Problem 2 [32 points] (Section 5.2 and 4.1): The data 'salary' from the alr4 library contains salary and other characteristics of all faculty members in a small Midwestern college in early 19805. Below are the description of selected variables in the data file: Variable Notation Description Sex S 1 = Female, 0 = Male Rank 1 = Assistant Professor, 2 = Associate Professor, 3 = Full Professor R Year X Number of years in current rank Y Salary Annual salary (in USS} Let U, and U3 be the dummy variables for Associate Professor and Full Professor respectively. Consider the following model: J' 3 Model 1: E(Y| S = 5,1: = j,X = x) = :70 + ,8 x + as + 20301:}, H31 .Ujs) =2 J' (a) [3 points] Obtain the OLS estimates for (am, 331,13\