In this presentation, we will look at different hypothesis testing using the ‘mtcars’ dataset. We will be comparing the fuel efficiency in the different transmission types. We will then build a regression model to further understand what predicts mpg.

data(mtcars)
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

A p-value represents the probability of obtaining results either as extreme or more extreme than the results, under the assumption that the null hypothesis is true. The formula for a p-value is \[ \text{p-value} = P(\text{observed or more extreme} \mid H_0 \text{ true}) \] If the p-value is less than 0.05, we can reject the null hypothesis

This t-test compares average mpg between the different transmissions

t_test = t.test(mpg ~ am, data = mtcars)
t_test 

## 
##  Welch Two Sample t-test
## 
## data:  mpg by am
## t = -3.7671, df = 18.332, p-value = 0.001374
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -11.280194  -3.209684
## sample estimates:
## mean in group 0 mean in group 1 
##        17.14737        24.39231

I want to test weather there is a difference in average MPG between automatic and manual transmissions \[ H_0: \mu_{\text{auto}} = \mu_{\text{manual}} \\ H_a: \mu_{\text{auto}} \ne \mu_{\text{manual}} \] this is a two-sample t-test comparing average mpg between the two transmissions

ggplot(mtcars, aes(x = am, y= mpg, fill = am)) +
  geom_boxplot() + 
  labs(title = "MPG by Tranmission Type",
       x= "Transmission",
       y = "MPG")+
  theme_minimal()

Code for Linear Regression

model = lm(mpg ~ wt, data = mtcars)
summary(model)

## `geom_smooth()` using formula = 'y ~ x'