Consider the Partial Printout for an Interaction Regression Analysis of the Relationship

question 62

Essay

Consider the partial printout for an interaction regression analysis of the relationship between a dependent variable $y$ and two independent variables $x _ { 1 }$ and $x _ { 2 }$ .
ANOVA
$\begin{array}{llllll}\hline & d f & \text { SS } & \text { MS } & F & \text { Significance F } \\\hline \text { Regression } & 3 & 3393.677324 & 1131.225775 & 9391.974782 & 2.11084 \mathrm{E}-11 \\\text { Residual } & 6 & 0.722675987 & 0.120445998 & & \\\text { Total } & 9 & 3394.4 & & & \\\hline\end{array}$
$\begin{array}{lllllll}\hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 16.72197014 & 8.283997219 & 2.018587126 & 0.09007654 & -3.548255659 & 36.99219593 \\\mathrm{X} 1 & -3.037317759 & 2.678748705 & -1.133856921 & 0.300116382 & -9.591984506 & 3.517348987 \\\mathrm{X} 2 & -1.046522754 & 1.547132645 & -0.676427297 & 0.523973988 & -4.832222727 & 2.73917722 \\\mathrm{X} 1 \mathrm{X} 2 & 4.071685147 & 0.444059933 & 9.169224345 & 9.47663 \mathrm{E}-05 & 2.98510884 & 5.158261454 \\\hline\end{array}$


a. Write the prediction equation for the interaction model.
b. Test the overall utility of the interaction model using the global $F$ -test at $\alpha = .05$ .
c. Test the hypothesis (at $\alpha = .05 )$ that $x _ { 1 }$ and $x _ { 2 }$ interact positively.
d. Estimate the change in $y$ for each additional 1 -unit increase in $x _ { 1 }$ when $x _ { 2 } = 6$ .

---

Definitions:

Thrust Faulting

A type of fault in which the hanging wall moves upward relative to the footwall, common in regions of compression.

Volcanic Fields

Regions of the Earth's crust that are prone to volcanic activity and are scattered with multiple volcanoes.

Magma

A molten or semi-molten rock material beneath the Earth's surface from which igneous rock is formed by cooling.

Continental Crust

The relatively thick part of the Earth's crust that forms the large landmasses. It is generally older and more complex than the oceanic crust.