1. Research collected data on hourly wages, gender {female=1 if female and 0 otherwise}. married [married=1 if married and 0 otherwise}. living in a metropolitan area {SMEAzl if living in a metropolitan area and 0 otherwise}, set of dummy variables for the region, years of education, and vears of experience. This researcher estimated several models that are presented in the table below using the OLE estimator and data on hand. (1) {2) (3} (4) log(wage) 10g(wage) log(\\vage) log(wage) Cer'Std. err. Coe? Std. err. Coel'Std. err. Coeffx'S-td. err. = if female -0.433 -0.430 0.401 -0.406 (0.059) (0.055) (0.050) (0.048) =_ lfman'ied 0.1?0 0.196 0.18? 0.05? (0.061) (0.05?) (0.052) (0.055) =' if live in SMSA 0.290 0.222 0.219 (0. 061) (0 .05 ?) (0.0 54) =' ifiiving in the 1101111- -0.08? 0.0?6 -0.0?? central US (0. 0??) (0.0?0) (0.06 ?) =' ifiiving inthe -0.l9l 0.119 -0.152 southern region (0.0?2) (0.066) (0 .064) ='_ if living in the 0.061 0.092 0.059I western region (0.08?) (0.0?9) (0.0 ?6) years of education 0.0?0 0.0 ?3 (0.009) (0 .009) experience 0.035 (0.00?) Experience squared -0.001 (0.000) Constant 1 .?55 1.605 0.?32 0.498 0.059 0.089 0.142 0.150 Observations 26? 26? 26? 26? Rsquared 0.216 0.324 0.445 0.501 Adj. RSquared 0.210 0.309 0.430 a) How many models were estimated? (2pts) b) Write down the population model for the model estimated in column 4. (HINT: Make sure to clearly define the variable names) (3pts)d) Is the effect of living in SMSA statistically different than 0.211 from column 2? (5pts)e) Is the region of living an important factor in determining log wages? Explain why yes or why not. Use statistical test(s) to support your argument. (10pts)