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

question 144

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,what is the experimental unit for this analysis?

• A)A client on a weight-loss program.
• B)A month.
• C)A morning,afternoon,or evening session.
• D)A clinic.

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Definitions:

Mutualistic

A type of symbiotic relationship between two different species in which each benefits from the other.

Mycorrhizal Fungus

Fungi that form beneficial symbiotic relationships with the roots of plants, improving water and nutrient absorption for the plant and receiving carbohydrates in return.

Plant Root

The part of a plant that typically lies below the surface of the soil and functions in anchorage, water and nutrient absorption, and sometimes in storage.

Club Fungi

A group of fungi characterized by the production of spores on club-shaped structures called basidia.