Lecture+10+Multiple+Regression+Analysis++cont+

Lecture+10+Multiple+Regression+Analysis++cont+ - Lecture...

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Lecture 10, ECON 123A, Fall 2011 Dale J. Poirier 10-1 Lecture 10 Multiple Regression Analysis: Estimation (continued)
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Lecture 10, ECON 123A, Fall 2011 Dale J. Poirier 10-2 A “Partialling Out” Interpretation of Multiple Regression C Consider the case k = 2 and B Appendix 3A.2 shows where the are the OLS residuals from a simple regression of x 1 on x 2 . (3.22)
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Lecture 10, ECON 123A, Fall 2011 Dale J. Poirier 10-3 B Equation (3.22) shows that we can then do a simple regression of y on to obtain . B The residuals are the part of x i1 that is uncorrelated with x i2 . B is x i1 after the effects of x i2 have been partialled out . (3.22)
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Lecture 10, ECON 123A, Fall 2011 Dale J. Poirier 10-4 Comparison of Simple and Multiple Regression Estimates C Consider the two estimated regressions: Then it can be shown that where is the slope coefficient from the simple regression of x i2 on x i1 (i = 1, . .., n). (3.23)
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Lecture 10, ECON 123A, Fall 2011 Dale J. Poirier 10-5 C More generally, (3.23) can be generalized to where (j = 1, 2, . .., k) are the OLS estimators from the regression of y on x j (j = 1, 2, . .., k), (j = 1, 2, . .., k-1) are the OLS estimators from the regression of y on x j (j = 1, 2, . .., k-1), and (j = 1, 2, . .., k-1) are the OLS estimators from the regression of x k on x j (j = 1, 2, . .., k). (3.64)
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Lecture 10, ECON 123A, Fall 2011 Dale J. Poirier 10-6 C Two special cases exist in which the simple regression of y on x l will produce the same OLS estimate on x l as the regression of y on x l and x 2 . B The partial effect of x 2 on is zero in the sample, i.e, B x 1 and x 2 are uncorrelated in the sample, i.e, (3.23)
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Lecture 10, ECON 123A, Fall 2011 Dale J. Poirier 10-7 Goodness-of-Fit C SST, SSE, SSR, and R 2 are defined the same as for simple regression. 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+10+Multiple+Regression+Analysis++cont+ - Lecture...

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