# 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. Sep 20, 2017 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? Sep 20, 2017 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.) Sep 20, 2017 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. Sep 20, 2017 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) Sep 20, 2017 at 22:47