Introduction to Statistics on Cars

Nicholas Fullerton

2022-09-10

Lets Load Our Data Set!

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

Simple Linear Regression Example

model: \(\text{E(Y)} = \alpha + \beta\cdot \text{X}\)

Simple Linear Regression ggplot2 Tutorial

g <- ggplot(data = mtcars, aes(x = hp, y = mpg)) + geom_point() 
lr <- geom_smooth(method="lm") 
title <- ggtitle("Miles per Gallon vs Horsepower") 
g + lr + title

Multiple Linear Regression Example

model: \(\text{E(Y)} = \alpha + \beta_1\cdot X_1 + \beta_2\cdot X_2 + \beta_3\cdot X_3 + \text{...}\)

This is the multiple regression model with the independent variables of the displacement of the car and the weight of the car, the outcome variable is the 1/4 mile time

model <- lm(qsec ~ disp + wt, data = mtcars)
model

Call:
lm(formula = qsec ~ disp + wt, data = mtcars)

Coefficients:
(Intercept)         disp           wt  
   16.38484     -0.01899      1.81685

3D Scatter Plot of the Previous Slides Variables

Normal Curve of Cars Mile Per Gallon

Horsepower vs MPG Depending on Number of Forward Gears