Lecture10_2005

# Lecture10_2005 - Green Stats The Importance of"Importance...

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Green // Stats The Importance of “Importance” This lecture aims to distinguish among various meanings of the term “importance” as applied to regression results. I will use James E. Campbell’s regression analysis of presidential election outcomes (see class website for his October 2004 essay “Forecasting the Presidential Vote in 2004: Placing Preference Polls in Context” PS 36(4): 763-7 and the accompanying data) as a running example. The basic model is U cZ bX a Y + + + = , where Y is the share of the major party vote won by the “incumbent” party’s presidential candidate, X is the share of the major party support expressed in a September pre-election poll, and Z is a measure of 2 nd quarter economic performance. Before turning to the topic of importance, let’s review Professor Campbell’s regression results. First, let’s consider the bivariate relationship between X and Y: SEPTPOLL INPTYVOTE 70 65 60 55 50 45 40 62.5 60.0 57.5 55.0 52.5 50.0 47.5 45.0 2000 1996 1992 1988 1984 1980 1976 1972 1968 1964 1960 1956 1952 1948 Scatterplot of I NPTYVOTE vs SEPTPOLL This graph shows a strong and fairly linear relationship between poll results and election outcomes. Note that the point farthest from the regression line is 1980, a year that featured unusually poor economic performance. That “residual” suggests that the inclusion of an economic predictor might improve the fit. The corresponding bivariate regression analysis looks like this:

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The regression equation is INPTYVOTE = 24.0 + 0.553 SEPTPOLL Predictor Coef SE Coef T P Constant 24.007 4.693 5.12 0.000 SEPTPOLL 0.55250 0.08958 6.17 0.000 S = 2.94831 R-Sq = 76.0% R-Sq(adj) = 74.0% The results indicate that the actual vote increases, on average, by .55 for each one-point increase in pre-election poll results. The magnitude of this coefficient is somewhat surprising. Evidently, races are typically much closer than they appear in September. Even if the poll found zero support for the incumbent party’s candidate, he would still be expected to receive 24%; conversely, if the poll found 100% support, the actual vote share would be expected to be 79%. The value of s tells us that the disturbances have an estimated standard deviation of close to 3 percentage-points. That means that polls have somewhat limited utility as grounds for election forecasts, in that polls lack the accuracy to “call” a close election. Remember that the confidence interval and prediction intervals for forecasts are functions of s . One of the key arguments in Professor Campbell’s essay is the claim that economic conditions can be used to augment the explanatory and predictive accuracy of this bivariate regression model. This graph, which plots the fitted values (FITS1) from a regression of election outcomes on both pre-election polls and economic conditions, seems to support this argument. Notice that the points tend to lie closer to the regression line than in the previous scatterplot.
FITS1

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## This note was uploaded on 04/07/2008 for the course STAT 102 taught by Professor Jonathanreuning-schererdonaldgreen during the Fall '05 term at Yale.

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Lecture10_2005 - Green Stats The Importance of"Importance...

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