Suppose we have the following causal model: Y a₁ + ₁ X + u, X + a₂ + B₂Y + v, where E(u) = E(v) = 0, cov(u, v) = 0. The best linear prediction of Y given X is: Y = a₁ + ₁X + error. Similarly, the best linear prediction of Y given X is: X = a + ₂Y + error. Which of the following statements is/are true?

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter4: Estimating Demand
Section: Chapter Questions
Problem 1.4CE
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Suppose we have the following causal model:
Ya₁ + ₁ X + u,
X + a₂ + B₂Y + v,
where E(u) = E(v) = 0, cov(u, v)
The best linear prediction of Y given X is:
Y = a₁ + ß₁X + error.
Similarly, the best linear prediction of Y given X is:
X = a* + ß₂Y+ error.
Which of the following statements is/are true?
3* = 0 if and only if ₁ = 0
OB₁ B₂ if B₁ = B₂
B = 0 if 3₂ = 0
O B₁ = 0 if B = 0
= : 0.
=
Transcribed Image Text:Suppose we have the following causal model: Ya₁ + ₁ X + u, X + a₂ + B₂Y + v, where E(u) = E(v) = 0, cov(u, v) The best linear prediction of Y given X is: Y = a₁ + ß₁X + error. Similarly, the best linear prediction of Y given X is: X = a* + ß₂Y+ error. Which of the following statements is/are true? 3* = 0 if and only if ₁ = 0 OB₁ B₂ if B₁ = B₂ B = 0 if 3₂ = 0 O B₁ = 0 if B = 0 = : 0. =
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