MATH 456 Quiz 03

Given on 2026-03-02

Suppose we fit a model in R, such as

library(dplyr)
fit <- lm(y ~ x, data = df)

1. Provide R code to make a ggplot2 histogram of the standardized residuals.

2. Describe the shape we expect to see, if assumptions are satisfactorily met, from the histogram of standardized residuals?

3. Provide R code to make a ggplot2 scatter plot where the standardized residuals are on the y-axis and the predicted values yhat are on the x-axis.

4. Describe aspects of this plot that might indicate an improper fit of our model.

5. What do these two plots have in common, in the sense that both plots can help us identify the same modeling issue, albeit on different axes?