a. Show that when the ei

’s are the residuals from a simple linear regression.

b. Are the residuals from a simple linear regression independent of one another, positively correlated, or negatively correlated? Explain.

c. Show that for the residuals from a simple linear regression. (This result along with part

(a) shows that there are two linear restrictions on the ei

’s, resulting in a loss of 2 df when the squared residuals are used to estimate s2

.)

d. Is it true that ? Give a proof or a counter example.