# How much parabolic distortion in residual plots can be tolerated?

I have been banging my head against the wall these pas few weeks trying to fit regressions to model outputs and I can't get the parabolic trends out of my residual plots.

First things first:

My model outputs the Carrot Color based on Soil Quality and Soil Temperature inputs.

Plots of model outputs:

So I tried finding a regression to be able to find the Carrot Color based on the inputs without having to re-run my numerical model every time.

The residual plots I get from it are:

I used the linear regression from the Analysis Toolpack on Excel and fed it the Carrot Color as the ouput, the Log10(Soil Temperature) and Soil Quality as inputs.

What the graph below shows is that the regression never actually over-estimates massively. It does however, underestimate for value above 10. Can I go along with that as a "conservative approach" as long I as I use the regression on the values within the range of values used to build the regression ?

EDIT:

Following a suggestion in the comments I tried adding a interaction term of the form Log10(Soil Quality * Soil Temperature). The overall R^2 of the regression reduced slightly, and the P-value of the interaction term is of 0.62

• Have you tried adding an interaction term? – GeoMatt22 Oct 25 '16 at 16:29
• No, how would that look like ? – Sorade Oct 25 '16 at 17:58
• As in the link I gave: $z = ( a x + b y + c ) + d xy + \mathrm{error}$. So you add $xy$ as an extra "predictor variable", in addition to $x$ and $y$ alone. If $x$ and $y$ are correlated, this extra term would have a "parabolic" component. – GeoMatt22 Oct 25 '16 at 18:54
• Thanks I'll try that. However I thought that the variables should be independent from one another. If they have a relationship through an interaction term would that go against it ? – Sorade Oct 26 '16 at 7:53
• @GeoMatt22 : I added the interaction term (see EDIT in question), however it's p-value is of 0.62. If my understanding of p-value is correct the closer to 1 the value is the more likely that the coefficient for the variable is due to chance, and that this variable should not be included in the regression. – Sorade Oct 26 '16 at 9:21