a. (5) From the multiple regression model we want to test the following hypothesis: Ho: β1-0...

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a. (5) From the multiple regression model we want to test the following hypothesis: Ho: β1-0 and β2-β3 and β5-1 Rewrite the null hypothesis Ho in the form of RB-r using the matrix R and two vectors B and r b. (5) Consider the following wage regression result: log(wage) 3.240.06educ 0.51Female 0.01educ Female, where educ denotes years of education and Female is a dummy variable for females. What is the return to schooling for male workers? What is the return to schooling for female workers? (5) Calculate the following matrix multiplication: c. 1 21x 0 1 d. (5) Recall that we can write the OLS estimation in matrix form as follows The projection matrix on space of X is defined as Px X(XX)-X. The residual vector (not the error term) is defined as 0-Y-X1. Prove that P,0-0.

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NOTE:The number of years in "educ" is not given for school.So general formula is used.Plug years of education for schooling in your country for problem(b)

as, a) P.th», th,%. 야3y, f t1,Yu, ‘ ts+,. .11. We want lest to P,o.tobo 0 0 - 3-24+ 0.06.adu 24 10.06 u og wage: 오 3.24 ↑ 0.0 6·edue 12due , ;ク о.yous cd 오du eoh on numby. log ωage): 3.24 + 0,06 edue-o-si.l . 0.01 edue. I 2.33 .05 edu c 3 05 adue 63a32

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