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Introductory Econometrics 4th Edition by Jeffrey Wooldridge
Edition 4ISBN: 978-0324660609Introductory Econometrics 4th Edition by Jeffrey Wooldridge
Edition 4ISBN: 978-0324660609 Exercise 17
Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6: 
You would like to test the null hypothesis H 0 : 1 - 2 = 1.
(i) Let
1 and 
2 denote the OLS estimators of 1 and 2. Find Var( 
1 - 3 
2 ) in terms of the variances of ji1 and J52 and the covariance between them. What is the standard error of 
1 - 3 
2
(ii) Write the t statistic for testing H 0 :
1 - 3 
2 =1
(iii) Define
. Write a regression equation involving 0 , 1 1 and 3 that allows you to directly obtain 
1 and its standard error.
You would like to test the null hypothesis H 0 : 1 - 2 = 1.
(i) Let
1 and 2 denote the OLS estimators of 1 and 2. Find Var( 1 - 3 2 ) in terms of the variances of ji1 and J52 and the covariance between them. What is the standard error of 1 - 3 2 (ii) Write the t statistic for testing H 0 :
1 - 3 2 =1(iii) Define
. Write a regression equation involving 0 , 1 1 and 3 that allows you to directly obtain 1 and its standard error.Explanation
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Consider the multiple linear regression ...
Introductory Econometrics 4th Edition by Jeffrey Wooldridge
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