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 10

Multiple Choice

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, 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(X1).
• B)There is sufficient evidence (at \(\alpha\) = 0.05)to indicate that the relationship between weight loss (Y)and months on program (X1)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(X1).
• D)There is insufficient evidence (at \(\alpha\) = 0.05)to indicate that the relationship between weight loss (Y)and months on program(X1)varies with session time.

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Definitions:

Long-Term Vision

A strategic outlook that focuses on achieving goals and objectives over an extended period, shaping the future direction of an individual or organization.

Organizational Objectives

The established goals that guide a company or organization's activities and direction, aimed at achieving overall success and fulfillment of its mission.

Cost Containment

Strategies or approaches implemented to control, reduce, or maintain the level of expenses.

Production Targets

Specific goals or quotas set for the amount of goods or services to be produced within a certain timeframe.