Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6:

y 5 b0 1 b1x1 1 b2x2 1 b3x3 1 u.

You would like to test the null hypothesis H0: b1 2 3b2 5 1.

(i) Let b^

1 and b^

2 denote the OLS estimators of b1 and b2. Find Var1b^

1 2 3b^

2 2 in terms of the variances of b^

1 and b^

2 and the covariance between them. What is the standard error of b^

1 2 3b^

2?

(ii) Write the t statistic for testing H0: b1 2 3b2 5 1.

(iii) Define u1 5 b1 2 3b2 and u^

1 5 b^

1 2 3b^

2. Write a regression equation involving b0, u1, b2, and b3 that allows you to directly obtain u^

1 and its standard error.