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- From: Mathematics, Statistics and Probability
- Posted on: Sat 23 Jan, 2016
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Question 1
Shown below are rental and leasing revenue figures for office machinery and equipment in the United States over a seven-year period according to the U.S. Census Bureau. Use these data to run a linear regression and then forecast the rental and leasing revenue for the year 2012.
Year (x) Rental and Leasing ($ millions) (y)
2004 5860
2005 6632
2006 7125
2007 6000
2008 4380
2009 3326
2010 2642
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 satis?ed). 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 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? How can you tell?
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, finds the quality of the work environment to be scored at 75, works 60 hours per week and rates her opportunities for advancement to be at 30, what would you expect her job satisfaction score to be?
JOB SATISFACTION (y) RELATIONSHIP WITH SUPERVISOR (x1) OVERALL QUALITY OF WORK ENVIRONMENT (x2) TOTAL HOURS WORKED PER-WEEK (x3) OPPORTUNITIES FOR ADVANCEMENT (x4)
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 12
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. Can the bond rate be predicted by the prime interest rate? 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 value from the chart (right click on the line, select “Add Trendline” and select options to show these metrics).
Prime Interest Rate (x) Bond Rate (y)
16 5
6 12
8 9
4 15
7 7
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