Section 13.2 alludes to two circumstances in which the regression calculations are not well defined.

(a) Toward the end of section 13.2, we make the claim that the results pertaining to regression slopes in chapters 11 and 12 don’t depend on the values of the associated explanatory variables, “as long as these values vary across observations.” Why did we have to add this qualification?

What happens if the value of an explanatory variable does not vary across observations?

(b) Demonstrate that the sample CORR(x1i, x2i) = −1 if equation (13.10) is true. Recall the consequences from chapter 12.