a. Could a linear regression result in residuals 23, –27, 5, 17, –8, 9, and 15? Why or w...

a. Could a linear regression result in residuals 23, –27, 5, 17, –8, 9, and 15? Why or why not?

b. Could a linear regression result in residuals 23, –27, 5, 17, –8, –12, and 2 corresponding to x values 3, –4, 8, 12, –14, –20, and 25? Why or why not? [Hint: See Exercise 10.]

Reference exercise 10

a. Show that when the e_i’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 e_i’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.