## brandVolkswagen -0.328 0.127 -0.060 -2.584 0.010 -0.577 -0.079
## brandVolvo 0.195 0.130 0.022 1.492 0.136 -0.061 0.450
## fuelDiesel 0.368 0.035 0.222 10.422 0.000 0.299 0.437
## fuelLPG 0.232 0.055 0.019 4.234 0.000 0.125 0.340
## fuelPetrol 0.152 0.035 0.091 4.324 0.000 0.083 0.221
## -------------------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 3
##
## - owner added
##
## Model Summary
## -------------------------------------------------------------
## R 0.955 RMSE 0.246
## R-Squared 0.912 Coef. Var 1.892
## Adj. R-Squared 0.912 MSE 0.061
## Pred R-Squared 0.911 MAE 0.187
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4938.715 41 120.456 1990.699 0.0000
## Residual 475.848 7864 0.061
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -225.836 1.822 -123.926 0.000 -229.408 -222.264
## year 0.118 0.001 0.551 130.738 0.000 0.116 0.120
## transmissionManual -0.068 0.011 -0.028 -6.044 0.000 -0.090 -0.046
## engine 0.000 0.000 0.149 20.042 0.000 0.000 0.000
## max_power 0.008 0.000 0.350 50.571 0.000 0.008 0.008
## brandAshok -0.418 0.275 -0.006 -1.520 0.128 -0.958 0.121
## brandAudi 0.084 0.131 0.007 0.640 0.522 -0.173 0.340
## brandBMW 0.326 0.127 0.048 2.570 0.010 0.077 0.575
## brandChevrolet -0.573 0.125 -0.116 -4.597 0.000 -0.817 -0.328
## brandDaewoo 0.136 0.188 0.003 0.721 0.471 -0.234 0.505
## brandDatsun -0.561 0.128 -0.061 -4.394 0.000 -0.811 -0.311
## brandFiat -0.439 0.129 -0.038 -3.388 0.001 -0.692 -0.185
## brandForce -0.441 0.159 -0.015 -2.765 0.006 -0.753 -0.128
## brandFord -0.330 0.124 -0.086 -2.660 0.008 -0.574 -0.087
## brandHonda -0.168 0.124 -0.048 -1.351 0.177 -0.412 0.076
## brandHyundai -0.231 0.124 -0.105 -1.866 0.062 -0.474 0.012
## brandIsuzu -0.327 0.166 -0.010 -1.974 0.048 -0.653 -0.002
## brandJaguar 0.232 0.128 0.026 1.812 0.070 -0.019 0.483
## brandJeep -0.205 0.132 -0.015 -1.546 0.122 -0.464 0.055
## brandKia -0.118 0.175 -0.003 -0.673 0.501 -0.460 0.225
## brandLand 0.630 0.160 0.021 3.941 0.000 0.316 0.943
## brandLexus 0.400 0.132 0.032 3.024 0.003 0.141 0.660
## brandMahindra -0.332 0.124 -0.118 -2.684 0.007 -0.575 -0.090
## brandMaruti -0.173 0.124 -0.096 -1.399 0.162 -0.416 0.070
## brandMercedes-Benz 0.197 0.129 0.020 1.528 0.127 -0.056 0.450
## brandMG 0.148 0.189 0.003 0.782 0.434 -0.223 0.518
## brandMitsubishi -0.065 0.140 -0.003 -0.466 0.641 -0.339 0.209
## brandNissan -0.279 0.127 -0.034 -2.208 0.027 -0.527 -0.031
## brandOpel 0.076 0.275 0.001 0.278 0.781 -0.463 0.616
## brandRenault -0.313 0.125 -0.063 -2.504 0.012 -0.557 -0.068
## brandSkoda -0.266 0.126 -0.037 -2.111 0.035 -0.513 -0.019
## brandTata -0.652 0.124 -0.227 -5.264 0.000 -0.895 -0.409
## brandToyota 0.000 0.124 0.000 0.001 0.999 -0.243 0.243
## brandVolkswagen -0.308 0.125 -0.056 -2.467 0.014 -0.553 -0.063
## brandVolvo 0.206 0.128 0.023 1.602 0.109 -0.046 0.457
## fuelDiesel 0.362 0.035 0.218 10.400 0.000 0.293 0.430
## fuelLPG 0.217 0.054 0.017 4.010 0.000 0.111 0.323
## fuelPetrol 0.139 0.035 0.083 4.004 0.000 0.071 0.207
## ownerFourth -0.152 0.021 -0.026 -7.368 0.000 -0.193 -0.112
## ownerSecond -0.090 0.007 -0.047 -12.619 0.000 -0.104 -0.076
## ownerTest 0.677 0.113 0.021 6.002 0.000 0.456 0.898
## ownerThird -0.125 0.012 -0.037 -10.154 0.000 -0.149 -0.101
## -------------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.955 RMSE 0.246
## R-Squared 0.912 Coef. Var 1.892
## Adj. R-Squared 0.912 MSE 0.061
## Pred R-Squared 0.911 MAE 0.187
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4938.715 41 120.456 1990.699 0.0000
## Residual 475.848 7864 0.061
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -225.836 1.822 -123.926 0.000 -229.408 -222.264
## year 0.118 0.001 0.551 130.738 0.000 0.116 0.120
## transmissionManual -0.068 0.011 -0.028 -6.044 0.000 -0.090 -0.046
## engine 0.000 0.000 0.149 20.042 0.000 0.000 0.000
## max_power 0.008 0.000 0.350 50.571 0.000 0.008 0.008
## brandAshok -0.418 0.275 -0.006 -1.520 0.128 -0.958 0.121
## brandAudi 0.084 0.131 0.007 0.640 0.522 -0.173 0.340
## brandBMW 0.326 0.127 0.048 2.570 0.010 0.077 0.575
## brandChevrolet -0.573 0.125 -0.116 -4.597 0.000 -0.817 -0.328
## brandDaewoo 0.136 0.188 0.003 0.721 0.471 -0.234 0.505
## brandDatsun -0.561 0.128 -0.061 -4.394 0.000 -0.811 -0.311
## brandFiat -0.439 0.129 -0.038 -3.388 0.001 -0.692 -0.185
## brandForce -0.441 0.159 -0.015 -2.765 0.006 -0.753 -0.128
## brandFord -0.330 0.124 -0.086 -2.660 0.008 -0.574 -0.087
## brandHonda -0.168 0.124 -0.048 -1.351 0.177 -0.412 0.076
## brandHyundai -0.231 0.124 -0.105 -1.866 0.062 -0.474 0.012
## brandIsuzu -0.327 0.166 -0.010 -1.974 0.048 -0.653 -0.002
## brandJaguar 0.232 0.128 0.026 1.812 0.070 -0.019 0.483
## brandJeep -0.205 0.132 -0.015 -1.546 0.122 -0.464 0.055
## brandKia -0.118 0.175 -0.003 -0.673 0.501 -0.460 0.225
## brandLand 0.630 0.160 0.021 3.941 0.000 0.316 0.943
## brandLexus 0.400 0.132 0.032 3.024 0.003 0.141 0.660
## brandMahindra -0.332 0.124 -0.118 -2.684 0.007 -0.575 -0.090
## brandMaruti -0.173 0.124 -0.096 -1.399 0.162 -0.416 0.070
## brandMercedes-Benz 0.197 0.129 0.020 1.528 0.127 -0.056 0.450
## brandMG 0.148 0.189 0.003 0.782 0.434 -0.223 0.518
## brandMitsubishi -0.065 0.140 -0.003 -0.466 0.641 -0.339 0.209
## brandNissan -0.279 0.127 -0.034 -2.208 0.027 -0.527 -0.031
## brandOpel 0.076 0.275 0.001 0.278 0.781 -0.463 0.616
## brandRenault -0.313 0.125 -0.063 -2.504 0.012 -0.557 -0.068
## brandSkoda -0.266 0.126 -0.037 -2.111 0.035 -0.513 -0.019
## brandTata -0.652 0.124 -0.227 -5.264 0.000 -0.895 -0.409
## brandToyota 0.000 0.124 0.000 0.001 0.999 -0.243 0.243
## brandVolkswagen -0.308 0.125 -0.056 -2.467 0.014 -0.553 -0.063
## brandVolvo 0.206 0.128 0.023 1.602 0.109 -0.046 0.457
## fuelDiesel 0.362 0.035 0.218 10.400 0.000 0.293 0.430
## fuelLPG 0.217 0.054 0.017 4.010 0.000 0.111 0.323
## fuelPetrol 0.139 0.035 0.083 4.004 0.000 0.071 0.207
## ownerFourth -0.152 0.021 -0.026 -7.368 0.000 -0.193 -0.112
## ownerSecond -0.090 0.007 -0.047 -12.619 0.000 -0.104 -0.076
## ownerTest 0.677 0.113 0.021 6.002 0.000 0.456 0.898
## ownerThird -0.125 0.012 -0.037 -10.154 0.000 -0.149 -0.101
## -------------------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 4
##
## - seats added
##
## Model Summary
## -------------------------------------------------------------
## R 0.955 RMSE 0.245
## R-Squared 0.913 Coef. Var 1.886
## Adj. R-Squared 0.912 MSE 0.060
## Pred R-Squared 0.911 MAE 0.186
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4942.068 42 117.668 1958.171 0.0000
## Residual 472.495 7863 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -224.513 1.825 -123.044 0.000 -228.090 -220.936
## year 0.117 0.001 0.548 129.721 0.000 0.116 0.119
## transmissionManual -0.076 0.011 -0.031 -6.754 0.000 -0.098 -0.054
## engine 0.000 0.000 0.120 14.463 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.284 0.000 0.008 0.009
## brandAshok -0.536 0.275 -0.007 -1.951 0.051 -1.075 0.002
## brandAudi 0.066 0.131 0.006 0.509 0.611 -0.189 0.322
## brandBMW 0.319 0.127 0.047 2.518 0.012 0.071 0.567
## brandChevrolet -0.620 0.124 -0.126 -4.985 0.000 -0.863 -0.376
## brandDaewoo 0.083 0.188 0.002 0.443 0.658 -0.285 0.452
## brandDatsun -0.605 0.127 -0.066 -4.750 0.000 -0.854 -0.355
## brandFiat -0.466 0.129 -0.040 -3.610 0.000 -0.719 -0.213
## brandForce -0.460 0.159 -0.015 -2.896 0.004 -0.771 -0.149
## brandFord -0.351 0.124 -0.092 -2.833 0.005 -0.594 -0.108
## brandHonda -0.193 0.124 -0.055 -1.561 0.118 -0.436 0.049
## brandHyundai -0.258 0.124 -0.118 -2.088 0.037 -0.500 -0.016
## brandIsuzu -0.342 0.165 -0.010 -2.069 0.039 -0.666 -0.018
## brandJaguar 0.222 0.128 0.025 1.740 0.082 -0.028 0.472
## brandJeep -0.204 0.132 -0.015 -1.547 0.122 -0.463 0.054
## brandKia -0.140 0.174 -0.004 -0.803 0.422 -0.481 0.202
## brandLand 0.580 0.159 0.019 3.638 0.000 0.267 0.892
## brandLexus 0.407 0.132 0.032 3.085 0.002 0.148 0.665
## brandMahindra -0.391 0.124 -0.139 -3.164 0.002 -0.633 -0.149
## brandMaruti -0.210 0.123 -0.116 -1.700 0.089 -0.452 0.032
## brandMercedes-Benz 0.193 0.129 0.019 1.505 0.132 -0.059 0.445
## brandMG 0.118 0.188 0.003 0.624 0.532 -0.252 0.487
## brandMitsubishi -0.089 0.139 -0.005 -0.637 0.524 -0.362 0.184
## brandNissan -0.299 0.126 -0.036 -2.371 0.018 -0.546 -0.052
## brandOpel 0.057 0.274 0.001 0.207 0.836 -0.481 0.595
## brandRenault -0.349 0.124 -0.070 -2.800 0.005 -0.593 -0.105
## brandSkoda -0.284 0.126 -0.039 -2.260 0.024 -0.530 -0.038
## brandTata -0.684 0.124 -0.238 -5.542 0.000 -0.927 -0.442
## brandToyota -0.036 0.124 -0.010 -0.293 0.770 -0.279 0.206
## brandVolkswagen -0.329 0.125 -0.060 -2.638 0.008 -0.573 -0.084
## brandVolvo 0.194 0.128 0.022 1.518 0.129 -0.057 0.445
## fuelDiesel 0.354 0.035 0.213 10.218 0.000 0.286 0.422
## fuelLPG 0.207 0.054 0.017 3.846 0.000 0.102 0.313
## fuelPetrol 0.131 0.035 0.079 3.796 0.000 0.063 0.199
## ownerFourth -0.155 0.021 -0.026 -7.524 0.000 -0.195 -0.114
## ownerSecond -0.090 0.007 -0.047 -12.692 0.000 -0.104 -0.076
## ownerTest 0.678 0.112 0.021 6.031 0.000 0.457 0.898
## ownerThird -0.126 0.012 -0.037 -10.250 0.000 -0.150 -0.102
## seats 0.034 0.005 0.039 7.470 0.000 0.025 0.043
## -------------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.955 RMSE 0.245
## R-Squared 0.913 Coef. Var 1.886
## Adj. R-Squared 0.912 MSE 0.060
## Pred R-Squared 0.911 MAE 0.186
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4942.068 42 117.668 1958.171 0.0000
## Residual 472.495 7863 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -224.513 1.825 -123.044 0.000 -228.090 -220.936
## year 0.117 0.001 0.548 129.721 0.000 0.116 0.119
## transmissionManual -0.076 0.011 -0.031 -6.754 0.000 -0.098 -0.054
## engine 0.000 0.000 0.120 14.463 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.284 0.000 0.008 0.009
## brandAshok -0.536 0.275 -0.007 -1.951 0.051 -1.075 0.002
## brandAudi 0.066 0.131 0.006 0.509 0.611 -0.189 0.322
## brandBMW 0.319 0.127 0.047 2.518 0.012 0.071 0.567
## brandChevrolet -0.620 0.124 -0.126 -4.985 0.000 -0.863 -0.376
## brandDaewoo 0.083 0.188 0.002 0.443 0.658 -0.285 0.452
## brandDatsun -0.605 0.127 -0.066 -4.750 0.000 -0.854 -0.355
## brandFiat -0.466 0.129 -0.040 -3.610 0.000 -0.719 -0.213
## brandForce -0.460 0.159 -0.015 -2.896 0.004 -0.771 -0.149
## brandFord -0.351 0.124 -0.092 -2.833 0.005 -0.594 -0.108
## brandHonda -0.193 0.124 -0.055 -1.561 0.118 -0.436 0.049
## brandHyundai -0.258 0.124 -0.118 -2.088 0.037 -0.500 -0.016
## brandIsuzu -0.342 0.165 -0.010 -2.069 0.039 -0.666 -0.018
## brandJaguar 0.222 0.128 0.025 1.740 0.082 -0.028 0.472
## brandJeep -0.204 0.132 -0.015 -1.547 0.122 -0.463 0.054
## brandKia -0.140 0.174 -0.004 -0.803 0.422 -0.481 0.202
## brandLand 0.580 0.159 0.019 3.638 0.000 0.267 0.892
## brandLexus 0.407 0.132 0.032 3.085 0.002 0.148 0.665
## brandMahindra -0.391 0.124 -0.139 -3.164 0.002 -0.633 -0.149
## brandMaruti -0.210 0.123 -0.116 -1.700 0.089 -0.452 0.032
## brandMercedes-Benz 0.193 0.129 0.019 1.505 0.132 -0.059 0.445
## brandMG 0.118 0.188 0.003 0.624 0.532 -0.252 0.487
## brandMitsubishi -0.089 0.139 -0.005 -0.637 0.524 -0.362 0.184
## brandNissan -0.299 0.126 -0.036 -2.371 0.018 -0.546 -0.052
## brandOpel 0.057 0.274 0.001 0.207 0.836 -0.481 0.595
## brandRenault -0.349 0.124 -0.070 -2.800 0.005 -0.593 -0.105
## brandSkoda -0.284 0.126 -0.039 -2.260 0.024 -0.530 -0.038
## brandTata -0.684 0.124 -0.238 -5.542 0.000 -0.927 -0.442
## brandToyota -0.036 0.124 -0.010 -0.293 0.770 -0.279 0.206
## brandVolkswagen -0.329 0.125 -0.060 -2.638 0.008 -0.573 -0.084
## brandVolvo 0.194 0.128 0.022 1.518 0.129 -0.057 0.445
## fuelDiesel 0.354 0.035 0.213 10.218 0.000 0.286 0.422
## fuelLPG 0.207 0.054 0.017 3.846 0.000 0.102 0.313
## fuelPetrol 0.131 0.035 0.079 3.796 0.000 0.063 0.199
## ownerFourth -0.155 0.021 -0.026 -7.524 0.000 -0.195 -0.114
## ownerSecond -0.090 0.007 -0.047 -12.692 0.000 -0.104 -0.076
## ownerTest 0.678 0.112 0.021 6.031 0.000 0.457 0.898
## ownerThird -0.126 0.012 -0.037 -10.250 0.000 -0.150 -0.102
## seats 0.034 0.005 0.039 7.470 0.000 0.025 0.043
## -------------------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 5
##
## - km_driven added
##
## Model Summary
## -------------------------------------------------------------
## R 0.956 RMSE 0.245
## R-Squared 0.913 Coef. Var 1.882
## Adj. R-Squared 0.913 MSE 0.060
## Pred R-Squared 0.911 MAE 0.186
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4943.970 43 114.976 1920.856 0.0000
## Residual 470.593 7862 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -220.928 1.929 -114.534 0.000 -224.710 -217.147
## year 0.116 0.001 0.540 120.770 0.000 0.114 0.117
## transmissionManual -0.073 0.011 -0.030 -6.519 0.000 -0.095 -0.051
## engine 0.000 0.000 0.123 14.757 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.319 0.000 0.008 0.009
## brandAshok -0.481 0.274 -0.007 -1.752 0.080 -1.018 0.057
## brandAudi 0.086 0.130 0.007 0.660 0.509 -0.169 0.341
## brandBMW 0.333 0.126 0.049 2.638 0.008 0.086 0.581
## brandChevrolet -0.597 0.124 -0.121 -4.806 0.000 -0.840 -0.353
## brandDaewoo 0.095 0.188 0.002 0.508 0.611 -0.272 0.463
## brandDatsun -0.579 0.127 -0.063 -4.558 0.000 -0.829 -0.330
## brandFiat -0.441 0.129 -0.038 -3.423 0.001 -0.694 -0.188
## brandForce -0.443 0.159 -0.015 -2.797 0.005 -0.754 -0.133
## brandFord -0.327 0.124 -0.085 -2.645 0.008 -0.569 -0.085
## brandHonda -0.168 0.124 -0.048 -1.360 0.174 -0.411 0.074
## brandHyundai -0.233 0.123 -0.106 -1.887 0.059 -0.475 0.009
## brandIsuzu -0.325 0.165 -0.010 -1.969 0.049 -0.648 -0.001
## brandJaguar 0.237 0.127 0.027 1.858 0.063 -0.013 0.487
## brandJeep -0.185 0.132 -0.014 -1.403 0.161 -0.443 0.073
## brandKia -0.126 0.174 -0.003 -0.724 0.469 -0.467 0.215
## brandLand 0.595 0.159 0.020 3.738 0.000 0.283 0.906
## brandLexus 0.430 0.132 0.034 3.265 0.001 0.172 0.688
## brandMahindra -0.368 0.123 -0.131 -2.985 0.003 -0.610 -0.127
## brandMaruti -0.186 0.123 -0.103 -1.505 0.132 -0.427 0.056
## brandMercedes-Benz 0.211 0.128 0.021 1.643 0.101 -0.041 0.462
## brandMG 0.142 0.188 0.003 0.755 0.450 -0.227 0.511
## brandMitsubishi -0.059 0.139 -0.003 -0.425 0.671 -0.332 0.214
## brandNissan -0.273 0.126 -0.033 -2.170 0.030 -0.520 -0.026
## brandOpel 0.067 0.274 0.001 0.245 0.806 -0.470 0.604
## brandRenault -0.322 0.124 -0.065 -2.592 0.010 -0.566 -0.079
## brandSkoda -0.259 0.125 -0.036 -2.063 0.039 -0.504 -0.013
## brandTata -0.660 0.123 -0.229 -5.352 0.000 -0.902 -0.418
## brandToyota -0.008 0.124 -0.002 -0.065 0.948 -0.250 0.234
## brandVolkswagen -0.304 0.124 -0.056 -2.446 0.014 -0.548 -0.060
## brandVolvo 0.207 0.128 0.023 1.620 0.105 -0.043 0.457
## fuelDiesel 0.356 0.035 0.214 10.286 0.000 0.288 0.424
## fuelLPG 0.206 0.054 0.016 3.825 0.000 0.100 0.311
## fuelPetrol 0.124 0.035 0.074 3.589 0.000 0.056 0.191
## ownerFourth -0.152 0.021 -0.026 -7.415 0.000 -0.193 -0.112
## ownerSecond -0.087 0.007 -0.046 -12.270 0.000 -0.101 -0.073
## ownerTest 0.677 0.112 0.021 6.040 0.000 0.458 0.897
## ownerThird -0.121 0.012 -0.036 -9.913 0.000 -0.145 -0.097
## seats 0.035 0.005 0.041 7.781 0.000 0.026 0.044
## km_driven 0.000 0.000 -0.023 -5.637 0.000 0.000 0.000
## -------------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.956 RMSE 0.245
## R-Squared 0.913 Coef. Var 1.882
## Adj. R-Squared 0.913 MSE 0.060
## Pred R-Squared 0.911 MAE 0.186
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4943.970 43 114.976 1920.856 0.0000
## Residual 470.593 7862 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------------
## (Intercept) -220.928 1.929 -114.534 0.000 -224.710 -217.147
## year 0.116 0.001 0.540 120.770 0.000 0.114 0.117
## transmissionManual -0.073 0.011 -0.030 -6.519 0.000 -0.095 -0.051
## engine 0.000 0.000 0.123 14.757 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.319 0.000 0.008 0.009
## brandAshok -0.481 0.274 -0.007 -1.752 0.080 -1.018 0.057
## brandAudi 0.086 0.130 0.007 0.660 0.509 -0.169 0.341
## brandBMW 0.333 0.126 0.049 2.638 0.008 0.086 0.581
## brandChevrolet -0.597 0.124 -0.121 -4.806 0.000 -0.840 -0.353
## brandDaewoo 0.095 0.188 0.002 0.508 0.611 -0.272 0.463
## brandDatsun -0.579 0.127 -0.063 -4.558 0.000 -0.829 -0.330
## brandFiat -0.441 0.129 -0.038 -3.423 0.001 -0.694 -0.188
## brandForce -0.443 0.159 -0.015 -2.797 0.005 -0.754 -0.133
## brandFord -0.327 0.124 -0.085 -2.645 0.008 -0.569 -0.085
## brandHonda -0.168 0.124 -0.048 -1.360 0.174 -0.411 0.074
## brandHyundai -0.233 0.123 -0.106 -1.887 0.059 -0.475 0.009
## brandIsuzu -0.325 0.165 -0.010 -1.969 0.049 -0.648 -0.001
## brandJaguar 0.237 0.127 0.027 1.858 0.063 -0.013 0.487
## brandJeep -0.185 0.132 -0.014 -1.403 0.161 -0.443 0.073
## brandKia -0.126 0.174 -0.003 -0.724 0.469 -0.467 0.215
## brandLand 0.595 0.159 0.020 3.738 0.000 0.283 0.906
## brandLexus 0.430 0.132 0.034 3.265 0.001 0.172 0.688
## brandMahindra -0.368 0.123 -0.131 -2.985 0.003 -0.610 -0.127
## brandMaruti -0.186 0.123 -0.103 -1.505 0.132 -0.427 0.056
## brandMercedes-Benz 0.211 0.128 0.021 1.643 0.101 -0.041 0.462
## brandMG 0.142 0.188 0.003 0.755 0.450 -0.227 0.511
## brandMitsubishi -0.059 0.139 -0.003 -0.425 0.671 -0.332 0.214
## brandNissan -0.273 0.126 -0.033 -2.170 0.030 -0.520 -0.026
## brandOpel 0.067 0.274 0.001 0.245 0.806 -0.470 0.604
## brandRenault -0.322 0.124 -0.065 -2.592 0.010 -0.566 -0.079
## brandSkoda -0.259 0.125 -0.036 -2.063 0.039 -0.504 -0.013
## brandTata -0.660 0.123 -0.229 -5.352 0.000 -0.902 -0.418
## brandToyota -0.008 0.124 -0.002 -0.065 0.948 -0.250 0.234
## brandVolkswagen -0.304 0.124 -0.056 -2.446 0.014 -0.548 -0.060
## brandVolvo 0.207 0.128 0.023 1.620 0.105 -0.043 0.457
## fuelDiesel 0.356 0.035 0.214 10.286 0.000 0.288 0.424
## fuelLPG 0.206 0.054 0.016 3.825 0.000 0.100 0.311
## fuelPetrol 0.124 0.035 0.074 3.589 0.000 0.056 0.191
## ownerFourth -0.152 0.021 -0.026 -7.415 0.000 -0.193 -0.112
## ownerSecond -0.087 0.007 -0.046 -12.270 0.000 -0.101 -0.073
## ownerTest 0.677 0.112 0.021 6.040 0.000 0.458 0.897
## ownerThird -0.121 0.012 -0.036 -9.913 0.000 -0.145 -0.097
## seats 0.035 0.005 0.041 7.781 0.000 0.026 0.044
## km_driven 0.000 0.000 -0.023 -5.637 0.000 0.000 0.000
## -------------------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 6
##
## - seller_type added
##
## Model Summary
## -------------------------------------------------------------
## R 0.956 RMSE 0.244
## R-Squared 0.913 Coef. Var 1.880
## Adj. R-Squared 0.913 MSE 0.060
## Pred R-Squared 0.911 MAE 0.185
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4944.989 45 109.889 1839.379 0.0000
## Residual 469.574 7860 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## ----------------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ----------------------------------------------------------------------------------------------------------------
## (Intercept) -220.511 1.933 -114.049 0.000 -224.302 -216.721
## year 0.115 0.001 0.539 120.285 0.000 0.114 0.117
## transmissionManual -0.067 0.011 -0.027 -5.888 0.000 -0.089 -0.045
## engine 0.000 0.000 0.123 14.756 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.294 0.000 0.008 0.009
## brandAshok -0.482 0.274 -0.007 -1.759 0.079 -1.020 0.055
## brandAudi 0.079 0.130 0.007 0.608 0.543 -0.176 0.334
## brandBMW 0.318 0.126 0.047 2.513 0.012 0.070 0.565
## brandChevrolet -0.595 0.124 -0.121 -4.800 0.000 -0.838 -0.352
## brandDaewoo 0.097 0.187 0.002 0.519 0.603 -0.270 0.465
## brandDatsun -0.578 0.127 -0.063 -4.551 0.000 -0.827 -0.329
## brandFiat -0.438 0.129 -0.038 -3.402 0.001 -0.691 -0.186
## brandForce -0.451 0.158 -0.015 -2.844 0.004 -0.761 -0.140
## brandFord -0.330 0.124 -0.086 -2.670 0.008 -0.572 -0.088
## brandHonda -0.173 0.124 -0.049 -1.396 0.163 -0.415 0.070
## brandHyundai -0.232 0.123 -0.106 -1.883 0.060 -0.474 0.010
## brandIsuzu -0.320 0.165 -0.010 -1.944 0.052 -0.644 0.003
## brandJaguar 0.217 0.127 0.025 1.700 0.089 -0.033 0.467
## brandJeep -0.180 0.132 -0.014 -1.370 0.171 -0.438 0.078
## brandKia -0.132 0.174 -0.004 -0.757 0.449 -0.472 0.209
## brandLand 0.576 0.159 0.019 3.622 0.000 0.264 0.887
## brandLexus 0.406 0.132 0.032 3.084 0.002 0.148 0.665
## brandMahindra -0.367 0.123 -0.131 -2.977 0.003 -0.609 -0.125
## brandMaruti -0.185 0.123 -0.103 -1.506 0.132 -0.427 0.056
## brandMercedes-Benz 0.204 0.128 0.020 1.593 0.111 -0.047 0.456
## brandMG 0.118 0.188 0.003 0.629 0.529 -0.250 0.487
## brandMitsubishi -0.063 0.139 -0.003 -0.453 0.651 -0.336 0.210
## brandNissan -0.272 0.126 -0.033 -2.162 0.031 -0.519 -0.025
## brandOpel 0.064 0.274 0.001 0.234 0.815 -0.472 0.600
## brandRenault -0.321 0.124 -0.065 -2.584 0.010 -0.565 -0.078
## brandSkoda -0.268 0.125 -0.037 -2.136 0.033 -0.513 -0.022
## brandTata -0.658 0.123 -0.229 -5.338 0.000 -0.899 -0.416
## brandToyota -0.013 0.124 -0.004 -0.107 0.915 -0.255 0.229
## brandVolkswagen -0.305 0.124 -0.056 -2.454 0.014 -0.549 -0.061
## brandVolvo 0.203 0.128 0.023 1.595 0.111 -0.047 0.453
## fuelDiesel 0.351 0.035 0.211 10.144 0.000 0.283 0.419
## fuelLPG 0.202 0.054 0.016 3.766 0.000 0.097 0.308
## fuelPetrol 0.120 0.034 0.072 3.479 0.001 0.052 0.188
## ownerFourth -0.149 0.021 -0.025 -7.231 0.000 -0.189 -0.108
## ownerSecond -0.084 0.007 -0.044 -11.729 0.000 -0.098 -0.070
## ownerTest 0.658 0.112 0.020 5.864 0.000 0.438 0.878
## ownerThird -0.117 0.012 -0.035 -9.543 0.000 -0.141 -0.093
## seats 0.036 0.005 0.042 7.895 0.000 0.027 0.045
## km_driven 0.000 0.000 -0.021 -5.327 0.000 0.000 0.000
## seller_typeIndividual -0.037 0.009 -0.017 -4.072 0.000 -0.055 -0.019
## seller_typeTrustmark Dealer -0.016 0.019 -0.003 -0.837 0.403 -0.053 0.021
## ----------------------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.956 RMSE 0.244
## R-Squared 0.913 Coef. Var 1.880
## Adj. R-Squared 0.913 MSE 0.060
## Pred R-Squared 0.911 MAE 0.185
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4944.989 45 109.889 1839.379 0.0000
## Residual 469.574 7860 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## ----------------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ----------------------------------------------------------------------------------------------------------------
## (Intercept) -220.511 1.933 -114.049 0.000 -224.302 -216.721
## year 0.115 0.001 0.539 120.285 0.000 0.114 0.117
## transmissionManual -0.067 0.011 -0.027 -5.888 0.000 -0.089 -0.045
## engine 0.000 0.000 0.123 14.756 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.294 0.000 0.008 0.009
## brandAshok -0.482 0.274 -0.007 -1.759 0.079 -1.020 0.055
## brandAudi 0.079 0.130 0.007 0.608 0.543 -0.176 0.334
## brandBMW 0.318 0.126 0.047 2.513 0.012 0.070 0.565
## brandChevrolet -0.595 0.124 -0.121 -4.800 0.000 -0.838 -0.352
## brandDaewoo 0.097 0.187 0.002 0.519 0.603 -0.270 0.465
## brandDatsun -0.578 0.127 -0.063 -4.551 0.000 -0.827 -0.329
## brandFiat -0.438 0.129 -0.038 -3.402 0.001 -0.691 -0.186
## brandForce -0.451 0.158 -0.015 -2.844 0.004 -0.761 -0.140
## brandFord -0.330 0.124 -0.086 -2.670 0.008 -0.572 -0.088
## brandHonda -0.173 0.124 -0.049 -1.396 0.163 -0.415 0.070
## brandHyundai -0.232 0.123 -0.106 -1.883 0.060 -0.474 0.010
## brandIsuzu -0.320 0.165 -0.010 -1.944 0.052 -0.644 0.003
## brandJaguar 0.217 0.127 0.025 1.700 0.089 -0.033 0.467
## brandJeep -0.180 0.132 -0.014 -1.370 0.171 -0.438 0.078
## brandKia -0.132 0.174 -0.004 -0.757 0.449 -0.472 0.209
## brandLand 0.576 0.159 0.019 3.622 0.000 0.264 0.887
## brandLexus 0.406 0.132 0.032 3.084 0.002 0.148 0.665
## brandMahindra -0.367 0.123 -0.131 -2.977 0.003 -0.609 -0.125
## brandMaruti -0.185 0.123 -0.103 -1.506 0.132 -0.427 0.056
## brandMercedes-Benz 0.204 0.128 0.020 1.593 0.111 -0.047 0.456
## brandMG 0.118 0.188 0.003 0.629 0.529 -0.250 0.487
## brandMitsubishi -0.063 0.139 -0.003 -0.453 0.651 -0.336 0.210
## brandNissan -0.272 0.126 -0.033 -2.162 0.031 -0.519 -0.025
## brandOpel 0.064 0.274 0.001 0.234 0.815 -0.472 0.600
## brandRenault -0.321 0.124 -0.065 -2.584 0.010 -0.565 -0.078
## brandSkoda -0.268 0.125 -0.037 -2.136 0.033 -0.513 -0.022
## brandTata -0.658 0.123 -0.229 -5.338 0.000 -0.899 -0.416
## brandToyota -0.013 0.124 -0.004 -0.107 0.915 -0.255 0.229
## brandVolkswagen -0.305 0.124 -0.056 -2.454 0.014 -0.549 -0.061
## brandVolvo 0.203 0.128 0.023 1.595 0.111 -0.047 0.453
## fuelDiesel 0.351 0.035 0.211 10.144 0.000 0.283 0.419
## fuelLPG 0.202 0.054 0.016 3.766 0.000 0.097 0.308
## fuelPetrol 0.120 0.034 0.072 3.479 0.001 0.052 0.188
## ownerFourth -0.149 0.021 -0.025 -7.231 0.000 -0.189 -0.108
## ownerSecond -0.084 0.007 -0.044 -11.729 0.000 -0.098 -0.070
## ownerTest 0.658 0.112 0.020 5.864 0.000 0.438 0.878
## ownerThird -0.117 0.012 -0.035 -9.543 0.000 -0.141 -0.093
## seats 0.036 0.005 0.042 7.895 0.000 0.027 0.045
## km_driven 0.000 0.000 -0.021 -5.327 0.000 0.000 0.000
## seller_typeIndividual -0.037 0.009 -0.017 -4.072 0.000 -0.055 -0.019
## seller_typeTrustmark Dealer -0.016 0.019 -0.003 -0.837 0.403 -0.053 0.021
## ----------------------------------------------------------------------------------------------------------------
##
##
##
## No more variables to be added/removed.
##
##
## Final Model Output
## ------------------
##
## Model Summary
## -------------------------------------------------------------
## R 0.956 RMSE 0.244
## R-Squared 0.913 Coef. Var 1.880
## Adj. R-Squared 0.913 MSE 0.060
## Pred R-Squared 0.911 MAE 0.185
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 4944.989 45 109.889 1839.379 0.0000
## Residual 469.574 7860 0.060
## Total 5414.563 7905
## ------------------------------------------------------------------------
##
## Parameter Estimates
## ----------------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ----------------------------------------------------------------------------------------------------------------
## (Intercept) -220.511 1.933 -114.049 0.000 -224.302 -216.721
## year 0.115 0.001 0.539 120.285 0.000 0.114 0.117
## transmissionManual -0.067 0.011 -0.027 -5.888 0.000 -0.089 -0.045
## engine 0.000 0.000 0.123 14.756 0.000 0.000 0.000
## max_power 0.008 0.000 0.356 51.294 0.000 0.008 0.009
## brandAshok -0.482 0.274 -0.007 -1.759 0.079 -1.020 0.055
## brandAudi 0.079 0.130 0.007 0.608 0.543 -0.176 0.334
## brandBMW 0.318 0.126 0.047 2.513 0.012 0.070 0.565
## brandChevrolet -0.595 0.124 -0.121 -4.800 0.000 -0.838 -0.352
## brandDaewoo 0.097 0.187 0.002 0.519 0.603 -0.270 0.465
## brandDatsun -0.578 0.127 -0.063 -4.551 0.000 -0.827 -0.329
## brandFiat -0.438 0.129 -0.038 -3.402 0.001 -0.691 -0.186
## brandForce -0.451 0.158 -0.015 -2.844 0.004 -0.761 -0.140
## brandFord -0.330 0.124 -0.086 -2.670 0.008 -0.572 -0.088
## brandHonda -0.173 0.124 -0.049 -1.396 0.163 -0.415 0.070
## brandHyundai -0.232 0.123 -0.106 -1.883 0.060 -0.474 0.010
## brandIsuzu -0.320 0.165 -0.010 -1.944 0.052 -0.644 0.003
## brandJaguar 0.217 0.127 0.025 1.700 0.089 -0.033 0.467
## brandJeep -0.180 0.132 -0.014 -1.370 0.171 -0.438 0.078
## brandKia -0.132 0.174 -0.004 -0.757 0.449 -0.472 0.209
## brandLand 0.576 0.159 0.019 3.622 0.000 0.264 0.887
## brandLexus 0.406 0.132 0.032 3.084 0.002 0.148 0.665
## brandMahindra -0.367 0.123 -0.131 -2.977 0.003 -0.609 -0.125
## brandMaruti -0.185 0.123 -0.103 -1.506 0.132 -0.427 0.056
## brandMercedes-Benz 0.204 0.128 0.020 1.593 0.111 -0.047 0.456
## brandMG 0.118 0.188 0.003 0.629 0.529 -0.250 0.487
## brandMitsubishi -0.063 0.139 -0.003 -0.453 0.651 -0.336 0.210
## brandNissan -0.272 0.126 -0.033 -2.162 0.031 -0.519 -0.025
## brandOpel 0.064 0.274 0.001 0.234 0.815 -0.472 0.600
## brandRenault -0.321 0.124 -0.065 -2.584 0.010 -0.565 -0.078
## brandSkoda -0.268 0.125 -0.037 -2.136 0.033 -0.513 -0.022
## brandTata -0.658 0.123 -0.229 -5.338 0.000 -0.899 -0.416
## brandToyota -0.013 0.124 -0.004 -0.107 0.915 -0.255 0.229
## brandVolkswagen -0.305 0.124 -0.056 -2.454 0.014 -0.549 -0.061
## brandVolvo 0.203 0.128 0.023 1.595 0.111 -0.047 0.453
## fuelDiesel 0.351 0.035 0.211 10.144 0.000 0.283 0.419
## fuelLPG 0.202 0.054 0.016 3.766 0.000 0.097 0.308
## fuelPetrol 0.120 0.034 0.072 3.479 0.001 0.052 0.188
## ownerFourth -0.149 0.021 -0.025 -7.231 0.000 -0.189 -0.108
## ownerSecond -0.084 0.007 -0.044 -11.729 0.000 -0.098 -0.070
## ownerTest 0.658 0.112 0.020 5.864 0.000 0.438 0.878
## ownerThird -0.117 0.012 -0.035 -9.543 0.000 -0.141 -0.093
## seats 0.036 0.005 0.042 7.895 0.000 0.027 0.045
## km_driven 0.000 0.000 -0.021 -5.327 0.000 0.000 0.000
## seller_typeIndividual -0.037 0.009 -0.017 -4.072 0.000 -0.055 -0.019
## seller_typeTrustmark Dealer -0.016 0.019 -0.003 -0.837 0.403 -0.053 0.021
## ----------------------------------------------------------------------------------------------------------------forwardstepwisemodel = lm(log(selling_price)~year+transmission+engine+max_power+brand+fuel,data=car_details)
backwardsmodel = lm(log(selling_price)~year + km_driven + fuel+ seller_type + transmission + owner + engine + max_power + seats +brand,data=car_details)set.seed(1236)
library(leaps)
#We are now trainning and testing our forward selection model and backwards model.
trainIndex<-createDataPartition(car_details$selling_price,p=.8,list=F) #p: proportion of data in train
training<-car_details[trainIndex,]
validate<-car_details[-trainIndex,]
reg.fwd=regsubsets(log(selling_price)~year + log(km_driven) + fuel+ seller_type + transmission + owner + mileage + log(engine) + log(max_power) + log(seats) + brand,data=car_details,method="forward",nvmax=20)
coef(reg.fwd,10)## (Intercept) year fuelDiesel transmissionManual
## -226.1113271 0.1159377 0.2082455 -0.2636134
## log(engine) log(max_power) brandBMW brandChevrolet
## 0.2496920 0.8859295 0.5864387 -0.3490934
## brandLexus brandTata brandToyota
## 0.7793731 -0.4118995 0.2519476reg.bwd=regsubsets(log(selling_price)~year + log(km_driven) + fuel+ seller_type + transmission + owner + mileage + log(engine) + log(max_power) + log(seats) + brand,data=car_details,method="backward",nvmax=20)
coef(reg.bwd,10)## (Intercept) year fuelDiesel log(max_power) brandChevrolet
## -223.8820918 0.1147257 0.2251209 1.3125028 -0.4701862
## brandFord brandHonda brandHyundai brandMahindra brandTata
## -0.2681248 -0.1752410 -0.1929691 -0.1481669 -0.5454645
## brandVolkswagen
## -0.2991710#Creating a prediction function
predict.regsubsets =function (object , newdata ,id ,...){
form=as.formula (object$call [[2]])
mat=model.matrix(form ,newdata )
coefi=coef(object ,id=id)
xvars=names(coefi)
mat[,xvars]%*%coefi
}
valMSE<-c()
#note my index, i, is to 20 since that is how many predictors I went up to during fwd selection
for (i in 1:10){
predictions<-predict.regsubsets(object=reg.fwd,newdata=validate,id=i)
valMSE[i]<-mean((log(validate$selling_price)-predictions)^2)
}
par(mfrow=c(1,1))
plot(1:10,sqrt(valMSE),type="l",xlab="# of predictors",ylab="test vs train RMSE",ylim=c(0.2381315,0.5360795))
index<-which(valMSE==min(valMSE))
points(index,sqrt(valMSE[index]),col="red",pch=10)
trainMSE<-summary(reg.fwd)$rss/nrow(training)
lines(1:20,sqrt(trainMSE),lty=3,col="blue") 
ForwardRSME = sqrt(valMSE[index])
ForwardRSME## [1] 0.2648139for (i in 1:10){
predictions<-predict.regsubsets(object=reg.bwd,newdata=validate,id=i)
valMSE[i]<-mean((log(validate$selling_price)-predictions)^2)
}
par(mfrow=c(1,1))
plot(1:10,sqrt(valMSE),type="l",xlab="# of predictors",ylab="test vs train RMSE",ylim=c(0.2381315,0.5360795))
index1<-which(valMSE==min(valMSE))
points(index1,sqrt(valMSE[index]),col="red",pch=10)
trainMSE<-summary(reg.bwd)$rss/nrow(training)
lines(1:20,sqrt(trainMSE),lty=3,col="blue") 
BackwardRSME = sqrt(valMSE[index1])
BackwardRSME## [1] 0.289365#Adjusted R-Squared for Forward
max(forward$adjr)## [1] 0.9127792#Adjusted R-squared for Backwards
max(backward$adjr)## [1] 0.9127792forwardstepwisemodeltest = lm(log(selling_price)~year+transmission+engine+max_power+brand+fuel,data=validate)
summary(forwardstepwisemodeltest)##
## Call:
## lm(formula = log(selling_price) ~ year + transmission + engine +
## max_power + brand + fuel, data = validate)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.23124 -0.14483 0.01187 0.15199 1.39104
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.351e+02 3.564e+00 -65.972 < 2e-16 ***
## year 1.224e-01 1.761e-03 69.521 < 2e-16 ***
## transmissionManual -9.968e-02 2.486e-02 -4.010 6.36e-05 ***
## engine 2.850e-04 2.825e-05 10.091 < 2e-16 ***
## max_power 8.299e-03 3.751e-04 22.122 < 2e-16 ***
## brandAudi 2.727e-01 2.808e-01 0.971 0.33169
## brandBMW 7.736e-01 2.569e-01 3.011 0.00264 **
## brandChevrolet -1.322e-01 2.520e-01 -0.525 0.59999
## brandDatsun -6.413e-02 2.586e-01 -0.248 0.80416
## brandFiat 4.931e-02 2.639e-01 0.187 0.85181
## brandForce -1.010e-01 3.523e-01 -0.287 0.77429
## brandFord 1.879e-01 2.502e-01 0.751 0.45270
## brandHonda 2.858e-01 2.504e-01 1.141 0.25386
## brandHyundai 2.350e-01 2.494e-01 0.942 0.34624
## brandJaguar 6.167e-01 2.632e-01 2.343 0.01924 *
## brandJeep 2.290e-01 2.706e-01 0.846 0.39764
## brandLand 1.112e+00 3.527e-01 3.153 0.00165 **
## brandLexus 7.584e-01 2.723e-01 2.785 0.00542 **
## brandMahindra 1.205e-01 2.499e-01 0.482 0.62970
## brandMaruti 3.142e-01 2.492e-01 1.261 0.20741
## brandMercedes-Benz 5.344e-01 2.663e-01 2.007 0.04495 *
## brandMG 5.442e-01 3.531e-01 1.541 0.12352
## brandMitsubishi 7.500e-01 2.879e-01 2.605 0.00927 **
## brandNissan 2.789e-01 2.590e-01 1.077 0.28183
## brandRenault 1.442e-01 2.516e-01 0.573 0.56667
## brandSkoda 2.033e-01 2.550e-01 0.797 0.42539
## brandTata -1.948e-01 2.496e-01 -0.781 0.43516
## brandToyota 3.975e-01 2.507e-01 1.586 0.11296
## brandVolkswagen 1.583e-01 2.520e-01 0.628 0.53004
## brandVolvo 6.082e-01 2.589e-01 2.350 0.01892 *
## fuelDiesel 3.971e-01 7.665e-02 5.181 2.50e-07 ***
## fuelLPG 6.397e-02 1.456e-01 0.439 0.66049
## fuelPetrol 1.974e-01 7.645e-02 2.582 0.00992 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2487 on 1546 degrees of freedom
## Multiple R-squared: 0.9149, Adjusted R-squared: 0.9132
## F-statistic: 519.5 on 32 and 1546 DF, p-value: < 2.2e-16backwardsmodel = lm(log(selling_price)~year + km_driven + fuel+ seller_type + transmission + owner + engine + max_power + seats +brand,data=validate)
summary(backwardsmodel)##
## Call:
## lm(formula = log(selling_price) ~ year + km_driven + fuel + seller_type +
## transmission + owner + engine + max_power + seats + brand,
## data = validate)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.32522 -0.14595 0.00501 0.16520 1.15487
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.119e+02 4.310e+00 -49.158 < 2e-16 ***
## year 1.109e-01 2.128e-03 52.100 < 2e-16 ***
## km_driven -7.826e-07 1.597e-07 -4.900 1.06e-06 ***
## fuelDiesel 3.755e-01 7.487e-02 5.015 5.93e-07 ***
## fuelLPG -5.100e-04 1.421e-01 -0.004 0.997137
## fuelPetrol 1.462e-01 7.487e-02 1.953 0.050967 .
## seller_typeIndividual -1.505e-02 1.994e-02 -0.755 0.450544
## seller_typeTrustmark Dealer 1.591e-02 4.156e-02 0.383 0.701952
## transmissionManual -9.104e-02 2.471e-02 -3.685 0.000237 ***
## ownerFourth -1.938e-01 4.350e-02 -4.454 9.03e-06 ***
## ownerSecond -7.572e-02 1.585e-02 -4.778 1.93e-06 ***
## ownerTest 3.717e-01 2.450e-01 1.517 0.129371
## ownerThird -1.259e-01 2.841e-02 -4.431 1.00e-05 ***
## engine 2.500e-04 3.037e-05 8.231 3.90e-16 ***
## max_power 8.403e-03 3.684e-04 22.809 < 2e-16 ***
## seats 3.072e-02 9.375e-03 3.277 0.001074 **
## brandAudi 2.749e-01 2.757e-01 0.997 0.318935
## brandBMW 7.197e-01 2.536e-01 2.837 0.004608 **
## brandChevrolet -1.681e-01 2.468e-01 -0.681 0.495804
## brandDatsun -1.123e-01 2.534e-01 -0.443 0.657623
## brandFiat 6.679e-03 2.591e-01 0.026 0.979441
## brandForce -2.156e-01 3.449e-01 -0.625 0.532067
## brandFord 1.508e-01 2.460e-01 0.613 0.540063
## brandHonda 2.369e-01 2.460e-01 0.963 0.335656
## brandHyundai 1.931e-01 2.451e-01 0.788 0.430751
## brandJaguar 5.509e-01 2.596e-01 2.122 0.033966 *
## brandJeep 1.929e-01 2.667e-01 0.723 0.469619
## brandLand 1.001e+00 3.450e-01 2.902 0.003765 **
## brandLexus 7.476e-01 2.687e-01 2.782 0.005469 **
## brandMahindra 5.018e-02 2.448e-01 0.205 0.837615
## brandMaruti 2.617e-01 2.445e-01 1.070 0.284605
## brandMercedes-Benz 4.770e-01 2.623e-01 1.819 0.069129 .
## brandMG 5.018e-01 3.459e-01 1.451 0.147031
## brandMitsubishi 6.662e-01 2.832e-01 2.353 0.018771 *
## brandNissan 2.283e-01 2.546e-01 0.897 0.369947
## brandRenault 9.561e-02 2.470e-01 0.387 0.698702
## brandSkoda 1.767e-01 2.507e-01 0.705 0.481015
## brandTata -2.457e-01 2.452e-01 -1.002 0.316347
## brandToyota 3.508e-01 2.459e-01 1.426 0.153954
## brandVolkswagen 1.224e-01 2.478e-01 0.494 0.621429
## brandVolvo 5.556e-01 2.552e-01 2.177 0.029642 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2423 on 1538 degrees of freedom
## Multiple R-squared: 0.9196, Adjusted R-squared: 0.9175
## F-statistic: 439.8 on 40 and 1538 DF, p-value: < 2.2e-16backwardsmodeltest = lm(log(selling_price)~year + km_driven + fuel+ seller_type + transmission + owner + engine + max_power + seats +brand,data=training)
summary(backwardsmodeltest)##
## Call:
## lm(formula = log(selling_price) ~ year + km_driven + fuel + seller_type +
## transmission + owner + engine + max_power + seats + brand,
## data = training)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.27015 -0.14574 0.01206 0.15821 1.88029
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.226e+02 2.172e+00 -102.509 < 2e-16 ***
## year 1.165e-01 1.078e-03 108.017 < 2e-16 ***
## km_driven -2.306e-07 6.305e-08 -3.658 0.000256 ***
## fuelDiesel 3.451e-01 3.894e-02 8.862 < 2e-16 ***
## fuelLPG 2.259e-01 5.853e-02 3.860 0.000114 ***
## fuelPetrol 1.129e-01 3.882e-02 2.909 0.003640 **
## seller_typeIndividual -4.314e-02 1.026e-02 -4.203 2.67e-05 ***
## seller_typeTrustmark Dealer -2.438e-02 2.139e-02 -1.140 0.254435
## transmissionManual -5.975e-02 1.287e-02 -4.644 3.49e-06 ***
## ownerFourth -1.379e-01 2.329e-02 -5.922 3.34e-09 ***
## ownerSecond -8.411e-02 8.023e-03 -10.485 < 2e-16 ***
## ownerTest 7.100e-01 1.267e-01 5.604 2.18e-08 ***
## ownerThird -1.143e-01 1.365e-02 -8.370 < 2e-16 ***
## engine 1.909e-04 1.535e-05 12.440 < 2e-16 ***
## max_power 8.204e-03 1.787e-04 45.920 < 2e-16 ***
## seats 3.702e-02 5.200e-03 7.119 1.20e-12 ***
## brandAudi 9.302e-02 1.315e-01 0.707 0.479367
## brandBMW 3.052e-01 1.274e-01 2.396 0.016616 *
## brandChevrolet -6.102e-01 1.245e-01 -4.902 9.70e-07 ***
## brandDaewoo 9.027e-02 1.877e-01 0.481 0.630672
## brandDatsun -6.032e-01 1.282e-01 -4.704 2.61e-06 ***
## brandFiat -4.584e-01 1.304e-01 -3.516 0.000441 ***
## brandForce -4.320e-01 1.649e-01 -2.621 0.008800 **
## brandFord -3.628e-01 1.239e-01 -2.927 0.003437 **
## brandHonda -1.846e-01 1.241e-01 -1.488 0.136893
## brandHyundai -2.483e-01 1.236e-01 -2.009 0.044553 *
## brandIsuzu -3.174e-01 1.652e-01 -1.921 0.054767 .
## brandJaguar 2.182e-01 1.286e-01 1.698 0.089624 .
## brandJeep -1.839e-01 1.339e-01 -1.374 0.169532
## brandKia -1.425e-01 1.741e-01 -0.818 0.413110
## brandLand 5.635e-01 1.655e-01 3.405 0.000666 ***
## brandLexus 4.094e-01 1.339e-01 3.058 0.002237 **
## brandMahindra -3.817e-01 1.237e-01 -3.086 0.002036 **
## brandMaruti -2.063e-01 1.235e-01 -1.671 0.094711 .
## brandMercedes-Benz 2.218e-01 1.294e-01 1.714 0.086663 .
## brandMG 1.158e-01 2.133e-01 0.543 0.587166
## brandMitsubishi -1.716e-01 1.436e-01 -1.195 0.232164
## brandNissan -3.018e-01 1.266e-01 -2.384 0.017168 *
## brandOpel 6.366e-02 2.739e-01 0.232 0.816200
## brandRenault -3.351e-01 1.248e-01 -2.685 0.007270 **
## brandSkoda -2.891e-01 1.261e-01 -2.293 0.021883 *
## brandTata -6.700e-01 1.236e-01 -5.423 6.09e-08 ***
## brandToyota -1.416e-02 1.240e-01 -0.114 0.909085
## brandVolkswagen -3.228e-01 1.249e-01 -2.584 0.009788 **
## brandVolvo 2.042e-01 1.291e-01 1.582 0.113636
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2446 on 6282 degrees of freedom
## Multiple R-squared: 0.9124, Adjusted R-squared: 0.9118
## F-statistic: 1488 on 44 and 6282 DF, p-value: < 2.2e-16ols_plot_resid_fit(backwardsmodel)
ols_plot_resid_lev(backwardsmodel)
ols_plot_resid_qq(backwardsmodel)
ols_plot_resid_hist(backwardsmodel)
ols_plot_resid_fit(backwardsmodeltest)
ols_plot_resid_lev(backwardsmodeltest)
ols_plot_resid_qq(backwardsmodeltest)
ols_plot_resid_hist(backwardsmodeltest)
Objective 2: Complex Models
Problem Statement: We are through a process of comparing multiple models using K-fold Cross Validation to test our model against each other for that can predict best for future data. We will have model 3, which will focus on logging the y and x variables as a Log-Log model. Model 4 will have a Log-Log transformation, but will also include more complexities in interactions.
Model 3: Log-Log Transformation : We will logging every numerical variables in both the response and predictor variables.
Model 4: Log-Log Transformation with Interactions: We performed a full interactions on our 2nd model, and selected the variables that were statistically significant.
Model Selections
#Model 3: Log-Log Transformation
model3 = lm(log(selling_price)~year + log(km_driven) + fuel+ seller_type + transmission + owner + mileage + log(engine) + log(max_power) + log(seats) + brand,data=car_details)
summary(model3)##
## Call:
## lm(formula = log(selling_price) ~ year + log(km_driven) + fuel +
## seller_type + transmission + owner + mileage + log(engine) +
## log(max_power) + log(seats) + brand, data = car_details)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.27879 -0.14445 0.01046 0.15066 1.57962
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.092e+02 2.250e+00 -92.976 < 2e-16 ***
## year 1.075e-01 1.121e-03 95.836 < 2e-16 ***
## log(km_driven) -4.296e-02 4.299e-03 -9.992 < 2e-16 ***
## fuelDiesel 2.955e-01 3.390e-02 8.715 < 2e-16 ***
## fuelLPG 2.132e-01 5.275e-02 4.041 5.37e-05 ***
## fuelPetrol 9.820e-02 3.407e-02 2.882 0.00396 **
## seller_typeIndividual -2.374e-02 8.922e-03 -2.661 0.00780 **
## seller_typeTrustmark Dealer -4.014e-02 1.859e-02 -2.159 0.03091 *
## transmissionManual -9.115e-02 1.109e-02 -8.221 2.33e-16 ***
## ownerFourth -1.584e-01 2.007e-02 -7.891 3.40e-15 ***
## ownerSecond -8.296e-02 7.007e-03 -11.839 < 2e-16 ***
## ownerTest 6.204e-01 1.097e-01 5.657 1.59e-08 ***
## ownerThird -1.206e-01 1.202e-02 -10.038 < 2e-16 ***
## mileage 2.026e-03 1.252e-03 1.619 0.10554
## log(engine) 3.580e-01 2.420e-02 14.793 < 2e-16 ***
## log(max_power) 7.589e-01 1.607e-02 47.214 < 2e-16 ***
## log(seats) 2.586e-01 2.802e-02 9.231 < 2e-16 ***
## brandAshok -5.499e-01 2.680e-01 -2.052 0.04019 *
## brandAudi 2.733e-01 1.273e-01 2.147 0.03179 *
## brandBMW 5.092e-01 1.233e-01 4.128 3.70e-05 ***
## brandChevrolet -6.237e-01 1.215e-01 -5.133 2.93e-07 ***
## brandDaewoo 7.283e-02 1.837e-01 0.396 0.69184
## brandDatsun -6.071e-01 1.244e-01 -4.880 1.08e-06 ***
## brandFiat -4.985e-01 1.262e-01 -3.950 7.89e-05 ***
## brandForce -4.634e-01 1.549e-01 -2.992 0.00278 **
## brandFord -3.852e-01 1.210e-01 -3.183 0.00146 **
## brandHonda -2.504e-01 1.212e-01 -2.066 0.03888 *
## brandHyundai -2.865e-01 1.208e-01 -2.371 0.01777 *
## brandIsuzu -2.219e-01 1.612e-01 -1.377 0.16868
## brandJaguar 3.638e-01 1.246e-01 2.920 0.00351 **
## brandJeep 3.639e-02 1.285e-01 0.283 0.77705
## brandKia -2.168e-01 1.700e-01 -1.275 0.20224
## brandLand 6.176e-01 1.557e-01 3.968 7.33e-05 ***
## brandLexus 6.777e-01 1.291e-01 5.250 1.56e-07 ***
## brandMahindra -3.941e-01 1.207e-01 -3.265 0.00110 **
## brandMaruti -2.117e-01 1.208e-01 -1.753 0.07963 .
## brandMercedes-Benz 3.859e-01 1.253e-01 3.079 0.00208 **
## brandMG 6.888e-02 1.839e-01 0.375 0.70803
## brandMitsubishi -3.378e-02 1.360e-01 -0.248 0.80393
## brandNissan -3.382e-01 1.233e-01 -2.743 0.00610 **
## brandOpel -1.293e-01 2.676e-01 -0.483 0.62904
## brandRenault -3.367e-01 1.218e-01 -2.765 0.00571 **
## brandSkoda -3.488e-01 1.227e-01 -2.843 0.00447 **
## brandTata -6.883e-01 1.207e-01 -5.703 1.22e-08 ***
## brandToyota -2.251e-02 1.209e-01 -0.186 0.85231
## brandVolkswagen -3.640e-01 1.218e-01 -2.989 0.00281 **
## brandVolvo 2.883e-01 1.247e-01 2.312 0.02080 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2389 on 7859 degrees of freedom
## Multiple R-squared: 0.9172, Adjusted R-squared: 0.9167
## F-statistic: 1891 on 46 and 7859 DF, p-value: < 2.2e-16#Model 3: Assumptions Checks for Normality & Constant Variance
par(mfrow=c(2,2))
plot(model3)## Warning: not plotting observations with leverage one:
## 4246## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
par(mfrow=c(1,1))
#Full Interaction
Interactionmodel = lm(log(selling_price)~(year + log(km_driven) + fuel+ seller_type + transmission + owner + mileage + log(engine) + log(max_power) + log(seats) + brand)^2,data=car_details)
summary(Interactionmodel)##
## Call:
## lm(formula = log(selling_price) ~ (year + log(km_driven) + fuel +
## seller_type + transmission + owner + mileage + log(engine) +
## log(max_power) + log(seats) + brand)^2, data = car_details)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.2367 -0.1101 0.0000 0.1231 1.5111
##
## Coefficients: (260 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) 8.486e+05 5.406e+05 1.570
## year -3.552e+02 2.263e+02 -1.570
## log(km_driven) -9.744e+03 6.201e+03 -1.571
## fuelDiesel -1.499e+02 9.036e+01 -1.659
## fuelLPG -8.899e+01 6.365e+01 -1.398
## fuelPetrol -9.656e-01 3.287e+01 -0.029
## seller_typeIndividual 6.715e+00 8.171e+00 0.822
## seller_typeTrustmark Dealer -1.236e+02 6.032e+01 -2.048
## transmissionManual -1.293e+01 1.046e+01 -1.236
## ownerFourth 2.880e+01 1.200e+01 2.400
## ownerSecond 2.161e+01 1.844e+01 1.172
## ownerTest 9.307e+00 3.771e+00 2.468
## ownerThird 2.831e+03 1.803e+03 1.570
## mileage -2.838e+00 2.024e+00 -1.402
## log(engine) -3.672e+03 2.339e+03 -1.570
## log(max_power) -1.797e+02 5.374e+01 -3.344
## log(seats) 1.311e+02 1.803e+01 7.269
## brandAshok 1.240e+04 7.901e+03 1.569
## brandAudi -8.484e+05 5.406e+05 -1.569
## brandBMW -8.484e+05 5.406e+05 -1.569
## brandChevrolet -8.485e+05 5.406e+05 -1.570
## brandDaewoo -8.208e+05 5.248e+05 -1.564
## brandDatsun -8.486e+05 5.406e+05 -1.570
## brandFiat -8.484e+05 5.406e+05 -1.569
## brandForce -1.173e+06 7.469e+05 -1.571
## brandFord -8.485e+05 5.406e+05 -1.569
## brandHonda -8.485e+05 5.406e+05 -1.569
## brandHyundai -8.485e+05 5.406e+05 -1.569
## brandIsuzu 8.986e+05 5.720e+05 1.571
## brandJaguar -8.498e+05 5.416e+05 -1.569
## brandJeep -8.484e+05 5.406e+05 -1.569
## brandKia -7.883e+05 5.002e+05 -1.576
## brandLand 5.247e+06 3.341e+06 1.570
## brandLexus -5.936e+03 3.783e+03 -1.569
## brandMahindra -8.485e+05 5.406e+05 -1.569
## brandMaruti -8.485e+05 5.406e+05 -1.569
## brandMercedes-Benz -8.485e+05 5.406e+05 -1.569
## brandMG -8.223e+05 5.234e+05 -1.571
## brandMitsubishi -8.498e+05 5.405e+05 -1.572
## brandNissan -8.485e+05 5.406e+05 -1.569
## brandOpel -1.367e+03 8.711e+02 -1.570
## brandRenault -8.484e+05 5.406e+05 -1.569
## brandSkoda -8.485e+05 5.406e+05 -1.570
## brandTata -8.485e+05 5.406e+05 -1.569
## brandToyota -8.485e+05 5.406e+05 -1.569
## brandVolkswagen -8.484e+05 5.406e+05 -1.569
## brandVolvo -8.202e+05 5.228e+05 -1.569
## year:log(km_driven) 6.897e-03 1.378e-03 5.003
## year:fuelDiesel 1.222e-02 1.606e-02 0.761
## year:fuelLPG 4.810e-02 3.086e-02 1.558
## year:fuelPetrol 2.163e-03 1.608e-02 0.134
## year:seller_typeIndividual -3.177e-03 4.064e-03 -0.782
## year:seller_typeTrustmark Dealer 5.945e-02 2.957e-02 2.010
## year:transmissionManual 6.494e-03 5.186e-03 1.252
## year:ownerFourth -1.495e-02 5.994e-03 -2.494
## year:ownerSecond 2.667e-03 2.428e-03 1.099
## year:ownerTest NA NA NA
## year:ownerThird 3.869e-05 4.187e-03 0.009
## year:mileage -1.758e-04 4.105e-04 -0.428
## year:log(engine) -8.722e-04 9.136e-03 -0.095
## year:log(max_power) 4.973e-02 5.476e-03 9.082
## year:log(seats) -6.642e-02 8.862e-03 -7.494
## year:brandAshok NA NA NA
## year:brandAudi 3.551e+02 2.263e+02 1.569
## year:brandBMW 3.551e+02 2.263e+02 1.569
## year:brandChevrolet 3.551e+02 2.263e+02 1.570
## year:brandDaewoo 3.537e+02 2.263e+02 1.563
## year:brandDatsun 3.552e+02 2.263e+02 1.570
## year:brandFiat 3.551e+02 2.263e+02 1.569
## year:brandForce 5.293e+02 3.369e+02 1.571
## year:brandFord 3.551e+02 2.263e+02 1.569
## year:brandHonda 3.551e+02 2.263e+02 1.570
## year:brandHyundai 3.551e+02 2.263e+02 1.570
## year:brandIsuzu -4.887e+02 3.111e+02 -1.571
## year:brandJaguar 3.557e+02 2.267e+02 1.569
## year:brandJeep 3.550e+02 2.263e+02 1.569
## year:brandKia 3.389e+02 2.149e+02 1.577
## year:brandLand -2.574e+03 1.639e+03 -1.570
## year:brandLexus NA NA NA
## year:brandMahindra 3.551e+02 2.263e+02 1.570
## year:brandMaruti 3.551e+02 2.263e+02 1.570
## year:brandMercedes-Benz 3.551e+02 2.263e+02 1.570
## year:brandMG 3.556e+02 2.263e+02 1.571
## year:brandMitsubishi 3.550e+02 2.263e+02 1.569
## year:brandNissan 3.551e+02 2.263e+02 1.570
## year:brandOpel NA NA NA
## year:brandRenault 3.551e+02 2.263e+02 1.569
## year:brandSkoda 3.551e+02 2.263e+02 1.570
## year:brandTata 3.551e+02 2.263e+02 1.570
## year:brandToyota 3.551e+02 2.263e+02 1.570
## year:brandVolkswagen 3.551e+02 2.263e+02 1.569
## year:brandVolvo 3.552e+02 2.264e+02 1.569
## log(km_driven):fuelDiesel 5.703e-03 5.312e-02 0.107
## log(km_driven):fuelLPG 7.372e-02 1.146e-01 0.643
## log(km_driven):fuelPetrol 3.080e-02 5.298e-02 0.581
## log(km_driven):seller_typeIndividual -7.959e-03 1.424e-02 -0.559
## log(km_driven):seller_typeTrustmark Dealer 7.170e-02 6.454e-02 1.111
## log(km_driven):transmissionManual 1.348e-02 1.551e-02 0.869
## log(km_driven):ownerFourth 1.275e-02 5.230e-02 0.244
## log(km_driven):ownerSecond 2.273e-02 1.214e-02 1.872
## log(km_driven):ownerTest 8.583e-02 2.817e-01 0.305
## log(km_driven):ownerThird 1.282e-02 2.726e-02 0.470
## log(km_driven):mileage 1.799e-04 1.878e-03 0.096
## log(km_driven):log(engine) 1.227e-01 3.809e-02 3.222
## log(km_driven):log(max_power) -7.690e-02 2.534e-02 -3.035
## log(km_driven):log(seats) -1.092e-01 3.886e-02 -2.809
## log(km_driven):brandAshok NA NA NA
## log(km_driven):brandAudi 9.730e+03 6.201e+03 1.569
## log(km_driven):brandBMW 9.730e+03 6.201e+03 1.569
## log(km_driven):brandChevrolet 9.730e+03 6.201e+03 1.569
## log(km_driven):brandDaewoo 9.731e+03 6.201e+03 1.569
## log(km_driven):brandDatsun 9.730e+03 6.201e+03 1.569
## log(km_driven):brandFiat 9.730e+03 6.201e+03 1.569
## log(km_driven):brandForce 1.001e+04 6.376e+03 1.569
## log(km_driven):brandFord 9.730e+03 6.201e+03 1.569
## log(km_driven):brandHonda 9.730e+03 6.201e+03 1.569
## log(km_driven):brandHyundai 9.730e+03 6.201e+03 1.569
## log(km_driven):brandIsuzu 8.358e+03 5.327e+03 1.569
## log(km_driven):brandJaguar 9.733e+03 6.203e+03 1.569
## log(km_driven):brandJeep 9.730e+03 6.201e+03 1.569
## log(km_driven):brandKia 9.719e+03 6.193e+03 1.569
## log(km_driven):brandLand -5.639e+03 3.587e+03 -1.572
## log(km_driven):brandLexus NA NA NA
## log(km_driven):brandMahindra 9.730e+03 6.201e+03 1.569
## log(km_driven):brandMaruti 9.730e+03 6.201e+03 1.569
## log(km_driven):brandMercedes-Benz 9.730e+03 6.201e+03 1.569
## log(km_driven):brandMG 9.730e+03 6.201e+03 1.569
## log(km_driven):brandMitsubishi 9.730e+03 6.201e+03 1.569
## log(km_driven):brandNissan 9.730e+03 6.201e+03 1.569
## log(km_driven):brandOpel NA NA NA
## log(km_driven):brandRenault 9.730e+03 6.201e+03 1.569
## log(km_driven):brandSkoda 9.730e+03 6.201e+03 1.569
## log(km_driven):brandTata 9.730e+03 6.201e+03 1.569
## log(km_driven):brandToyota 9.730e+03 6.201e+03 1.569
## log(km_driven):brandVolkswagen 9.730e+03 6.201e+03 1.569
## log(km_driven):brandVolvo 9.728e+03 6.200e+03 1.569
## fuelDiesel:seller_typeIndividual 1.046e-01 3.294e-02 3.176
## fuelLPG:seller_typeIndividual -8.712e-03 2.360e-01 -0.037
## fuelPetrol:seller_typeIndividual NA NA NA
## fuelDiesel:seller_typeTrustmark Dealer -4.638e-02 2.626e-01 -0.177
## fuelLPG:seller_typeTrustmark Dealer NA NA NA
## fuelPetrol:seller_typeTrustmark Dealer NA NA NA
## fuelDiesel:transmissionManual 3.015e-03 4.493e-02 0.067
## fuelLPG:transmissionManual NA NA NA
## fuelPetrol:transmissionManual NA NA NA
## fuelDiesel:ownerFourth 3.253e-01 9.337e-01 0.348
## fuelLPG:ownerFourth 5.811e-01 9.342e-01 0.622
## fuelPetrol:ownerFourth 1.768e-01 9.264e-01 0.191
## fuelDiesel:ownerSecond 6.296e-02 7.841e-02 0.803
## fuelLPG:ownerSecond 1.181e-01 1.227e-01 0.963
## fuelPetrol:ownerSecond 5.973e-02 7.945e-02 0.752
## fuelDiesel:ownerTest 3.724e+00 2.013e+00 1.851
## fuelLPG:ownerTest NA NA NA
## fuelPetrol:ownerTest NA NA NA
## fuelDiesel:ownerThird -9.087e-02 1.733e-01 -0.524
## fuelLPG:ownerThird -5.103e-02 2.198e-01 -0.232
## fuelPetrol:ownerThird -2.275e-01 1.739e-01 -1.308
## fuelDiesel:mileage -3.765e-02 2.037e-02 -1.848
## fuelLPG:mileage -2.282e-02 2.402e-02 -0.950
## fuelPetrol:mileage -2.869e-02 2.025e-02 -1.417
## fuelDiesel:log(engine) -1.044e+00 7.651e-01 -1.364
## fuelLPG:log(engine) -1.966e+00 1.324e+00 -1.485
## fuelPetrol:log(engine) -9.199e-01 7.670e-01 -1.199
## fuelDiesel:log(max_power) 9.108e-01 5.155e-01 1.767
## fuelLPG:log(max_power) 1.406e+00 9.217e-01 1.525
## fuelPetrol:log(max_power) 9.244e-01 5.192e-01 1.780
## fuelDiesel:log(seats) -1.558e-01 5.342e-01 -0.292
## fuelLPG:log(seats) NA NA NA
## fuelPetrol:log(seats) -8.823e-02 5.418e-01 -0.163
## fuelDiesel:brandAshok NA NA NA
## fuelLPG:brandAshok NA NA NA
## fuelPetrol:brandAshok NA NA NA
## fuelDiesel:brandAudi 1.306e+02 8.417e+01 1.551
## fuelLPG:brandAudi NA NA NA
## fuelPetrol:brandAudi NA NA NA
## fuelDiesel:brandBMW 1.303e+02 8.417e+01 1.548
## fuelLPG:brandBMW NA NA NA
## fuelPetrol:brandBMW NA NA NA
## fuelDiesel:brandChevrolet 1.305e+02 8.417e+01 1.550
## fuelLPG:brandChevrolet 6.474e-01 3.336e-01 1.941
## fuelPetrol:brandChevrolet NA NA NA
## fuelDiesel:brandDaewoo NA NA NA
## fuelLPG:brandDaewoo NA NA NA
## fuelPetrol:brandDaewoo NA NA NA
## fuelDiesel:brandDatsun NA NA NA
## fuelLPG:brandDatsun NA NA NA
## fuelPetrol:brandDatsun NA NA NA
## fuelDiesel:brandFiat 1.301e+02 8.417e+01 1.546
## fuelLPG:brandFiat NA NA NA
## fuelPetrol:brandFiat NA NA NA
## fuelDiesel:brandForce NA NA NA
## fuelLPG:brandForce NA NA NA
## fuelPetrol:brandForce NA NA NA
## fuelDiesel:brandFord 1.305e+02 8.417e+01 1.550
## fuelLPG:brandFord NA NA NA
## fuelPetrol:brandFord NA NA NA
## fuelDiesel:brandHonda 1.301e+02 8.417e+01 1.546
## fuelLPG:brandHonda NA NA NA
## fuelPetrol:brandHonda NA NA NA
## fuelDiesel:brandHyundai 1.298e+02 8.417e+01 1.542
## fuelLPG:brandHyundai -2.015e-01 2.885e-01 -0.698
## fuelPetrol:brandHyundai -3.976e-01 3.743e-01 -1.062
## fuelDiesel:brandIsuzu NA NA NA
## fuelLPG:brandIsuzu NA NA NA
## fuelPetrol:brandIsuzu NA NA NA
## fuelDiesel:brandJaguar NA NA NA
## fuelLPG:brandJaguar NA NA NA
## fuelPetrol:brandJaguar NA NA NA
## fuelDiesel:brandJeep 1.405e+02 8.442e+01 1.664
## fuelLPG:brandJeep NA NA NA
## fuelPetrol:brandJeep NA NA NA
## fuelDiesel:brandKia NA NA NA
## fuelLPG:brandKia NA NA NA
## fuelPetrol:brandKia NA NA NA
## fuelDiesel:brandLand NA NA NA
## fuelLPG:brandLand NA NA NA
## fuelPetrol:brandLand NA NA NA
## fuelDiesel:brandLexus NA NA NA
## fuelLPG:brandLexus NA NA NA
## fuelPetrol:brandLexus NA NA NA
## fuelDiesel:brandMahindra 1.304e+02 8.417e+01 1.550
## fuelLPG:brandMahindra NA NA NA
## fuelPetrol:brandMahindra NA NA NA
## fuelDiesel:brandMaruti 1.301e+02 8.417e+01 1.545
## fuelLPG:brandMaruti NA NA NA
## fuelPetrol:brandMaruti -2.929e-01 2.440e-01 -1.200
## fuelDiesel:brandMercedes-Benz 1.302e+02 8.417e+01 1.547
## fuelLPG:brandMercedes-Benz NA NA NA
## fuelPetrol:brandMercedes-Benz NA NA NA
## fuelDiesel:brandMG NA NA NA
## fuelLPG:brandMG NA NA NA
## fuelPetrol:brandMG NA NA NA
## fuelDiesel:brandMitsubishi NA NA NA
## fuelLPG:brandMitsubishi NA NA NA
## fuelPetrol:brandMitsubishi NA NA NA
## fuelDiesel:brandNissan 1.306e+02 8.417e+01 1.551
## fuelLPG:brandNissan NA NA NA
## fuelPetrol:brandNissan NA NA NA
## fuelDiesel:brandOpel NA NA NA
## fuelLPG:brandOpel NA NA NA
## fuelPetrol:brandOpel NA NA NA
## fuelDiesel:brandRenault 1.307e+02 8.417e+01 1.553
## fuelLPG:brandRenault NA NA NA
## fuelPetrol:brandRenault NA NA NA
## fuelDiesel:brandSkoda 1.305e+02 8.417e+01 1.550
## fuelLPG:brandSkoda NA NA NA
## fuelPetrol:brandSkoda NA NA NA
## fuelDiesel:brandTata 1.302e+02 8.417e+01 1.546
## fuelLPG:brandTata NA NA NA
## fuelPetrol:brandTata NA NA NA
## fuelDiesel:brandToyota 1.304e+02 8.417e+01 1.549
## fuelLPG:brandToyota NA NA NA
## fuelPetrol:brandToyota NA NA NA
## fuelDiesel:brandVolkswagen 1.301e+02 8.417e+01 1.546
## fuelLPG:brandVolkswagen NA NA NA
## fuelPetrol:brandVolkswagen NA NA NA
## fuelDiesel:brandVolvo NA NA NA
## fuelLPG:brandVolvo NA NA NA
## fuelPetrol:brandVolvo NA NA NA
## seller_typeIndividual:transmissionManual 1.069e-02 2.817e-02 0.379
## seller_typeTrustmark Dealer:transmissionManual 1.091e-01 7.810e-02 1.396
## seller_typeIndividual:ownerFourth NA NA NA
## seller_typeTrustmark Dealer:ownerFourth NA NA NA
## seller_typeIndividual:ownerSecond -8.511e-02 2.758e-02 -3.086
## seller_typeTrustmark Dealer:ownerSecond -1.977e-01 1.646e-01 -1.201
## seller_typeIndividual:ownerTest NA NA NA
## seller_typeTrustmark Dealer:ownerTest NA NA NA
## seller_typeIndividual:ownerThird -1.091e-01 1.083e-01 -1.007
## seller_typeTrustmark Dealer:ownerThird NA NA NA
## seller_typeIndividual:mileage -5.288e-03 4.374e-03 -1.209
## seller_typeTrustmark Dealer:mileage -5.141e-03 3.786e-02 -0.136
## seller_typeIndividual:log(engine) -1.824e-01 9.520e-02 -1.917
## seller_typeTrustmark Dealer:log(engine) -4.914e-01 6.323e-01 -0.777
## seller_typeIndividual:log(max_power) 9.036e-02 6.456e-02 1.400
## seller_typeTrustmark Dealer:log(max_power) 8.319e-01 4.721e-01 1.762
## seller_typeIndividual:log(seats) 1.967e-01 1.044e-01 1.884
## seller_typeTrustmark Dealer:log(seats) 1.689e+00 1.776e+00 0.951
## seller_typeIndividual:brandAshok NA NA NA
## seller_typeTrustmark Dealer:brandAshok NA NA NA
## seller_typeIndividual:brandAudi 3.152e-01 3.458e-01 0.911
## seller_typeTrustmark Dealer:brandAudi NA NA NA
## seller_typeIndividual:brandBMW 3.276e-01 3.360e-01 0.975
## seller_typeTrustmark Dealer:brandBMW NA NA NA
## seller_typeIndividual:brandChevrolet 3.034e-01 3.359e-01 0.903
## seller_typeTrustmark Dealer:brandChevrolet NA NA NA
## seller_typeIndividual:brandDaewoo NA NA NA
## seller_typeTrustmark Dealer:brandDaewoo NA NA NA
## seller_typeIndividual:brandDatsun 3.246e-01 3.431e-01 0.946
## seller_typeTrustmark Dealer:brandDatsun NA NA NA
## seller_typeIndividual:brandFiat 2.008e-01 4.005e-01 0.501
## seller_typeTrustmark Dealer:brandFiat NA NA NA
## seller_typeIndividual:brandForce -4.455e+02 2.829e+02 -1.575
## seller_typeTrustmark Dealer:brandForce NA NA NA
## seller_typeIndividual:brandFord 3.820e-01 3.293e-01 1.160
## seller_typeTrustmark Dealer:brandFord 1.249e-02 2.628e-01 0.048
## seller_typeIndividual:brandHonda 4.645e-01 3.295e-01 1.410
## seller_typeTrustmark Dealer:brandHonda 3.624e-02 1.928e-01 0.188
## seller_typeIndividual:brandHyundai 4.154e-01 3.286e-01 1.264
## seller_typeTrustmark Dealer:brandHyundai -8.597e-02 2.482e-01 -0.346
## seller_typeIndividual:brandIsuzu -8.761e+02 5.586e+02 -1.568
## seller_typeTrustmark Dealer:brandIsuzu NA NA NA
## seller_typeIndividual:brandJaguar -2.560e+00 2.587e+00 -0.990
## seller_typeTrustmark Dealer:brandJaguar NA NA NA
## seller_typeIndividual:brandJeep 4.335e-01 3.572e-01 1.214
## seller_typeTrustmark Dealer:brandJeep NA NA NA
## seller_typeIndividual:brandKia NA NA NA
## seller_typeTrustmark Dealer:brandKia NA NA NA
## seller_typeIndividual:brandLand NA NA NA
## seller_typeTrustmark Dealer:brandLand NA NA NA
## seller_typeIndividual:brandLexus NA NA NA
## seller_typeTrustmark Dealer:brandLexus NA NA NA
## seller_typeIndividual:brandMahindra 3.145e-01 3.307e-01 0.951
## seller_typeTrustmark Dealer:brandMahindra NA NA NA
## seller_typeIndividual:brandMaruti 3.868e-01 3.296e-01 1.174
## seller_typeTrustmark Dealer:brandMaruti 5.754e-02 2.586e-01 0.222
## seller_typeIndividual:brandMercedes-Benz 4.403e-01 3.340e-01 1.319
## seller_typeTrustmark Dealer:brandMercedes-Benz NA NA NA
## seller_typeIndividual:brandMG NA NA NA
## seller_typeTrustmark Dealer:brandMG NA NA NA
## seller_typeIndividual:brandMitsubishi 8.653e-01 4.684e-01 1.847
## seller_typeTrustmark Dealer:brandMitsubishi NA NA NA
## seller_typeIndividual:brandNissan 6.189e-01 3.394e-01 1.823
## seller_typeTrustmark Dealer:brandNissan -2.120e-01 2.624e-01 -0.808
## seller_typeIndividual:brandOpel NA NA NA
## seller_typeTrustmark Dealer:brandOpel NA NA NA
## seller_typeIndividual:brandRenault 4.214e-01 3.320e-01 1.270
## seller_typeTrustmark Dealer:brandRenault NA NA NA
## seller_typeIndividual:brandSkoda 2.756e-01 3.340e-01 0.825
## seller_typeTrustmark Dealer:brandSkoda 1.053e-01 2.582e-01 0.408
## seller_typeIndividual:brandTata 4.978e-01 3.305e-01 1.506
## seller_typeTrustmark Dealer:brandTata NA NA NA
## seller_typeIndividual:brandToyota 4.517e-01 3.302e-01 1.368
## seller_typeTrustmark Dealer:brandToyota NA NA NA
## seller_typeIndividual:brandVolkswagen 3.462e-01 3.310e-01 1.046
## seller_typeTrustmark Dealer:brandVolkswagen NA NA NA
## seller_typeIndividual:brandVolvo NA NA NA
## seller_typeTrustmark Dealer:brandVolvo NA NA NA
## transmissionManual:ownerFourth -2.425e-01 1.168e-01 -2.076
## transmissionManual:ownerSecond -5.049e-02 3.204e-02 -1.576
## transmissionManual:ownerTest NA NA NA
## transmissionManual:ownerThird 7.272e-02 6.670e-02 1.090
## transmissionManual:mileage -2.071e-03 6.754e-03 -0.307
## transmissionManual:log(engine) -2.178e-01 1.673e-01 -1.302
## transmissionManual:log(max_power) 9.605e-02 1.302e-01 0.737
## transmissionManual:log(seats) 3.990e-01 1.740e-01 2.293
## transmissionManual:brandAshok NA NA NA
## transmissionManual:brandAudi NA NA NA
## transmissionManual:brandBMW NA NA NA
## transmissionManual:brandChevrolet 3.252e-01 1.133e-01 2.872
## transmissionManual:brandDaewoo NA NA NA
## transmissionManual:brandDatsun 2.783e-01 2.326e-01 1.196
## transmissionManual:brandFiat NA NA NA
## transmissionManual:brandForce NA NA NA
## transmissionManual:brandFord 1.738e-01 9.651e-02 1.801
## transmissionManual:brandHonda 1.361e-01 7.192e-02 1.892
## transmissionManual:brandHyundai 1.767e-01 6.508e-02 2.716
## transmissionManual:brandIsuzu NA NA NA
## transmissionManual:brandJaguar NA NA NA
## transmissionManual:brandJeep 1.644e-01 2.836e-01 0.580
## transmissionManual:brandKia NA NA NA
## transmissionManual:brandLand NA NA NA
## transmissionManual:brandLexus NA NA NA
## transmissionManual:brandMahindra 5.296e-03 8.519e-02 0.062
## transmissionManual:brandMaruti 1.713e-01 6.732e-02 2.544
## transmissionManual:brandMercedes-Benz 2.948e-01 1.712e-01 1.722
## transmissionManual:brandMG NA NA NA
## transmissionManual:brandMitsubishi NA NA NA
## transmissionManual:brandNissan 2.556e-01 1.037e-01 2.466
## transmissionManual:brandOpel NA NA NA
## transmissionManual:brandRenault -4.212e-02 9.546e-02 -0.441
## transmissionManual:brandSkoda 2.342e-01 9.690e-02 2.417
## transmissionManual:brandTata -2.257e-02 8.126e-02 -0.278
## transmissionManual:brandToyota 2.069e-01 8.251e-02 2.507
## transmissionManual:brandVolkswagen NA NA NA
## transmissionManual:brandVolvo NA NA NA
## ownerFourth:mileage 9.564e-03 7.980e-03 1.198
## ownerSecond:mileage 3.219e-03 3.075e-03 1.047
## ownerTest:mileage -6.029e-01 2.831e-01 -2.129
## ownerThird:mileage -1.542e-02 5.986e-03 -2.576
## ownerFourth:log(engine) 1.546e-01 1.803e-01 0.857
## ownerSecond:log(engine) 5.819e-02 5.631e-02 1.034
## ownerTest:log(engine) NA NA NA
## ownerThird:log(engine) -1.991e-01 1.050e-01 -1.897
## ownerFourth:log(max_power) -8.458e-02 1.129e-01 -0.749
## ownerSecond:log(max_power) -2.341e-02 3.565e-02 -0.657
## ownerTest:log(max_power) NA NA NA
## ownerThird:log(max_power) -6.766e-03 6.510e-02 -0.104
## ownerFourth:log(seats) -2.280e-02 1.518e-01 -0.150
## ownerSecond:log(seats) 9.461e-03 6.628e-02 0.143
## ownerTest:log(seats) NA NA NA
## ownerThird:log(seats) 5.665e-02 1.091e-01 0.519
## ownerFourth:brandAshok NA NA NA
## ownerSecond:brandAshok NA NA NA
## ownerTest:brandAshok NA NA NA
## ownerThird:brandAshok NA NA NA
## ownerFourth:brandAudi -6.049e-01 3.045e-01 -1.986
## ownerSecond:brandAudi -2.758e+01 1.779e+01 -1.550
## ownerTest:brandAudi NA NA NA
## ownerThird:brandAudi -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandBMW -4.402e-01 2.855e-01 -1.542
## ownerSecond:brandBMW -2.761e+01 1.779e+01 -1.552
## ownerTest:brandBMW NA NA NA
## ownerThird:brandBMW -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandChevrolet 2.037e-01 1.193e-01 1.708
## ownerSecond:brandChevrolet -2.759e+01 1.779e+01 -1.550
## ownerTest:brandChevrolet NA NA NA
## ownerThird:brandChevrolet -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandDaewoo NA NA NA
## ownerSecond:brandDaewoo NA NA NA
## ownerTest:brandDaewoo NA NA NA
## ownerThird:brandDaewoo NA NA NA
## ownerFourth:brandDatsun NA NA NA
## ownerSecond:brandDatsun -2.750e+01 1.779e+01 -1.546
## ownerTest:brandDatsun NA NA NA
## ownerThird:brandDatsun -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandFiat NA NA NA
## ownerSecond:brandFiat -2.782e+01 1.779e+01 -1.563
## ownerTest:brandFiat NA NA NA
## ownerThird:brandFiat -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandForce NA NA NA
## ownerSecond:brandForce NA NA NA
## ownerTest:brandForce NA NA NA
## ownerThird:brandForce NA NA NA
## ownerFourth:brandFord -1.508e-01 1.362e-01 -1.107
## ownerSecond:brandFord -2.765e+01 1.779e+01 -1.554
## ownerTest:brandFord NA NA NA
## ownerThird:brandFord -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandHonda 1.955e-02 2.463e-01 0.079
## ownerSecond:brandHonda -2.764e+01 1.779e+01 -1.553
## ownerTest:brandHonda NA NA NA
## ownerThird:brandHonda -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandHyundai 7.451e-02 1.045e-01 0.713
## ownerSecond:brandHyundai -2.763e+01 1.779e+01 -1.553
## ownerTest:brandHyundai NA NA NA
## ownerThird:brandHyundai -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandIsuzu NA NA NA
## ownerSecond:brandIsuzu NA NA NA
## ownerTest:brandIsuzu NA NA NA
## ownerThird:brandIsuzu NA NA NA
## ownerFourth:brandJaguar NA NA NA
## ownerSecond:brandJaguar -2.933e+01 1.908e+01 -1.537
## ownerTest:brandJaguar NA NA NA
## ownerThird:brandJaguar NA NA NA
## ownerFourth:brandJeep NA NA NA
## ownerSecond:brandJeep -2.739e+01 1.779e+01 -1.539
## ownerTest:brandJeep NA NA NA
## ownerThird:brandJeep NA NA NA
## ownerFourth:brandKia NA NA NA
## ownerSecond:brandKia NA NA NA
## ownerTest:brandKia NA NA NA
## ownerThird:brandKia NA NA NA
## ownerFourth:brandLand NA NA NA
## ownerSecond:brandLand NA NA NA
## ownerTest:brandLand NA NA NA
## ownerThird:brandLand NA NA NA
## ownerFourth:brandLexus NA NA NA
## ownerSecond:brandLexus NA NA NA
## ownerTest:brandLexus NA NA NA
## ownerThird:brandLexus NA NA NA
## ownerFourth:brandMahindra 7.751e-02 1.273e-01 0.609
## ownerSecond:brandMahindra -2.764e+01 1.779e+01 -1.553
## ownerTest:brandMahindra NA NA NA
## ownerThird:brandMahindra -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandMaruti 6.648e-02 1.050e-01 0.633
## ownerSecond:brandMaruti -2.761e+01 1.779e+01 -1.552
## ownerTest:brandMaruti NA NA NA
## ownerThird:brandMaruti -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandMercedes-Benz NA NA NA
## ownerSecond:brandMercedes-Benz -2.774e+01 1.779e+01 -1.559
## ownerTest:brandMercedes-Benz NA NA NA
## ownerThird:brandMercedes-Benz -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandMG NA NA NA
## ownerSecond:brandMG NA NA NA
## ownerTest:brandMG NA NA NA
## ownerThird:brandMG NA NA NA
## ownerFourth:brandMitsubishi NA NA NA
## ownerSecond:brandMitsubishi -2.762e+01 1.780e+01 -1.552
## ownerTest:brandMitsubishi NA NA NA
## ownerThird:brandMitsubishi -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandNissan -4.715e-02 2.404e-01 -0.196
## ownerSecond:brandNissan -2.754e+01 1.779e+01 -1.548
## ownerTest:brandNissan NA NA NA
## ownerThird:brandNissan -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandOpel NA NA NA
## ownerSecond:brandOpel NA NA NA
## ownerTest:brandOpel NA NA NA
## ownerThird:brandOpel NA NA NA
## ownerFourth:brandRenault NA NA NA
## ownerSecond:brandRenault -2.758e+01 1.779e+01 -1.550
## ownerTest:brandRenault NA NA NA
## ownerThird:brandRenault -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandSkoda NA NA NA
## ownerSecond:brandSkoda -2.770e+01 1.779e+01 -1.557
## ownerTest:brandSkoda NA NA NA
## ownerThird:brandSkoda -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandTata -8.712e-02 1.185e-01 -0.735
## ownerSecond:brandTata -2.770e+01 1.779e+01 -1.557
## ownerTest:brandTata NA NA NA
## ownerThird:brandTata -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandToyota -1.972e-03 1.348e-01 -0.015
## ownerSecond:brandToyota -2.765e+01 1.779e+01 -1.554
## ownerTest:brandToyota NA NA NA
## ownerThird:brandToyota -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandVolkswagen NA NA NA
## ownerSecond:brandVolkswagen -2.766e+01 1.779e+01 -1.554
## ownerTest:brandVolkswagen NA NA NA
## ownerThird:brandVolkswagen -2.829e+03 1.803e+03 -1.569
## ownerFourth:brandVolvo NA NA NA
## ownerSecond:brandVolvo NA NA NA
## ownerTest:brandVolvo NA NA NA
## ownerThird:brandVolvo NA NA NA
## mileage:log(engine) 5.405e-02 9.803e-03 5.514
## mileage:log(max_power) -1.463e-02 8.448e-03 -1.732
## mileage:log(seats) 1.985e-02 1.002e-02 1.980
## mileage:brandAshok NA NA NA
## mileage:brandAudi 2.868e+00 1.841e+00 1.557
## mileage:brandBMW 2.826e+00 1.841e+00 1.535
## mileage:brandChevrolet 2.858e+00 1.841e+00 1.552
## mileage:brandDaewoo NA NA NA
## mileage:brandDatsun 2.949e+00 1.842e+00 1.601
## mileage:brandFiat 2.927e+00 1.844e+00 1.588
## mileage:brandForce NA NA NA
## mileage:brandFord 2.835e+00 1.841e+00 1.540
## mileage:brandHonda 2.877e+00 1.841e+00 1.562
## mileage:brandHyundai 2.877e+00 1.841e+00 1.563
## mileage:brandIsuzu NA NA NA
## mileage:brandJaguar 2.151e+00 1.174e+00 1.831
## mileage:brandJeep 2.764e+00 1.848e+00 1.496
## mileage:brandKia NA NA NA
## mileage:brandLand NA NA NA
## mileage:brandLexus NA NA NA
## mileage:brandMahindra 2.843e+00 1.841e+00 1.544
## mileage:brandMaruti 2.885e+00 1.841e+00 1.567
## mileage:brandMercedes-Benz 2.840e+00 1.841e+00 1.542
## mileage:brandMG NA NA NA
## mileage:brandMitsubishi 1.613e+01 1.368e+01 1.179
## mileage:brandNissan 2.798e+00 1.842e+00 1.519
## mileage:brandOpel NA NA NA
## mileage:brandRenault 2.807e+00 1.841e+00 1.524
## mileage:brandSkoda 2.835e+00 1.842e+00 1.539
## mileage:brandTata 2.883e+00 1.841e+00 1.566
## mileage:brandToyota 2.866e+00 1.841e+00 1.557
## mileage:brandVolkswagen 2.865e+00 1.841e+00 1.556
## mileage:brandVolvo NA NA NA
## log(engine):log(max_power) 1.449e-01 8.081e-02 1.793
## log(engine):log(seats) 7.018e-01 2.183e-01 3.215
## log(engine):brandAshok NA NA NA
## log(engine):brandAudi 3.671e+03 2.339e+03 1.570
## log(engine):brandBMW 3.671e+03 2.339e+03 1.570
## log(engine):brandChevrolet 3.672e+03 2.339e+03 1.570
## log(engine):brandDaewoo NA NA NA
## log(engine):brandDatsun 3.673e+03 2.339e+03 1.571
## log(engine):brandFiat 3.669e+03 2.339e+03 1.569
## log(engine):brandForce NA NA NA
## log(engine):brandFord 3.671e+03 2.339e+03 1.570
## log(engine):brandHonda 3.672e+03 2.339e+03 1.570
## log(engine):brandHyundai 3.671e+03 2.339e+03 1.570
## log(engine):brandIsuzu NA NA NA
## log(engine):brandJaguar 3.758e+03 2.396e+03 1.568
## log(engine):brandJeep 3.631e+03 2.339e+03 1.552
## log(engine):brandKia NA NA NA
## log(engine):brandLand NA NA NA
## log(engine):brandLexus NA NA NA
## log(engine):brandMahindra 3.672e+03 2.339e+03 1.570
## log(engine):brandMaruti 3.671e+03 2.339e+03 1.570
## log(engine):brandMercedes-Benz 3.672e+03 2.339e+03 1.570
## log(engine):brandMG NA NA NA
## log(engine):brandMitsubishi 3.880e+03 2.348e+03 1.652
## log(engine):brandNissan 3.671e+03 2.339e+03 1.570
## log(engine):brandOpel NA NA NA
## log(engine):brandRenault 3.670e+03 2.339e+03 1.569
## log(engine):brandSkoda 3.672e+03 2.339e+03 1.570
## log(engine):brandTata 3.672e+03 2.339e+03 1.570
## log(engine):brandToyota 3.672e+03 2.339e+03 1.570
## log(engine):brandVolkswagen 3.672e+03 2.339e+03 1.570
## log(engine):brandVolvo NA NA NA
## log(max_power):log(seats) -4.623e-01 1.284e-01 -3.601
## log(max_power):brandAshok NA NA NA
## log(max_power):brandAudi 7.961e+01 5.255e+01 1.515
## log(max_power):brandBMW 7.991e+01 5.255e+01 1.521
## log(max_power):brandChevrolet 7.999e+01 5.254e+01 1.522
## log(max_power):brandDaewoo NA NA NA
## log(max_power):brandDatsun 7.721e+01 5.255e+01 1.469
## log(max_power):brandFiat 8.034e+01 5.254e+01 1.529
## log(max_power):brandForce NA NA NA
## log(max_power):brandFord 8.084e+01 5.254e+01 1.539
## log(max_power):brandHonda 8.010e+01 5.254e+01 1.525
## log(max_power):brandHyundai 8.025e+01 5.254e+01 1.527
## log(max_power):brandIsuzu NA NA NA
## log(max_power):brandJaguar NA NA NA
## log(max_power):brandJeep 1.503e+02 7.007e+01 2.145
## log(max_power):brandKia NA NA NA
## log(max_power):brandLand NA NA NA
## log(max_power):brandLexus NA NA NA
## log(max_power):brandMahindra 7.994e+01 5.254e+01 1.521
## log(max_power):brandMaruti 8.036e+01 5.254e+01 1.530
## log(max_power):brandMercedes-Benz 7.965e+01 5.254e+01 1.516
## log(max_power):brandMG NA NA NA
## log(max_power):brandMitsubishi 5.274e+01 6.014e+01 0.877
## log(max_power):brandNissan 7.963e+01 5.254e+01 1.515
## log(max_power):brandOpel NA NA NA
## log(max_power):brandRenault 7.978e+01 5.254e+01 1.518
## log(max_power):brandSkoda 7.993e+01 5.254e+01 1.521
## log(max_power):brandTata 8.042e+01 5.254e+01 1.531
## log(max_power):brandToyota 8.021e+01 5.254e+01 1.527
## log(max_power):brandVolkswagen 7.978e+01 5.254e+01 1.518
## log(max_power):brandVolvo NA NA NA
## log(seats):brandAshok NA NA NA
## log(seats):brandAudi 1.601e+00 5.694e-01 2.811
## log(seats):brandBMW 2.652e-01 4.564e-01 0.581
## log(seats):brandChevrolet 3.230e-01 2.485e-01 1.300
## log(seats):brandDaewoo NA NA NA
## log(seats):brandDatsun 6.420e-01 3.156e-01 2.034
## log(seats):brandFiat NA NA NA
## log(seats):brandForce NA NA NA
## log(seats):brandFord 5.508e-01 4.205e-01 1.310
## log(seats):brandHonda 3.735e-01 2.421e-01 1.543
## log(seats):brandHyundai 9.771e-01 3.429e-01 2.849
## log(seats):brandIsuzu NA NA NA
## log(seats):brandJaguar NA NA NA
## log(seats):brandJeep NA NA NA
## log(seats):brandKia NA NA NA
## log(seats):brandLand NA NA NA
## log(seats):brandLexus NA NA NA
## log(seats):brandMahindra 2.525e-02 1.954e-01 0.129
## log(seats):brandMaruti 5.378e-01 2.172e-01 2.476
## log(seats):brandMercedes-Benz 2.770e-01 5.578e-01 0.497
## log(seats):brandMG NA NA NA
## log(seats):brandMitsubishi NA NA NA
## log(seats):brandNissan NA NA NA
## log(seats):brandOpel NA NA NA
## log(seats):brandRenault 5.313e-01 2.461e-01 2.159
## log(seats):brandSkoda 2.231e+00 6.659e-01 3.350
## log(seats):brandTata -5.360e-02 2.127e-01 -0.252
## log(seats):brandToyota NA NA NA
## log(seats):brandVolkswagen NA NA NA
## log(seats):brandVolvo NA NA NA
## Pr(>|t|)
## (Intercept) 0.116507
## year 0.116491
## log(km_driven) 0.116122
## fuelDiesel 0.097232 .
## fuelLPG 0.162148
## fuelPetrol 0.976567
## seller_typeIndividual 0.411195
## seller_typeTrustmark Dealer 0.040557 *
## transmissionManual 0.216588
## ownerFourth 0.016423 *
## ownerSecond 0.241328
## ownerTest 0.013623 *
## ownerThird 0.116447
## mileage 0.160926
## log(engine) 0.116403
## log(max_power) 0.000830 ***
## log(seats) 3.99e-13 ***
## brandAshok 0.116691
## brandAudi 0.116603
## brandBMW 0.116595
## brandChevrolet 0.116572
## brandDaewoo 0.117828
## brandDatsun 0.116546
## brandFiat 0.116606
## brandForce 0.116271
## brandFord 0.116590
## brandHonda 0.116579
## brandHyundai 0.116575
## brandIsuzu 0.116216
## brandJaguar 0.116687
## brandJeep 0.116625
## brandKia 0.115057
## brandLand 0.116355
## brandLexus 0.116663
## brandMahindra 0.116576
## brandMaruti 0.116586
## brandMercedes-Benz 0.116584
## brandMG 0.116216
## brandMitsubishi 0.115961
## brandNissan 0.116578
## brandOpel 0.116559
## brandRenault 0.116617
## brandSkoda 0.116571
## brandTata 0.116584
## brandToyota 0.116580
## brandVolkswagen 0.116623
## brandVolvo 0.116720
## year:log(km_driven) 5.77e-07 ***
## year:fuelDiesel 0.446574
## year:fuelLPG 0.119211
## year:fuelPetrol 0.893013
## year:seller_typeIndividual 0.434316
## year:seller_typeTrustmark Dealer 0.044420 *
## year:transmissionManual 0.210523
## year:ownerFourth 0.012657 *
## year:ownerSecond 0.271967
## year:ownerTest NA
## year:ownerThird 0.992628
## year:mileage 0.668552
## year:log(engine) 0.923944
## year:log(max_power) < 2e-16 ***
## year:log(seats) 7.44e-14 ***
## year:brandAshok NA
## year:brandAudi 0.116593
## year:brandBMW 0.116582
## year:brandChevrolet 0.116557
## year:brandDaewoo 0.118021
## year:brandDatsun 0.116529
## year:brandFiat 0.116590
## year:brandForce 0.116236
## year:brandFord 0.116578
## year:brandHonda 0.116566
## year:brandHyundai 0.116561
## year:brandIsuzu 0.116257
## year:brandJaguar 0.116683
## year:brandJeep 0.116651
## year:brandKia 0.114820
## year:brandLand 0.116359
## year:brandLexus NA
## year:brandMahindra 0.116561
## year:brandMaruti 0.116574
## year:brandMercedes-Benz 0.116573
## year:brandMG 0.116164
## year:brandMitsubishi 0.116681
## year:brandNissan 0.116562
## year:brandOpel NA
## year:brandRenault 0.116605
## year:brandSkoda 0.116560
## year:brandTata 0.116572
## year:brandToyota 0.116568
## year:brandVolkswagen 0.116616
## year:brandVolvo 0.116729
## log(km_driven):fuelDiesel 0.914512
## log(km_driven):fuelLPG 0.520215
## log(km_driven):fuelPetrol 0.560990
## log(km_driven):seller_typeIndividual 0.576343
## log(km_driven):seller_typeTrustmark Dealer 0.266620
## log(km_driven):transmissionManual 0.384779
## log(km_driven):ownerFourth 0.807410
## log(km_driven):ownerSecond 0.061243 .
## log(km_driven):ownerTest 0.760605
## log(km_driven):ownerThird 0.638072
## log(km_driven):mileage 0.923675
## log(km_driven):log(engine) 0.001278 **
## log(km_driven):log(max_power) 0.002414 **
## log(km_driven):log(seats) 0.004977 **
## log(km_driven):brandAshok NA
## log(km_driven):brandAudi 0.116659
## log(km_driven):brandBMW 0.116662
## log(km_driven):brandChevrolet 0.116665
## log(km_driven):brandDaewoo 0.116630
## log(km_driven):brandDatsun 0.116661
## log(km_driven):brandFiat 0.116661
## log(km_driven):brandForce 0.116623
## log(km_driven):brandFord 0.116659
## log(km_driven):brandHonda 0.116659
## log(km_driven):brandHyundai 0.116659
## log(km_driven):brandIsuzu 0.116684
## log(km_driven):brandJaguar 0.116701
## log(km_driven):brandJeep 0.116656
## log(km_driven):brandKia 0.116619
## log(km_driven):brandLand 0.115956
## log(km_driven):brandLexus NA
## log(km_driven):brandMahindra 0.116661
## log(km_driven):brandMaruti 0.116659
## log(km_driven):brandMercedes-Benz 0.116661
## log(km_driven):brandMG 0.116650
## log(km_driven):brandMitsubishi 0.116654
## log(km_driven):brandNissan 0.116664
## log(km_driven):brandOpel NA
## log(km_driven):brandRenault 0.116662
## log(km_driven):brandSkoda 0.116658
## log(km_driven):brandTata 0.116661
## log(km_driven):brandToyota 0.116658
## log(km_driven):brandVolkswagen 0.116661
## log(km_driven):brandVolvo 0.116666
## fuelDiesel:seller_typeIndividual 0.001498 **
## fuelLPG:seller_typeIndividual 0.970560
## fuelPetrol:seller_typeIndividual NA
## fuelDiesel:seller_typeTrustmark Dealer 0.859797
## fuelLPG:seller_typeTrustmark Dealer NA
## fuelPetrol:seller_typeTrustmark Dealer NA
## fuelDiesel:transmissionManual 0.946509
## fuelLPG:transmissionManual NA
## fuelPetrol:transmissionManual NA
## fuelDiesel:ownerFourth 0.727589
## fuelLPG:ownerFourth 0.533945
## fuelPetrol:ownerFourth 0.848625
## fuelDiesel:ownerSecond 0.422078
## fuelLPG:ownerSecond 0.335792
## fuelPetrol:ownerSecond 0.452257
## fuelDiesel:ownerTest 0.064278 .
## fuelLPG:ownerTest NA
## fuelPetrol:ownerTest NA
## fuelDiesel:ownerThird 0.599989
## fuelLPG:ownerThird 0.816365
## fuelPetrol:ownerThird 0.190827
## fuelDiesel:mileage 0.064574 .
## fuelLPG:mileage 0.342003
## fuelPetrol:mileage 0.156614
## fuelDiesel:log(engine) 0.172628
## fuelLPG:log(engine) 0.137547
## fuelPetrol:log(engine) 0.230472
## fuelDiesel:log(max_power) 0.077257 .
## fuelLPG:log(max_power) 0.127248
## fuelPetrol:log(max_power) 0.075052 .
## fuelDiesel:log(seats) 0.770546
## fuelLPG:log(seats) NA
## fuelPetrol:log(seats) 0.870650
## fuelDiesel:brandAshok NA
## fuelLPG:brandAshok NA
## fuelPetrol:brandAshok NA
## fuelDiesel:brandAudi 0.120907
## fuelLPG:brandAudi NA
## fuelPetrol:brandAudi NA
## fuelDiesel:brandBMW 0.121592
## fuelLPG:brandBMW NA
## fuelPetrol:brandBMW NA
## fuelDiesel:brandChevrolet 0.121148
## fuelLPG:brandChevrolet 0.052354 .
## fuelPetrol:brandChevrolet NA
## fuelDiesel:brandDaewoo NA
## fuelLPG:brandDaewoo NA
## fuelPetrol:brandDaewoo NA
## fuelDiesel:brandDatsun NA
## fuelLPG:brandDatsun NA
## fuelPetrol:brandDatsun NA
## fuelDiesel:brandFiat 0.122223
## fuelLPG:brandFiat NA
## fuelPetrol:brandFiat NA
## fuelDiesel:brandForce NA
## fuelLPG:brandForce NA
## fuelPetrol:brandForce NA
## fuelDiesel:brandFord 0.121195
## fuelLPG:brandFord NA
## fuelPetrol:brandFord NA
## fuelDiesel:brandHonda 0.122247
## fuelLPG:brandHonda NA
## fuelPetrol:brandHonda NA
## fuelDiesel:brandHyundai 0.123089
## fuelLPG:brandHyundai 0.485014
## fuelPetrol:brandHyundai 0.288100
## fuelDiesel:brandIsuzu NA
## fuelLPG:brandIsuzu NA
## fuelPetrol:brandIsuzu NA
## fuelDiesel:brandJaguar NA
## fuelLPG:brandJaguar NA
## fuelPetrol:brandJaguar NA
## fuelDiesel:brandJeep 0.096152 .
## fuelLPG:brandJeep NA
## fuelPetrol:brandJeep NA
## fuelDiesel:brandKia NA
## fuelLPG:brandKia NA
## fuelPetrol:brandKia NA
## fuelDiesel:brandLand NA
## fuelLPG:brandLand NA
## fuelPetrol:brandLand NA
## fuelDiesel:brandLexus NA
## fuelLPG:brandLexus NA
## fuelPetrol:brandLexus NA
## fuelDiesel:brandMahindra 0.121284
## fuelLPG:brandMahindra NA
## fuelPetrol:brandMahindra NA
## fuelDiesel:brandMaruti 0.122315
## fuelLPG:brandMaruti NA
## fuelPetrol:brandMaruti 0.230017
## fuelDiesel:brandMercedes-Benz 0.121839
## fuelLPG:brandMercedes-Benz NA
## fuelPetrol:brandMercedes-Benz NA
## fuelDiesel:brandMG NA
## fuelLPG:brandMG NA
## fuelPetrol:brandMG NA
## fuelDiesel:brandMitsubishi NA
## fuelLPG:brandMitsubishi NA
## fuelPetrol:brandMitsubishi NA
## fuelDiesel:brandNissan 0.120924
## fuelLPG:brandNissan NA
## fuelPetrol:brandNissan NA
## fuelDiesel:brandOpel NA
## fuelLPG:brandOpel NA
## fuelPetrol:brandOpel NA
## fuelDiesel:brandRenault 0.120489
## fuelLPG:brandRenault NA
## fuelPetrol:brandRenault NA
## fuelDiesel:brandSkoda 0.121140
## fuelLPG:brandSkoda NA
## fuelPetrol:brandSkoda NA
## fuelDiesel:brandTata 0.122053
## fuelLPG:brandTata NA
## fuelPetrol:brandTata NA
## fuelDiesel:brandToyota 0.121339
## fuelLPG:brandToyota NA
## fuelPetrol:brandToyota NA
## fuelDiesel:brandVolkswagen 0.122171
## fuelLPG:brandVolkswagen NA
## fuelPetrol:brandVolkswagen NA
## fuelDiesel:brandVolvo NA
## fuelLPG:brandVolvo NA
## fuelPetrol:brandVolvo NA
## seller_typeIndividual:transmissionManual 0.704390
## seller_typeTrustmark Dealer:transmissionManual 0.162619
## seller_typeIndividual:ownerFourth NA
## seller_typeTrustmark Dealer:ownerFourth NA
## seller_typeIndividual:ownerSecond 0.002038 **
## seller_typeTrustmark Dealer:ownerSecond 0.229772
## seller_typeIndividual:ownerTest NA
## seller_typeTrustmark Dealer:ownerTest NA
## seller_typeIndividual:ownerThird 0.314164
## seller_typeTrustmark Dealer:ownerThird NA
## seller_typeIndividual:mileage 0.226763
## seller_typeTrustmark Dealer:mileage 0.891973
## seller_typeIndividual:log(engine) 0.055333 .
## seller_typeTrustmark Dealer:log(engine) 0.437127
## seller_typeIndividual:log(max_power) 0.161629
## seller_typeTrustmark Dealer:log(max_power) 0.078045 .
## seller_typeIndividual:log(seats) 0.059586 .
## seller_typeTrustmark Dealer:log(seats) 0.341583
## seller_typeIndividual:brandAshok NA
## seller_typeTrustmark Dealer:brandAshok NA
## seller_typeIndividual:brandAudi 0.362067
## seller_typeTrustmark Dealer:brandAudi NA
## seller_typeIndividual:brandBMW 0.329614
## seller_typeTrustmark Dealer:brandBMW NA
## seller_typeIndividual:brandChevrolet 0.366443
## seller_typeTrustmark Dealer:brandChevrolet NA
## seller_typeIndividual:brandDaewoo NA
## seller_typeTrustmark Dealer:brandDaewoo NA
## seller_typeIndividual:brandDatsun 0.344178
## seller_typeTrustmark Dealer:brandDatsun NA
## seller_typeIndividual:brandFiat 0.616134
## seller_typeTrustmark Dealer:brandFiat NA
## seller_typeIndividual:brandForce 0.115327
## seller_typeTrustmark Dealer:brandForce NA
## seller_typeIndividual:brandFord 0.246044
## seller_typeTrustmark Dealer:brandFord 0.962103
## seller_typeIndividual:brandHonda 0.158670
## seller_typeTrustmark Dealer:brandHonda 0.850906
## seller_typeIndividual:brandHyundai 0.206159
## seller_typeTrustmark Dealer:brandHyundai 0.729023
## seller_typeIndividual:brandIsuzu 0.116829
## seller_typeTrustmark Dealer:brandIsuzu NA
## seller_typeIndividual:brandJaguar 0.322311
## seller_typeTrustmark Dealer:brandJaguar NA
## seller_typeIndividual:brandJeep 0.224929
## seller_typeTrustmark Dealer:brandJeep NA
## seller_typeIndividual:brandKia NA
## seller_typeTrustmark Dealer:brandKia NA
## seller_typeIndividual:brandLand NA
## seller_typeTrustmark Dealer:brandLand NA
## seller_typeIndividual:brandLexus NA
## seller_typeTrustmark Dealer:brandLexus NA
## seller_typeIndividual:brandMahindra 0.341607
## seller_typeTrustmark Dealer:brandMahindra NA
## seller_typeIndividual:brandMaruti 0.240576
## seller_typeTrustmark Dealer:brandMaruti 0.823934
## seller_typeIndividual:brandMercedes-Benz 0.187372
## seller_typeTrustmark Dealer:brandMercedes-Benz NA
## seller_typeIndividual:brandMG NA
## seller_typeTrustmark Dealer:brandMG NA
## seller_typeIndividual:brandMitsubishi 0.064718 .
## seller_typeTrustmark Dealer:brandMitsubishi NA
## seller_typeIndividual:brandNissan 0.068312 .
## seller_typeTrustmark Dealer:brandNissan 0.419247
## seller_typeIndividual:brandOpel NA
## seller_typeTrustmark Dealer:brandOpel NA
## seller_typeIndividual:brandRenault 0.204271
## seller_typeTrustmark Dealer:brandRenault NA
## seller_typeIndividual:brandSkoda 0.409294
## seller_typeTrustmark Dealer:brandSkoda 0.683389
## seller_typeIndividual:brandTata 0.132058
## seller_typeTrustmark Dealer:brandTata NA
## seller_typeIndividual:brandToyota 0.171363
## seller_typeTrustmark Dealer:brandToyota NA
## seller_typeIndividual:brandVolkswagen 0.295581
## seller_typeTrustmark Dealer:brandVolkswagen NA
## seller_typeIndividual:brandVolvo NA
## seller_typeTrustmark Dealer:brandVolvo NA
## transmissionManual:ownerFourth 0.037913 *
## transmissionManual:ownerSecond 0.115114
## transmissionManual:ownerTest NA
## transmissionManual:ownerThird 0.275663
## transmissionManual:mileage 0.759077
## transmissionManual:log(engine) 0.193032
## transmissionManual:log(max_power) 0.460886
## transmissionManual:log(seats) 0.021888 *
## transmissionManual:brandAshok NA
## transmissionManual:brandAudi NA
## transmissionManual:brandBMW NA
## transmissionManual:brandChevrolet 0.004096 **
## transmissionManual:brandDaewoo NA
## transmissionManual:brandDatsun 0.231581
## transmissionManual:brandFiat NA
## transmissionManual:brandForce NA
## transmissionManual:brandFord 0.071809 .
## transmissionManual:brandHonda 0.058516 .
## transmissionManual:brandHyundai 0.006625 **
## transmissionManual:brandIsuzu NA
## transmissionManual:brandJaguar NA
## transmissionManual:brandJeep 0.562172
## transmissionManual:brandKia NA
## transmissionManual:brandLand NA
## transmissionManual:brandLexus NA
## transmissionManual:brandMahindra 0.950430
## transmissionManual:brandMaruti 0.010969 *
## transmissionManual:brandMercedes-Benz 0.085022 .
## transmissionManual:brandMG NA
## transmissionManual:brandMitsubishi NA
## transmissionManual:brandNissan 0.013693 *
## transmissionManual:brandOpel NA
## transmissionManual:brandRenault 0.659039
## transmissionManual:brandSkoda 0.015665 *
## transmissionManual:brandTata 0.781170
## transmissionManual:brandToyota 0.012185 *
## transmissionManual:brandVolkswagen NA
## transmissionManual:brandVolvo NA
## ownerFourth:mileage 0.230765
## ownerSecond:mileage 0.295197
## ownerTest:mileage 0.033250 *
## ownerThird:mileage 0.010027 *
## ownerFourth:log(engine) 0.391257
## ownerSecond:log(engine) 0.301400
## ownerTest:log(engine) NA
## ownerThird:log(engine) 0.057916 .
## ownerFourth:log(max_power) 0.453744
## ownerSecond:log(max_power) 0.511444
## ownerTest:log(max_power) NA
## ownerThird:log(max_power) 0.917219
## ownerFourth:log(seats) 0.880656
## ownerSecond:log(seats) 0.886496
## ownerTest:log(seats) NA
## ownerThird:log(seats) 0.603664
## ownerFourth:brandAshok NA
## ownerSecond:brandAshok NA
## ownerTest:brandAshok NA
## ownerThird:brandAshok NA
## ownerFourth:brandAudi 0.047017 *
## ownerSecond:brandAudi 0.121107
## ownerTest:brandAudi NA
## ownerThird:brandAudi 0.116624
## ownerFourth:brandBMW 0.123170
## ownerSecond:brandBMW 0.120743
## ownerTest:brandBMW NA
## ownerThird:brandBMW 0.116620
## ownerFourth:brandChevrolet 0.087681 .
## ownerSecond:brandChevrolet 0.121096
## ownerTest:brandChevrolet NA
## ownerThird:brandChevrolet 0.116638
## ownerFourth:brandDaewoo NA
## ownerSecond:brandDaewoo NA
## ownerTest:brandDaewoo NA
## ownerThird:brandDaewoo NA
## ownerFourth:brandDatsun NA
## ownerSecond:brandDatsun 0.122198
## ownerTest:brandDatsun NA
## ownerThird:brandDatsun 0.116647
## ownerFourth:brandFiat NA
## ownerSecond:brandFiat 0.117981
## ownerTest:brandFiat NA
## ownerThird:brandFiat 0.116646
## ownerFourth:brandForce NA
## ownerSecond:brandForce NA
## ownerTest:brandForce NA
## ownerThird:brandForce NA
## ownerFourth:brandFord 0.268373
## ownerSecond:brandFord 0.120281
## ownerTest:brandFord NA
## ownerThird:brandFord 0.116642
## ownerFourth:brandHonda 0.936727
## ownerSecond:brandHonda 0.120411
## ownerTest:brandHonda NA
## ownerThird:brandHonda 0.116664
## ownerFourth:brandHyundai 0.476016
## ownerSecond:brandHyundai 0.120517
## ownerTest:brandHyundai NA
## ownerThird:brandHyundai 0.116637
## ownerFourth:brandIsuzu NA
## ownerSecond:brandIsuzu NA
## ownerTest:brandIsuzu NA
## ownerThird:brandIsuzu NA
## ownerFourth:brandJaguar NA
## ownerSecond:brandJaguar 0.124310
## ownerTest:brandJaguar NA
## ownerThird:brandJaguar NA
## ownerFourth:brandJeep NA
## ownerSecond:brandJeep 0.123747
## ownerTest:brandJeep NA
## ownerThird:brandJeep NA
## ownerFourth:brandKia NA
## ownerSecond:brandKia NA
## ownerTest:brandKia NA
## ownerThird:brandKia NA
## ownerFourth:brandLand NA
## ownerSecond:brandLand NA
## ownerTest:brandLand NA
## ownerThird:brandLand NA
## ownerFourth:brandLexus NA
## ownerSecond:brandLexus NA
## ownerTest:brandLexus NA
## ownerThird:brandLexus NA
## ownerFourth:brandMahindra 0.542727
## ownerSecond:brandMahindra 0.120411
## ownerTest:brandMahindra NA
## ownerThird:brandMahindra 0.116640
## ownerFourth:brandMaruti 0.526589
## ownerSecond:brandMaruti 0.120816
## ownerTest:brandMaruti NA
## ownerThird:brandMaruti 0.116633
## ownerFourth:brandMercedes-Benz NA
## ownerSecond:brandMercedes-Benz 0.119086
## ownerTest:brandMercedes-Benz NA
## ownerThird:brandMercedes-Benz 0.116619
## ownerFourth:brandMG NA
## ownerSecond:brandMG NA
## ownerTest:brandMG NA
## ownerThird:brandMG NA
## ownerFourth:brandMitsubishi NA
## ownerSecond:brandMitsubishi 0.120748
## ownerTest:brandMitsubishi NA
## ownerThird:brandMitsubishi 0.116647
## ownerFourth:brandNissan 0.844472
## ownerSecond:brandNissan 0.121687
## ownerTest:brandNissan NA
## ownerThird:brandNissan 0.116621
## ownerFourth:brandOpel NA
## ownerSecond:brandOpel NA
## ownerTest:brandOpel NA
## ownerThird:brandOpel NA
## ownerFourth:brandRenault NA
## ownerSecond:brandRenault 0.121214
## ownerTest:brandRenault NA
## ownerThird:brandRenault 0.116634
## ownerFourth:brandSkoda NA
## ownerSecond:brandSkoda 0.119593
## ownerTest:brandSkoda NA
## ownerThird:brandSkoda 0.116648
## ownerFourth:brandTata 0.462303
## ownerSecond:brandTata 0.119608
## ownerTest:brandTata NA
## ownerThird:brandTata 0.116620
## ownerFourth:brandToyota 0.988331
## ownerSecond:brandToyota 0.120168
## ownerTest:brandToyota NA
## ownerThird:brandToyota 0.116636
## ownerFourth:brandVolkswagen NA
## ownerSecond:brandVolkswagen 0.120144
## ownerTest:brandVolkswagen NA
## ownerThird:brandVolkswagen 0.116634
## ownerFourth:brandVolvo NA
## ownerSecond:brandVolvo NA
## ownerTest:brandVolvo NA
## ownerThird:brandVolvo NA
## mileage:log(engine) 3.63e-08 ***
## mileage:log(max_power) 0.083298 .
## mileage:log(seats) 0.047692 *
## mileage:brandAshok NA
## mileage:brandAudi 0.119397
## mileage:brandBMW 0.124916
## mileage:brandChevrolet 0.120724
## mileage:brandDaewoo NA
## mileage:brandDatsun 0.109429
## mileage:brandFiat 0.112422
## mileage:brandForce NA
## mileage:brandFord 0.123702
## mileage:brandHonda 0.118262
## mileage:brandHyundai 0.118149
## mileage:brandIsuzu NA
## mileage:brandJaguar 0.067071 .
## mileage:brandJeep 0.134797
## mileage:brandKia NA
## mileage:brandLand NA
## mileage:brandLexus NA
## mileage:brandMahindra 0.122572
## mileage:brandMaruti 0.117251
## mileage:brandMercedes-Benz 0.123069
## mileage:brandMG NA
## mileage:brandMitsubishi 0.238241
## mileage:brandNissan 0.128708
## mileage:brandOpel NA
## mileage:brandRenault 0.127467
## mileage:brandSkoda 0.123797
## mileage:brandTata 0.117480
## mileage:brandToyota 0.119600
## mileage:brandVolkswagen 0.119727
## mileage:brandVolvo NA
## log(engine):log(max_power) 0.073066 .
## log(engine):log(seats) 0.001310 **
## log(engine):brandAshok NA
## log(engine):brandAudi 0.116505
## log(engine):brandBMW 0.116495
## log(engine):brandChevrolet 0.116461
## log(engine):brandDaewoo NA
## log(engine):brandDatsun 0.116283
## log(engine):brandFiat 0.116697
## log(engine):brandForce NA
## log(engine):brandFord 0.116546
## log(engine):brandHonda 0.116451
## log(engine):brandHyundai 0.116484
## log(engine):brandIsuzu NA
## log(engine):brandJaguar 0.116824
## log(engine):brandJeep 0.120615
## log(engine):brandKia NA
## log(engine):brandLand NA
## log(engine):brandLexus NA
## log(engine):brandMahindra 0.116473
## log(engine):brandMaruti 0.116512
## log(engine):brandMercedes-Benz 0.116381
## log(engine):brandMG NA
## log(engine):brandMitsubishi 0.098531 .
## log(engine):brandNissan 0.116488
## log(engine):brandOpel NA
## log(engine):brandRenault 0.116588
## log(engine):brandSkoda 0.116416
## log(engine):brandTata 0.116473
## log(engine):brandToyota 0.116443
## log(engine):brandVolkswagen 0.116478
## log(engine):brandVolvo NA
## log(max_power):log(seats) 0.000319 ***
## log(max_power):brandAshok NA
## log(max_power):brandAudi 0.129819
## log(max_power):brandBMW 0.128383
## log(max_power):brandChevrolet 0.127950
## log(max_power):brandDaewoo NA
## log(max_power):brandDatsun 0.141817
## log(max_power):brandFiat 0.126305
## log(max_power):brandForce NA
## log(max_power):brandFord 0.123941
## log(max_power):brandHonda 0.127411
## log(max_power):brandHyundai 0.126700
## log(max_power):brandIsuzu NA
## log(max_power):brandJaguar NA
## log(max_power):brandJeep 0.032019 *
## log(max_power):brandKia NA
## log(max_power):brandLand NA
## log(max_power):brandLexus NA
## log(max_power):brandMahindra 0.128198
## log(max_power):brandMaruti 0.126174
## log(max_power):brandMercedes-Benz 0.129562
## log(max_power):brandMG NA
## log(max_power):brandMitsubishi 0.380513
## log(max_power):brandNissan 0.129693
## log(max_power):brandOpel NA
## log(max_power):brandRenault 0.128967
## log(max_power):brandSkoda 0.128256
## log(max_power):brandTata 0.125916
## log(max_power):brandToyota 0.126906
## log(max_power):brandVolkswagen 0.128952
## log(max_power):brandVolvo NA
## log(seats):brandAshok NA
## log(seats):brandAudi 0.004952 **
## log(seats):brandBMW 0.561174
## log(seats):brandChevrolet 0.193754
## log(seats):brandDaewoo NA
## log(seats):brandDatsun 0.041948 *
## log(seats):brandFiat NA
## log(seats):brandForce NA
## log(seats):brandFord 0.190336
## log(seats):brandHonda 0.122844
## log(seats):brandHyundai 0.004393 **
## log(seats):brandIsuzu NA
## log(seats):brandJaguar NA
## log(seats):brandJeep NA
## log(seats):brandKia NA
## log(seats):brandLand NA
## log(seats):brandLexus NA
## log(seats):brandMahindra 0.897194
## log(seats):brandMaruti 0.013322 *
## log(seats):brandMercedes-Benz 0.619524
## log(seats):brandMG NA
## log(seats):brandMitsubishi NA
## log(seats):brandNissan NA
## log(seats):brandOpel NA
## log(seats):brandRenault 0.030878 *
## log(seats):brandSkoda 0.000811 ***
## log(seats):brandTata 0.801022
## log(seats):brandToyota NA
## log(seats):brandVolkswagen NA
## log(seats):brandVolvo NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2094 on 7529 degrees of freedom
## Multiple R-squared: 0.939, Adjusted R-squared: 0.936
## F-statistic: 308.4 on 376 and 7529 DF, p-value: < 2.2e-16#Model 4: Log-Log Transformation with Interactions
model4 = lm(log(selling_price)~seller_type + owner + log(max_power)+log(seats)+year:log(km_driven)+year:seller_type+year:owner+year:log(max_power)+year:log(seats)+log(km_driven):log(engine)+log(km_driven):log(max_power)+log(km_driven):log(seats)+fuel:seller_type,data=car_details)
summary(model4)##
## Call:
## lm(formula = log(selling_price) ~ seller_type + owner + log(max_power) +
## log(seats) + year:log(km_driven) + year:seller_type + year:owner +
## year:log(max_power) + year:log(seats) + log(km_driven):log(engine) +
## log(km_driven):log(max_power) + log(km_driven):log(seats) +
## fuel:seller_type, data = car_details)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.69634 -0.17324 0.01407 0.19863 1.42516
##
## Coefficients: (4 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.014e+00 7.559e-01 1.342 0.17978
## seller_typeIndividual 3.908e+01 7.142e+00 5.472 4.59e-08
## seller_typeTrustmark Dealer 6.075e+01 2.139e+01 2.840 0.00452
## ownerFourth 2.117e+01 1.185e+01 1.786 0.07414
## ownerSecond -5.530e+00 4.695e+00 -1.178 0.23893
## ownerTest 4.008e-01 1.336e-01 3.000 0.00271
## ownerThird 8.709e+00 7.954e+00 1.095 0.27357
## log(max_power) -1.062e+02 5.032e+00 -21.114 < 2e-16
## log(seats) 1.336e+02 1.341e+01 9.963 < 2e-16
## year:log(km_driven) 2.253e-04 3.412e-05 6.603 4.29e-11
## seller_typeIndividual:year -1.939e-02 3.543e-03 -5.473 4.56e-08
## seller_typeTrustmark Dealer:year -3.014e-02 1.061e-02 -2.841 0.00451
## ownerFourth:year -1.061e-02 5.900e-03 -1.798 0.07216
## ownerSecond:year 2.718e-03 2.332e-03 1.165 0.24388
## ownerTest:year NA NA NA NA
## ownerThird:year -4.386e-03 3.956e-03 -1.109 0.26752
## log(max_power):year 5.407e-02 2.463e-03 21.956 < 2e-16
## log(seats):year -6.619e-02 6.571e-03 -10.073 < 2e-16
## log(km_driven):log(engine) 2.704e-02 2.169e-03 12.470 < 2e-16
## log(max_power):log(km_driven) -1.481e-01 1.353e-02 -10.952 < 2e-16
## log(seats):log(km_driven) -1.735e-02 3.305e-02 -0.525 0.59956
## seller_typeDealer:fuelDiesel 1.971e-01 1.888e-02 10.437 < 2e-16
## seller_typeIndividual:fuelDiesel 6.613e-02 4.189e-02 1.579 0.11445
## seller_typeTrustmark Dealer:fuelDiesel 3.166e-01 6.492e-02 4.877 1.10e-06
## seller_typeDealer:fuelLPG 3.490e-01 2.973e-01 1.174 0.24042
## seller_typeIndividual:fuelLPG 5.881e-02 6.567e-02 0.896 0.37049
## seller_typeTrustmark Dealer:fuelLPG NA NA NA NA
## seller_typeDealer:fuelPetrol NA NA NA NA
## seller_typeIndividual:fuelPetrol -6.502e-02 4.168e-02 -1.560 0.11879
## seller_typeTrustmark Dealer:fuelPetrol NA NA NA NA
##
## (Intercept)
## seller_typeIndividual ***
## seller_typeTrustmark Dealer **
## ownerFourth .
## ownerSecond
## ownerTest **
## ownerThird
## log(max_power) ***
## log(seats) ***
## year:log(km_driven) ***
## seller_typeIndividual:year ***
## seller_typeTrustmark Dealer:year **
## ownerFourth:year .
## ownerSecond:year
## ownerTest:year
## ownerThird:year
## log(max_power):year ***
## log(seats):year ***
## log(km_driven):log(engine) ***
## log(max_power):log(km_driven) ***
## log(seats):log(km_driven)
## seller_typeDealer:fuelDiesel ***
## seller_typeIndividual:fuelDiesel
## seller_typeTrustmark Dealer:fuelDiesel ***
## seller_typeDealer:fuelLPG
## seller_typeIndividual:fuelLPG
## seller_typeTrustmark Dealer:fuelLPG
## seller_typeDealer:fuelPetrol
## seller_typeIndividual:fuelPetrol
## seller_typeTrustmark Dealer:fuelPetrol
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2963 on 7880 degrees of freedom
## Multiple R-squared: 0.8722, Adjusted R-squared: 0.8718
## F-statistic: 2152 on 25 and 7880 DF, p-value: < 2.2e-16#Model 4: Assumptions Checks for Normality & Constant Variance
par(mfrow=c(2,2))
plot(model4)## Warning: not plotting observations with leverage one:
## 87
par(mfrow=c(1,1))Check for Multicollinearity
library(car)
vif(model3)## GVIF Df GVIF^(1/(2*Df))
## year 2.600387 1 1.612572
## log(km_driven) 1.981451 1 1.407640
## fuel 3.161550 3 1.211481
## seller_type 1.591715 2 1.123224
## transmission 1.946547 1 1.395187
## owner 1.520722 4 1.053795
## mileage 3.532693 1 1.879546
## log(engine) 8.286529 1 2.878633
## log(max_power) 4.396950 1 2.096891
## log(seats) 2.634614 1 1.623150
## brand 12.805004 30 1.043413Model 3: Analysis and CV
We are performing a 10-fold Cross Validation on Model 3: Log-Log.
library(caret)
set.seed(1234)
#K-fold in R
fitControl<-trainControl(method="repeatedcv",number=10,repeats=1)
# GLM-NET Regression
model3.fit <-train(log(selling_price)~year + log(km_driven) + fuel+ seller_type + transmission + owner + mileage + log(engine) + log(max_power) + log(seats) + brand,data=car_details,
method="glmnet",
trControl=fitControl
)
model3.fit## glmnet
##
## 7906 samples
## 11 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 7115, 7117, 7115, 7114, 7116, 7115, ...
## Resampling results across tuning parameters:
##
## alpha lambda RMSE Rsquared MAE
## 0.10 0.001225234 0.2399509 0.9163021 0.1825900
## 0.10 0.012252339 0.2402596 0.9161643 0.1832508
## 0.10 0.122523390 0.2588323 0.9096556 0.2004956
## 0.55 0.001225234 0.2399593 0.9162856 0.1825074
## 0.55 0.012252339 0.2432187 0.9144250 0.1862673
## 0.55 0.122523390 0.3224806 0.8715201 0.2461546
## 1.00 0.001225234 0.2400233 0.9162450 0.1826446
## 1.00 0.012252339 0.2487024 0.9109560 0.1908623
## 1.00 0.122523390 0.3701479 0.8373480 0.2792515
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 0.1 and lambda = 0.001225234.plot(model3.fit)
#Investigating Coefficients
opt.pen=model3.fit$finalModel$lambdaOpt #penalty term
coef(model3.fit$finalModel,opt.pen)## 47 x 1 sparse Matrix of class "dgCMatrix"
## s1
## (Intercept) -2.069102e+02
## year 1.062673e-01
## log(km_driven) -4.485407e-02
## fuelDiesel 1.999200e-01
## fuelLPG 1.052826e-01
## fuelPetrol .
## seller_typeIndividual -2.565623e-02
## seller_typeTrustmark Dealer -3.473901e-02
## transmissionManual -9.706906e-02
## ownerFourth -1.597758e-01
## ownerSecond -8.367145e-02
## ownerTest 6.030412e-01
## ownerThird -1.209117e-01
## mileage 1.754633e-03
## log(engine) 3.555482e-01
## log(max_power) 7.581255e-01
## log(seats) 2.497229e-01
## brandAshok -2.112746e-01
## brandAudi 5.446524e-01
## brandBMW 7.803403e-01
## brandChevrolet -3.339577e-01
## brandDaewoo 3.138094e-01
## brandDatsun -3.099876e-01
## brandFiat -2.058802e-01
## brandForce -1.533179e-01
## brandFord -9.668456e-02
## brandHonda 3.219341e-02
## brandHyundai .
## brandIsuzu 4.261551e-02
## brandJaguar 6.343486e-01
## brandJeep 3.134596e-01
## brandKia 4.252805e-02
## brandLand 8.747236e-01
## brandLexus 9.511224e-01
## brandMahindra -1.036325e-01
## brandMaruti 7.048418e-02
## brandMercedes-Benz 6.548605e-01
## brandMG 3.217798e-01
## brandMitsubishi 2.344810e-01
## brandNissan -4.737655e-02
## brandOpel 9.216913e-02
## brandRenault -4.545970e-02
## brandSkoda -6.231059e-02
## brandTata -3.992461e-01
## brandToyota 2.591875e-01
## brandVolkswagen -7.510168e-02
## brandVolvo 5.599281e-01#Lasso
model3.fit2 <-train(log(selling_price)~year + log(km_driven) + fuel+ seller_type + transmission + owner + mileage + log(engine) + log(max_power) + log(seats) + brand, data= car_details,
method="glmnet",
trControl=fitControl,
tuneGrid=expand.grid(data.frame(alpha=1,lambda=seq(0,.0001,0.001225234)))
)
model3.fit2## glmnet
##
## 7906 samples
## 11 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 7115, 7116, 7116, 7116, 7115, 7115, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 0.2398488 0.9159191 0.1824349
##
## Tuning parameter 'alpha' was held constant at a value of 1
## Tuning
## parameter 'lambda' was held constant at a value of 0opt.pen<-model3.fit2$finalModel$lambdaOpt #penalty term
coef(model3.fit2$finalModel,opt.pen)## 47 x 1 sparse Matrix of class "dgCMatrix"
## s1
## (Intercept) -2.095110e+02
## year 1.075856e-01
## log(km_driven) -4.271943e-02
## fuelDiesel 2.036947e-01
## fuelLPG 1.043446e-01
## fuelPetrol .
## seller_typeIndividual -2.378267e-02
## seller_typeTrustmark Dealer -3.182166e-02
## transmissionManual -9.365287e-02
## ownerFourth -1.541180e-01
## ownerSecond -8.158551e-02
## ownerTest 5.964948e-01
## ownerThird -1.173971e-01
## mileage 7.408238e-04
## log(engine) 3.441777e-01
## log(max_power) 7.658442e-01
## log(seats) 2.385269e-01
## brandAshok -1.885408e-01
## brandAudi 5.429752e-01
## brandBMW 7.814060e-01
## brandChevrolet -3.325954e-01
## brandDaewoo 3.203155e-01
## brandDatsun -3.068605e-01
## brandFiat -2.046429e-01
## brandForce -1.452522e-01
## brandFord -9.539412e-02
## brandHonda 3.295954e-02
## brandHyundai .
## brandIsuzu 3.020797e-02
## brandJaguar 6.336519e-01
## brandJeep 3.045146e-01
## brandKia 2.951595e-02
## brandLand 8.658050e-01
## brandLexus 9.591507e-01
## brandMahindra -1.017708e-01
## brandMaruti 7.363051e-02
## brandMercedes-Benz 6.535521e-01
## brandMG 3.078471e-01
## brandMitsubishi 2.328600e-01
## brandNissan -4.488947e-02
## brandOpel 8.678013e-02
## brandRenault -4.348605e-02
## brandSkoda -5.898076e-02
## brandTata -3.997711e-01
## brandToyota 2.605621e-01
## brandVolkswagen -7.501231e-02
## brandVolvo 5.590886e-01# Ridge
model3.fit3 <-train(log(selling_price)~year + log(km_driven) + fuel+ seller_type + transmission + owner + mileage + log(engine) + log(max_power) + log(seats) + brand, data= car_details,
method="glmnet",
trControl=fitControl,
tuneGrid=expand.grid(data.frame(alpha=0,lambda=seq(0,.0001,0.001225234)))
)
model3.fit3## glmnet
##
## 7906 samples
## 11 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 7115, 7115, 7115, 7115, 7116, 7115, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 0.2433077 0.9145063 0.1868609
##
## Tuning parameter 'alpha' was held constant at a value of 0
## Tuning
## parameter 'lambda' was held constant at a value of 0opt.pen<-model3.fit3$finalModel$lambdaOpt #penalty term
coef(model3.fit3$finalModel,opt.pen)## 47 x 1 sparse Matrix of class "dgCMatrix"
## s1
## (Intercept) -1.841407e+02
## year 9.508011e-02
## log(km_driven) -6.209052e-02
## fuelDiesel 1.255712e-01
## fuelLPG 1.822508e-02
## fuelPetrol -7.399838e-02
## seller_typeIndividual -4.360822e-02
## seller_typeTrustmark Dealer -3.913061e-02
## transmissionManual -1.360622e-01
## ownerFourth -1.986559e-01
## ownerSecond -9.905936e-02
## ownerTest 6.100970e-01
## ownerThird -1.457993e-01
## mileage 5.512657e-03
## log(engine) 3.765664e-01
## log(max_power) 7.119546e-01
## log(seats) 2.872342e-01
## brandAshok -2.405191e-01
## brandAudi 5.207847e-01
## brandBMW 7.346900e-01
## brandChevrolet -3.263879e-01
## brandDaewoo 1.749336e-01
## brandDatsun -2.921224e-01
## brandFiat -2.009769e-01
## brandForce -1.356172e-01
## brandFord -9.266541e-02
## brandHonda 3.074049e-02
## brandHyundai 1.817096e-03
## brandIsuzu 8.837955e-02
## brandJaguar 5.980826e-01
## brandJeep 3.542346e-01
## brandKia 6.752880e-02
## brandLand 8.521382e-01
## brandLexus 8.995931e-01
## brandMahindra -9.230047e-02
## brandMaruti 4.875968e-02
## brandMercedes-Benz 6.214552e-01
## brandMG 3.381247e-01
## brandMitsubishi 2.156949e-01
## brandNissan -4.757289e-02
## brandOpel 1.239820e-02
## brandRenault -4.258662e-02
## brandSkoda -7.675141e-02
## brandTata -3.797384e-01
## brandToyota 2.512732e-01
## brandVolkswagen -6.694023e-02
## brandVolvo 5.299899e-01#Linear Regression
model3.fit4 <-train(log(selling_price)~year + log(km_driven) + fuel+ seller_type + transmission + owner + mileage + log(engine) + log(max_power) + log(seats) + brand, data= car_details,
method="lm",
trControl=fitControl,
)## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleadingmodel3.fit4## Linear Regression
##
## 7906 samples
## 11 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 7114, 7116, 7115, 7116, 7116, 7115, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 0.2399183 0.9159655 0.1821006
##
## Tuning parameter 'intercept' was held constant at a value of TRUEopt.pen<-model3.fit2$finalModel #penalty term
coef(model3.fit4$finalModel)## (Intercept) year
## -2.092296e+02 1.074785e-01
## `log(km_driven)` fuelDiesel
## -4.295498e-02 2.954685e-01
## fuelLPG fuelPetrol
## 2.131892e-01 9.819511e-02
## seller_typeIndividual `seller_typeTrustmark Dealer`
## -2.374293e-02 -4.013692e-02
## transmissionManual ownerFourth
## -9.114765e-02 -1.584106e-01
## ownerSecond ownerTest
## -8.295973e-02 6.203986e-01
## ownerThird mileage
## -1.206168e-01 2.026341e-03
## `log(engine)` `log(max_power)`
## 3.580122e-01 7.589138e-01
## `log(seats)` brandAshok
## 2.585940e-01 -5.499034e-01
## brandAudi brandBMW
## 2.732699e-01 5.091633e-01
## brandChevrolet brandDaewoo
## -6.237420e-01 7.282616e-02
## brandDatsun brandFiat
## -6.071410e-01 -4.984592e-01
## brandForce brandFord
## -4.634127e-01 -3.851812e-01
## brandHonda brandHyundai
## -2.504477e-01 -2.864624e-01
## brandIsuzu brandJaguar
## -2.219154e-01 3.637892e-01
## brandJeep brandKia
## 3.639235e-02 -2.168083e-01
## brandLand brandLexus
## 6.175933e-01 6.776607e-01
## brandMahindra brandMaruti
## -3.940817e-01 -2.117147e-01
## `brandMercedes-Benz` brandMG
## 3.859378e-01 6.887980e-02
## brandMitsubishi brandNissan
## -3.377626e-02 -3.382484e-01
## brandOpel brandRenault
## -1.292909e-01 -3.367175e-01
## brandSkoda brandTata
## -3.488428e-01 -6.883353e-01
## brandToyota brandVolkswagen
## -2.251295e-02 -3.640466e-01
## brandVolvo
## 2.882826e-01#K Fold CV for Knn
#Setting k fold parameters
fitControl<-trainControl(method="repeatedcv",number=10,repeats=1)
#training the model via 10fold cv
knn3.fit1<-train(log(selling_price)~year + log(km_driven) + fuel+ seller_type + transmission + owner + mileage + log(engine) + log(max_power) + log(seats) + brand,
data=car_details,
method="knn",
trControl=fitControl
)
plot(knn3.fit1)
knn3.fit1## k-Nearest Neighbors
##
## 7906 samples
## 11 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 7115, 7116, 7114, 7116, 7116, 7114, ...
## Resampling results across tuning parameters:
##
## k RMSE Rsquared MAE
## 5 0.2532729 0.9065338 0.1736135
## 7 0.2560757 0.9045084 0.1760120
## 9 0.2610793 0.9008049 0.1797211
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was k = 5.Model 4: Analysis and CV
We are performing a 10-fold Cross Validation on Model 4: Log-Log with Interactions.
# GLM-NET Regression
model4.fit <-train(log(selling_price)~seller_type + owner + log(max_power)+log(seats)+year:log(km_driven)+year:seller_type+year:owner+year:log(max_power)+year:log(seats)+log(km_driven):log(engine)+log(km_driven):log(max_power)+log(km_driven):log(seats)+fuel:seller_type,data=car_details,
method="glmnet",
trControl=fitControl
)
model4.fit## glmnet
##
## 7906 samples
## 8 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 7114, 7116, 7114, 7116, 7116, 7116, ...
## Resampling results across tuning parameters:
##
## alpha lambda RMSE Rsquared MAE
## 0.10 0.001245231 0.3811374 0.7886392 0.2977562
## 0.10 0.012452311 0.4212485 0.7412933 0.3285344
## 0.10 0.124523110 0.4333487 0.7311947 0.3368804
## 0.55 0.001245231 0.3758046 0.7945859 0.2935515
## 0.55 0.012452311 0.4217409 0.7410662 0.3290074
## 0.55 0.124523110 0.4646746 0.7069512 0.3608330
## 1.00 0.001245231 0.3432727 0.8292658 0.2678723
## 1.00 0.012452311 0.4274919 0.7341496 0.3339256
## 1.00 0.124523110 0.5066420 0.6613770 0.3948735
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.001245231.plot(model4.fit)
#Investigating Coefficients
opt.pen=model3.fit$finalModel$lambdaOpt #penalty term
coef(model3.fit$finalModel,opt.pen)## 47 x 1 sparse Matrix of class "dgCMatrix"
## s1
## (Intercept) -2.069102e+02
## year 1.062673e-01
## log(km_driven) -4.485407e-02
## fuelDiesel 1.999200e-01
## fuelLPG 1.052826e-01
## fuelPetrol .
## seller_typeIndividual -2.565623e-02
## seller_typeTrustmark Dealer -3.473901e-02
## transmissionManual -9.706906e-02
## ownerFourth -1.597758e-01
## ownerSecond -8.367145e-02
## ownerTest 6.030412e-01
## ownerThird -1.209117e-01
## mileage 1.754633e-03
## log(engine) 3.555482e-01
## log(max_power) 7.581255e-01
## log(seats) 2.497229e-01
## brandAshok -2.112746e-01
## brandAudi 5.446524e-01
## brandBMW 7.803403e-01
## brandChevrolet -3.339577e-01
## brandDaewoo 3.138094e-01
## brandDatsun -3.099876e-01
## brandFiat -2.058802e-01
## brandForce -1.533179e-01
## brandFord -9.668456e-02
## brandHonda 3.219341e-02
## brandHyundai .
## brandIsuzu 4.261551e-02
## brandJaguar 6.343486e-01
## brandJeep 3.134596e-01
## brandKia 4.252805e-02
## brandLand 8.747236e-01
## brandLexus 9.511224e-01
## brandMahindra -1.036325e-01
## brandMaruti 7.048418e-02
## brandMercedes-Benz 6.548605e-01
## brandMG 3.217798e-01
## brandMitsubishi 2.344810e-01
## brandNissan -4.737655e-02
## brandOpel 9.216913e-02
## brandRenault -4.545970e-02
## brandSkoda -6.231059e-02
## brandTata -3.992461e-01
## brandToyota 2.591875e-01
## brandVolkswagen -7.510168e-02
## brandVolvo 5.599281e-01#Lasso
model4.fit2 <-train(log(selling_price)~seller_type + owner + log(max_power)+log(seats)+year:log(km_driven)+year:seller_type+year:owner+year:log(max_power)+year:log(seats)+log(km_driven):log(engine)+log(km_driven):log(max_power)+log(km_driven):log(seats)+fuel:seller_type, data= car_details,
method="glmnet",
trControl=fitControl,
tuneGrid=expand.grid(data.frame(alpha=1,lambda=seq(0,.0001,.001245231)))
)
model4.fit2## glmnet
##
## 7906 samples
## 8 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 7115, 7117, 7116, 7116, 7115, 7115, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 0.301215 0.8673106 0.2329125
##
## Tuning parameter 'alpha' was held constant at a value of 1
## Tuning
## parameter 'lambda' was held constant at a value of 0opt.pen<-model3.fit2$finalModel$lambdaOpt #penalty term
coef(model3.fit2$finalModel,opt.pen)## 47 x 1 sparse Matrix of class "dgCMatrix"
## s1
## (Intercept) -2.095110e+02
## year 1.075856e-01
## log(km_driven) -4.271943e-02
## fuelDiesel 2.036947e-01
## fuelLPG 1.043446e-01
## fuelPetrol .
## seller_typeIndividual -2.378267e-02
## seller_typeTrustmark Dealer -3.182166e-02
## transmissionManual -9.365287e-02
## ownerFourth -1.541180e-01
## ownerSecond -8.158551e-02
## ownerTest 5.964948e-01
## ownerThird -1.173971e-01
## mileage 7.408238e-04
## log(engine) 3.441777e-01
## log(max_power) 7.658442e-01
## log(seats) 2.385269e-01
## brandAshok -1.885408e-01
## brandAudi 5.429752e-01
## brandBMW 7.814060e-01
## brandChevrolet -3.325954e-01
## brandDaewoo 3.203155e-01
## brandDatsun -3.068605e-01
## brandFiat -2.046429e-01
## brandForce -1.452522e-01
## brandFord -9.539412e-02
## brandHonda 3.295954e-02
## brandHyundai .
## brandIsuzu 3.020797e-02
## brandJaguar 6.336519e-01
## brandJeep 3.045146e-01
## brandKia 2.951595e-02
## brandLand 8.658050e-01
## brandLexus 9.591507e-01
## brandMahindra -1.017708e-01
## brandMaruti 7.363051e-02
## brandMercedes-Benz 6.535521e-01
## brandMG 3.078471e-01
## brandMitsubishi 2.328600e-01
## brandNissan -4.488947e-02
## brandOpel 8.678013e-02
## brandRenault -4.348605e-02
## brandSkoda -5.898076e-02
## brandTata -3.997711e-01
## brandToyota 2.605621e-01
## brandVolkswagen -7.501231e-02
## brandVolvo 5.590886e-01# Ridge
model4.fit3 <-train(log(selling_price)~seller_type + owner + log(max_power)+log(seats)+year:log(km_driven)+year:seller_type+year:owner+year:log(max_power)+year:log(seats)+log(km_driven):log(engine)+log(km_driven):log(max_power)+log(km_driven):log(seats)+fuel:seller_type, data= car_details,
method="glmnet",
trControl=fitControl,
tuneGrid=expand.grid(data.frame(alpha=0,lambda=seq(0,.0001,0.001225234)))
)
model4.fit3## glmnet
##
## 7906 samples
## 8 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 7116, 7115, 7115, 7114, 7115, 7115, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 0.42679 0.7346005 0.3319185
##
## Tuning parameter 'alpha' was held constant at a value of 0
## Tuning
## parameter 'lambda' was held constant at a value of 0opt.pen<-model4.fit3$finalModel$lambdaOpt #penalty term
coef(model4.fit3$finalModel,opt.pen)## 30 x 1 sparse Matrix of class "dgCMatrix"
## s1
## (Intercept) 8.321400e+00
## seller_typeIndividual -7.139072e-02
## seller_typeTrustmark Dealer -4.507660e-03
## ownerFourth -3.180724e-01
## ownerSecond -1.411036e-01
## ownerTest 3.650476e-01
## ownerThird -2.258316e-01
## log(max_power) 6.279495e-01
## log(seats) 2.065152e-01
## year:log(km_driven) -5.994444e-05
## seller_typeIndividual:year -2.086630e-05
## seller_typeTrustmark Dealer:year 1.207293e-07
## ownerFourth:year -1.560798e-04
## ownerSecond:year -6.685285e-05
## ownerTest:year 1.856494e-04
## ownerThird:year -1.105778e-04
## log(max_power):year 4.019206e-04
## log(seats):year 2.749230e-04
## log(km_driven):log(engine) -1.003748e-02
## log(max_power):log(km_driven) -3.827043e-03
## log(seats):log(km_driven) -2.745488e-02
## seller_typeDealer:fuelDiesel 2.015330e-01
## seller_typeIndividual:fuelDiesel 1.197186e-01
## seller_typeTrustmark Dealer:fuelDiesel 3.929615e-01
## seller_typeDealer:fuelLPG -3.591113e-01
## seller_typeIndividual:fuelLPG -8.346211e-02
## seller_typeTrustmark Dealer:fuelLPG .
## seller_typeDealer:fuelPetrol -1.147943e-01
## seller_typeIndividual:fuelPetrol -2.024836e-01
## seller_typeTrustmark Dealer:fuelPetrol -7.271465e-02#Linear Regression
model4.fit4 <-train(log(selling_price)~seller_type + owner + log(max_power)+log(seats)+year:log(km_driven)+year:seller_type+year:owner+year:log(max_power)+year:log(seats)+log(km_driven):log(engine)+log(km_driven):log(max_power)+log(km_driven):log(seats)+fuel:seller_type, data= car_details,
method="lm",
trControl=fitControl,
)## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleading
## Warning in predict.lm(modelFit, newdata): prediction from a rank-deficient fit
## may be misleadingmodel4.fit4## Linear Regression
##
## 7906 samples
## 8 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 7116, 7115, 7115, 7114, 7116, 7116, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 0.2968222 0.8714683 0.2289652
##
## Tuning parameter 'intercept' was held constant at a value of TRUEopt.pen<-model3.fit2$finalModel #penalty term
coef(model3.fit4$finalModel)## (Intercept) year
## -2.092296e+02 1.074785e-01
## `log(km_driven)` fuelDiesel
## -4.295498e-02 2.954685e-01
## fuelLPG fuelPetrol
## 2.131892e-01 9.819511e-02
## seller_typeIndividual `seller_typeTrustmark Dealer`
## -2.374293e-02 -4.013692e-02
## transmissionManual ownerFourth
## -9.114765e-02 -1.584106e-01
## ownerSecond ownerTest
## -8.295973e-02 6.203986e-01
## ownerThird mileage
## -1.206168e-01 2.026341e-03
## `log(engine)` `log(max_power)`
## 3.580122e-01 7.589138e-01
## `log(seats)` brandAshok
## 2.585940e-01 -5.499034e-01
## brandAudi brandBMW
## 2.732699e-01 5.091633e-01
## brandChevrolet brandDaewoo
## -6.237420e-01 7.282616e-02
## brandDatsun brandFiat
## -6.071410e-01 -4.984592e-01
## brandForce brandFord
## -4.634127e-01 -3.851812e-01
## brandHonda brandHyundai
## -2.504477e-01 -2.864624e-01
## brandIsuzu brandJaguar
## -2.219154e-01 3.637892e-01
## brandJeep brandKia
## 3.639235e-02 -2.168083e-01
## brandLand brandLexus
## 6.175933e-01 6.776607e-01
## brandMahindra brandMaruti
## -3.940817e-01 -2.117147e-01
## `brandMercedes-Benz` brandMG
## 3.859378e-01 6.887980e-02
## brandMitsubishi brandNissan
## -3.377626e-02 -3.382484e-01
## brandOpel brandRenault
## -1.292909e-01 -3.367175e-01
## brandSkoda brandTata
## -3.488428e-01 -6.883353e-01
## brandToyota brandVolkswagen
## -2.251295e-02 -3.640466e-01
## brandVolvo
## 2.882826e-01#K Fold CV for Knn
#Setting k fold parameters
fitControl<-trainControl(method="repeatedcv",number=10,repeats=1)
#training the model via 10fold cv
knn4.fit<-train(log(selling_price)~seller_type + owner + log(max_power)+log(seats)+year:log(km_driven)+year:seller_type+year:owner+year:log(max_power)+year:log(seats)+log(km_driven):log(engine)+log(km_driven):log(max_power)+log(km_driven):log(seats)+fuel:seller_type,
data=car_details,
method="knn",
trControl=fitControl
)
plot(knn4.fit)
knn4.fit## k-Nearest Neighbors
##
## 7906 samples
## 8 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 1 times)
## Summary of sample sizes: 7113, 7116, 7116, 7115, 7115, 7116, ...
## Resampling results across tuning parameters:
##
## k RMSE Rsquared MAE
## 5 0.4006258 0.7670181 0.2848739
## 7 0.4028559 0.7638635 0.2883927
## 9 0.4053819 0.7605780 0.2919711
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was k = 5.