TABLE 14-12
a Weight-Loss Clinic Wants to Use Regression $Y=\beta_{0}+\beta_{1} X_{1}+\beta_{2} X_{2}+\beta_{3} X_{3}+\beta_{4} X_{1} X_{2}+\beta_{5} X_{1} X_{3}+\varepsilon$

question 216

Multiple Choice

TABLE 14-12
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)
X}2 ^{= 1 if morning session, 0 if not
X}3 ^{= 1 if afternoon session, 0 if not (Base level = evening session)}
Data for 12 clients on a weight- loss program at the clinic were collected and used to fit the interaction model:
$Y=\beta_{0}+\beta_{1} X_{1}+\beta_{2} X_{2}+\beta_{3} X_{3}+\beta_{4} X_{1} X_{2}+\beta_{5} X_{1} X_{3}+\varepsilon$

Partial output from Microsoft Excel follows:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.73514 \\\text { R Square } & 0.540438 \\\text { Adjusted R Square } & 0.157469 \\\text { Standard Error } & 12.4147 \\\text { Observations } & 12 \\\hline\end{array}\end{array}$$

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

$\begin{array}{lcccr}\hline & \text {Coefficients }& \text { Standard Error }& \text { t Stat }& \text { p -value} \\\hline \text {Intercept }& 0.089744 & 14.127 & 0.0060 & 0.9951 \\ \text {Length (X1) }& 6.22538 & 2.43473 & 2.54956 & 0.0479 \\ \text {Morn Ses (X2) }& 2.217272 & 22.1416 & 0.100141 & 0.9235 \\ \text {Aft Ses (X3) } & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\ \text {Length*Morn Ses} & 0.77058 & 3.562 & 0.216334 & 0.8359 \\ \text {Length * Aft Ses} & -0.54147 & 3.35988 & -0.161158 & 0.8773 \\\hline\end{array}$

-Referring to Table 14-12, in terms of the þ's in the model, give the average change in weight-loss (Y) for every 1 month increase in time in the program (X1) when attending the morning session.

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Definitions:

Sleeping

A natural periodic state of rest for the mind and body, characterized by altered consciousness and reduced interactions with surroundings.

Dreaming

The experience of envisioned images, sounds, or other sensations during sleep.

Brain Imaging Technology

Techniques and tools used to visualize the structure or function of the brain, such as MRI or CT scans.

Variability

Variability refers to the extent to which data points in a statistical distribution or set differ from each other and from the mean of the set, indicating the spread or dispersion of the dataset.