Lecture 10 Prof. Arkonac's Slides (Ch 6.7 - 7.3) for ECO 4000

Lecture 10 Prof. Arkonac's Slides (Ch 6.7 - 7.3) for ECO 4000

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Unformatted text preview: Multiple Regression (cont’) Multicollinearity, Hypothesis Testing in Multiple Regression ECO 4000, Statistical Analysis for Economics and Finance Fall 2010 Lecture 10 Prof: Seyhan Arkonac, PhD 1 Last thing we did last time was; Multicollinearity: (a) perfect multicollinearity: including both male and female in a regression, STATA drops one. (b) imperfect multicollinearity (often this is called as multicollinearity) : occurs when any two or more regressors have high correlation. 2 3 Multicollinearity, Perfect and Imperfect (SW Section 6.7) Some more examples of perfect multicollinearity The example from earlier: you include STR twice. Second example: regress TestScore on a constant, D , and B , where: D i = 1 if STR ≤ 20, = 0 otherwise; B i = 1 if STR >20, = 0 otherwise, so B i = 1 – D i and there is perfect multicollinearity Would there be perfect multicollinearity if the intercept (constant) were somehow dropped (that is, omitted or suppressed) in this regression? This example is a special case of… 4 The dummy variable trap Suppose you have a set of multiple binary (dummy) variables, which are mutually exclusive and exhaustive – that is, there are multiple categories and every observation falls in one and only one category (Freshmen, Sophomores, Juniors, Seniors, Other). If you include all these dummy variables and a constant, you will have perfect multicollinearity – this is sometimes called the dummy variable trap . Why is there perfect multicollinearity here ? Solutions to the dummy variable trap : 1. Omit one of the groups (e.g. Senior), or 2. Omit the intercept What are the implications of (1) or (2) for the interpretation of the coefficients? Perfect Multicollinearity: . reg ahe age female male Source | SS df MS Number of obs = 7986-------------+------------------------------ F( 2, 7983) = 164.89 Model | 24300.9748 2 12150.4874 Prob > F = 0.0000 Residual | 588266.294 7983 73.6898777 R-squared = 0.0397-------------+------------------------------ Adj R-squared = 0.0394 Total | 612567.269 7985 76.7147487 Root MSE = 8.5843------------------------------------------------------------------------------ ahe | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- age | .4415421 .0332389 13.28 0.000 .3763852 .5066989 female |-2.346755 .1950323 -12.03 0.000 -2.729069 -1.964441 male | (dropped) _cons | 4.606864 .9990293 4.61 0.000 2.648505 6.565222------------------------------------------------------------------------------ 5 Perfect Multicollinearity with no intercept: . reg ahe age female male, noconstant Source | SS df MS Number of obs = 7986-------------+------------------------------ F( 3, 7983) =10270.68 Model | 2270534.96 3 756844.986 Prob > F = 0.0000 Residual | 588266.294 7983 73.6898777 R-squared = 0.7942-------------+------------------------------ Adj R-squared = 0.7941 Total | 2858801.25 7986 357.976616 Root MSE = 8.5843------------------------------------------------------------------------------...
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This note was uploaded on 05/05/2011 for the course ECON 4000 taught by Professor Arkonac during the Spring '11 term at CUNY Baruch.

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Lecture 10 Prof. Arkonac's Slides (Ch 6.7 - 7.3) for ECO 4000

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