Your Textbook Discussed the Regression Model When X Is a Binary

Essay

Your textbook discussed the regression model when X is a binary variable $$Y _ { i } = \beta _ { 0 } + \beta _ { 1 } D _ { i } + u _ { i } , i = 1 , \ldots , n$$ Let $Y$ represent wages, and let $D$ be one for females, and 0 for males. Using the OLS formula for the slope coefficient, prove that $\widehat { \beta } _ { 1 }$ is the difference between the average wage for males and the average wage for females.