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

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Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6: y=B₁ + B₁x₁ + B₂x₂ + B ₂x₂ + U You would like to test the null hypothesis H₁: B₁-3B₂ = 1. (i) Let B, B₁, B and B, denotes the OLS estimators. Find Var (B₁-3₂ |X) in terms of the variance and covariance of ₂; What is the standard error of ß, -3B₂? (ii) Write the t statistic for testing Ho: B₁-3p₂ = 1 (iii) Define =B₁-3₂ and = 3₁-3₂; Write a regression equation involving B₁, 0, B₂ and B, that allows you to directly obtain and its standard error. Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6: y=B₁ + B₁x₁ + B₂x₂ + B ₂x₂ + U You would like to test the null hypothesis H₁: B₁-3B₂ = 1. (i) Let B, B₁, B and B, denotes the OLS estimators. Find Var (B₁-3₂ |X) in terms of the variance and covariance of ₂; What is the standard error of ß, -3B₂? (ii) Write the t statistic for testing Ho: B₁-3p₂ = 1 (iii) Define =B₁-3₂ and = 3₁-3₂; Write a regression equation involving B₁, 0, B₂ and B, that allows you to directly obtain and its standard error.