In: Math
name and draw two diagnostic plots used to evaluate linear regression and how they would look if all model assumptions are met.
1. Residuals vs Fitted
This plot shows if residuals have non-linear patterns. There could be a non-linear relationship between predictor variables and an outcome variable and the pattern could show up in this plot if the model doesn’t capture the non-linear relationship. If you find equally spread residuals around a horizontal line without distinct patterns, that is a good indication you don’t have non-linear relationships.
Let’s look at residual plots from a ‘good’ model and a ‘bad’ model. The good model data are simulated in a way that meets the regression assumptions very well, while the bad model data are not.
What do you think? Do you see differences between the two cases? I don’t see any distinctive pattern in Case 1, but I see a parabola in Case 2, where the non-linear relationship was not explained by the model and was left out in the residuals.
2. Normal Q-Q
This plot shows if residuals are normally distributed. Do residuals follow a straight line well or do they deviate severely? It’s good if residuals are lined well on the straight dashed line.
What do you think? Of course they wouldn’t be a perfect straight line and this will be your call. Case 2 definitely concerns me. I would not be concerned by Case 1 too much, although an observation numbered as 38 looks a little off. Let’s look at the next plot while keeping in mind that #38 might be a potential problem