# Question: For prediction intervals an important inference assumption is a constant

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.

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.

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