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 x1 and x2. $$\begin{array}{l}\text { ANOVA }\\\begin{array} { l l l l l l } \hline & d f & \text { SS } & \text { MS } & F & \text { Significance } F \\\hline \text { Regression } & 3 & 3393.677324 & 1131.225775 & 9391.974782 & 2.11084 \mathrm { E } - 11 \\\text { Residual } & 6 & 0.722675987 & 0.120445998 & & \\\text { Total } & 9 & 3394.4 & & & \\\hline\\\end{array}\\\begin{array} { l l l l l l l } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 16.72197014 & 8.283997219 & 2.018587126 & 0.09007654 & - 3.548255659 & 36.99219593 \\\text { X1 } & - 3.037317759 & 2.678748705 & - 1.133856921 & 0.300116382 & - 9.591984506 & 3.517348987 \\\text { X2 } & - 1.046522754 & 1.547132645 & - 0.676427297 & 0.523973988 & - 4.832222727 & 2.73917722 \\\text { X1X2 } & 4.071685147 & 0.444059933 & 9.169224345 & 9.47663 \mathrm { E } - 05 & 2.98510884 & 5.158261454 \\\hline\end{array}\end{array}$$ 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 $x _ { 2 } = 6$ . 3 Test for Interaction Between Two Variables