Chapter 5 Forecasting

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 ? = 0.2, ? = 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.

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

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

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.

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.

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?

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.

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.

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.

90) What is the basic additive decomposition model (in regression terms)?

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

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

93) Briefly describe the structure of a scatter diagram for a time series.

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

95) Briefly describe the consumer market survey forecasting method.

96) Describe the naïve forecasting method.

Topic: MEASURES OF FORECAST ACCURACY

97) Briefly describe why the scatter diagram is helpful.

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

99) List four measures of historical forecasting errors.

100) In general terms, describe what TIME SERIES forecasting models are.

101) List four components of TIME SERIES data.

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.

103) State the mathematical expression for exponential smoothing.

104) 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.

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

106) In general terms, describe the difference between a general linear regression model and a trend projection.

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

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.

109) List the steps to develop a forecast using the decomposition method.

110) What is one advantage of using causal models over TIME SERIES or qualitative models?

111) Discuss the use of a tracking signal.