Lenovo uses the​ ZX-81 chip in some of its laptop computers. The prices for the chip during the last 12 months were as​ follows: Month Price Per Chip Month Price Per Chip
January $1.80 July 1.80
February 1.67 August 1.83
March 1.70 September 1.70
April 1.85 October 1.65
May 1.90 November 1.70
June 1.87 December 1.75

a. Use a 2-month moving average on all the data and plot the averages and the prices.
b. Use a three-month moving average and add the three-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=0.1, then α=0.3, and finally α=0.5. Using MAD, which α is the best?