This is a regression analysis document. With the increase in
production of Electric vehicles it is important to understand the
correlation behind price changes. This document shows the linear model
of milage vs average price of electric vehicles. From this model we can
determine the coefficient of determination, allowing us to see if the
model is strong or weak. You can refer to the dataset on the following
link: https://www.kaggle.com/datasets/iannjuguna/electric-car-prices.
This dataset was posted on September 25, 2022
Importing Excel spreadsheet as an R dataframe
library("readxl")
df<-read_excel("Electric cars.xlsx")
# Preview of the spreadsheet
head(df)
## # A tibble: 6 × 6
## Year `BEV average price (USD)` `Global Sales Volume` Mileage `Lithium Ion B…`
## <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2010 64032 50000 127 1191
## 2 2011 51736 60000 139 924
## 3 2012 52084 80000 160 726
## 4 2013 56028 150000 189 668
## 5 2014 44776 224700 210 592
## 6 2015 42340 380100 211 384
## # … with 1 more variable: AveragePriceOfNewCar <dbl>
Average price of the new car is the y variable, while range
(mileage) in kilometers is the x variable.
#Setting the x and y variables from the spreadsheet into seperate variables for easy file access
x<-df$Mileage
y<-df$AveragePriceOfNewCar
print("Printing X values to test if pushed correctly")
## [1] "Printing X values to test if pushed correctly"
print(x)
## [1] 127 139 160 189 210 211 233 267 304 336 338 349 400
print("Printing Y values to test if pushed correctly")
## [1] "Printing Y values to test if pushed correctly"
print(y)
## [1] 37500 37311 36874 37826 37519 38240 38455 38350 38365 40546 44021 49185
## [13] 48000
Plotting the dataset
#Plotting the dataset
plot(x,y, main="Electric Cars", xlab="Range (Mileage) in Kilometers", ylab="Average Price of New Car", col="blue")
Running the cor function on the dataset to find the correlation
between the two variables
cor(x,y)
## [1] 0.8155397
Running the lm function on the dataset to find the linear regression
line
cars1<-lm(y~x)
# Equation of the linear regression line
cars1
##
## Call:
## lm(formula = y ~ x)
##
## Coefficients:
## (Intercept) x
## 30469.94 38.64
Plotting the linear regression line
#Plotting the linear regression line
plot(x,y, main="Electric Cars", xlab="Range (Mileage) in Kilometers", ylab="Average Price of New Car", col="blue")
abline(lm(y~x))
Summary of the dataset
summary(cars1)$coef
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30469.94300 2190.055443 13.912864 2.509358e-08
## x 38.64013 8.267068 4.673982 6.781452e-04
rSquare <-summary(cars1)$r.squared
outputVar <- paste("The coefficient of determination is", rSquare, "so the model is moderatly positive. This means that the model is not very strong, but it is not weak either.")
outputVar
## [1] "The coefficient of determination is 0.665104927228271 so the model is moderatly positive. This means that the model is not very strong, but it is not weak either."
intercetp <-summary(cars1)$coef[1]
slope <-summary(cars1)$coef[2]
outputVar <- paste("The Equation of the regression line is: ŷ = b0 + b1x. p̂ = ", intercetp, "+", slope, "x")
outputVar
## [1] "The Equation of the regression line is: ŷ = b0 + b1x. p̂ = 30469.9429989069 + 38.640129026727 x"
Calculating the Anova of the linear model
anova(cars1)
## Analysis of Variance Table
##
## Response: y
## Df Sum Sq Mean Sq F value Pr(>F)
## x 1 139323361 139323361 21.846 0.0006781 ***
## Residuals 11 70152400 6377491
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Anova Analysis
SSR<-anova(cars1)$Sum[1]
SSE<-anova(cars1)$Sum[2]
SST<- SSR+SSE
output1 <- paste("The sum of squares for the regression is", SSR)
output2 <- paste("The sum of squares for the error is", SSE)
output3 <- paste("The total sum of squares is", SSR,"+", SSE,"=",SST)
output4 <- paste("We can calculate the R^2 value from the total sum of squares and the sum of squares for the regression. R^2 = SSR/SST = ", SSR,"/",SST,"=", SSR/SST)
output1
## [1] "The sum of squares for the regression is 139323360.827154"
output2
## [1] "The sum of squares for the error is 70152400.2497694"
output3
## [1] "The total sum of squares is 139323360.827154 + 70152400.2497694 = 209475761.076923"
output4
## [1] "We can calculate the R^2 value from the total sum of squares and the sum of squares for the regression. R^2 = SSR/SST = 139323360.827154 / 209475761.076923 = 0.665104927228272"
Plotting the final graph with the linear regresison model
plot(x,y, main= "Range vs Average Price")
abline(cars1$coef,lty=1)
