(Statistical Inference) Given the following model,

yi = 1 + 2xi + 3zi + i.

I have collected data and computed the following moment matrix with M = [1, x, z, y] for you:

M'M =

[120 150 80 450

150 300 250 2000

80 250 600 1200

450 2000 1200 25000 ]

(a) How many observations have I collected? What are the average values for each variable, that is

y, x, and z?

(b) Using OLS formula to compute the coefficient estimates, 1, 2, and 3. What is the residual

variance, the variance-covariance matrix of estimates, and the R2 for this regression?

[Hint: e'e = Y'Y 'X'Y ]

(c) Test the hypothesis of 1) 3 = 3 and 2)1 + 2 = 0 separately.

(d) Test the hypotheses of 3 = 3 and 1 + 2 = 0 simultaneously. Comparing (c) and (d), what

do you conclude?