Question: Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6: y=B + Bx + Bx +

Consider the multiple regression model with three independent variables, under the classical linear model

Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6: y=B + Bx + Bx + B x + U You would like to test the null hypothesis H: B-3B = 1. (i) Let B, B, B and B, denotes the OLS estimators. Find Var (B-3 |X) in terms of the variance and covariance of ; What is the standard error of , -3B? (ii) Write the t statistic for testing Ho: B-3p = 1 (iii) Define =B-3 and = 3-3; Write a regression equation involving B, 0, B and B, that allows you to directly obtain and its standard error.

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