Economist
an Economist Is in the Process of Developing a Model

question 14

Short Answer

Economist
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 (x₁)and the interest rate (x₂).She proposes the first-order model with interaction $$y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 } + \epsilon$$ A random sample of 20 daily observations was taken.The computer output is shown below. The regression equation is:
$$y = 115.6 + 22.3 x _ { 1 } + 14.7 x _ { 2 } - 1.36 x _ { 1 } x _ { 2 }$$
$\begin{array}{|l|ccc|}\hline \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } \\\hline \text { Constant } & 115.6 & 78.1 & 1.480 \\x_{1} & 22.3 & 7.1 & 3.141 \\x_{2} & 14.7 & 6.3 & 2.333 \\x_{1} x_{2} & -1.36 & 0.52 & -2.615 \\\hline\end{array}$

$$\mathrm { S } = 20.9 \quad \mathrm { R } - \mathrm { Sq } = 55.4 \%$$
ANAL YSIS OF VARIANCE
$\begin{array}{|l|llll|}\hline \text { Source of Variation } & \text { DF } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 8661 & 2887.0 & 6.626 \\\text { Error } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}$

-Is there sufficient evidence at the 1% significance level to conclude that the interest rate and the price of gold are linearly related?
Test statistic = ____________________ = ____________________
Critical Value = ____________________
Conclusion: _____________________
Interpretation: _____________________________________________________

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Definitions:

Account

A record or statement of financial expenditure and receipts relating to a specific period or purpose; also used to refer to a customer's relationship with a financial institution.

Simple Interest

Interest computed solely on the initial amount invested, excluding any previously earned interest.

Investment

The undertaking of investing resources, usually capital, with the foresight of amassing income or profits.

Months

Units of time, typically used to measure periods within a year, consisting of 28 to 31 days.