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business
business statistics a first course

Questions and Answers of Business Statistics A First Course

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
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
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
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
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
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
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 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.
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
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
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
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
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
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
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
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
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
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
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
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,
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)
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)
“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
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,
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
Given the information in Exercise 15.13, determine the linear regression equation describing January–May burned acreage in Florida as a function of January–May rainfall in the state, then
The General Aviation Manufacturers Asso ciation has reported annual flying hours and fuel consumption for airplanes with a single, piston-driven engine as listed in file XR15057. Data are in millions
Given the information below, calculate SST, SSR, and SSE, determine the coefficient of determination, then use ANOVA and the 0.05 level in testing whether r2 is significantly different from zero. X:
Given the information below, calculate SST, SSR, and SSE, determine the coefficient of determination, then use ANOVA and the 0.05 level in testing whether r2 is significantly different from zero. X:
In a regression analysis, the sum of the squared deviations between y and }y is SST 5 200.0. If the sum of the squared deviations about the regression line is SSE 5 40.0, what is the coefficient of
In a regression analysis, the sum of the squared deviations between y and }y is SST 5 120.0. If the coefficient of correlation is r 5 0.7, what are the values of SSE and SSR?
How is analysis of variance related to regression analysis?
1 5.0x, and the standard deviation of the slope is listed as sb1 5 2.25.a. At the 0.05 level of significance, can we conclude that no linear relationship exists within the population of x and y
A computer analysis of 30 pairs of observations results in the least-squares regression equation yˆ 5
For the regression line developed in Exercise 15.38,a. Use the 0.05 level in testing whether the population coefficient of correlation could be zero.b. Use the 0.05 level in testing whether the
For the regression line developed in Exercise 15.37,a. Use the 0.05 level in testing whether the population coefficient of correlation could be zero.b. Use the 0.05 level in testing whether the
Based on sample data, the 95% confidence interval for the slope of the population regression line is found to be from 4.2 to 6.7. Based on this information, what is the most accurate statement that
Based on sample data, the 90% confidence interval for the slope of the population regression line is found to be from 2.5 to 1.4. Based on this information, what is the most accurate statement that
For n 5 37 data points, r2 5 0.29. At the 0.02 level of significance, can we conclude that the true coefficient of correlation could be zero?
For n 5 15 data points, r2 5 0.81. At the 0.05 level of significance, can we conclude that the true coefficient of correlation could be zero?
Testing the null hypothesis that the slope of the true regression line equals zero is equivalent to testing whether the true coefficient of correlation could be zero. Why?
For each of the 20 top-grossing U.S. films made during the 1990s, file XR15043 lists the domestic gross ticket sales versus foreign gross ticket sales (both in millions of U.S. dollars). Determine
For each of 10 popular prescription drugs, file XR15042 lists the retail price (in U.S. dollars) for the drug in several different countries, including the United States, Canada, Great Britain, and
Given the information in Exercise 15.12, determine and interpret the coefficients of correlation and determination for gross revenue versus the number of equity partners.
Given the information in Exercise 15.13, determine and interpret the coefficients of correlation and determination for January–May burned acreage in Florida versus January–May rainfall in the
It has been reported that the average American male consumes 3774 calories per day and that 72.2%of American males are overweight. This information, along with data for seven other countries, is
The following table compares U.S. population(millions) with U.S. per-capita consumption of bottled water (gallons).a. Determine the least-squares regression line and the value of r.b. What proportion
The Insurance Institute for Highway Safety has listed the following ratings based on collision and comprehensive claims for 12 makes of midsize fourdoor cars from the 2005–2007 model years. Higher
For a set of data, the total variation or sum of squares for y is SST 143.0, and the error sum of squares is SSE 24.0. What proportion of the variation in y is explained by the regression
In regression and correlation analysis, what are the two components of the total amount of variation in the y values? Define the coefficient of determination in terms of these components.
For the data in Exercise 15.23, and with y touchdown percentage and x interception percentage, determine and interpret the coefficients of correlation and determination.
The coefficient of correlation between variables y and x is 0.90. Calculate and interpret the value of the coefficient of determination.
The values of y and x are inversely related, and 64% of the variation in y is explained by the regression equation. What is the coefficient of correlation?
Differentiate between the coefficients of correlation and determination. What information does each one offer that the other does not?
Given the information in Exercise 15.12, determine and interpret the 90% confidence and prediction intervals associated with gross revenue when there are 200 equity partners.
Given the information in Exercise 15.13, determine and interpret the 90% confidence and prediction intervals associated with burned acreage in Florida when the January–May rainfall in the state is
Repeat Exercise 15.27, but with average retail units sold per dealer as the independent variable and with the 95% interval estimates assuming a dealer group for which the average number of retail
Information describing 98 of the top automobile dealership groups in the United States is provided in computer database file DEALERS. For calendar year 1999, the data include the number of dealers,
For the data in Exercise 15.10, find the standard error of estimate, then construct the 95% prediction interval for boat trailer sales during a year in which the number of boats sold is 500,000.(
For the data in Exercise 15.9, find the standard error of estimate, then construct the 95% prediction interval for the amount of stock owned by an individual employee who has been with the firm for 5
Repeat parts (a)–(e) of Exercise 15.23, but using the interception percentage as the independent variable, and for a quarterback who claims his interception percentage will be just 3.0% next year.
For the National Football League, ratings for the all-time leading passers were as shown below. Also shown for each quarterback is the percentage of passes that were interceptions, along with the
For the summary data provided in Exercise 15.21, construct a 95% prediction interval for an individual y value whenevera. x 5 2.b. x 5 3.c. x 5 4.
For n 6 data points, the following quantities have been calculated:a. Determine the least-squares regression line.b. Determine the standard error of estimate.c. Construct the 95% confidence interval
For a set of 8 data points, the sum of the squared differences between observed and estimated values of y is 34.72. Given this information, what is the standard error of estimate?
What happens to the width of a prediction interval for y as the x value on which the interval estimate is based gets farther away from the mean of x? Why?
For a given value of x, which will be wider, a 95%confidence interval or a 95% prediction interval? Explain.
Differentiate between a confidence interval and a prediction interval.
Is it possible for the standard error of estimate to be equal to zero? If so, under what circumstances?
What is the standard error of estimate, and what role does it play in simple linear regression and correlation analysis?
For the leading health maintenance organization(HMO) firms, data file XR15014 lists the number of persons enrolled in the HMO along with the number of plans the firm administers. Given these data,
The Florida ecosystem is heavily reliant on wet and dry seasons, and is particularly dependent on the winter and spring rainfall that helps reduce damage due to wildfires. Data file XR15013 lists the
For the top law firms in the world in terms of profit per equity partner, data file XR15012 lists the number of equity partners and the gross revenue($ millions) for the most recent fiscal year.
A media analyst studying popular movies has generated the accompanying table, which shows gross ticket sales during the initial 2 weeks following release compared to total gross sales during the
The following data represent x 5 boat sales and y boat trailer sales from 1995 through 2000.a. Determine the least-squares regression line and interpret its slope.b. Estimate, for a year during
For a sample of 8 employees, a personnel director has collected the following data on ownership of company stock versus years with the firm.a. Determine the least-squares regression line and
Determine the least-squares regression line for the data in Exercise 15.7, then calculate the sum of the squared deviations between y and y ˆ.
A scatter diagram includes the data points (x 5 3, y 5 8), (x 5 5, y 5 18), (x 5 7, y 5 30), and(x 5 9, y 5 32). Two regression lines are proposed:(1) y ˆ 5 5 1 3x, and (2) y ˆ 5 22 1 4x. Using the
Determine the least-squares regression line for the data in Exercise 15.5, then calculate the sum of the squared deviations between y and yˆ.
A scatter diagram includes the data points (x 5 2, y 5 10), (x 5 3, y 5 12), (x 5 4, y 5 20), and(x 5 5, y 5 16). Two regression lines are proposed:(1) y ˆ 5 10 1 x, and (2) yˆ 5 8 1 2x. Using the
What is the least-squares criterion, and what does it have to do with obtaining a regression line for a given set of data?
In the linear regression equation, y ˆ 5 b0 1 b1x, why is the term at the left given as y ˆ instead of simply y?
What assumptions are required in using the linear regression model?
Explain each term in the linear regression model, yi 5 0 1 1xi 1 i.
14.86 Apply either the chi-square or the Kolmogorov-Smirnov test for normality to the data described in Exercise 14.85. At the 0.05 level of significance, could the data have come from a normal
14.85 The weights (in ounces) of the first 34 units in a production run of cast-iron flywheels are in file XR14085.Using the 0.10 level of significance, test the randomness of this sequence of
14.84 Five computer operators have been asked to rate four different workstation arrangements in terms of comfort with 1 5 very uncomfortable to 10 5 very comfortable. Their ratings are in file
14.83 Reacting to a skeptical reader who doubts that so-called wine connoisseurs can really tell the difference between cheap and expensive wines, the dining editor of a city newspaper sets up a test
14.82 Comparing the attitudes of customers at three restaurants, a researcher selects a random sample of customers from each and asks each person to rate the restaurant on a scale of 50 to 100, with
14.81 A new taxi driver will be making regular trips from the airport to a downtown hotel. She has heard conflicting opinions as to which of two routes takes less time. When she randomly selects
14.80 Two applicants for a component assembly position with an electronics firm have been asked to complete each of six tasks that their jobs would typically involve. For each assigned task, file
14.79 In the past, telephone solicitors for a home improvement firm have been paid an hourly wage. A small-scale experiment has been set up in which five solicitors are given further incentive in the

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