Question

2. Consider a simple linear regression i ion model for a response variable Y, a single predictor variable ,i1.., n, and having Gaussian (i.e. normally distributed) errors: This model is often called "regression through the origin" since E(X) = 0 if xi = 0 (a) Write down the likelihood function for the parameters β and σ2 (b) Find the MLEs for β and σ2, explicitly showing that they are unique maximizers of the likelihood function Hint: The function g(x)log(x) +1-x for r >0 takes only nonpositive values.) (c) Compute the me an and variance of β, the MLE for ß. In your own words, what does the Gauss-Markov theorem tell us about this variance? (d) Let Ý, Ari be the fitted values and ei-Y;-Yi the residuals. Compute (e) Propose an unbiased estimator for σ2 based on your answer to part d)

Answer 1

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