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# Regression Analysis & Hypothesis Testing

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7. A taxicab company manager believes that the monthly repair costs (y) of cabs are related to age (x) of the cabs. Eight cabs are selected randomly and from their records we obtained the following data:

ï" x =134, ï" y = 410, ï" x2 =3 020, ï"y2=24000, and ï" xy =8340.

Estimate the linear regression line.

8. Using the data given in the taxicab company problem (the above problem) compute R2, interpret its meaning.

9. You are interested in comparing four methods of teaching. You randomly assign 20 students to each of the four methods and then administer a standardized test at the end of the study.

What null hypotheses are you interested in testing?
What statistical procedure might you use to test the hypothesis?

11. Suppose you are interested in determining the average number of years that employees of a company stay with the company. If past information shows a standard deviation of 7 months, what size sample should be taken so that at 95% confidence the sampling error will be 2 months or less?

12. We are interested in determining whether or not the variances of the sales at two small grocery stores are equal. A sample of 16 days of sales at each store indicated the following:

Store A Store B
n1 = 16 n2 = 16
Mean 1 = 300 Mean 2 = 310
S1 = \$12 S2 = \$10

Are the variances of the populations (from which these samples came) equal? Use
? =0.05

https://brainmass.com/math/interpolation-extrapolation-and-regression/regression-analysis-hypothesis-testing-412813

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis, regression analysis and sample size. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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## Multiple Regression Analysis and Hypothesis Test

The Excel file contains this data on weekly gross revenues, television advertising expenditures, and newspaper advertising expenditures for Showtime Movie Theaters, all measured in thousands of dollars.

96 5.0 1.5
90 2.0 2.0
95 4.0 1.5
92 2.5 2.5
95 3.0 3.3
94 3.5 2.3
94 2.5 4.2
94 3.0 2.5

a. Find an estimated regression equation relating weekly gross revenue to television expenditures and newspaper advertising expenditures.

b. Using a conservative measure that compensates for the number of independent variables in the model, comment on the goodness of fit. How much variability is accounted for in this regression model?

c. Does an overall test of significance say that the model is valid?

d. What is the outcome of individual t-tests for significance on the two independent variables?

e. Estimate gross revenues for Showtime given outlays of 4.5K\$ for TV and 1.7K\$ for newspaper advertising.

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