THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

Essay

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
An economist is in the process of developing a model to predict the price of gold.She believes that the two most important variables are the price of a barrel of oil (x₁)and the interest rate (x₂).She proposes the model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₃ + ε.A random sample of 20 daily observations was taken.The computer output is shown below.
THE REGRESSION EQUATION IS
y = 115.6 + 22.3x₁ + 14.7x₂ - 1.36x₁x₂

S = 20.9 R-Sq = 55.4%
ANALYSIS OF VARIANCE

-Suppose that a regression relationship is given by Y = β₀ + β₁X₁ + β₂X₂ + ε.If the simple linear regression of Y on X₁ is estimated from a sample of n observations,the resulting slope estimate will generally be biased for β₁.But if the sample correlation between X₁ and X₂ is 0,the slope will not be biased for β₁.
How does X₂ affect β₁ if the sample correlation between X₁ and X₂ is zero?