During your studies you take a human geography class and the professor tells you that additional years of experience are supposed to result in higher income; you reason that this is because experience is related toon the job training. Therefore, measuring age instead can be a substitute for experience. So, you estimate an original model (1) and a transformed model (2):

y= 647.40 + 10.30X1339.56X2, RA2= 0.13 (1)

log10y= 6.34 + 0.02X1log100.42X2, RA2= 0.17 (2)

whereyis monthly income in dollars,X1is age measured in years, andX2is a binary variable, which takes on the value of 1 if the individual is female and 0 if the individual is male.

You ask a stats professor for advice on your models and they point out to you that age-earning profiles typically take on a specific shape best explained by a different model that includes age2(X12) which you find is:

log10y= 3.64 + 0.15X1log100.29X20.01X12, RA2= 0.28 (3)

a) Interpret the coeffcient for a female in models (1) and (2) carefully, while con- trolling for age, given that for model (2)b2can be interpreted by evaluating 10b2and the result can be expressed as a percent.

(b)Is model (3) a better model than model (2)? And why do you think the age variable (X1) in model (3) is so much larger relative to its value in model (2)?