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Dell uses the CR5 chip in some of its laptop computers. The prices for the chip during the past 12 months were as follows Answer

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 ($)
January 1.8
February 1.67
March 1.7
April 1.85
May 1.9
June 1.87
July 1.8
August 1.83
September 1.7
October 1.65
November 1.7
December 1.75
  1. Use a 2-month moving average on all the data and plot the averages and the prices.
  2. Ans:
Month Price per Chip ($) 2-month moving average
January 1.8
February 1.67
March 1.7 1.735
April 1.85 1.685
May 1.9 1.775
June 1.87 1.875
July 1.8 1.885
August 1.83 1.835
September 1.7 1.815
October 1.65 1.765
November 1.7 1.675
December 1.75 1.675
December + 1 Month 1.725

 

  1. Use a 3-month moving average and add the 3-month plot to the graph created in part (a).
  2. Ans:
Month Price per Chip ($) 3-month moving average
January 1.8
February 1.67
March 1.7
April 1.85 1.72
May 1.9 1.74
June 1.87 1.82
July 1.8 1.87
August 1.83 1.86
September 1.7 1.83
October 1.65 1.78
November 1.7 1.73
December 1.75 1.68
December + 1 Month 1.70

 

 

 

  1. Which is better (using the mean absolute deviation): the 2-month average or the 3-month average?
  2. Ans:
Month Price per Chip ($) 2-month moving average Error Absolute
January 1.8
February 1.67
March 1.7 1.735 -0.035 0.03
April 1.85 1.685 0.165 0.17
May 1.9 1.775 0.125 0.13
June 1.87 1.875 -0.005 0.00
July 1.8 1.885 -0.085 0.09
August 1.83 1.835 -0.005 0.00
September 1.7 1.815 -0.115 0.12
October 1.65 1.765 -0.115 0.12
November 1.7 1.675 0.025 0.03
December 1.75 1.675 0.075 0.08
MAD 0.08

 

Month Price per Chip ($) 3-month moving average Error Absolute
January 1.8
February 1.67
March 1.7
April 1.85 1.72 0.13 0.13
May 1.9 1.74 0.16 0.16
June 1.87 1.82 0.05 0.05
July 1.8 1.87 -0.07 0.07
August 1.83 1.86 -0.03 0.03
September 1.7 1.83 -0.13 0.13
October 1.65 1.78 -0.13 0.13
November 1.7 1.73 -0.03 0.03
December 1.75 1.68 0.07 0.07
MAD 0.09

 

The lower MAD is the more accurate, i.e. has lower error. So, forecast using the 2-month average is better.

 

 

 

  1. 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?

Ans:

Month Price per Chip ($) Forecast using exponential smoothing ( alpha = 0.1) Error Absolute
January 1.8 1.8 0.00 0.000
February 1.67 1.8 -0.13 0.130
March 1.7 1.79 -0.09 0.087
April 1.85 1.78 0.07 0.072
May 1.9 1.79 0.11 0.115
June 1.87 1.80 0.07 0.073
July 1.8 1.80 0.00 0.004
August 1.83 1.80 0.03 0.026
September 1.7 1.81 -0.11 0.106
October 1.65 1.80 -0.15 0.146
November 1.7 1.78 -0.08 0.081
December 1.75 1.77 -0.02 0.023
MAD 0.072

 

 

 

Month Price per Chip ($) Forecast using exponential smoothing ( alpha = 0.3) Error Absolute
January 1.8 1.8 0.00 0.000
February 1.67 1.8 -0.13 0.130
March 1.7 1.76 -0.06 0.061
April 1.85 1.74 0.11 0.107
May 1.9 1.77 0.13 0.125
June 1.87 1.81 0.06 0.058
July 1.8 1.83 -0.03 0.030
August 1.83 1.82 0.01 0.009
September 1.7 1.82 -0.12 0.124
October 1.65 1.79 -0.14 0.136
November 1.7 1.75 -0.05 0.046
December 1.75 1.73 0.02 0.018
MAD 0.070

 

 

 

Month Price per Chip ($) Forecast using exponential smoothing ( alpha = 0.5) Error Absolute
January 1.8 1.8 0.00 0.000
February 1.67 1.8 -0.13 0.130
March 1.7 1.74 -0.03 0.035
April 1.85 1.72 0.13 0.133
May 1.9 1.78 0.12 0.116
June 1.87 1.84 0.03 0.028
July 1.8 1.86 -0.06 0.056
August 1.83 1.83 0.00 0.002
September 1.7 1.83 -0.13 0.129
October 1.65 1.76 -0.11 0.114
November 1.7 1.71 -0.01 0.007
December 1.75 1.70 0.05 0.046
MAD 0.066

 

We see that MAD is lowest for Forecast using exponential smoothing (alpha = 0.5), and so this is better.

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