# residual vs. QQ-plot in multiple regression

I'm working on a Kaggle multiple regression tutorial competition and inspecting plots of my residuals. I followed a suggestion and log transformed several independent variables and the dependent variable. These are the plots I got after fitting a Ridge regression model (sample size is 1500):  I'm trying to determine how to interpret these plots, and to better understand which is useful for which purposes. I believe that the first two plots illustrate that the regression assumptions of linearity, additivity, and homoscedasticity are not violated, although at lower prices my model tends to underestimate. I think that the pattern in the QQ-plot shows a distribution more heavily tailed than normal, so the variance is higher than expected for a normal distribution, and so the normality of error assumption is violated. Is this a correct assessment? And if my goal is prediction rather than inference, should I be concerned with this QQ-plot? I also did not divide the residuals by their standard deviation because I could not find enough information about when this step is necessary.

• To me the summary line on the first graph is tilted. Is that an illusion? Should be residual = 0. – Nick Cox Sep 20 '17 at 21:20
• It does seem slightly tilted. Is this a concern I should address in any particular way to build a more accurate model? – Austin Sep 20 '17 at 21:24
• Tell us how it is produced! (Someone familiar with ridge regression may be able to explain that it need not be flat -- I have never used it.) – Nick Cox Sep 20 '17 at 21:27
• Thanks, but syntax in unspecified software doesn't explain to most people how the line was calculated. Also, although it is clear from plain regression that residuals have mean zero, I am asking openly whether that is also true for the ridge flavour. – Nick Cox Sep 20 '17 at 21:35
• @NIck With shrinkage (using ridge regression) you would expect the residual plot would not necessarily be quite flat (though I'd have thought it would go the other way) – Glen_b Sep 20 '17 at 22:47