Suppose that the true relationship between y; and ; is as follows, Yi =B₁ + B₂x₁ + Uj The error term satisfies that E[ui] = 0 and Var(u) = 1. You find another variable zi whose sample correlation with ₂ is equal to -1. Select correct statement(s).
Suppose that the true relationship between y; and ; is as follows, Yi =B₁ + B₂x₁ + Uj The error term satisfies that E[ui] = 0 and Var(u) = 1. You find another variable zi whose sample correlation with ₂ is equal to -1. Select correct statement(s).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
![Suppose that the true relationship between y; and ; is as follows,
Yi = B₁ + B₂xi + Ui
The error term satisfies that E[u₂] = 0 and Var(u) = 1. You find
another variable zi whose sample correlation with x is equal to -1.
Select correct statement(s).
Because the correlation is equal to -1, we have %₁ = -₂.
O If we add z; in the regression model along with ;, R² will be increased.
Adding z; along with in the regression model is not plausible because
of the perfect multicollinearity.
O If we estimate the model y₁ = a₁ + a2%; + e₁, the estimator of a2 will
be equal to -3₂, where B₂ is the OLS estimator of 32](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7afc2de4-22ca-41c7-9e00-d318df3d7e5d%2Fda8d6e22-ea4a-4544-a371-f973f4d0c0fc%2F26t3k1b_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that the true relationship between y; and ; is as follows,
Yi = B₁ + B₂xi + Ui
The error term satisfies that E[u₂] = 0 and Var(u) = 1. You find
another variable zi whose sample correlation with x is equal to -1.
Select correct statement(s).
Because the correlation is equal to -1, we have %₁ = -₂.
O If we add z; in the regression model along with ;, R² will be increased.
Adding z; along with in the regression model is not plausible because
of the perfect multicollinearity.
O If we estimate the model y₁ = a₁ + a2%; + e₁, the estimator of a2 will
be equal to -3₂, where B₂ is the OLS estimator of 32
Expert Solution
Step 1: Given information
It is given that the relationship between variables yi and xi is
yi = β1 + β2xi + ui
We have another variable zi whose sample correlation with xi is -1
Step by step
Solved in 3 steps
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