Lecture+15+Multiple+Regression+Analysis+-+Further+Issues

# Lecture+15+Multiple+Regression+Analysis+-+Further+Issues -...

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Lecture 15, ECON 123A, Fall 2011 Dale J. Poirier 15-1 Lecture 15 Multiple Regression Analysis: Further Issues C This chapter brings together several issues in multiple regression analysis not covered in earlier chapters. C These topics are not as fundamental as the material in Chapters 3 and 4, but they are important for applying multiple regression to a broad range of empirical problems.

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Lecture 15, ECON 123A, Fall 2011 Dale J. Poirier 15-2 6.1 Effects of Data Scaling on OLS Statistics C In Chapter 2 on bivariate regression, we briefly discussed the effects of changing the units of measurement on the OLS intercept and slope estimates. We also showed that changing the units of measurement did not affect R 2 . We now return to the issue of data scaling and examine the effects of rescaling the dependent or independent variables on standard errors, t statistics, F statistics, and confidence intervals. C We will discover that everything we expect to happen, does happen. When variables are rescaled, the coefficients, standard errors, confidence intervals, t statistics, and F statistics change in ways that preserve all measured effects and testing outcomes.
Lecture 15, ECON 123A, Fall 2011 Dale J. Poirier 15-3 B Often, data scaling is used for cosmetic purposes, such as to reduce the number of zeros after a decimal point in an estimated coefficient. By judiciously choosing units of measurement, we can improve the appearance of an estimated equation while changing nothing that is essential. C We begin with an equation relating infant birth weight to cigarette smoking and family income: where bwght = child birth weight (in ounces), cigs = number of cigarettes smoked by the mother while pregnant (per day), faminc = annual family income, in thousands of dollars.

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Lecture 15, ECON 123A, Fall 2011 Dale J. Poirier 15-4
Lecture 15, ECON 123A, Fall 2011 Dale J. Poirier 15-5 C The estimates of this equation, obtained using the data in BWGHT.RAW, are given in the first column of Table 6.1. Standard errors are listed in parentheses. B The estimate on cigs says that if a woman smoked 5 more cigarettes per day, birth weight is predicted to be about .4634(5) = 2.317 ounces less. B The t statistic on cigs is -5.06, so the variable is very statistically significant.

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Dale J. Poirier 15-6 C Suppose we decide to measure birth weight in pounds, rather than in ounces. Let bwghtlbs = bwght /16. What happens to our OLS statistics if we use this as the dependent variable in our equation? B Divide (6.1) by 16: B Each new coefficient will be the corresponding old coefficient divided by 16. < To verify this, the regression of bwghtlbs on cigs , and faminc is reported in column (2) of Table 6.1. B
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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+15+Multiple+Regression+Analysis+-+Further+Issues -...

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