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business
business statistics a first course
Questions and Answers of
Business Statistics A First Course
For the situation and variables in Exercise 17.8, fit an exponential model and use it to estimate the world record time for the 100-meter dash in the year 2014. The underlying data are in file
For the situation and variables in Exercise 17.7, fit an exponential model and use it to estimate the average room rate for a market in which the average occupancy rate is 70%. The underlying data
Following data transformation, regression analysis results in the estimation equation log yˆ 5 3.15 1 0.473 log x1 1 0.354 log x2. Trans form this equation to the equivalent multiplicative model
Following data transformation, regression analysis results in the estimation equation log yˆ 5 20.179 10.140x. Transform this equation to the equivalent exponential model with estimation equation
For a small sample of suburban homes recently sold, the selling price ($), living space (square feet), and suburban area (Sunny Haven, Easy Acres, or Rolling Hills) have been recorded. Given the data
An efficiency expert has studied 12 employees who perform similar assembly tasks, recording productivity(units per hour), number of years of experience, and which one of three popular assembly
A researcher has observed 50 automatic teller machine (ATM) users outside the gift shop of a museum, and the data are in file XR17028. With y 5 amount withdrawn(dollars), x1 5 time required for the
In a PC World comparison of computer hard drives, data describing the drives included the following variables: price (dollars), disk capacity (gigabytes), and rotational speed (RPM). The data are in
The dean of a law school has developed a regression equation for estimating the starting salary (thousands of dollars) of a new graduate on the basis of two independent variables: x1 5 the score
The manager of an ice cream store has developed a regression equation for estimating the number of customers on the basis of two independent variables: x1 5 the high temperature (degrees Fahrenheit)
Repeat Exercise 17.23, but for clients whose risk levels have been specified as low, medium, high, or very high.
Data to be used in a linear regression analysis involving clients of an investment counselor include information regarding the risk level each client has specified:low, medium, or high. Determine the
Repeat Exercise 17.21, but assume that more information is available regarding the specific type of credit card that was used for the purchase, that is, Visa, MasterCard, or other.
For a sample of 100 recent credit-card customers of a company’s on-line store, the following data are available: the dollar amount of merchandise ordered during the visit, how much time (minutes)
Repeat Exercise 17.19, but using a second-order model with interaction. Interpreting the R2 value, to what extent has inclusion of the squared terms improved the model’s explanatory power?
For the Car and Driver information described in Exercise 17.9, it would seem reasonable that the number of seconds required to accelerate to 60 mph would depend on both a car’s weight and its
Repeat Exercise 17.17, using the data in file XR17017, but with y 5 total operating revenue (millions of dollars), x1 5 number of aircraft, and x2 5 number of employees.
The Air Transport Association has reported the following kinds of information describing 23 individual U.S. airlines: total operating revenue, number of aircraft, number of employees, and number of
Auto Rental News has reported U.S. operations data for 15 top rental-car companies. Using data file XR17016, with y 5 rental revenue (millions of dollars), x1 5 thousands of cars in service, and x2 5
The personnel director of the communications firm in Exercise 17.5 has just provided another variable describing the company’s technical sales representatives:their scores on a sales aptitude test
The regression model yˆ 5 200 1 5x1 2 2x2 has been fitted to a set of data. If x2 5 10, what will be the effect on yˆ if x1 increases by 1 unit? Will your answer change if x2 5 20? Given the
In Exercise 17.12, suppose the researcher wishes to use one of the models in this section, but is uncertain as to whether y might be nonlinearly related to x1 and/or x2.Also, the researcher doesn’t
A researcher suspects that the dependent variable y is linearly related to both x1 and x2, but believes there is little or no interaction between the two predictor variables.Of the models in this
For the 20 top-grossing U.S. films of the 1990s, data have been reported for y foreign gross ticket sales and x 5 domestic gross ticket sales, both in millions of dollars. The printout here shows
Repeat Exercise 17.9, but for a third-order model and using y 5 top speed (mph) as the dependent variable.During the 1960s, manufacturers of the so-called “muscle cars” were accused of
An early edition of Car and Driver magazine reported the engine horsepower, top speed (mph), curb weight(pounds), and 0–60 mph acceleration time (seconds) for a selection of automobiles that ranged
During the years 2005–2009, the world record for the 100-meter dash was repeatedly broken as never before. The years and corresponding record times are in data file XR17008 and shown in the table.
A travel research firm has reported average occupancy and room rates for hotels in 26 U.S. hotel markets.The data are also in file XR17007. For y 5 average room rate (dollars) and x 5 average
As the number of cable television subscribers has increased, the number of subscribers to satellite tele vi sion services has increased as well. For y 5 number of satellite subscribers and x 5 number
A communications firm employs a large number of technical sales representatives who make personal visits to potential customers. For data collected on y 5 average amount of sales per call and x 5
As the temperature increases, an experimental lubricant initially decreases in viscosity (resistance to flow), then increases, then decreases again. Of the polynomial models discussed in this
As x increases, y decreases, and at an increasing rate. If a second-order polynomial model were fitted to the scatterplot of the data, what would be the signs of the partial regression coefficients
As x increases, y increases, but at a decreasing rate.If a second-order polynomial model were fitted to the scatterplot of the data, what would be the signs of the partial regression coefficients in
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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.(
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
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
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
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
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.
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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