Chapter 12

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  • Topic: Regression analysis, Least squares, Linear least squares
  • Pages : 4 (672 words )
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  • Published : December 13, 2011
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Chapter 12 & 13

1. A sales manager collected the following data on salespersons’ annual sales and years of experience.

Years of Annual Sales
Salesperson Experience ($1000s)

1 1 80
2 3 97
3 4 92
4 4 102
5 6 103
6 8 111
7 10 119
8 10 123
9 11 117
10 13 136

a.Develop a scatter diagram for these data with years of experience as the independent variable.
b.Develop an estimated regression equation that can be used to predict annual sales given the years of experience. c.Use the estimated regression equation to predict annual sales for a salesperson with nine years of experience.

2. Diane's Beauty Salon is currently hiring beauticians at its new location in a popular mall. Diane wants to know what commission percentage to pay the beauticians based on experience. A survey of 12 licensed beauticians was taken with the following results.

Commission Years of Commission Years of Percentage (y) Experience (x) Percentage (y) Experience (x)
24 2 25 4
18 1 44 12
30 5 33 8
41 10 24 3
35 8 20 1
35 7 40 10

a.Find the least squares line equation.
b.What percentage of the variation in commission percentage is explained by the variation in years of experience? c.Interpret the coefficient value for years of experience in the least squares equation. d.Estimate the commission percentage for a beautician with 6 years of experience.

3. Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance con- tract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars).

Weekly MachineUsage (hours)|Annual MaintenanceExpense ($100s)| ||
13|17.0|
10|22.0|
20|30.0|
28|37.0|
32|47.0|...
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