You work for Motor Trend, a magazine about the automobile industry. Looking at a data set of a collection of cars, they are interested in exploring the relationship between a set of variables and miles per gallon (MPG) (outcome). They are particularly interested in the following two questions:
Take the mtcars data set and write up an analysis to answer their question using regression models and exploratory data analyses.
Your report must be:
Written as a PDF printout of a compiled (using knitr) R markdown document. Do not use any packages that are not in R-base or the library datasets. Brief. Roughly the equivalent of 2 pages or less for the main text. Supporting figures in an appendix can be included up to 5 total pages including the 2 for the main report. The appendix can only include figures. Include a first paragraph executive summary.
data(mtcars)
#Results omited for not having enought space and not needed.
summary(mtcars)
mtcars$cyl <- factor(mtcars$cyl)
mtcars$vs <- factor(mtcars$vs)
mtcars$gear <- factor(mtcars$gear)
mtcars$carb <- factor(mtcars$carb)
mtcars$am <- factor(mtcars$am,labels=c('Automatic','Manual'))
#Result shown in the Appendix
summary(mtcars)
full.model <- lm(mpg ~ ., data = mtcars)
best.model <- step(full.model, direction = "backward")
#Result shown in the Appendix
summary(best.model)
t.test(mpg ~ am, data = mtcars)
##
## Welch Two Sample t-test
##
## data: mpg by am
## t = -3.767, df = 18.33, p-value = 0.001374
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -11.28 -3.21
## sample estimates:
## mean in group Automatic mean in group Manual
## 17.15 24.39
#Result shown in the Appendix
boxplot(mpg ~ am, data = mtcars, col = "blue", ylab = "miles per gallon")
According to these results, cars with a manual transmission are better for mpg than cars with an automatic transmission. The rate of change of the conditional mean mpg with respect to am is about 1.8, and we are 95% confident that this value varies between -1.06 and 4.68. There are however some limitations to this study. To name a few:
Exploratory analysis
summary(mtcars)
## mpg cyl disp hp drat
## Min. :10.4 4:11 Min. : 71.1 Min. : 52.0 Min. :2.76
## 1st Qu.:15.4 6: 7 1st Qu.:120.8 1st Qu.: 96.5 1st Qu.:3.08
## Median :19.2 8:14 Median :196.3 Median :123.0 Median :3.69
## Mean :20.1 Mean :230.7 Mean :146.7 Mean :3.60
## 3rd Qu.:22.8 3rd Qu.:326.0 3rd Qu.:180.0 3rd Qu.:3.92
## Max. :33.9 Max. :472.0 Max. :335.0 Max. :4.93
## wt qsec vs am gear carb
## Min. :1.51 Min. :14.5 0:18 Automatic:19 3:15 1: 7
## 1st Qu.:2.58 1st Qu.:16.9 1:14 Manual :13 4:12 2:10
## Median :3.33 Median :17.7 5: 5 3: 3
## Mean :3.22 Mean :17.8 4:10
## 3rd Qu.:3.61 3rd Qu.:18.9 6: 1
## Max. :5.42 Max. :22.9 8: 1
Regression model
summary(best.model)
##
## Call:
## lm(formula = mpg ~ cyl + hp + wt + am, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.939 -1.256 -0.401 1.125 5.051
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.7083 2.6049 12.94 7.7e-13 ***
## cyl6 -3.0313 1.4073 -2.15 0.0407 *
## cyl8 -2.1637 2.2843 -0.95 0.3523
## hp -0.0321 0.0137 -2.35 0.0269 *
## wt -2.4968 0.8856 -2.82 0.0091 **
## amManual 1.8092 1.3963 1.30 0.2065
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.41 on 26 degrees of freedom
## Multiple R-squared: 0.866, Adjusted R-squared: 0.84
## F-statistic: 33.6 on 5 and 26 DF, p-value: 1.51e-10
boxplot(mpg ~ am, data = mtcars, col = "blue", ylab = "miles per gallon")
par(mfrow=c(2, 2))
plot(best.model)
