1. (20 points) Consider the following regression model that tests for personal differences in hours worked: hours Bo + Biurban + Beduc + B3age + Bage2 + 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 | Model 442.532288 4 110.633072 Residual 48302.8089 930 51.9385042 Total 48745.3412 934 52.1898728 where SS Coef. Std. Err. hours | urban | .1668028 educ | .2992042 .5254225 .1080452 -.2002188 1.914023 .0039179 .0018749 age | age2 | _cons | 42.07806 31.52459 df Zhours = Zhours = and the regression result is (a) At what age is average hours worked minimized? Show your work. (b) Instead of the regression above, the following regression model is estimated: MS hours-Phours sd(hours) Interpret the coefficient estimate on educ do + djurban +82%educ +d3age + dage2 + u, Number of obs = F( 4, 930) = Prob > F R-squared = Zhours 0.302 +0.023 urban+ .091 Zeduc (4.376) (.073) (.033) 1 = Adj R-squared = Root MSE = t P>|t| [95% Conf. Interval] XXXXX XXXXX XXXXXXXXX XXXXXXXXX XXXXX XXXXX XXXXXXXXX XXXXXXXXX XXXXX XXXXX XXXXXXXXX XXXXXXXXX XXXXX XXXXX XXXXXXXXX XXXXXXXXX XXXXX XXXXX XXXXXXXXX XXXXXXXXX and educ 935 2.13 0.0752 0.0091 0.0048 7.2068 educ-Peduc sd(educ) 0.028 age + 0.001 age2 (0.265) (.004) (2) (c) Derive analytically the relations between the sets of parameters {Bo, B1, B2, B3, B4} and {80, 81, 82, 83, 84}.