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# Regression Analysis

A 1998 article in Fortune magazine entitled " The 100 Best Companies to Work for in America" (January 12, 1998) contained data on the 100 companies. These data are included in the data file called Best-Companies ( attached). Two variables of interest are the revenues of the company and the number of hours of training per year per employee. (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 the company is to be used to predict the number of hours of training per year per employee.

b) Synovus Financial had 902 million dollars in revenue in a recent year. If it were to increase its revenue by 10% what change would you expect to see in the number of hours of training per year per employee?

c) Would you feel comfortable using the revenue of one of the 100 companies to determine the number of hours of training per year per employee with a simple linear regression model? Conduct a statistical procedure to answer this question.

d) Synovus has 8,827 employees. Using a new regression model with number of US employees as the independent variable, predict the number of hours of training per year per employee for Synovus.

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

f) Referring to part e, 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 part d and discuss why the widths of the two are different.

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

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

#### Solution Summary

A 1998 article in Fortune magazine entitled " The 100 Best Companies to Work for in America" (January 12, 1998) contained data on the 100 companies. These data are included in the data file called Best-Companies ( attached). Two variables of interest are the revenues of the company and the number of hours of training per year per employee. (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 the company is to be used to predict the number of hours of training per year per employee.

b) Synovus Financial had 902 million dollars in revenue in a recent year. If it were to increase its revenue by 10% what change would you expect to see in the number of hours of training per year per employee?

c) Would you feel comfortable using the revenue of one of the 100 companies to determine the number of hours of training per year per employee with a simple linear regression model? Conduct a statistical procedure to answer this question.

d) Synovus has 8,827 employees. Using a new regression model with number of US employees as the independent variable, predict the number of hours of training per year per employee for Synovus.

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

f) Referring to part e, 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 part d and discuss why the widths of the two are different.

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

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

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