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I was reading of cases in which linear models in least-squares regression were found to be

innefective, despite values of r, r^2 being close to 1 (obviously, both go together ).

I think the issue has to see with the distribution of the residuals being distinctively non-linear (and, definitely, not being normal), e.g., having a histogram that looks like a parabola, or a cubic, etc.

Just curious to see if someone knows of some examples and/or results in this respect, and of what other checks can be made to see if a linear model makes sense for a data set. Checks I know of are Lack-of-fit Sum of Squares F-test and inference for regression (with Ho:= Slope is zero.)

Thanks.

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# When is Linear Model not Good despite r^2 close to 1?

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