Project for Regression Models at Coursera

Executive summary

This project aims at answering the two questions:

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

We conclude that:

• Manual transmission is better than automatic for MPG.
• Compared with automatic transmissions, manual transmittions have an additional 2.94mpg.

Exploratory Analysis

We begin by inspecting the distribution of mpg for different types of transmission, please find figure 1 in appendix.

We also inspect the difference of mean and standard deviation for mpg with different transmission types. As shown below, we can see the mean and standard deviation for mpg with different transmission types are significantly different.

data(mtcars)
summary(mtcars$mpg[mtcars$am==0])

##    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==0])

## [1] 3.834

summary(mtcars$mpg[mtcars$am==1])

##    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==1])

## [1] 6.167

Model Selection & Fitting

Here we choose models by AIC in a stepwise algorithm.

For transmission type 0 (atomatic), we get the model.

lm1 <- step(lm(mpg ~ ., data=mtcars))

Residual standard error for this model is:

summary(lm1)$sigma

## [1] 2.459

The coefficients suggest that, compared with automatic transmissions, manual transmittions have an additional 2.94mpg.

To identify whether wt and qsec have significant influences to the model. We build models with and without wt and qsec respectively. We, then, use residual standard error to measure the performance of different models

The second model is:

lm2 <- lm(mpg ~ am + wt, data=mtcars)

Residual standard error for this model is:

summary(lm2)$sigma

## [1] 3.098

The third model is:

lm3 <- lm(mpg ~ am + qsec, data=mtcars)

Residual standard error for this model is:

summary(lm3)$sigma

## [1] 3.487

The fourth model is:

lm4 <- lm(mpg ~ am, data=mtcars)

Residual standard error for this model is:

summary(lm4)$sigma

## [1] 4.902

As we can see, the first model (lm(formula = mpg ~ wt + qsec + am, data = mtcars)) has the smallest residual standard error.

We visualize residuals in figure 2 of appendix, from these figures, we can see, there is no significant relationship between residuals and fitted values.

Appendix

boxplot(mtcars$mpg ~ mtcars$am,main='Figure 1. Box plot of mpg for different transmission', xlab='Transmission', ylab='mpg')

Figure 2. Residual Plot

par(mfrow = c(2, 2))
plot(lm1)