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

-An economist estimates the regression model y_i= β₀ + β₁x₁_i+ β₂x₂_i + ε_i.The estimates of the parameters β₁ and β₂ are not very large compared with their respective standard errors.But the size of the coefficient of determination indicates quite a strong relationship between the dependent variable and the pair of independent variables.Having obtained these results,the economist strongly suspects the presence of multicollinearity.Since his chief interest is in the influence of X₁ on the dependent variable,he decides that he will avoid the problem of multicollinearity by regressing Y on X₁ alone.Comment on this strategy.

Question

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

-An economist estimates the regression model y_i= β₀ + β₁x₁_i+ β₂x₂_i + ε_i.The estimates of the parameters β₁ and β₂ are not very large compared with their respective standard errors.But the size of the coefficient of determination indicates quite a strong relationship between the dependent variable and the pair of independent variables.Having obtained these results,the economist strongly suspects the presence of multicollinearity.Since his chief interest is in the influence of X₁ on the dependent variable,he decides that he will avoid the problem of multicollinearity by regressing Y on X₁ alone.Comment on this strategy.

Quizplus · Accepted Answer

The Answer of 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 (x 1 )and the interest rate (x 2 ).She proposes the model y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 1 x 3 + ε.A random sample of 20 daily observations was taken.The computer output is shown below. THE REGRESSION EQUATION IS y = 115.6 + 22.3x 1 + 14.7x 2 - 1.36x 1 x 2 S = 20.9 R-Sq = 55.4% ANALYSIS OF VARIANCE -An economist estimates the regression model y_i= β₀ + β₁x₁_i+ β₂x₂_i + ε_i.The estimates of the parameters β₁ and β₂ are not very large compared with their respective standard errors.But the size of the coefficient of determination indicates quite a strong relationship between the dependent variable and the pair of independent variables.Having obtained these results,the economist strongly suspects the presence of multicollinearity.Since his chief interest is in the influence of X₁ on the dependent variable,he decides that he will avoid the problem of multicollinearity by regressing Y on X₁ alone.Comment on this strategy.