Question: R File Edit Format Workspace Packages & Data Misc Window reg_sim (1).R set.seed(2024) sim_itr Question 4 Consider the simple linear regression model y =

R File Edit Format Workspace Packages & Data Misc Window reg_sim (1).R set.seed(2024) sim_itr Question 4 Consider the simple linear regression model y = 50+ 10x + & where is NID(0, 16). Suppose that n = 20 pairs of observations are used to fit this model, where the values of x are kept as 1, 1.5, ..., 10, 10.5 for each sample. The least squares estimation is applied to estimate the regression coefficients. reg_sim. R repeats the sample generating process and the least squares estimation specified above for 10,000 times. (a) Find E(B) and Var(B1). (b) Find the sample mean and the sample variance of the 1000 estimates of 1. Are they consistent with the values obtained in (a)? (c) How to reduce Var(B) without increasing the sample size and Var(E)? (d) Verify your method in (c) by simulation. Report the sample variance of and modifications in reg_sim. R.

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