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how that the expression for B₁ is given by 8₁ Hint = S XY 8XX Σ₁(X; - X)(Y₂ - Y) Σ' 1(X, − x)2

how that the expression for B₁ is given by 8₁ Hint = S XY 8XX Σ₁(X; - X)(Y₂ - Y) Σ' 1(X, − x)2

MATLAB: An Introduction with Applications
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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In regression analysis with (X₁, X₂,..., X₂) and (Y₁, Y₂, …, Y) such that Y₁ = Bo + B₁X₁ + €; where id N (0,0²) Let 3 and 3₁ be the maximum likelihood estimators for 30, 3₁. €1, €2,..., En
Transcribed Image Text:In regression analysis with (X₁, X₂,..., X₂) and (Y₁, Y₂, …, Y) such that Y₁ = Bo + B₁X₁ + €; where id N (0,0²) Let 3 and 3₁ be the maximum likelihood estimators for 30, 3₁. €1, €2,..., En
2. Write down the log-likelihood function (Bo, B₁, 0²) for the unknown parameters and using the fact that d -l(B₁, B₁,0²) 23, 80, 81,0²) dßo d dß₁ -l(Bo, B1,0²) show that the expression for B₁ is given by ₁ and then solve it. SXY 8XX (X - 36 - Î;X;) – 0 - 3o = i=1 = - Σα (Y – Bo – BiXi)Xi=0 Σ₁(X₁-X) (Y₁ - Y) Σ1(X₂ - X)² Hint You may find it useful to first get an relationship for Bo and then show that 72 2 (Y - B - BLX)X=0. Using this straightforward derivation you can write down the second likelihood equation in terms of Σ(Y₁ – Bo – B₁X;) (Xi – X) i=1
Transcribed Image Text:2. Write down the log-likelihood function (Bo, B₁, 0²) for the unknown parameters and using the fact that d -l(B₁, B₁,0²) 23, 80, 81,0²) dßo d dß₁ -l(Bo, B1,0²) show that the expression for B₁ is given by ₁ and then solve it. SXY 8XX (X - 36 - Î;X;) – 0 - 3o = i=1 = - Σα (Y – Bo – BiXi)Xi=0 Σ₁(X₁-X) (Y₁ - Y) Σ1(X₂ - X)² Hint You may find it useful to first get an relationship for Bo and then show that 72 2 (Y - B - BLX)X=0. Using this straightforward derivation you can write down the second likelihood equation in terms of Σ(Y₁ – Bo – B₁X;) (Xi – X) i=1
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