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

question 27

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 $y =$ $115.6 + 22.3 x _ { 1 } + 14.7 x _ { 2 } - 1.36 x _ { 1 } x _ { 2 }$ . $$\begin{array} { | c | r r r | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & T \\\hline \text { Constant } & 115.6 & 78.1 & 1.480 \\x _ { 1 } & 22.3 & 7.1 & 3.141 \\x _ { 2 } & 14.7 & 6.3 & 2.333 \\x _ { 1 } x _ { 2 } & - 1.36 & 0.52 & - 2.615 \\\hline\end{array}$$ S = 20.9 R-Sq = 55.4%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | r r r r | } \hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \\\hline \text { Regression } & 3 & 8661 & 2887.0 & 6.626 \\\text { Error } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}\end{array}$$ Interpret the coefficient $b _ { 1 }$ .

---

Definitions:

Insecure

Feeling uncertain or lacking confidence in oneself, which can affect emotional well-being and interpersonal relationships.

Destructively Obedient

Following orders without moral consideration, leading to harmful actions that the individual might not ordinarily commit.

Legitimate Authority Figures

Individuals who are recognized and respected for having lawful or moral power and control within a given context.

Electric Shocks

A sudden discharge of electrical energy through a part of the body, often used for medical therapy or as a laboratory method of study.