Description
Test Bank Quantitative Analysis for Management 12th Edition Render Stair Hanna Hale\
SAMPLE
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
2
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.
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
3
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
4
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.
5
Answer: FALSE
Diff: 2
Topic: ADJUSTING FOR SEASONAL VARIATIONS
29) A seasonal index of 1 means that the season is average.
Answer: TRUE
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
6
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
7
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
8
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
9
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
10
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
11
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
12
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
13
A) decomposition
B) smoothing
C) tracking signal
D) regression
E) moving average
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
14
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
15
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
16
74) For the data below:
Month Automobile
Battery Sales Month Automobile
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.
17
Answer:
(a) scatter diagram
(b)
Month
Automobile
Battery Sales
3-Month
Moving Avg. Absolute 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
18
75) For the data below:
Month Automobile
Tire Sales Month Automobile
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.
19
Answer:
(a) scatter diagram
(b)
Month
Automobile
Tire Sales
3-Month
Tire Average
Squared
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
20
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.
21
Answer:
(a) scatter diagram
(b)
Year Number of
Automobiles Forecast Error Error
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
22
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.
Month Automobile
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.
Month Automobile
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
23
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
24
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:
Month # of applicants Ft Tt FITt
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
25
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
26
85) For the data below:
Year Automobile
Sales Year Automobile
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
27
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)
Quarter Year 1 Year 2 Average twoyear
demand
Quarterly
demand
Average
seasonal 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
28
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
29
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)?
30
Answer: = a + b1X1 + b2
X2 + b3X3 + b4X4
Where X1 = time period; X2 = 1 if quarter 2, 0 otherwise; X3 = 1 if quarter 3, 0 otherwise; 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
31
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
32
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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