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

question 57

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
$$y = 115.6 + 22.3 x _ { 1 } + 14.7 x _ { 2 } - 1.36 x _ { 1 } x _ { 2 }$$
$\begin{array}{|c|rrc|}\hline \text { Predictor } & \text { Coef } & \text { S2Dev } & T \\\hline \text { Constant } & 115.6 & 78.1 & 1.480 \\x_{1} & 22.3 & 7.1 & 3.141 \\x_{2} & 14.7 & 6.3 & 2.333 \\x_{1} x_{2} & -1.36 & 0.52 & -2.615 \\\hline\end{array}$
$$\mathrm { S } = 20.9 \quad \mathrm { R } - \mathrm { Sq } = 55.4 \%$$
ANALYSIS OF VARIANCE
$\begin{array}{|l|rrrr|}\hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \\\hline \text { Regression } & 3 & 8661 & 2887.0 & 6.626 \\\text { Error } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}$ Is there sufficient evidence at the 1% significance level to conclude that the interaction term should be retained?

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Definitions:

Merge

The combination of two or more entities into one, often seen in the context of companies or organizations.

Oligopolies

Market structures characterized by a small number of firms that have significant control over market prices and competition.

Tacit Collusion

An unspoken, informal agreement among competitors to limit competition, such as by fixing prices or dividing market territories, without explicit communication.

Price Effect

The impact that a change in the price of a good or service has on consumers' demand for that good or service.