Just question 4

3. ( 30 points) Simulate n=1,000 observations of the following process: yi=2+3xi+i, where xiN(0,4) and iN(0,1), with xii. Set the seed to 1234 . Now, using the same simulated data for xi and yi, determine b0,b1,sv, s.e e(b0),s.e(b1) and R2 in the following Simple Linear Regression-SLR: yi=0+1xi+vi, where viN(0,v2). 4. (30 points) Run exactly the same simulation as in the previous question, but now assume that corr(xi,i)=0.95 (Hint: you can simulate xiN(0,4) first and then generate i= 21(0.95xi+10.952zi), where ziN(0,2) and xizi). Now, using the same simulated data for xi and yi, estimate the SLR: yi=0+1xi+vi, where viN(0,v2) With these results, perform the following t-test: H0:1=3H1:1=3 At the 95% confidence level (i.e., =0.05 ), can you reject the null hypothesis? If you rejected the null, what is the most likely reason