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

question 182

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:
$$\begin{array}{l}\text { Regression Statistics }\\\begin{array} { l c } \hline \text { Multiple R } & 0.73514 \\\text { R Square } & 0.540438 \\\text { Adjusted R Square } & 0.157469 \\\text { Standard Error } & 12.4147 \\\text { Observations } & 12\end{array}\end{array}$$ 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, what null hypothesis would you test to determine whether the slope of the linear relationship between weight-loss (Y) and time in the program (X1) varies according to time of session?

Grasp the concept of concrete operational thinking and its applications in problem solving.

Understand the structure and assumptions behind intelligence testing, including historical applications and implications.

Identify methods used in psychological research and the interpretation of study results.

Recognize key factors in cognitive development, including metacognition, memory, and intelligence theory.

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