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lect10_103t_2010_Compatibility_Mode_

# lect10_103t_2010_Compatibility_Mode_ - Dummy Variables in...

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5/10/2010 1 Dummy Variables in MR - VIII We also may be interested in the effects of multiple sets of categorical variables, e.g. the effects of both the sex of an individual, and their ethnicity. In this case, there needs to be an “excluded” group for each set of categories, e.g. Ethnicity: let’s choose “Other” as the excluded group Hispanic i = 1 if observation i is Hispanic, Hispanic i = 0 otherwise Black i = 1 if observation i is Black, Black i = 0 otherwise Sex: let’s choose “Male” as the excluded group Female i = 1 if observation i is Female, Female i = 0 otherwise What do these regression results say about average wages for Hispanic Females, Black Males, Other Males, etc………? circumflexnosp4char Wage = 17.40 6.08Hispanic 4.59Black 2.90Female (1.02) (1.10) (1.04) (0.97) i i i i - - - Hypothesis Testing in MR There are two types of hypothesis tests we can do in multiple regression. 1) Hypothesis tests involving a single coefficient , e.g. a test whether β 5 =1, or a test whether β 3 =0. 2) Hypothesis tests involving multiple coefficients , e.g. a test whether β 5 =2* β 3 , or a test whether β 1 = β 2 = β 4 =0. These are sometimes called joint hypothesis tests, because they test conditions on multiple coefficients jointly, or together. Tests of the form 1) can be done using t STAT ’s, just like in basic regression analysis. As discussed last week, these are done exactly like in simple regression. Tests of the form 2) will be done with a new statistic , the F- statistic, or F STAT .

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5/10/2010 2 Hypothesis Tests for a Single Coefficient - I One new issue regarding tests for a single coefficient: When using dummy variables, remember that we had to choose an excluded group. In our PS2 example we had: Regression A (with “Other” as the excluded group) Regression B (with “Hispanic” as the excluded group) Again, these regressions are really exactly the same (they both say average wages for Others is 16.08, average wages for Blacks is 11.57, and average wages for Hispanics is 10.19) But because the variables are coded differently, the coefficients measure different aspects of the relationship, so the t STAT ’s on the coefficients test different things. circumflexnosp4char Wage = 16.08 5.89Hispanic 4.51Black (0.69) (1.09) (1.84) i i i - - circumflexnosp4char Wage = 10.19 + 1.38Black 5.89Other (0.85) (1.94) (1.09) i i i + Hypothesis Tests for a Single Coefficient - II For example, in Regression A, the coefficient on the variable Black i measures the difference between average wages for Blacks and average wages for Others. (since Other is the excluded group). Hence the t STAT for the hypothesis test that this coefficient equals 0 tests the hypothesis that Blacks and Others have equal average wages. On the other hand, in Regression B, the coefficient on the variable Black i measures the difference between average wages for Blacks and average wages for Hispanics. (since Hispanics is now the excluded group). Hence the t STAT for the hypothesis test that this coefficient equals 0 tests the hypothesis that Blacks and Hispanics have equal average wages.
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lect10_103t_2010_Compatibility_Mode_ - Dummy Variables in...

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