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1. Let B₁ and 32 denote the OLS estimators of B1 and 32 in the regression: yi= Bo + Bixi + B2x12 + Ui. Let B1 denote the OLS estimators of B1 in the regression yi= Bo + Bixi + V₁. Let 81==1(x₁1 - x₁)(x₁2 - x₂)/₁1(x₁₁ - X₁)². a) ₁ is the OLS estimator of a slope parameter from what regression model? b) Show that 1(Vi-Bo-Bixi₁ - B2xiz) (Xi1 - x₁) = 0. c) Prove that B₁ =B₁ +812. Explain the situations in which omitting x2 from the model will NOT bias the OLS estimate of ₁. [Hint. Plug in for Bo=y-B₁x₁-B₂x₂ into (b). Then push through the summation and solve for B₁ to complete the derivation.]

1. Let B₁ and 32 denote the OLS estimators of B1 and 32 in the regression: yi= Bo + Bixi + B2x12 + Ui. Let B1 denote the OLS estimators of B1 in the regression yi= Bo + Bixi + V₁. Let 81==1(x₁1 - x₁)(x₁2 - x₂)/₁1(x₁₁ - X₁)². a) ₁ is the OLS estimator of a slope parameter from what regression model? b) Show that 1(Vi-Bo-Bixi₁ - B2xiz) (Xi1 - x₁) = 0. c) Prove that B₁ =B₁ +812. Explain the situations in which omitting x2 from the model will NOT bias the OLS estimate of ₁. [Hint. Plug in for Bo=y-B₁x₁-B₂x₂ into (b). Then push through the summation and solve for B₁ to complete the derivation.]

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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please answer b and c. 

1. Let B₁ and 32 denote the OLS estimators of ₁ and 2 in the regression: yi= Bo + Bixi1 + B2x₁2 + Ui. Let B₁ denote the OLS estimators of B₁ in the regression yi= Bo + B1x1 + Vi. Let 8₁==1(x₁ - x₁)(Xi2 — X₂) / Σ=1(Xi1 — X1₁)². a) ₁ is the OLS estimator of a slope parameter from what regression model? b) Show that 1(Vi-Bo-Bixi1 - B2x₁2)(x₁₁ - x₁) = 0. c) Prove that B₁ =B₁ + ☎1ß₂. Explain the situations in which omitting x₂ from the model will NOT bias the OLS estimate of ₁. [Hint. Plug in for Bo=ỹ - B₁x₁-B₂x₂ into (b). Then push through the summation and solve for B₁ to complete the derivation.]
Transcribed Image Text:1. Let B₁ and 32 denote the OLS estimators of ₁ and 2 in the regression: yi= Bo + Bixi1 + B2x₁2 + Ui. Let B₁ denote the OLS estimators of B₁ in the regression yi= Bo + B1x1 + Vi. Let 8₁==1(x₁ - x₁)(Xi2 — X₂) / Σ=1(Xi1 — X1₁)². a) ₁ is the OLS estimator of a slope parameter from what regression model? b) Show that 1(Vi-Bo-Bixi1 - B2x₁2)(x₁₁ - x₁) = 0. c) Prove that B₁ =B₁ + ☎1ß₂. Explain the situations in which omitting x₂ from the model will NOT bias the OLS estimate of ₁. [Hint. Plug in for Bo=ỹ - B₁x₁-B₂x₂ into (b). Then push through the summation and solve for B₁ to complete the derivation.]
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