(Hamermesh and Parker, 2005, Economics of Education Review) Install an R package \"AER\". Type \"install.packages(\"AER\")\" in your R console. Then type \"library(AER)\" to use the pack- age. The data set \"TeachingBatings\" can be now loaded using \"data(TeachingRatings)\". The data contains course evaluations, course characteristics, and professor charactoristics for 463 courses for the academic years 2000-2002 at the University of Texas at Austin. Carefully read the data description Which can be found by typing \"help(TeachingRatings)\" or \"?TeachingRat- ings\". a) Run a regression of course evaluation (eval) on instructor's beauty rating (beauty). Briey explain the result. b) You may omit important variables that can explain course evaluation. First, compute the correlation between beauty rating (beauty) and age (age). Suggest Whether the effect of age on course evaluation is positive or negative. Given the correlation and your guess on the effect of age on course evaluation, explain Whether the estimate of beauty rating in (a) is overestimated or underestmated. 0) Run a regression of course evaluation (eval) on instructor's beauty rating (beauty) and age (age). Does the estimate of the effect of beauty rating chage from (a)? Explain Why or Why not. (1) Compare the regression results from (a) and (c). Does it improve the model t? Do you want to add age in your regression? Explain. e) Run a regression of course evaluation (eval) on instructor's beauty rating (beauty), age, gender, minority, native, tenure, division, and credits. Explain the results. Are the esti- mated coeicients on included regressors in line With your expectation? f) Compare the results in (a) and (c). Is the model t improved When you add more regressors? Explain Why or Why not. g) The effects of beauty rating on course evaluation may differ between male and female instructors. Further include the interaction between beauty rating and gender (beauty * gender). Explain the results