Refer to Exercise 20.18. Use regression analysis to calculate the linear and quadratic trends. Which line fits better? Data from Exercise 20.18: Plot the following time series. Would the linear or quadratic model fit better?
> Many people suffer from heartburn. It appears, however, that the problem may increase with age. A researcher for a pharmaceutical company wanted to determine whether age and the incidence and extent of heartburn are related. A random sample of 325 adults
> Do cell phones cause cancer? This is a multibillion- dollar question. Currently, dozens of lawsuits are pending that claim cell phone use has caused cancer. To help shed light on the issue, several scientific research projects have been undertaken. One s
> Slow play of golfers is a serious problem for golf clubs. Slow play results in fewer rounds of golf and less profits for public course owners. To examine this problem, a random sample of British and American golf courses was selected. The amount of time
> At the completion of most courses in universities and colleges, a course evaluation is undertaken. Some professors believe that the way in which students fill out the evaluations is based on how well the student is doing in the course. To test this theor
> Refer to Example 16.2. If the required condition is not satisfied conduct another more appropriate test to determine whether odometer reading and price are related. Data from Example 16.2:
> Feminist organizations often use the issue of who does the housework in two-career families as a gauge of equality. Suppose that a study was undertaken and a random sample of 125 two-career families was taken. The wives were asked to report the number of
> These problems can be solved manually or by creating an Excel spreadsheet. a. Given the following statistics calculate the value of the test statistic to determine whether the population locations differ. t1 = 250 n1 = 15 t2 = 215 n2 = 15 b. Repeat par
> For Exercises 20.7 and 20.8, draw the time series and the two sets of exponentially smoothed values. Does there appear to be a trend component in the time series?
> Repeat Exercise 20.7 with w = .8.
> Apply exponential smoothing with w = .1 to help detect the components of the following time series. Period 1 2 3 4 5 Time Series 12 18 16 24 17 Period 6 7 8 9. 10 Time Series 16 25 21 23 14
> For Exercises 20.4 and 20.5, graph the time series and the two moving averages.
> The number of housing starts (in 1,000s) in the northeast United States for the years 2004 to 2009 were recorded. a. Use the 2004–2008 data to calculate the seasonal indexes. b. Use the indexes and regression analysis to forecast the number of housing st
> Using the seasonal indexes and trend line, forecast revenues for the next four quarters.
> An article in the journal Appetite (December 2003) described an experiment to determine the effect that breakfast meals have on school children. A sample of 29 children was tested on four successive days, having a different breakfast each day. The breakf
> Determine the seasonal indexes.
> For Exercise 20.4, compute the five-period moving averages.
> Use regression analysis to determine the trend line.
> Discuss why exponential smoothing is not recommended as a forecasting tool in this problem.
> Apply the trend line and seasonal indexes from Exercise 20.29 to forecast accounts receivable for the next four quarters.
> Refer to Exercise 20.28. Use the seasonal indexes and trend line to forecast the number of pizzas to be sold for each of the next 7 days. Data from Exercise 20.28: The owner of a pizzeria wants to forecast the number of pizzas she will sell each day. Sh
> Use the seasonal indexes and trend line from Exercise 20.27 to forecast the number of cable subscribers for the next four quarters.
> Refer to Exercise 20.26. Forecast next year’s merchandise trade balance using the following methods. a. Autoregressive forecasting model. b. Exponential smoothing method with w = .7. Data from Exercise 20.26: Foreign trade is important to the United Sta
> Refer to Exercise 20.25. Forecast next year’s enrollment using the following methods. a. Autoregressive forecasting model. b. Exponential smoothing method with w = .5. Data from Exercise 20.25: College and university enrollment increased sharply during
> Use the seasonal indexes and trend line to forecast the quarterly earnings for the years 2014 and 2015 in Exercise 20.24.
> In the last decade, society in general and the judicial system in particular have altered their opinions on the seriousness of drunken driving. In most jurisdictions, driving an automobile with a blood alcohol level in excess of .08 is a felony. Because
> Refer to Exercise 20.23. Use the seasonal indexes and the trend line to forecast the time series for the next four quarters. Data from Exercise 20.23: Given the following time series, compute the seasonal indexes. The regression equation is y^ = 47.7 −
> For the following time series, compute the three-period moving averages. Period Time Series Period Time Series 1 16 7 24 2 22 8 29 3 19 9 21 4 24 10 23 5 30 11 19 15 6. 26 12
> Use the seasonal indexes and trend line to forecast the time series for the next 5 days in Exercise 20.22.
> Apply exponential smoothing with w = .4 to forecast the next four quarters in Exercise 20.15.
> The following autoregressive equation was developed. Forecast the next value if the last observed value was 11. y^ = 155 + 21yt−1
> Use the following autoregressive equation to forecast the next value of the time series if the last observed value is 65. y^ = 625 − 1.3yt−1
> The following trend line and seasonal indexes were computed from 4 weeks of daily observations. Forecast the 7 values for next week. y^ = 120 + 2.3t t = 1, 2, . . . , 28 Day Seasonal Index Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1.5
> The following trend line and seasonal indexes were computed from 10 years of quarterly observations. Forecast the next year’s time series. y^ = 150 + 3t t = 1, 2, . . . , 40 Quarter Seasonal Index 1 .7 2 1.2 3 1.5 .6
> Three forecasting techniques were used to predict the values of a time series. These values are given in the following table. Compute MAD and SSE for each technique to determine which was most accurate. Period 1 4 Forecast (Model 1) 21 27 29 31 35 Fo
> Calculate MAD and SSE for the forecasts that follow. Period 1 2 4 Forecast 63 72 86 71 60 Actual 57 60 70 75 70 3.
> The marketing manager of a large ski resort wants to advertise that his ski resort has the shortest lift lines of any resort in the area. To avoid the possibility of a false advertising liability suit, he collects data on the times skiers wait in line at
> Two forecasting models were used to predict the future values of a time series. These are shown here together with the actual values. Compute MAD and SSE for each model to determine which was more accurate. Period 2 3 4 Forecast (Model 1) 7.5 6.3 5.4
> For the actual and forecast values of a time series shown here, calculate MAD and SSE Period 1 2 4 5 Forecast 173 186 192 211 223 Actual Value 166 179 195 214 220 LO 3.
> For Exercises 20.1 and 20.2, graph the time series and the two moving averages.
> A manufacturer of ski equipment is in the process of reviewing his accounts receivable. He noticed that there appears to be a seasonal pattern with the accounts receivable increasing in the winter months and decreasing during the summer. The quarterly ac
> The owner of a pizzeria wants to forecast the number of pizzas she will sell each day. She recorded the numbers sold daily for the past 4 weeks. Calculate the seasonal (daily) indexes.
> The number of cable television subscribers has increased over the past 5 years. The marketing manager for a cable company has recorded the numbers of subscribers for the past 24 quarters. a. Plot the numbers. b. Compute the seasonal (quarterly) indexes.
> Foreign trade is important to the United States. No country exports and imports more. However, there has been a large trade imbalance in many sectors. To measure the extent of the problem, an economist recorded the difference between exports and imports
> College and university enrollment increased sharply during the 1970s and 1980s. However, since then, the rate of growth has slowed. To help forecast future enrollments, an economist recorded the total U.S. college and university enrollment from 1993 to 2
> The quarterly earnings (in $millions) of a large soft-drink manufacturer have been recorded for the years 2013–2016. These data are listed here. Compute the seasonal indexes given the regression line y^ = 61.75 + 1.18t (t = 1, 2, . . .
> Given the following time series, compute the seasonal indexes. The regression equation is y^ = 47.7 − 1.06t (t = 1, 2, . . . , 20) Year Quarter 1 2 3 4 5 1 55 41 43 36 50 2 44 38 39 32 25 3 46 37 39 30 24 4 39 30 35 25 22
> Researchers at the University of Washington conducted an experiment to determine whether the herbal remedy Echinacea is effective in treating children’s colds and other respiratory infection (National Post, December 3, 2003). A sample of 524 children wer
> For the following time series, compute the seasonal (daily) indexes. The regression line is y^ = 16.8 + .366t (t = 1, 2, . . . , 20) Week Day 1 2 3 4 Monday Tuesday Wednesday Thursday Friday 12 11 14 17 18 17 16 21 16 19 16 20 25 24 28 24 31 27 25 32
> Refer to Exercise 20.19. Use regression analysis to calculate the linear and quadratic trends. Which line fits better? Data from Exercise 20.19: Plot the following time series to determine which of the trend models appears to fit better.
> Compute the five-period moving averages for the time series in Exercise 20.1.
> Plot the following time series to determine which of the trend models appears to fit better. Period 1 2. 4 5 Time Series 55 57 53 49 47 Period 6 7 8 9 10 Time Series 39 41 33 28 20 3.
> Plot the following time series. Would the linear or quadratic model fit better? Period 1 3 4 5 6 7 8 Time Series .5 .6 1.3 2.7 4.1 6.9 10.8 19.2 2.
> Repeat Exercise 20.15, using exponential smoothing with w = .8.
> Repeat Exercise 20.15, using exponential smoothing with w = .4.
> The following quarterly sales of a department store chain were recorded for the years 2013–2016. a. Calculate the four-quarter centered moving averages. b. Graph the time series and the moving averages. c. What can you conclude from yo
> For Exercise 20.13, compute the five-day moving averages, and superimpose these on the same graph. Does this help you answer part (c) of Exercise 20.13?
> We expect the demand for a product depends on its price: The higher the price, the lower the demand. However, this may not be entirely true. In an experiment conducted by professors at Northwestern University and MIT, a mail-order dress was available at
> The following daily sales figures have been recorded in a medium-size merchandising firm. a. Compute the three-day moving averages. b. Plot the time series and the moving averages on a graph. c. Does there appear to be a seasonal (weekly) pattern? W
> For Exercises 20.10 and 20.11, draw the time series and the two sets of exponentially smoothed values. Does there appear to be a trend component in the time series?
> Repeat Exercise 20.10 with w = .8.
> Apply exponential smoothing with w = .1 to help detect the components of the following time series. Period 1 2 4 5 Time Series 38 43 42 45 46 3. Period 6 7 8 9 10 Time Series 48 50 49 46 45
> For the following time series, compute the three-period moving averages. Period Time Series Period Time Series 1 48 7 43 41 8 52 37 9 60 32 10 48 36 11 41 31 12 30 N34 56
> The coach and the general manager of a team in the National Hockey League are trying to decide what kinds of players to draft. To help in making their decision, they need to know which variables are most closely related to the goals differential—the diff
> The manager of a large hotel on the Riviera in southern France wanted to forecast the monthly vacancy rate (as a percentage) during the peak season. After considering a long list of potential variables, she identified two variables that she believed were
> The manager of the food concession at a major league baseball stadium wanted to be able to predict the attendance of a game 24 hours in advance to prepare the correct amount of food for sale. He believed that the two most important factors were the home
> Refer to Exercise 17.14. The dean of the school of business wanted to improve the regression model, which was developed to describe the relationship between MBA program GPA and undergraduate GPA, GMAT score, and years of work experience. The dean now bel
> A person starting a new job always takes a certain amount of time to adjust fully. In repetitive task situations, such as on an assembly line, significant productivity gains can occur within a few days. In an experiment to study this phenomenon, the aver
> Does driving an ABS-equipped car change the behavior of drivers? To help answer this question, the following experiment was undertaken. A random sample of 200 drivers who currently operate cars without ABS were selected. Each person was given an identica
> The maintenance of swimming pools is quite costly because of all the chlorine that is needed to keep the water clear and relatively free of germs. A chain of hotels (all with outdoor pools) seeking to reduce costs decided to analyze the factors that dete
> A growing segment of the textile industry in the United States is based on piecework, wherein workers are paid for each unit they produce, instead of receiving an hourly wage. The manager of one such company has observed that inexperienced workers perfor
> After analyzing whether the number of ads is related to the number of customers, the manager in Exercise 16.99 decided to determine whether the advertising made any difference. As a result, he reorganized the experiment. Each week he advertised several t
> Refer to Exercise 18.44. a. Estimate a second-order model with interaction. b. Is this model valid in predicting the number of accidents? Test at the 10% significance level. Data from Exercise 18.44: The number of car accidents on a particular stretch o
> The number of car accidents on a particular stretch of highway seems to be related to the number of vehicles that travel over it and the speed at which they are traveling. A city alderman has decided to ask the county sheriff to provide him with statisti
> Car designers have been experimenting with ways to improve gas mileage for many years. An important element in this research is the way in which a car’s speed affects how quickly fuel is burned. Competitions whose objective is to drive the farthest on th
> A fast-food restaurant chain whose menu features hamburgers and chicken sandwiches is about to add a fish sandwich to its menu. There was considerable debate among the executives about the likely demand and what the appropriate price should be. A recentl
> Refer to Exercise 17.17 a. Use stepwise regression to compute the regression equation. b. Compare the output with that produced in Exercise 17.17. Data from Exercise 17.17: La Quinta Motor Inns is a moderately priced chain of motor inns located across t
> Refer to Exercise 17.16. a. Use stepwise regression to compute the regression equation. b. Compare the output with that produced in Exercise 17.16. Data from Exercise 17.16: The pollster also recorded the following variables in addition to the variable
> Discuss how the factor values and weights affect the final result. Explain the strengths and weaknesses of the statistical analysis.
> The cost of workplace injuries is high for the individual worker, for the company, and for society. It is in everyone’s interest to rehabilitate the injured worker as quickly as possible. A statistician working for an insurance company has investigated t
> Re-do Example 18.4 by assigning your own values to each factor and to the weights. What conclusion did you reach?
> Re-do Example 18.4. Change the weights for knowledge and training to 15% and for working conditions to 25%. What effect does this have on the conclusion? Briefly explain why the result was predictable.
> Pay equity for men and women has been an ongoing source of conflict for a number of years in North America. Suppose that a statistics practitioner is investigating the factors that affect salary differences between male and female university professors.
> The general manager of a supermarket chain believes that sales of a product are influenced by the amount of space the product is allotted on shelves. If true, this would have great significance, because the more profitable items could be given more shelf
> Absenteeism is a serious employment problem in most countries. It is estimated that absenteeism reduces potential output by more than 10%. Two economists launched a research project to learn more about the problem. They randomly selected 100 organization
> Refer to Exercise 16.139. The gender of the student was recorded where 1 = male and 0 = female. a. Does the inclusion of gender improve the model? b. Predict with 95% confidence the height of a female whose index finger is 6.5 cm long. c. Predict with 95
> Refer to Exercise 16.132, where a simple linear regression model was used to analyze the relationship between welding machine breakdowns and the age of the machine. The analysis proved to be so useful to company management that it decided to expand the m
> Profitable banks are ones that make good decisions on loan applications. Credit scoring is the statistical technique that helps banks make that decision. However, many branches overturn credit scoring recommendations, whereas other banks do not use the t
> Graph y versus x1 for x2 = 2, 4, and 5 for each of the following equations. a. y = 0.5 + 1x1 − 0.7x2 − 1.2x21 + 1.5x22 b. y = 0.5 + 1x1 − 0.7x2 − 1.2x21 + 1.5x22 + 2x1x2
> Refer to Exercise 17.12 where the amount of time to unload a truck was analyzed. The manager realized that another variable, the time of day, may affect unloading time. He recorded the following codes: 1 = morning, 2 = early afternoon, and 3 = late after
> In the door-to-door selling of vacuum cleaners, various factors influence sales. The Birk Vacuum Cleaner Company considers its sales pitch and overall package to be extremely important. As a result, it often thinks of new ways to sell its product. Becaus
> Recall Exercise 16.6 where a statistics practitioner analyzed the relationship between the length of a commercial and viewers’ memory of the commercial’s product. However, in the experiment not only was the length varied but also the type of commercial.
> The manager of an amusement park would like to be able to predict daily attendance in order to develop more accurate plans about how much food to order and how many ride operators to hire. After some consideration, he decided that the following three fac
> Refer to Exercise 17.10, where a multiple regression analysis was performed to predict men’s longevity based on the parents’ and grandparents’ longevity. In addition to these data, suppose that the actuary also recorded whether the man was a smoker (1 =
> Refer to Exercise 17.14. a. Predict with 95% confidence the MBA program GPA of a BEng whose undergraduate GPA was 9.0, whose GMAT score as 700, and who has had 10 years of work experience. b. Repeat part (a) for a BA student. Data from Exercise 17.14: T
> Refer to Exercise 17.14. After considering the results of the initial study, the dean realized that she may have omitted an important variable— the type of undergraduate degree. She returned to her sample of students and recorded the type of undergraduat
> In a study of computer applications, a survey asked which microcomputer a number of companies used. The following indicator variables were created. Which computer is being referred to by each of the following pairs of values? a. I1 = 0; I2 = 1 b. I1 = 1
> Create and identify indicator variables to represent the following nominal variables. a. Religious affiliation (Catholic, Protestant, and others) b. Working shift (8 a.m. to 4 p.m., 4 p.m. to 12 midnight, and 12 midnight to 8 a.m.) c. Supervisor (Jack Jo
> How many indicator variables must be created to represent a nominal independent variable that has five categories?
> The production manager of a chemical plant wants to determine the roles that temperature and pressure play in the yield of a particular chemical produced at the plant. From past experience, she believes that when pressure is held constant, lower and high
> Graph y versus x1 for x2 = 1, 2, and 3 for each of the following equations. a. y = 1 + 2x1 + 4x2 b. y = 1 + 2x1 + 4x2 − x1x2
