Chapter 13.1, Problem 1E

Suppose the variables x = commuting distance and y = commuting time are related according to the simple linear regression model with σ = 10.

a. If n = 5 observations are made at the x values x₁ = 5, x₂ = 10, x₃ =15, x₄ = 20, and x₅ = 25, calculate the standard deviations of the five corresponding residuals.

b. Repeat part (a) for x₁ = 5, x₂ = 10, x₃ = 15, x₄ = 20, and x₅ = 50.

c. What do the results of parts (a) and (b) imply about the deviation of the estimated line from the observation made at the largest sampled x value?