With the assumptions of this section, show that a regression of Yi on Xi gives unbiased estimates, conditionally on the Xi’s, of a and b in (17).

Show also that a regression of Zi on Xi and Yi gives unbiased estimates, conditionally on the Xi’s and Yi’s, of

c, d, and e in (18). Hints. What are the design matrices in the two regressions? Can you verify assumptions (4.2)–(4.5)? [Cross-references: (4.2) is equation (2) in chapter 4.]