In this project we explore the relationship between miles per gallon (MPG) and a set of variables from the Motor Trends car dataset.
I 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:
*“Is an automatic or manual transmission better for MPG” *“Quantify the MPG difference between automatic and manual transmissions”
library(ggplot2)
library(GGally)
data("mtcars")As now We have loaded the data in our Environment, Now lets look at the Data set.
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
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 ...
Lets Convert the "am" into a categorical Variable.
mtcars$am <- as.factor(mtcars$am)
levels(mtcars$am) <- c("Automatic","Manual")To get a better understanding of correlation of variable "mpg" and "am", I started my EDA with a Boxplot.
It can be clearly seen that Manual Transmission is better for MPG.
ggplot(mtcars, aes(x= am, y= mpg, fill=am))+geom_boxplot()+labs(fill="Transmission", x=" ")
At first we will look at the overall collinearity of our Dataset.
ggpairs(mtcars,ggplot2::aes(color=am),
upper = list(continuous = wrap("smooth", size = 1)),
lower = list(continuous = wrap("smooth", size = 1)))
As we can see multi-collinearity in the above plot, So that means we cannot fit the model with all the variables. So we need to select only the important features. So for that We will use step-wise regression method also known as Backwards Regression.
model = step(lm(data = mtcars, mpg ~ . ),trace = FALSE)
summary(model)##
## 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 ***
## amManual 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-11
Intercept is amAutomatic. Which means that the origin is amAutomatic and the values of other features are calculated w.r.t to that origin. So now, we can clearly see the difference between Manual and Automatic in Numbers i.e. Cars with manual transmission have 2.9358 (say 3) more miles per gallon than automatic transmissions
plot(model)
From the Above Analysis, both of the Answers are pretty clear.
Boxplot justifies the Answer of first Question. And our step-wise regression technique quantify the difference between Automatic and Manual Transmission i.e. Cars with manual transmission have 2.9358 (say 3) more miles per gallon than automatic transmissions.