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

question 42

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 $$y =$$ $$115.6 + 22.3 x _ { 1 } + 14.7 x _ { 2 } - 1.36 x _ { 1 } x _ { 2 }$$ . $$\begin{array} { | c | r r c | } \hline \text { Predictor } & \text { Coef } & \text { SiDev } & T \\\hline \text { Constant } & 115.6 & 78.1 & 1.480 \\x _ { 1 } & 22.3 & 7.1 & 3.141 \\x _ { 2 } & 14.7 & 6.3 & 2.333 \\x _ { 1 } x _ { 2 } & - 1.36 & 0.52 & - 2.615 \\\hline\end{array}$$ S = 20.9 R-Sq = 55.4%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | r r r c | } \hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \\\hline \text { Regression } & 3 & 8661 & 2887.0 & 6.626 \\\text { Error } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}\end{array}$$ Do these results allow us at the 5% significance level to conclude that the model is useful in predicting the price of gold?

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Definitions:

Collective Bargaining Rights

The legal right granted to employees to negotiate terms and conditions of employment through chosen representatives with their employer.

Landrum-Griffin Act

A US federal law enacted in 1959 to regulate labor unions' internal affairs and their officials' relationships with employers.

NLRB

The National Labor Relations Board, a U.S. federal agency responsible for enforcing U.S. labor law in relation to collective bargaining and unfair labor practices.

Political Influence

The power to affect governmental actions, policies, or decisions, often exercised through lobbying or electoral activities.