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Consider the simple lincar model Y, = Be + B,x, + C. where -N(0,0²); i= 1,2, --,n. 1. Show that a) Y-IIN(8 + B1*i,g?) (i) a* =(S - S,) c) Cov(Br.B) (Show all results used as part of your answer) that Kar(&1

Consider the simple lincar model Y, = Be + B,x, + C. where -N(0,0²); i= 1,2, --,n. 1. Show that a) Y-IIN(8 + B1*i,g?) (i) a* =(S - S,) c) Cov(Br.B) (Show all results used as part of your answer) that Kar(&1

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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Consider the simple linear model Y, = Be + Bix, + C. where --N(0,a); i = 1,2, .., n. 1. Show that a) Y-IIN(B + B1*i,g²) b) (i) L = L(B.Pa:y) = (2ro) žexp - - Po + B,x,| (ü) a = (Sx - PSy) c) Cov(Be.B) = d) B, is an unhiased estimator of B, and that Var(B) = o 2. Derive the statisic for testing Ho: B - Bio versus H,: ß1 + Pin. (You must also state the distribution and critical region for the lest). 3. Constract a 100(1 – a)% confidence interval for 8,. %3D (Show all results used as part of your answer) %3D
Transcribed Image Text:Consider the simple linear model Y, = Be + Bix, + C. where --N(0,a); i = 1,2, .., n. 1. Show that a) Y-IIN(B + B1*i,g²) b) (i) L = L(B.Pa:y) = (2ro) žexp - - Po + B,x,| (ü) a = (Sx - PSy) c) Cov(Be.B) = d) B, is an unhiased estimator of B, and that Var(B) = o 2. Derive the statisic for testing Ho: B - Bio versus H,: ß1 + Pin. (You must also state the distribution and critical region for the lest). 3. Constract a 100(1 – a)% confidence interval for 8,. %3D (Show all results used as part of your answer) %3D
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