2. Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6: y=Bo+ Bixi+B2x2 + B3x3 + u. You would like to test the null hypothesis Ho: B1-3ẞ2 = 1. a. Let Band 2 denote the OLS estimators of B1 and B2. Find Var(B₁ - 3B2) in terms of the variances of B₁ and B2 and the covariance between them. What is the standard error of B₁ - 3B2 ? b. Write the t statistic for testing Ho: B1-3ẞ2=1. c. Define B1-3ẞ2 and ₁ = B₁ - 3B2. Write a regression equation involving Bo, 1, B2 and B3 that allows you to directly obtain ₁ and its standard error.
2. Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6: y=Bo+ Bixi+B2x2 + B3x3 + u. You would like to test the null hypothesis Ho: B1-3ẞ2 = 1. a. Let Band 2 denote the OLS estimators of B1 and B2. Find Var(B₁ - 3B2) in terms of the variances of B₁ and B2 and the covariance between them. What is the standard error of B₁ - 3B2 ? b. Write the t statistic for testing Ho: B1-3ẞ2=1. c. Define B1-3ẞ2 and ₁ = B₁ - 3B2. Write a regression equation involving Bo, 1, B2 and B3 that allows you to directly obtain ₁ and its standard error.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 5EA
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