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(e) Consider the model Y; = Bo + B,X; +u; where E (u;|X;) = 0, observations (Yi, X;) are independent and identi- cally distributed and 0 < E (Y*) < ∞, 0 < E (X÷) < ∞. Suppose X; is measured with error and so X; is observed instead of X;, X; = X;+wi, where Ew; = 0, var (w;) = o², cov (Wi, X;) = 0 and cov (wi, u;) = 0. In this case, it can be shown that Does 3, overestimate or underestimate the true value of B,? What can be said about 3, if there is a very small or very large amount of measurement error?

(e) Consider the model Y; = Bo + B,X; +u; where E (u;|X;) = 0, observations (Yi, X;) are independent and identi- cally distributed and 0 < E (Y*) < ∞, 0 < E (X÷) < ∞. Suppose X; is measured with error and so X; is observed instead of X;, X; = X;+wi, where Ew; = 0, var (w;) = o², cov (Wi, X;) = 0 and cov (wi, u;) = 0. In this case, it can be shown that Does 3, overestimate or underestimate the true value of B,? What can be said about 3, if there is a very small or very large amount of measurement error?

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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(e) Consider the model Y; = Bo+ B1X; + u; where E (u;|X;) = 0, observations (Y;, X;) are independent and identi- cally distributed and 0 < E (Y*) <∞, 0 < E (X;) <o. Suppose X; is measured with error and so X; is observed instead of X;, X; = X;+wi, where Ew; = 0, var (w;) = o², cov (wi, X;) = 0 and cov (wi, U;) = 0. In this case, it can be shown that %3D -B1. Does 3, overestimate or underestimate the true value of 3,? What can be said about 31 if there is a very small or very large amount of measurement error? (f) In part (e), if we could estimate o?/o, how could we correct for the bias in B1?
Transcribed Image Text:(e) Consider the model Y; = Bo+ B1X; + u; where E (u;|X;) = 0, observations (Y;, X;) are independent and identi- cally distributed and 0 < E (Y*) <∞, 0 < E (X;) <o. Suppose X; is measured with error and so X; is observed instead of X;, X; = X;+wi, where Ew; = 0, var (w;) = o², cov (wi, X;) = 0 and cov (wi, U;) = 0. In this case, it can be shown that %3D -B1. Does 3, overestimate or underestimate the true value of 3,? What can be said about 31 if there is a very small or very large amount of measurement error? (f) In part (e), if we could estimate o?/o, how could we correct for the bias in B1?
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