The Owner of a Large Chain of Health Spas Has

question 9

Essay

The owner of a large chain of health spas has selected eight of her smaller clubs for a test in which she varies the size of the newspaper ad , and the amount of the initiation fee discount to see how this might affect the number of prospective members who visit each club during the following week. The results are shown in the table below: The results of a multiple regression analysis are below.
-(A) Determine the least-squares multiple regression equation.
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(B) Interpret the Y-intercept of the regression equation.
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(C) Interpret the partial regression coefficients.
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(D) What is the estimated number of new visitors to a club if the size of the ad is 6 column-inches and a $100 discount is offered?
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(E) Determine the approximate 95% prediction interval for the number of new visitors to a given club when the ad is 5 column-inches and the discount is $80.
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(F) What is the value for the percentage of variation explained, and exactly what does it indicate?
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(G) At the 0.05 level, is the overall regression equation in (A) significant?
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(H) Use the 0.05 level in concluding whether each partial regression coefficient differs significantly from zero.
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(I Interpret the results of the preceding tests in (H) and (I) in the context of the two explanatory variables described in the problem.
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(J) Construct a 95% confidence interval for each partial regression coefficient in the population regression equation.

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Definitions:

Spiral Pattern

A motif or structure that coils in a continuous and gradually widening curve around a central point.

Transtheoretical Model

A model of behavior change that assesses an individual's readiness to act on a new healthier behavior and provides strategies to guide the individual through the stages of change.

Pretreatment Stage

The initial phase in therapy where assessment and evaluation of the client's needs and goals are conducted.

Stages-Of-Change

A model in psychology that maps out the phases individuals undergo when changing behavior, including precontemplation, contemplation, preparation, action, and maintenance.