The modely 1 1 x 1 1 ,y 2 2 x 2 2 satisfies all the assumptions of the classical multivariate regression model All variables have zero means The following sample second moment matrix is obtained from a sample of 20 observations a Compute the FGLS estimates of 1 and 2 b Test the hypothesis that 1 2 c Compute the maximum likelihood estimates of the model parameters d Use the likelihood ratio test to test the hypothesis in part b yi y2 X1 X2 yi 20 6 4 3 y2 6 10 3 X1 3 5 2 X2 6 2 10 643

Question: The modely 1 = 1 x 1 + 1 ,y 2 = 2 x 2 + 2 satisfies all the assumptions

The modely₁= β₁x₁+ ε₁,y₂= β₂x₂+ ε₂

satisfies all the assumptions of the classical multivariate regression model. All variables have zero means. The following sample second-moment matrix is obtained from a sample of 20 observations:

yi y2 X1 X2 yi [20 6 4 3] y2 6 10

a. Compute the FGLS estimates of β₁ and β₂.

b. Test the hypothesis that β₁ = β₂.

c. Compute the maximum likelihood estimates of the model parameters.

d. Use the likelihood ratio test to test the hypothesis in part b.

yi y2 X1 X2 yi [20 6 4 3] y2 6 10 3 X1 3 5 2 X2 6 2 10 643

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