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business statistics a first course
Introduction To Business Statistics 7th Edition Ronald M. Weiers - Solutions
The models in this section include the first-, second-, and third-order polynomials. What would be the form of a fifth-order polynomial? Would such a polynomial model tend to be practical for use with business data?
What percentage of the variation in days of sick leave this year is explained by the regression equation you generated for question 1? To the extent that there is unexplained variation in the number of sick days taken this year, what other variables —including possible variables not in the
Use a multiple regression model to estimate the number of days of sick leave this year as a function of two variables: days of sick leave taken last year and whether the employee is a participant in the exercise program.Interpret the partial regression coefficients in the equation. Specifically,
Use a multiple regression model to estimate PRICE as a function of SQFEET, BEDROOMS, AGE, DALLAS, and EASTON.a. Interpret the partial regression coefficients in the equation. Specifically, comment on the sign and numerical value of the partial regression coefficient for EASTON in terms of the claim
Considering the claim that the two houses in question did not sell for their fair market value:a. Compare the selling prices of the two houses to the average selling price of all houses sold in the most recent three-month period. Does the difference appear to be substantial?b. Provide at least two
With variable 7 (attitude toward Springdale Mall) as the dependent variable, perform a multiple regression analysis using variables 21 (good var iety of sizes/styles), 22 (sales staff helpful/friendly), 26 (gender), and 28 (marital status) as the four indepen dent variables.If possible, have the
Data file XR16058 lists the following data for a sample of automatic teller machine (ATM) customers:time (seconds) to complete their transaction, estimated age, and gender (1 5 male, 0 5 female).a. Determine the multiple regression equation and interpret the partial regression coefficients.b. What
In Exercise 16.56, what would be the estimated selling price of a house occupying a 0.01-acre lot, with 100 square feet of living area and no central air conditioning?Considering the nature of this “house,” does this selling price seem reasonable? If not, might the computer have made an error
Data file XR16056 lists the following information for a sample of local homes sold recently: selling price (dollars), lot size (acres), living area (square feet), and whether the home is air conditioned (1 5 AyC, 0 5 no AyC).a. Determine the multiple regression equation and interpret the partial
An admissions counselor, examining the usefulness of x1 5 total SAT score and x2 5 high school class rank in predicting y 5 freshman grade point average (GPA) at her university, has collected the sample data shown here and listed in file XR16055. Rank in high school class is expressed as a
A university placement director is interested in the effect that grade point average (GPA) and the number of university activities listed on the résumé might have on the starting salaries of this year’s graduating class. He has collected these data for a sample of 10 graduates:a. Determine the
Annual per-capita consumption of all fresh fruits versus that of apples and grapes from 1998 through 2003 was as shown in the table.a. Determine the multiple regression equation and interpret the partial regression coefficients.b. What is the estimated per-capita consumption of all fresh fruits
Interested in the possible relationship between the size of his tip versus the size of the check and the number of diners in the party, a food server has recorded the following for a sample of 8 checks:a. Determine the multiple regression equation and interpret the partial regression
A safety researcher has measured the speed of automobiles passing his vantage point near an interstate highway. He has also recorded the number of occupants and whether the driver was wearing a seat belt. The data are shown in the following table with seat belt users coded as 1, nonusers as 0.
For 12 recent clients, a weight-loss clinic has collected the following data. (Session is coded as 1 for day, 0 for evening. Gender is coded as 1 for male, 0 for female.) Using a computer statistical package, carry out a multiple regression analysis, interpret the partial regression coefficients,
What is multicollinearity, and how can it adversely affect multiple regression analysis? How can we tell whether multicollinearity is present?( DATA SET ) Note: Exercises 16.50 and 16.51 require a computer and statistical software.
For the regression equation in Exercise 16.47, the estimated number of persons swimming on a zero-degree weekday would be 100 persons. Since this level of pool attendance is unlikely on such a day, does this mean that an error was made in constructing the regression equation?Explain.
A multiple regression equation has been developed for y 5 daily attendance at a community swimming pool, x1 5 temperature (degrees Fahrenheit), and x2 5 weekend versus weekday (x2 5 1 for Saturday and Sunday, and 0 for the other days of the week). For the regression equation shown below, interpret
What is a dummy variable, and how is it useful to multiple regression? Give an example of three dummy variables that could be used in describing your home town.
Of all U.S. credit unions, 67% have a “courtesy overdraft” policy that automatically covers overdrafts, with the median fee for each overdraft being approximately$25. For 14 federal credit unions with a courtesy overdraft policy, the accompanying table shows their fee income, total assets, and
An efficiency expert wants to determine whether the time an assembly worker requires to perform a standard task might be related to (1) the number of years on the job and (2) the score on a pre-employment aptitude test. The following data have been collected.a. Determine the multiple regression
For the regression equation obtained in Exercise 16.19, analyze the residuals by (a) constructing a histogram, (b) utilizing the normal probability plot, and(c) plotting the residuals versus each of the independent variables. Do any of the assumptions of the multiple regression model appear to have
For the regression equation obtained in Exercise 16.18, analyze the residuals by (a) constructing a histogram, (b) utilizing the normal probability plot, and (c) plotting the residuals versus each of the independent variables. Do any of the assumptions of the multiple regression model appear to
For the regression equation obtained in Exercise 16.13, analyze the residuals by (a) constructing a histogram, (b) utilizing the normal probability plot, and(c) plotting the residuals versus each of the independent variables. Do any of the assumptions of the multiple regression model appear to have
For the regression equation obtained in Exercise 16.12, analyze the residuals by (a) constructing a histogram, (b) utilizing the normal probability plot, and(c) plotting the residuals versus each of the independent variables. Do any of the assumptions of the multiple regression model appear to have
For the regression equation obtained in Exercise 16.11, analyze the residuals by (a) constructing a histogram, (b) utilizing the normal probability plot, and(c) plotting the residuals versus each of the independent variables. Do any of the assumptions of the multiple regression model appear to have
Given the printout in Exercise 16.15, briefly summarize the overall results in the context of that exercise:a. Identify and interpret each of the partial regression coefficients.b. What proportion of the variation in y is explained by the equation?c. At what p-value is the overall regression
Discuss residual analysis in terms of the assumptions required for using the multiple regression model.
What role does the normal probability plot play in examining whether the multiple regression model is appropriate for a given set of data?
Information describing 98 of the top automobile dealership groups in the United States is provided in computer database file DEALERS. For each group, the data include (1) total group revenue during 1999, (2) the number of retail vehicles sold that year, and (3) the number of dealerships in the
The computer database GROWCO describes the characteristics of 100 companies identified by Fortune as among the fastest growing. Three of the variables listed are(1) estimated stock price/earnings ratio next year, (2) annual revenue growth (as a percentage), and (3) annual earnings per share growth
Referring to the least-squares regression equation and printout obtained in Exercise 16.19:a. At the 0.05 level, is the overall regression equation significant?b. Use the 0.05 level in concluding whether each partial regression coefficient differs significantly from zero.
Referring to the least-squares regression equation and printout obtained in Exercise 16.18:a. At the 0.10 level, is the overall regression equation significant?b. Use the 0.10 level in concluding whether each partial regression coefficient differs significantly from zero.
Given the printout in Exercise 16.15, (a) determine the 90% confidence interval for each partial regression coefficient, and (b) interpret each significance test in the context of that exercise.( DATA SET ) Note: Exercises 16.32–16.35 require a computer and statistical software.
For the multiple regression equation obtained in Exercise 16.12:a. At the 0.05 level, is the overall regression equation significant?b. Use the 0.05 level in concluding whether each partial regression coefficient differs significantly from zero.c. Interpret the results of the preceding tests in the
For the multiple regression equation obtained in Exercise 16.11:a. At the 0.05 level, is the overall regression equation significant?b. Use the 0.05 level in concluding whether each partial regression coefficient differs significantly from zero.c. Interpret the results of the preceding tests in the
What is the relationship between (a) the results of the hypothesis test examining whether b3 differs significantly from zero at the 0.02 level and (b) the 98%confidence interval for 3?
For the multiple regression equation obtained in Exercise 16.11, what is the coefficient of multiple determination and exactly what does it mean?
For the multiple regression equation obtained in Exercise 16.12, what is the coefficient of multiple determination and exactly what does it mean?
Given the printout in Exercise 16.15, identify the coefficient of multiple determination and interpret its value in terms of that exercise.( DATA SET ) Note: Exercises 16.26 and 16.27 require a computer and statistical software.
Among the results of a multiple regression analysis are the following sum-of-squares terms: SST, SSR, and SSE. What does each term represent, and how do the terms contribute to our understanding of the relationship between y and the set of independent variables?
What is the coefficient of multiple determination, and what does it tell us about the relationship between y and the independent variables?
For the multiple regression equation obtained in Exercise 16.13, determine the approximatea. 95% confidence interval for the mean crispness rating of pies that are baked 5.0 minutes at 300 degrees.b. 95% prediction interval for the crispness rating of a pie that is baked 5.0 minutes at 300 degrees.
For the multiple regression equation obtained in Exercise 16.12, determine the approximatea. 95% confidence interval for the mean overall rating of cars that receive ratings of 8 on ride, 7 on handling, and 9 on driver comfort.b. 95% prediction interval for the overall rating of a car that has
For the multiple regression equation obtained in Exercise 16.11, determine the approximatea. 95% confidence interval for the mean number of new visitors for clubs using a 5-column-inch ad and offering an $80 discount.b. 95% prediction interval for the number of new visitors to a given club when the
In considering whether to implement a program where selected entering freshmen would be required to take a precalculus refresher course before moving on to calculus, a university’s business college has given mathematical proficiency tests to a sample of entering freshmen. The college hopes to use
In testing eight value notebook computers, PC World reported various physical and performance measures of each. Data included overall rating, street price, PC WorldBench 4 performance score, and battery life, with the results shown here.a. From these data, obtain the multiple regression equation
The regression equation yˆ 5 5.0 1 1.0x1 1 2.5x2 has been fitted to 20 data points. The means of x1 and x2 are 25 and 40, respectively. The sum of the squared differences between observed and predicted values of y has been calculated as SSE 5 173.5, and the sum of squared differences between y
Given the printout in Exercise 16.15, determine the approximatea. 90% confidence interval for the mean rating on test 4 for units that have been rated at 300, 500, and 400 on the first three tests.b. 90% prediction interval for the rating a unit will get on test 4 if its ratings are 300, 500, and
The president of the fast-food chain believes that a new franchise being planned for construction in a suburban neighborhood would have experienced$6.0 million in counter sales and $4.0 million in drive-through sales had it been in operation during the preceding year. For these sales figures, what
For franchises having counter sales of $6.0 million and drive-through sales of$4.0 million, what is the approximate 95% confidence interval for their average net profit?
During its manufacture, a product is subjected to four different tests, each giving a score of 200 to 800. An efficiency expert claims the fourth test to be unnecessary since its results can be predicted based on the first three.The following Minitab printout is an analysis of scores received by a
The following data have been reported for a sample of 10 major U.S. zoological parks:a. Determine the least-squares multiple regression equation.b. Interpret the y-intercept and partial regression coefficients.c. What is the estimated budget for a zoological park that draws an annual attendance of
The makers of a pie crust mix have baked test pies and collected the following data on y 5 amount of crispness (a rating of 1 to 100), x1 5 minutes in the oven, and x2 5 oven temperature(degrees Fahrenheit).a. Determine the least-squares multiple regression equation.b. Interpret the y-intercept and
In testing 9 sedans, an automotive publication rated each on 13 different characteristics, including ride, handling, and driver comfort. Each vehicle also received an overall rating. Scores for each vehicle were as follows.a. Determine the least-squares multiple regression equation.b. Interpret the
The owner of a large chain of health spas has selected eight of her smaller clubs for a test in which she varies the size of the newspaper ad and the amount of the initiation fee discount to see how this might affect the number of prospective members who visit each club during the following week.
A study describes operating costs for comparable manufacturing plants operating in 15 different U.S. metropolitan areas. From the costs obtained in the study, the following multiple regression equation was developed:yˆ 5 1.0 1 1.1x1 1 2.8x2, with yˆ 5 total operating cost, x1 5 labor cost, and x2
Last year’s utility bill (in dollars) for a sample of homes is estimated by the multiple regression equation yˆ 5 300 1 7x1 1 13x2, where x1 is the number of occupants and x2 is the number of rooms in the home.a. Identify the y-intercept and partial regression coefficients.b. If 3 people live in
For the multiple regression equation yˆ 5 100 1 20x1 2 3x2 1 120x3:a. Identify the y-intercept and partial regression coefficients.b. If x1 5 12, x2 5 5, and x3 5 10, what is the estimated value of y?c. If x3 were to increase by 4, what change would be necessary in x2 in order for the estimated
In simple linear regression, the regression equation is a straight line. In multiple regression, what geometric form is taken by the regression equation when there are two independent variables? When there are three or more independent variables?
What assumptions are required in using the multiple regression model?
Explain each of the terms in the multiple regression model.
For the regression equation obtained in Exercise 15.95, analyze the residuals by (a) constructing a histogram,(b) using a normal probability plot, (c) plotting the residuals versus the x values, and (d) plotting the residuals versus the order in which they were observed. Do any of the assumptions
Computer database GROWCO describes the characteristics of 100 companies identified by Fortune as among the fastest growing. Two of the variables listed are (1) estimated stock price/earnings ratio next year and (2) annual revenue growth (as a percentage). Source:“Fortune’s 100 Fastest-Growing
For the regression equation obtained in Exercise 15.93, analyze the residuals by (a) constructing a histogram, (b) using a normal probability plot, (c) plotting the residuals versus the x values, and (d) plotting the residuals versus the order in which they were observed.Do any of the assumptions
The National Association of Realtors has reported data on housing affordability for 1990–1999, and values for two of the variables are listed in file XR15093. Representing affordability is y average monthly mortgage payment as a percentage of median household income.Representing the cost of a
For the regression equation obtained in Exercise 15.91, analyze the residuals by (a) constructing a histo gram, (b) using a normal probability plot, (c) plotting the residuals versus the x values, and (d) plotting the residuals versus the order in which they were observed.Do any of the assumptions
A university administrator has collected data on total Scholastic Aptitude Test (SAT) score versus freshman grade point average (GPA) for a sample of students who recently finished their first year at the university.The data are listed in file XR15091. Given these data:a. Determine the
A physical-fitness researcher tests 25 professional football players, finding that the time required to run 40 yards (y, in seconds) is related to weight (x, in pounds)by the least-squares equation yˆ 2.0 0.038x.According to this equation, a person weighing 200 pounds would run the 40-yard
Given the data and regression analysis for Exercise 15.76, construct and interpret the 95% confidence and prediction intervals associated with 1.4 million housing starts.
Given the data and regression analysis for Exercise 15.73, construct and interpret the 90% confidence and prediction intervals associated with a 3-year annualized rate of return of 7.0%.
Given the data and regression analysis for Exercise 15.72, construct and interpret the 95% confidence and prediction intervals associated with a score of 60 on the sales aptitude test.
For the ANOVA portion of the printout shown in Exercise 15.85, explain the exact meaning of each number in the “SS” and “F” columns.
A tire company has carried out tests in which rolling resistance (pounds) and inflation pressure (pounds per square inch, or psi) have been measured for psi values ranging from 20 to 45. The regression analysis is summarized in the following Minitab printout:a. To the greatest number of decimal
For the ANOVA portion of the printout shown in Exercise 15.83, explain the exact meaning of each number in the “SS” and “F” columns.
The following Minitab output describes the results of a production experiment in which n 10 different steel bars were subjected to tempering times ranging from 6 to 10 seconds, then measured for tensile strength(thousands of pounds):a. To the greatest number of decimal places in the printout, what
For the regression analysis of the data in Exer cise 15.81:a. Use the 0.10 level in testing whether the population coeffi cient of correlation could be zero.b. Use the 0.10 level in testing whether the population regression equation could have a slope of zero.c. Construct the 90% confi dence
As part of its ongoing testing and reporting program, the Insurance Institute for Highway Safety has crashed vehicles into a barrier intended to represent another vehicle’s bumper, then recorded the cost of repairs necessary to fix whatever damage has occurred.In these tests, the simulated bumper
For the regression analysis of the data in Exercise 15.79:a. Use the 0.05 level in testing whether the population coeffi cient of correlation could be zero.b. Use the 0.05 level in testing whether the population regression equation could have a slope of zero.c. Construct the 95% confi dence
The following data describe U.S. motor vehicle travel and fuel consumption from 2002 through 2006.The data represent billions of gallons consumed and billions of miles traveled, respectively.a. Determine the least-squares equation line for predicting fuel consumption on the basis of driving
For the regression analysis of the data in Exercise 15.77:a. Use the 0.10 level in testing whether the population coeffi cient of correlation could be zero.b. Use the 0.10 level in testing whether the population regression equation could have a slope of zero.c. Construct the 90% confi dence
In the early 1900s, population, prices, wages, and individual life insurance policy face amounts were all incredibly low compared to their counterparts of today.The following data show the number of life insurance policies (millions) and their total face amounts ($ millions)for five years selected
The data in the table describe retail furniture store sales ($ billions) versus housing starts over a 5-year time period.a. Determine the least-squares regression equation for predicting retail furniture store sales on the basis of housing starts.b. Determine and interpret the coeffi cients of
For 2004 through 2008, Coca-Cola annual operating revenues and net incomes were as shown below.Determine the least-squares regression line and interpret its slope. Estimate net income if the operating revenue is $30 billion. Year 2004 x = Operating Revenue $21.74 billion y = Net Income $4.85
Peoples Energy, Inc. reports the following data for operating revenue and net income for 2001–2005.Determine the least-squares regression line and interpret its slope. Estimate the net income if the operating revenue figure is $2500 million. x = Operating Revenue y = Net Income (Millions) Year
As of mid-June 2009, five U.S. Government Bond mutual funds were reported as having generated the 1-year and 3-year (annualized) rates of return shown below.a. Determine the least-squares regression line and interpret its slope.b. For a U.S. Government Bond mutual fund with a 3-year annualized rate
Prior to being hired, the five salespersons for a computer store were given a standard sales aptitude test.For each individual, the score achieved on the aptitude test and the number of computer systems sold during the first 3 months of their employment are shown here.Determine the least-squares
McDonald’s Corporation has reported the following values for total revenues and net income during the 1998 to 2005 period. All data are in billions of dollars:Determine the least-squares regression equation line for estimating net income and interpret its slope. For a year in which total revenues
For high school seniors entering college, and for y grade point average for the freshman year, x Scholastic Aptitude Test score would tend to be directly related to y. Provide an example of another personal variable that might be directly related to y along with an example of a personal variable
For households in a community, many different variables can be observed or measured. If y monthly mortgage payment, x annual income would probably be directly related to y. For y monthly mortgage payment, provide an example of an x variable likely to be(a) directly related to y, (b) inversely
For the regression equation obtained in Exercise 15.59, analyze the residuals by (a) constructing a histogram, (b) using a normal probability plot, (c) plotting the residuals versus the x values, and (d) plotting the residuals versus the order in which they were observed. Do any of the assumptions
For the regression equation obtained in Exercise 15.57, analyze the residuals by (a) constructing a histogram, (b) using a normal probability plot,(c) plotting the residuals versus the x values, and(d) plotting the residuals versus the order in which they were observed. Do any of the assumptions of
For the y and x values listed in file XR15066, obtain the simple linear regression equation, then analyze the residuals by (a) constructing a histogram, (b) using a normal probability plot, (c) plotting the residuals versus the x values, and (d) plotting the residuals versus the order in which they
For the y and x values listed in file XR15065, obtain the simple linear regression equation, then analyze the residuals by (a) constructing a histogram, (b) using a normal probability plot, (c) plotting the residuals versus the x values, and (d) plotting the residuals versus the order in which they
“The Ford Edsel was sold only in the 1957–1959 model years, but the company made a big mistake in dropping it. If they had just fitted a regression line to the sales for these 3 years and extended it to 2006, they could have seen that it would have been one of the ten sales leaders of that
A firm finds the coefficient of correlation between y 5 annual sales and x 5 annual expen diture on research and development to be r 5 10.90. Comment on the likely direction of causation, if any, between these variables.
What is spurious correlation? Provide a real or hypothetical example where two variables might exhibit such a relationship.
What is residual analysis, and what information can it provide?
In regression analysis, what is a “residual”?
Computer database GROWCO describes the characteristics of 100 companies identified by Fortune as the fastest growing. Two of the variables listed are revenue and net income (millions of dollars) for the most recent four quarters. Determine the linear regression equation describing net income as a
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