Transcription of Chapter 7, Dummy Variable - Miami University
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Chapter 7, Dummy Variable - Miami University
Chapter 7, Dummy Dummy Variable takes on 1 and 0 only. The number 1 and 0 have no numerical(quantitative) meaning. The two numbers are used to represent groups. In shortdummy Variable is categorical (qualitative).(a)For instance, we may have a sample (or population) that includes both femaleand male. Then a Dummy Variable can be defined asD= 1 for female andD= 0for male. Such a Dummy Variable divides the sample into two subsamples (or twosub-populations): one for female and one for male.(b) Dummy Variable follows Bernoulli distribution. The distribution is characterizedby the parameterpD={1;with probabilityp0;with probability 1 p(1) using Dummy Variable as regressorY= 0+ 1D+u(2)Regression (2) can be broken into two separate regressions asY={ 0+u;whenD= 0( 0+ 1) +u;whenD= 1(3)Taking expectation of (3) leads toE(YjD= 0) = 0(4)E(YjD= 1) = 0+ 1(5)and 0=E(YjD= 0)(6) 1=E(YjD= 1) E(YjD= 0)(7)Therefore 0is the mean ofYconditional onD= 0 (or mean ofYin the subpopulationwithD= 0), 1is the differencein meanYbetween the two mean is the estimate for population mean, so we have the following interpre-tation for the estimated coefficients in (2) 0= yD=0(8) 1= yD=1 yD=0(9)where yD=0denotes the averageYin the sub-sample for whichD= 0; yD=1denotesthe averageYin the sub-sample for whichD= 1:Equation (2) pro}}
Chapter 7, Dummy Variable 1. A dummy variable takes on 1 and 0 only. The number 1 and 0 have no numerical (quantitative) meaning. The two numbers are used to represent groups. In short dummy variable is categorical (qualitative). (a) For instance, we may have a sample (or population) that includes both female and male.
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