TABLE 14-11 A Weight-Loss Clinic Wants to Use Regression Analysis to Build

question 348

Multiple Choice

TABLE 14-11
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
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 + β₅X₁X₂ + ε
Partial output from Microsoft Excel follows:

-Referring to Table 14-11, what null hypothesis would you test to determine whether the slope of the linear relationship between weight-loss (Y) and time in the program (X₁) varies according to time of session?

• A) H₀: β₁ = β₂ = β₃ = β₄ = β₅ = 0
• B) H₀: β₂ = β₃ = β₄ = β₅ = 0
• C) H₀: β₄ = β₅ = 0
• D) H₀: β₂ = β₃ = 0

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Definitions:

Collectively Exhaustive

A condition in which all possible outcomes or events are considered or covered in a scenario or experiment.

Mutually Exclusive

Events that cannot occur at the same time, meaning the occurrence of one event excludes the occurrence of another.

Probability

A measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Random Experiment

A process or action that leads to different outcomes, often uncertain and subject to chance.