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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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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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