Suppose I fit a linear regression to some data (say, weight vs. height), and all the standard linear regression assumptions are satisfied (in particular, the data is homoscedastic). For example, here's a random figure pulled from amstat.org that looks like it satisfies what I'm thinking of:
Now I'm doing some exploratory data analysis, so I want to look at examples where the linear regression is particularly off; that is, I want to sort all the individuals by how badly the regression predicts their weight from their height (so that, say, I can look at further details, like whether people whose weight the model underpredicts tend to eat a lot of junk food). My question is:
- Should I sort all the individuals by their raw residuals?
- Or should I sort all the individuals by the residuals as a percentage of the prediction, i.e., by
residual weight / predicted weight?
On the one hand, it seems like sorting by raw residuals might be the way to go, since standard linear regression errors are based off the squared residuals, and not the residual percentages. On the other hand, someone who weighs 70kg when their predicted weight is 50kg seems much more of an outlier than someone who weighs 120kg when their predicted weight is 100kg.
Is it just a matter of preference or the particular model at hand?