Consider the regression model with the heterogeneous coefficient. Y₁ = Boi + BX, +%₂ where (v. X₁. Boi. Bu) are i.i.d random variables with Bo=E (Boi) and B₁ = E (Bu) It is possible to show that the model can be written as Y,= Bo + B,X, +u, where u, = (Boi-Bo) + (B₁-B₁) X1 + v And, it is also possible to show that E[u[X]-0 when we assume that E (Boi Xi) Bo. E (BulXi) B₁. and E (v₁|X₁) = 0. (you don't need to prove these results here.) Based on these results, we can conclude that under the current setting, regression of Y on X and an intercept will yield a consistent estimation of the ( ). Fill the parenthesis with three words. A
Consider the regression model with the heterogeneous coefficient. Y₁ = Boi + BX, +%₂ where (v. X₁. Boi. Bu) are i.i.d random variables with Bo=E (Boi) and B₁ = E (Bu) It is possible to show that the model can be written as Y,= Bo + B,X, +u, where u, = (Boi-Bo) + (B₁-B₁) X1 + v And, it is also possible to show that E[u[X]-0 when we assume that E (Boi Xi) Bo. E (BulXi) B₁. and E (v₁|X₁) = 0. (you don't need to prove these results here.) Based on these results, we can conclude that under the current setting, regression of Y on X and an intercept will yield a consistent estimation of the ( ). Fill the parenthesis with three words. A
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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![Consider the regression model with the heterogeneous coefficient.
Y₁ = Boi + B₁X₁ + %₁
where (v₁, X₁. Boi, B₁) are i.i.d random variables with Bo= E (Bo) and B₁ = E (B₁)
It is possible to show
that the model can be written as Y, = Bo + B₁X₁ + u, where u, =
(Bu-Bi Xitô
= (Bor-Bo) +
And, it is also possible to show that E[u[X]=0 when we assume
that E (Boi Xi) Bo. E (BX) = B₁, and E (v₁|X₁) = 0.
(you don't need to prove these results here.) Based on these results, we can conclude
that under the current setting, regression of Y on X and an intercept will yield a
consistent estimation of the ( ). Fill the parenthesis with three words.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b2e714b-077a-4877-9b39-06f1ff24f4d8%2F182c656d-91e4-4d54-bfff-a6b6055a88cb%2Fg3r3ade_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the regression model with the heterogeneous coefficient.
Y₁ = Boi + B₁X₁ + %₁
where (v₁, X₁. Boi, B₁) are i.i.d random variables with Bo= E (Bo) and B₁ = E (B₁)
It is possible to show
that the model can be written as Y, = Bo + B₁X₁ + u, where u, =
(Bu-Bi Xitô
= (Bor-Bo) +
And, it is also possible to show that E[u[X]=0 when we assume
that E (Boi Xi) Bo. E (BX) = B₁, and E (v₁|X₁) = 0.
(you don't need to prove these results here.) Based on these results, we can conclude
that under the current setting, regression of Y on X and an intercept will yield a
consistent estimation of the ( ). Fill the parenthesis with three words.
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