Lecture+16+Multiple+Regression+Analysis+-+Further+Issues++cont+

Lecture+16+Multiple+Regression+Analysis+-+Further+Issues++cont+

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Lecture 16, ECON 123A, Fall 2011 16-1 Dale J. Poirier Lecture 16 Multiple Regression Analysis: Further Issues (cont.) 6.3 More on Goodness-of-Fit and Selection of Regressors C Until now, we have not focused much on the size of R in evaluating our 2 regression models, because beginning students tend to put too much weight on R . 2 C As we will see shortly, choosing a set of explanatory variables based on the size of the R can lead to nonsensical models. 2 C In Chapter 10, we will discover that R s obtained from time series 2 regressions can be artificially high and result in misleading conclusions.
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Lecture 16, ECON 123A, Fall 2011 16-2 Dale J. Poirier C Nothing about the classical linear model assumptions requires that R be 2 above any particular value; R is simply an estimate of how much 2 12 k variation in y is explained by x , x , . .., x in the population. B We have seen several regressions that have had pretty small R s. 2 Although this means that we have not accounted for several factors that affect y, this does not mean that the factors in u are correlated with the independent variables. B The zero conditional mean assumption MLR.4 is what determines whether we get unbiased estimators of the ceteris paribus effects of the independent variables, and the size of the R has no direct bearing 2 on this.
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Lecture 16, ECON 123A, Fall 2011 16-3 Dale J. Poirier B A small R does imply that the error variance is large relative to the 2 variance of y, which means we may have a hard time precisely j estimating the $ . < But remember, we saw in Section 3.4 that a large error variance can be offset by a large sample size: if we have enough data, we may be able to precisely estimate the partial effects even though we have not controlled for many unobserved factors. < Whether or not we can get precise enough estimates depends on the application.
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Lecture 16, ECON 123A, Fall 2011 16-4 Dale J. Poirier Example (p. 199): Suppose that some incoming students at a large university are randomly given grants to buy computer equipment. C If the amount of the grant is truly randomly determined, we can estimate the ceteris paribus effect of the grant amount on subsequent college grade point average by using simple regression analysis. B Because of random assignment, all of the other factors that affect GPA would be uncorrelated with the amount of the grant. C The grant amount would likely explain little of the variation in GPA, so the R from such a regression would probably be very small. 2 C But, if we have a large sample size, we still might get a reasonably precise estimate of the effect of the grant.
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Lecture 16, ECON 123A, Fall 2011 16-5 Dale J. Poirier Example (p. 199): A good illustration of where poor explanatory power has j nothing to do with unbiased estimation of the $ is given by analyzing the data set in APPLE.RAW. Unlike the other data sets we have used, the key explanatory variables in APPLE.RAW were set experimentally - that is, without regard to other factors that might affect the dependent variable. The variable we would like to explain, ecolbs , is the (hypothetical) pounds of “ecologically friendly” (“ecolabeled”) apples a family would demand.
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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+16+Multiple+Regression+Analysis+-+Further+Issues++cont+

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