Consider the Monte Carlo analysis (Below)
• First follow Exercise 5.1 to derive the mean and variance of simulated residuals eps2; call the variance sigma^2.
Using the function simreg2 (which deviates from the Normal model by using residuals generated from the non-normal distribution of resid2), consider the estimate s^2 of the variance of regression residuals conditional on X.
• Prove that s^2 is an unbiased and consistent estimator of sigma^2.
• Run 1,000 simulated regressions with sample size 100. Compute the t-statistic for testing the hypothesis beta2-beta1=0.1 (the third coefficient minus the second in the regression, since the intercept is beta0), and plot its density. What can you say about this density?