Using Residual Plots to Assess Assumptions

Residual plots are essential for assessing assumptions!

Residuals have constant variance across all values of X

In this plot, the variance of residuals is not constant across all values of x. The variance is higher for higher values of x, violating the assumption of constant variance. This is also known as heteroscedasticity.

Residuals do not vary by value of X

Residuals should be normally distributed across all values of X. In the example above, you can see that the residuals are more likely to be above or below the predicted line depending on the value of X. 

Residuals are normally distributed across values of X

This scatterplot violates the assumption that residuals are normally distributed across values of X because there are clear outliers at certain values of X (around x = -.5 and x = .5), and the distribution of residuals appears skewed towards the top of the plot. 

Note: The distribution of X or Y does not necessarily need to be normal! To assess normality using the eye test, look at the plot above from the side (where e is the x-axis) and assess normality as a histogram or bar chart at all values of X!