Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 14.2, Problem 1P
The file P14_01.xlsx contains data on 100 consumers who drink beer. Some of them prefer light beer, and others prefer regular beer. A major beer producer believes that the following variables might be useful in discriminating between these two groups: gender, marital status, annual income level, and age.
- a. Use logistic regression to classify the consumers on the basis of these explanatory variables. How successful is it? Which variables appear to be most important in the classification?
- b. Consider a new customer: Male, Married, Income $42,000, Age 47. Use the logistic regression equation to estimate the probability that this customer prefers Regular. How would you classify this person?
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A golf club manufacturer is trying to determine how the price of a set of clubs affects the demand for clubs. The file P10_50.xlsx contains the price of a set of clubs and the monthly sales.
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Interpret your best-fitting equation.
Using the best-fitting equation, predict sales during a month in which the price is $470.
File data:
Price
Demand
$400
20,000
$420
19,000
$440
17,000
$460
16,000
$500
14,000
$380
22,000
$290
31,000
$340
26,000
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An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.
- Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume.- What is the variable cost per unit produced?- Compute the coefficient of determination. What percentage of the variation in total cost can be explained by production volume?- The company’s production schedule shows 500 units must be produced next month. Predict the total cost for this operation.
MarkLines is an online portal (www.marklines.com) that reports automotive industry data. The table below shows the number of cars sold in the United States from January to November in 2017 and 2018. The top 22 manufacturers, plus others, are listed here. Sales data often is reported in this way to compare current sales to last year’s sales.
Car Sales
Manufacturer
Jan.-Nov.2017
Jan.-Nov.2018
GM (Est.)
2,691,493
2,654,568
Ford
2,334,290
2,265,590
Toyota
2,211,533
2,205,762
Fiat Chrysler
1,887,430
2,038,684
Honda
1,492,112
1,449,713
Nissan
1,455,238
1,345,157
Hyundai
621,961
612,225
Subaru
584,614
615,594
Kia
546,629
542,245
Mercedes (includes Sprinter)
332,990
318,012
BMW
271,432
276,657
VW
309,395
322,017
Mazda
262,577
274,455
Audi
199,534
200,558
Tesla (Est.)
40,320
106,050
Land Rover
66,759
81,526
Volvo
71,828
89,437
Mitsubishi
95,185
109,088
Porsche
51,507…
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- An antique collector believes that the price received for a particular item increases with its age and with the number of bidders. The file P13_14.xlsx contains data on these three variables for 32 recently auctioned comparable items. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Is the antique collector correct in believing that the price received for the item increases with its age and with the number of bidders? Interpret the standard error of estimate and the R-square value for these data.arrow_forwardThe file P13_04.xlsx lists the monthly sales for a company (in millions of dollars) for a 10-year period. a. Fit an exponential trend line to these data. b. By what percentage do you estimate that the company will grow each month? c. Why cant a high rate of exponential growth continue for a long time? d. Rather than an exponential curve, what type of curve might better represent the growth of a new technology?arrow_forwardThe file P13_27.xlsx contains yearly data on the proportion of Americans under the age of 18 living below the poverty level. a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model? Why? b. Use simple exponential smoothing to forecast these data, using a smoothing constant of 0.1. c. Repeat part b, but search for the smoothing constant that makes RMSE as small as possible. Create a chart of the series with the forecasts superimposed from this optimal smoothing constant. Does it make much of an improvement over the model in part b? d. Write a short report to summarize your results. Considering the chart in part c, would you say the forecasts are good?arrow_forward
- Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semifragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P13_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semifragile cargo.arrow_forwardThe file P13_01.xlsx contains the monthly number of airline tickets sold by a travel agency. a. Does a linear trend appear to fit these data well? If so, estimate and interpret the linear trend model for this time series. Also, interpret the R2 and se values. b. Provide an indication of the typical forecast error generated by the estimated model in part a. c. Is there evidence of some seasonal pattern in these sales data? If so, characterize the seasonal pattern.arrow_forwardThe management of a technology company is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees; see the file P13_08.xlsx. Estimate simple linear regression equations to identify which of the following has the strongest linear relationship with annual salary: the employees gender, age, number of years of relevant work experience prior to employment at the company, number of years of employment at the company, or number of years of post secondary education. Provide support for your conclusion.arrow_forward
- A small computer chip manufacturer wants to forecast monthly ozperating costs as a function of the number of units produced during a month. The company has collected the 16 months of data in the file P13_34.xlsx. a. Determine an equation that can be used to predict monthly production costs from units produced. Are there any outliers? b. How could the regression line obtained in part a be used to determine whether the company was efficient or inefficient during any particular month?arrow_forwardManagement of a home appliance store would like to understand the growth pattern of the monthly sales of Blu-ray disc players over the past two years. Managers have recorded the relevant data in the file P13_33.xlsx. a. Create a scatterplot for these data. Comment on the observed behavior of monthly sales at this store over time. b. Estimate an appropriate regression equation to explain the variation of monthly sales over the given time period. Interpret the estimated regression coefficients. c. Analyze the estimated equations residuals. Do they suggest that the regression equation is adequate? If not, return to part b and revise your equation. Continue to revise the equation until the results are satisfactory.arrow_forwardThe file P13_20.xlsx contains the monthly sales of iPod cases at an electronics store for a two-year period. Use the moving averages method, with spans of your choice, to forecast sales for the next six months. Does this method appear to track sales well? If not, what might be the reason?arrow_forward
- The file P13_03.xlsx contains monthly data on production levels and production costs during a four-year period for a company that produces a single product. Use simple regression on all of the data to see how Total Cost is related to Units Produced. Use the resulting equation to predict total cost in month 49, given that the proposed production level for that month is 450 units. Do you see anything wrong with the analysis? How should you modify your analysis if your main task is to find an equation useful for predicting future costs, and you know that the company installed new machinery at the end of month 18? Write a concise memo to management that describes your findings.arrow_forwardThe file P13_21.xlsx contains the weekly sales of rakes at a hardware store for a two-year period. Use the moving averages method, with spans of your choice, to forecast sales for the next 30 weeks. Does this method appear to track sales well? If not, what might be the reason?arrow_forwardBelow you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. Coefficients Standard Error Constant 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 Analysis of Variance Source ofVariation Degrees ofFreedom Sum ofSquares MeanSquare F Regression 4853 2426.5 Error 485.3 The t value obtained from the table which is used to test an individual parameter at the 1% level is a. 2.977. b. 2.921. c. 3.012. d. 2.650.arrow_forward
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