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

question 246

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 morning session.

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

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Definitions:

Low-Mach Personality

An individual who shows low manipulativeness, tends to be direct and honest, and prefers not to manipulate others for personal gain.

Exploitative

Utilizing someone or something unfairly for one's own advantage, often without regard for the welfare of the other party.

Personality Differences

The variations among individuals' behavioral traits, emotional responses, and thought processes, which can impact their interactions and performance in various settings.

Authoritarian Personality

A personality type characterized by adherence to strict obedience and control over others, often without consideration for their opinions or feelings.