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 σ2.)
d. Is it true that ? Give a proof or a counter example.
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