Observations on yare to be taken when x 10 20 30 40 and

Question

Observations on Yare to be taken when X = 10, 20, 30, 40, and 50, respectively. The true regression function is E{Y) = 20 + l0X. The error terms are independent and normally distributed with

a. Generate a random Y observation for each X level and calculate both the ordinary and weighted least squares estimates of the regression coefficient ß₁ in the simple linear regression function.

b. Repeal pan (a) 200 times. generating new random numbers each time.

c. Calculate the mean and variance of the 200 ordinary least squares estimates of ß₁ and do the same for the 200 weighted least squares estimates.

d. Do both the ordinary least squares and weighted least squares estimators appear to be unbiased? Explain. Which estimator appears to be more precise here? Comment.