An Economist Is in the Process of Developing a Model $\left( x _ { 1 } \right)$

question 20

Essay

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 $\left( x _ { 1 } \right)$ and the interest rate $\left( x _ { 2 } \right)$ She proposes the first-order model with interaction: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 3 } + \varepsilon$ .
A random sample of 20 daily observations was taken. The computer output is shown below.
THE REGRESSION EQUATION IS $$y = 115.6 + 22.3 x _ { 1 } + 14.7 x _ { 2 } - 1.36 x _ { 1 } x _ { 2 } \text {. }$$
$\begin{array}{|c|rrc|}\hline \text { Predictor } & \text { Coef } & \text { SDDev } & T \\\hline \text { Constant } & 115.6 & 78.1 & 1.480 \\x_{1} & 22.3 & 7.1 & 3.141 \\x_{2} & 14.7 & 6.3 & 2.333 \\x_{1} x_{2} & -1.36 & 0.52 & -2.615 \\\hline\end{array}$
$$\mathrm { S } = 20.9 \quad \mathrm { R } - \mathrm { Sq } = 55.4 \%$$
ANALYSIS OF VARIANCE
$\begin{array}{|l|rrrc|}\hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & F \\\hline \text { Regression } & 3 & 8661 & 2887.0 & 6.626 \\\text { Error } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}$ Is there sufficient evidence at the 1% significance level to conclude that the price of a barrel of oil and the price of gold are linearly related?

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Definitions:

Personal Assets

Items of value owned by an individual, including real estate, bank accounts, investments, and personal property.

Objectivity Principle

The objectivity principle in accounting states that financial information presented in the accounts of a business should be based on objective evidence and be verifiable, avoiding personal opinions or biases.

External Users

individuals or entities outside of a company who use its financial information, such as investors, creditors, and government agencies.

Shareholders

Individuals or entities that own a portion of a corporation's stock, thus having a share in its ownership and profits.