Motor_Trend
Astha
2024-11-03
##Executive Summary As an analyst for Motor Trend, an automobile industry magazine, you are examining a dataset of various car models to investigate the relationship between certain variables and miles per gallon (MPG), the outcome of interest. Specifically, Motor Trend wants to answer two key questions:
- “Which transmission type—automatic or manual—yields better MPG?”
- “What is the MPG difference between automatic and manual transmissions?”
A regression analysis was conducted, revealing that beyond transmission type, the number of cylinders, horsepower, and weight significantly impact MPG.
##Data Processing
Begin by loading the dataset and conducting basic exploratory data
analysis.
library(datasets)
data(mtcars)Transform the class of some variables.
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'))To determine whether an automatic or manual transmission is better for MPG, we can start by visualizing the data with a boxplot of MPG by transmission type. This provides a quick look at the distribution of MPG for each type (see Appendix 2).
From the boxplot, it appears that manual transmissions may offer better MPG than automatic ones.
To statistically test this observation, we can perform a t-test comparing the MPG values between the two transmission types. This will help determine if the difference in MPG is significant or likely due to random variation.
t.test(mtcars$mpg~mtcars$am)##
## Welch Two Sample t-test
##
## data: mtcars$mpg by mtcars$am
## t = -3.7671, df = 18.332, p-value = 0.001374
## alternative hypothesis: true difference in means between group Automatic and group Manual is not equal to 0
## 95 percent confidence interval:
## -11.280194 -3.209684
## sample estimates:
## mean in group Automatic mean in group Manual
## 17.14737 24.39231With a p-value of 0.001374 (less than 0.05), we reject the null hypothesis, which states there is no difference in MPG between transmission types. This result supports the conclusion that manual transmission provides better MPG than automatic transmission, assuming all other factors remain constant.
Quantifying MPG
To quantify the MPG difference between automatic and manual
transmissions, and to see if other variables impact MPG, we conducted a
multivariate linear regression using all available variables. A stepwise
regression using R’s step function was applied to select
predictors based on criteria like AIC.
The results indicate that the optimal model includes the variables
cyl6, cyl8, hp, wt,
and amManual. This model explains approximately 86.59% of
the variance in MPG. Specifically: - The number of cylinders negatively
affects MPG, with reductions of 3.03 miles for 6 cylinders and 2.16
miles for 8 cylinders. - Horsepower also reduces MPG by 0.03 miles per
unit increase. - Weight has a negative impact, decreasing MPG by 2.5
miles for every 1,000 pounds.
Conversely, manual transmission shows an improvement, delivering an average of 1.81 MPG more than automatic transmission.
The residual plots suggest a random scatter, indicating that some transformation might be beneficial for achieving linearity (see Appendix 3).
Multi = lm(data = mtcars, mpg~.)
Best = step(Multi, 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 70.438summary(Best)##
## 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-10Conclusion
On average, manual transmission outperforms automatic transmission by 1.81 MPG. However, transmission type alone does not account for all MPG variation; other critical factors include the number of cylinders, horsepower, and weight, each of which significantly impacts MPG. ##Appendix
pairs(mtcars)
boxplot(mpg~am, data = mtcars,
xlab = "Transmission",
ylab = "Miles per Gallon",
main = "MPG by Transmission Type")
par(mfrow = c(2,2))
plot(Best)