Mileage of Automatic vs Manual Transmission Cars
Executive Summary
Exploring the relationship between various factors influencing the mileage of cars and quantifying the difference between automatic and manual transmission. The analysis supports the general assumption that manual transmission is better for Mileage. Linear Model Regression hints that, on average, a manaul transmission gives 1.80 MPG higher than automatic transmission with an uncerainty of ± 1.40 MPG.
Loading Data
library(datasets)
library(ggplot2)
library(car)
library(stats)
head(mtcars)## mpg cyl disp hp drat wt qsec vs transmission gear
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 Manual 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 Manual 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 Manual 4
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 Automatic 3
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 Automatic 3
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 Automatic 3
## carb
## Mazda RX4 4
## Mazda RX4 Wag 4
## Datsun 710 1
## Hornet 4 Drive 1
## Hornet Sportabout 2
## Valiant 1Exploratory Data Analysis
- There seems to be a significant effect of the transmission type on the mileage which can be seen in the boxplot.
- But it is important notice the influence of other variables like the number of cylinders, weight of the car and horsepower on MPG.
- Hence a linear model is to be built with appropriate regressors to estimate the adjusted influence of any particular variable.
par(mfrow=c(1,2))
colnames(mtcars)[9]<-"transmission"
mtcars$transmission[mtcars$transmission=="0"]<-"Automatic"
mtcars$transmission[mtcars$transmission=="1"]<-"Manual"
mtcars$transmission <- as.factor(mtcars$transmission)
boxplot(mtcars$mpg~mtcars$transmission,
ylab="Miles pre Gallon",col=c("salmon","gold"))
title("MPG vs Transmission")
plot(mtcars$wt,mtcars$mpg,col=mtcars$cyl,pch=17,
ylab="Miles per Gallon",xlab="Weight")
title("MPG vs Weight vs Cyl")
legend("topright", title="No. of Cyl",
c("4","6","8"),pch=17, col=c("black","red","green"), horiz=FALSE)
Model Selection
- Starting with just transmission, 5 linear models are built progressively adding a variable.
- It is important to note that qsec(1/4 mile time) is directly related to the horse power and hence is omitted from our list of models.
- Best model is then chosen by comparing the variances of these models using the function ‘anova()’.
# Building possible models
lm1 <- lm(mpg~transmission,data=mtcars)
lm2 <- lm(mpg~transmission+cyl,data=mtcars)
lm3 <- lm(mpg~transmission+cyl+hp,data=mtcars)
lm4 <- lm(mpg~transmission+cyl+hp+wt,data=mtcars)
lm5 <- lm(mpg~transmission+cyl+hp+wt+carb,data=mtcars)
anova(lm1,lm2,lm3,lm4,lm5)## Analysis of Variance Table
##
## Model 1: mpg ~ transmission
## Model 2: mpg ~ transmission + cyl
## Model 3: mpg ~ transmission + cyl + hp
## Model 4: mpg ~ transmission + cyl + hp + wt
## Model 5: mpg ~ transmission + cyl + hp + wt + carb
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 30 720.90
## 2 28 264.50 2 456.40 37.7751 2.783e-08 ***
## 3 27 197.20 1 67.30 11.1399 0.002647 **
## 4 26 151.03 1 46.17 7.6433 0.010547 *
## 5 25 151.03 1 0.00 0.0000 0.999841
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Summary of the selected model
summary(lm4)##
## Call:
## lm(formula = mpg ~ transmission + cyl + hp + wt, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9387 -1.2560 -0.4013 1.1253 5.0513
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.70832 2.60489 12.940 7.73e-13 ***
## transmissionManual 1.80921 1.39630 1.296 0.20646
## cyl6 -3.03134 1.40728 -2.154 0.04068 *
## cyl8 -2.16368 2.28425 -0.947 0.35225
## hp -0.03211 0.01369 -2.345 0.02693 *
## wt -2.49683 0.88559 -2.819 0.00908 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.41 on 26 degrees of freedom
## Multiple R-squared: 0.8659, Adjusted R-squared: 0.8401
## F-statistic: 33.57 on 5 and 26 DF, p-value: 1.506e-10Results
- From the analysis of the variance, the best model is lm4 which depends on the factors transmission type,number of cylinders, horsepower and weight.
- It can be inferred from the estimate of these variables that manual transmission gives 1.80 MPG more than automatic transmission(Intercept) considering the effect of other significant variables with a standard deviation of 1.40 MPG.
- It is important to note that the manual transmission by itself without considering the effect of other variables gives 7.245 MPG higher than automatic transmission .
Diagnostics
- Maximum values of Standardized difference of Betas(dfbetas) and Leverages(hatvalues) of the chosen model are calculated which lie withing welcomed range.
- The same is reflected in the residual plots below.
maxvalues <- c(Maximum.Beta=max(dfbetas(lm4)),
Maximum.Hatvalue=max(hatvalues(lm4)))
round(maxvalues,3)## Maximum.Beta Maximum.Hatvalue
## 0.939 0.471Residual Plot
par(mfrow=c(2,2))
plot(lm4)
Appendix
Source of Data:
The data was extracted from the 1974 Motor Trend US magazine, and comprises fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973-74 models). Henderson and Velleman (1981), Building multiple regression models interactively. Biometrics, 37, 391-411.
Variables:
The data frame(mtcars) with 32 observations on 11 variables.
- [, 1] mpg Miles/(US) gallon
- [, 2] cyl Number of cylinders
- [, 3] disp Displacement (cu.in.)
- [, 4] hp Gross horsepower
- [, 5] drat Rear axle ratio
- [, 6] wt Weight (lb/1000)
- [, 7] qsec 1/4 mile time
- [, 8] vs V/S
- [, 9] am Transmission (0 = automatic, 1 = manual)
- [,10] gear Number of forward gears
- [,11] carb Number of carburetors