C calculate the mean of the 100 estimates of b1amp39 does

Question

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 Y_I  .........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?