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? .
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| 17|30. 5| 24|32. 5| 31|39. 0| 40|51. 5| 38|40. 0| a. Develop a scatter diagram for these data with weekly machine usage as the independent variable. b. Develop the estimated regression equation that relates annual maintenance expense to weekly machine usage. c. Interpret the x coefficient value in the estimated regression equation. d. Jensen expects to use the new machine 30 hours per week. If the maintenance contract costs $3000 per year, would ou recommend purchasing it? Why or why not? 4. Data on advertising expenditure and revenue (in thousands of dollars) for the Four Sea- sons Restaurant follow. Advertising Expenditure|Revenue| || 1|19| 2|32| 4|44| 6|40| 10|52| 14|53| 20|54| a. Develop a scatter diagram for these data with advertising expenditure as the independent variable. b. Develop an estimated regression equation that can be used to predict revenue given the advertising expenditure. c. Use the estimated regression equation to predict revenue when the advertising expenditure is $8,000. . A statistics professor investigated some of the factors that affect an individual student’s final grade in his course. She proposed a multiple regression model, where y is the final grade (out of 100), x1 is the number of lectures skipped, x2 is the number of late assignments, and x3 is the mid-term test grade (out of 100). The professor recorded the data for 50 randomly selected students. The regression equation is: y = 41. 6 – 3. 18×1 – 1. 17×2 + 0. 63×3 Interpret the coefficient values for x1 , x2 , and x3 6.
A statistician wanted to determine if the demographic variables of age, education, and income influence the number of hours of television watched per week. A random sample of 25 adults was selected to estimate the multiple regression model, where y is the number of hours of television watched last week, x1 is the age (in years), x2 is the number of years of education, and x3 is income (in $1,000). The regression equation is: y = 22. 3 + 0. 41×1 – 0. 29×2 – 0. 12×3 Interpret the coefficient values for x1 , x2 , and x3