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Minitab Technical Support Document

Winters’ Method - Additive Model

Initial Values for Seasonal Indices

1. Run regression using the data values as the Y variable, and a vector of 1 through 24 as the X variable. So for

your data:

Y X

1.00 1

1.00 2

527.00 3

819.45 4

719.04 5

1498.47 6

788.42 7

501.08 8

307.90 9

20.30 10

1.00 11

1.00 12

83.00 13

668.21 14

1121.28 15

1386.84 16

1031.18 17

988.60 18

1380.30 19

1005.97 20

233.69 21

211.87 22

2.00 23

2.40 24

The residuals from this regression model will be needed in the next step.

2. Run regression using the residuals as the Y variable, and 12 indicator variables (z.1 through z.12) as the X

variables. Fit the regression model without an intercept (constant) term. So for your data:

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Minitab Technical Support Document

Winters’ Method - Additive Model

Initial Values for Seasonal Indices

Residuals z.1 z.2 z.3 z.4 z.5 z.6 z.7 z.8 z.9 z.10 z.11 z.12

-508.261 1 0 0 0 0 0 0 0 0 0 0 0

-512.170 0 1 0 0 0 0 0 0 0 0 0 0

9.926 0 0 1 0 0 0 0 0 0 0 0 0

298.460 0 0 0 1 0 0 0 0 0 0 0 0

194.145 0 0 0 0 1 0 0 0 0 0 0 0

969.667 0 0 0 0 0 1 0 0 0 0 0 0

255.705 0 0 0 0 0 0 1 0 0 0 0 0

-35.538 0 0 0 0 0 0 0 1 0 0 0 0

-232.625 0 0 0 0 0 0 0 0 1 0 0 0

-524.137 0 0 0 0 0 0 0 0 0 1 0 0

-547.346 0 0 0 0 0 0 0 0 0 0 1 0

-551.254 0 0 0 0 0 0 0 0 0 0 0 1

-473.161 1 0 0 0 0 0 0 0 0 0 0 0

108.141 0 1 0 0 0 0 0 0 0 0 0 0

557.303 0 0 1 0 0 0 0 0 0 0 0 0

818.952 0 0 0 1 0 0 0 0 0 0 0 0

459.378 0 0 0 0 1 0 0 0 0 0 0 0

412.890 0 0 0 0 0 1 0 0 0 0 0 0

800.684 0 0 0 0 0 0 1 0 0 0 0 0

422.451 0 0 0 0 0 0 0 1 0 0 0 0

-353.739 0 0 0 0 0 0 0 0 1 0 0 0

-379.468 0 0 0 0 0 0 0 0 0 1 0 0

-593.247 0 0 0 0 0 0 0 0 0 0 1 0

The coefficients from this regression model are the initial values for the Seasonal Indices. The coefficients are:

Period COEF1

1 -490.711

2 -202.014

3 283.615

4 558.706

5 326.762

6 691.278

7 528.195

8 193.456

9 -293.182

10 -451.803

11 -570.297

12 -574.005

Note: The indicator variables z.1 through z.12 indicate which month of the period that each data point belongs

to. For example, the variable z.1 is equal to1 for the first month of the period, and it is equal to 0 otherwise; z.2

is equal to1 for the second month of the period, and it is equal to 0 otherwise; etc.