Chapter 11.7, Problem 74E

a.

To determine

Show the expression of the variance of the i^th residual is $V\left(e_i\right)={\sigma }^2\left[1-\left(\frac{1}{n}+\frac{{\left(x_i-\overline{x}\right)}^2}{S_{xx}}\right)\right]$

Explain the reason of unit standard deviation of the studentized residual.

b.

To determine

Explain whether the standardized residuals have unit standard deviation or not.

c.

To determine

Explain the behavior of the studentized residual for the sample values which are close to the middle range of x.

d.

To determine

Explain the behavior of the studentized residual for the sample values which are close to the any end of the range of x.