103lect7hand

103lect7hand - Dummy Variables - I We next consider the...

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Dummy Variables - I • We next consider the case when X i is a dummy variable , or binary variable. • A dummy variable is a variable that takes on only the values 0 or 1. Often categorical variables are “quantified” in this way, e.g. X i = 1 if female, X i = 0 if male, X i = 1 if use advertising campaign A, X i = 0 if use advertising campaign B. Dummy Variables - II • Nothing major changes when X i is a dummy variable. However, the interpretation of the estimated coefficients β 0 and β 1 is a bit different. • Example: Sales i = β 0 + β 1 AdCampaign i + u i – AdCampaign i =1 if use advertising campaign A in region i – AdCampaign i =0 if use advertising campaign B in region i –S a l e s i = unit sales in region i • Suppose we regress Sales i on AdCampaign i and get estimated coefficients β 0 and β 1 . What do these coefficients tell us? • Recall predicted value formula…… Dummy Variables - III • The predicted value formula says that when advertising campaign A is used, (i.e. when AdCampaign i =1) predicted sales are: • When advertising campaign B is used (i.e. AdCampaign i =0), predicted sales are: • So the estimated coefficient β 1 measures the difference in predicted sales between the two campaigns. n 01 ˆˆ Sales AdCampaign ii ββ =+ n Sales i β n 0 ˆ Sales i =
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Dummy Variables - IV • Therefore, if we want to test whether the two ad campaigns generate the same amount of sales, we should test the null hypothesis that the slope coefficient β 1 =0. • Suppose regression results are: •T h e t STAT for the hypothesis test that β 1 =0 is 1.46. Hence we cannot reject the null hypothesis that the campaigns generate equivalent amounts of sales.
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This note was uploaded on 05/26/2008 for the course ECON 103 taught by Professor Sandrablack during the Spring '07 term at UCLA.

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103lect7hand - Dummy Variables - I We next consider the...

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