Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6: y = Bo + Bixi + Bzx2 + Bztz + u. You would like to test the null hypothesis H,: B1 – 3B2 = 1. (i) Let Bj and B denote the OLS estimators of ß1 and B,. Find Var(ß – 3B,) in terms of the vari- ances of Bj and Bz and the covariance between them. What is the standard error of Bi – 3B? |(ii) Write the t statistic for testing Họ: B1 – 3B2 = 1. |(iii) Define 0, = Bi – 3B2 and ô, = B1 – 3B. Write a regression equation involving Bo. 01. B2- and Bz that allows you to directly obtain ô, 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 = Bo + Bixi + Bzx2 + Bztz + u. You would like to test the null hypothesis H,: B1 – 3B2 = 1. (i) Let Bj and B denote the OLS estimators of ß1 and B,. Find Var(ß – 3B,) in terms of the vari- ances of Bj and Bz and the covariance between them. What is the standard error of Bi – 3B? |(ii) Write the t statistic for testing Họ: B1 – 3B2 = 1. |(iii) Define 0, = Bi – 3B2 and ô, = B1 – 3B. Write a regression equation involving Bo. 01. B2- and Bz that allows you to directly obtain ô, 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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