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

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
$\begin{array}{llllll}\hline & \text { df } & \text { SS } & \text { MS } & F & \text { Significance F } \\\hline \text { Regression } & 3 & 3393.677324 & 1131.225775 & 9391.974782 & 2.11084 \mathrm{E}-11 \\\text { Residual } & 6 & 0.722675987 & 0.120445998 & & \\\text { Total } & 9 & 3394.4 & & & \\\hline\end{array}$


$\begin{array}{lllllll} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 16.72197014 & 8.283997219 & 2.018587126 & 0.09007654 & -3.548255659 & 36.99219593 \\\text { X1 }_{1} & -3.037317759 & 2.678748705 & -1.133856921 & 0.300116382 & -9.591984506 & 3.517348987 \\\text { X2 }_{2} & -1.046522754 & 1.547132645 & -0.676427297 & 0.523973988 & -4.832222727 & 2.73917722 \\\text { X1X2 }_{1} & 4.071685147 & 0.444059933 & 9.169224345 & 9.47663 \mathrm{E}-05 & 2.98510884 & 5.158261454\end{array}$


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 $x _ { 2 } = 6$ .