Curvilinearity
We look at the linearity of the scatterplot, the normality of the variances (normal probability plot), and the equality of the variances (residuals versus plots).
Linearity | Normal variances | Equal variance | Conclusion |
|---|---|---|---|
Violated. Curvilinear scatterplot, and curvilinear residuals versus fits plot | Not violated. Normal probability plot close to the diagonal. | Not violated. Residuals versus fits plot may be curvilinear, but is not megaphone-shaped. | Transform the predictor. This is useful when only the linearity assumption is violated. Generally, but not always, transforming the predictor will correct the non-linearity. |
Not violated. We see a linear scatterplot. | Might be violated. Normal probability plot might be s-shaped. | Might be violated. Residuals versus fits plot might be megaphone-shaped. | Transform the response. This is useful when either normal variances or equal variance assumptions are violated. Generally but not always, transforming the response will correct problems with the errors (and may help a bit with non-linearity). |
Violated. | Violated. | Violated. | Transform the predictor and the response. This is useful when everything appears to be violated. |