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The true regression model is Y1
pendent N (0, 25).
a. Generate II independent random numbers from N(O, 25). Use the first random number. £0, obtain the 10 error terms ε1..... ε10. and then calculate the 10 observations YI .........Y10 corresponding to X1 = I. X2 = 2 ..... X 10 = 10. Fit a linear regression function by ordinary least squares and calculate MSE.
b. Repeat part (a) 100 times, using new random numbers each time.
c. Calculate the mean of the 100 estimates of b1' Does it appear that hi is an unbiased destination of ß1 despite the presence of positive autocorrelation?
d. Calculate the mean of the 100 estimates of MSE. Does it appear that MSE is a biased' estimator of σ2? If so. does the magnitude of the bias appear to be small or large?
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