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# Linear Regression and Correlation

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Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales (\$ thousands) last month for each client sampled.

Linear Regression and Correlation

Number of Sales Number of Sales
Contacts, (\$ thousands), Contacts, (\$ thousands),
X Y X Y

14 24 23 30
12 14 48 90
20 28 50 85
16 30 55 120
46 80 50 110

a. Determine the regression equation.
b. Determine the estimated sales if 40 contacts are made.
c. Determine the standard error of estimate.
d. Suppose a large sample is selected (instead of just 10). About 95 percent of the predictions regarding sales would occur between what two values?

The following table lists the annual amounts of glass cullet produced by Kimble Glass
Works, Inc.

Scrap Code Tons
Year
1999 1 2.0
2000 2 4.0
2001 3 3.0
2002 4 5.0
2003 5 6.0

Determine the least squares trend equation. Estimate the amount of scrap for the year
2005.

Victor Anderson, the owner of Anderson Belts, Inc., is studying absenteeism among his employees. His workforce is small, consisting of only five employees. For the last three years he recorded the following number of employee absences, in days, for each quarter.

Quarter
Year I I III IV
2001 4 10 7 3
2002 5 12 9 4
2003 6 16 12 4

Determine a typical seasonal index for each of the four quarters.

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