### Solutions Essentials of Modern Business Statistics with Microsoft Office Excel - 7th Edition - Chapter 15

15.1 The estimated regression equation for a model involving two independent variables and 10 observations follows....
a. Interpret b1 and b2 in this estimated regression equation.
b. Predict y when x1 = 180 and x2 = 310.

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15.2 Consider the following data for a dependent variable y and two independent variables, x1 and x2....
a. Develop an estimated regression equation relating y to x1. Predict y if x1 = 45.
b. Develop an estimated regression equation relating y to x2. Predict y if x2 = 15.
c. Develop an estimated regression equation relating y to x1 and x2. Predict y if x1 = 45 and x2 = 15.

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15.3 In a regression analysis involving 30 observations, the following estimated regression equation was obtained....
a. Interpret b1, b2, b3, and b4 in this estimated regression equation.
b. Predict y when x1 = 10, x2 = 5, x3 = 1, and x4 = 2.

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15.4 A shoe store developed the following estimated regression equation relating sales to inventory investment and advertising expenditures....wherex1 = inventory investment (\$1000s)x2 = advertising expenditures (\$1000s)y = sales (\$1000s)
a. Predict the sales resulting from a \$15,000 investment in inventory and an advertising budget of \$10,000.
b. Interpret b1 and b2 in this estimated regression equation.

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15.5 The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow....
a. Develop an estimated regression equation with the amount of television advertising as the independent variable.
b. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables.
c. Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)? Interpret the coefficient in each case.
d. Predict weekly gross revenue for a week when \$3500 is spent on television advertising and \$1800 is spent on newspaper advertising?

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15.6 The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 NFL teams for the 2011 season (NFL website, February 12, 2012)....
a. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt.
b. Develop the estimated regression equation that could be used to predict the percentage of games won given the number of interceptions thrown per attempt.
c. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt and the number of interceptions thrown per attempt.
d. The average number of passing yards per attempt for the Kansas City Chiefs was 6.2 and the number of interceptions thrown per attempt was .036. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. (Note: For the 2011 season the Kansas City Chiefs’ record was 7 wins and 9 losses.) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs.

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15.7
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15.8 The Condé Nast Traveler Gold List for 2012 provided ratings for the top 20 small cruise ships (Condé Nast Traveler website, March 1, 2012). The following data are the scores each ship received based upon the results from Condé Nast Traveler’s annual Readers’ Choice Survey. Each score represents the percentage of respondents who rated a ship as excellent or very good on several criteria, including Shore Excursions and Food/Dining. An overall score was also reported and used to rank the ships. The highest ranked ship, the Seabourn Odyssey, has an overall score of 94.4, the highest component of which is 97.8 for Food/Dining....
a. Determine an estimated regression equation that can be used to predict the overall score given the score for Shore Excursions.
b. Consider the addition of the independent variable Food/Dining. Develop the estimated regression equation that can be used to predict the overall score given the scores for Shore Excursions and Food/Dining.
c. Predict the overall score for a cruise ship with a Shore Excursions score of 80 and a Food/Dining Score of 90.

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15.9 The Professional Golfers Association (PGA) maintains data on performance and earnings for members of the PGA Tour. For the 2012 season Bubba Watson led all players in total driving distance, with an average of 309.2 yards per drive. Some of the factors thought to influence driving distance are club head speed, ball speed, and launch angle. For the 2012 season Bubba Watson had an average club head speed of 124.69 miles per hour, an average ball speed of 184.98 miles per hour, and an average launch angle of 8.79 degrees. The WEBfile named PGADrivingDist contains data on total driving distance and the factors related to driving distance for 190 members of the PGA Tour (PGA Tour website, November 1, 2012). Descriptions for the variables in the data set follow.
Club Head Speed: Speed at which the club impacts the ball (mph)Ball Speed: Peak speed of the golf ball at launch (mph)Launch Angle: Vertical launch angle of the ball immediately after leaving the club (degrees)Total Distance: The average number of yards per drive
a. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the club head speed.
b. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the ball speed.
c. A recommendation has been made to develop an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive. Do you agree with this? Explain.
d. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the ball speed and the launch angle.
e. Suppose a new member of the PGA Tour for 2013 has a ball speed of 170 miles per hour and a launch angle of 11 degrees. Use the estimated regression equation in part (d) to predict the average number of yards per drive for this player.

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15.10 Major League Baseball (MLB) consists of teams that play in the American League and the National League. MLB collects a wide variety of team and player statistics. Some of the statistics often used to evaluate pitching performance are as follows: ERA: The average number of earned runs given up by the pitcher per nine innings. An earned run is any run that the opponent scores off a particular pitcher except for runs scored as a result of erroros or passed balls. SO/IP: The average number of strikeouts per inning pitched. HR/IP: The average number of home runs per inning pitched. R/IP: The number of runs given up per inning pitched.The following data show values for these statistics for a random sample of 20 pitchers from the American League for the 2011 season (MLB website, March 1, 2012)....
a. Develop an estimated regression equation that can be used to predict the average number of runs given up per inning given the average number of strikeouts per inning pitched.
b. Develop an estimated regression equation that can be used to predict the average number of runs given up per inning given the average number of home runs per inning pitched.
c. Develop an estimated regression equation that can be used to predict the average number of runs given up per inning given the average number of strikeouts per inning pitched and the average number of home runs per inning pitched.
d. A. J. Burnett, a pitcher for the New York Yankees, had an average number of strikeouts per inning pitched of .91 and an average number of home runs per inning of .16. Use the estimated regression equation developed in part (c) to predict the average number of runs given up per inning for A. J. Burnett. (Note: The actual value for R/IP was .6.)
e. Suppose a suggestion was made to also use the earned run average as another independent variable in part (c). What do you think of this suggestion?

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15.11 In exercise 1, the following estimated regression equation based on 10 observations was presented....The values of SST and SSR are 6724.125 and 6216.375, respectively.
a. Find SSE.
b. Compute R2.
c. Compute ....
d. Comment on the goodness of fit.

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15.12 In exercise 2, 10 observations were provided for a dependent variable y and two independent variables x1 and x2; for these data SST 5 = 15,182.9 and SSR = 14,052.2.
a. Compute R2.
b. Compute ...
c. Does the estimated regression equation explain a large amount of the variability in the data? Explain.

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15.13 In exercise 3, the following estimated regression equation based on 30 observations was presented....The values of SST and SSR are 1805 and 1760, respectively.
a. Compute R2.
b. Compute ...
c. Comment on the goodness of fit.

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15.14 In exercise 4, the following estimated regression equation relating sales to inventory investment and advertising expenditures was given....The data used to develop the model came from a survey of 10 stores; for those data, SST = 16,000 and SSR = 12,000.
a. For the estimated regression equation given, compute R2.
b. Compute ....
c. Does the model appear to explain a large amount of variability in the data? Explain.

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15.15 In exercise 5, the owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1) and newspaper advertising (x2). The estimated regression equation was...The computer solution provided SST = 25.5 and SSR = 23.435.
a. Compute and interpret R2 and ....
b. When television advertising was the only independent variable, R2 = .653 and ... = .595. Do you prefer the multiple regression results? Explain.

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15.16 In exercise 6, data were given on the average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 National Football League (NFL) teams for the 2011 season (NFL website, February 12, 2012).
a. Did the estimated regression equation that uses only the average number of passing yards per attempt as the independent variable to predict the percentage of games won provide a good fit?
b. Discuss the benefit of using both the average number of passing yards per attempt and the number of interceptions thrown per attempt to predict the percentage of games won.

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15.17 In part (d) of exercise 9, data contained in the WEBfile named PGADrivingDist (PGA Tour website, November 1, 2012) was used to develop an estimated regression equation to predict the average number of yards per drive given the ball speed and the launch angle.
a. Does the estimated regression equation provide a good fit to the data? Explain.
b. In part (b) of exercise 9, an estimated regression equation was developed using only ball speed to predict the average number of yards per drive. Compare the fit obtained using just ball speed to the fit obtained using ball speed and the launch angle.

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15.18 Refer to exercise 10, where Major League Baseball (MLB) pitching statistics were reported for a random sample of 20 pitchers from the American League for the 2011 season (MLB website, March 1, 2012).
a. In part (c) of exercise 10, an estimated regression equation was developed relating the average number of runs given up per inning pitched given the average number of strikeouts per inning pitched and the average number of home runs per inning pitched. What are the values of R2 and ...?
b. Does the estimated regression equation provide a good fit to the data? Explain.
c. Suppose the earned run average (ERA) is used as the dependent variable in part (c) instead of the average number of runs given up per inning pitched. Does the estimated regression equation that uses the ERA provide a good fit to the data? Explain.

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15.19 In exercise 1, the following estimated regression equation based on 10 observations was presented....Here SST = 6724.125, SSR = 6216.375, sb1 = .0813, and sb2 = .0567.
a. Compute MSR and MSE.
b. Compute F and perform the appropriate F test. Use α = .05.
c. Perform a t test for the significance of β1Use α = .05.
d. Perform a t test for the significance of β2. Use α = .05.

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15.20 Refer to the data presented in exercise 2. The estimated regression equation for these data is...Here SST = 15,182.9, SSR = 14,052.2, sb1 = .2471, and sb2 = .9484.
a. Test for a significant relationship among x1, x2, and y. Use α = .05.
b. Is β1 significant? Use α = .05.
c. Is β2 significant? Use α = .05.

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15.21 The following estimated regression equation was developed for a model involving two independent variables....After x2 was dropped from the model, the least squares method was used to obtain an estimated regression equation involving only x1 as an independent variable....
a. Give an interpretation of the coefficient of x1 in both models.
b. Could multicollinearity explain why the coefficient of x1 differs in the two models? If so, how?

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15.22 In exercise 4, the following estimated regression equation relating sales to inventory investment and advertising expenditures was given....The data used to develop the model came from a survey of 10 stores; for these data SST = 16,000 and SSR = 12,000.
a. Compute SSE, MSE, and MSR.
b. Use an F test and a .05 level of significance to determine whether there is a relationship among the variables.

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15.23 Refer to exercise 5.
a. Use α = .01 to test the hypothesesH0: β1 = β2 = 0Ha: β1 and/or β2 is not equal to zerofor the model y = β0 + β1x1 + β2x2 + ϵ, wherex1 = television advertising (\$1000s)x2 = newspaper advertising (\$1000s)
b. Use α = .05 to test the significance of β1. Should x1 be dropped from the model?
c. Use α = .05 to test the significance of β2. Should x2 be dropped from the model?

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15.24 The National Football League (NFL) records a variety of performance data for individuals and teams. A portion of the data showing the average number of passing yards obtained per game on offense (OffPass Yds/G), the average number of yards given up per game on defense (DefYds/G), and the precentage of games won (Win%), for the 2011 season follows (ESPN website, November 3, 2012)....
a. Develop an estimated regression equation that can be used to predict the percentage of games won given the average number of passing yards obtained per game on offense and the average number of yards given up per game on defense.
b. Use the F test to determine the overall significance of the relationship. What is your conclusion at the .05 level of significance?
c. Use the t test to determine the significance of each independent variable. What is your conclusion at the .05 level of significance?

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15.25 The Condé Nast Traveler Gold List for 2012 provided ratings for the top 20 small cruise ships (Condé Nast Traveler website, March 1, 2012). The following data are the scores each ship received based upon the results from Condé Nast Traveler’s annual Readers’ Choice Survey. Each score represents the percentage of respondents who rated a ship as excellent or very good on several criteria, including Itineraries/Schedule, Shore Excursions, and Food/Dining. An overall score was also reported and used to rank the ships The highest ranked ship, the Seabourn Odyssey, has an overall score of 94.4, the highes component of which is 97.8 for Food/Dining....
a. Determine the estimated regression equation that can be used to predict the overall score given the scores for Itineraries/Schedule, Shore Excursions, and Food/Dining.
b. Use the F test to determine the overall significance of the relationship. What is your conclusion at the .05 level of significance?
c. Use the t test to determine the significance of each independent variable. What is your conclusion at the .05 level of significance?
d. Remove any independent variable that is not significant from the estimated regression equation. What is your recommended estimated regression equation?

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15.26 In exercise 10, data showing the values of several pitching statistics for a random sample of 20 pitchers from the American League of Major League Baseball were provided (MLB website, March 1, 2012). In part (c) of this exercise an estimated regression equation was developed to predict the average number of runs given up per inning pitched (R/IP) given the average number of strikeouts per inning pitched (SO/IP) and the average number of home runs per inning pitched (HR/IP).
a. Use the F test to determine the overall significance of the relationship. What is your conclusion at the .05 level of significance?
b. Use the t test to determine the significance of each independent variable. What is your conclusion at the .05 level of significance?

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15.27 In exercise 1, the following estimated regression equation based on 10 observations was presented....
a. Develop a point estimate of the mean value of y when x1 = 180 and x2 = 310.
b. Predict an individual value of y when x1 = 180 and x2 = 310.

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15.28 Refer to the data in exercise 2. The estimated regression equation for those data is...
a. Develop a point estimate of the mean value of y when x1 = 45 and x2 = 15.
b. Develop a 95% prediction interval for y when x1 = 45 and x2 = 15.

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15.29 In exercise 5, the owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1) and newspaper advertising (x2). The estimated regression equation was...
a. What is the gross revenue expected for a week when \$3500 is spent on television advertising (x1 = 3.5) and \$1800 is spent on newspaper advertising (x2 = 1.8)?
b. Provide a 95% prediction interval for next week’s revenue, assuming that the advertising expenditures will be allocated as in part (a).

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15.30
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15.31 The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with electronic trades handled by discount brokers. As part of the survey, members were asked to rate their satisfaction with the trade price and the speed of execution, as well as provide an overall satisfaction rating. Possible responses (scores) were no opinion (0), unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker, summary scores were calculated by computing a weighted average of the scores provided by each respondent. A portion of the survey results follows (AAII website, February 7, 2012)....
a. Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker.
b. Finger Lakes Investments has developed a new electronic trading system and would like to predict overall customer satisfaction assuming they can provide satisfactory levels of service levels (3) for both trade price and speed of execution. Use the estimated regression equation developed in part (a) to predict overall satisfaction level for Finger Lakes Investments if they can achieve these performance levels.
c. Develop a 95% prediction interval of overall satisfaction for Finger Lakes Investments assuming they achieve service levels of 3 for both trade price and speed of execution.

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15.32 Consider a regression study involving a dependent variable y, a quantitative independent variable x1, and a categorical independent variable with two levels (level 1 and level 2).
a. Write a multiple regression equation relating x1 and the categorical variable to y.
b. What is the expected value of y corresponding to level 1 of the categorical variable?
c. What is the expected value of y corresponding to level 2 of the categorical variable?
d. Interpret the parameters in your regression equation.

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15.33 Consider a regression study involving a dependent variable y, a quantitative independent variable x1, and a categorical independent variable with three possible levels (level 1, level 2, and level 3).
a. How many dummy variables are required to represent the categorical variable?
b. Write a multiple regression equation relating x1 and the categorical variable to y.
c. Interpret the parameters in your regression equation.

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15.34 Management proposed the following regression model to predict sales at a fast-food outlet. y = β0 + β1x1 + β2x2 + β3x3 + ϵwhere x1 = number of competitors within one mile x2 = population within one mile (1000s) ... y = sales (\$1000s)The following estimated regression equation was developed after 20 outlets were surveyed....
a. What is the expected amount of sales attributable to the drive-up window?
b. Predict sales for a store with two competitors, a population of 8000 within 1 mile, and no drive-up window.
c. Predict sales for a store with one competitor, a population of 3000 within 1 mile, and a drive-up window.

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15.35 Refer to the Johnson Filtration problem introduced in this section. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a list showing which repairperson performed the service. The revised data follow....
a. Ignore for now the months since the last maintenance service (x1) and the repairperson who performed the service. Develop the estimated simple linear regression equation to predict the repair time (y) given the type of repair (x2). Recall that x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical.
b. Does the equation that you developed in part (a) provide a good fit for the observed data? Explain.
c. Ignore for now the months since the last maintenance service and the type of repair associated with the machine. Develop the estimated simple linear regression equation to predict the repair time given the repairperson who performed the service. Let x3 = 0 if Bob Jones performed the service and x3 = 1 if Dave Newton performed the service.
d. Does the equation that you developed in part (c) provide a good fit for the observed data? Explain.

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15.36 This problem is an extension of the situation described in exercise 35.
a. Develop the estimated regression equation to predict the repair time given the number of months since the last maintenance service, the type of repair, and the repairperson who performed the service.
b. At the .05 level of significance, test whether the estimated regression equation developed in part (a) represents a significant relationship between the independent variables and the dependent variable.
c. Is the addition of the independent variable x3, the repairperson who performed the service, statistically significant? Use α = .05. What explanation can you give for the results observed?

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15.37
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15.38 A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker.......
a. Develop an estimated regression equation that relates risk of a stroke to the person’s age, blood pressure, and whether the person is a smoker.
b. Is smoking a significant factor in the risk of a stroke? Explain. Use α = .05.
c. What is the probability of a stroke over the next 10 years for Art Speen, a 68-year-old smoker who has blood pressure of 175? What action might the physician recommend for this patient?

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15.39
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15.40
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15.41
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15.42
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15.43
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15.44 The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student’s SAT mathematics score and high-school GPA. ...where x1 = high-school grade point average x2 = SAT mathematics score y = final college grade point average
a. Interpret the coefficients in this estimated regression equation.
b. Predict the final college GPA for a student who has a high-school average of 84 and a score of 540 on the SAT mathematics test.

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15.45 The personnel director for McCormick Publisher Services developed the following estimated regression equation relating an employee’s score on a job satisfaction test to his or her length of service and pay grade. ...where x1 = length of service (years) x2 = pay grade y = job satisfaction test score (higher scores indicate greater job satisfaction)
a. Interpret the coefficients in this estimated regression equation.
b. Predict the job satisfaction test score for an employee who has four years of service and has a pay grade of 6.

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15.46 A partial computer output from a regression analysis using Excel’s Regression tool follows.
a. Compute the missing entries in this output.
b. Using α = .05, test for overall significance.
c. Use the t test and α = .05 to test H0: β1 = 0 and H0: β2 = 0....

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15.47 Recall that in exercise 44, the admissions officer for Clearwater College developed the following estimated regression equation relating final college GPA to the student’s SAT mathematics score and high-school GPA. ...where x1 = high-school grade point average x2 = SAT mathematics score y = final college grade point averageA portion of the Excel Regression tool output follows....
a. Complete the missing entries in this output.
b. Using α = .05, test for overall significance.
c. Did the estimated regression equation provide a good fit to the data? Explain.
d. Use the t test and α = .05 to test H0: = 0 and H0: β2 = 0.

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15.48 Recall that in exercise 45 the personnel director for McCormick Publisher Services developed the following estimated regression equation relating an employee’s score on a job satisfaction test to length of service and pay grade. ...where x1 = length of service (years) x2 = pay grade y = job satisfaction test score (higher scores indicate greater job satisfaction)A portion of the Excel Regression tool output follows....
a. Complete the missing entries in this output.
b. Using α = .05, test for overall significance.
c. Did the estimated regression equation provide a good fit to the data? Explain.
d. Use the t test and α = .05 to test H0: β1 = 0 and H0: β2 = 0.

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15.49
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15.50
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15.51
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15.52 The National Basketball Association (NBA) records a variety of statistics for each team. Five of these statistics are the percentage of games won (Win%), the percentage of field goals made (FG%), the percentage of three-point shots made (3P%), the percentage of free throws made (FT%), the average number of offensive rebounds per game (RBOff), and the average number of defensive rebounds per game (RBDef). The data contained in the WEBfile named NBAStats show the values of these statistics for the 30 teams in the NBA for the 2011-2012 season (ESPN website, October 3, 2012). A portion of the data follows....
a. Develop an estimated regression equation that can be used to predict the percentage of games won given the percentage of field goals made. At the .05 level of significance, test for a significant relationship.
b. Provide an interpretation for the slope of the estimated regression equation developed in part (a).
c. Develop an estimated regression equation that can be used to predict the percentage of games won given the percentage of field goals made, the percentage of three-point shots made, the percentage of free throws made, the average number of offensive rebounds per game, and the average number of defensive rebounds per game.
d. For the estimated regression equation developed in part (c), remove any independent variables that are not significant at the .05 level of significance and develop a new estimated regression equation using the remaining independent variables.
e. Assuming the estimated regression equation developed in part (d) can be used for the 2012-2013 season, predict the percentage of games won for a team with the following values for the four independent variables: FG% = 45, 3P% = 35, RBOff = 12, and RBDef = 30.

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### Solutions Essentials of Modern Business Statistics with Microsoft Office Excel - 7th Edition - Chapter 14

14.1 Given are five observations for two variables, x and y....
a. Develop a scatter diagram for these data.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Try to approximate the relationship between x and y by drawing a straight line through the data.
d. Develop the estimated regression equation by computing the values of b0 and b1 using equations (12.6) and (12.7).
e. Use the estimated regression equation to predict the value of y when x = 4.

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14.2 Given are five observations for two variables, x and y....
a. Develop a scatter diagram for these data.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Try to approximate the relationship between x and y by drawing a straight line through the data.
d. Develop the estimated regression equation by computing the values of b0 and b1 using equations (12.6) and (12.7).
e. Use the estimated regression equation to predict the value of y when x = 10.

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14.3 Given are five observations collected in a regression study on two variables....
a. Develop a scatter diagram for these data.
b. Develop the estimated regression equation for these data.
c. Use the estimated regression equation to predict the value of y when x = 6.

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14.4 The following data give the percentage of women working in five companies in the retail and trade industry. The percentage of management jobs held by women in each company is also shown....
a. Develop a scatter diagram for these data with the percentage of women working in the company as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Try to approximate the relationship between the percentage of women working in the company and the percentage of management jobs held by women in that company.
d. Develop the estimated regression equation by computing the values of b0 and b1.
e. Predict the percentage of management jobs held by women in a company that has 60% women employees.

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14.5 Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected....
a. Develop a scatter diagram with the line speed as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Use the least squares method to develop the estimated regression equation.
d. Predict the number of defective parts found for a line speed of 25 feet per minute.

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14.6 The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the average number of passing yards per attempt (Yds/Att) and the percentage of games won (WinPct) for a random sample of 10 NFL teams for the 2011 season (NFL website, February 12, 2012)....
a. Develop a scatter diagram with the number of passing yards per attempt on the horizontal axis and the percentage of games won on the vertical axis.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt.
d. Provide an interpretation for the slope of the estimated regression equation.
e. For the 2011 season, the average number of passing yards per attempt for the Kansas City Chiefs was 6.2. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. (Note: For the 2011 season the Kansas City Chiefs’ record was 7 wins and 9 losses.) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs.

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14.7 A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons....
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 9 years of experience
.
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14.8 The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion (0), unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker, summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follows (AAII website, February 7, 2012)....
a. Develop a scatter diagram for these data with the speed of execution as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Develop the least squares estimated regression equation.
d. Provide an interpretation for the slope of the estimated regression equation.
e. Suppose Zecco.com developed new software to increase its speed of execution rating. If the new software is able to increase Zecco.com’s speed of execution rating from the current value of 2.5 to the average speed of execution rating for the other 10 brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating?

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14.9 Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011 Hertz had 320,000 cars in service and annual revenue of approximately \$4.2 billion. The following data show the number of cars in service (1000s) and the annual revenue (\$ millions) for six smaller car rental companies (Auto Rental News website, August 7, 2012)....
a. Develop a scatter diagram with the number of cars in service as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Use the least squares method to develop the estimated regression equation.
d. For every additional car placed in service, estimate how much annual revenue will change.
e. Fox Rent A Car has 11,000 cars in service. Use the estimated regression equation developed in part (c) to predict annual revenue for Fox Rent A Car.

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14.10
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14.11 To help consumers in purchasing a laptop computer, Consumer Reports calculates an overall test score for each computer tested based upon rating factors such as ergonomics, portability, performance, display, and battery life. Higher overall scores indicate better test results. The following data show the average retail price and the overall score for ten 13-inch models (Consumer Reports website, October 25, 2012)....
a. Develop a scatter diagram with price as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Use the least squares method to develop the estimated regression equation.
d. Provide an interpretation of the slope of the estimated regression equation.
e. Another laptop that Consumer Reports tested is the Acer Aspire S3-951-6646 Ultrabook; the price for this laptop was \$700. Predict the overall score for this laptop using the estimated regression equation developed in part (c).

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14.12
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14.13 A large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was selected and the following data were collected....
a. Develop a scatter diagram for these data. Does a linear relationship appear reasonable? Explain.
b. Develop the least squares estimated regression equation that relates the distance to work to the number of days absent.
c. Predict the number of days absent for an employee who lives 5 miles from the hospital.

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14.14 Using a global-positioning-system (GPS)–based navigator for your car, you enter a destination and the system will plot a route, give spoken turn-by-turn directions, and show your progress along the route. Today, even budget units include features previously available only on more expensive models. Consumer Reports conducted extensive tests of GPS-based navigators and developed an overall rating based on factors such as ease of use, driver information, display, and battery life. The following data show the price and rating for a sample of 20 GPS units with a 4.3-inch screen that Consumer Reports tested (Consumer Reports website, April 17, 2012)....
a. Develop a scatter diagram with price as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Use the least squares method to develop the estimated regression equation.
d. Predict the rating for a GPS system with a 4.3-inch screen that has a price of \$200.

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14.15 The data from exercise 1 follow....The estimated regression equation for these data is ....
a. Compute SSE, SST, and SSR using equations (12.8), (12.9), and (12.10).
b. Compute the coefficient of determination r2. Comment on the goodness of fit.
c. Compute the sample correlation coefficient.

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14.16 The data from exercise 2 follow....The estimated regression equation for these data is ....
a. Compute SSE, SST, and SSR.
b. Compute the coefficient of determination r2. Comment on the goodness of fit.
c. Compute the sample correlation coefficient.

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14.17 The data from exercise 3 follow....The estimated regression equation for these data is .... What percentage of the total sum of squares can be accounted for by the estimated regression equation? What is the value of the sample correlation coefficient?
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14.18 The following data show the brand, price (\$), and the overall score for six stereo headphones that were tested by Consumer Reports (Consumer Reports website, March 5, 2012). The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ..., where x = price (\$) and y = overall score....
a. Compute SST, SSR, and SSE.
b. Compute the coefficient of determination r2. Comment on the goodness of fit.
c. What is the value of the sample correlation coefficient?

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14.19 In exercise 7 a sales manager collected the following data on x = annual sales and y = years of experience. The estimated regression equation for these data is .......
a. Compute SST, SSR, and SSE.
b. Compute the coefficient of determination r2. Comment on the goodness of fit.
c. What is the value of the sample correlation coefficient?

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14.20 Bicycling, the world’s leading cycling magazine, reviews hundreds of bicycles throughout the year. Its “Road-Race” category contains reviews of bikes used by riders primarily interested in racing. One of the most important factors in selecting a bike for racing is the weight of the bike. The following data show the weight (pounds) and price (\$) for 10 racing bikes reviewed by the magazine (Bicycling website, March 8, 2012)....
a. Use the data to develop an estimated regression equation that could be used to estimate the price for a bike given the weight.
b. Compute r2. Did the estimated regression equation provide a good fit?
c. Predict the price for a bike that weighs 15 pounds.

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14.21 An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation....
a. Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume.
b. What is the variable cost per unit produced?
c. Compute the coefficient of determination. What percentage of the variation in total cost can be explained by production volume?
d. The company’s production schedule shows 500 units must be produced next month. Predict the total cost for this operation.

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14.22 Refer to exercise 9, where the following data were used to investigate the relationship between the number of cars in service (1000s) and the annual revenue (\$millions) for six smaller car rental companies (Auto Rental News website, August 7, 2012)....With x = cars in service (1000s) and y = annual revenue (\$ millions), the estimated regression equation is .... For these data SSE = 1043.03.
a. Compute the coefficient of determination r2.
b. Did the estimated regression equation provide a good fit? Explain.
c. What is the value of the sample correlation coefficient? Does it reflect a strong or weak relationship between the number of cars in service and the annual revenue?

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14.23 The data from exercise 1 follow....
a. Compute the mean square error using equation (12.15).
b. Compute the standard error of the estimate using equation (12.16).
c. Compute the estimated standard deviation of b1 using equation (12.18).
d. Use the t test to test the following hypotheses (α = .05):...
e. Use the F test to test the hypotheses in part (d) at a .05 level of significance. Present the results in the analysis of variance table format.

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14.24 The data from exercise 2 follow....
a. Compute the mean square error using equation (12.15).
b. Compute the standard error of the estimate using equation (12.16).
c. Compute the estimated standard deviation of b1 using equation (12.18).
d. Use the t test to test the following hypotheses (α = .05):...
e. Use the F test to test the hypotheses in part (d) at a .05 level of significance. Present the results in the analysis of variance table format.

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14.25 The data from exercise 3 follow....
a. What is the value of the standard error of the estimate?
b. Test for a significant relationship by using the t test. Use α = .05.
c. Use the F test to test for a significant relationship. Use α = .05. What is your conclusion?

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14.26 In exercise 18 the data on price (\$) and the overall score for six stereo headphones tested by Consumer Reports were as follows (Consumer Reports website, March 5, 2012)....
a. Does the t test indicate a significant relationship between price and the overall score? What is your conclusion? Use α = .05.
b. Test for a significant relationship using the F test. What is your conclusion? Use α = .05.
c. Show the ANOVA table for these data.

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14.27 To identify high-paying jobs for people who do not like stress, the following data were collected showing the average annual salary (\$1000s) and the stress tolerance for a variety of occupations (Business Insider, November 8, 2013)....The stress tolerance for each job is rating on a scale from 0 to 100, where a lower rating indicates less stress.
a. Develop a scatter diagram for these data with average annual salary as the independent variable. What does the scatter diagram indicate about the relationship between the two variables?
b. Use these data to develop an estimated regression equation that can be used to predict stress tolerance given the average annual salary.
c. At the .05 level of significance, does there appear to be a significant statistical relationship between the two variables?
d. Would you feel comfortable in predicting the stress tolerance for a different occupation given the average annual salary for the occupation? Explain.
e. Does the relationship between average annual salary and stress tolerance for these data seem reasonable to you? Explain.

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14.28 In exercise 8, ratings data on x = the quality of the speed of execution and y = overall satisfaction with electronic trades provided the estimated regression equation ... (AAII website, February 7, 2012). At the .05 level of significance, test whether speed of execution and overall satisfaction are related. Show the ANOVA table. What is your conclusion?
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14.29 Refer to exercise 21, where data on production volume and cost were used to develop an estimated regression equation relating production volume and cost for a particular manufacturing operation. Use α = .05 to test whether the production volume is significantly related to the total cost. Show the ANOVA table. What is your conclusion?
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14.30 Refer to exercise 9, where the following data were used to investigate the relationship between the number of cars in service (1000s) and the annual revenue (\$ millions) for six smaller car rental companies (Auto Rental News website, August 7, 2012)....With x = cars in service (1000s) and y = annual revenue (\$ millions), the estimated regression equation is .... For these data SSE = 1043.03 and SST = 10,568. Do these results indicate a significant relationship between the number of cars in service and the annual revenue?
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14.31 In exercise 20, data on x = weight (pounds) and y = price (\$) for 10 road-racing bikes provided the estimated regression equation ... (Bicycling website, March 8, 2012). For these data SSE = 7,102,922.54 and SST = 52,120,800. Use the F test to determine whether the weight for a bike and the price are related at the .05 level of significance.
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14.32 The data from exercise 1 follow....
a. Use equation (12.23) to estimate the standard deviation of ... when x = 4.
b. Use expression (12.24) to develop a 95% confidence interval for the expected value of y when x = 4.
c. Use equation (12.26) to estimate the standard deviation of an individual value of y when x = 4.
d. Use expression (12.27) to develop a 95% prediction interval for y when x = 4.

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14.33 The data from exercise 2 follow....
a. Estimate the standard deviation of ... when x = 8.
b. Develop a 95% confidence interval for the expected value of y when x = 8.
c. Estimate the standard deviation of an individual value of y when x = 8.
d. Develop a 95% prediction interval for y when x = 8.

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14.34 The data from exercise 3 follow....Develop the 95% confidence and prediction intervals when x = 12. Explain why these two intervals are different.
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14.35 The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor’s degree in business administration....The estimated regression equation for these data is ... and MSE = 21,284.
a. Develop a point estimate of the starting salary for a student with a GPA of 3.0.
b. Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA.
c. Develop a 95% prediction interval for Ryan Dailey, a student with a GPA of 3.0.
d. Discuss the differences in your answers to parts (b) and (c).

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14.36 In exercise 7, the data on y = annual sales (\$ 1000s) for new customer accounts and x = number of years of experience for a sample of 10 salespersons provided the estimated regression equation .... For these data ..., and s = 4.6098.
a. Develop a 95% confidence interval for the mean annual sales for all salespersons with nine years of experience.
b. The company is considering hiring Tom Smart, a salesperson with nine years of experience. Develop a 95% prediction interval of annual sales for Tom Smart.
c. Discuss the differences in your answers to parts (a) and (b).

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14.37 In exercise 5, the following data on x = the number of defective parts found and y = the line speed (feet per minute) for a production process at Brawdy Plastics provided the estimated regression equation .......For these data SSE = 16. Develop a 95% confidence interval for the mean number of defective parts for a line speed of 25 feet per minute.
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14.38 Refer to exercise 21, where data on the production volume x and total cost y for a particular manufacturing operation were used to develop the estimated regression equation .......
a. The company’s production schedule shows that 500 units must be produced next month. Predict the total cost for next month.
b. Develop a 99% prediction interval for the total cost for next month.
c. If an accounting cost report at the end of next month shows that the actual production cost during the month was \$6000, should managers be concerned about incurring such a high total cost for the month? Discuss.

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14.39 In exercise 12, the following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation .... For these data SSE = 1541.4....
a. Predict the amount spent on entertainment for a particular city that has a daily room rate of \$89.
b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of \$89.
c. The average room rate in Chicago is \$128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago.

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14.40 The commercial division of a real estate firm conducted a study to determine the extent of the relationship between annual gross rents (\$1000s) and the selling price (\$1000s) for apartment buildings. Data were collected on several properties sold, and Excel’s Regression tool was used to develop an estimated regression equation. A portion of the regression output follows....
a. How many apartment buildings were in the sample?
b. Write the estimated regression equation.
c. Use the t test to determine whether the selling price is related to annual gross rents. Use α = .05.
d. Use the F test to determine whether the selling price is related to annual gross rents. Use α = .05.
e. Predict the selling price of an apartment building with gross annual rents of \$50,000.

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14.41 A portion of the regression output for an application relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal follows....
a. Write the estimated regression equation.
b. Use a t test to determine whether monthly maintenance expense is related to usage at the .05 level of significance.
c. Did the estimated regression equation provide a good fit? Explain.

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14.42 A regression model relating the number of salespersons at a branch office to annual sales at the office (in thousands of dollars) provided the following regression output....
a. Write the estimated regression equation.
b. Compute the F statistic and test the significance of the relationship at the .05 level of significance.
c. Compute the t statistic and test the significance of the relationship at the .05 level of significance.
d. Predict the annual sales at the Memphis branch office. This branch employs 12 salespersons.

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14.43
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14.44 Automobile racing, high-performance driving schools, and driver education programs run by automobile clubs continue to grow in popularity. All these activities require the participant to wear a helmet that is certified by the Snell Memorial Foundation, a not-for-profit organization dedicated to research, education, testing, and development of helmet safety standards. Snell “SA” (Sports Application) rated professional helmets are designed for auto racing and provide extreme impact resistance and high fire protection. One of the key factors in selecting a helmet is weight, since lower weight helmets tend to place less stress on the neck. The following data show the weight and price for 18 SA helmets (SoloRacer website, April 20, 2008)....
a. Develop a scatter diagram with weight as the independent variable.
b. Does there appear to be any relationship between these two variables?
c. Develop the estimated regression equation that could be used to predict the price given the weight.
d. Test for the significance of the relationship at the .05 level of significance.
e. Did the estimated regression equation provide a good fit? Explain.

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14.45 Given are data for two variables, x and y....
a. Develop an estimated regression equation for these data.
b. Compute the residuals.
c. Develop a plot of the residuals against the independent variable x. Do the assumptions about the error terms seem to be satisfied?
d. Compute the standardized residuals.
e. Develop a plot of the standardized residuals against .... What conclusions can you draw from this plot?

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14.46 The following data were used in a regression study....
a. Develop an estimated regression equation for these data.
b. Construct a plot of the residuals. Do the assumptions about the error term seem to be satisfied?

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14.47 Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow....
a. Let x equal advertising expenditures and y equal revenue. Use the method of least squares to develop a straight line approximation of the relationship between the two variables.
b. Test whether revenue and advertising expenditures are related at a .05 level of significance.
c. Prepare a residual plot of ... versus .... Use the result from part (a) to obtain the values of ....
d. What conclusions can you draw from residual analysis? Should this model be used, or should we look for a better one?

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14.48 Refer to exercise 7, where an estimated regression equation relating years of experience and annual sales was developed.
a. Compute the residuals and construct a residual plot for this problem.
b. Do the assumptions about the error terms seem reasonable in light of the residual plot?

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14.49
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14.50 Consider the following data for two variables, x and y....
a. Develop a scatter diagram for these data. Does the scatter diagram indicate any outliers in the data? In general, what implications does this finding have for simple linear regression?
b. Compute the standardized residuals for these data. Do the data include any outliers? Explain.

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14.51 Consider the following data for two variables, x and y....
a. Develop a scatter diagram for these data. Does the scatter diagram indicate any influential observations? Explain.
b. Compute the standardized residuals for these data. Do the data include any outliers? Explain.
c. Do there appear to be any influential observations in these data? Explain.

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14.52 Charity Navigator is America’s leading independent charity evaluator. The following data show the total expenses (\$), the percentage of the total budget spent on administrative expenses, the percentage spent on fundraising, and the percentage spent on program expenses for 10 supersized charities (Charity Navigator website, April 12, 2012). Administrativ expenses include overhead, administrative staff and associated costs, and organization; meetings. Fundraising expenses are what a charity spends to raise money, and program expenses are what the charity spends on the programs and services it exists to deliver. The sum of the three percentages does not add to 100% because of rounding....
a. Develop a scatter diagram with fundraising expenses (%) on the horizontal axis and program expenses (%) on the vertical axis. Looking at the data, do there appear to be any outliers and/or influential observations?
b. Develop an estimated regression equation that could be used to predict program expenses (%) given fundraising expenses (%).
c. Does the value for the slope of the estimated regression equation make sense in the context of this problem situation?
d. Use residual analysis to determine whether any outliers and/or influential observations are present. Briefly summarize your findings and conclusions.

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14.53 Many countries, especially those in Europe, have significant gold holdings. But many of these countries also have massive debts. The following data show the total value of gold holdings in billions of U.S. dollars and the debt as a percentage of the gross domestic product for nine countries (WordPress and Trading Economics websites, February 24, 2012)....
a. Develop a scatter diagram for the total value of a country’s gold holdings (\$ billions) as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? Do there appear to be any outliers and/or influential observations? Explain.
c. Using the entire data set, develop the estimated regression equation that can be used to predict the debt of a country given the total value of its gold holdings.
d. Suppose that after looking at the scatter diagram in part (a) that you were able to visually identify what appears to be an influential observation. Drop this observation from the data set and fit an estimated regression equation to the remaining data. Compare the estimated slope for the new estimated regression equation to the estimated slope obtained in part (c). Does this approach confirm the conclusion you reached in part (d)? Explain.

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14.54 The following data show the annual revenue (\$ millions) and the estimated team value (\$ millions) for the 30 Major League Baseball teams (Forbes website, January 16, 2014).......
a. Develop a scatter diagram with Revenue on the horizontal axis and Value on the vertical axis. Looking at the scatter diagram, does it appear that there are any outliers and/ or influential observations in the data?
b. Develop the estimated regression equation that can be used to predict team value given the annual revenue.
c. Use residual analysis to determine whether any outliers and/or influential observations are present. Briefly summarize your findings and conclusions.

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14.55 The Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 (S&P 500) indexes are used as measures of overall movement in the stock market. The DJIA is based on the price movements of 30 large companies; the S&P 500 is an index composed of 500 stocks. Some say the S&P 500 is a better measure of stock market performance because it is broader based. The closing price for the DJIA and the S&P 500 for 15 weeks, beginning with January 6, 2012, follow (Barron’s website, April 17, 2012)....
a. Develop a scatter diagram with DJIA as the independent variable.
b. Develop the estimated regression equation.
c. Test for a significant relationship. Use α = .05.
d. Did the estimated regression equation provide a good fit? Explain.
e. Suppose that the closing price for the DJIA is 13,500. Predict the closing price for the S&P 500.
f. Should we be concerned that the DJIA value of 13,500 used to predict the S&P 500 value in part (e) is beyond the range of the data used to develop the estimated regression equation?

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14.56
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14.57
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14.58 Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract 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)....
a. Develop the estimated regression equation that relates annual maintenance expense to weekly usage.
b. Test the significance of the relationship in part (a) at a .05 level of significance.
c. Jensen expects to use the new machine 30 hours per week. Develop a 95% prediction interval for the company’s annual maintenance expense.
d. If the maintenance contract costs \$3000 per year, would you recommend purchasing it? Why or why not?

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14.59 The regional transit authority for a major metropolitan area wants to determine whether there is any relationship between the age of a bus and the annual maintenance cost. A sample of 10 buses resulted in the following data....
a. Develop the least squares estimated regression equation.
b. Test to see whether the two variables are significantly related with α = .05.
c. Did the least squares line provide a good fit to the observed data? Explain.
d. Develop a 95% prediction interval for the maintenance cost for a specific bus that is 4 years old.

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14.60
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14.61 The Toyota Camry is one of the best-selling cars in North America. The cost of a previously owned Camry depends upon many factors, including the model year, mileage, and condition. To investigate the relationship between the car’s mileage and the sales price for a 2007 model year Camry, the following data show the mileage and sale price for 19 sales (PriceHub website, February 24, 2012)....
a. Develop a scatter diagram with the car mileage on the horizontal axis and the price on the vertical axis.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Develop the estimated regression equation that could be used to predict the price (\$1000s) given the miles (1000s).
d. Test for a significant relationship at the .05 level of significance.
e. Did the estimated regression equation provide a good fit? Explain.

f. Provide an interpretation for the slope of the estimated regression equation.
g. Suppose that you are considering purchasing a previously owned 2007 Camry that has been driven 60,000 miles. Using the estimated regression equation developed in part (c), predict the price for this car. Is this the price you would offer the seller?

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