Instruction 13-9
a Weight-Loss Clinic Wants to Use Regression Analysis

question 157

Multiple Choice

Instruction 13-9
A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in kilograms) .Two variables thought to effect 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 kilograms)
X₁ = Length of time in weight-loss program (in months)
X₂ = 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
Partial output from Microsoft Excel follows:
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.73514 \\ \text { R Square } & 0.540438 \\ \text { Adjusted R Square } & 0.157469 \\ \text { Standard Error } & 12.4147 \\ \text { Observations } & 12 \end{array}$
ANOVA
$\begin{array} { c c c c c } F = 5.41118 & \text { Significance } F = 0.040201 & & \\ & & & & \\ \text { Intercept } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\ \text { Length } \left( X _ { 1 } \right) & 0.089744 & 14.127 & 0.0060 & 0.9951 \\ \text { Morn Ses } \left( X _ { 2 } \right) & 6.22538 & 2.43473 & 2.54956 & 0.0479 \\ \text { Aft Ses } \left( X _ { 3 } \right) & 2.217272 & 22.1416 & 0.100141 & 0.9235 \\ \text { Length*Morn Ses } & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\ \text { Length*Aft Ses } & 0.77058 & 3.562 & 0.216334 & 0.8359 \\ & - 0.54147 & 3.35988 & - 0.161158 & 0.8773 \end{array}$
-Referring to Instruction 13-9,in terms of the ?'s in the model,give the mean change in weight-loss (Y) for every 1 month increase in time in the program (X₁) when attending the afternoon session.

• A)?₁ + ?₄
• B)?₁ + ?₅
• C)?₁
• D)?₄ + ?₅

---

Definitions:

Proxy Euthanasia

The act of making a decision to end another person’s life to relieve them from incurable diseases or intolerable suffering, usually when the individual is incapable of making the decision themselves due to medical conditions.

Passive Euthanasia

The withholding or withdrawal of life-sustaining treatments, allowing a patient to die naturally, often in cases of terminal illness.

Deep Depression

A severe form of depression characterized by intense feelings of sadness, hopelessness, and a lack of interest or pleasure in activities.

Passive Euthanasia

The act of allowing a person to die by withholding or withdrawing medical interventions, such as life support, without taking direct action to cause death.