Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN: 9781305658004
Author: Ron Larson
Publisher: Cengage Learning
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1. Is this null hypothesis always testable? Why or why not?
2. Consider the case that this null hypothesis is testable. Construct a
statistical test and its rejection region for H0 .
Transcribed Image Text:Consider the multiple regression model for n y-data yı, ., Yn, (n is sample size)
....
y = X,B1 + X,B2 + ɛ
where y = (y1, ., Yn)', X1 and X2 are random except the intercept term (i.e., the
vector of 1) included in X1. Conditional on X1 and X2, the random error vector
ɛ is jointly normal with zero expectation and variance-covariance matrix V,
which does not depend on X1 and X2. V is not a diagonal matrix (i.e., some
off-diagonal elements are nonzero). B1 and B2 are vectors of two different
sets of regression coefficients; B1 has two regression coefficients and B2 has
four regression coefficients. B = (B1 , B½)'; that is, B is a column vector of
six regression coefficients.
a) V is completely known (i.e., the values of all elements of V are given).
Let W be a matrix of k rows (k > 1) and four columns of given real
numbers. Of interest are the hypotheses
Họ: WB2 = 0 versus H1: WB2 ÷ 0 .
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