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2. Consider the simple regression model y = Bo+BID + u, where D is a binary variable. a) Let y be y; with D;= 1, yo be y; with Di= 0, and Σ₁ Y₁ = ¹₁ ₁₁ + 1 Vio, No Nº Σi=1 ³io = Ďÿ₁+ (1 − ¯)ÿ· N No where N₁ + No = N. Show that y = ₁₁ N N₁ b) Show that the OLS estimator: B₁ [Hint: Note that Diyi = yil and D² = D₁. Therefore ₁ = Σ', Divi - Σ, Dyi - Σ,5D + 2,55 _Σ1 vi-521-52, Di + NDy Σ1D} - ND = ΣDi-ND² Σ₁(Di-D)(yi - y) Σ1(D; – D)2 can be written as ₁ - Yo N

2. Consider the simple regression model y = Bo+BID + u, where D is a binary variable. a) Let y be y; with D;= 1, yo be y; with Di= 0, and Σ₁ Y₁ = ¹₁ ₁₁ + 1 Vio, No Nº Σi=1 ³io = Ďÿ₁+ (1 − ¯)ÿ· N No where N₁ + No = N. Show that y = ₁₁ N N₁ b) Show that the OLS estimator: B₁ [Hint: Note that Diyi = yil and D² = D₁. Therefore ₁ = Σ', Divi - Σ, Dyi - Σ,5D + 2,55 _Σ1 vi-521-52, Di + NDy Σ1D} - ND = ΣDi-ND² Σ₁(Di-D)(yi - y) Σ1(D; – D)2 can be written as ₁ - Yo N

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2. Consider the simple regression model y =Bo+BiD + u, where D is a binary variable. a) Let ya be y; with D;= 1, yo be y; with Di= 0, and Σ₁ Yi = ¹₁ ₁₁ + 1 Vio D₁ Yios where N₁ + No = N. Show that y=+No=Dỹ₁+ (1 − Ď)ÿ¸· b) Show that the OLS estimator: B₁- Σ₁(Di-D)(yi - Y) Σ₁=1(Di-D)² [Hint: Note that Diy: = y₁1 and D² = D₁. Therefore B₁ = i=1 Σ., Divi - Σ., Dyi - Σ15D, +Σ,53_ Σ 1 vi - 5Σ1 - 52, Di + NDy Σ1 D} - ND? = -2 can be written as ₁ - Yo Σ₁ Di-ND² i=1
Transcribed Image Text:2. Consider the simple regression model y =Bo+BiD + u, where D is a binary variable. a) Let ya be y; with D;= 1, yo be y; with Di= 0, and Σ₁ Yi = ¹₁ ₁₁ + 1 Vio D₁ Yios where N₁ + No = N. Show that y=+No=Dỹ₁+ (1 − Ď)ÿ¸· b) Show that the OLS estimator: B₁- Σ₁(Di-D)(yi - Y) Σ₁=1(Di-D)² [Hint: Note that Diy: = y₁1 and D² = D₁. Therefore B₁ = i=1 Σ., Divi - Σ., Dyi - Σ15D, +Σ,53_ Σ 1 vi - 5Σ1 - 52, Di + NDy Σ1 D} - ND? = -2 can be written as ₁ - Yo Σ₁ Di-ND² i=1
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