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Suppose that Yi = Bo + B₁X₁ + €į, i = 1, ..., n where E(€;) = 0 and Var (e;) = o². Let 3 and 3₁ be the least squares estimates. a) Find Var(ŝo) (treating the Xi's as fixed). b) The observed residuals are defined by ê; = Y; – Bo – Â₁ Xį. Show that Σ₁ ê; = 0. c) Show that Σ₁ ê¿Ỹ; = 0. What is the interpretation of this result? d) Suppose you did a regression of Y's on the observed residuals. (In other words, reat the ê¿ as the X₂'s.) What intercept and slope would you get?

Suppose that Yi = Bo + B₁X₁ + €į, i = 1, ..., n where E(€;) = 0 and Var (e;) = o². Let 3 and 3₁ be the least squares estimates. a) Find Var(ŝo) (treating the Xi's as fixed). b) The observed residuals are defined by ê; = Y; – Bo – Â₁ Xį. Show that Σ₁ ê; = 0. c) Show that Σ₁ ê¿Ỹ; = 0. What is the interpretation of this result? d) Suppose you did a regression of Y's on the observed residuals. (In other words, reat the ê¿ as the X₂'s.) What intercept and slope would you get?

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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Suppose that Y = Bo + BıXite, i - 1,..., n where E(€;) = 0 and Var(e;) = o². Let 3o and 3₁ be the least squares estimates. (a) Find Var(Bo) (treating the X's as fixed). (b) The observed residuals are defined by ê; = Y; – Bo – Â₁ Xį. Show that Σ₁ ê; = 0. i=1 (c) Show that ₁ ê¡¿Ÿ¿ = 0. What is the interpretation of this result? (d) Suppose you did a regression of Y's on the observed residuals. (In other words, treat the ê¿ as the X;'s.) What intercept and slope would you get?
Transcribed Image Text:Suppose that Y = Bo + BıXite, i - 1,..., n where E(€;) = 0 and Var(e;) = o². Let 3o and 3₁ be the least squares estimates. (a) Find Var(Bo) (treating the X's as fixed). (b) The observed residuals are defined by ê; = Y; – Bo – Â₁ Xį. Show that Σ₁ ê; = 0. i=1 (c) Show that ₁ ê¡¿Ÿ¿ = 0. What is the interpretation of this result? (d) Suppose you did a regression of Y's on the observed residuals. (In other words, treat the ê¿ as the X;'s.) What intercept and slope would you get?
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