library(kableExtra)
library(tidyverse)
library(stargazer)

Top 5 rows of data set

data(mtcars)
mtcars[1:5,] %>%
  kable() %>%
  kable_styling(bootstrap_options = c("striped","bordered"), full_width = F)
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

Is an automatic or manual transmission better for MPG? (Mile per Gallon)

ave_mpg <- mtcars %>%
  group_by(am) %>%
  summarise(ave_mpg = mean(mpg))
automatic = ave_mpg[ave_mpg$am==0,'ave_mpg']
manual = ave_mpg[ave_mpg$am==1,'ave_mpg']
mtcars %>% 
  mutate(Type = ifelse(am == 0,'Automatic','Manual')) %>%
  ggplot(mapping = aes(x=Type,y=mpg)) +
  geom_boxplot(outlier.colour="black", outlier.shape=16,
             outlier.size=2, notch=FALSE)

Average MPG for manual is 24.3923077 and average MPG for automatic is 17.1473684. Manual is better for MPG.

Quantify the MPG difference between automatic and manual transmissions

Hypothesis testing

H0: Average MPG of manual and automatic are the same

H1: Manual is better for MPG

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  24.39231

P-value = 0.00137 < 0.05. Reject null hypothesis and conclude that manual is better for MPG

Linear Regression models

Models:

model1 <- lm(mpg~am,data=mtcars)
model2 <- lm(mpg~am + wt + hp,data=mtcars)
stargazer(model1,model2,digits=4, type = "html", header = FALSE)
Dependent variable:
mpg
(1) (2)
am 7.2449*** 2.0837
(1.7644) (1.3764)
wt -2.8786***
(0.9050)
hp -0.0375***
(0.0096)
Constant 17.1474*** 34.0029***
(1.1246) (2.6427)
Observations 32 32
R2 0.3598 0.8399
Adjusted R2 0.3385 0.8227
Residual Std. Error 4.9020 (df = 30) 2.5375 (df = 28)
F Statistic 16.8603*** (df = 1; 30) 48.9600*** (df = 3; 28)
Note: p<0.1; p<0.05; p<0.01

Model 1 explains 36% of the variance and model 2 explains 84% of the variance.

According to model 2, keeping everything else constant, manual transmissions have 2.08 MPG than automatic