SCENARIO 17-6
a Weight-Loss Clinic Wants to Use Regression Analysis

question 39

Short Answer

SCENARIO 17-6
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: $\begin{aligned} Y & = \text { Weight-loss (in pounds) } \\ X _ { 1 } & = \text { Length of time in weight-loss program (in months) } \\ X _ { 2 } & = 1 \text { if morning session, } 0 \text { if not } \\ X _ { 3 } & = 1 \text { if afternoon session, } 0 \text { if not } \quad \text { (Base level = evening session) } \end{aligned}$
Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: $\quad Y = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \beta _ { 3 } X _ { 3 } + \beta _ { 4 } X _ { 1 } X _ { 2 } + \beta _ { 5 } X _ { 1 } X _ { 3 } + \varepsilon$

Partial output from Microsoft Excel follows:

$\begin{array}{ll}{\text { Regression Statistics }} \\\text { Multiple R } & 0.73514 \\\text { R Square } & 0.540438 \\\text { Adjusted R Square } & 0.157469 \\\text { Standard Error } & 12.4147 \\\text { Observations } & 12\end{array}$

$\text { ANOVA }$
$F=5.41118 \quad \text { Significance } F=0.040201$

$\begin{array}{ccccc} & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\\text { Intercept } & 0.089744 & 14.127 & 0.0060 & 0.9951 \\\text { Length }\left(X_{1}\right) & 6.22538 & 2.43473 & 2.54956 & 0.0479 \\\text { Morn Ses }\left(X_{2}\right) & 2.217272 & 22.1416 & 0.100141 & 0.9235 \\\text { Aft Ses }\left(X_{3}\right) & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\\text { Length*Morn Ses } & 0.77058 & 3.562 & 0.216334 & 0.8359 \\\text { Length"Aft Ses } & -0.54147 & 3.35988 & -0.161158 & 0.8773\end{array}$


-Referring to Scenario 17-6, 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 in 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 in program $\left( X _ { 1 } \right)$ depends on session time.
c) There is sufficient evidence (at $\alpha = 0.10$ ) to indicate that the session time (morning, afternoon, evening) affects weight-loss $( Y )$ .
d) There is insufficient evidence (at $\alpha = 0.10$ ) to indicate that the relationship between weight-loss $( Y )$ and months in program $\left( X _ { 1 } \right)$ depends on session time.

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