Due: Nov. 5th. Worth 3% of your mark. Upload your answers to the assignment 2 dropbox on UM Learn.

  1. Exercise question 7, from Chapter 5.

    OR

    Run the following code several times, changing just one thing each time you run it. Do this in order to show that the LS estimator is consistent. Your answer should include several histograms.

    nrep <- 1000 # The number of times the experiment will run.
n <- 100 # Set the sample size.
beta1 <- 3 # Set the true value for the intercept.
beta2 <- -2 # Set the true value for the slope.
x <- rnorm(n) # Generates a Normally distributed regressor.
b2 <- numeric(nrep) # Setup an empty vector to store the LS estimates.

for(i in 1:nrep) { # Start the simulation loop.
  y <- beta1 + beta2 * x + rnorm(n) # Generate the y variable according to the true population model.
  b2[i] <- lm(y ~ x)$coefficients[2] # Estimate and store the value for b2
}

hist(b2, xlim = c(-2.5,-1.5)) # View the simulated sampling distribution

  2. Any exercise question that does not include an answer key.