Monte Carlo Exercise
In order to illustrate the sampling theory for the least squares estimator, we will perform a Monte Carlo experiment based on the following statistical model and the attached design matrix
y = Xβ + e = 10 + 0.4x_{1} + 0.6x_{2} + e
e~N(0,0.0625)
Generate 1000 samples of 20 observations each and compute the least squares sample estimates of β_1,β_2,and β_3 Obtain the average of each parameter and compare it to the true population parameter.
Pick one parameter and provide a plot of its frequency distribution.
Compute the covariance matrix of each sample and compare with the true covariance matrix.
What can you conclude about the sampling distribution of the least squares.
Attachment:- Design Matrix X.rar