Homework3.pdf - ECO 321 Fall 2019 Homework 3 Due October 18 by 5 pm Cut and paste at the end of your submission the R code you have used to show your

Homework3.pdf - ECO 321 Fall 2019 Homework 3 Due October 18...

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ECO 321 Fall 2019 Homework 3 Due October 18 by 5 pm Cut and paste at the end of your submission the R code you have used to show your work. 1. Let us consider the following regression model for a sample of n 3rd grade students TestScore i = β 0 + β 1 SmallClass i + u i , i = 1 , . . . , n, (1) where SmallClass i is a binary variable that takes value 1 if the student belongs to a small class and 0 otherwise; and TestScore is the student’s score in a standardized test taken at the end of the year. Let TestScore = Y and SmallClass = X . Also let n 1 the number of students who attend small classes and n 0 the number of students who attend large classes, such that n 0 + n 1 = n . Recall that the OLS estimators are given by ˆ β 1 = n i =1 ( y i - ¯ Y ) ( x i - ¯ X ) n i =1 ( x i - ¯ X ) 2 , ˆ β 0 = ¯ Y - ˆ β 1 ¯ X. (a) Let y i, 0 a student i for which the value of X is 0; and y i, 1 a student i for which the value of X is 1. Show that n X i =1 ( y i - ¯ Y ) ( x i - ¯ X ) = n 0 n n 1 X i =1 y i, 1 - n 1 n n 0 X i =1 y i, 0 (b) Show that n X i =1 ( x i - ¯ X ) 2 = n 1 n 0 n .
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