MPG Analysis Automatic vs Manual Transmissions
Ed Loessi
March 24, 2018
Introduction - Executive Summary
In this project I am utilizing data from the 1974 Motor Trend Magazine Study covering 32 vehicles. The purpose of this particular analysis is to determine which type of transmission is better for higher gas mileage, an automatic transmission, or a manual transmission, and to build a best fit model comparing the two transmissions and other important variables. In completing this analysis, I performed basic exploratory, tested a few linear models, and utilized a stepwise model to determine the best combination of variables to determine a vehicle’s MPG. The final analysis showed that the MPG for a vehicle is in fact higher when equipped with a manual transmission and that a model that contains the weight of the vehicle, its quarter-mile race time, and its transmission type will allow you to explain approximately 85% using the Multiple R-squared.
Load the initial dataset
The first step is to load the dataset and create factors for the vs and am variables for future processing.
data(mtcars)
mtcars$vs <- as.factor(mtcars$vs)
mtcars$am <- as.factor(mtcars$am)Summarize and review the data
The next step is to look through the number of observations of which there are 32 and the number or variables of which there are 11. Additional I ran a pairs comparison to test the connections that the variables show between eachother. Note - the Appendix (Figure 1) contains the pairs grid.
Observations and Variables
You can see the breakout of the variables as well as a number of the observations.
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 : Factor w/ 2 levels "0","1": 1 1 2 2 1 2 1 2 2 2 ...
## $ am : Factor w/ 2 levels "0","1": 2 2 2 1 1 1 1 1 1 1 ...
## $ gear: num 4 4 4 3 3 3 3 4 4 4 ...
## $ carb: num 4 4 1 1 2 1 4 2 2 4 ...Key statistical summary
The summary can be reviewed to better understand some of the key statistical data.
summary(mtcars)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs am
## Min. :2.760 Min. :1.513 Min. :14.50 0:18 0:19
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1:14 1:13
## Median :3.695 Median :3.325 Median :17.71
## Mean :3.597 Mean :3.217 Mean :17.85
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90
## Max. :4.930 Max. :5.424 Max. :22.90
## gear carb
## Min. :3.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:2.000
## Median :4.000 Median :2.000
## Mean :3.688 Mean :2.812
## 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :8.000Automatic vs Manual Transmission Plotting
I ran an initial boxplot to see what the differences were between a manual and automatic transmission regarding MPG. The boxplot shows that the manual transmission performs better in terms of having a higher MPG.
boxplot(mpg ~ am, data = mtcars,
col = c("dark green", " dark blue"),
xlab = "Miles per Gallon",
ylab = "Transmission Type",
main = "Miles Per Gallon by Type of Transmission",
names= c("automatic trans","manual trans"),
horizontal= T) 
T-test for the automatic vs. manual transmissions
The t-test below renders a p-value of 0.001374 which is < 0.05 the standard marker for significance meaning that there is a difference between the two transmissions when measured against the dependent variable of MPG.
auto=subset(mtcars,select=mpg,am==0)
manual=subset(mtcars,select=mpg,am==1)
t.test(auto,manual)##
## Welch Two Sample t-test
##
## data: auto and manual
## 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 of x mean of y
## 17.14737 24.39231Trial a series of linear regression models
In the next several steps I used a simple regression model to understand the mpg and transmission relationship, then a multivariate model to understand all of the variables in relation to the mpg, then a stepwise regression to choose the best variables to combine to determine mpg.
Simple Regression model
The simple regression model below shows that the manual transmission would be expected to outperform the automatic transmission by 7.24 miles per gallon given no other variables to consider and that it would explain 36% of the variance.
regSIM <- lm(mpg~am,mtcars)
summary(regSIM) ##
## 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 ***
## am1 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: 0.000285Multivariate model
The multivariate model takes into account all variables. However in this model the manual transmission only outperforms the automatice transmission by 2.5 miles per gallon. This model explains 86% of the variance. However, in this model many of the variables are not significant.
regTOT <- lm(mpg~.,mtcars)
summary(regTOT)##
## Call:
## lm(formula = mpg ~ ., data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4506 -1.6044 -0.1196 1.2193 4.6271
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.30337 18.71788 0.657 0.5181
## cyl -0.11144 1.04502 -0.107 0.9161
## disp 0.01334 0.01786 0.747 0.4635
## hp -0.02148 0.02177 -0.987 0.3350
## drat 0.78711 1.63537 0.481 0.6353
## wt -3.71530 1.89441 -1.961 0.0633 .
## qsec 0.82104 0.73084 1.123 0.2739
## vs1 0.31776 2.10451 0.151 0.8814
## am1 2.52023 2.05665 1.225 0.2340
## gear 0.65541 1.49326 0.439 0.6652
## carb -0.19942 0.82875 -0.241 0.8122
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.65 on 21 degrees of freedom
## Multiple R-squared: 0.869, Adjusted R-squared: 0.8066
## F-statistic: 13.93 on 10 and 21 DF, p-value: 3.793e-07Stepwise regression
In order to find the best set of variables I used the stepwise model below. The variables of weight, quarter-mile race time, and transmission type when combined provide the strongest model while explaining 85% of the variance. In this model, the manual transmission outperforms the automatic transmission by 2.93 miles per gallon.
regSR=step(regTOT,trace=0)
summary(regSR)##
## Call:
## lm(formula = mpg ~ wt + qsec + am, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4811 -1.5555 -0.7257 1.4110 4.6610
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.6178 6.9596 1.382 0.177915
## wt -3.9165 0.7112 -5.507 6.95e-06 ***
## qsec 1.2259 0.2887 4.247 0.000216 ***
## am1 2.9358 1.4109 2.081 0.046716 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.459 on 28 degrees of freedom
## Multiple R-squared: 0.8497, Adjusted R-squared: 0.8336
## F-statistic: 52.75 on 3 and 28 DF, p-value: 1.21e-11Final Analysis
The final model above shows that weight, quarter-mile race time, and transmission type are all statistically significant regarding the MPG. This model shows that the MPG when all other factors are held constant will improve by 2.93 miles per gallon over the automatic transmission, which answers the original question of which transmission is better for a higher MPG (manual transmission).
Appendix
Graph 1 - Pairs Analysis
pairs(mtcars)
Graph 2 - Residuals Analysis
plot(regSR, which=c(1:1))