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# Linear Regression and Correlation Analysis

A 1998 article in Fortune magazine titled the 100 Best Companies to Workd for in America (January 12, 1998) contained data on the 100 companies. Three variabled of interest are the revenues of each company, the number of hours of training per year per employee and the number of employees. (Note you will need to omit companies with data marked N.A. before completing the analysis).

a. Compute the linear regression equation based on the sample data if the revenue of each company is to be used to predict the number of hours of training per year per employee.

b. Would you feel comfotable using the revenue of one of the 100 companies to determine the number of hours of traning per year per employee with a simple linear gregreesion model? Conduct a statistical procedure to answer this question.

c. Synovus Financial has 8,827 employees. Predict the number of hours of trainging per year employee for Synovus

d. Referring to part c, develop and interpret a 90% prediction interval for the average training hours per employee for companies with 8,827 employees.

e. Referring to part d, what is the 90% confidence interval for average training hours per employee for companies with 40,000 employees? Compare this interval with the one computed in pard d and discuss why the widths of the two are different.

f. Referring to parts d and e, at what number of employees would the width of a 90% prediction interval for average training hours be minimized?

g. Referring to parts d and e, develop and interpret a 90% prediction interval for the actual training hours per employee for Synovus.

#### Solution Preview

A 1998 article in Fortune magazine titled the 100 Best Companies to Workd for in America (January 12, 1998) contained data on the 100 companies. Three variabled of interest are the revenues of each company, the number of hours of training per year per employee and the number of employees. (Note you will need to omit companies with data marked N.A. before completing the analysis)

a. compute the linear regression equation based on the sample data if the revenue of each company is to be used to predict the number of hours of training per year per employee.

The linear regression equation is (training hours) = 39.812 - 0.0001(revenue).

b. Would you feel comfotable using the revenue of one of the 100 companies to determine the number of hours of traning per year per employee with a simple linear gregreesion model? Conduct a statistical procedure to answer this question.

No, I would not be comfortable using the revenue to predict the number of training hours. The slope of the regression line is very close to 0, ...

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