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 36

Short Answer

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: $$\begin{array}{l}\begin{array} { l r } \hline \text { Multiple R } & 0.7308 \\\text { R Square } & 0.5341 \\\text { Adjusted R Square } & 0.4675 \\\text { Standard Error } & 43.3275 \\\text { Observations } & 25\\\hline\end{array}\\\text { ANOVA }\\\begin{array} { l r r l l r } \hline & d f & & { \text { SS } } & { \text { MS } } & \text { Significance } F \\\hline \text { Regression } & 3 & 45194.0661 & 15064.6887 & 8.0248 & 0.0009 \\\text { Residual } & 21 & 39422.6542 & 1877.2692 & & \\\text { Total } & 24 & 84616.7203 & &\\\hline\end{array}\\\\\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 99\% } & \text { Upper 99\% } \\\hline\text { Intercept } & -20.7298 & 22.3710 & -0.9266 & 0.3646 & -84.0702 & 42.6106 \\\text { Length } & 7.2472 & 1.4992 & 4.8340 & 0.0001 & 3.0024 & 11.4919 \\\text { Morn } & 90.1981 & 40.2336 & 2.2419 & 0.0359 & -23.7176 & 204.1138 \\\text { Length x Morn } & -5.1024 & 3.3511 & -1.5226 & 0.1428 & -14.5905&4.3857\\\hline\end{array}\end{array}$$
-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:

Operant Conditioning

A method of learning that occurs through rewards and punishments for behavior.

Deviant People

Individuals who significantly deviate from societal norms in behavior, beliefs, or attitudes, often leading to social disapproval.

Modeling

A behavior modification technique that involves observing the behavior of others (the models) and participating with them in performing the desired behavior.

Vicariously

Experiencing something indirectly or through another person's experience, often used in the context of learning or emotional experiences.