Lecture+13+Multiple+Regression+Analysis+-+Inference+cont+

Lecture+13+Multiple+Regression+Analysis+-+Inference+cont+ -...

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Lecture 13, ECON 123A, Fall 2011 Dale J. Poirier 13-1 Lecture 13 Multiple Regression Analysis: Inference (continued) Economic, or Practical, versus Statistical Significance (continued) Example 4.6 (Participation Rates in 401 (k) Plans): Example 3.3 used data on 401(k) plans to estimate a model describing participation rates in terms of the firm’s match rate and age of the plan. Including a measure of firm size = total number of employees ( totemp ), the estimated equation is
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Lecture 13, ECON 123A, Fall 2011 Dale J. Poirier 13-2 C The smallest t statistic in absolute value is that on the variable totemp : t = -.00013/.00004 = -3.25, and this is statistically significant at very small significance levels. (The two-tailed p-value for this t statistic is about .001.) Thus, all of the variables are statistically significant at rather small significance levels. C How big, in a practical sense, is the coefficient on totemp ? Holding mrate and age fixed, if a firm grows by 10,000 employees, the participation rate falls by 10,000(.00013) = 1.3 percentage points. This is a huge increase in number of employees with only a modest effect on the participation rate. Thus, although firm size does affect the participation rate, the effect is not practically very large.
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Lecture 13, ECON 123A, Fall 2011 Dale J. Poirier 13-3 C The previous example shows that it is especially important to interpret the magnitude of the coefficient, in addition to looking at t statistics, when working with large samples. B With large sample sizes, parameters can be estimated very precisely. B Standard errors are often quite small relative to the coefficient estimates, which usually results in statistical significance. C We saw last class that some researchers insist on using smaller significance levels as the sample size increases, partly as a way to offset the fact that standard errors are getting smaller.
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Lecture 13, ECON 123A, Fall 2011 Dale J. Poirier 13-4 Guidelines for discussing the economic and statistical significance of a variable in a multiple regression model: C Check for statistical significance. If the variable is statistically significant, discuss the magnitude of the coefficient to get an idea of its practical or economic importance. B This latter step can require some care, depending on how the independent and dependent variables appear in the equation. B In particular, what are the units of measurement ? B Do the variables appear in logarithmic form ?
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Lecture 13, ECON 123A, Fall 2011 Dale J. Poirier 13-5 C If a variable is not statistically significant at the usual levels (l0%, 5%, or 1%), you might still ask if the variable has the expected effect on y and whether that effect is practically large. 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+13+Multiple+Regression+Analysis+-+Inference+cont+ -...

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