In this presentation I will hope to use simple linear regression to look at the relationship between a car’s weight and mileage. I will be using the mtcars dataset. The response variable is mpg (miles per gallon), and the predictor variables is wt (weight).
2026-03-07
Introduction
Example Data
This is what the data looks like:
## mpg wt ## Mazda RX4 21.0 2.620 ## Mazda RX4 Wag 21.0 2.875 ## Datsun 710 22.8 2.320 ## Hornet 4 Drive 21.4 3.215 ## Hornet Sportabout 18.7 3.440 ## Valiant 18.1 3.460
Scatterplot of mpg vs wt
Interactive Plotly Plot
Simple Linear Regression
Residual Plot
Regression Equation
The simple regression model is: \[ Y_i = \beta_0 + \beta_1 x_i + \varepsilon_i \]
Testing our Simple Regression
We will be making a prediction to see how accurate our regression is. Suppose a car weighs 3 thousand pounds. Then the predicted mpg is: \[ Y_i = b_0 + b_1(3.0) \]
## (Intercept) wt ## 37.285126 -5.344472
So the fuel efficient is about:
## (Intercept) ## 21.25
Conclusion
In this dataset heavier cars are the ones that are most likely to have lower mileage. The scatterplot and regression line show a negative relationship. The residual plot shows the linear model is reasonable, however there is some curvature so not perfectly linear.