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

question 86

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%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | r r r c | } \hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \\\hline \text { Regression } & 3 & 8661 & 2887.0 & 6.626 \\\text { Error } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}\end{array}$$ Interpret the coefficient $b _ { 1 }$ .

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Definitions:

Paid-In Capital

Paid-In Capital is the amount of money investors have paid to a company in exchange for shares of its stock, reflecting the additional capital contributed by shareholders over the par value of the shares.

Par Value

The face value of a stock or bond as stated by the issuing company, which does not necessarily match the market value.

Common Stock

A type of equity security that represents ownership in a corporation, entitling the holder to vote on corporate matters and receive dividends.

Dividends in Arrears

Unpaid dividends on cumulative preferred stock, which must be paid out before any dividends can be issued to common stockholders.