4. In this question, you will simulate data and perform various analyses. (The idea behind this question is to use simulation to evaluate the performance of your model and estimation approach). a. Generate two predictor variables of length n = 200 from a normal distribution with mean 0 and standard deviation of 2. Generate a response vector Y of length n = 200 using your predictors according to the model y =1+ 2x1+ 5x2 + E where random error from a N(0, 1) distribution. Estimate the least squares regression line to your data. What is the estimated line? b. Estimate the variance for each of the three regression coefficients. How do these compare to the theoretical values for the variance of these predictors (you can compute the theoretical values since you know the x's and also the variance of the errors)? c. For your data, test the hypothesis: Ho : B1 = 0 vs H1 : 31 / 0; assuming x2 is in the model. Use a significance level of a=0.05. d. Repeat parts a. and c. 1000 times. What proportion of times do you reject Ho