SCENARIO 13-11
a Weight-Loss Clinic Wants to Use Regression Analysis $$Y = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \beta _ { 3 } X _ { 1 } X _ { 2 } + \varepsilon$$

question 198

True/False

SCENARIO 13-11
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)
X1 = Length of time in weight-loss program (in months)
X2 = 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: $$Y = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \beta _ { 3 } X _ { 1 } X _ { 2 } + \varepsilon$$ Output from Microsoft Excel follows: $\begin{array}{lr}{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7308 \\\text { R Square } & 0.5341 \\\text { Adjusted R Square } & 0.4675 \\\text { Standard Error } & 43.3275 \\\text { Observations } & 25\\\hline\end{array}$

$\text { ANOVA }$
$\begin{array}{lrrrrr}\hline&\text { df } & \text { SS }&M S &F & \text { Significance } F\\\hline\text { Regression } & 3 & 45194.0661 & 15064.6887 & 8.0248 & 0.0009 \\\text { Residual } & 21 & 39422.6542 & 1877.2692 & & \\\text { Total } & 24 & 84616.7203 & &\\\hline \end{array}$


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

-Referring to SCENARIO 13-11, the overall model for predicting weight loss(Y) is statistically significant at the 0.05 level.

---

Definitions:

Containment

A foreign policy strategy aimed at stopping the expansion of an enemy or ideology, particularly communism during the Cold War.

Indian Removal Program

A government policy in the 1830s that forced Native American tribes to relocate from their ancestral lands in the southeastern United States to designated territory west of the Mississippi River.

American Expansionism

A policy or ideology aiming at expanding the territorial or economic influence of the United States across other nations and territories.

Civilian Control

The principle that military leaders remain under the oversight and authority of civilian government leaders.