For prediction intervals, an important inference assumption is a constant residual standard deviation of y values at different x values. In practice, the residual standard deviation often tends to be larger when μy is larger.
a. Sketch a hypothetical scatter-plot for which this happens, using observations for the previous year on x = family income and y = amount donated to charity.
b. Explain why a 95% prediction interval would not work well at very small or at very large x values.