Tupperware's Forecasting Techniques

1. Tupperware only uses both qualitative and quantitative forecasting techniques, culminating in a final forecast that is the consensus of all participating managers. False (Global company profile: Tupperware Corporation, moderate)

2. The forecasting time horizon and the forecasting techniques used tend to vary over the life cycle of a product. True (What is forecasting? moderate)

3. Sales forecasts are an input to financial planning, while demand forecasts impact human resource decisions. True (Types of forecasts, moderate)

4. Forecasts of individual products tend to be more accurate than forecasts of product families.

False (Seven steps in the forecasting system, moderate)

5. Most forecasting techniques assume that there is some underlying stability in the system. True (Seven steps in the forecasting system, moderate)

6. The sales force composite forecasting method relies on salespersons’ estimates of expected sales. True (Forecasting approaches, easy)

7. A time-series model uses a series of past data points to make the forecast. True (Forecasting approaches, moderate)

8. The quarterly "make meeting" of Lexus dealers is an example of a sales force composite forecast.

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True (Forecasting approaches, easy)

9. Cycles and random variations are both components of time series. True (Time-series forecasting, easy)

10. A naive forecast for September sales of a product would be equal to the sales in August. True (Time-series forecasting, easy)

11. One advantage of exponential smoothing is the limited amount of record keeping involved. True (Time-series forecasting, moderate)

12. The larger the number of periods in the simple moving average forecasting method, the greater the method's responsiveness to changes in demand. False (Time-series forecasting, moderate)

13. Forecast including trend is an exponential smoothing technique that utilizes two smoothing constants: one for the average level of the forecast and one for its trend.

True (Time-series forecasting, easy)

14. Mean Squared Error and Coefficient of Correlation are two measures of the overall error of a forecasting model. False (Time-series forecasting, easy)

15. In trend projection, the trend component is the slope of the regression equation. True (Time-series forecasting, easy)

16. In trend projection, a negative regression slope is mathematically impossible. False (Time-series forecasting, moderate)

17. Seasonal indexes adjust raw data for patterns that repeat at regular time intervals. True (Time-series forecasting, moderate)

18. If a quarterly seasonal index has been calculated at 1.55 for the October-December quarter, then raw data for that quarter must be multiplied by 1.55 so that the quarter can be fairly compared to other quarters. False (Time-series forecasting: Seasonal variation in data, moderate)

19. The best way to forecast a business cycle is by finding a leading variable. True (Time-series forecasting, moderate)

20. Linear-regression analysis is a straight-line mathematical model to describe the functional relationships between independent and dependent variables. True (Associative forecasting methods: Regression and correlation
analysis, easy)

21. The larger the standard error of the estimate, the more accurate the forecasting model. False (Associative forecasting methods: Regression and correlation analysis, easy)

22. A trend projection equation with a slope of 0.78 means that there is a 0.78 unit rise in Y for every unit of time that passes. True (Time-series forecasting: Trend projections, moderate)

23. In a regression equation where Y is demand and X is advertising, a coefficient of determination (R2) of .70 means that 70% of the variance in advertising is explained by demand. False (Associative forecasting methods: Regression and correlation analysis, moderate)

24. Tracking limits should be within ± 8 MADs for low-volume stock items. True (Monitoring and controlling forecasts, moderate)

25. If a forecast is consistently greater than (or less than) actual values, the forecast is said to be biased. True (Monitoring and controlling forecasts, moderate)

26. Focus forecasting tries a variety of computer models and selects the best one for a particular application. True (Monitoring and controlling forecasts, moderate)

27. Many service firms use point-of-sale computers to collect detailed records needed for accurate short-term forecasts. True (Forecasting in the service sector, moderate)
MULTIPLE CHOICE

28. Tupperware's use of forecasting
a.involves only a few statistical tools
b.concentrates on the low-level dealer, and is not aggregated at the company level
c.relies on the fact that all of its products are in the maturity phase of the life cycle
d.is a major source of its competitive edge over its rivals
e.takes inputs from sales, marketing, and finance, but not from production
d (Global company profile, moderate)

29. Which of the following statements regarding Tupperware's forecasting is false?
a.Tupperware's fifty profit centers generate the basic set of projections.
b.Tupperware uses at least three quantitative forecasting techniques.
c.Tupperware uses only quantitative forecasting techniques.
d."Sales per active dealer" is one of three key forecasting variables (factors).
e."Jury of executive opinion" is the ultimate forecasting tool used at Tupperware.
c (Global company profile, moderate)

30. Forecasts
a.become more accurate with longer time horizons
b.are rarely perfect
c.are more accurate for individual items than for groups of items
d.all of the above
e.none of the above
b (What is forecasting? moderate)

31. One use of short-range forecasts is to determine
a.production planning
b.inventory budgets
c.research and development plans
d.facility location
e.job assignments
e (What is forecasting? moderate)

32. Forecasts are usually classified by time horizon into three categories
a.short-range, medium-range, and long-range
b.finance/accounting, marketing, and operations
c.strategic, tactical, and operational
d.exponential smoothing, regression, and time series
e.departmental, organizational, and industrial
a (What is forecasting? easy)

33. A forecast with a time horizon of about 3 months to 3 years is typically called a
a.long-range forecast
b.medium-range forecast
c.short-range forecast
d.weather forecast
e.strategic forecast
b (What is forecasting? moderate)
34. Forecasts used for new product planning, capital expenditures, facility location or expansion, and R&D typically utilize a
a.short-range time horizon
b.medium-range time horizon
c.long-range time horizon
d.naive method, because there is no data history
e.all of the above
c (What is forecasting? moderate)

35. The three major types of forecasts used by business organizations are
a.strategic, tactical, and operational
b.economic, technological, and demand
c.exponential smoothing, Delphi, and regression
d.causal, time-series, and seasonal
e.departmental, organizational, and territorial
b (Types of forecasts, moderate)

36. Which of the following is not a step in the forecasting process?
a.Determine the use of the forecast.
b.Eliminate any assumptions.
c.Determine the time horizon.
d.Select forecasting model.
e.Validate and implement the results.
b (The strategic importance of forecasting, moderate)

37. The two general approaches to forecasting are
a.qualitative and quantitative
b.mathematical and statistical
c.judgmental and qualitative
d.historical and associative
e.judgmental and associative
a (Forecasting approaches, easy)

38. Which of the following uses three types of participants: decision makers, staff personnel, and respondents?
a.executive opinions
b.sales force composites
c.the Delphi method
d.consumer surveys
e.time series analysis
c (Forecasting approaches, moderate)

39. The forecasting model that pools the opinions of a group of experts or managers is known as the
a.sales force composition model
b.multiple regression
c.jury of executive opinion model
d.consumer market survey model
e.management coefficients model
c (Forecasting approaches, moderate)
40. Which of the following is not a type of qualitative forecasting?
a.executive opinions
b.sales force composites
c.consumer surveys
d.the Delphi method
e.moving average
e (Forecasting approaches, moderate)

41. Which of the following techniques uses variables such as price and promotional expenditures, which are related to product demand, to predict demand?
a.associative models
b.exponential smoothing
c.weighted moving average
d.simple moving average
e.time series
a (Forecasting approaches, moderate)

42. Which of the following statements about time series forecasting is true?
a.It is based on the assumption that future demand will be the same as past demand.
b.It makes extensive use of the data collected in the qualitative approach.
c.The analysis of past demand helps predict future demand.
d.Because it accounts for trends, cycles, and seasonal patterns, it is more powerful than causal forecasting.
e.All of the above are true.
c (Time-series forecasting, moderate)

43. Time series data may exhibit which of the following behaviors?
a.trend
b.random variations
c.seasonality
d.cycles
e.They may exhibit all of the above.
e (Time-series forecasting, moderate)

44. Gradual, long-term movement in time series data is called
a.seasonal variation
b.cycles
c.trends
d.exponential variation
e.random variation
c (Time-series forecasting, moderate)

45. Which of the following is not present in a time series?
a.seasonality
b.operational variations
c.trend
d.cycles
e.random variations
b (Time-series forecasting, moderate)

46. The fundamental difference between cycles and seasonality is the
a.duration of the repeating patterns
b.magnitude of the variation
c.ability to attribute the pattern to a cause
d.all of the above
e.none of the above
a (Time-series forecasting, moderate)

47. In time series, which of the following cannot be predicted?
a.large increases in demand
b.technological trends
c.seasonal fluctuations
d.random fluctuations
e.large decreases in demand
d (Time-series forecasting, moderate)

48. What is the approximate forecast for May using a four-month moving average?

49. Which time series model below assumes that demand in the next period will be equal to the most recent period's demand?
a.naive approach
b.moving average approach
c.weighted moving average approach
d.exponential smoothing approach
e.none of the above
a (Time-series forecasting, easy)

50. Which of the following is not a characteristic of simple moving averages?
a.It smoothes random variations in the data.
b.It has minimal data storage requirements.
c.It weights each historical value equally.
d.It lags changes in the data.
e.It smoothes real variations in the data.
b (Time-series forecasting, moderate)

51. A six-month moving average forecast is better than a three-month moving average forecast if demand
a.is rather stable
b.has been changing due to recent promotional efforts
c.follows a downward trend
d.follows a seasonal pattern that repeats itself twice a year
e.follows an upward trend
a (Time-series forecasting, moderate)

52. Increasing the number of periods in a moving average will accomplish greater smoothing, but at the expense of
a.manager understanding
b.accuracy
c.stability
d.responsiveness to changes
e.All of the above are diminished when the number of periods increases.
d (Time-series forecasting, moderate)

53. Which of the following statements comparing the weighted moving average technique and exponential smoothing is true?
a.Exponential smoothing is more easily used in combination with the Delphi method.
b.More emphasis can be placed on recent values using the weighted moving average.
c.Exponential smoothing is considerably more difficult to implement on a computer.
d.Exponential smoothing typically requires less record keeping of past data.
e.Exponential smoothing allows one to develop forecasts for multiple periods, whereas weighted moving averages does not.
d (Time-series forecasting, moderate)

54. Which time series model uses past forecasts and past demand data to generate a new forecast?
a.naive
b.moving average
c.weighted moving average
d.exponential smoothing
e.regression analysis
d (Time-series forecasting, moderate)

55. Which is not a characteristic of exponential smoothing?
a.smoothes random variations in the data
b.easily altered weighting scheme
c.weights each historical value equally
d.has minimal data storage requirements
e.none of the above; they are all characteristics of exponential smoothing
c (Time-series forecasting, moderate)

56. Which of the following smoothing constants would make an exponential smoothing forecast equivalent to a naive forecast?
a.0
b.1 divided by the number of periods
c.0.5
d.1.0
e.cannot be determined
d (Time-series forecasting, moderate)

57. Given an actual demand of 103, a previous forecast value of 99, and an alpha of .4, the exponential smoothing forecast for the next period would be
a.94.6
b.97.4
c.100.6
d.101.6
e.103.0
c (Time-series forecasting, moderate)

58. A forecast based on the previous forecast plus a percentage of the forecast error is a(n)
a.qualitative forecast
b.naive forecast
c.moving average forecast
d.weighted moving average forecast
e.exponentially smoothed forecast
e (Time-series forecasting, moderate)

59. Given an actual demand of 61, a previous forecast of 58, and an of .3, what would the forecast for the next period be using simple exponential smoothing?
a.45.5
b.57.1
c.58.9
d.61.0
e.65.5
c (Time-series forecasting, moderate)

60. Which of the following values of alpha would cause exponential smoothing to respond the most slowly to forecast errors?
a.0.10
b.0.20
c.0.40
d.0.80
e.cannot be determined
a (Time-series forecasting, moderate)

61. A forecasting method has produced the following over the past five months. What is the mean absolute deviation?

62. The primary purpose of the mean absolute deviation (MAD) in forecasting is to
a.estimate the trend line
b.eliminate forecast errors
c.measure forecast accuracy
d.seasonally adjust the forecast
e.all of the above
c (Time-series forecasting, moderate)

63. Given forecast errors of -1, 4, 8, and -3, what is the mean absolute deviation?
a.2
b.3
c.4
d.8
e.16
c (Time-series forecasting, moderate)

64. The last four months of sales were 8, 10, 15, and 9 units. The last four forecasts were 5, 6, 11, and 12 units. The Mean Absolute Deviation (MAD) is
a.2
b.-10
c.3.5
d.9
e.10.5
c (Time-series forecasting, moderate)

65. A time series trend equation is 25.3 + 2.1 X. What is your forecast for period 7?
a.23.2
b.25.3
c.27.4
d.40.0
e.cannot be determined
d (Time-series forecasting, moderate)
66. For a given product demand, the time series trend equation is 53 - 4 X. The negative sign on the slope of the equation
a.is a mathematical impossibility
b.is an indication that the forecast is biased, with forecast values lower than actual values
c.is an indication that product demand is declining
d.implies that the coefficient of determination will also be negative
e.implies that the RSFE will be negative
c (Time-series forecasting, moderate)

67. In trend-adjusted exponential smoothing, the forecast including trend (FIT) consists of
a.an exponentially smoothed forecast and an estimated trend value
b.an exponentially smoothed forecast and a smoothed trend factor
c.the old forecast adjusted by a trend factor
d.the old forecast and a smoothed trend factor
e.a moving average and a trend factor
b (Time-series forecasting, moderate)

68. Which of the following is true regarding the two smoothing constants of the Forecast Including Trend (FIT) model?
a.One constant is positive, while the other is negative.
b.They are called MAD and RSFE.
c.Alpha is always smaller than beta.
d.One constant smoothes the regression intercept, whereas the other smoothes the regression slope.
e.Their values are determined independently.
e (Time-series forecasting, moderate)

69. Demand for a certain product is forecast to be 800 units per month, averaged over all 12 months of the year. The product follows a seasonal pattern, for which the January monthly index is 1.25. What is the seasonally-adjusted sales forecast for January?

a.640 units
b.798.75 units
c.800 units
d.1000 units
e.cannot be calculated with the information given
a (Time-series forecasting, moderate)

70. A seasonal index for a monthly series is about to be calculated on the basis of three years' accumulation of data. The three previous July values were 110, 150, and 130. The average over all months is 190. The approximate seasonal index for July is

a.0.487
b.0.684
c.1.462
d.2.053
e. cannot be calculated with the information given
b (Time-series forecasting, moderate)

71. A fundamental distinction between trend projection and linear regression is that
a.trend projection uses least squares while linear regression does not
b.only linear regression can have a negative slope
c.in trend projection the independent variable is time; in linear regression the independent variable need not be time, but can be any variable with explanatory power
d.linear regression tends to work better on data that lack trends
e.trend projection uses two smoothing constants, not just one
c (Associative forecasting methods: Regression and correlation analysis, moderate)

72. The percent of variation in the dependent variable that is explained by the regression equation is measured by the
a.mean absolute deviation
b.slope
c.coefficient of determination
d.correlation coefficient
e.intercept
c (Associative forecasting methods: Regression and correlation analysis, moderate)

73. The degree or strength of a linear relationship is shown by the
a.alpha
b.mean
c.mean absolute deviation
d.correlation coefficient
e.RSFE
d (Associative forecasting methods: Regression and correlation analysis, moderate)

74. If two variables were perfectly correlated, the correlation coefficient r would equal
a.0
b.less than 1
c.exactly 1
d.-1 or +1
e.greater than 1
d (Associative forecasting methods: Regression and correlation analysis, moderate)

75. The last four weekly values of sales were 80, 100, 105, and 90 units. The last four forecasts were 60, 80, 95, and 75 units. These forecasts illustrate
a.qualitative methods
b.adaptive smoothing
c.slope
d.bias
e.trend projection
d (Monitoring and controlling forecasts, easy)

76. The tracking signal is the
a.standard error of the estimate
b.running sum of forecast errors (RSFE)
c.mean absolute deviation (MAD)
d.ratio RSFE/MAD
e.mean absolute percentage error (MAPE)
d (Monitoring and controlling forecasts, moderate)

77. Computer monitoring of tracking signals and self-adjustment if a signal passes a preset limit is characteristic of
a.exponential smoothing including trend
b.adaptive smoothing
c.trend projection
d.focus forecasting
e.multiple regression analysis
b (Monitoring and controlling forecasts, moderate)

78. Many services maintain records of sales noting
a.the day of the week
b.unusual events
c.weather
d.holidays
e.all of the above
e (Forecasting in the service sector, moderate)

79. Taco Bell's unique employee scheduling practices are partly the result of using
a.point-of-sale computers to track food sales in 15 minute intervals
b.focus forecasting
c.a six-week moving average forecasting technique
d.multiple regression
e.a and c are both correct
e (Forecasting in the service sector, moderate)

96. A skeptical manager asks what short-range forecasts can be used for. Give her three possible uses/purposes. Any three of: planning purchasing, job scheduling, work force levels, job assignments, production levels. (What is forecasting? moderate)

97. A skeptical manager asks what long-range forecasts can be used for. Give her three possible uses/purposes. Any three of: planning new products, capital expenditures, facility location or expansion, research and development. (What is forecasting? moderate)

98. Describe the three forecasting time horizons and their use. Forecasting time horizons are: short range—generally less than three months, used for purchasing, job scheduling, work force levels, production levels; medium range—usually from three months up to three years, used for sales planning, production planning and budgeting, cash budgeting, analyzing operating plans; long range—usually three years or more, used for new product development, capital expenditures, facility planning, and R&D. (What is forecasting? moderate)

99. List and briefly describe the three major types of forecasts. The three types are economic, technological, and demand; economic refers to macroeconomic, growth and financial variables; technological refers to forecasting amount of technological advance, or futurism; demand refers to product demand. (Types of forecasts, moderate)

100. List the seven steps involved in forecasting.
1. Determine the use of the forecast.
2. Select the items that are to be forecast.
3. Determine the time horizon of the forecast.
4. Select the forecasting model(s).
5. Gather the data needed to make the forecast.
6. Make the forecast.
7. Validate the forecasting mode and implement the results.
(Seven steps in the forecasting process, moderate)

101. What are the realities of forecasting that companies face? First, forecasts are seldom perfect. Second, most forecasting techniques assume that there is some underlying stability in the system. Finally, both product family and aggregated forecasts are more accurate than individual product forecasts. (Seven steps in the forecasting system, moderate)

102. What are the differences between quantitative and qualitative forecasting methods? Quantitative methods use mathematical models to analyze historical data. Qualitative methods incorporate such factors as the decision maker's intuition, emotions, personal experiences, and value systems in determining the forecast. (Forecasting approaches, moderate)

103. List four quantitative forecasting methods.
The list includes naive, moving averages, exponential smoothing, trend projection, and linear regression. (Forecasting approaches, moderate)

104. What is a time-series forecasting model?
A time series forecasting model is any mathematical model that uses historical values of the quantity of interest to predict future values of that quantity. (Forecasting approaches, easy)

105. What is the difference between an associative model and a time-series model? A time series model uses only historical values of the quantity of
interest to predict future values of that quantity. The associative model, on the other hand, attempts to identify underlying causes or factors that control the variation of the quantity of interest, predict future values of these factors, and use these predictions in a model to predict future values of the specific quantity of interest. (Forecasting approaches, moderate)

106. Name and discuss three qualitative forecasting methods. Qualitative forecasting methods include: jury of executive opinion, where high-level managers arrive at a group estimate of demand; sales force composite, where salespersons’ estimates are aggregated; Delphi method, where respondents provide inputs to a group of decision makers; the group of decision makers, often experts, then make the actual forecast; consumer market survey, where consumers are queried about their future purchase plans. (Forecasting approaches, moderate)

107. List the four components of a time series. Which one of these is rarely forecast? Why is this so? Trend, seasonality, cycles, and random variation. Since random variations follow no discernible pattern, they cannot be predicted, and thus are not forecast. (Time-series forecasting, moderate)

108. Compare seasonal effects and cyclical effects.
A cycle is longer (typically several years) than a season (typically days, weeks, months, or quarters). A cycle has variable duration, while a season has fixed duration and regular repetition. (Time-series forecasting, moderate)

109. Distinguish between a moving average model and an exponential smoothing model. Exponential smoothing is a weighted moving average model wherein previous values are weighted in a specific manner--in particular, all previous values are weighted with a set of weights that decline exponentially. (Time-series forecasting, moderate)

110. Describe three popular measures of forecast accuracy.
Measures of forecast accuracy include: (a) MAD (mean absolute deviation). This is a sum of the absolute values of individual errors divided by the number of periods of data. (b) MSE (mean squared error). This is the average of the squared differences between the forecast and observed values. (c) MAPE (mean absolute percent error) is independent of the magnitude of the variable being forecast. (Forecasting approaches: Measuring forecast error, moderate)

111. Give an example—other than a restaurant or other food-service firm—of an organization that experiences an hourly seasonal pattern. (That is, each hour of the day has a pattern that tends to repeat day after day.) Explain. Answer will vary. However, two non-food examples would be banks and movie theaters. (Time-series forecasting, moderate) 112. Explain the role of regression models (time series and otherwise) in forecasting. That is, how is trend projection able to forecast? How is regression used for causal forecasting? For trend projection, the independent variable is time. The trend projection equation has a slope that is the change in demand per period. To forecast the demand for period t, perform the calculation a + bt. For causal forecasting, the independent variables are predictors of the forecast value or dependent variable. The slope of the regression equation is the change in the Y variable per unit change in the X variable. (Time-series forecasting, difficult)

113. List three advantages of the moving average forecasting model. List three disadvantages of the moving average forecasting model. Two advantages of the model are that it uses simple calculations, it smoothes out sudden fluctuations, and it is easy for users to understand. The disadvantages are that the averages always stay within past ranges, that they require extensive record keeping of past data, and that they do not pick up on trends very well. (Time-series forecasting, moderate)

114. What does it mean to "decompose" a time series?
To decompose a time series means to break past data down into components of trends, seasonality, cycles, and random blips, and to project them forward. (Time-series forecasting, easy)

115. Distinguish a dependent variable from an independent variable. The independent variable causes some behavior in the dependent variable; the dependent variable shows the effect of changes in the independent variable. (Associative forecasting methods: Regression and correlation, moderate)

116. Explain, in your own words, the meaning of the coefficient of determination. The coefficient of determination measures the amount (percent) of total variation in the data that is explained by the model. (Associative forecasting methods: Regression and correlation, moderate)

117. What is a tracking signal? How is it calculated? Explain the connection between adaptive smoothing and tracking signals. A tracking signal is a measure of how well the forecast actually predicts. Its calculation is the ratio of RSFE to MAD. The larger the absolute tracking signal, the worse the forecast is performing. Adaptive smoothing sets limits to the tracking signal, and makes changes to its forecasting models when the tracking signal goes beyond those limits. (Monitoring and controlling forecasts, moderate)

118. What is focus forecasting?
It is a forecasting method that tries a variety of computer models, and selects the one that is best for a particular application. (Monitoring and controlling forecasts, easy)

124. A management analyst is using exponential smoothing to predict merchandise returns at an upscale branch of a department store chain. Given an actual number of returns of 154 items in the most recent period completed, a forecast of 172 items for that period, and a smoothing constant of 0.3, what is the forecast for the next period? How would the forecast be changed if the smoothing constant were 0.6? Explain the difference in terms of alpha and responsiveness. 166.6; 161.2 The larger the smoothing constant in an exponentially smoothed forecast, the more responsive the forecast. (Time-series forecasting, easy)

126. The following trend projection is used to predict quarterly demand: Y = 250 - 2.5t, where t = 1 in the first quarter of 2004. Seasonal (quarterly) relatives are Quarter 1 = 1.5; Quarter 2 = 0.8; Quarter 3 = 1.1; and Quarter 4 = 0.6. What is the seasonally adjusted forecast for the four quarters of 2006?

PeriodProjectionAdjusted
9 227.5341.25
10 225180.00
11222.5224.75
12220132.00
(Time-series forecasting, moderate)

127. Jim's department at a local department store has tracked the sales of a product over the last ten weeks. Forecast demand using exponential smoothing with an alpha of 0.4, and an initial forecast of 28.0. Calculate MAD and the tracking signal. What do you recommend?

130. A small family-owned restaurant uses a seven-day moving average model to determine manpower requirements. These forecasts need to be seasonalized because each day of the week has its own demand pattern. The seasonal relatives for each day of the week are: Monday, 0.445; Tuesday, 0.791; Wednesday, 0.927; Thursday, 1.033; Friday, 1.422; Saturday, 1.478; and Sunday 0.903. Average daily demand based on the most recent moving average is 194 patrons. What is the seasonalized forecast for each day of next week? The average value multiplied by each day's seasonal index. Monday: 194 x .445 = 86; Tuesday: 194 x .791 = 153; Wednesday: 194 x .927 = 180; Thursday: 194 x 1.033 = 200; Friday: 194 x 1.422 = 276; Saturday: 194 x 1.478 = 287; and Sunday: 194 x .903 = 175. (Associative forecasting methods: Regression and correlation, moderate)

131. A restaurant has tracked the number of meals served at lunch over the last four weeks. The data shows little in terms of trends, but does display substantial variation by day of the week. Use the following information to determine the seasonal (daily) index for this restaurant.

132. A firm has modeled its experience with industrial accidents and found that the number of accidents per year (Y) is related to the number of employees (X) by the regression equation Y = 3.3 + 0.049*X. R-Square is 0.68. The regression is based on 20 annual observations. The firm intends to employ 480 workers next year. How many accidents do you project? How much confidence do you have in that forecast? Y = 3.3 + 0.049 * 480 = 3.3 + 23.52 = 26.52 accidents. This is not a time series, so next year = year 21 is of no relevance. Confidence comes from the coefficient of determination; the model explains 68% of the variation in number of accidents, which seems respectable. (Associative forecasting methods: Regression and correlation, moderate)

133. Demand for a certain product is forecast to be 8,000 units per month, averaged over all 12 months of the year. The product follows a seasonal pattern, for which the January monthly index is 1.25. What is the seasonally-adjusted sales forecast for January? 8,000 x 1.25 = 10,000 (Time-series forecasting, easy)

134. A seasonal index for a monthly series is about to be calculated on the basis of three years' accumulation of data. The three previous July values were 110, 135, and 130. The average over all months is 160. The approximate seasonal index for July is (110 + 135 + 130)/3 = 125; 125/160 = 0.781 (Time-series forecasting, moderate)

135. Marie Bain is the production manager at a company that manufactures hot water heaters. Marie needs a demand forecast for the next few years to help decide whether to add new production capacity. The company's sales history (in thousands of units) is shown in the table below. Use exponential smoothing with trend adjustment, to forecast demand for period 6. The initial forecast for period 1 was 11 units; the initial estimate of trend was 0. The smoothing constants are = .3 and · = .3

136. The quarterly sales for specific educational software over the past three years are given in the following table. Compute the four seasonal factors.

137. An innovative restaurateur owns and operates a dozen "Ultimate Low-Carb" restaurants in northern Arkansas. His signature item is a cheese-encrusted beef medallion wrapped in lettuce. Sales (X, in millions of dollars) is related to Profits (Y, in hundreds of thousands of dollars) by the regression equation Y = 8.21 + 0.76 X. What is your forecast of profit for a store with sales of $40 million? $50 million?

Students must recognize that sales is the independent variable and profits is dependent; the problem is not a time series. A store with $40 million in sales: 40 x 0.76 = 30.4; 30.4 + 8.21 = 38.61, or $3,861,000 in profit; $50 million in sales is estimated to profit 46.21 or $4,621,000. (Associative forecasting methods: Regression and correlation, moderate)

138. Arnold Tofu owns and operates a chain of 12 vegetable protein "hamburger" restaurants in northern Louisiana. Sales figures and profits for the stores are in the table below. Sales are given in millions of dollars; profits are in hundreds of thousands of dollars. Calculate a regression line for the data. What is your forecast of profit for a store with sales of $24 million? $30 million?

Students must recognize that "sales" is the independent variable and profits is dependent. Store number is not a variable, and the problem is not a time series. The regression equation is Y = 5.936 + 1.421 X (Y = profit, X = sales). A store with $24 million in sales is estimated to profit 40.04 or $4,004,000; $30 million in sales should yield 48.566 or $4,856,600 in profit. (Associative forecasting methods: Regression and correlation, moderate)

139. The department manager using a combination of methods has forecast sales of toasters at a local department store. Calculate the MAD for the
manager's forecast. Compare the manager's forecast against a naive forecast. Which is better?