Effect of Transmission Type on a Car’s MileageShridhara Aithal

Friday, July 24, 2015

Executive Summary

This report is to identify the effect of transmission type (automatic vs. manual) on a car’s mileage. Weperform some analysis on mtcars dataset to determine whether manual transmission is better than automaticand quantify the difference if any.

Our analysis shows that cars with manual transmission have a better mileage than the cars with automatictransmission. Holding all other variables constant, manual transmission give an average of 7.25mpg morethan automatic transmission.

Analysis

We first load mtcars dataset and do a bit of preprocessing and basic analysis to understand the data.

library(dplyr)library(ggplot2)

data(mtcars)mtcars$am <- factor(mtcars$am, labels = c("Automatic", "Manual"))c <- group_by(mtcars, am)summarize(c, mean(mpg))

## Source: local data frame [2 x 2]#### am mean(mpg)## 1 Automatic 17.14737## 2 Manual 24.39231

c <- group_by(mtcars, cyl, am)summarize(c, mean(mpg))

## Source: local data frame [6 x 3]## Groups: cyl#### cyl am mean(mpg)## 1 4 Automatic 22.90000## 2 4 Manual 28.07500## 3 6 Automatic 19.12500## 4 6 Manual 20.56667## 5 8 Automatic 15.05000## 6 8 Manual 15.40000

From the summary, we see that on an average, manual transmission has better mpg than automatic whetherwe consider number of cylinders or not.

We now fit a model and see what the model predicts.

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fit <- lm(mpg ~ am, data = mtcars)summary(fit)$coefficients

## Estimate Std. Error t value Pr(>|t|)## (Intercept) 17.147368 1.124603 15.247492 1.133983e-15## amManual 7.244939 1.764422 4.106127 2.850207e-04

From the coefficients of the model we see that manual transmission has a positive slope (a difference of7.25mpg) in comparison with automatic transmission and the relationship is significant (with a low p-value)

We now plot the residuals to see their characteristics

qplot(mtcars$am, resid(fit)) + geom_boxplot() + ylab("Residuals (mpg)") +xlab("Transmission") + ggtitle("Residuals")

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Automatic ManualTransmission

Res

idua

ls (

mpg

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Residuals

From the plot we see that the residuals for manual transmission have a greater variation than that ofautomatic transmission.

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