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

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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 – Sales 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 0 1 ˆ ˆ Sales AdCampaign i i β β = + n 0 1 ˆ ˆ Sales i β β = + n 0 ˆ Sales i β =
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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: The 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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