(c) Use the results in (a) and (b) to conclude that B1 = Y1 - Yo, upon an appropriate definition of Y, and Yo. (d) Show that Y = (n1)Y1 + (no) Yo. (e) Using the result in (d), finally show that Bo = Yo.1. Let us consider the following regression model for a sample of n female workers WorkHoursi = [30 + lChildi + ui, i: 1,. . .,n, (1) where Childi is a binary variable that takes value 1 if the individual has one or more child and 0 otherwise; and WorkHours is the individual's usual hours worked per week in past 12 months. Let WeeklyPay = Y and Child 2 X. Also let an the number of individuals who has a one or more than one child and no the number of female worker who does not have a child, such that no + m = n. Recall that the OLS estimators are given by 221:1 (92' Y) (532' X) 221:1 (Iii _ XV a=Yax 81: (a) Let 39130 an individual i's working hours for which the value of X is 0; and 31231 an individual i's working hour for which the value of X is 1. Show that n n1 \"0 Z (Elil7) (IaX) = $213121 E21910 i=1 TL (b) Show that