Question 2: Consider the regression model x B0) +€i, x, B®) + €i, xB8) + Ei, Yi i = 1, .., n1, i = n1 + 1, ..., n1 + n2, i = n1 + n2 +1, .., n1 + n2+n3, i = 1, .., n, n = n1 + n2 + n3, Yi Yi IIDN(0, 0²), 2) where ß(1), B²), and 3(8) are K ×1 parameter vectors, ɛ¡ is 1 x 1, x¡ is 1 × K and non-random. We want to test Ho : B(1) = B(2) = 3(3) against the alternative that Họ is not true. Derive the test statistic for testing Ho and derive its distribution under Ho.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 43E
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Question 2:
Consider the regression model
X; B4) + Ei,
x; B2) + Ei,
x; 3(3) + Ei, i = n1 + n2 + 1, ..., n1 + n2 + n3,
IIDN(0,0²), i= 1,..., n, n = n1 +n2 + n3,
Yi
i = 1, .., n1,
Yi
i = n1 + 1, ..., nị + n2,
Yi
Ei
where B1), B(2), and ß(3) are K × 1 parameter vectors, ɛ; is 1 × 1, x; is 1 × K and non-random.
We want to test
Họ : B(1) = B(2) = 3(3)
against the alternative that Họ is not true. Derive the test statistic for testing Ho and derive
its distribution under Ho.
Transcribed Image Text:Question 2: Consider the regression model X; B4) + Ei, x; B2) + Ei, x; 3(3) + Ei, i = n1 + n2 + 1, ..., n1 + n2 + n3, IIDN(0,0²), i= 1,..., n, n = n1 +n2 + n3, Yi i = 1, .., n1, Yi i = n1 + 1, ..., nị + n2, Yi Ei where B1), B(2), and ß(3) are K × 1 parameter vectors, ɛ; is 1 × 1, x; is 1 × K and non-random. We want to test Họ : B(1) = B(2) = 3(3) against the alternative that Họ is not true. Derive the test statistic for testing Ho and derive its distribution under Ho.
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