Automatic, Manual Transmition and MPG

Executive Summary

In this report we will be comparing the effect of having an automatic or manual transmition and the performance this has on MPG using a regression analysis. We will be using a dataset from the 1974 Motor Trend magazine to answer the following inquiries:

• Is an automatic or manual transmission better for MPG
• Quantify the MPG difference between automatic and manual transmissions

The conclusion for our analysis was: * Manual transmition is better than automatic transmition for MPG by a factor of 2.9358 MPG.

Data Preprocessing

First we load the data. Then we will change the variable mtcars$am from numeric value to a factor value. This variable is the one that says if the car transmition is either automatic or manual (0 = automatic, 1 = manual)

data(mtcars)
mtcars$am <- as.factor(mtcars$am)
levels(mtcars$am) <- c("Automatic", "Manual")

Exploratory analysis

We will now perform some basic exploratory analysis to get to know more about the data.

summary(mtcars$mpg[mtcars$am=="Automatic"])

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    10.4    15.0    17.3    17.1    19.2    24.4

sd(mtcars$mpg[mtcars$am=="Automatic"])

## [1] 3.834

summary(mtcars$mpg[mtcars$am=="Manual"])

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    15.0    21.0    22.8    24.4    30.4    33.9

sd(mtcars$mpg[mtcars$am=="Manual"])

## [1] 6.167

We see that the standard deviation and mean from automatic and manual transmition and significantly different.

Model selection

We will build a model using all the variables as predictors using the step method in conjunction with lm.

model <- step(lm(mpg ~ ., data=mtcars))

summary(model)

## 
## Call:
## lm(formula = mpg ~ wt + qsec + am, data = mtcars)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -3.481 -1.556 -0.726  1.411  4.661 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    9.618      6.960    1.38  0.17792    
## wt            -3.917      0.711   -5.51    7e-06 ***
## qsec           1.226      0.289    4.25  0.00022 ***
## amManual       2.936      1.411    2.08  0.04672 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.46 on 28 degrees of freedom
## Multiple R-squared:  0.85,   Adjusted R-squared:  0.834 
## F-statistic: 52.7 on 3 and 28 DF,  p-value: 1.21e-11

By looking at the summary(model) we can see that the intercept is at 9.6178 mpg and for the manual transmition we get 2.9358 which means that a car with manual transmition have an additional 2.9358 mpg compared with automatic transmition cars.

Appendix

par(mfrow = c(2, 2))
plot(model)

boxplot(mtcars$mpg ~ mtcars$am, main='MPG for automatic and manual transmition', xlab='Transmission', ylab='MPG')