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:

Latent Learning

The process by which something is learned but not immediately manifested in an observable change in behavior.

Observational Learning

The process of learning behaviors by watching and imitating others, as proposed by Bandura's social learning theory.

Learned Helplessness

A situation where someone feels unable to control their life, due to a traumatic incident or repeated failures.

Contingency Blocking

A phenomenon in classical conditioning where a previously learned association prevents the acquisition of a new association because the first stimulus is a better predictor of the outcome.