a. Interpret b1 and b2 in this estimated regression equation.
b. Estimate 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. Estimate y if x1 = 45.
b. Develop an estimated regression equation relating y to x2. Estimate y if x2 = 15.
c. Develop an estimated regression equation relating y to x1 and x2. Estimate 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. Estimate 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....Where...
a. Estimate 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 estimate 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. What is the estimate of the weekly gross revenue for a week when $3500 is spent on television advertising and $1800 is spent on newspaper advertising?
Get solution
15.6 In baseball, a team’s success is often thought to be a function of the team’s hitting and pitching performance. One measure of hitting performance is the number of home runs the team hits, and one measure of pitching performance is the earned run average for the team’s pitching staf
f. It is generally believed that teams that hit more home runs and have a lower earned run average will win a higher percentage of the games played. The following data show the proportion of games won, the number of team home runs (HR), and the earned run average (ERA) for the 16 teams in the National League for the 2003 Major League Baseball season (http://www.usatoday.com, January 7, 2004)....
a. Determine the estimated regression equation that could be used to predict the proportion of games won given the number of team home runs.
b. Determine the estimated regression equation that could be used to predict the proportion of games won given the earned run average for the team’s pitching staff.
c. Determine the estimated regression equation that could be used to predict the proportion of games won given the number of team home runs and the earned run average for the team’s pitching staff.
d. For the 2003 season San Diego won only 39.5% of the games they played, the lowest in the National League. To improve next year’s record, the team is trying to acquire new players who will increase the number of team home runs to 180 and decrease the earned run average for the team’s pitching staff to 4.0. Use the estimated regression equation developed in part (c) to estimate the percentage of games San Diego will win if they have 180 team home runs and have an earned run average of 4.0.
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15.7
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15.8
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15.9 Waterskiing and wakeboarding are two popular water-sports. Finding a model that best suits your intended needs, whether it is waterskiing, wakeboading, or general boating, can be a difficult task. WaterSki magazine did extensive testing for 88 boats and provided a wide variety of information to help consumers select the best boat. A portion of the data they reported for 20 boats with a length of between 20 and 22 feet follows (WaterSki, January/February 2006). Beam is the maximum width of the boat in inches, HP is the horsepower of the boat’s engine, and TopSpeed is the top speed in miles per hour (mph).......
a. Using these data, develop an estimated regression equation relating the top speed with the boat’s beam and horsepower rating.
b. The Svfara SV609 has a beam of 85 inches and an engine with a 330 horsepower rating. Use the estimated regression equation developed in part (a) to estimate the top speed for the Svfara SV609.
Get solution
15.10 The National Basketball Association (NBA) records a variety of statistics for each team. Four of these statistics are the proportion of games won (PCT), the proportion of field goals made by the team (FG%), the proportion of three-point shots made by the team’s opponent (Opp 3 Pt%), and the number of turnovers committed by the team’s opponent (Opp TO). The following data show the values of these statistics for the 29 teams in the NBA for a portion of the 2004 season (http://www.nba.com, January 3, 2004)....
a. Determine the estimated regression equation that can be used to predict the proportion of games won given the proportion of field goals made by the team.
b. Provide an interpretation for the slope of the estimated regression equation developed in part (a).
c. Determine the estimated regression equation that can be used to predict the proportion of games won given the proportion of field goals made by the team, the proportion of three-point shots made by the team’s opponent, and the number of turnovers committed by the team’s opponent.
d. Discuss the practical implications of the estimated regression equation developed in part (c).
e. Estimate the proportion of games won for a team with the following values for the three independent variables: FG% = .45, Opp 3 Pt% = .34, and Opp TO = 17.
Get solution
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 = 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.
Get solution
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.
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15.16
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15.17 In exercise 9, an estimated regression equation was developed relating the top speed for a boat to the boat’s beam and horsepower rating.
a. Compute and interpret and R2 and R2a.
b. Does the estimated regression equation provide a good fit to the data? Explain.
Get solution
15.18 Refer to exercise 10, where data were reported on a variety of statistics for the 29 teams in the National Basketball Association for a portion of the 2004 season (http://www.nba. com, January 3, 2004).
a. In part (c) of exercise 10, an estimated regression equation was developed relating the proportion of games won given the percentage of field goals made by the team, the proportion of three-point shots made by the team’s opponent, and the number of turnovers committed by the team’s opponent. What are the values of R2 and R2a?
b. Does the estimated regression equation 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, ... and ....
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 β1. Use 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, ..., and ....
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?
Get solution
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 dataSST = 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 hypotheses...for the model y = β0 + β1x1 + β2x2 + ϵ, where...
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
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15.25 Barron’s conducts an annual review of online brokers, including both brokers that can be accessed via a Web browser, as well as direct-access brokers that connect customers directly with the broker’s network server. Each broker’s offerings and performance are evaluated in six areas, using a point value of 0-5 in each category. The results are weighted to obtain an overall score, and a final star rating, ranging from zero to five stars, is assigned to each broker. Trade execution, ease of use, and range of offerings are three of the areas evaluated. A point value of 5 in the trade execution area means the order entry and execution process flowed easily from one step to the next. A value of 5 in the ease of use area means that the site was easy to use and can be tailored to show what the user wants to see. A value of 5 in the range offerings area means that all of the investment transactions can be executed online. The following data show the point values for trade execution, ease of use, range of offerings, and the star rating for a sample of 10 of the online brokers that Barron’s evaluated (Barron’s, March 10, 2003)....
a. Determine the estimated regression equation that can be used to predict the star rating given the point values for execution, ease of use, and range of offerings.
b. Use the F test to determine the overall significance of the relationship. What is the 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? Compare the R2 with the value of R2 from part (a). Discuss the differences.
Get solution
15.26 In exercise 10 an estimated regression equation was developed relating the proportion of games won given the proportion of field goals made by the team, the proportion of three-point shots made by the team’s opponent, and the number of turnovers committed by the team’s opponent.
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. Develop a point estimate for 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 95% confidence interval for 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% confidence interval for the mean revenue of all weeks with the expenditures listed in part (a).
c. Provide a 95% prediction interval for next week’s revenue, assuming that the advertising expenditures will be allocated as in part (a).
Get solution
15.30 In exercise 9 an estimated regression equation was developed relating the top speed for a boat to the boat’s beam and horsepower rating.
a. Develop a point estimate the mean top speed of a boat with a beam of 85 inches and an engine with a 330 horsepower rating.
b. The Svfara SV609 has a beam of 85 inches and an engine with a 330 horsepower rating. Develop a 95% confidence interval for the mean top speed for the Svfara SV609.
Get solution
15.31 The Buyer’s Guide section of the Web site for Car and Driver magazine provides reviews and road tests for cars, trucks, SUVs, and vans. The average ratings of overall quality, vehicle styling, braking, handling, fuel economy, interior comfort, acceleration, dependability, fit and finish, transmission, and ride are summarized for each vehicle using a scale ranging from 1 (worst) to 10 (best). A portion of the data for 14 Sports/GT cars is shown here (http://www.caranddriver.com, January 7, 2004)....
a. Develop an estimated regression equation using handling, dependability, and fit and finish to predict overall quality.
b. Another Sports/GT car rated by Car and Driver is the Honda Accord. The ratings for handling, dependability, and fit and finish for the Honda Accord were 8.28, 9.06, and 8.07, respectively. Estimate the overall rating for this car.
c. Provide a 95% prediction interval for overall quality for the Honda Accord described in part (b).
d. The overall rating reported by Car and Driver for the Honda Accord was 8.65. How does this rating compare to the estimates you developed in parts (b) and (d)?
Get solution
15.32 Consider a regression study involving a dependent variable y, a categorical independent variable x1, and a categorical 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....Where...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 one mile, and no drive-up window.
c. Predict sales for a store with one competitor, a population of 3000 within one 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 Data for two variables, x and y, follow....
a. Develop the estimated regression equation for these data.
b. Plot the standardized residuals versus ŷ. Do there appear to be any outliers in these data? Explain.
c. Compute the studentized deleted residuals for these data. At the .05 level of significance, can any of these observations be classified as an outlier? Explain.
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15.40 Data for two variables, x and y, follow....
a. Develop the estimated regression equation for these data.
b. Compute the studentized deleted residuals for these data. At the .05 level of significance, can any of these observations be classified as an outlier? Explain.
c. Compute the leverage values for these data. Do there appear to be any influential observations in these data? Explain.
d. Compute Cook’s distance measure for these data. Are any observations influential? Explain.
Get solution
15.41 Exercise 5 gave the following data on weekly gross revenue, television advertising, and newspaper advertising for Showtime Movie Theaters....
a. Find an estimated regression equation relating weekly gross revenue to television and newspaper advertising.
b. Plot the standardized residuals against ŷ. Does the residual plot support the assumptions about ϵ? Explain.
c. Check for any outliers in these data. What are your conclusions?
d. Are there any influential observations? Explain.
Get solution
15.42 The following data show the curb weight, horsepower, and 1/4-mile speed for 16 popular sports and GT cars. Suppose that the price of each sports and GT car is also available. The complete data set is as follows:... ...
a. Find the estimated regression equation, which uses price and horsepower to predict 1/4-mile speed.
b. Plot the standardized residuals against ŷ. Does the residual plot support the assumption about ϵ? Explain.
c. Check for any outliers. What are your conclusions?
d. Are there any influential observations? Explain.
Get solution
15.43 The Ladies Professional Golfers Association (LPGA) maintains statistics on performance and earnings for members of the LPGA Tour. Year-end performance statistics for the 30 players who had the highest total earnings in LPGA Tour events for 2005 appear in the file named LPGA (LPGA website, 2006). Earnings ($1000s) is the total earnings in thousands of dollars; Scoring Avg. is the average score for all events; Greens in Reg. is the percentage of time a player is able to hit the green in regulation; and Putting Avg. is the average number of putts taken on greens hit in regulation. A green is considered hit in regulation if any part of the ball is touching the putting surface and the difference between the value of par for the hole and the number of strokes taken to hit the green is at least 2.
a. Develop an estimated regression equation that can be used to predict the average score for all events given the percentage of time a player is able to hit the green in regulation and the average number of putts taken on greens hit in regulation.
b. Plot the standardized residuals against ŷ. Does the residual plot support the assumption about ϵ? Explain.
c. Check for any outliers. What are your conclusions?
d. Are there any influential observations? Explain.
Get solution
15.44 Refer to the Simmons Stores example introduced in this section. The dependent variable is coded as y = 1 if the customer used the coupon and 0 if not. Suppose that the only information available to help predict whether the customer will use the coupon is the customer’s credit card status, coded as x = 1 if the customer has a Simmons credit card and x = 0 if not.
a. Write the logistic regression equation relating x to y.
b. What is the interpretation of E( y) when x = 0?
c. For the Simmons data in Table 15.11, use Minitab to compute the estimated logit.
d. Use the estimated logit computed in part (c) to compute an estimate of the probability of using the coupon for customers who do not have a Simmons credit card and an estimate of the probability of using the coupon for customers who have a Simmons credit card.
e. What is the estimate of the odds ratio? What is its interpretation?
Get solution
15.45 In Table 15.12 we provided estimates of the probability using the coupon in the Simmons Stores catalog promotion. Adifferent value is obtained for each combination of values for the independent variables.
a. Compute the odds in favor of using the coupon for a customer with annual spending of $4000 who does not have a Simmons credit card (x1 = 4, x2 = 0).
b. Use the information in Table 15.12 and part (a) to compute the odds ratio for the Simmons credit card variable x2 = 0, holding annual spending constant at x1 = 4.
c. In the text, the odds ratio for the credit card variable was computed using the information in the $2000 column of Table 15.12. Did you get the same value for the odds ratio in part (b)?
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15.46 Community Bank would like to increase the number of customers who use payroll direct deposit. Management is considering a new sales campaign that will require each branch manager to call each customer who does not currently use payroll direct deposit. As an incentive to sign up for payroll direct deposit, each customer contacted will be offered free checking for two years. Because of the time and cost associated with the new campaign, management would like to focus their efforts on customers who have the highest probability of signing up for payroll direct deposit. Management believes that the average monthly balance in a customer’s checking account may be a useful predictor of whether the customer will sign up for direct payroll deposit. To investigate the relationship between these two variables, Community Bank tried the new campaign using a sample of 50 checking account customers who do not currently use payroll direct deposit. The sample data show the average monthly checking account balance (in hundreds of dollars) and whether the customer contacted signed up for payroll direct deposit (coded 1 if the customer signed up for payroll direct deposit and 0 if not). The data are contained in the data set named Bank; a portion of the data follows....
a. Write the logistic regression equation relating x to y.
b. For the Community Bank data, use Minitab to compute the estimated logistic regression equation.
c. Conduct a test of significance using the G test statistic. Use α = .05.
d. Estimate the probability that customers with an average monthly balance of $1000 will sign up for direct payroll deposit.
e. Suppose Community Bank only wants to contact customers who have a .50 or higher probability of signing up for direct payroll deposit. What is the average monthly balance required to achieve this level of probability?
f. What is the estimate of the odds ratio? What is its interpretation?
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15.47 Over the past few years the percentage of students who leave Lakeland College at the end of the first year has increased. Last year Lakeland started a voluntary one-week orientation program to help first-year students adjust to campus life. If Lakeland is able to show that the orientation program has a positive effect on retention, they will consider making the program a requirement for all first-year students. Lakeland’s administration also suspects that students with lower GPAs have a higher probability of leaving Lakeland at the end of the first year. In order to investigate the relation of these variables to retention, Lakeland selected a random sample of 100 students from last year’s entering class. The data are contained in the data set named Lakeland; a portion of the data follows....The dependent variable was coded as y = 1 if the student returned to Lakeland for the sophomore year and y = 0 if not. The two independent variables are:...
a. Write the logistic regression equation relating x1 and x2 to y.
b. What is the interpretation of E(y) when x2 = 0?
c. Use both independent variables and Minitab to compute the estimated logit.
d. Conduct a test for overall significance using α = .05.
e. Use α = .05 to determine whether each of the independent variables is significant.
f. Use the estimated logit computed in part (c) to compute an estimate of the probability that students with a 2.5 grade point average who did not attend the orientation program will return to Lakeland for their sophomore year. What is the estimated probability for students with a 2.5 grade point average who attended the orientation program?
g. What is the estimate of the odds ratio for the orientation program? Interpret it.
h. Would you recommend making the orientation program a required activity? Why or why not?
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15.48 Consumer Reports conducted a taste test on 19 brands of boxed chocolates. The following data show the price per serving, based on the FDA serving size of 1.4 ounces, and the quality rating for the 19 chocolates tested (Consumer Reports, February 2002)....Suppose that you would like to determine whether products that cost more rate higher in quality. For the purpose of this exercise, use the following binary dependent variable:y = 1 if the quality rating is very good or excellent and 0 if good or fair
a. Write the logistic regression equation relating x = price per serving to y.
b. Use Minitab to compute the estimated logit.
c. Use the estimated logit computed in part (b) to compute an estimate of the probability a chocolate that has a price per serving of $4.00 will have a quality rating of very good or excellent.
d. What is the estimate of the odds ratio? What is its interpretation?
Get solution
15.49 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...
a. Interpret the coefficients in this estimated regression equation.
b. Estimate 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
15.50 The personnel director for Electronics Associates developed the following estimated regression equation relating an employee’s score on a job satisfaction test to his or her length of service and wage rate....where...
a. Interpret the coefficients in this estimated regression equation.
b. Develop an estimate of the job satisfaction test score for an employee who has four years of service and makes $6.50 per hour.
Get solution
15.51 A partial computer output from a regression analysis follows....
a. Compute the missing entries in this output.
b. Use the F test and α = .05 to see whether a significant relationship is present.
c. Use the t test and α = .05 to test H0: β1 = 0 and H0: β2 = 0.
d. Compute ....
Get solution
15.52 Recall that in exercise 49, 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...A portion of the Minitab computer output follows....
a. Complete the missing entries in this output.
b. Use the F test and a .05 level of significance to see whether a significant relationship is present.
c. Use the t test and α = .05 to test H0: β1 = 0 and H0: β2 = 0.
d. Did the estimated regression equation provide a good fit to the data? Explain.
Get solution
15.53 Recall that in exercise 50 the personnel director for Electronics Associates developed the following estimated regression equation relating an employee’s score on a job satisfaction test to length of service and wage rate....where...A portion of the Minitab computer output follows....
a. Complete the missing entries in this output.
b. Compute F and test using α = .05 to see whether a significant relationship is present.
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.
Get solution
15.54
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15.55 Consumer Reports provided extensive testing and ratings for 24 treadmills. An overall score, based primarily on ease of use, ergonomics, exercise range, and quality, was developed for each treadmill tested. In general, a higher overall score indicates better performance. The following data show the price, the quality rating, and overall score for the 24 treadmills (Consumer Reports, February 2006).......
a. Use these data to develop an estimated regression equation that could be used to estimate the overall score given the price.
b. Use α = .05 to test for overall significance.
c. To incorporate the effect of quality, a categorical variable with three levels, we used two dummy variables: Quality-E and Quality-VG. Each variable was coded 0 or 1 as follows....Develop an estimated regression equation that could be used to estimate the overall score given the price and the quality rating.
d. For the estimated regression equation developed in part (c), test for overall significance using α = .10.
e. For the estimated regression equation developed in part (c), use the t test to determine the significance of each independent variable. Use α = .10.
f. Develop a standardized residual plot. Does the pattern of the residual plot appear to be reasonable?
g. Do the data contain any outliers or influential observations?
h. Estimate the overall score for a treadmill with a price of $2000 and a good quality rating. How much would the estimate change if the quality rating were very good? Explain.
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15.56
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15.57
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