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:

Personality Traits

Enduring characteristics that describe an individual's behavior, such as extroversion, agreeableness, and conscientiousness.

Individualism

A theory that champions the importance of individuals' right to act freely rather than being under collective or governmental restraint.

Social Framework

The structure of societal norms, beliefs, and values that shape individuals' interactions and behaviors within a community.

Inherited Characteristics

are traits or qualities passed down from parents to offspring through genes.