Question: Consider the simple regression model Y i = 0 + 1 D i + U i , i = 1, . . . , n,

Consider the simple regression model Y_i = ₀ + ₁D_i + U_i, i = 1, . . . , n, where D_i is a binary indicator that takes value 1 ("success") for a fraction p of the data, with 0 < p < 1, and value 0 ("failure") otherwise. Show that the OLS intercept is equal to the average value of Y among the successes and the OLS slope coefficient is equal to the difference between the average value of Y among the successes and the average value of Y among the failures. Comment on this result.

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