THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

question 70

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

-Is there sufficient evidence at the 1% significance level to conclude that the interest rate and the price of gold are linearly related?

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Definitions:

Squared Deviations

The squared differences between individual values and the mean of a dataset, used in statistical analysis to measure variance.

Scatter Diagram

A visual depiction employing points to illustrate the connection between two numerical variables.

Cov(X,Y)

The covariance between two variables X and Y, measuring how changes in one variable are associated with changes in the other.

Sample Slope Coefficient

A parameter in a linear regression equation that represents the change in the dependent variable for a one-unit change in the independent variable.