A.   Regress the response variable on the explanatory variable. What is the residual at the last point (5,0)?

B.   Regress the first four response variables on the first four explanatory variables. What is the studentized residual at the last point (5,0)?

C.   Explain intuitively why the residual is correlated with the response variable.

D.   Is the studentized residual correlated with the response variable? Why or why not?

If the residuals, Ei = Yi - Yi^ , then how could Ei and Yi not be correlated? Is this related to why we plot residual against the Yi^ values in order to detect nonconstant spread?

[NEAS: Correct. The residual is always correlated with the observed response values. We examine the correlation with the fitted values to test for heteroscedasticity.]