# Interpreting Residual Plots

I was hoping to get some input on people's thought process when looking at residual plots of a linear regression to assess the fit / whether assumptions are met. I included a plot of a model I'm currently working on as an example. I was always taught when looking at such a plot, it's best not to be so picky i.e. we're looking for serious deviations. Generally the first thing I usually look for is any apparent trend (i.e. what I want is a shapeless cloud of points centered around 0), and then look for evidence of uneven vertical spread, and then check qq plot for normality. Upon initial inspection of my plots, I thought the qq plot looked "normal enough" and there was no apparent trend in my residuals vs. fitted plot. However, it did look like there was evidence of uneven vertical spread (i.e. heteroskedasticity). Now it seems to me like what I thought was uneven vertical spread was really just a downward sloping trend. What do you guys think?

• If you have the response bound $y \geqslant L$ then you have the residual bound $r \geqslant L - \hat{y}$, and since $\hat{y}$ is the horizontal axis of the residual plot, you see the diagonal lower bound on the residuals in that plot. If instead you had an upper bound $y \leqslant U$ then you would get the residual bound $r \leqslant U-\hat{y}$, so yes, you would see a similar diaogonal upper bound at the top of the residual plot. – Ben Mar 19 '20 at 22:13