1. Let us consider the following regression model for a sample of a female workers WorkHoursi = n + IChildi + tar-1 1i: 1, . . . ,n1 {1] where Childl- is a binary rvariable that takes value 1 if the individual has one or more child and otherwise; and WorkHours is the individual's usual hours worked per week in past 12 months. Let WeaklyPay = Y and Child 2 X. Also let m the number of individuals who has a one or more than one child and ma the number of female worker who does not have a child, such that nu + in = n. Recall that the OLE estimators are given by Eli-i=1 [95' Y) {Ii 2). EL {3.- - 1"?)2 ' g =17\" Elli. t: {a} Let Has an individual 'i's working hours for which the value of X is U; and y\" an individual it's working hour for which the value of X is 11 Show that "0 _ _ n n1 n1 =1 [gtY] (It-X}=:Zyt,1-: yea i=1 i=1 {b} Show that iaaq. i=1 n {1:} Use the results in [a] and [b] to conclude that 5'1 = 1?] 17a, upon an appropriate denition of l7] and 17"\". (d) Show that l} = MIXED'1 + {nnfn}:.. {e} Using the result in {a}, nally Show that a.) = if\