Question 1 (40%) In class we have introduced the Ordinary Lease Squares (OLS) method: N (Bo, B1) = arg min Clyi - (Po + Bizz)]? In order the minimize the objective function, estimated coefficients (8o, 81 ) need to satisfy the following first order conditions (F.O.C.s): a ly - (30 + Biz.) = 0 a 8 [ u - (80 + Biz. ) ] ? =0 Therefore, E-2[12 - (30 + B ,17) = 0 E -2 1: - (30 + 3 121) 21=0 Prove that these two F.O.C.s of the OLS method lead to the following results: Bo = y - BIT A = Lil(Ti - T) (yi - y)Question 2 (60%) Suppose that a researcher would like to study the effect of various factors on the income, and gets a good random sample of a large size (/ = 5,777) from the population. The researcher use the following regression model: In (inc) = cons + Bjedu + Byexpr + Byfemale + Bamarr + Bs (erpr) + in which inc stands for income per month, edu for years of education, expr for working experience (in years), and female and marr are two dummy variables indicating whether the subject is female and whether the subject is married. The computer gives the following results: reg lging edu expr female marr expre Source SS df MS Number of obs 1I 5,778 F (5, 5772) 735.27 Model 2873 . 72659 5 574. 745319 Prob > F 0.0000 Residual 4511 . 83934 5,772 . 781676947 R-squared 0. 3891 Adj R-squared 0. 3886 Total 7385.56593 5,777 1.27844312 Root MSE . 88412 lginc Coef. Std. Err. t P>ItI [954 Conf. Interval] edu 1517716 . 0031451 48.26 0. 000 145606 .1579372 expr -. 0015997 0048689 -0.33 0. 743 - . 0111446 0079452 female -. 2898737 . 023885 -12. 14 0.000 - .3366972 -. 2430502 marr -. 0336541 0486495 -0. 69 0. 489 - . 1290254 . 0617171 expre -. 0000631 . 0001084 -0. 58 0. 561 - . 0002756 . 0001494 cons 7.55469 . 0592657 127. 47 0. 000 7. 438507 7. 670873i. In accordance with the regression results, which independent variables significantly affect (at the o = 5% significance level) the value of the dependent variable? ii. Interpret the coefficients that are significantly different from 0 at the o = 5% significance level, excluding the coefficient for the constant. iii. Why does the researcher choose not to add both non female and female to the model? iv. What is the motivation of adding (expr) to the model