# Normality of residuals versus AIC and "best" fit

Hoping to get some insight into normality of residuals vs the "best" fit of the model.

After running a simple linear regression and checking normality of the residuals, I logged my outcome variable and this significantly improved the normality of residuals. See below:

After graphing with geom_smooth(), I noted that perhaps the relationship was not linear but rather a second-order polynomial .

I compared the models with AIC and poly^2 was considered a better fit.

                df      AIC
PT~Age          3    496.7536
PT~poly(Age,2)  4    490.3009


My problem comes in when checking the residuals of the model of second order polynomial. I can see they are not normally distributed when compared to a simple linear regression.

My question is, what is more important here? Do I go with the simple linear regression or the second-order polynomial (which visually seems to fit my data better)? I should also add that on a physiological level this does make sense with respect to where the inflection is starting at around 50.

• Commented May 23 at 3:30
• While useful the difference in AIC doesn't quite answer my question as I am asking about the assumptions of the model vs "best" fit. Commented May 23 at 3:44
• Comments are not intended to be answers; that's what answers are for. Commented May 23 at 3:46
• If I understand this correctly, curvature in the relationship is visible and plausible. The problem is that a quadratic shape doesn't match what I see, or at least a different story, which is an approximately flat relationship at first with a decline from about age 55. (Given my own age, I am rather alarmed at the latter.) You don't have an enormous sample size and in any case need not to jump straight here to "So, it's quadratic!". I see the fuss about AIC and BIC as a utter side-issue compared with the question of choosing a functional form. Something like a spline approach may help. Commented May 24 at 8:33
• I agree with @NickCox that a spline approach is probably better than a polynomial. Reading this the first time, I mistook the plotted function as the fitted function, and here I think polynomials do worse with distributions that have flat distributions for a large part of the scatterplot. Commented May 24 at 9:03