Consider the regression model Y = B0 + B1 X1 + B2 X2 + u. Suppose you want to test the null hypothesis H0: B1 + B2 = 0, versus the alternative hypothesis H1: B1+ B2 != 0 (!= means "not equal to"). The data set consists of 100 observations. (a) Suppose we use an F-statistic to conduct the test. What are the degrees of freedom associated with this test statistic? (b) Let G(.) be the CDF of the F-distribution for the F-statistic in part (b). Denote the actual F-statistic by F_act. Suppose someone says that you should reject the null at the 5% significance level if G(F_act)<0.05. Explain whether you agree with this approach. (c) Suppose you find that the F-test in part (b)-(c) and the test in part (a) yield very different p-values. Do you think this result is correct? Briefly explain your reasoning.
Consider the regression model Y = B0 + B1 X1 + B2 X2 + u. Suppose you want to test the null hypothesis H0: B1 + B2 = 0, versus the alternative hypothesis H1: B1+ B2 != 0 (!= means "not equal to"). The data set consists of 100 observations. (a) Suppose we use an F-statistic to conduct the test. What are the degrees of freedom associated with this test statistic? (b) Let G(.) be the CDF of the F-distribution for the F-statistic in part (b). Denote the actual F-statistic by F_act. Suppose someone says that you should reject the null at the 5% significance level if G(F_act)<0.05. Explain whether you agree with this approach. (c) Suppose you find that the F-test in part (b)-(c) and the test in part (a) yield very different p-values. Do you think this result is correct? Briefly explain your reasoning.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider the regression model Y = B0 + B1 X1 + B2 X2 + u. Suppose you want to
test the null hypothesis H0: B1 + B2 = 0, versus the alternative hypothesis H1: B1+
B2 != 0 (!= means "not equal to"). The data set consists of 100 observations.
(a) Suppose we use an F-statistic to conduct the test. What are the degrees of
freedom associated with this test statistic?
(b) Let G(.) be the CDF of the F-distribution for the F-statistic in part (b). Denote
the actual F-statistic by F_act. Suppose someone says that you should reject the null
at the 5% significance level if G(F_act)<0.05. Explain whether you agree with this
approach.
(c) Suppose you find that the F-test in part (b)-(c) and the test in part (a) yield
very different p-values. Do you think this result is correct? Briefly explain your
reasoning.
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