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TABLE 14-12
a Weight-Loss Clinic Wants to Use Y=β0+β1X1+β2X2+β3X3+β4X1X2+β5X1X3+ε 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 87

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
X3 = 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=β0+β1X1+β2X2+β3X3+β4X1X2+β5X1X3+ε 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:
 Regression Statistics  Multiple R 0.73514 R Square 0.540438 Adjusted R Square 0.157469 Standard Error 12.4147 Observations 12\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 Significance F=0.040201F = 5.41118 \quad\text { Significance } F = 0.040201

Coefficients  Standard Error  t Stat  p -valueIntercept 0.08974414.1270.00600.9951Length (X1) 6.225382.434732.549560.0479Morn Ses (X2) 2.21727222.14160.1001410.9235Aft Ses (X3) 11.82333.15453.5589010.0165Length*Morn Ses0.770583.5620.2163340.8359Length * Aft Ses0.541473.359880.1611580.8773\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, which of the following statements is supported by the analysis shown?

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Definitions:

Price Stability

An economic objective aiming to maintain a steady rate of inflation, allowing for predictable planning and investing.

Interest Inelastic

A situation where the demand for or the supply of a good or service does not significantly change in response to changes in interest rates.

Reverend Thomas Malthus

An 18th-century economist known for his theory on population growth, suggesting that population increases geometrically, whereas food supply increases arithmetically, leading to inevitable shortages.

Population Growth

The increase in the number of individuals in a population, commonly expressed as an annual percentage.

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