Question
Asked Nov 11, 2019
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For the data set, perform exponential smoothing with alpha = 0.1 to determine the forecast for week 20.  

week Sales (1000s of gallons)
1 17
2 21
3 19
4 23
5 18
6 16
7 20
8 18
9 22
10 20
11 15
12 22
13 31
14 34
15 31
16 33
17 28
18 32
19 30
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Expert Answer

Step 1

Given data and forecast for the following week is shown here

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week Sales (1000s of gallons) (A) (Ft) Forecast Еггor (At-Ft) 17 0.00 1 17.00 17.00 2 21 4.00 3 19 17.40 1.60 23 17.56 5.44 18.10 5 18 -0.10 18.09 6 16 -2.09 7 20 17.88 2.12 18 18.10 -0.10 22 18.09 3.91 20 18.48 10 1.52 -3.63 11 15 18.63 12 22 18.27 3.73 13 31 18.64 12.36 14 34 19.88 14.12 15 31 21.29 9.71 16 33 22.26 10.74 23.33 17 28 4.67 18 32 23.80 8.20 5.38 19 30 24.62 4

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Step 2

Forecast formula

Ft+1 = Ft + α (At - Ft)

Assuming the forecast for week 1 is same as actual sales

F2 = F1 + α (A1 – F1) = 17 + 0.1 x 0 = 17

F3 = F2 + α (A2 – F2) = 17 + 0.1 x 4 = 17.4

F4 = F3 + α (A3 – F3) = 17.4 + 0.1 x 1.60 = 17.56

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