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 ?
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