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Plotting and Trends

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(1) Year 1 2 3 4 5 6 7 8 9 10 11
Demand 7 9 5 9 13 8 12 13 9 11 7

a) Plot the above data on a graph. Do you observe any trend, cycles, or random variations?
b) Starting in year 4 and going to year 12, forecast demand using a 3-year moving average. Plot your forecast on the same graph as the original data.
c) Starting in year 4 and going to year 12, forecast demand using a 3-year moving average with weights of .1, .3, and .6, using .6 for the most recent year. Plot this forecast on the same graph.

(2) The monthly sales for Telco Batteries, Inc., were as follows:
Month Sales
January 20
February 21
March 15
April 14
May 13
June 16
July 17
August 18
September 20
October 20
November 21
December 23

a) Plot the monthly sales data.
b) Forecast January sales using each of the following:
i) Naive method.
ii) A 3-month moving average.
iii) A 6-month weighted average using .1, .1, .1, .2, .2, and .3, with the heaviest weights applied to the most recent months.
iv) Exponential smoothing using an α = .3 and a September forecast of 18.
v) A trend projection.
c) With the data given, which method would allow you to forecast next March's sales?

(3) Dell uses the CR5 chip in some of its laptop computers. The prices for the chip during the past 12 months were as follows:
Month Price per Chip
January $1.80
February $1.67
March $1.70
April $1.85
May $1.90
June $1.87
July $1.80
August $1.83
September $1.70
October $1.65
November $1.70
December $1.75

a) Use a 2-month moving average on all the data and plot the averages and the prices.
b) Use a 3-month moving average and add the 3-month plot to the graph created in part (a).
c) Which is better (using the mean absolute deviation): the 2-month average or the 3-month average?
d) Compute the forecasts for each month using exponential smoothing, with an initial forecast for January of $1.80. Use α = .1, then α = .3, and finally α = .5. Using MAD, which α is the best?

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Graphing, Trends and Forecasting

5.
(a) Plot the data on U.S. general aviation shipments. (b) Describe the pattern and discuss possible causes. (c) Would a fitted trend be helpful? Explain. (d) Make a similar graph for 1992-2003 only. Would a fitted trend be helpful in making a prediction for 2004? (e) Fit a trend model of your choice to the 1992-2003 data. (f) Make a forecast for 2004, using either the fitted trend model or a judgment forecast. Why is it best to ignore earlier years in this data set? Airplanes
Make a forecast for 2004, using either the fitted trend model or a judgment forecast. Why is it best to ignore earlier years in this data set? Airplanes
U.S. Manufactured General Aviation Shipments, 1966-2003
Year Planes
1966 15,587
1967 13,484
1968 13,556
1969 12,407
1970 7,277
1971 7,346
1972 9,774
1973 13,646
1974 14,166
1975 14,056
1976 15,451
1977 16,904
1978 17,811
1979 17,048
1980 11,877
1981 9,457
1982 4,266
1983 2,691
1984 2,431
1985 2,029
1986 1,495
1987 1,085
1988 1,143
1989 1,535
1990 1,134
1991 1,021
1992 856
1993 870
1994 881
1995 1,028
1996 1,053
1997 1,482
1998 2,115
1999 2,421
2000 2,714
2001 2,538
2002 2,169
2003 2,090

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