Category:
Mathematics

Question 1

Shown below are rental and leasing revenue figures for office machinery and equipment in the United States over a 7-year period according to the U.S. Census Bureau. Use these data and the regression tool in the data analysis tool pack to run a linear regression.

Based on the formula you get from the regression output, answer the following questions:

a) What is the forecast for the rental and leasing revenue for the year

2011?

b) How confident are you in this forecast? Explain your answer by citing the relevant metrics.

Year Rental and Leasing (millions)

2004 5,860

2005 6,632

2006 7,125

2007 6,000

2008 4,380

2009 3,326

2010 2,642

Question 2

Suppose a researcher gathered survey data from 19 employees and asked the employees to rate their job satisfaction on a scale from 0 to 100 (with 100 being perfectly satisfied). Suppose the following data represent the results of this survey. Assume that relationship with supervisor is rated on a scale from 0 to 50 (0 represents

a poor relationship and 50 represents an excellent relationship);overall quality of the work environment is rated on a scale from 0 to 100 (0 represents poor work environment and 100 rep resents an excellent work environment);and opportunities for advancement is rated on a scale from 0 to 50 (0 represents no opportunities and 50 represents excellent opportunities).Answer the following questions:

A) What is the regression formula?

B) How reliable do you think the estimates will be based on this formula? Explain your answer by citing the relevant metrics.

C) Are there any variables that do not appear to be good predictors of job satisfaction?

How can you tell?

D) If a new employee reports that her relationship with her supervisor is 40, rates her

opportunities for advancement to be at 30, finds the quality of the

work environment to be at 75,and works 60 hours per week, what wouldyou

expect her job satisfaction score to be?

Job Satisfaction Relationship with Supervisor Opportunities for advancement Overall quality of work environment Total hours worked per week

55 27 65 50 42

20 12 13 60 28

85 40 79 45 7

65 35 53 65 48

45 29 43 40 32

70 42 62 50 41

35 22 18 75 18

60 34 75 40 32

95 50 84 45 48

65 33 68 60 11

85 40 72 55 33

10 5 10 50 21

75 37 64 45 42

80 42 82 40 46

50 31 46 60 48

90 47 95 55 30

75 36 82 70 39

45 20 42 40 22

65 32 73 55 21

Question 3

Investment analysts generally believe the interest rate on bonds is inversely related to the prime interest rate for loans; that is, bonds perform well when lending rates are down and perform poorly when interest rates are up.

Use the following data to construct a scatter graph and then fit a regression line to the data. Report the regression formula and the r-squared values from the chart (right click on the data points, select Add Trend line, and select options to show these metrics).

Do you think the bond rate can be predicted by the prime interest rate? Justify your answer using the relevant metrics.

Bond Rate Prime Interest Rate

5% 16%

12 6

9 8

15 4

7 7