## Regression for Dummies

An important regression special case is bivariate regression with a dummy regressor. The conditional expectation of Yt given a dummy variable, Z{, takes on two values. Write them in Greek, like this:

FAY^Zi = 0| = tf

= = « +

so that

is the difference in expected Yt with the dummy regressor, Zf, switched on and off.

Using this notation, we can write

ВДг|2Л = E[rtZi = 0| + (£[yjz( ^Ц-ElWi И01)г,

= or + ^Zj, (2.8)

This shows that E[Ff|Zf] is a linear function of Zf, with slope j8 and intercept a. Because the CEF with a single dummy variable is linear, regression fits this CEF perfectly. As a result, the regression slope must also be j8 = E[Ff|Zf = 1] – E[Ff|Zf = 0], the difference in expected Yt with Z; switched on and off.

Regression for dummies is important because dummy regressors...

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