Plotting and Trends

(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?