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ch chapter 4 test bank

Operations Management (‫)سوباق ناطلسلا ةعماج‬

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Quantitative Analysis for Management, 12e (Render)

Chapter 5 Forecasting

1) A medium-term forecast typically covers a two- to four-year time horizon.

Answer: FALSE
Diff: 2
Topic: INTRODUCTION

2) Regression is always a superior forecasting method to exponential smoothing, so

regression should be used whenever the appropriate software is available.
Answer: FALSE
Diff: 1
Topic: INTRODUCTION

3) The three categories of forecasting models are time series, quantitative, and qualitative.
Answer: FALSE
Diff: 2
Topic: TYPES OF FORECASTING MODELS

4) TIME SERIES models attempt to predict the future by using historical data.
Answer: TRUE
Diff: 2
Topic: TYPES OF FORECASTING MODELS

5) TIME SERIES models rely on judgment in an attempt to incorporate qualitative or

subjective factors into the forecasting model.
Answer: FALSE
Diff: 1
Topic: TYPES OF FORECASTING MODELS

6) A moving average forecasting method is a causal forecasting method.

Answer: FALSE
Diff: 2
Topic: TYPES OF FORECASTING MODELS

7) An exponential forecasting method is a TIME SERIES forecasting method.

Answer: TRUE
Diff: 2
Topic: TYPES OF FORECASTING MODELS

8) A trend-projection forecasting method is a causal forecasting method.

Answer: FALSE
Diff: 2
Topic: TYPES OF FORECASTING MODELS

9) Qualitative models produce forecasts that are a little better than simple guesses or coin
tosses.
Answer: FALSE
Diff: 1
Topic: TYPES OF FORECASTING MODELS

10) The most common quantitative causal model is regression analysis.

Answer: TRUE
Diff: 2
Topic: TYPES OF FORECASTING MODELS

11) Qualitative models attempt to incorporate judgmental or subjective factors into the
forecasting model.

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Answer: TRUE
Diff: 1
Topic: TYPES OF FORECASTING MODELS

12) A scatter diagram is useful to determine if a relationship exists between two variables.
Answer: TRUE
Diff: 1
Topic: SCATTER DIAGRAMS AND TIME SERIES

13) The Delphi method solicits input from customers or potential customers regarding their
future purchasing plans.
Answer: FALSE
Diff: 2
Topic: TYPES OF FORECASTING MODELS

14) The naïve forecast for the next period is the actual value observed in the current period.
Answer: TRUE
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY

15) Mean absolute deviation (MAD) is simply the sum of forecast errors.
Answer: FALSE
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY

16) TIME SERIES models enable the forecaster to include specific representations of various
qualitative and quantitative factors.
Answer: FALSE
Diff: 2
Topic: COMPONENTS OF A TIME SERIES

17) Four components of time series are trend, moving average, exponential smoothing, and
seasonality.
Answer: FALSE
Diff: 2
Topic: COMPONENTS OF A TIME SERIES

18) The fewer the periods over which one takes a moving average, the more accurately the
resulting forecast mirrors the actual data of the most recent time periods.
Answer: TRUE
Diff: 2
Topic: COMPONENTS OF A TIME SERIES

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19) In a weighted moving average, the weights assigned must sum to 1.

Answer: FALSE
Diff: 2
Topic: COMPONENTS OF A TIME SERIES

20) A scatter diagram for a time series may be plotted on a two-dimensional graph with the
horizontal axis representing the variable to be forecast (such as sales).
Answer: FALSE
Diff: 2
Topic: COMPONENTS OF A TIME SERIES

21) Scatter diagrams can be useful in spotting trends or cycles in data over time.
Answer: TRUE
Diff: 1
Topic: COMPONENTS OF A TIME SERIES

22) Exponential smoothing cannot be used for data with a trend.

Answer: FALSE
Diff: 2
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY

23) In a second order exponential smoothing, a low β gives less weight to more recent
trends.
Answer: TRUE
Diff: 2
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY

24) An advantage of exponential smoothing over a simple moving average is that

exponential smoothing requires one to retain less data.
Answer: TRUE
Diff: 2
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY
AACSB: Reflective Thinking

25) When the smoothing constant α = 0, the exponential smoothing model is equivalent to
the naïve forecasting model.
Answer: FALSE
Diff: 3
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY
AACSB: Analytic Skills

26) Multiple regression models use dummy variables to adjust for seasonal variations in an
additive TIME SERIES model.
Answer: TRUE
Diff: 2
Topic: FORECASTING MODELS—TREND, SEASONAL, AND RANDOM VARIATIONS

27) Multiple regression can be used to develop a multiplicative decomposition model.

Answer: FALSE
Diff: 2
Topic: FORECASTING MODELS—TREND, SEASONAL, AND RANDOM VARIATIONS

28) A seasonal index must be between -1 and +1.

Answer: FALSE
Diff: 2
Topic: ADJUSTING FOR SEASONAL VARIATIONS

29) A seasonal index of 1 means that the season is average.

Answer: TRUE
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Diff: 2
Topic: ADJUSTING FOR SEASONAL VARIATIONS

30) The process of isolating linear trend and seasonal factors to develop a more accurate
forecast is called regression.
Answer: FALSE
Diff: 2
Topic: ADJUSTING FOR SEASONAL VARIATIONS

31) When the smoothing constant α = 1, the exponential smoothing model is equivalent to
the naïve forecasting model.
Answer: TRUE
Diff: 3
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY
AACSB: Analytic Skills

32) Multiple regression may be used to forecast both trend and seasonal components
present in a time series.
Answer: TRUE
Diff: 2
Topic: FORECASTING MODELS—TREND, SEASONAL, AND RANDOM VARIATIONS

33) Adaptive smoothing is analogous to exponential smoothing where the coefficients α and
β are periodically updated to improve the forecast.
Answer: TRUE
Diff: 2
Topic: MONITORING AND CONTROLLING FORECASTS

34) Bias is the average error of a forecast model.

Answer: TRUE
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY

35) Which of the following is not classified as a qualitative forecasting model?

A) exponential smoothing
B) Delphi method
C) jury of executive opinion
D) sales force composite
E) consumer market survey
Answer: A
Diff: 1
Topic: TYPES OF FORECASTING MODELS

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36) A judgmental forecasting technique that uses decision makers, staff personnel, and
respondent to determine a forecast is called
A) exponential smoothing.
B) the Delphi method.
C) jury of executive opinion.
D) sales force composite.
E) consumer market survey.
Answer: B
Diff: 2
Topic: TYPES OF FORECASTING MODELS

37) Which of the following is considered a causal method of forecasting?

A) exponential smoothing
B) moving average
C) Holt's method
D) Delphi method
E) None of the above
Answer: E
Diff: 2
Topic: TYPES OF FORECASTING MODELS

38) A graphical plot with sales on the Y axis and time on the X axis is a
A) scatter diagram.
B) trend projection.
C) radar chart.
D) line graph.
E) bar chart.
Answer: A
Diff: 2
Topic: FORECASTING MODELS—TREND AND RANDOM VARIATIONS

39) Which of the following statements about scatter diagrams is true?

A) Time is always plotted on the y-axis.
B) It can depict the relationship among three variables simultaneously.
C) It is helpful when forecasting with qualitative data.
D) The variable to be forecasted is placed on the y-axis.
E) It is not a good tool for understanding TIME SERIES data.
Answer: D
Diff: 2
Topic: COMPONENTS OF A TIME SERIES

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40) Which of the following is a technique used to determine forecasting accuracy?

A) exponential smoothing
B) moving average
C) regression
D) Delphi method
E) mean absolute percent error
Answer: E
Diff: 1
Topic: MEASURES OF FORECAST ACCURACY

41) A medium-term forecast is considered to cover what length of time?

A) 2-4 weeks
B) 1 month to 1 year
C) 2-4 years
D) 5-10 years
E) 20 years
Answer: B
Diff: 2
Topic: INTRODUCTION

42) When is the exponential smoothing model equivalent to the naïve forecasting model?
A) α = 0
B) α = 0.5
C) α = 1
D) during the first period in which it is used
E) never
Answer: C
Diff: 3
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY
AACSB: Analytic Skills

43) Enrollment in a particular class for the last four semesters has been 120, 126, 110, and
130. Suppose a one-semester moving average was used to forecast enrollment (this is
sometimes referred to as a naïve forecast). Thus, the forecast for the second semester
would be 120, for the third semester it would be 126, and for the last semester it would be
110. What would the MSE be for this situation?
A) 196.00
B) 230.67
C) 100.00
D) 42.00
E) None of the above
Answer: B
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY
AACSB: Analytic Skills

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44) Which of the following methods tells whether the forecast tends to be too high or too
low?
A) MAD
B) MSE
C) MAPE
D) decomposition
E) bias
Answer: E
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY

45) Assume that you have tried three different forecasting models. For the first, the MAD =
2.5, for the second, the MSE = 10.5, and for the third, the MAPE = 2.7. We can then say:
A) the third method is the best.
B) the second method is the best.
C) methods one and three are preferable to method two.
D) method two is least preferred.
E) None of the above
Answer: E
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY

46) Which of the following methods gives an indication of the percentage of forecast error?
A) MAD
B) MSE
C) MAPE
D) decomposition
E) bias
Answer: C
Diff: 1
Topic: MEASURES OF FORECAST ACCURACY

47) Daily demand for newspapers for the last 10 days has been as follows: 12, 13, 16, 15,
12, 18, 14, 12, 13, 15 (listed from oldest to most recent). Forecast sales for the next day
using a two-day moving average.
A) 14
B) 13
C) 15
D) 28
E) 12.5
Answer: A
Diff: 2
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY
AACSB: Analytic Skills

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48) As one increases the number of periods used in the calculation of a moving average,
A) greater emphasis is placed on more recent data.
B) less emphasis is placed on more recent data.
C) the emphasis placed on more recent data remains the same.
D) it requires a computer to automate the calculations.
E) one is usually looking for a long-term prediction.
Answer: B
Diff: 2
Topic: COMPONENTS OF A TIME SERIES
AACSB: Reflective Thinking

49) Enrollment in a particular class for the last four semesters has been 122, 128, 100, and
155 (listed from oldest to most recent). The best forecast of enrollment next semester,
based on a three-semester moving average, would be
A) 116.7.
B) 126.3.
C) 168.3.
D) 135.0.
E) 127.7.
Answer: E
Diff: 1
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY
AACSB: Analytic Skills

50) Which of the following methods produces a particularly stiff penalty in periods with large
forecast errors?
A) MAD
B) MSE
C) MAPE
D) decomposition
E) bias
Answer: B
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY
AACSB: Reflective Thinking

51) The process of isolating linear trend and seasonal factors to develop more accurate
forecasts is called
A) regression.
B) decomposition.
C) smoothing.
D) monitoring.
E) None of the above
Answer: B
Diff: 2
Topic: FORECASTING MODELS—TREND, SEASONAL, AND RANDOM VARIATIONS

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52) Sales for boxes of Girl Scout cookies over a 4-month period were forecasted as follows:
100, 120, 115, and 123. The actual results over the 4-month period were as follows: 110,
114, 119, 115. What was the MAD of the 4-month forecast?
A) 0
B) 5
C) 7
D) 108
E) None of the above
Answer: C
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY
AACSB: Analytic Skills

53) Sales for boxes of Girl Scout cookies over a 4-month period were forecasted as follows:
100, 120, 115, and 123. The actual results over the 4-month period were as follows: 110,
114, 119, 115. What was the MSE of the 4-month forecast?
A) 0
B) 5
C) 7
D) 108
E) None of the above
Answer: E
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY
AACSB: Analytic Skills

54) Daily demand for newspapers for the last 10 days has been as follows: 12, 13, 16, 15,
12, 18, 14, 12, 13, 15 (listed from oldest to most recent). Forecast sales for the next day
using a three-day weighted moving average where the weights are 3, 1, and 1 (the highest
weight is for the most recent number).
A) 12.8
B) 13.0
C) 70.0
D) 14.0
E) None of the above
Answer: D
Diff: 2
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY
AACSB: Analytic Skills

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55) Daily demand for newspapers for the last 10 days has been as follows: 12, 13, 16, 15,
12, 18, 14, 12, 13, 15 (listed from oldest to most recent). Forecast sales for the next day
using a two-day weighted moving average where the weights are 3 and 1.
A) 14.5
B) 13.5
C) 14
D) 12.25
E) 12.75
Answer: A
Diff: 2
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY
AACSB: Analytic Skills

56) Which of the following is not considered to be one of the components of a time series?
A) trend
B) seasonality
C) variance
D) cycles
E) random variations
Answer: C
Diff: 2
Topic: COMPONENTS OF A TIME SERIES

57) Which of the following statements about the decomposition method is/are false?
A) The process of "deseasonalizing" involves multiplying by a seasonal index.
B) Dummy variables are used in a regression model as part of an additive approach to
seasonality.
C) Computing seasonal indices is the first step of the decomposition method.
D) Data is "deseasonalized" after the trend line is found.
E) Decomposition can involve additive or multiplicative methods with respect to seasonality.
Answer: D
Diff: 3
Topic: FORECASTING MODELS—TREND, SEASONAL, AND RANDOM VARIATIONS

58) Enrollment in a particular class for the last four semesters has been 120, 126, 110, and
130 (listed from oldest to most recent). Develop a forecast of enrollment next semester
using exponential smoothing with an alpha = 0.2. Assume that an initial forecast for the first
semester was 120 (so the forecast and the actual were the same).
A) 118.96
B) 121.17
C) 130
D) 120
E) None of the above
Answer: B
Diff: 3
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY
AACSB: Analytic Skills

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59) Demand for soccer balls at a new sporting goods store is forecasted using the following
regression equation:
Y = 98 + 2.2X where X is the number of months that the store has been in existence. Let
April be represented by
X = 4. April is assumed to have a seasonality index of 1.15. What is the forecast for soccer
ball demand for the month of April (rounded to the nearest integer)?
A) 123
B) 107
C) 100
D) 115
E) None of the above
Answer: B
Diff: 2
Topic: FORECASTING MODELS—TREND AND RANDOM VARIATIONS
AACSB: Analytic Skills

60) A TIME SERIES forecasting model in which the forecast for the next period is the actual
value for the current period is the
A) Delphi model.
B) Holt's model.
C) naïve model.
D) exponential smoothing model.
E) weighted moving average.
Answer: C
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY
AACSB: Analytic Skills

61) In picking the smoothing constant for an exponential smoothing model, we should look
for a value that
A) produces a nice-looking curve.
B) equals the utility level that matches with our degree of risk aversion.
C) produces values which compare well with actual values based on a standard measure of
error.
D) causes the least computational effort.
E) None of the above
Answer: C
Diff: 1
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY

62) Which of the following is not considered one of the steps to developing the
decomposition method?
A) compute seasonal indices using CMAs
B) deseasonalize the data by dividing each number by its seasonal index
C) find the equation of the trend line using the deseasonlized data
D) forecast for future periods using the trend line
E) add the seasonal index to the trend forecast
Answer: E
Diff: 3
Topic: FORECASTING MODELS—TREND, SEASONAL, AND RANDOM VARIATIONS

63) A method to measure how well predictions fit actual data is

A) decomposition
B) smoothing
C) tracking signal
D) regression
E) moving average

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Answer: C
Diff: 2
Topic: MONITORING AND CONTROLLING FORECASTS

64) If the Q1 demand for a particular year is 200 and the seasonal index is 0.85, what is the
deseasonalized demand value for Q1?
A) 170
B) 185
C) 215
D) 235.29
E) 250
Answer: D
Diff: 2
Topic: FORECASTING METHODS—TREND, SEASONAL, AND RANDOM VARIATIONS

65) In the exponential smoothing with trend adjustment forecasting method, β is the
A) slope of the trend line.
B) new forecast.
C) Y-axis intercept.
D) independent variable.
E) trend smoothing constant.
Answer: E
Diff: 2
Topic: FORECASTING MODELS—TREND AND RANDOM VARIATIONS

66) Using the additive decomposition model, what would be the period 2, Q3 forecast using
the following equation: = 20 + 3.2X1 + 1.5X2 + 0.8X3 + 0.6X4?
A) 23.2
B) 25
C) 27
D) 27.2
E) 27.9
Answer: D
Diff: 2
Topic: FORECASTING MODELS—TREND, SEASONAL, AND RANDOM VARIATIONS

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67) The computer monitoring of tracking signals and self-adjustment is referred to as

A) exponential smoothing.
B) adaptive smoothing.
C) trend projections.
D) trend smoothing.
E) running sum of forecast errors (RFSE).
Answer: B
Diff: 2
Topic: MONITORING AND CONTROLLING FORECASTS

68) Which of the following is not a characteristic of trend projections?

A) The variable being predicted is the Y variable.
B) Time is the X variable.
C) It is useful for predicting the value of one variable based on time trend.
D) A negative intercept term always implies that the dependent variable is decreasing over
time.
E) They are often developed using linear regression.
Answer: D
Diff: 2
Topic: FORECASTING MODELS—TREND AND RANDOM VARIATIONS

69) A tracking signal was calculated for a particular set of demand forecasts. This tracking
signal was positive. This would indicate that
A) demand is greater than the forecast.
B) demand is less than the forecast.
C) demand is equal to the forecast.
D) the MAD is negative.
E) None of the above
Answer: A
Diff: 2
Topic: MONITORING AND CONTROLLING FORECASTS

70) A seasonal index of ________ indicates that the season is average.

A) 10
B) 100
C) 0.5
D) 0
E) 1
Answer: E
Diff: 2
Topic: ADJUSTING FOR SEASONAL VARIATIONS

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71) The errors in a particular forecast are as follows: 4, -3, 2, 5, -1. What is the tracking
signal of the forecast?
A) 0.4286
B) 2.3333
C) 5
D) 1.4
E) 2.5
Answer: B
Diff: 3
Topic: MONITORING AND CONTROLLING FORECASTS
AACSB: Analytic Skills

72) Demand for a particular type of battery fluctuates from one week to the next. A study of
the last six weeks provides the following demands (in dozens): 4, 5, 3, 2, 8, 10 (last week).
(a) Forecast demand for the next week using a two-week moving average.
(b) Forecast demand for the next week using a three-week moving average.
Answer:
(a) (8 + 10)/2 = 9
(b) (2 + 8 + 10)/3 = 6.67
Diff: 1
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY
AACSB: Analytic Skills

73) Daily high temperatures in the city of Houston for the last week have been: 93, 94, 93,
95, 92, 86, 98 (yesterday).
(a) Forecast the high temperature today using a three-day moving average.
(b) Forecast the high temperature today using a two-day moving average.
(c) Calculate the mean absolute deviation based on a two-day moving average, covering all
days in which you can have a forecast and an actual temperature.
Answer:
(a) (92 + 86 + 98)/3 = 92
(b) (86 + 98)/2 = 92
(c) MAD = ( + + + + ) / 5 = 20.5 / 5 = 4.1
Diff: 2
Topic: VARIOUS
AACSB: Analytic Skills

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74) For the data below:

Automobile Automobile
Month Month
Battery Sales Battery Sales
January 20 July 17
February 21 August 18
March 15 September 20
April 14 October 20
May 13 November 21
June 16 December 23

(a) Develop a scatter diagram.

(b) Develop a three-month moving average.
(c) Compute MAD.

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Answer:
(a) scatter diagram

(b)

Automobile 3-Month Absolute

Month Battery Sales Moving Avg. Deviation
January 20 - -
February 21 - -
March 15 - -
April 14 18.67 4.67
May 13 16.67 3.67
June 16 14 2
July 17 14.33 2.67
August 18 15.33 3.67
September 20 17 3
October 20 18.33 1.67
November 21 19.33 1.67
December 23 20.33 2.67
January - 21.33 -

(c) MAD = 2.85

Diff: 3
Topic: VARIOUS
AACSB: Analytic Skills

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75) For the data below:

Automobile Automobile
Month Month
Tire Sales Tire Sales
January 80 July 68
February 84 August 100
March 60 September 80
April 56 October 80
May 52 November 84
June 64 December 92

(a) Develop a scatter diagram.

(b) Compute a three-month moving average.
(c) Compute the MSE.

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Answer:
(a) scatter diagram

(b)
Automobile 3-Month Squared
Month Tire Sales Tire Average Error
January 80 - -
February 84 - -
March 60 - -
April 56 74.7 349.69
May 52 66.7 216.09
June 64 56.0 64
July 68 57.3 114.49
August 100 61.3 1497.69
September 80 77.3 7.29
October 80 82.7 7.29
November 84 86.7 7.29
December 92 81.3 114.49
January - 85.33

(c) MSE = 264.26

Diff: 3
Topic: VARIOUS
AACSB: Analytic Skills

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76) For the data below:

Year Automobile Sales Year Automobile Sales

1990 116 1997 119
1991 105 1998 34
1992 29 1999 34
1993 59 2000 48
1994 108 2001 53
1995 94 2002 65
1996 27 2003 111

(a) Develop a scatter diagram.

(b) Develop a six-year moving average forecast.
(c) Find MAPE.

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Answer:
(a) scatter diagram

(b)
Number of Error
Year Forecast Error
Automobiles Actual
1990 116 X
1991 105 X
1992 29 X
1993 59 X
1994 108 X
1995 94 X
1996 27 85.2 -58.2 2.15
9 119 70.3 48.7 0.41
1998 34 72.7 -38.7 1.14
1999 34 73.5 -39.5 1.16
2000 48 69.3 -21.3 0.44
2001 53 59.3 -6.3 0.12
2002 65 52.5 12.5 0.19
2003 111 58.8 52.2 0.47

(c) MAPE = .76 ∗ 100% = 76%

Diff: 3
Topic: VARIOUS
AACSB: Analytic Skills

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77) Use simple exponential smoothing with α = 0.3 to forecast battery sales for February
through May. Assume that the forecast for January was for 22 batteries.

Automobile
Month
Battery Sales
January 42
February 33
March 28
April 59

Answer: Forecasts for February through May are: 28, 29.5, 29.05, and 38.035.
Diff: 2
Topic: VARIOUS
AACSB: Analytic Skills

78) Average starting salaries for students using a placement service at a university have
been steadily increasing. A study of the last four graduating classes indicates the following
average salaries: $30,000, $32,000, $34,500, and $36,000 (last graduating class). Predict
the starting salary for the next graduating class using a simple exponential smoothing model
with α = 0.25. Assume that the initial forecast was $30,000 (so that the forecast and the
actual were the same).
Answer: Forecast for next period = $32,625
Diff: 2
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY
AACSB: Analytic Skills

79) Use simple exponential smoothing with α = 0.33 to forecast the tire sales for February
through May. Assume that the forecast for January was for 22 sets of tires.

Automobile
Month
Battery Sales
January 28
February 21
March 39
April 34

Answer: Forecast for Feb. through May = 23.98, 22.9966, 28.2777, and 30.1661
Diff: 2
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY
AACSB: Analytic Skills

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80) The following table represents the new members that have been acquired by a fitness
center.

Month New members

Jan 45
Feb 60
March 57
April 65

Assuming α = 0.3, β = 0.4, an initial forecast of 40 for January, and an initial trend
adjustment of 0 for January, use exponential smoothing with trend adjustment to come up
with a forecast for May on new members.
Answer:
Month New members Ft Tt FITt
Jan 45 40 0 40
Feb 60 41.5 0.6 42.1
March 57 47.47 2.748 50.218
April 65 52.2526 3.56184 55.81444
May 58.57011 4.664107 63.23422

May forecast = 58.57

Diff: 3
Topic: FORECASTING MODELS—TREND AND RANDOM VARIATIONS
AACSB: Analytic Skills

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81) The following table represents the number of applicants at a popular private college in
the last four years.

Month New members

2007 10,067
2008 10,940
2009 11,116
2010 10,999

Assuming α = 0.2, β = 0.3, an initial forecast of 10,000 for 2007, and an initial trend
adjustment of 0 for 2007, use exponential smoothing with trend adjustment to come up with
a forecast for 2011 on the number of applicants.

Answer:
# of Ft Tt FITt
Month
applicants
2007 10,067 10,000 0 10000
2008 10,940 10013.4 4.02 10017.42
2009 11,116 10201.94 59.3748 10261.31
2010 10,999 10432.25 110.6562 10542.9
2011 10634.12 138.0219 10772.15

2011 Forecast = 10,634

Diff: 3
Topic: FORECASTING MODELS—TREND AND RANDOM VARIATIONS
AACSB: Analytic Skills

82) Given the following data, if MAD = 1.25, determine what the actual demand must have
been in period 2 (A2).

Time Period Actual (A) Forecast (F)

1 2 3 1
2 A2 = ? 4 -
3 6 5 1
4 4 6 2

Answer: A2 = 3 or A2 = 5
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY
AACSB: Analytic Skills

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83) Calculate (a) MAD, (b) MSE, and (c) MAPE for the following forecast versus actual sales
figures. (Please round to four decimal places for MAPE.)

Forecast Actual
100 95
110 108
120 123
130 130

Answer:
(a) MAD = 10/4 = 2.5
(b) MSE = 38/4 = 9.5
(c) MAPE = (0.0956/4)100 = 2.39%
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY
AACSB: Analytic Skills

84) Use the sales data given below to determine:

Year Sales (units) Year Sales (units)

1995 130 1999 169
1996 140 2000 182
1997 152 2001 194
1998 160 2002 ?

(a) The least squares trend line.

(b) The predicted value for 2002 sales.
(c) The MAD.
(d) The unadjusted forecasting MSE.
Answer:
(a) = 119.14 + 10.46X
(b) 119.14 + 10.46(8) = 202.82
(c) MAD = 1.01
(d) MSE = 1.71
Diff: 3
Topic: VARIOUS
AACSB: Analytic Skills

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85) For the data below:

Automobile Automobile
Year Year
Sales Sales
1990 116 1977 119
1991 105 1998 34
1992 29 1999 34
1993 59 2000 48
1994 108 2001 53
1995 94 2002 65
1996 27 2003 111

(a) Determine the least squares regression line.

(b) Determine the predicted value for 2004.
(c) Determine the MAD.
(d) Determine the unadjusted forecasting MSE.
Answer:
(a) = 85.15 - 1.8X
(b) 85.15 - 1.8 (15) = 58.15
(c) MAD = 30.09
(d) MSE = 1,121.66
Diff: 3
Topic: VARIOUS
AACSB: Analytic Skills

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86) Given the following gasoline data:

Quarter Year 1 Year 2

1 150 156
2 140 148
3 185 201
4 160 174

(a) Compute the seasonal index for each quarter.

(b) Suppose we expect year 3 to have annual demand of 800. What is the forecast value for
each quarter in year 3?
Answer:
(a)
Average
Average two- Quarterly
Quarter Year 1 Year 2 seasonal
year demand demand
index
1 150 156 153 164.25 .932
2 140 148 144 164.25 .877
3 185 201 193 164.25 1.175
4 160 174 167 164.25 1.017

(b)
Quarter Forecast
1 200 * .932 = 186.00
2 200 * .877 = 175.34
3 200 * 1.175 = 235.01
4 200 * 1.017 = 203.35
Diff: 3
Topic: ADJUSTING FOR SEASONAL VARIATIONS
AACSB: Analytic Skills

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87) Given the following data and seasonal index:

(a) Compute the seasonal index using only year 1 data.

(b) Determine the deseasonalized demand values using year 2 data and year 1's seasonal
indices.
(c) Determine the trend line on year 2's deseasonalized data.
(d) Forecast the sales for the first 3 months of year 3, adjusting for seasonality.
Answer:
(a) and (b)

(c) y = 11.96 + .29X

(d) Jan = [11.96 + .29 (13)] * .87 = 13.69
Feb = [11.96 + .29 (14)] * .67 = 12.18
Mar = [11.96 + .29 (15)] * .55 = 8.97
Diff: 3
Topic: ADJUSTING FOR SEASONAL VARIATIONS
AACSB: Analytic Skills

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88) Wick's Ski Shop is looking to forecast ski sales on a quarterly basis based on the
historical data listed in the table below:

Use the steps to develop a forecast using the decomposition method to answer the following
questions:
(a) Using the CMAs, calculate the seasonal indices for Q1, Q2, Q3, and Q4.
(b) Find the equation for the trend line using deseasonalized data.
(c) Find the year 5 quarterly forecasts.
Answer:
(a) Q1 — 2.1174, Q2 — 0.6129, Q3 — 0.3320, Q4 — 0.9324
(b) y = 227.73 + 4.32X
(c) Q1 forecast — 637.66, Q2 forecast — 187.22, Q3 forecast — 102.85, Q4 forecast —
292.88
Diff: 3
Topic: FORECASTING MODELS—TREND, SEASONAL, AND RANDOM VARIATIONS

89) The following table represents the actual vs. forecasted amount of new customers
acquired by a major credit card company:

Month Actual Forecast

Jan 1024 1010
Feb 1057 1025
March 1049 1141
April 1069 1053
May 1065 1059

(a) What is the tracking signal?

(b) Based on the answer in part (a), comment on the accuracy of this forecast.
Answer:
Month Actual Forecast Error RSFE
Jan 1024 1010 14 14 14
Feb 1057 1025 32 46 32
March 1049 1141 -92 -46 92
April 1069 1053 16 -30 16
May 1065 1059 6 -24 6

(a) RSFE/MAD = -24/32 = -0.75 MAD

(b) The answer in part (a) indicates an accurate forecast, one where overall, the actual
amount of new customers was slightly less than the forecast.
Diff: 3
Topic: MONITORING AND CONTROLLING FORECASTS
AACSB: Analytic Skills

90) What is the basic additive decomposition model (in regression terms)?
Answer: = a + b1X1 + b2X2 + b3X3 + b4X4
Where X1 = time period; X2 = 1 if quarter 2, 0 otherwise; X3 = 1 if quarter 3, 0 otherwise;

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X4 = 1 if quarter 4, 0 otherwise.
Diff: 2
Topic: TYPES OF FORECASTING MODELS

91) In general terms, describe what causal forecasting models are.

Answer: Causal forecasting models incorporate variables or factors that might influence the
quantity being forecasted.
Diff: 2
Topic: TYPES OF FORECASTING MODELS

92) In general terms, describe what qualitative forecasting models are.

Answer: Qualitative forecasting models attempt to incorporate judgmental or subjective
factors into the model.
Diff: 2
Topic: TYPES OF FORECASTING MODELS

93) Briefly describe the structure of a scatter diagram for a time series.
Answer: A scatter diagram for a time series may be plotted on a two-dimensional graph with
the horizontal axis representing the time period, while the variable to be forecast (such as
sales) is placed on the vertical axis.
Diff: 2
Topic: COMPONENTS OF A TIME SERIES

94) Briefly describe the jury of executive opinion forecasting method.

Answer: The jury of executive opinion forecasting model uses the opinions of a small group
of high-level managers, often in combination with statistical models, and results in a group
estimate of demand.
Diff: 2
Topic: TYPES OF FORECASTING MODELS

95) Briefly describe the consumer market survey forecasting method.

Answer: It is a forecasting method that solicits input from customers or potential customers
regarding their future purchasing plans.
Diff: 2
Topic: TYPES OF FORECASTING MODELS

96) Describe the naïve forecasting method.

Answer: The forecast for the next period is the actual value observed in the current period.
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY

97) Briefly describe why the scatter diagram is helpful.

Answer: Scatter diagrams show the relationships between model variables.
Diff: 1
Topic: COMPONENTS OF A TIME SERIES

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98) Explain, briefly, why most forecasting error measures use either the absolute or the
square of the error.
Answer: A deviation is equally important whether it is above or below the actual. This also
prevents negative errors from canceling positive errors that would understate the true size
of the errors.
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY

99) List four measures of historical forecasting errors.

Answer: MAD, MSE, MAPE, and Bias
Diff: 2
Topic: MEASURES OF FORECAST ACCURACY

100) In general terms, describe what TIME SERIES forecasting models are.
Answer: forecasting models that make use of historical data
Diff: 1
Topic: COMPONENTS OF A TIME SERIES

101) List four components of TIME SERIES data.

Answer: trend, seasonality, cycles, and random variations
Diff: 2
Topic: COMPONENTS OF A TIME SERIES

102) Explain, briefly, why the larger number of periods included in a moving average
forecast, the less well the forecast identifies rapid changes in the variable of interest.
Answer: The larger the number of periods included in the moving average forecast, the less
the average is changed by the addition or deletion of a single number.
Diff: 2
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY

103) State the mathematical expression for exponential smoothing.

Answer: Ft+1 = Ft + α(Yt - Ft)
Diff: 2
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY

104) Explain, briefly, why, in the exponential smoothing forecasting method, the larger the
value of the smoothing constant, α, the better the forecast will be in allowing the user to see
rapid changes in the variable of interest.
Answer: The larger the value of α, the greater is the weight placed on the most recent
values.
Diff: 2
Topic: FORECASTING MODELS—RANDOM VARIATIONS ONLY

105) In exponential smoothing, discuss the difference between α and β.

Answer: α is a weight applied to adjust for the difference between last period actual and
forecasted value. β is a trend smoothing constant.
Diff: 2
Topic: FORECASTING MODELS—TREND AND RANDOM VARIATIONS

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106) In general terms, describe the difference between a general linear regression model
and a trend projection.
Answer: A trend projection is a regression model where the independent variable is always
time.
Diff: 2
Topic: FORECASTING MODELS—TREND AND RANDOM VARIATIONS

107) In general terms, describe a centered moving average.

Answer: An average of the values centered at a particular point in time. This is used to
compute seasonal indices when trend is present.
Diff: 2
Topic: ADJUSTING FOR SEASONAL VARIATIONS

108) The decomposition approach to forecasting (using trend and seasonal components)
may be helpful when attempting to forecast a TIME SERIES. Could an analogous approach be
used in multiple regression analysis? Explain briefly.
Answer: An analogous approach would be possible using time as one independent variable
and using a set of dummy variables to represent the seasons.
Diff: 2
Topic: FORECASTING MODELS—TREND, SEASONAL, AND RANDOM VARIATIONS

109) List the steps to develop a forecast using the decomposition method.
Answer:
1. Compute seasonal indices using CMAs.
2. Deseasonalize the data by dividing each number by its seasonal index.
3. Find the equation of a trend line using the deseasonalized data.
4. Forecast for future periods using the trend line.
5. Multiply the trend line forecast by the appropriate seasonal index.
Diff: 2
Topic: FORECASTING MODELS—TREND, SEASONAL, AND RANDOM VARIATIONS

110) What is one advantage of using causal models over TIME SERIES or qualitative models?
Answer: Use of the causal model requires that the forecaster gain an understanding of the
relationships, not merely the frequency of variation; i.e., the forecaster gains a greater
understanding of the problem than the other methods.
Diff: 2
Topic: TYPES OF FORECASTING MODELS
AACSB: Reflective Thinking

111) Discuss the use of a tracking signal.

Answer: A tracking signal measures how well predictions fit actual data. By setting tracking
limits, a manager is signaled to reevaluate the forecasting method.
Diff: 2
Topic: MONITORING AND CONTROLLING FORECASTS

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