Suppose the Variables X=commuting Distance and Y=commuting Time Are Related $\sigma = 10 .$

Essay

Suppose the variables x=commuting distance and y=commuting time are related according to the simple linear regression model with $\sigma = 10 .$
a. If n=5 observations are made at the x values $x _ { 1 } = 4 , x _ { 2 } = 9 , x _ { 3 } = 14 , x _ { 4 } = 19 , \text { and } x _ { 5 } = 24$
calculate the standard deviations of the five corresponding residuals.
b. Repeat part (a) for $x _ { 1 } = 4 , x _ { 2 } = 9 , x _ { 3 } = 14 , x _ { 4 } = 19 , \text { and } x _ { 5} = 49$
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?