Studentized Residuals. Show that in a simple linear regression model the variance of the ith residual is

(a) Explain why ri has unit standard deviation (for known).

(b) Do the standardized residuals have unit standard deviation?

(c) Discuss the behavior of the studentized residual when the sample value xi is very close to the middle of the range of x.

(d) Discuss the behavior of the studentized residual when the sample value xi is very near one end of the range of x.

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Hint: 814)-1-(1-7) S II (xx)27 cov (Y, Y)+(-)] The ith studentized residual for this model is defined as e (x-x)2 + n S