Executive Summary

Motor Trend is a magazine about the automobile industry. It is interested in exploring the relationship between a set of variables and miles per gallon (MPG) (outcome), particularly:

“Is an automatic or manual transmission better for MPG” “Quantify the MPG difference between automatic and manual transmissions” Using a data set from Motor Trend Magazine along with linear regression and hypothesis testing, it can be concluded that there is a significant difference between the MPG of automatic and manual transmission cars.

To quantify the MPG difference between automatic and manual transmission cars, a linear regression model that took into account the weight, the type of transmission and the acceleration (qsec) was used. Controlling for these factors, manual transmission cars have a better fuel efficiency of 2.94 MPG more than automatic transmission cars.

library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.1.3
library(dplyr)
## Warning: package 'dplyr' was built under R version 4.1.3
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

Reading DATA 

data("mtcars")
str(mtcars)
## 'data.frame':    32 obs. of  11 variables:
##  $ mpg : num  21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
##  $ cyl : num  6 6 4 6 8 6 8 4 4 6 ...
##  $ disp: num  160 160 108 258 360 ...
##  $ hp  : num  110 110 93 110 175 105 245 62 95 123 ...
##  $ drat: num  3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
##  $ wt  : num  2.62 2.88 2.32 3.21 3.44 ...
##  $ qsec: num  16.5 17 18.6 19.4 17 ...
##  $ vs  : num  0 0 1 1 0 1 0 1 1 1 ...
##  $ am  : num  1 1 1 0 0 0 0 0 0 0 ...
##  $ gear: num  4 4 4 3 3 3 3 4 4 4 ...
##  $ carb: num  4 4 1 1 2 1 4 2 2 4 ...

Processing the DATA 

mtcars$am<-as.factor(mtcars$am)
levels(mtcars$am)<-c("AT", "MT")

aggregate(mpg~am, data=mtcars, mean)
##   am      mpg
## 1 AT 17.14737
## 2 MT 24.39231
atData<-mtcars[mtcars$am == "AT",]
mtData<-mtcars[mtcars$am == "MT",]
t.test(atData$mpg, mtData$mpg)
## 
##  Welch Two Sample t-test
## 
## data:  atData$mpg and mtData$mpg
## t = -3.7671, df = 18.332, p-value = 0.001374
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -11.280194  -3.209684
## sample estimates:
## mean of x mean of y 
##  17.14737  24.39231

Graphs 

ggplot(data = mtcars, aes(mpg)) + geom_histogram(color = "blue", fill = "pink") + facet_grid(.~am) + labs(x = "Miles per Gallon", y = "Frequency", title = "MPG Histogram for AT and MT cars")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(data = mtcars, aes(am,mpg)) + geom_boxplot(color = "blue", fill = "pink") + labs(x= "Transmission", y = "MPG", title = "MPG: AT vs MT")

ggplot(data = mtcars, aes(am,mpg)) + geom_boxplot(color = "blue", fill = "pink") + labs(x= "Transmission", y = "MPG", title = "MPG: AT vs MT")

Linear Models ### Model 1: Regress mpg against am

fit_1 <-lm(mpg~am, data = mtcars)
summary(fit_1)
## 
## Call:
## lm(formula = mpg ~ am, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.3923 -3.0923 -0.2974  3.2439  9.5077 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   17.147      1.125  15.247 1.13e-15 ***
## amMT           7.245      1.764   4.106 0.000285 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.902 on 30 degrees of freedom
## Multiple R-squared:  0.3598, Adjusted R-squared:  0.3385 
## F-statistic: 16.86 on 1 and 30 DF,  p-value: 0.000285
fit_2 = step(lm(data = mtcars, mpg ~ .),trace=0,steps=10000) 
summary(fit_2)
## 
## Call:
## lm(formula = mpg ~ wt + qsec + am, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4811 -1.5555 -0.7257  1.4110  4.6610 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   9.6178     6.9596   1.382 0.177915    
## wt           -3.9165     0.7112  -5.507 6.95e-06 ***
## qsec          1.2259     0.2887   4.247 0.000216 ***
## amMT          2.9358     1.4109   2.081 0.046716 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.459 on 28 degrees of freedom
## Multiple R-squared:  0.8497, Adjusted R-squared:  0.8336 
## F-statistic: 52.75 on 3 and 28 DF,  p-value: 1.21e-11

ANOVA of the 2 Models 

fit_step<-lm(mpg~ am + wt + qsec, data = mtcars)
anova(fit_1, fit_step)
## Analysis of Variance Table
## 
## Model 1: mpg ~ am
## Model 2: mpg ~ am + wt + qsec
##   Res.Df    RSS Df Sum of Sq      F   Pr(>F)    
## 1     30 720.90                                 
## 2     28 169.29  2    551.61 45.618 1.55e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
par(mfrow = c(2,2))
plot(fit_2)