Regression Models - Course Project

Prepare Data

library(datasets)
library(ggplot2)
data(mtcars)

mtcars$am <- factor(mtcars$am, labels=c("Automatic", "Manual"))

Is an automatic or manual transmission better for MPG?

Let’s make a t test to understand if means of mpg variables for each transmission type are significantly different.

ttest<-t.test(mpg~am, data=mtcars)
print(ttest)

## 
##  Welch Two Sample t-test
## 
## data:  mpg by am
## 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 in group Automatic    mean in group Manual 
##                17.14737                24.39231

According to t test, there is a significance difference of means of mpg variables for each tranmission type. Let’s validate by plotting.

plt<-ggplot(mtcars, aes(am, mpg, group=am,color=am)) + geom_boxplot()
print(plt)

Quantify the MPG difference between automatic and manual transmissions

To understand which variables most effect the lm, we will use step function.

stepmodel<-step(lm(mpg~., data=mtcars), trace=0)
print(stepmodel)

## 
## Call:
## lm(formula = mpg ~ wt + qsec + am, data = mtcars)
## 
## Coefficients:
## (Intercept)           wt         qsec     amManual  
##       9.618       -3.917        1.226        2.936

It seems that wt, qsec and am variables are the variables that effect the lm. We will train run lm again by using variables wt and qsec, controled by am.

model<-lm(mpg~ am:(wt+qsec),data=mtcars)
print(model)

## 
## Call:
## lm(formula = mpg ~ am:(wt + qsec), data = mtcars)
## 
## Coefficients:
##      (Intercept)    amAutomatic:wt       amManual:wt  amAutomatic:qsec  
##          13.9692           -3.1759           -6.0992            0.8338  
##    amManual:qsec  
##           1.4464

• Increasing weight for cars which have manual tranmission decreases the mpg more than increasing weight for cars which have automatic tranmission. Let’s plot this.

plt<-ggplot(mtcars, aes(wt, mpg, group=am,color=am)) + geom_line()
print(plt)

• Increasing qsec for cars which have manual tranmission increases the mpg more than increasing qsec for cars which have automatic tranmission. Let’s plot this.

plt<-ggplot(mtcars, aes(qsec, mpg, group=am,color=am)) + geom_line()
print(plt)