Motor Trend Car Road Tests - Effects of transmission on MPG
Rishabh Shukla
In this project, we will analyze the mtcars data set and explore the relationship between a set of variables and miles per gallon (MPG) which will be our outcome.
- Is an automatic or manual transmission better for MPG
- Quantify the MPG difference between automatic and manual transmissions
Exploratory Data Analysis
First we will load the data and do the data transformation. All the required variables are factored accordingly.
data(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'))
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 : Factor w/ 3 levels "4","6","8": 2 2 1 2 3 2 3 1 1 2 ...
## $ 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 "Automatic","Manual": 2 2 2 1 1 1 1 1 1 1 ...
## $ gear: Factor w/ 3 levels "3","4","5": 2 2 2 1 1 1 1 2 2 2 ...
## $ carb: Factor w/ 6 levels "1","2","3","4",..: 4 4 1 1 2 1 4 2 2 4 ...We will than draw a qplot for observing the relationship of the variables.Next we do draw the box plot to see the effect in case of manual and automatic
## Warning: package 'ggplot2' was built under R version 3.2.3
This plot clearly depicts an increase in the mpg when the transmission is Manual The plot here will depict all the relationship among different variables. we have to take only that variable which are correlated with mpg
We will build a temp model with all variables as predictor and perform stepwise method selection to select significant predictor for the final model.
temp_model <- lm(mpg ~ ., data = mtcars)
final_model <- step(temp_model, direction = "both")## Start: AIC=76.4
## mpg ~ cyl + disp + hp + drat + wt + qsec + vs + am + gear + carb
##
## Df Sum of Sq RSS AIC
## - carb 5 13.5989 134.00 69.828
## - gear 2 3.9729 124.38 73.442
## - am 1 1.1420 121.55 74.705
## - qsec 1 1.2413 121.64 74.732
## - drat 1 1.8208 122.22 74.884
## - cyl 2 10.9314 131.33 75.184
## - vs 1 3.6299 124.03 75.354
## <none> 120.40 76.403
## - disp 1 9.9672 130.37 76.948
## - wt 1 25.5541 145.96 80.562
## - hp 1 25.6715 146.07 80.588
##
## Step: AIC=69.83
## mpg ~ cyl + disp + hp + drat + wt + qsec + vs + am + gear
##
## Df Sum of Sq RSS AIC
## - gear 2 5.0215 139.02 67.005
## - disp 1 0.9934 135.00 68.064
## - drat 1 1.1854 135.19 68.110
## - vs 1 3.6763 137.68 68.694
## - cyl 2 12.5642 146.57 68.696
## - qsec 1 5.2634 139.26 69.061
## <none> 134.00 69.828
## - am 1 11.9255 145.93 70.556
## - wt 1 19.7963 153.80 72.237
## - hp 1 22.7935 156.79 72.855
## + carb 5 13.5989 120.40 76.403
##
## Step: AIC=67
## mpg ~ cyl + disp + hp + drat + wt + qsec + vs + am
##
## Df Sum of Sq RSS AIC
## - drat 1 0.9672 139.99 65.227
## - cyl 2 10.4247 149.45 65.319
## - disp 1 1.5483 140.57 65.359
## - vs 1 2.1829 141.21 65.503
## - qsec 1 3.6324 142.66 65.830
## <none> 139.02 67.005
## - am 1 16.5665 155.59 68.608
## - hp 1 18.1768 157.20 68.937
## + gear 2 5.0215 134.00 69.828
## - wt 1 31.1896 170.21 71.482
## + carb 5 14.6475 124.38 73.442
##
## Step: AIC=65.23
## mpg ~ cyl + disp + hp + wt + qsec + vs + am
##
## Df Sum of Sq RSS AIC
## - disp 1 1.2474 141.24 63.511
## - vs 1 2.3403 142.33 63.757
## - cyl 2 12.3267 152.32 63.927
## - qsec 1 3.1000 143.09 63.928
## <none> 139.99 65.227
## + drat 1 0.9672 139.02 67.005
## - hp 1 17.7382 157.73 67.044
## - am 1 19.4660 159.46 67.393
## + gear 2 4.8033 135.19 68.110
## - wt 1 30.7151 170.71 69.574
## + carb 5 13.0509 126.94 72.095
##
## Step: AIC=63.51
## mpg ~ cyl + hp + wt + qsec + vs + am
##
## Df Sum of Sq RSS AIC
## - qsec 1 2.442 143.68 62.059
## - vs 1 2.744 143.98 62.126
## - cyl 2 18.580 159.82 63.466
## <none> 141.24 63.511
## + disp 1 1.247 139.99 65.227
## + drat 1 0.666 140.57 65.359
## - hp 1 18.184 159.42 65.386
## - am 1 18.885 160.12 65.527
## + gear 2 4.684 136.55 66.431
## - wt 1 39.645 180.88 69.428
## + carb 5 2.331 138.91 72.978
##
## Step: AIC=62.06
## mpg ~ cyl + hp + wt + vs + am
##
## Df Sum of Sq RSS AIC
## - vs 1 7.346 151.03 61.655
## <none> 143.68 62.059
## - cyl 2 25.284 168.96 63.246
## + qsec 1 2.442 141.24 63.511
## - am 1 16.443 160.12 63.527
## + disp 1 0.589 143.09 63.928
## + drat 1 0.330 143.35 63.986
## + gear 2 3.437 140.24 65.284
## - hp 1 36.344 180.02 67.275
## - wt 1 41.088 184.77 68.108
## + carb 5 3.480 140.20 71.275
##
## Step: AIC=61.65
## mpg ~ cyl + hp + wt + am
##
## Df Sum of Sq RSS AIC
## <none> 151.03 61.655
## - am 1 9.752 160.78 61.657
## + vs 1 7.346 143.68 62.059
## + qsec 1 7.044 143.98 62.126
## - cyl 2 29.265 180.29 63.323
## + disp 1 0.617 150.41 63.524
## + drat 1 0.220 150.81 63.608
## + gear 2 1.361 149.66 65.365
## - hp 1 31.943 182.97 65.794
## - wt 1 46.173 197.20 68.191
## + carb 5 5.633 145.39 70.438The final model obtained from above computation consist of variables cyl,wt and hp as cofounders and am as independent variable.
summary(final_model)##
## Call:
## lm(formula = mpg ~ cyl + hp + wt + am, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9387 -1.2560 -0.4013 1.1253 5.0513
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.70832 2.60489 12.940 7.73e-13 ***
## cyl6 -3.03134 1.40728 -2.154 0.04068 *
## cyl8 -2.16368 2.28425 -0.947 0.35225
## hp -0.03211 0.01369 -2.345 0.02693 *
## wt -2.49683 0.88559 -2.819 0.00908 **
## amManual 1.80921 1.39630 1.296 0.20646
## ---
## 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: 0.8659, Adjusted R-squared: 0.8401
## F-statistic: 33.57 on 5 and 26 DF, p-value: 1.506e-10R^2 value is .84 is maximum obtained from the mode.Thus we can conclude that 84% variability is explained by the above model.
Residuals and Diagnostics
We will now plot the residual and examine its behaviour.
As we can see from the plot that values are scatterd properply all along the graph so it implies that we can use linear model and that our final model is the best one.