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Introductory EconometricsIntuition, Proof, and Practice$
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Jeffrey Zax

Print publication date: 2011

Print ISBN-13: 9780804772624

Published to Stanford Scholarship Online: June 2013

DOI: 10.11126/stanford/9780804772624.001.0001

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Understanding and Interpreting Regression with Two x's

Understanding and Interpreting Regression with Two x's

Chapter:
(p.453) Chapter 12 Understanding and Interpreting Regression with Two x's
Source:
Introductory Econometrics
Publisher:
Stanford University Press
DOI:10.11126/stanford/9780804772624.003.0012

This chapter begins by deriving the variances of the slopes from a given equation. These are used first to address the issue of multicollinearity. It then turns to the issue of interpreting regression results. The slopes obtained when the sum of squared errors for the regression of the same equation is minimized are best linear unbiased (BLU) estimates of the population coefficients. If the population relationship includes two explanatory variables, the precision of these slopes depends heavily on the extent to which the two explanatory variables are related. Including an irrelevant variable is inefficient, but does not create bias. Everything that was done in Chapters 8 through 10 holds with two explanatory variables, either exactly or with minor, sensible extensions.

Keywords:   regression analysis, explanatory variables, slopes, multicollinearity, variance, sum of squared errors, population relationship

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