I am trying to fit a model to predict housing prices. My residual plots look like the following:
Should I be concerned about the large hump for the higher quantiles? Would a transformation on the response variable help?
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$\begingroup$ Plot of the quantiles of what? $\endgroup$– DaveCommented Jul 25, 2020 at 14:37
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$\begingroup$ Why do you care if the fitted values are normal? $\endgroup$– DaveCommented Jul 25, 2020 at 14:40
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$\begingroup$ @Dave *the residuals $\endgroup$– 324Commented Jul 25, 2020 at 14:51
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$\begingroup$ What do the other diagnostics say? I am concerned about that hump, but I wonder if it has something to do with the variance increasing for expensive houses. $\endgroup$– DaveCommented Jul 25, 2020 at 15:11
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1$\begingroup$ Log price is often a much better scale to work on than price. $\endgroup$– Nick CoxCommented Jul 26, 2020 at 1:33
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1 Answer
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You have something to think about which is much more important than the normality assumption, and your last plot is helpful.
Residuals vs leverage You have some data points with a very high leverage. If you are not used to leverage, Leverage and Influence. I would guess the points with high leverage corresponds to a high fitted value, which leads to ...
Residuals vs fitted This plot might indicate a variance increasing with fitted vales, and that is what @Dave indicated in his comment ... but for the very highest fitted values the trend of increasing spread is not followed. That can maybe be explained with high leverage of those points (investigate!), which tends to draw the fitted model to themselves, as if high leverage points have a gravitational force. You could also investigate this by some robust fitting.
Normal QQ until you have thought about the first two points, don't even bother to look at this plot.
answered Jul 25, 2020 at 20:20
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$\begingroup$ Did this solve your problem? If not, please tell what is unclear, if yes, you can upvote and accept. $\endgroup$ Commented Jul 27, 2020 at 19:29