Motor Trend magazine: Automatic or Manual Transmission
Colleen
3/31/2022
Executive Summary
In this analysis, I will be using data from the 1974 Motor Trend magazine to explore the relationship between 2 variables and miles per gallon (mpg). I will be answering the following two questions in my analysis:
1.“Is an automatic or manual transmission better for MPG”
2.”Quantify the MPG difference between automatic and manual transmissions”
In order to answer these questions I will utilize a knitr document to complete the following:
-Provide exploratory data
-Provide visual analysis
1. Is an automatic or manual transmission better for MPG
Obtain Data from the 1974 Motor Trend US magazine and load the library.
library(datasets)
data(mtcars)
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
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000Review Automatic vs. manual transmission mpg’s
Automatic Transmission
summary(mtcars[mtcars$am==0,])## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. :120.1 Min. : 62.0
## 1st Qu.:14.95 1st Qu.:6.000 1st Qu.:196.3 1st Qu.:116.5
## Median :17.30 Median :8.000 Median :275.8 Median :175.0
## Mean :17.15 Mean :6.947 Mean :290.4 Mean :160.3
## 3rd Qu.:19.20 3rd Qu.:8.000 3rd Qu.:360.0 3rd Qu.:192.5
## Max. :24.40 Max. :8.000 Max. :472.0 Max. :245.0
## drat wt qsec vs am
## Min. :2.760 Min. :2.465 Min. :15.41 Min. :0.0000 Min. :0
## 1st Qu.:3.070 1st Qu.:3.438 1st Qu.:17.18 1st Qu.:0.0000 1st Qu.:0
## Median :3.150 Median :3.520 Median :17.82 Median :0.0000 Median :0
## Mean :3.286 Mean :3.769 Mean :18.18 Mean :0.3684 Mean :0
## 3rd Qu.:3.695 3rd Qu.:3.842 3rd Qu.:19.17 3rd Qu.:1.0000 3rd Qu.:0
## Max. :3.920 Max. :5.424 Max. :22.90 Max. :1.0000 Max. :0
## gear carb
## Min. :3.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:2.000
## Median :3.000 Median :3.000
## Mean :3.211 Mean :2.737
## 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :4.000 Max. :4.000Manual Transmission
summary(mtcars[mtcars$am==1,])## mpg cyl disp hp drat
## Min. :15.00 Min. :4.000 Min. : 71.1 Min. : 52.0 Min. :3.54
## 1st Qu.:21.00 1st Qu.:4.000 1st Qu.: 79.0 1st Qu.: 66.0 1st Qu.:3.85
## Median :22.80 Median :4.000 Median :120.3 Median :109.0 Median :4.08
## Mean :24.39 Mean :5.077 Mean :143.5 Mean :126.8 Mean :4.05
## 3rd Qu.:30.40 3rd Qu.:6.000 3rd Qu.:160.0 3rd Qu.:113.0 3rd Qu.:4.22
## Max. :33.90 Max. :8.000 Max. :351.0 Max. :335.0 Max. :4.93
## wt qsec vs am gear
## Min. :1.513 Min. :14.50 Min. :0.0000 Min. :1 Min. :4.000
## 1st Qu.:1.935 1st Qu.:16.46 1st Qu.:0.0000 1st Qu.:1 1st Qu.:4.000
## Median :2.320 Median :17.02 Median :1.0000 Median :1 Median :4.000
## Mean :2.411 Mean :17.36 Mean :0.5385 Mean :1 Mean :4.385
## 3rd Qu.:2.780 3rd Qu.:18.61 3rd Qu.:1.0000 3rd Qu.:1 3rd Qu.:5.000
## Max. :3.570 Max. :19.90 Max. :1.0000 Max. :1 Max. :5.000
## carb
## Min. :1.000
## 1st Qu.:1.000
## Median :2.000
## Mean :2.923
## 3rd Qu.:4.000
## Max. :8.000The mean mpg of the manual transmission (24.4) is greater than the mean mpg of the automatic transmission (17.1), making Manual transmission better for MPG’s.
2. Quantify the MPG difference between automatic and manual transmissions
boxplot(mpg ~ am, data = mtcars, xlab = "Transmission", ylab = "Miles per gallon", main="Miles per gallon by Transmission Type")
As displayed visually in the above boxplot, the manual transmission shows a higher mean of MPG.
Hypothesis Testing
aggregate(mpg~am, data = mtcars, mean)## am mpg
## 1 0 17.14737
## 2 1 24.39231The mean transmission for manual is 7.24mpg higher than automatic
auto <- mtcars[mtcars$am == 0,]
manual <- mtcars[mtcars$am == 1,]
t.test(auto$mpg, manual$mpg)##
## Welch Two Sample t-test
##
## data: auto$mpg and manual$mpg
## 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 24.39231There is a major difference between mpg of manual and automatic transmissions.
m<-lm(mpg~am,data=mtcars)
summary(m)##
## 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: 0.000285From the above, we may conclude that automatic run at 17.15mpg, while manual have 7.24 more mpg.
model <- lm(mpg~am + wt + hp + cyl, data = mtcars)
anova(m,model)## Analysis of Variance Table
##
## Model 1: mpg ~ am
## Model 2: mpg ~ am + wt + hp + cyl
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 30 720.9
## 2 27 170.0 3 550.9 29.166 1.274e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The final model is shown below:
summary(model)##
## Call:
## lm(formula = mpg ~ am + wt + hp + cyl, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4765 -1.8471 -0.5544 1.2758 5.6608
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36.14654 3.10478 11.642 4.94e-12 ***
## am 1.47805 1.44115 1.026 0.3142
## wt -2.60648 0.91984 -2.834 0.0086 **
## hp -0.02495 0.01365 -1.828 0.0786 .
## cyl -0.74516 0.58279 -1.279 0.2119
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.509 on 27 degrees of freedom
## Multiple R-squared: 0.849, Adjusted R-squared: 0.8267
## F-statistic: 37.96 on 4 and 27 DF, p-value: 1.025e-10conclusion
It can be concluded from above that on average, manual transmissions have 1.478 moer MPG than automatic transmissions.
Visual Appendix
plot(model)
