12.50 Assumption violated For prediction intervals, an important inference assumption is a constant standard deviation s of y values at different x values. In practice, the standard deviation often tends to be larger when my is larger.

a. Sketch a hypothetical scatterplot for which this happens, using observations 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.