a. Show that
n i
1 ei
0 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
n i
1 xi ei
0 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 2

.)

d. Is it true that
n i
1 e*i
0? Give a proof or a counter example.