1. (20 points) Consider the following regression model that tests for personal differences in hours worked: hours = Bo + Biurban + Breduc + Bsage + BAage2 + u, (1) where hours is average hours worked per week, urban is a dummy variable that takes on a value of 1 if the respondent lives in metropolitan area, and 0 otherwise, educ is the years of education of the respondent, age is the age of the respondent, and age2 is the squared value of respondent's age. The results from this regression are below: Source SS df MS Number of obs = 935 F( 4, 930) = 2. 13 Model 442. 532288 4 110. 633072 Prob > F 0. 0752 Residual 48302 .8089 930 51.9385042 R-squared 0. 0091 Adj R-squared = 0. 0048 Total | 48745 . 3412 934 52. 1898728 Root MSE = 7. 2068 hours Coef. Std. Err. P> t [95% Conf. Interval] urban . 1668028 5254225 XXXXX XXXXX XXXXXXXXX XXXXXXXXX educ . 2992042 1080452 XXXXX XXXXX XXXXXXXXX XXXXXXXXX age - . 2002188 1.914023 XXXXX XXXXX XXXXXXXXX XXXXXXXXX age2 0039179 . 0018749 XXXXX XXXXX XXXXXXXXX XXXXXXXXX _cons 42. 07806 31.52459 XXXXX XXXXX XXXXXXXXX XXXXXXXXX (a) At what age is average hours worked minimized? Show your work. (b) Instead of the regression above, the following regression model is estimated: Zhours = do + durban + 62Zeduc + 63age + bage2 + u, (2) where hours - Hhours Zhours= and Zeduc = educ - Reduc sd(hours) sd(educ) and the regression result is Zhours = 0.302 + 0.023 urban + .091 Zeduc - 0.028 age + 0.001 age2 (4.376) (.073) (.033) (0.265) (.004) Interpret the coefficient estimate on Zeduc. (c) Derive analytically the relations between the sets of parameters { Bo, B1, B2, B3, B4} and {60, 61, 62, 83, 64}