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Author

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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 30 Nov 2010 14:09:25 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/30/t1291126053z9t2obeeyphb9hq.htm/, Retrieved Sun, 28 Apr 2024 17:03:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103485, Retrieved Sun, 28 Apr 2024 17:03:58 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

318

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Explorative Data Analysis] [Monthly US soldie...] [2010-11-02 12:07:39] [b98453cac15ba1066b407e146608df68]
- RMP     [Exponential Smoothing] [Soldiers] [2010-11-30 14:09:25] [d76b387543b13b5e3afd8ff9e5fdc89f] [Current]
- RMPD      [Recursive Partitioning (Regression Trees)] [BEL20-RP1(no cat)] [2010-12-22 17:58:31] [d672a41e0af7ff107c03f1d65e47fd32] 
-   P         [Recursive Partitioning (Regression Trees)] [BEL20-RP2(cat)] [2010-12-22 18:45:42] [d672a41e0af7ff107c03f1d65e47fd32] 
-   P           [Recursive Partitioning (Regression Trees)] [BEL20-RP(crossval...] [2010-12-25 19:22:30] [d672a41e0af7ff107c03f1d65e47fd32] 
- R P       [Exponential Smoothing] [Us soldiers] [2011-11-30 11:28:26] [27e29806e0b1d1351a97bc4ee4116294] 
- R P       [Exponential Smoothing] [Paper: ES] [2011-12-18 09:16:50] [54b1f171ce7a12209ffa11b565e1dcf5] 
- R P       [Exponential Smoothing] [Paper: ES] [2011-12-18 10:23:16] [54b1f171ce7a12209ffa11b565e1dcf5] 
- R P       [Exponential Smoothing] [deel 4 exp smooth...] [2012-12-09 11:01:23] [885d0a915dae889a27a534b235a2244f] 
- R P       [Exponential Smoothing] [paper single expo...] [2012-12-11 11:13:51] [1edfe4f7de973a74350ac08c1294a22c] 
-   P         [Exponential Smoothing] [paper double expo...] [2012-12-11 11:30:08] [1edfe4f7de973a74350ac08c1294a22c] 
-   P         [Exponential Smoothing] [paper triple expo...] [2012-12-11 11:39:36] [1edfe4f7de973a74350ac08c1294a22c] 
- RMP       [Exponential Smoothing] [] [2012-12-18 19:57:55] [147786ccb76fa00e429d4b9f5f28b291] 
- RMP       [Exponential Smoothing] [] [2014-11-19 14:37:40] [d253a55552bf9917a397def3be261e30] 
-  M          [Exponential Smoothing] [] [2014-11-19 14:38:11] [d253a55552bf9917a397def3be261e30] 
- RMP       [Exponential Smoothing] [] [2014-11-19 16:27:06] [bcf5edf18529a33bd1494456d2c6cb9a] 
- RMP       [Exponential Smoothing] [WS8 ES] [2014-11-19 18:17:52] [46c7ebd23dbdec306a09830d8b7528e7] 
- RM        [Exponential Smoothing] [ws 8 t] [2014-11-20 21:14:51] [be945163e51ed825733188af308451be] 
- RMP       [Exponential Smoothing] [lhlk] [2014-11-20 22:03:18] [e596eb22b7565c1d1947422243452583] 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103485&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103485&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103485&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.458869668359626
beta	0.0711214003445339
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.458869668359626 \tabularnewline
beta & 0.0711214003445339 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103485&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.458869668359626[/C][/ROW]
[ROW][C]beta[/C][C]0.0711214003445339[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103485&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103485&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.458869668359626
beta	0.0711214003445339
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	47	23	24
4	35	27.7961229219759	7.20387707802414
5	30	25.1201162836198	4.87988371638025
6	43	21.5369567997076	21.4630432002924
7	82	26.2637623544902	55.7362376455098
8	40	48.5364746637534	-8.53647466375342
9	47	41.0377970700929	5.96220292990706
10	19	40.3867020513055	-21.3867020513055
11	52	26.4880593558425	25.5119406441575
12	136	34.9423750303279	101.057624969672
13	80	81.3603752266012	-1.36037522660121
14	42	80.7374651764547	-38.7374651764547
15	54	61.6991275175825	-7.6991275175825
16	66	56.6520770494322	9.3479229505678
17	81	59.7324746798525	21.2675253201475
18	63	68.9764916278734	-5.97649162787336
19	137	65.5240100402184	71.4759899597816
20	72	99.9447743311122	-27.9447743311122
21	107	87.8323751036235	19.1676248963765
22	58	97.9639710141695	-39.9639710141695
23	36	79.6576288063808	-43.6576288063808
24	52	58.2315925624452	-6.23159256244519
25	79	53.7758583091664	25.2241416908336
26	77	64.5774077011363	12.4225922988637
27	54	69.9101313010682	-15.9101313010682
28	84	61.7225930704797	22.2774069295203
29	48	71.7851911187162	-23.7851911187162
30	96	59.9348195806636	36.0651804193364
31	83	76.724971696032	6.27502830396799
32	66	80.0501149835696	-14.0501149835696
33	61	73.5901346387314	-12.5901346387314
34	53	67.3892102383725	-14.3892102383725
35	30	59.8931462142082	-29.8931462142082
36	74	44.3072198506079	29.6927801493921
37	69	57.0325050989402	11.9674949010598
38	59	62.0147592058215	-3.01475920582153
39	42	60.0237233058568	-18.0237233058568
40	65	50.5573166450362	14.4426833549638
41	70	56.4601027609435	13.5398972390565
42	100	62.3905083964867	37.6094916035133
43	63	80.5931236258233	-17.5931236258233
44	105	72.8907735462262	32.1092264537738
45	82	89.0432235276487	-7.04322352764866
46	81	86.9999429774815	-5.99994297748148
47	75	85.2395813679951	-10.2395813679951
48	102	81.1996049158271	20.8003950841729
49	121	92.081762488406	28.9182375115939
50	98	107.632711515864	-9.63271151586369
51	76	105.179431440454	-29.1794314404538
52	77	92.8044705010255	-15.8044705010255
53	63	86.0510873918158	-23.0510873918158
54	37	75.22016890505	-38.22016890505
55	35	56.1812864741518	-21.1812864741518
56	23	44.2697694860844	-21.2697694860844
57	40	31.6235017570103	8.37649824298966
58	29	32.8543778868524	-3.85437788685239
59	37	28.3470865733748	8.65291342662523
60	51	29.8614036298067	21.1385963701933
61	20	37.7948895543533	-17.7948895543533
62	28	27.282235415999	0.717764584001024
63	13	25.2879013151935	-12.2879013151935
64	22	16.9246403858033	5.07535961419669
65	25	16.6944899028475	8.30551009715252
66	13	18.2176115884078	-5.21761158840782
67	16	13.3651037911309	2.63489620886909
68	13	12.2018646749922	0.798135325007793
69	16	10.2218392094178	5.77816079058217
70	17	10.7155692748114	6.28443072518861
71	9	11.6467065032089	-2.64670650320886
72	17	8.39323928681646	8.60676071318354
73	25	10.5845323779945	14.4154676220055
74	14	15.9117202036859	-1.91172020368588
75	8	13.6844669109560	-5.68446691095602
76	7	9.54049943294032	-2.54049943294032
77	10	6.7562929180657	3.2437070819343
78	7	6.73214317967641	0.267856820323587
79	10	5.35120764742861	4.64879235257139
80	3	6.13226599610745	-3.13226599610745

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 47 & 23 & 24 \tabularnewline
4 & 35 & 27.7961229219759 & 7.20387707802414 \tabularnewline
5 & 30 & 25.1201162836198 & 4.87988371638025 \tabularnewline
6 & 43 & 21.5369567997076 & 21.4630432002924 \tabularnewline
7 & 82 & 26.2637623544902 & 55.7362376455098 \tabularnewline
8 & 40 & 48.5364746637534 & -8.53647466375342 \tabularnewline
9 & 47 & 41.0377970700929 & 5.96220292990706 \tabularnewline
10 & 19 & 40.3867020513055 & -21.3867020513055 \tabularnewline
11 & 52 & 26.4880593558425 & 25.5119406441575 \tabularnewline
12 & 136 & 34.9423750303279 & 101.057624969672 \tabularnewline
13 & 80 & 81.3603752266012 & -1.36037522660121 \tabularnewline
14 & 42 & 80.7374651764547 & -38.7374651764547 \tabularnewline
15 & 54 & 61.6991275175825 & -7.6991275175825 \tabularnewline
16 & 66 & 56.6520770494322 & 9.3479229505678 \tabularnewline
17 & 81 & 59.7324746798525 & 21.2675253201475 \tabularnewline
18 & 63 & 68.9764916278734 & -5.97649162787336 \tabularnewline
19 & 137 & 65.5240100402184 & 71.4759899597816 \tabularnewline
20 & 72 & 99.9447743311122 & -27.9447743311122 \tabularnewline
21 & 107 & 87.8323751036235 & 19.1676248963765 \tabularnewline
22 & 58 & 97.9639710141695 & -39.9639710141695 \tabularnewline
23 & 36 & 79.6576288063808 & -43.6576288063808 \tabularnewline
24 & 52 & 58.2315925624452 & -6.23159256244519 \tabularnewline
25 & 79 & 53.7758583091664 & 25.2241416908336 \tabularnewline
26 & 77 & 64.5774077011363 & 12.4225922988637 \tabularnewline
27 & 54 & 69.9101313010682 & -15.9101313010682 \tabularnewline
28 & 84 & 61.7225930704797 & 22.2774069295203 \tabularnewline
29 & 48 & 71.7851911187162 & -23.7851911187162 \tabularnewline
30 & 96 & 59.9348195806636 & 36.0651804193364 \tabularnewline
31 & 83 & 76.724971696032 & 6.27502830396799 \tabularnewline
32 & 66 & 80.0501149835696 & -14.0501149835696 \tabularnewline
33 & 61 & 73.5901346387314 & -12.5901346387314 \tabularnewline
34 & 53 & 67.3892102383725 & -14.3892102383725 \tabularnewline
35 & 30 & 59.8931462142082 & -29.8931462142082 \tabularnewline
36 & 74 & 44.3072198506079 & 29.6927801493921 \tabularnewline
37 & 69 & 57.0325050989402 & 11.9674949010598 \tabularnewline
38 & 59 & 62.0147592058215 & -3.01475920582153 \tabularnewline
39 & 42 & 60.0237233058568 & -18.0237233058568 \tabularnewline
40 & 65 & 50.5573166450362 & 14.4426833549638 \tabularnewline
41 & 70 & 56.4601027609435 & 13.5398972390565 \tabularnewline
42 & 100 & 62.3905083964867 & 37.6094916035133 \tabularnewline
43 & 63 & 80.5931236258233 & -17.5931236258233 \tabularnewline
44 & 105 & 72.8907735462262 & 32.1092264537738 \tabularnewline
45 & 82 & 89.0432235276487 & -7.04322352764866 \tabularnewline
46 & 81 & 86.9999429774815 & -5.99994297748148 \tabularnewline
47 & 75 & 85.2395813679951 & -10.2395813679951 \tabularnewline
48 & 102 & 81.1996049158271 & 20.8003950841729 \tabularnewline
49 & 121 & 92.081762488406 & 28.9182375115939 \tabularnewline
50 & 98 & 107.632711515864 & -9.63271151586369 \tabularnewline
51 & 76 & 105.179431440454 & -29.1794314404538 \tabularnewline
52 & 77 & 92.8044705010255 & -15.8044705010255 \tabularnewline
53 & 63 & 86.0510873918158 & -23.0510873918158 \tabularnewline
54 & 37 & 75.22016890505 & -38.22016890505 \tabularnewline
55 & 35 & 56.1812864741518 & -21.1812864741518 \tabularnewline
56 & 23 & 44.2697694860844 & -21.2697694860844 \tabularnewline
57 & 40 & 31.6235017570103 & 8.37649824298966 \tabularnewline
58 & 29 & 32.8543778868524 & -3.85437788685239 \tabularnewline
59 & 37 & 28.3470865733748 & 8.65291342662523 \tabularnewline
60 & 51 & 29.8614036298067 & 21.1385963701933 \tabularnewline
61 & 20 & 37.7948895543533 & -17.7948895543533 \tabularnewline
62 & 28 & 27.282235415999 & 0.717764584001024 \tabularnewline
63 & 13 & 25.2879013151935 & -12.2879013151935 \tabularnewline
64 & 22 & 16.9246403858033 & 5.07535961419669 \tabularnewline
65 & 25 & 16.6944899028475 & 8.30551009715252 \tabularnewline
66 & 13 & 18.2176115884078 & -5.21761158840782 \tabularnewline
67 & 16 & 13.3651037911309 & 2.63489620886909 \tabularnewline
68 & 13 & 12.2018646749922 & 0.798135325007793 \tabularnewline
69 & 16 & 10.2218392094178 & 5.77816079058217 \tabularnewline
70 & 17 & 10.7155692748114 & 6.28443072518861 \tabularnewline
71 & 9 & 11.6467065032089 & -2.64670650320886 \tabularnewline
72 & 17 & 8.39323928681646 & 8.60676071318354 \tabularnewline
73 & 25 & 10.5845323779945 & 14.4154676220055 \tabularnewline
74 & 14 & 15.9117202036859 & -1.91172020368588 \tabularnewline
75 & 8 & 13.6844669109560 & -5.68446691095602 \tabularnewline
76 & 7 & 9.54049943294032 & -2.54049943294032 \tabularnewline
77 & 10 & 6.7562929180657 & 3.2437070819343 \tabularnewline
78 & 7 & 6.73214317967641 & 0.267856820323587 \tabularnewline
79 & 10 & 5.35120764742861 & 4.64879235257139 \tabularnewline
80 & 3 & 6.13226599610745 & -3.13226599610745 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103485&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]47[/C][C]23[/C][C]24[/C][/ROW]
[ROW][C]4[/C][C]35[/C][C]27.7961229219759[/C][C]7.20387707802414[/C][/ROW]
[ROW][C]5[/C][C]30[/C][C]25.1201162836198[/C][C]4.87988371638025[/C][/ROW]
[ROW][C]6[/C][C]43[/C][C]21.5369567997076[/C][C]21.4630432002924[/C][/ROW]
[ROW][C]7[/C][C]82[/C][C]26.2637623544902[/C][C]55.7362376455098[/C][/ROW]
[ROW][C]8[/C][C]40[/C][C]48.5364746637534[/C][C]-8.53647466375342[/C][/ROW]
[ROW][C]9[/C][C]47[/C][C]41.0377970700929[/C][C]5.96220292990706[/C][/ROW]
[ROW][C]10[/C][C]19[/C][C]40.3867020513055[/C][C]-21.3867020513055[/C][/ROW]
[ROW][C]11[/C][C]52[/C][C]26.4880593558425[/C][C]25.5119406441575[/C][/ROW]
[ROW][C]12[/C][C]136[/C][C]34.9423750303279[/C][C]101.057624969672[/C][/ROW]
[ROW][C]13[/C][C]80[/C][C]81.3603752266012[/C][C]-1.36037522660121[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]80.7374651764547[/C][C]-38.7374651764547[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]61.6991275175825[/C][C]-7.6991275175825[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]56.6520770494322[/C][C]9.3479229505678[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]59.7324746798525[/C][C]21.2675253201475[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]68.9764916278734[/C][C]-5.97649162787336[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]65.5240100402184[/C][C]71.4759899597816[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]99.9447743311122[/C][C]-27.9447743311122[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]87.8323751036235[/C][C]19.1676248963765[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]97.9639710141695[/C][C]-39.9639710141695[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]79.6576288063808[/C][C]-43.6576288063808[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]58.2315925624452[/C][C]-6.23159256244519[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]53.7758583091664[/C][C]25.2241416908336[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]64.5774077011363[/C][C]12.4225922988637[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]69.9101313010682[/C][C]-15.9101313010682[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]61.7225930704797[/C][C]22.2774069295203[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]71.7851911187162[/C][C]-23.7851911187162[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]59.9348195806636[/C][C]36.0651804193364[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]76.724971696032[/C][C]6.27502830396799[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]80.0501149835696[/C][C]-14.0501149835696[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]73.5901346387314[/C][C]-12.5901346387314[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]67.3892102383725[/C][C]-14.3892102383725[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]59.8931462142082[/C][C]-29.8931462142082[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]44.3072198506079[/C][C]29.6927801493921[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]57.0325050989402[/C][C]11.9674949010598[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]62.0147592058215[/C][C]-3.01475920582153[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]60.0237233058568[/C][C]-18.0237233058568[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]50.5573166450362[/C][C]14.4426833549638[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]56.4601027609435[/C][C]13.5398972390565[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]62.3905083964867[/C][C]37.6094916035133[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]80.5931236258233[/C][C]-17.5931236258233[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]72.8907735462262[/C][C]32.1092264537738[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]89.0432235276487[/C][C]-7.04322352764866[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]86.9999429774815[/C][C]-5.99994297748148[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]85.2395813679951[/C][C]-10.2395813679951[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]81.1996049158271[/C][C]20.8003950841729[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]92.081762488406[/C][C]28.9182375115939[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]107.632711515864[/C][C]-9.63271151586369[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]105.179431440454[/C][C]-29.1794314404538[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]92.8044705010255[/C][C]-15.8044705010255[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]86.0510873918158[/C][C]-23.0510873918158[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]75.22016890505[/C][C]-38.22016890505[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]56.1812864741518[/C][C]-21.1812864741518[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]44.2697694860844[/C][C]-21.2697694860844[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]31.6235017570103[/C][C]8.37649824298966[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]32.8543778868524[/C][C]-3.85437788685239[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]28.3470865733748[/C][C]8.65291342662523[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]29.8614036298067[/C][C]21.1385963701933[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]37.7948895543533[/C][C]-17.7948895543533[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]27.282235415999[/C][C]0.717764584001024[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]25.2879013151935[/C][C]-12.2879013151935[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]16.9246403858033[/C][C]5.07535961419669[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]16.6944899028475[/C][C]8.30551009715252[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]18.2176115884078[/C][C]-5.21761158840782[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]13.3651037911309[/C][C]2.63489620886909[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]12.2018646749922[/C][C]0.798135325007793[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]10.2218392094178[/C][C]5.77816079058217[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]10.7155692748114[/C][C]6.28443072518861[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]11.6467065032089[/C][C]-2.64670650320886[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]8.39323928681646[/C][C]8.60676071318354[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]10.5845323779945[/C][C]14.4154676220055[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]15.9117202036859[/C][C]-1.91172020368588[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]13.6844669109560[/C][C]-5.68446691095602[/C][/ROW]
[ROW][C]76[/C][C]7[/C][C]9.54049943294032[/C][C]-2.54049943294032[/C][/ROW]
[ROW][C]77[/C][C]10[/C][C]6.7562929180657[/C][C]3.2437070819343[/C][/ROW]
[ROW][C]78[/C][C]7[/C][C]6.73214317967641[/C][C]0.267856820323587[/C][/ROW]
[ROW][C]79[/C][C]10[/C][C]5.35120764742861[/C][C]4.64879235257139[/C][/ROW]
[ROW][C]80[/C][C]3[/C][C]6.13226599610745[/C][C]-3.13226599610745[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103485&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103485&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	47	23	24
4	35	27.7961229219759	7.20387707802414
5	30	25.1201162836198	4.87988371638025
6	43	21.5369567997076	21.4630432002924
7	82	26.2637623544902	55.7362376455098
8	40	48.5364746637534	-8.53647466375342
9	47	41.0377970700929	5.96220292990706
10	19	40.3867020513055	-21.3867020513055
11	52	26.4880593558425	25.5119406441575
12	136	34.9423750303279	101.057624969672
13	80	81.3603752266012	-1.36037522660121
14	42	80.7374651764547	-38.7374651764547
15	54	61.6991275175825	-7.6991275175825
16	66	56.6520770494322	9.3479229505678
17	81	59.7324746798525	21.2675253201475
18	63	68.9764916278734	-5.97649162787336
19	137	65.5240100402184	71.4759899597816
20	72	99.9447743311122	-27.9447743311122
21	107	87.8323751036235	19.1676248963765
22	58	97.9639710141695	-39.9639710141695
23	36	79.6576288063808	-43.6576288063808
24	52	58.2315925624452	-6.23159256244519
25	79	53.7758583091664	25.2241416908336
26	77	64.5774077011363	12.4225922988637
27	54	69.9101313010682	-15.9101313010682
28	84	61.7225930704797	22.2774069295203
29	48	71.7851911187162	-23.7851911187162
30	96	59.9348195806636	36.0651804193364
31	83	76.724971696032	6.27502830396799
32	66	80.0501149835696	-14.0501149835696
33	61	73.5901346387314	-12.5901346387314
34	53	67.3892102383725	-14.3892102383725
35	30	59.8931462142082	-29.8931462142082
36	74	44.3072198506079	29.6927801493921
37	69	57.0325050989402	11.9674949010598
38	59	62.0147592058215	-3.01475920582153
39	42	60.0237233058568	-18.0237233058568
40	65	50.5573166450362	14.4426833549638
41	70	56.4601027609435	13.5398972390565
42	100	62.3905083964867	37.6094916035133
43	63	80.5931236258233	-17.5931236258233
44	105	72.8907735462262	32.1092264537738
45	82	89.0432235276487	-7.04322352764866
46	81	86.9999429774815	-5.99994297748148
47	75	85.2395813679951	-10.2395813679951
48	102	81.1996049158271	20.8003950841729
49	121	92.081762488406	28.9182375115939
50	98	107.632711515864	-9.63271151586369
51	76	105.179431440454	-29.1794314404538
52	77	92.8044705010255	-15.8044705010255
53	63	86.0510873918158	-23.0510873918158
54	37	75.22016890505	-38.22016890505
55	35	56.1812864741518	-21.1812864741518
56	23	44.2697694860844	-21.2697694860844
57	40	31.6235017570103	8.37649824298966
58	29	32.8543778868524	-3.85437788685239
59	37	28.3470865733748	8.65291342662523
60	51	29.8614036298067	21.1385963701933
61	20	37.7948895543533	-17.7948895543533
62	28	27.282235415999	0.717764584001024
63	13	25.2879013151935	-12.2879013151935
64	22	16.9246403858033	5.07535961419669
65	25	16.6944899028475	8.30551009715252
66	13	18.2176115884078	-5.21761158840782
67	16	13.3651037911309	2.63489620886909
68	13	12.2018646749922	0.798135325007793
69	16	10.2218392094178	5.77816079058217
70	17	10.7155692748114	6.28443072518861
71	9	11.6467065032089	-2.64670650320886
72	17	8.39323928681646	8.60676071318354
73	25	10.5845323779945	14.4154676220055
74	14	15.9117202036859	-1.91172020368588
75	8	13.6844669109560	-5.68446691095602
76	7	9.54049943294032	-2.54049943294032
77	10	6.7562929180657	3.2437070819343
78	7	6.73214317967641	0.267856820323587
79	10	5.35120764742861	4.64879235257139
80	3	6.13226599610745	-3.13226599610745

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
81	3.24060975992207	-43.515313575402	49.9965330952461
82	1.78625538258464	-50.3120403948589	53.8845511600282
83	0.331901005247214	-57.2424823466158	57.9062843571102
84	-1.12245337209021	-64.3087232372839	62.0638164931035
85	-2.57680774942764	-71.5113739157706	66.3577584169154
86	-4.03116212676506	-78.8501136282416	70.7877893747115
87	-5.48551650410249	-86.3240266303458	75.3529936221408
88	-6.93987088143991	-93.9318176680923	80.0520759052125
89	-8.39422525877734	-101.671953087675	84.8835025701201
90	-9.84857963611477	-109.542754868370	89.8455955961403
91	-11.3029340134522	-117.542464090177	94.936596063273
92	-12.7572883907896	-125.669284131773	100.154707350194

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 3.24060975992207 & -43.515313575402 & 49.9965330952461 \tabularnewline
82 & 1.78625538258464 & -50.3120403948589 & 53.8845511600282 \tabularnewline
83 & 0.331901005247214 & -57.2424823466158 & 57.9062843571102 \tabularnewline
84 & -1.12245337209021 & -64.3087232372839 & 62.0638164931035 \tabularnewline
85 & -2.57680774942764 & -71.5113739157706 & 66.3577584169154 \tabularnewline
86 & -4.03116212676506 & -78.8501136282416 & 70.7877893747115 \tabularnewline
87 & -5.48551650410249 & -86.3240266303458 & 75.3529936221408 \tabularnewline
88 & -6.93987088143991 & -93.9318176680923 & 80.0520759052125 \tabularnewline
89 & -8.39422525877734 & -101.671953087675 & 84.8835025701201 \tabularnewline
90 & -9.84857963611477 & -109.542754868370 & 89.8455955961403 \tabularnewline
91 & -11.3029340134522 & -117.542464090177 & 94.936596063273 \tabularnewline
92 & -12.7572883907896 & -125.669284131773 & 100.154707350194 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103485&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]81[/C][C]3.24060975992207[/C][C]-43.515313575402[/C][C]49.9965330952461[/C][/ROW]
[ROW][C]82[/C][C]1.78625538258464[/C][C]-50.3120403948589[/C][C]53.8845511600282[/C][/ROW]
[ROW][C]83[/C][C]0.331901005247214[/C][C]-57.2424823466158[/C][C]57.9062843571102[/C][/ROW]
[ROW][C]84[/C][C]-1.12245337209021[/C][C]-64.3087232372839[/C][C]62.0638164931035[/C][/ROW]
[ROW][C]85[/C][C]-2.57680774942764[/C][C]-71.5113739157706[/C][C]66.3577584169154[/C][/ROW]
[ROW][C]86[/C][C]-4.03116212676506[/C][C]-78.8501136282416[/C][C]70.7877893747115[/C][/ROW]
[ROW][C]87[/C][C]-5.48551650410249[/C][C]-86.3240266303458[/C][C]75.3529936221408[/C][/ROW]
[ROW][C]88[/C][C]-6.93987088143991[/C][C]-93.9318176680923[/C][C]80.0520759052125[/C][/ROW]
[ROW][C]89[/C][C]-8.39422525877734[/C][C]-101.671953087675[/C][C]84.8835025701201[/C][/ROW]
[ROW][C]90[/C][C]-9.84857963611477[/C][C]-109.542754868370[/C][C]89.8455955961403[/C][/ROW]
[ROW][C]91[/C][C]-11.3029340134522[/C][C]-117.542464090177[/C][C]94.936596063273[/C][/ROW]
[ROW][C]92[/C][C]-12.7572883907896[/C][C]-125.669284131773[/C][C]100.154707350194[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103485&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103485&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
81	3.24060975992207	-43.515313575402	49.9965330952461
82	1.78625538258464	-50.3120403948589	53.8845511600282
83	0.331901005247214	-57.2424823466158	57.9062843571102
84	-1.12245337209021	-64.3087232372839	62.0638164931035
85	-2.57680774942764	-71.5113739157706	66.3577584169154
86	-4.03116212676506	-78.8501136282416	70.7877893747115
87	-5.48551650410249	-86.3240266303458	75.3529936221408
88	-6.93987088143991	-93.9318176680923	80.0520759052125
89	-8.39422525877734	-101.671953087675	84.8835025701201
90	-9.84857963611477	-109.542754868370	89.8455955961403
91	-11.3029340134522	-117.542464090177	94.936596063273
92	-12.7572883907896	-125.669284131773	100.154707350194

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code