a. Interpret b1 and b2 in this estimated regression equation.
b. Predict y when x1 = 180 and x2 = 310.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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?
Get solution
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?
Get solution
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?
Get solution
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?
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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.
Get solution
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....
Get solution
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.
Get solution
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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