Consider the simple linear model Y; = Bo + B1Xi + €¿, where e~N(0,0²); i = 1,2, .. 1. Show that a) Y~IIN(Bo + Bıxi,o²) b) (i) L = L(Bo, ß1;y) = (2ro²)äexp|- Vi – Bo + Brx1)*] (ii) ô² = -(Sx - B,Sy) %3D 2ng?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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Consider the simple linear model Y, = Bo + B1x; + €j, where e;~N(0,0?); i = 1, 2, ., n.
1. Show that
a) Y;~IIN(Bo + B1xi, o?)
%3D
...
b) (i) L = L(Bo, Pai y) = (2no?)žexp|- LVi – Bo + Bixi)*|
(ii) ô? = (Sx - BiSy)
c) Cov(Bo, Bi) =
d) Bi is an unbiased estimator of ß1 and that Var(B1) = o =
%3D
(Show all results used as part of your answer)
%3D
Sxx
%3D
Sxx
Transcribed Image Text:Consider the simple linear model Y, = Bo + B1x; + €j, where e;~N(0,0?); i = 1, 2, ., n. 1. Show that a) Y;~IIN(Bo + B1xi, o?) %3D ... b) (i) L = L(Bo, Pai y) = (2no?)žexp|- LVi – Bo + Bixi)*| (ii) ô? = (Sx - BiSy) c) Cov(Bo, Bi) = d) Bi is an unbiased estimator of ß1 and that Var(B1) = o = %3D (Show all results used as part of your answer) %3D Sxx %3D Sxx
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