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

question 7

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

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

Circular Thickness

The width measured along the circumference of an object, often relevant in gears or circular parts.

Pitch Diameter

The effective diameter of a screw thread, halfway between the major and minor diameters, crucial for thread engagement and measurement.

Diametral Pitch

The ratio of the number of teeth to the pitch diameter of a gear, indicating how densely the teeth are packed.

Chordal Thickness

A measurement of the thickness of an object at the midpoint of a chord, often used in reference to circular objects to specify a specific section's thickness.