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Introduction To Business Statistics 7th Edition Ronald M. Weiers - Solutions

For the multiple regression equation ŷ = 100 + 20x1 – 3x2 + 120x3: a. Identify the y-intercept and partial regression coefficients. b. If x1 = 12, x2 = 5, and x3 = 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
Last year’s utility bill (in dollars) for a sample of homes is estimated by the multiple regression equation ŷ = 300 + 7x1 + 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
For several years, Thorndike Sports Equipment has been a minority stockholder in the Snow Kingdom Ski Resort and Conference Center. The Thorn dikes visit Snow Kingdom several times each winter to meet with management and find out how business is going. In addition, the visits give them a chance for
This case involves the variables shown here and described in data file SHOPPING. Information like that gained from this case could provide management with useful insights into how two or more variables (including dummy variables) can help describe consumers’ overall attitude toward a shopping
Sam Easton started out as a real estate agent in Atlanta ten years ago. After working two years for a national real estate firm, he transferred to Dallas, Texas, and worked for another realty agency. His friends and relatives convinced him that with his experience and knowledge of the real estate
In Chapters 11 and 14, we visited Circuit Systems, Inc., a company that was concerned about the effectiveness of its new program for reducing the cost of absenteeism among hourly workers. Besides allowing employees to be paid for unused sick leave, the program also pays $200 toward membership in a
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?
Repeat Exercise 17.9, but for a third-order model and using y = top speed (mph) as the dependent variable. During the 1960s, manufacturers of the so-called “muscle cars” were accused of deliberately understating the massive amount of horsepower these engines produced. Examining the curve for
For the 20 top-grossing U.S. films of the 1990s, data have been reported for y = foreign gross ticket sales and x = domestic gross ticket sales, both in millions of dollars. The printout here shows the results for a second order polynomial model fitted to the data. What amount of foreign gross
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 have any idea as to whether interaction might exist between x1 and x2. Of the models in this
The regression model ŷ = 200 + 5x1 – 2x2 has been fitted to a set of data. If x2 = 10, what will be the effect on ŷ if x1 increases by 1 unit? Will your answer change if x2 = 20? Given the preceding, comment on whether interaction appears to exist between x1 and x2.
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 they were recently given. Using data file XR17015, with y = average dollar sales per call, x1 =
Auto Rental News has reported U.S. operations data for 15 top rental-car companies. Using data file XR17016, with y = rental revenue (millions of dollars), x1 = thousands of cars in service, and x2 = number of rental locations: a. Fit a first-order model of the form E(y) = β0 + β1x1 + β2x2.
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 aircraft departures. Using data file XR17017, with y = total operating revenue (millions of dollars),
Repeat Exercise 17.17, using the data in file XR17017, but with y = total operating revenue (millions of dollars), x1 = number of aircraft, and x2 = number of employees. Repeat exercise The Air Transport Association has reported the following kinds of information describing 23 individual U.S.
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 horsepower. Further, it would be logical to assume that horsepower and weight might interact. Using data
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 model?
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? In exercise For the Car and Driver information described in Exercise 17.9, it would seem reasonable that the
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) the customer spent at the site during the purchase visit, and whether the customer used a Visa credit
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. Repeat exercise For a sample of 100 recent credit-card customers of a company’s on-line store, the following data
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 number of qualitative independent variables that will be required to represent this information
Repeat Exercise 17.23, but for clients whose risk levels have been specified as low, medium, high, or very high. Repeat exercise 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,
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 = the high temperature (degrees Fahrenheit) for the day, and x2 = whether the day is during the weekend (coded as 1) or is a weekday (coded as
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 = the score achieved on the Law School Admission Test (LSAT) at the time of application, and x2 = whether the new
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 file XR17027. With y = price, x1 = disk capacity, and x2 = rotational speed (coded as 1 = 7200 RPM
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 = amount withdrawn (dollars), x1 = time required for the transaction (seconds), and x2 = gender (1 = female, 0 = male), determine the linear regression
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 methods the individual has chosen to use in performing the task. Given the data shown here, determine the
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 in the model?
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 shown here, determine the linear regression equation for estimating selling price based on the
Following data transformation, regression analysis results in the estimation equation log ŷ = – 0.179 + 0.140x. Transform this equation to the equivalent exponential model with estimation equation ŷ = b0b1x. (The base of the logarithms is 10.)
Following data transformation, regression analysis results in the estimation equation log ŷ = 3.15 + 0.473 log x1 +1 0.354 log x2. Trans form this equation to the equivalent multiplicative model with estimation equation ŷ = b0 x1b11x2b22. (The base of the logarithms is 10.)
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 are in file XR17007. In exercise A travel research firm has reported average occupancy and room rates
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 XR17008.In exercise
For the situation and variables in Exercise 17.17, fit a multiplicative model and use it to estimate the total operating revenue for an airline with 2000 employees and 10,000 departures. The underlying data are in file XR17017. In exercise The Air Transport Association has reported the following
For the situation and variables in Exercise 17.16, fit a multiplicative model and use it to estimate the rental revenue for a company with 80,000 cars in service and 2500 rental locations. The underlying data are in file XR17016. In exercise Auto Rental News has reported U.S. operations data for 15
One of the indicators that multicollinearity is present is when a variable that is known to be an important predictor ends up having a partial regression coefficient that is not significant. What are some of the other signals for the presence of multicollinearity?
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 section, which one would tend to be most applicable for such data? What would be the signs of the partial
For the situation and variables in Exercise 17.16, use data file XR17016 and generate a correlation matrix for the independent variables. Examine the correlation matrix and comment on the possible presence of multicollinearity. In exercise Auto Rental News has reported U.S. operations data for 15
For the situation and variables in Exercise 17.17, use data file XR17017 and generate a correlation matrix for these independent variables: number of aircraft, number of employees, and number of aircraft departures. Examine the correlation matrix and comment on the possible presence of
Circulation (millions) for Sunday newspapers versus morning and evening daily papers for 1999€“2007 are shown here. The data are also in file XR17044. With Sunday circulation as the dependent variable, generate the correlation matrix for the independent variables and comment on the
For the years 1998€“2008, production in the U.S. energy sector included the quantities shown here. The variables represent total energy production as well as energy production from nonrenewable fossil fuels. The units are in quadrillion Btu and the data are also in file XR17045. For these
What is stepwise regression, and when is it desirable to make use of this multiple regression technique?
In general, on what basis are independent variables selected for entry into the equation during stepwise regression?
The two largest values in a correlation matrix are the 0.850 correlation between y and x4, and the 0.790 correlation between y and x9. During a stepwise regression analysis, x4 is the first independent variable brought into the equation. Will x9 necessarily be next? If not, why not?
The following Minitab printout is for a stepwise regression with 10 independent variables and 50 observations:a. List the order in which the independent variables have been introduced. b. What is the multiple regression equation after two independent variables have been introduced? c. As of step 3,
A communications firm employs a large number of technical sales representatives who make personal visits to potential customers. For data collected on y = average amount of sales per call and x = number of years of experience, the accompanying scatter diagram has been constructed. If a third-order
For the data in Exercise 17.44, and using Sunday circulation as the dependent variable, perform conventional multiple regression and stepwise regression analyses on the data, then compare the results of the two approaches. The data are in file XR17044. We suggest that Minitab users specify
For the data in Exercise 17.45, and using total nonrenewable energy production as the dependent variable, perform conventional multiple regression and stepwise regression analyses on the data, then compare the results of the two approaches. The data are in file XR17045.In exerciseWe suggest that
For the situation, data, and variables described in Exercise 17.16, perform conventional multiple regression and stepwise regression analyses on the data, then compare the results of the two approaches. The data are in file XR17016. In exercise Auto Rental News has reported U.S. operations data for
For the situation, data, and variables described in Exercise 17.15, perform conventional multiple regression and stepwise regression analyses on the data, then compare the results of the two approaches. The data are in file XR17015. In exercise The personnel director of the communications firm in
For the situation and data described in Exercise 17.17, perform conventional multiple regression and stepwise regression analyses on the data, then compare the results of the two approaches. Use total operating revenue as the dependent variable and number of aircraft, number of employees, and
An officer training program has 9 board members who provide ratings for the candidates. The high and low scores are dropped before the overall rating is computed. For a sample of 28 persons from the most recent class of candidates, the overall ratings and ratings by the individual board members are
Using the data file for Exercise 17.55: a. Apply stepwise regression with the rating by board member 1 as the dependent variable and the ratings by the other 8 members as the set of independent variables from which to select. Interpret the results. b. Using only the independent variables introduced
Using the data file for Exercise 17.55: a. Apply stepwise regression with the rating by board member 9 as the dependent variable and the ratings by the other 8 members as the set of independent variables from which to select, then interpret the results. b. Including only the independent variables
As reported by the Recording Industry Association of America, the percentage of recorded music dollar sales in CD format was as shown here for the years 2000 through 2007. The data are also in file XR17058. Using x = 1 through 8 to represent years 2000€“2007, fit a second-order polynomial
J.K. Rowling’s popular Harry Potter books have tended to become thicker with each new edition. The publication year and page count for U.S. editions for the first seven books were as shown on the next page. The data are also in file XR17059. Using year codes so that x = 1 corresponds to 1998, the
As the number of cable television subscribers has increased, the number of subscribers to satellite television services has increased as well. For y = number of satellite subscribers and x = number of cable subscribers, the scatter diagram shown here has been constructed. Of the polynomial models
For 1995 through the first half of 2009, PricewaterhouseCoopers and the National Venture Capital Association reported quarterly venture capital investments (trillions of dollars) and the number of investment deals as shown in data file XR17060. Generate a scatter diagram with the number of deals as
Each workstation in the final assembly area of a large manufacturing facility has a “backlog” area to hold units that are to be processed. A production engineer believes there could be a relationship between the number of units in the backlog area and the productivity of the worker.
The data in the table show the number of years it took for selected technological innovations to spread to 25% of the U.S. population. The data are also in file XR17062. For y = years to spread and x = years past 1800 (e.g., the code for 1975 is 175), generate a scatter diagram and apply an
The data in file XR17063 include the wind chill index (how cold it “feels”) at different combinations of outside temperature (degrees Fahrenheit) and wind speed (miles per hour). For y = wind chill index, x1 = actual outside temperature, and x2 = wind speed, fit a first order polynomial model
For loans at insured commercial banks, the Federal Financial Institutions Examination Council has reported the percentage of various kinds of loans that were at least 30 days in delinquency during each of the years shown in the table. The data are also listed in file XR17064. For y = percent of all
The production engineer for the manufacturing plant in Exercise 17.61 has just included another variable: the worker’s gender, coded as 1 = female and 0 5 male. File XR17065 contains the expanded set of data. With y = productivity (units/hour), x1 = number of units in the backlog area, and x2 =
The sales director for an industrial supplies firm has collected information describing the performance and personal characteristics of 80 members of her sales force. The data in file XR17066 include the percent of sales quota the salesperson achieved last year, age, number of years with the firm,
For the loan delinquency data in Exercise 17.64 and listed in file XR17064, fit a multiplicative model and use it to estimate the delinquency rate for all insured commercial bank loans when the delinquency rates for credit cards and residential loans are 4.0% and 2.0%, respectively.In exercise
The Dow Jones Global Indexes describe over 3000 companies worldwide that represent more than 80% of the equity capital in the world’s stock markets. Data file XR17068 shows the quarterly indexes for the world as a whole, and indexes for the United States, the Americas, Europe, and the
Data file XR17069 lists a variety of information for a selection of aircraft. The variables and their units are: operating cost (dollars per hour), number of seats, speed (mph), flight range (miles), and fuel consumption (gallons per hour). Considering operating cost per hour as the dependent
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 = average room rate (dollars) and x = average occupancy rate (percent), fit a second-order polynomial model to the data and determine the percentage of
Given the situation and variables described in Exercise 17.66 and data file XR17066, use y 5 percent of sales quota in performing a stepwise regression using the other variables as predictors. Interpret the results, including a commentary on which variables seem to be of greater importance in
The students in a training program have taken four tests along with a final exam, with the scores shown in the table. The data are also in file XR17071.a. Construct the correlation matrix for these variables. Does it appear that multicollinearity could be a problem if all of the independent
Repeat parts (b)–(d) of Exercise 17.71, with Test 1 as the dependent variable, and Test 2, Test 3, Test 4, and Final Exam as the independent variables. In exercise b. With y = final exam score and the independent variables as shown above, apply stepwise regression analysis to these data. d.
As indicated in the chapter-opening vignette, the National Football League quarterback passer rating is somewhat of a mystery to most observers. Data file XR17073 includes the passer rating for 32 NFL quarterbacks during the 2008 season, along with these ten performance measurements for each
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. Using x = 1 through 5 to represent years 2005€“2009, fit a secondorder polynomial
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 from large American “muscle cars” to small economy imports. The data are in file XR17009.
Ted Thorndike has been asked to pay another visit to the statistics class taught by his friend, Mary Stuart. One of the university€™s track athletes has an excellent chance to make the Olympics in the 1500 meters, known as the €œmetric mile,€ and Ted has brought along
They are coded according to the scheme described in Section 17.4. For a technology company, technology = 1 and the other dummy variables will be 0. For a financial services company, financial = 1 and the others will be 0. If a company is “other,” all six values will be 0. Thus, we need only six
The MBA program at Westmore University has undergone several dramatic changes over the past five years. During this time, the goal of the business school was to recruit as many students as possible into the MBA program in order to build up their student base and credit hour production. A massive
When we visited Easton Realty Company (A), in Chapter 16, Sam Easton was concerned about two former clients who complained that Easton Realty had underpriced their houses in order to get a quick sale and collect their realty fee. In defending his company against these charges, Mr. Easton obtained a
What are the four components of a time series, and to what kind of variation in the series does each refer?
For the data in Exercise 18.9, determine the centered moving average for N = 2; for N = 4.In exercise
According to the U.S. Energy Information Administration, a heating degree-day is a relative measurement of outdoor temperature that indicates how far the average daily temperature is below 65° Fahrenheit. The higher the number of heating degree-days, the greater the national demand for heating
For the data of Exercise 18.11: a. Obtain the centered moving average for N = 4; for N = 12. b. When N = 12 months, the centered moving average is relatively smooth compared to when N = 4. Aside from the fact that it includes a greater number of months at a time, is there any other reason why the
The following data describe the monthly volume for an urban courier service. Data are in thousands of pieces handled.a. Construct a graph of the time series. Does the overall trend appear to be upward or downward? b. Determine the three-month and five-month centered moving average curves and
For the data of Exercise 18.13: a. Obtain the centered moving average for N = 4; for N = 12. b. When N = 12 months, the centered moving average is relatively smooth compared to N = 4. Aside from the fact that it includes a greater number of months at a time, is there any other reason why the moving
The following data describe U.S. manufacturers€™ shipments of general aviation jet aircraft from 1989 through 2008.a. Construct a graph of the time series. Does the overall trend appear to be upward or downward? b. Determine the three-year and five-year centered moving average curves and
For the data of Exercise 18.11, fit an exponentially smoothed curve with smoothing constant Î± = 0.4; with smoothing constant Î± = 0.7. Which constant provides more €œsmoothing€ and why? Which curve is quicker to €œcatch up€
For the data of Exercise 18.13, fit an exponentially smoothed curve with smoothing constant Î± = 0.4; with smoothing constant Î± = 0.7. Which constant provides more €œsmoothing€ and why? Which curve is quicker to €œcatch up€
For the data of Exercise 18.15, determine the centered moving average for N = 2; for N = 4.In exercise
For the data of Exercise 18.15: a. Fit an exponentially smoothed curve with smoothing constant α = 0.6. b. For these data, describe the appearance of the exponentially smoothed curve when the smoothing constant is α = 0.0; when α = 1.0. Why is it not useful to assign either of these extreme
The seasonal indexes for a convention center’s bookings are 83, 120, 112, and 85 for quarters 1– 4, respectively. What percentage of the center’s annual bookings tend to occur during the second quarter?
The state of Texas has reported the following quarterly gross sales for the in-state accommodation and food services industry for the years 2004€“2008.a. Construct the four-quarter centered moving average for these data and determine the percentages of the moving average for the
A major amusement park has the following number of visitors each quarter from 2005 through 2009:a. Construct the four-quarter centered moving average for these data and determine the percentages of the moving average for the quarters. b. Determine the seasonal indexes for the quarters. c. Use the
Given the degree-day data of Exercise 18.11, (a) determine the monthly seasonal indexes for January through December, then (b) use these indexes to deseasonalize the original time series.In exercise
Given the data of Exercise 18.13, (a) determine the monthly seasonal indexes for January through December, then (b) use these indexes to deseasonalize the original time series.In exercise
A mail-order firm has found the following seasonal indexes for the number of calls received each month. Below the seasonal indexes is the actual number of calls (thousands) per month during 2009.a. Using the seasonal indexes, deseasonalize the data for 2009.b. The president of the firm is quite
The linear trend equation ŷ = 120 + 4.8x has been developed, where ŷ = estimated sales (thousands of dollars) and x = 1 for the year 1999. What level of sales would be forecast for 2013; for 2015?
An appliance repair shop owner has fitted the quadratic trend equation ŷ = 90 + 0.9x + 3x2 to a time series of annual repair orders, with y = the number of repair orders and x = 1 for 2005. Forecast the number of repair orders for 2013; for 2015.
Based on annual truck rentals over the years, a rental firm has developed the quadratic trend equation ŷ = 450 + 20x + 7.2x2, with x = 1 for 2005. Forecast y for 2013; for 2015.
When exponential smoothing is used in fitting a curve to a time series, the approach is slightly different from its application to forecasting. Compare the appropriate formulas and point out how they differ.
The U.S. trade deficit with Canada (billions of dollars) from 2000 through 2007 is reported as shown in the table. Using exponential smoothing and the smoothing constant Î± = 0.7, what deficit would have been forecast for 2008?

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