PROBLEM 1 A researcher is interested in estimating the trade-off between the average teacher salary and school characteristics for a subset of schools. Define lavgsal = log(avgsal) as the logarithm of average salary of teachers for a particular school and bs = avgben/avgsal where average benefits are bene- fits other than salary. 1) The regression results for lavgsal on bs are reported in listing 1. Can you reject H : Bi = 0 against a two-sided alternative? Can you reject Ho : B1 = -1 versus Ho: B1 >-1? 2) Now define the variable lbs = log(bs). The results of the regression of lavgsal on lbs are in listing 2. Interpret the coefficient on lbs. Do you prefer this model to the one presented in listing 1? 3) Introducing three more variables, school enrollment (enroll), staff size of the school (staff), and percentage of students that qaulify for free lunch (lunch) the results for the population model lavgsal = Bo+Bybs+Belenroll+ 1 B3lstaff + Balunch+u are reported in listing 3. Interpret all of the coeffi- cients carefully. Listing 1: Determinants of average salary. Call: Im (formula = lavgsal ~ bs) Residuals: Min 1Q -1.35039 -0.14368 Median 0.00689 3Q 0.14759 Max 0.74891 Coefficients : Estimate Std. Error t value Pr(>It D. (Intercept) 10.64757 0.05724 186.02 t D. (Intercept) 10.31332 0.06029 171.062 t). (Intercept) 13.7236149 0.1121095 122.413 -1? 2) Now define the variable lbs = log(bs). The results of the regression of lavgsal on lbs are in listing 2. Interpret the coefficient on lbs. Do you prefer this model to the one presented in listing 1? 3) Introducing three more variables, school enrollment (enroll), staff size of the school (staff), and percentage of students that qaulify for free lunch (lunch) the results for the population model lavgsal = Bo+Bybs+Belenroll+ 1 B3lstaff + Balunch+u are reported in listing 3. Interpret all of the coeffi- cients carefully. Listing 1: Determinants of average salary. Call: Im (formula = lavgsal ~ bs) Residuals: Min 1Q -1.35039 -0.14368 Median 0.00689 3Q 0.14759 Max 0.74891 Coefficients : Estimate Std. Error t value Pr(>It D. (Intercept) 10.64757 0.05724 186.02 t D. (Intercept) 10.31332 0.06029 171.062 t). (Intercept) 13.7236149 0.1121095 122.413