# ch07 - Multiple Regression Analysis y = 0 1x1 2x2 kxk u 5...

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Economics 20 - Prof. Anderson 1 Multiple Regression Analysis y = β 0 + β 1 x 1 + β 2 x 2 + . . . β k x k + u 5. Dummy Variables

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Economics 20 - Prof. Anderson 2 Dummy Variables A dummy variable is a variable that takes on the value 1 or 0 Examples: male (= 1 if are male, 0 otherwise), south (= 1 if in the south, 0 otherwise), etc. Dummy variables are also called binary variables, for obvious reasons
Economics 20 - Prof. Anderson 3 A Dummy Independent Variable Consider a simple model with one continuous variable ( x ) and one dummy ( d ) y = β 0 + δ 0 d + β 1 x + u This can be interpreted as an intercept shift If d = 0, then y = β 0 + β 1 x + u If d = 1, then y = ( β 0 + δ 0 ) + β 1 x + u The case of d = 0 is the base group

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Economics 20 - Prof. Anderson 4 Example of δ 0 > 0 x y { δ 0 } β 0 y = ( β 0 + δ 0 ) + β 1 x y = β 0 + β 1 x slope = β 1 d = 0 d = 1
Economics 20 - Prof. Anderson 5 Dummies for Multiple Categories We can use dummy variables to control for something with multiple categories Suppose everyone in your data is either a HS dropout, HS grad only, or college grad To compare HS and college grads to HS dropouts, include 2 dummy variables hsgrad = 1 if HS grad only, 0 otherwise; and colgrad = 1 if college grad, 0 otherwise

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Economics 20 - Prof. Anderson 6 Multiple Categories (cont) Any categorical variable can be turned into a set of dummy variables Because the base group is represented by
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