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

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 afternoon session.

A) $\beta_{1}+\beta_{5}$
B) $\beta_{4}+\beta_{5}$
C) $\beta_{1}+\beta_{4}$
D) $\beta_{1}$