Chapter 5

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```					                                            CHAPTER 5
Forecasting
TRUE/FALSE

5.1    Time-series models rely on judgment in an attempt to incorporate qualitative or subjective
factors into the forecasting model.

*5.2   Use of any forecasting procedure is somewhat subjective.

5.3    The coefficient of correlation expresses the degree or strength of a linear relationship.

*5.4   To make a forecast which is accurate over time requires that we collect data over time.

5.5    One of the most popular qualitative forecasting methods is the Delphi technique.

5.6    A disadvantage of the Delphi technique is that results are obtained slowly.

5.7    Often, a variety of dependent variables may be successfully used in a linear regression forecast of
a single independent variable.

5.8    A moving average forecasting method is a causal forecasting method.

5.9    An exponential forecasting method is a time-series forecasting method.

5.10   A trend projection forecasting method is a causal forecasting method.

5.11   Tupperware International has successfully identified a single forecasting tool to predict their
company’s product sales.

5.12   A scatter diagram is useful to determine if a relationship exists between two variables.

5.13   A seasonal index must be between –1 and +1.

5.14   Time-series models enable the forecaster to include specific representations of various
qualitative and quantitative factors.

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5.15   Qualitative models produce forecasts that are little better than simple guesses or coin tosses.

5.16   If you need to develop a forecast in a hurry, you probably should not contemplate using the
Delphi method.

5.17   If you need to develop a forecast of sales as a function of advertising expenditure and product
selling price, you should probably consider using one of the regression analysis models.

5.18   One of the benefits of the Delphi method is that no one forecaster is able to unduly influence any
other forecaster.

5.19   When one plots a scatter diagram, the independent variable (X) is always time.

5.20   One of the benefits of using a causal forecasting model is that we are able to eliminate the impact
of random error.

5.21   The fewer the periods over which one takes a moving average, the more accurately the resulting
forecast mirrors the actual data.

5.22   An advantage of exponential smoothing over a simple moving average is that exponential
smoothing requires one to retain less data.

5.23   An advantage of exponential smoothing over a simple moving average is that the exponential
smoothing model can be extended to include a trend term.

5.24   The notion of a seasonal index can only be associated with time-series forecasting.

5.25   A correlation coefficient of +0.75 implies that the forecasted variable increases as the
independent variable increases.

5.26   The purpose of a tracking signal is to help us estimate the forecast error at each data point.

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5.27    Adaptive smoothing is analogous to exponential smoothing where the coefficients  and  are
periodically updated to improve the forecast.

*5.28   One of the advantages of using a scatter diagram is that it may suggest types of formatting
techniques that are appropriate.

*5.29   One of the advantages of using a scatter diagram is that it may suggest types of formatting
techniques that are not appropriate.

*5.30   As a causal method, moving averages are preferable to exponential smoothing.

MULTIPLE CHOICE

5.31    A weighted moving average having the early periods more heavily weighted

(a)   is more responsive to recent demand changes.
(b)   is less responsive to recent demand.
(c)   places emphasis on the past demand data.
(d)   is always the most effective weighting scheme.
(e)   is not a time-series model.

5.32    One statistical method for developing a linear trend line is

(a)   "eyeballing."
(b)   the exponential smoothing method.
(c)   the causal forecasting method.
(e)   least squares.

5.33    In the linear regression equation, "b" is the

(a)   smoothing constant.
(b)   Y-axis intercept.
(c)   slope of the regression line.
(d)   independent variable.
(e)   dependent variable.

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

(a)   exponential smoothing
(b)   Delphi
(c)   executive opinion
(d)   sales force composite

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(e) consumer market survey

5.35   Which of the following is (are) not characteristic of the scatter diagram?

(a)   The independent variable is usually measured on the horizontal (X) axis.
(b)   The dependent variable is usually measured on the vertical (y) axis.
(c)   It is useful to get a quick idea as to whether any relationship exists.
(d)   It is helpful in determining what is cause and what is effect.
(e)   none of the above

5.36   Which of the following university/commercial statistical computer packages has a forecasting
technique?

(a)   BIOMED
(b)   SAS
(c)   SPSS
(d)   Minitab
(e)   all of the above

5.37   One thing not true about the coefficient of correlation is that it

(a)   can be squared to get the coefficient of determination.
(b)   can be any number between -1 and +1.
(c)   expresses the degree or strength of the relationship between variables.
(d)   can be used to calculate next year's sales.
(e)   is usually expressed as r.

5.38   If computing a causal linear regression model of Y = a + bX and the resultant r 2 is very near zero,
then one would be able to conclude that

(a)   Y = a + bX is a good forecasting method.
(b)   Y = a + bX is not a good forecasting method.
(c)   a multiple linear regression model is a good forecasting method for the data.
(d)   a multiple linear regression model is not a good forecasting method for the data.
(e)   none of the above

5.39   Daily demand for newspapers for the last 10 days has been as follows: 12, 13, 16, 15, 12, 18, 14,
12, 13, 15. Forecast sales for the next day using a 2-day moving average.

(a)   14
(b)   13
(c)   15
(d)   28
(e)   none of the above

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5.40    Daily demand for newspapers for the last 10 days has been as follows: 12, 13, 16, 15, 12, 18, 14,
12, 13, 15. Forecast sales for the next day using a 3-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

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5.41   Enrollment in a particular class for the last four semesters had been 120, 126, 110, and 130.
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

5.42   Enrollment in a particular class for the last four semesters had been 120, 126, 110, and 130.
Suppose a 1-semester moving average was used to forecast enrollment (this is sometimes referred
to as a naive 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

5.43   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.
(e)   none of the above

5.44   Regression was used to develop a model to predict sales based on advertising dollars spent. The
equation developed is Y = 1000 + 20X, where X is advertising dollars and Y is sales. If \$300 is
spent on advertising, what would be the best prediction for sales?

(a)   \$1,600
(b)   \$7,000
(c)   \$1,620
(d)   \$6,000
(e)   none of the above

5.45   Regression was used to develop a model to predict sales based on advertising dollars spent. The
equation developed is Y = 1000 + 20X - 2Z, where X is advertising dollars spent by your

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company, Z is the price for the product, and Y is sales. If \$800 is spent by your company on
advertising, and the price is set at \$100, what would be the best prediction for sales?

(a)   \$17,200
(b)   \$6,800
(c)   \$7,200
(d)   \$16,800
(e)   none of the above

5.46    An exponential smoothing model having a large 

(a)   is more responsive to recent demand changes.
(b)   is less responsive to recent demand.
(c)   places emphasis on the past demand data.
(d)   is always the most effective weighting scheme.
(e)   is not a time-series model.

5.47    In the exponential smoothing forecasting method,  is the

(a)   slope of the trend line.
(b)   new forecast.
(c)   Y-axis intercept.
(d)   independent variable.
(e)   trend smoothing constant.

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

(a)   Mean deviation
(b)   Squared Average Error
(c)   Mean Absolute Percent Error
(d)   Delphi Method
(e)   none of the above

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5.49   Calculation of a correlation coefficient is part of ________ analysis.

(a)   exponential smoothing
(b)   time-series
(c)   seasonal
(d)   marginal
(e)   regression

5.50   Which of the following is not a characteristic of regression analysis?

(a) The independent variable is usually called X.
(b) The dependent variable is usually called Y.
(c) It is useful in developing a forecast of one variable as a function of one or more other
variables.
(d) It is helpful in determining what is cause and what is effect.
(e) none of the above

5.51   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.

5.52   The diagram below illustrates data with a

(a) negative correlation coefficient.
(b) zero correlation coefficient.
(c) positive correlation coefficient.

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(d) correlation coefficient equal to +1.
(e) none of the above

5.53    A correlation coefficient of -1 implies that

(a)   both variables increase at exactly the same rate.
(b)   one variable increases at the same rate that the other variable decreases.
(c)   the two variables have no correlation.
(d)   both variables decrease at the same rate.
(e)   both variables increase at the same rate.

5.54    If computing a causal linear regression model, Y = a + bX, and the resultant r2 is very near zero,
then one should conclude that

(a)   Y = a + bX is a good forecasting method.
(b)   a time-series model would be preferable.
(c)   a multiple linear regression model would be preferable.
(d)   an exponential smoothing model would be preferable.
(e)   one's choice of independent variable was inappropriate.

5.55    Enrollment in a particular class for the last four semesters had been 120, 126, 110, and 135. The
best forecast of enrollment next semester, based on a 3-semester moving average, would be

(a)   126.
(b)   135.
(c)   120.
(d)   123.
(e)   125.

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5.56   The correlation coefficient resulting from a particular regression analysis was 0.25. What was
the slope of the regression line?

(a)   0.5
(b)   -0.5
(c)   0.0625
(d)   There is insufficient information to answer the question.
(e)   none of the above

5.57   A tracking signal was calculated for a particular set of demand forecasts. This tracking signal
was negative. This would indicate that

(a)   the trend portion of the model was inappropriate.
(b)   the nontrend portion of the model was inappropriate.
(c)   the EMSE is negative.
(e)   none of the above

5.58   Given that the MAD for the following forecast is 2.5, what is the actual value in period 2?

Period   Forecast      Actual
1        100          95
2        110
3        120          123
4        130          130

(a)   120
(b)   98
(c)   108
(d)   115
(e)   none

5.59   Given that the MSE for the following forecast is 9.5, what is the forecast value in period 3?

Period      Forecast            Actual
1           100                 95
2           110                108
3                              123
4            130               130

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(a)   108
(b)   118
(c)   128
(d)   115
(e)   none of the above

5.60    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

*5.61   Which of the following is not a problem with moving average models?

(a)   larger number of periods may smooth out real changes
(b)   they take a considerable period of time to construct
(c)   they don’t pick up trends in time to react to the trends
(d)   they require that lots of past data be kept
(e)   none of the above

*5.62   In picking the smoothing constant for an exponential smoothing model, we should look for a
value which

(a) produces a nice looking curve.
(b) produces the values you would like to see.
(c) produces values which compare well with actual values based on a standard measure of
error.
(d) cause the least computational effort.
(e) none of the above

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*5.63   Which of the following model types would likely be the best for predicting the number of
automobiles sold next year?

(a)   Delphi
(b)   Sales force composite
(c)   Regression
(d)   Multiple regression
(e)   none of the above

*5.64   For which of the following forecasts would you expect it to be most appropriate to use a multiple
regression model?

(a)   The likelihood of a student applicant being accepted at college.
(b)   The number of ice cream cones sold by a single store tomorrow.
(c)   The number of apples on a single apple tree at harvest time.
(d)   The average GPA in a class of seniors graduating from college.
(e)   None of the above

*5.65   When San Diego Hospital forecast the number of patient days for each upcoming month, they
used a simple regression model. Had they needed to forecast the number of available beds by
day for the upcoming months,

(a)   a simple regression model would have been more than adequate.
(b)   a moving average model would have been more appropriate.
(c)   a multiple regression model should have been used.
(d)   an exponential smoothing model would have been best.
(e)   none of the above

PROBLEMS

5.66    For the data below, develop a 3-month moving average forecast.

Month      Automobile         Month       Automobile
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

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5.67    Use exponential smoothing with  = 0.2 to forecast the battery sales. Assume the forecast for
January was 22 batteries.

Month        Automobile
Battery Sales
January             20
February            21
March               15
April               14

5.68    Use the sales data given below to determine:

(a) the least squares trend line
(b) the predicted value for 1982 sales

Year      Sales (units)   Year       Sales (units)
1975          100         1979           139
1976          110         1980           152
1977          122         1981           164
1978          130         1982             ?

5.69    City government has collected the following data on annual sales tax collections and new car
registrations:

Annual Sales          New Car           Annual Sales         New Car
Tax Collections      Registrations      Tax Collections     Registrations
(\$ millions)        (thousands)          (millions)        (thousands)
1.0                  10                 1.8                 14
1.4                  12                 2.1                 17
1.9                  15                 2.3                 20
2.0                  16

(a) Determine the least squares regression equation.
(b) Using the results of part (a), find the estimated sales tax collections if new car registrations
total 22.
(c) Calculate the coefficient of correlation.
(d) Calculate the coefficient of determination.

5.70    Let us hypothesize (imagine) that the number of automobile accidents in a certain region are
related to the regional number of registered automobiles in thousands (b1), alcoholic beverage

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sales in \$10,000 (b2), and decrease in the price of gasoline in cents (b3). Furthermore, imagine
that the regression formula has been calculated as:

Y = a + b1 X 1 + b2 X 2 + b3 X 3

where Y = the number of automobile accidents, a = 7.5, b1 = 3.5, b2 = 4.5, and b3 = 2.5

Calculate the expected number of automobile accidents under the following conditions:

X1     X2      X3
(a)    2      3       0
(b)    3      5       1
(c)    4      7       2

5.71   Calculate (a) MAD, (b) MSE, and (c) MAPE for the following forecast versus actual sales
figures.

Forecast     Actual
100         95
110         108
120         123
130         130

5.72   Demand for a particular type of battery fluctuates from one week to the next. A study of the last
6 weeks provides the following demands (in dozens): 4, 5, 3, 6, 7, 8 (last week).

(a) Forecast demand for the next week using a 2-week moving average.
(b) Forecast demand for the next week using a 3-week moving average.

5.73   Daily high temperatures in the city of Houston for the last week have been as follows:
93, 94, 93, 95, 96, 88, 90 (yesterday).

(a) Forecast the high temperature today using a 3-day moving average.
(b) Forecast the high temperature today using a 2-day moving average.
(c) Calculate the mean absolute deviation based on a 2-day moving average.

5.74   Average starting salaries for students using a placement service at a university have been steadily
increasing. A study of the last four graduating classes indicate the following average salaries:
\$20,000, \$22,000, \$23,000, and \$25,000 (last graduating class).

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Predict the starting salary for the next graduating class using an exponential smoothing model
with  = 0.2. Assume that the initial forecast was \$20,000 (so that the forecast and the actual
were the same).

5.75    A firm conducted a careful analysis of the cost of operating an automobile. The following model
was developed:

Y = 4000 + 0.20X, where Y = annual cost, X = miles driven

(a) If a car is driven 15,000 miles this year, what is the forecasted cost of operating this
automobile?

(b) If a car is driven 25,000 miles this year, what is the forecasted cost of operating this
automobile?

(c) Suppose that one car was driven 15,000 miles and the actual cost of operating was \$6,000,
while a second car was driven 25,000 miles and the actual operating cost was \$10,000.
Calculate the mean absolute deviation for this.

5.76    The following multiple regression model was developed to predict job performance as measured
by a company job performance evaluation index based on a pre-employment test score and

Y = 35 + 20X1 + 50X2, where Y = job performance evaluation index
X1 = pre-employment test score
X2 = college GPA

(a) Forecast the job performance index for an applicant who had a 3.0 GPA and scored 80 on the
pre-employment score.
(b) Forecast the job performance index for an applicant who had a 2.5 GPA and scored 70 on the
pre-employment score.

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5.77    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)   |FA|
1                2                 3           1
2             A2 = ?               4           -
3                6                 5           1
4                4                 6           2

*5.78                                                                                                For

Month        Automobile         Month      Automobile
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

*5.79   Use exponential smoothing with  = 0.3 to forecast the battery sales. Assume the forecast for
January was 22 batteries.

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Forecasting  CHAPTER 5

Month         Automobile
Tire Sales
January              20
February             21
March                15
April                14

*5.80   Use the sales data given below to determine:

(a) the least squares trend line
(b) the predicted value for 1982 sales

Year      Sales (units)   Year   Sales (units)
1995          130         1999       169
1996          140         2000       182
1997          152         2001       194
1998          160         2002         ?

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*5.81   For the data below

Year       Automobile         Year          Automobile
Sales                            Sales
1980       116                 1987         119
1981       105                 1988          34
1982        29                 1989          34
1983        59                 1990          48
1984       108                 1991          53
1985        94                 1992          65
1986        27                 1993         111

(a) Develop a 6-year moving average forecast.

5.82    In general terms, describe what time-series forecasting models are.

5.83    In general terms, describe what causal forecasting models are.

5.84    In general terms, describe what qualitative forecasting models are.

5.85    Briefly describe the Delphi forecasting method.

5.86    Briefly describe the executive opinion forecasting method.

5.88    Briefly describe the sales force composite forecasting method.

5.89    Briefly describe the consumer market survey forecasting method.

5.90    List the possible components of time-series data.

5.91    In general terms, describe an independent variable.

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Forecasting  CHAPTER 5

5.92    In general terms, describe a dependent variable.

5.93    The accuracy parameter of regression estimates is called the ________________.

5.94    List four measures of historical forecasting errors.

*5.95   In what way might it be said that all forecasting models are subjective?

*5.96   Explain, briefly, why most forecasting error measures use either the absolute or the square of the
error.

*5.97   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.

.

*5.98   Explain, briefly, why, in the exponential smoothing forecasting method, the larger the value of
the smoothing constant, , the better the forecast will be in allowing the user to see rapid changes
in the variable of interest.

*5.99   Explain, briefly, why the Delphi forecasting approach is probably the most useful of those
discussed when attempting to forecast fifty to one hundred years into the future.

*5.100 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.

*5.101 What are some of the basic assumptions we make when using simple linear or multiple
regression?

*5.102 What is one advantage of using causal models over time-series or qualitative models?

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