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 recently hired economics graduate observed that the demand curve would reveal a great deal about the relationship between price and demand. She convinced the executives to conduct an experiment. A random sample of 20 restaurants was drawn. The restaurants were almost identical in terms of sales and in the demographics of the surrounding area. At each restaurant, the fish sandwich was sold at a different price. The number of sandwiches sold over a 7-day period and the price were recorded. A first-order model and a second-order model were proposed. a. Write the equation for each model. b. Use regression analysis to estimate the coefficients and other statistics for each model. c. Which model seems to fit better? Explain. d. Use the better model to calculate the point prediction for weekly sales when the price is $2.95.
> 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.
> 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?
> 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
> 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
> the value of television commercials is by telephone surveys conducted shortly after commercials are aired. Respondents who watched a certain television station at a given time period, during which the commercial appeared, are asked whether they can recal
> The administrator of a school board in a large county was analyzing the average mathematics test scores in the schools under her control. She noticed that there were dramatic differences in scores among the schools. In an attempt to improve the scores of
> For many cities around the world, garbage is an increasing problem. Many North American cities have virtually run out of space to dump the garbage. A consultant for a large American city decided to gather data about the problem. She took a random sample
> The marketing manager for a chain of hardware stores needed more information about the effectiveness of the three types of advertising that the chain used. These are localized direct mailing (in which flyers describing sales and featured products are dis
> The admissions officer of a university is trying to develop a formal system to decide which students to admit to the university. She believes that determinants of success include the standard variables—high school grades and SAT scores. However, she also
> The manager of a tire store in Minneapolis has been concerned with the high cost of inventory. The current policy is to stock all the snow tires that are predicted to sell over the entire winter at the beginning of the season (end of October). The manage
> Refer to Exercise 16.131. Determine whether there is evidence of first-order autocorrelation. Data from Exercise 16.131: The manager of Colonial Furniture has been reviewing weekly advertising expenditures. During the past 6 months, all advertisements f
> Refer to Exercise 17.3. Is there evidence of positive first-order autocorrelation? Data from Exercise 17.3: The president of a company that manufactures drywall wants to analyze the variables that affect demand for his product. Drywall is used to constr
> Weekly sales of a company’s product (y) and those of its main competitor (x) were recorded for one year. a. Conduct a regression analysis of these data. b. Plot the residuals versus the time periods. Does there appear to be autocorrelation? c. Perform th
> Observations of variables y, x1, and x2 were taken over 100 consecutive time periods. a. Conduct a regression analysis of these data. b. Plot the residuals versus the time periods. Describe the graph. c. Perform the Durbin-Watson test. Is there evidence
> Test the following hypotheses with = .05. H0: There is no first-order autocorrelation. H1: There is negative first-order autocorrelation. n = 33, k = 4, d = 2.25
> The widespread use of salt on roads in Canada and the northern United States during the winter and acid precipitation throughout the year combine to cause rust on cars. Car manufacturers and other companies offer rustproofing services to help purchasers
> After a recent study, researchers reported on the effects of folic acid on the occurrence of spina bifida—a birth defect in which there is incomplete formation of the spine. A sample of 2,000 women who gave birth to children with spina bifida and who wer
> Test the following hypotheses with = .02. H0: There is no first-order autocorrelation. H1: There is first-order autocorrelation. n = 90, k = 5, d = 1.60
> Test the following hypotheses with = .05. H0: There is no first-order autocorrelation. H1: There is positive first-order autocorrelation. n = 50, k = 2, d = 1.38
> When one company buys another company, it is not unusual that some workers are terminated. The severance benefits offered to the laid-off workers are often the subject of dispute. Suppose that the Laurier Company recently bought the Western Company and s
> Given the following information, perform the Durbin-Watson test to determine whether first order autocorrelation exists: n = 25, k = 5,= .10, d = .90
> Exercise 13.19 described a survey that asked people between 18 and 34 years of age and 35 to 50 years of age how much time they spent listening to FM radio each day. Also recorded were the amounts spent on music throughout the year. Can we infer that a l
> In addition to the data recorded for Exercises 12.31 and 13.227, we recorded the grade point average of the students who held down parttime jobs. Determine whether there is evidence of a linear relationship between the hours spent at parttime jobs and th
> A computer dating service typically asks for various pieces of information such as height, weight, income, and so on. One such service requested the length of index fingers. The only plausible reason for this request is to act as a proxy on height. Women
> (Exercise 3.67 revisited) A very large contribution to profits for a movie theater is the sale of popcorn, soft drinks, and candy. A movie theater manager speculated that the longer the time between showings of a movie, the greater the sales of concessio
> Mutual funds minimize risks by diversifying the investments they make. There are mutual funds that specialize in particular types of investments. For example, the TD Precious Metal Mutual Fund buys shares in gold mining companies. The value of this mutua
> The analysis that the human resources manager performed in Exercise 16.18 indicated that the dexterity test is not a predictor of job performance. However, before discontinuing the test, he decided that the problem is that the statistical analysis was fl
> Automobile insurance appraisers examine cars that have been involved in accidental collisions and estimate the cost of repairs. An insurance executive claims that there are significant differences in the estimates from different appraisers. To support hi
> Some critics of television complain that the amount of violence shown on television contributes to violence in our society. Others point out that television also contributes to the high level of obesity among children. We may have to add financial proble
> Every year, the U.S. Federal Trade Commission rates cigarette brands according to their levels of tar and nicotine, substances that are hazardous to smokers’ health. Additionally, the commission includes the amount of carbon monoxide, which is a by-produ
