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

question 162

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, which of the following statements is supported by the analysis shown?

• A) There is sufficient evidence (at α = 0.05) of curvature in the relationship between weight-loss (
• Y) and months in program(X₁).
• B) There is sufficient evidence (at α = 0.05) to indicate that the relationship between weight-loss (
• Y) and months in program (X₁) depends on session time.
• C) There is sufficient evidence (at α = 0.10) to indicate that the session time (morning, afternoon, evening) affects weight-loss (
• Y).
• D) There is insufficient evidence (at α = 0.10) to indicate that the relationship between weight-loss (
• Y) and months in program(X₁) depends on session time.

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Definitions:

2-Methylpropane

An alkane with the chemical formula C4H10, also known as isobutane, characterized by a branched structure.

Conformers

Different spatial arrangements of atoms in a molecule that can be converted into one another by rotation around single bonds.

Butane

A gaseous hydrocarbon with the formula C4H10, existing in two isomeric forms and used as a fuel and a refrigerant.

Torsional Strain

A type of strain in molecules that occurs when atoms in a molecule are placed such that they cause repulsion by being in close proximity, often linked to bond angles and rotation around bonds.