Lecture+11+Multiple+Regression+Analysis++cont+

Lecture+11+Multiple+Regression+Analysis++cont+ - Lecture...

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Lecture 11, ECON 123A, Fall 2011 Dale J. Poirier 11-1 Lecture 11 Multiple Regression Analysis: Estimation (continued) We begin with some nice historical slides from Professor Charles Franklin at the University of Wisconsin.
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Lecture 11, ECON 123A, Fall 2011 Dale J. Poirier 11-2
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Lecture 11, ECON 123A, Fall 2011 Dale J. Poirier 11-9 Consider the standard multiple linear regression model y = Xß + u = X 1 ß 1 + X 2 ß 2 + u, where X = [X 1 , X 2 ], $ = [ $ 1 N , $ 2 N ] N , X j is n×k i , $ j is k j ×1 (j = 1, 2), and k 1 + k 2 = k.
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Lecture 11, ECON 123A, Fall 2011 Dale J. Poirier 11-10 C It is possible to show equals where M 1 is the idempotent matrix
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Lecture 11, ECON 123A, Fall 2011 Dale J. Poirier 11-11 B M 1 X 2 is the residual from regressing X 2 on X 1 . B is the slope estimator from a regression of y on M 1 X 2 . B If k 1 = 1 with then M 1 = I n - n -1 4 n 4 n N and M 1 X 2 converts X 2 to deviations from column means. In this case,
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Lecture 11, ECON 123A, Fall 2011 Dale J. Poirier 11-12 3.4 The Variance of the OLS Estimators We now obtain the variance of the OLS estimators so that, in addition to knowing the central tendencies of the we also have a measure of the spread in its sampling distribution. Assumption MLR.5 (Homoskedasticity): The error u has the same variance given any values of the explanatory variables. In other words, Var(u * x 1 , . .., x k ) = F 2. C When MLR.5 fails, the disturbance u is said to be heteroskedastic . C Appendix E provides further elaboration.
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Lecture 11, ECON 123A, Fall 2011 Dale J. Poirier 11-13
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Lecture 11, ECON 123A, Fall 2011 Dale J. Poirier 11-15 Theorem 3.2 (Sampling Variances of the OLS Slope Estimators): Under Assumptions MLR.l - MLR.5, conditional on the sample values of the independent variables, for j = 1, 2, . .., k, where is the total sample variation in x j , and is the R-squared from regressing x j on all other independent variables (and including an intercept). (3.51)
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Lecture 11, ECON 123A, Fall 2011 Dale J. Poirier 11-16 Definition: The variance inflation factor (VIF) for is VIF j = 1/(1 - ). C VIF j is the factor by which is higher because x j is not uncorrelated with all other regressors, i.e,.
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Lecture 11, ECON 123A, Fall 2011 Dale J. Poirier 11-17
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Lecture 11, ECON 123A, Fall 2011 Dale J. Poirier 11-18
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Dale J. Poirier 11-19 The Components of the OLS Variances: Multicollinearity Equation (3.51) shows that the variance of depends on three factors: F 2 , SST j , and . C
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This note was uploaded on 12/13/2011 for the course ECON 123a taught by Professor Staff during the Fall '08 term at UC Irvine.

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Lecture+11+Multiple+Regression+Analysis++cont+ - Lecture...

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