SCENARIO 13-11
a Weight-Loss Clinic Wants to Use Regression Analysis $$Y = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \beta _ { 3 } X _ { 1 } X _ { 2 } + \varepsilon$$

question 5

Multiple Choice

SCENARIO 13-11
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)
X2 = 1 if morning session, 0 if not
Data for 25 clients on a weight-loss program at the clinic were collected and used to fit the interaction
model: $$Y = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \beta _ { 3 } X _ { 1 } X _ { 2 } + \varepsilon$$ Output from Microsoft Excel follows: $\begin{array}{lr}{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7308 \\\text { R Square } & 0.5341 \\\text { Adjusted R Square } & 0.4675 \\\text { Standard Error } & 43.3275 \\\text { Observations } & 25\\\hline\end{array}$

$\text { ANOVA }$
$\begin{array}{lrrrrr}\hline&\text { df } & \text { SS }&M S &F & \text { Significance } F\\\hline\text { Regression } & 3 & 45194.0661 & 15064.6887 & 8.0248 & 0.0009 \\\text { Residual } & 21 & 39422.6542 & 1877.2692 & & \\\text { Total } & 24 & 84616.7203 & &\\\hline \end{array}$


$\begin{array}{lrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } &{\text { t Stat }} & \text { P-value } & \text { Lower 99\% } & \text { Upper 99\% } \\\hline \text { Intercept } & -20.7298 & 22.3710 & -0.9266 & 0.3646 & -84.0702 & 42.6106 \\\text { Length } & 7.2472 & 1.4992 & 4.8340 & 0.0001 & 3.0024 & 11.4919 \\\text { Morn } & 90.1981 & 40.2336 & 2.2419 & 0.0359 & -23.7176 & 204.1138 \\\text { Length x Morn } & -5.1024 & 3.3511 & -1.5226 & 0.1428 & -14.5905 & 4.3857 \\\hline\end{array}$

-Referring to SCENARIO 13-11, what null hypothesis would you test to determine whether the slope of the linear relationship between weight loss (Y) and time on the program (X1) varies according to time of session?

• A)\(H _ { 0 } : \beta _ { 1 } = 0\)
• B)\(H _ { 0 } : \beta _ { 2 } = 0\)
• C)\(H _ { 0 } : \beta _ { 3 } = 0\)
• D)\(H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = 0\)

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Definitions:

Attributional Styles

The way in which individuals explain the causes of events and behaviors, typically as internal or external to themselves.

Relationship-Enhancing

Activities or behaviors aimed at improving the quality and satisfaction of a personal relationship.

Internal Attributions

The process of explaining one's own behavior or the behavior of others based on internal characteristics or dispositions.

External Attributions

The process of attributing someone's behavior to external factors, such as the situation or environment.