The following analysis looks into the affect of miles per gallon (MPG) based on type of transmission. We look at the mtcars dataset and compare the impact on MPG from a manual transmission versus an automatic one. By doing the analysis below, we find that on average a MANUAL transmission will give you a higher MPG rate.

Getting Data

library(datasets)
data("mtcars")

Exploratory Data Analysis

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 ...
head(mtcars)
##                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
## Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

Standard Linear Model (LM)

CR <- lm(mpg ~ am, data = mtcars)
summary(CR)
## 
## 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 ***
## am             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

We see that transmission is very significant in determining MPG. If you have an automatic transmission, your average MPG is 17.147 while a manual transmission your average is +7.245 more making it 24.392 MPG.

From the plot, we have further support that manual transmissions tend to have higher MPG’s.

Poisson General Linear Model (GLM)

Running a Poisson GLM did not result in a better fit. It is the same as with a standard linear model.

Residuals and Residual Plots

Residuals

n <- length(mtcars$mpg)
e <- resid(CR)
yhat <- predict(CR)
max(abs(e -(mtcars$mpg - yhat)))
## [1] 4.840572e-14
max(abs(e - (mtcars$mpg  - coef(CR)[1] - coef(CR)[2] * mtcars$am)))
## [1] 4.840572e-14

Residual Plots

Confidence Intervals

confint(CR)
##                2.5 %   97.5 %
## (Intercept) 14.85062 19.44411
## am           3.64151 10.84837
confint(glm1)
## Waiting for profiling to be done...
##                 2.5 %    97.5 %
## (Intercept) 2.7312549 2.9484974
## mtcars$am   0.1976786 0.5070595

From this, we see that although the fit may not show a difference, the confidence of the Poisson GLM is greater than the standard linear model.