Lenovo uses the ZX-81 chip in some of its laptop computers. The prices for the c
ID: 391065 • Letter: L
Question
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
$1.901.90
July
$1.801.80
February
$1.611.61
August
$1.821.82
March
$1.601.60
September
$1.601.60
April
$1.851.85
October
$1.571.57
May
$1.901.90
November
$1.621.62
June
$1.951.95
December
$1.751.75
This exercise contains only part d.
With
alpha
= 0.1 and the initial forecast for October of
$1.83
using exponential smoothing, the forecast for periods 11 and 12 is (round your responses to two decimal places):
Month
Oct
Nov
Dec
Forecast
$1.83
With
alpha
= 0.3 and the initial forecast for October of
$1.76
using exponential smoothing, the forecast for periods 11 and 12 is (round your responses to two decimal places):
Month
Oct
Nov
Dec
Forecast
$1.76
With
alpha
= 0.5 and the initial forecast for October of
$1.72
using exponential smoothing, the forecast for periods 11 and 12 is (round your responses to two decimal places):
Month
Oct
Nov
Dec
Forecast
$1.72
Based on the months of October, November, and December, the mean absolute deviation using exponential smoothing where
alpha
= 0.1 and the initial forecast for
Octoberequals=$1.83
is
(round your response to three decimal places).
Based on the months of October, November, and December, the mean absolute deviation using exponential smoothing where
alpha
= 0.3 and the initial forecast for
Octoberequals=$1.76
is
(round your response to three decimal places).
Based on the months of October, November, and December, the mean absolute deviation using exponential smoothing where
alpha
= 0.5 and the initial forecast for
Octoberequals=$1.72
is
(round your response to three decimal places).
Based on the mean absolute deviation, the better forecast is achieved using alphaequals=
Month
Price Per Chip
Month
Price Per Chip
January
$1.901.90
July
$1.801.80
February
$1.611.61
August
$1.821.82
March
$1.601.60
September
$1.601.60
April
$1.851.85
October
$1.571.57
May
$1.901.90
November
$1.621.62
June
$1.951.95
December
$1.751.75
Explanation / Answer
Formula for exponential smoothing as follows:
Ft = alpha x At-1 + ( 1 – alpha) x Ft-1
Where, Ft , Ft-1 = Forecasts for period t and t-1 respectively
At-1 = actual price for period t
Alpha = exponential smoothing constant
Therefore , formula when alpha = 0.1 will be Ft = 0.1 x at-1 + 0.9 x ft-1
Formula when alpha =0.3 will be Ft = 0.3 x at-1 + 0.7 x ft-1
Formula when alpha = 0.5 will be Ft = 0.5 x At-1 + 0.5 x Ft-1
Also to be noted :
Absolute deviation for period t = Absolute difference between values Ft and At ( i.e. non negative values )
Based on above data , forecasts and absolute deviation values for October through December for different values of alpha ( alpha = 0.1, alpha = 0.3 and alpha =0.5) as follows :
Period
Actual price/ chip ($)
Forecast ( alpha = 0.1)
Absolute deviation
Forecast( alpha = 0.3)
Absolute deviation
Forecast( alpha = 0.5)
Absolute deviation
Oct
1.57
1.83
0.26
1.760
0.19
1.72
0.15
Nov
1.62
1.80
0.18
1.703
0.08
1.65
0.02
Dec
1.75
1.79
0.04
1.678
0.07
1.63
0.12
Sum =
0.48
0.34
0.29
Therefore ,
Mean absolute deviation for alpha of 0.1 = Sum of absolute deviation / 3 ( i.e. number of observations ) = 0.48 / 3 = 0.16
Mean absolute deviation for alpha of 0.3 = Sum of absolute deviation / 3 ( i.e. number of observations ) = 0.34/3 = 0.113
Mean absolute deviation for alpha = 0.5 = Sum of absolute deviation / 3 = 0.29/3 = 0.097
Period
Actual price/ chip ($)
Forecast ( alpha = 0.1)
Absolute deviation
Forecast( alpha = 0.3)
Absolute deviation
Forecast( alpha = 0.5)
Absolute deviation
Oct
1.57
1.83
0.26
1.760
0.19
1.72
0.15
Nov
1.62
1.80
0.18
1.703
0.08
1.65
0.02
Dec
1.75
1.79
0.04
1.678
0.07
1.63
0.12
Sum =
0.48
0.34
0.29
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