SCENARIO 14-11
a Weight-Loss Clinic Wants to Use Regression Analysis $Y=$

Short Answer

SCENARIO 14-11
A weight-loss clinic wants to use regression analysis to build a model for weight loss of a client
(measured in pounds). Two variables thought to affect weight loss are client's length of time on the
weight-loss program and time of session. These variables are described below: $Y=$ Weight loss (in pounds)
$X_{1}=$ Length of time in weight-loss program (in months)
$X_{2}=1$ if morning session, 0 if not
Data for 25 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: $Y=\beta_{0}+\beta_{1} X_{1}+\beta_{2} X_{2}+\beta_{3} X_{1} X_{2}+\varepsilon$

$\text { Output from Microsoft Excel follows: }$

$\begin{array}{lr}{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7308 \\\text { R Square } & 0.5341 \\\text { Adjusted R Square } & 0.4675 \\\text { Standard Error } & 43.3275 \\\text { Observations } & 25 \\\hline\end{array}$

$\text { ANOVA }$


$\begin{array}{lrrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } & {t \text { Stot }} & \rho_{\text {-value }} & \text { Lower 99\% } & \text { Upper 99\% } \\\hline \text { Intercept } & -20.7298 & 22.3710 & -0.9266 & 0.3646 & -84.0702 & 42.6106 \\\text { Length } & 7.2472 & 1.4992 & 4.8340 & 0.0001 & 3.0024 & 11.4919 \\\text { Morn } & 90.1981 & 40.2336 & 2.2419 & 0.0359 & -23.7176 & 204.1138 \\\text { Length × Morn } & -5.1024 & 3.3511 & -1.5226 & 0.1428 & -14.5905 & 4.3857\end{array}$


-Referring to Scenario 14-11, which of the following statements is supported by the analysis shown? a) There is sufficient evidence (at $\alpha = 0.05$ ) of curvature in the relationship between weight loss $( Y )$ and months on program $\left( X _ { 1 } \right)$ .
b) There is sufficient evidence (at $\alpha = 0.05$ ) to indicate that the relationship between weight loss $( Y )$ and months on program $\left( X _ { 1 } \right)$ varies with session time.
c) There is insufficient evidence (at $\alpha = 0.05$ ) of curvature in the relationship between weight loss $( Y )$ and months on program $\left( X _ { 1 } \right)$ .
d) There is insufficient evidence (at $\alpha = 0.05$ ) to indicate that the relationship between weight loss $( Y )$ and months on program $\left( X _ { 1 } \right)$ varies with session time.