Data Preparation

library(tidyverse)
library(caret)
library(GGally)
library(car)
library(lmtest)
library(data.table)
library(MLmetrics)
library(performance)

car <- read.csv('Used_Cars.csv')
rmarkdown::paged_table(car)

glimpse(car)

## Rows: 8,128
## Columns: 13
## $ X             <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1~
## $ name          <chr> "Maruti Swift Dzire VDI", "Skoda Rapid 1.5 TDI Ambition"~
## $ year          <int> 2014, 2014, 2006, 2010, 2007, 2017, 2007, 2001, 2011, 20~
## $ selling_price <int> 450000, 370000, 158000, 225000, 130000, 440000, 96000, 4~
## $ km_driven     <int> 145500, 120000, 140000, 127000, 120000, 45000, 175000, 5~
## $ fuel          <chr> "Diesel", "Diesel", "Petrol", "Diesel", "Petrol", "Petro~
## $ seller_type   <chr> "Individual", "Individual", "Individual", "Individual", ~
## $ transmission  <chr> "Manual", "Manual", "Manual", "Manual", "Manual", "Manua~
## $ owner         <chr> "First Owner", "Second Owner", "Third Owner", "First Own~
## $ mileage       <chr> "23.4 kmpl", "21.14 kmpl", "17.7 kmpl", "23.0 kmpl", "16~
## $ engine        <chr> "1248 CC", "1498 CC", "1497 CC", "1396 CC", "1298 CC", "~
## $ max_power     <chr> "74 bhp", "103.52 bhp", "78 bhp", "90 bhp", "88.2 bhp", ~
## $ seats         <int> 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, NA, 5, 5, 7, 5, 5~

car<- car %>%
  mutate(mileage = as.numeric(str_replace(mileage," kmpl| km/kg","")),
         engine = as.numeric(str_replace(engine," CC","")),
         max_power = as.numeric(str_replace(max_power," bhp","")),
         fuel = as.factor(fuel),
         seller_type = as.factor(seller_type),
         transmission = as.factor(transmission),
         owner = as.factor(owner)) %>% 
  select(-c(X,name))
  
str(car)

## 'data.frame':    8128 obs. of  11 variables:
##  $ year         : int  2014 2014 2006 2010 2007 2017 2007 2001 2011 2013 ...
##  $ selling_price: int  450000 370000 158000 225000 130000 440000 96000 45000 350000 200000 ...
##  $ km_driven    : int  145500 120000 140000 127000 120000 45000 175000 5000 90000 169000 ...
##  $ fuel         : Factor w/ 4 levels "CNG","Diesel",..: 2 2 4 2 4 4 3 4 2 2 ...
##  $ seller_type  : Factor w/ 3 levels "Dealer","Individual",..: 2 2 2 2 2 2 2 2 2 2 ...
##  $ transmission : Factor w/ 2 levels "Automatic","Manual": 2 2 2 2 2 2 2 2 2 2 ...
##  $ owner        : Factor w/ 5 levels "First Owner",..: 1 3 5 1 1 1 1 3 1 1 ...
##  $ mileage      : num  23.4 21.1 17.7 23 16.1 ...
##  $ engine       : num  1248 1498 1497 1396 1298 ...
##  $ max_power    : num  74 103.5 78 90 88.2 ...
##  $ seats        : int  5 5 5 5 5 5 5 4 5 5 ...

colSums(is.na(car))

##          year selling_price     km_driven          fuel   seller_type 
##             0             0             0             0             0 
##  transmission         owner       mileage        engine     max_power 
##             0             0           221           221           216 
##         seats 
##           221

car <- drop_na(car)
dim(car)

## [1] 7906   11

Exploratory Data Analysis

Exploratory data analysis is a phase where we explore the data variables, see if there are any pattern that can indicate any kind of correlation between variables.

First we want to know the distribution of our target variable which is selling_price

hist(car$selling_price, col="darkblue")

From the histogram it is known that most of the selling prices of used cars are below 2,000,000

Before we make the model, we need to split the data into train dataset and test dataset. We will use the train dataset to train the linear regression model. The test dataset will be used as a comparasion and see if the model get overfit and can not predict new data that hasn’t been seen during training phase. We will set 80% of the data as the training data and the rest of it as the testing data.

RNGkind(sample.kind = "Rounding")
set.seed(123)
intrain <- sample(x=nrow(car), size = nrow(car)*0.8)
car_train <- car[intrain,]
car_test <- car[-intrain,]

dim(car_train)

## [1] 6324   11

dim(car_test)

## [1] 1582   11

hist(car_train$selling_price, col= "darkblue")

hist(car_test$selling_price, col="darkblue")

ggcorr(car_train, label = T)

Modeling

The first model we can make is to use all variables (except selling_price) as predictor variables.

model0 <- lm(selling_price~1, car_train)
model_all <- lm(selling_price~., car_train)
summary(model_all)

## 
## Call:
## lm(formula = selling_price ~ ., data = car_train)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2707308  -197720    10512   153376  4458792 
## 
## Coefficients:
##                               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 -6.724e+07  4.289e+06 -15.676  < 2e-16 ***
## year                         3.335e+04  2.143e+03  15.564  < 2e-16 ***
## km_driven                   -9.389e-01  1.163e-01  -8.073 8.15e-16 ***
## fuelDiesel                  -3.289e+04  6.878e+04  -0.478 0.632578    
## fuelLPG                      1.536e+05  1.134e+05   1.355 0.175540    
## fuelPetrol                  -7.180e+04  6.914e+04  -1.039 0.299063    
## seller_typeIndividual       -2.481e+05  1.849e+04 -13.418  < 2e-16 ***
## seller_typeTrustmark Dealer -3.452e+05  3.855e+04  -8.956  < 2e-16 ***
## transmissionManual          -4.487e+05  2.206e+04 -20.336  < 2e-16 ***
## ownerFourth & Above Owner    4.160e+04  4.300e+04   0.967 0.333392    
## ownerSecond Owner           -4.278e+04  1.499e+04  -2.853 0.004343 ** 
## ownerTest Drive Car          2.631e+06  2.307e+05  11.403  < 2e-16 ***
## ownerThird Owner            -1.359e+04  2.576e+04  -0.528 0.597849    
## mileage                      1.483e+04  2.369e+03   6.261 4.07e-10 ***
## engine                       1.070e+02  2.643e+01   4.050 5.18e-05 ***
## max_power                    1.288e+04  2.890e+02  44.574  < 2e-16 ***
## seats                       -3.219e+04  8.812e+03  -3.653 0.000261 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 459300 on 6307 degrees of freedom
## Multiple R-squared:  0.6897, Adjusted R-squared:  0.6889 
## F-statistic: 876.3 on 16 and 6307 DF,  p-value: < 2.2e-16

The summary of model_all shows a lot of information. But for now, we may be better focus on the Pr(>|t|). This column shows the significant level of the variable toward the model. If the value is below 0.05, than we can safely assume that the variable has significant effect toward the model.

Linear Regression Assumption

As a statistical model, linear regression has several assumptions that need to be fulfilled so that the interpretation obtained is not biased. This assumption only needs to be fulfilled if the purpose of making a linear regression model is to want an interpretation or to see the effect of each predictor on the value of the target variable. If you only want to use linear regression to make predictions, then the model assumptions are not required to be met.

check_model(model_all)

Model Using Scaled Data

The picture above shows that the assumptions that are met are only multicollinearity, while the others are not appropriate. Now I will try to do data scaling on predictor variables and target variable to overcome Normality of Residual and Heterocesdasticity

# Scaling data
num_data <- car_train %>% 
  select(is.numeric) %>% 
  sapply(scale)

## Warning: Predicate functions must be wrapped in `where()`.
## 
##   # Bad
##   data %>% select(is.numeric)
## 
##   # Good
##   data %>% select(where(is.numeric))
## 
## i Please update your code.
## This message is displayed once per session.

fac_data <- car_train %>% select(is.factor)

## Warning: Predicate functions must be wrapped in `where()`.
## 
##   # Bad
##   data %>% select(is.factor)
## 
##   # Good
##   data %>% select(where(is.factor))
## 
## i Please update your code.
## This message is displayed once per session.

car_scale <- data.frame(num_data,fac_data)

model_scale <- lm(selling_price~., car_scale)
summary(model_scale)

## 
## Call:
## lm(formula = selling_price ~ ., data = car_scale)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.2874 -0.2401  0.0128  0.1862  5.4142 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                  0.805766   0.087509   9.208  < 2e-16 ***
## year                         0.155202   0.009972  15.564  < 2e-16 ***
## km_driven                   -0.067133   0.008316  -8.073 8.15e-16 ***
## mileage                      0.073018   0.011662   6.261 4.07e-10 ***
## engine                       0.065462   0.016163   4.050 5.18e-05 ***
## max_power                    0.560830   0.012582  44.574  < 2e-16 ***
## seats                       -0.037662   0.010310  -3.653 0.000261 ***
## fuelDiesel                  -0.039934   0.083522  -0.478 0.632578    
## fuelLPG                      0.186478   0.137646   1.355 0.175540    
## fuelPetrol                  -0.087191   0.083956  -1.039 0.299063    
## seller_typeIndividual       -0.301247   0.022450 -13.418  < 2e-16 ***
## seller_typeTrustmark Dealer -0.419179   0.046806  -8.956  < 2e-16 ***
## transmissionManual          -0.544820   0.026790 -20.336  < 2e-16 ***
## ownerFourth & Above Owner    0.050515   0.052218   0.967 0.333392    
## ownerSecond Owner           -0.051941   0.018205  -2.853 0.004343 ** 
## ownerTest Drive Car          3.194600   0.280164  11.403  < 2e-16 ***
## ownerThird Owner            -0.016501   0.031281  -0.528 0.597849    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5577 on 6307 degrees of freedom
## Multiple R-squared:  0.6897, Adjusted R-squared:  0.6889 
## F-statistic: 876.3 on 16 and 6307 DF,  p-value: < 2.2e-16

check_model(model_scale)

After creating a model with data that has been scaled, it turns out that the results given are not much different from the model_all and produce the same R value of 0.6889, and the assumptions that are met are only multicollinearity. For this reason, it is recommended to use other regression models on this data such as polynomial regression, random forest regression, etc.

Prediction

pred <- predict(model_all, newdata = car_test, interval = "prediction", level = 0.95)
head(pred)

##          fit       lwr       upr
## 2  693441.39 -207413.9 1594296.7
## 3   18287.87 -883617.2  920193.0
## 13  72350.87 -828574.5  973276.2
## 15 485480.94 -415205.7 1386167.6
## 20  98401.11 -802465.1  999267.3
## 22 518553.09 -382295.0 1419401.2

Evaluation

After making predictions from the data, we must find out whether the machine learning model that has been created can produce predictions with the smallest error. There are several ways to do model evaluation on the regression model. To perform model evaluation on the regression model, there are several metrics that can be used:

• R-Squared and Adj R-Squared : to determine how well the model explains the variance of the target variable
• Error value : to see if the prediction made produces the smallest error value

Error values that we will use to see the performance of the model are MAE (Mean Absolute Error) and MAPE. MAE shows the average of the absolute error values while MAPE shows how big the deviation is in percentage terms.

\[ MAE = \frac{\sum |\hat y - y|}{n} \] \[ MAPE = \frac{1}{n} \sum\frac{|\hat y - y|}{y} \]

min <- min(car$selling_price)
max <- max(car$selling_price)
mape <- MAPE(y_pred = pred, y_true = car_test$selling_price)
mae <- MAE(y_pred = pred, y_true = car_test$selling_price)

value <- c(min,max,mape,mae)
eval <- as.data.frame(value)
row.names(eval) <- c("min","max","mape","mae")
eval

##             value
## min  2.999900e+04
## max  1.000000e+07
## mape 2.263373e+00
## mae  7.127226e+05

When viewed from the MAPE (0.87), it means that the error in the prediction of this model is about 87% so that it can be said that linear regression is not suitable for predicting the selling price of used cars in this data.

Conclusion

The data is a history of used car sales sourced from kaggle.com. The purpose of this analysis is to create a model that can predict the selling price of a used car based on several existing features. linear regression models and tuning models have been used by means of feature selection but still give the same results. only one assumption of linear regression can be met, namely multicolinearity, while the assumptions of Normality of Residual, linearity, and homoscedasticity are not met.

From the results of the analysis that has been carried out I conclude that linear regression is not suitable for predicting the selling price of used cars in this data, it is recommended to use other regression models on this data such as polynomial regression, random forest regression, etc.