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)\(H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = 0\)

---

Definitions:

CT Scan

A medical imaging technique using computer-processed combinations of many X-ray measurements taken from different angles to produce cross-sectional images of specific areas of a scanned object.

Cross-Sectional View

A type of representation or diagram that shows a cut-through portion of an object, revealing its internal structure.

Rotate

The act or process of moving or turning around a central point or axis, often applied in various scientific and practical contexts.

X-Ray Camera

A specialized device designed to capture images using X-rays, allowing for the visualization of internal structures within the body.