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Consider the regression mode, y = a + Bx + ɛ; where, E (ɛ | x) = 0, E(ɛx) = 0, Var (ɛ|x)= oʻ, and Var [(a + Bx)|x] = 0. (a) Derive Var(y|x).

Consider the regression mode, y = a + Bx + ɛ; where, E (ɛ | x) = 0, E(ɛx) = 0, Var (ɛ|x)= oʻ, and Var [(a + Bx)|x] = 0. (a) Derive Var(y|x).

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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1. Consider the regression mode, y = a + ßx+ɛ; where, E (ɛ | x) = 0, E(ɛx) = 0, Var (ɛ|x)= oʻ, and Var [(a+ ßx)|x] = 0. (a) Derive Var(y|x). (b) The errors are homoscedastic [i.e, Var (ɛ\x)= o²] in this case. Based on the given regression equation, show that, Var(y|x) < Var (y).
Transcribed Image Text:1. Consider the regression mode, y = a + ßx+ɛ; where, E (ɛ | x) = 0, E(ɛx) = 0, Var (ɛ|x)= oʻ, and Var [(a+ ßx)|x] = 0. (a) Derive Var(y|x). (b) The errors are homoscedastic [i.e, Var (ɛ\x)= o²] in this case. Based on the given regression equation, show that, Var(y|x) < Var (y).
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