Economist
an Economist Is in the Process of Developing a Model

question 68

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
$\begin{array}{|l|llll|}\hline \text { Source of Variation } & \text { DF } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 8661 & 2887.0 & 6.626 \\\text { Error } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}$

-Do these results allow us at the 5% significance level to conclude that the model is useful in predicting the price of gold?
Test statistic = ____________________ = ____________________
Critical Value = ____________________
Conclusion: _________________________________
Interpretation: ______________________________________________________

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