Testing the General Linear Hypothesis (cont'd)Let the full model be y = ẞ0 + ẞ1×1 + ẞ2x2 + ẞ3x3 + ε.Construct the matrix D and the vector d.Hoẞ1 = 0► Hoẞ1 = ẞ3 = 0DB = (0100)/(༠ ༩༠༠)(DP = (010-1DA² Coo000= 0DEAO=(i)Testing the General Linear Hypothesis (cont'd)Let the full model be y = ẞ0 + ẞ1×1 + ẞ2×2 + B3x3 + ε.Construct the matrix D and the vector d.► Hoẞ1 = 0 and ẞ3= −1DHoẞ1+2ẞ2 = 30100·00016012ام=Ο=d()822(-1)38=1996667 1. (Chapter 3, pp. 65-67) Consider the multiple linear regression modely = ßo + ß1x1 + ẞ2x2 + ẞ3x3 + ß4×4 + ɛ.For the general linear hypothesis approach, find the appropriate D and d.(a) Hoẞ1+2ẞ₂ = 3B1 + B2(b) Ho:= ẞ32(c) Ho B1 B2, B3 = ẞ4=(d) Hoẞ12ẞ2 = 4ẞ3, ẞ1 +2ẞ2 = 0(e) Hoẞ₁ = B₂ = ß3 = ß4

The given multiple linear regression model is as follows.

Answered: 1. (Chapter 3, pp. 65-67) Consider the…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 62CR

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Question

Testing the General Linear Hypothesis (cont'd)
Let the full model be y = ẞ0 + ẞ1×1 + ẞ2x2 + ẞ3x3 + ε.
Construct the matrix D and the vector d.
Hoẞ1 = 0
► Hoẞ1 = ẞ3 = 0
DB = (0100)/
(༠ ༩༠༠)(
DP = (010-1
DA² Coo
000
= 0
DEAO
=
(i)
Testing the General Linear Hypothesis (cont'd)
Let the full model be y = ẞ0 + ẞ1×1 + ẞ2×2 + B3x3 + ε.
Construct the matrix D and the vector d.
► Hoẞ1 = 0 and ẞ3
= −1
D
Hoẞ1+2ẞ2 = 3
0100
·0001
6012
ام
=
Ο
=
d
()
822
(-1)
3
8=1
99
66
67

1. (Chapter 3, pp. 65-67) Consider the multiple linear regression model
y = ßo + ß1x1 + ẞ2x2 + ẞ3x3 + ß4×4 + ɛ.
For the general linear hypothesis approach, find the appropriate D and d.
(a) Hoẞ1+2ẞ₂ = 3
B1 + B2
(b) Ho:
= ẞ3
2
(c) Ho B1 B2, B3 = ẞ4
=
(d) Hoẞ12ẞ2 = 4ẞ3, ẞ1 +2ẞ2 = 0
(e) Hoẞ₁ = B₂ = ß3 = ß4

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