Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 13L / d / Solution

With a well-fitting Gaussian linear model, the residual-versus-fitted plot should be an unstructured horizontal band around zero with roughly constant width. The normal Q-Q plot should lie close to a straight line.

Here the residual spread grows with the fitted value and the response's discreteness produces pronounced bands, indicating nonconstant variance. The Q-Q plot bends strongly upward in the upper tail, indicating right-skewness or heavy positive tails and failure of Gaussian residuals. Thus both homoscedasticity and normality are doubtful.