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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 25 Apr 2016 22:40:37 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/25/t1461620596k191esazmb1e1in.htm/, Retrieved Mon, 06 May 2024 06:30:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294806, Retrieved Mon, 06 May 2024 06:30:25 +0000

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Estimated Impact

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

-     [Classical Decomposition] [Consumptieprijsin...] [2016-04-25 20:59:45] [e6773be784e85f51fb44487d8478f111]
- RMP     [Exponential Smoothing] [Consumptieprijsin...] [2016-04-25 21:40:37] [268d33ec1c95cc32f8abd6e0112b4a36] [Current]

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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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294806&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294806&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294806&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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.912480497339331
beta	0
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.912480497339331 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294806&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]0.912480497339331[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294806&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294806&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	0.912480497339331
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	98.82	98.62	0.199999999999989
4	99.39	98.7524960994679	0.637503900532138
5	99.33	99.2842059756812	0.0457940243187949
6	99.22	99.2759921297668	-0.0559921297667927
7	99.05	99.1749004033501	-0.124900403350111
8	98.83	99.0109312211833	-0.180931221183315
9	98.84	98.7958350104937	0.0441649895062568
10	98.89	98.7861347020834	0.103865297916599
11	98.8	98.8309097607826	-0.0309097607826487
12	99.4	98.7527052068911	0.647294793108941
13	98.89	99.2933490816323	-0.403349081632285
14	98.85	98.8753009110231	-0.0253009110231091
15	98.69	98.8022143231496	-0.112214323149601
16	98.48	98.6498209417535	-0.169820941753457
17	98.39	98.4448626443636	-0.054862644363638
18	98.35	98.3448015513494	0.00519844865063135
19	98.26	98.2995450343595	-0.0395450343594774
20	98.06	98.2134609617399	-0.153460961739853
21	98.14	98.0234308270493	0.11656917295069
22	98.17	98.0797979239578	0.0902020760422033
23	98.41	98.1121055591658	0.29789444083417
24	98.64	98.3339284266928	0.306071573307179
25	99.25	98.5632127681256	0.686787231874419
26	99.61	99.1398927230326	0.470107276967354
27	100.28	99.5188564449227	0.761143555077339
28	100.31	100.163385094606	0.146614905393733
29	100.55	100.247168336397	0.302831663602703
30	100.45	100.473496323412	-0.0234963234115924
31	100.78	100.402056386539	0.377943613460658
32	100.68	100.696922562916	-0.016922562916136
33	101.69	100.63148105429	1.05851894570982
34	98.09	101.547358948315	-3.45735894831458
35	99.13	98.3425863356759	0.787413664324077
36	99.18	99.0110859477101	0.168914052289864
37	96.22	99.1152167261512	-2.8952167261512
38	96.11	96.4233879279676	-0.313387927967611
39	96	96.0874275555956	-0.0874275555955819
40	95.96	95.9576516161846	0.00234838381541635
41	97.95	95.9097944706164	2.04020552938358
42	98.43	97.7214422267428	0.708557773257198
43	98.32	98.3179873760782	0.00201262392180013
44	97.45	98.2698238561553	-0.819823856155324
45	96.42	97.4717505761601	-1.05175057616006
46	95.36	96.4620486873486	-1.1020486873486
47	95.1	95.4064507530246	-0.306450753024606
48	95.54	95.0768204174947	0.463179582505319
49	94.07	95.4494627532966	-1.37946275329658
50	93.48	94.1407298941074	-0.660729894107433
51	92.86	93.4878267517253	-0.627826751725323
52	90.98	92.8649470850681	-1.88494708506806
53	91.45	91.0949696314268	0.355030368573154
54	91.16	91.3689279187131	-0.208927918713059
55	90.71	91.1282852675377	-0.418285267537698
56	90.31	90.6966081185852	-0.386608118585187
57	89.78	90.2938357502632	-0.513835750263169
58	91.02	89.7749706493123	1.24502935068769
59	90.77	90.8610356504299	-0.0910356504298733
60	90.69	90.72796739485	-0.0379673948500141

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 98.82 & 98.62 & 0.199999999999989 \tabularnewline
4 & 99.39 & 98.7524960994679 & 0.637503900532138 \tabularnewline
5 & 99.33 & 99.2842059756812 & 0.0457940243187949 \tabularnewline
6 & 99.22 & 99.2759921297668 & -0.0559921297667927 \tabularnewline
7 & 99.05 & 99.1749004033501 & -0.124900403350111 \tabularnewline
8 & 98.83 & 99.0109312211833 & -0.180931221183315 \tabularnewline
9 & 98.84 & 98.7958350104937 & 0.0441649895062568 \tabularnewline
10 & 98.89 & 98.7861347020834 & 0.103865297916599 \tabularnewline
11 & 98.8 & 98.8309097607826 & -0.0309097607826487 \tabularnewline
12 & 99.4 & 98.7527052068911 & 0.647294793108941 \tabularnewline
13 & 98.89 & 99.2933490816323 & -0.403349081632285 \tabularnewline
14 & 98.85 & 98.8753009110231 & -0.0253009110231091 \tabularnewline
15 & 98.69 & 98.8022143231496 & -0.112214323149601 \tabularnewline
16 & 98.48 & 98.6498209417535 & -0.169820941753457 \tabularnewline
17 & 98.39 & 98.4448626443636 & -0.054862644363638 \tabularnewline
18 & 98.35 & 98.3448015513494 & 0.00519844865063135 \tabularnewline
19 & 98.26 & 98.2995450343595 & -0.0395450343594774 \tabularnewline
20 & 98.06 & 98.2134609617399 & -0.153460961739853 \tabularnewline
21 & 98.14 & 98.0234308270493 & 0.11656917295069 \tabularnewline
22 & 98.17 & 98.0797979239578 & 0.0902020760422033 \tabularnewline
23 & 98.41 & 98.1121055591658 & 0.29789444083417 \tabularnewline
24 & 98.64 & 98.3339284266928 & 0.306071573307179 \tabularnewline
25 & 99.25 & 98.5632127681256 & 0.686787231874419 \tabularnewline
26 & 99.61 & 99.1398927230326 & 0.470107276967354 \tabularnewline
27 & 100.28 & 99.5188564449227 & 0.761143555077339 \tabularnewline
28 & 100.31 & 100.163385094606 & 0.146614905393733 \tabularnewline
29 & 100.55 & 100.247168336397 & 0.302831663602703 \tabularnewline
30 & 100.45 & 100.473496323412 & -0.0234963234115924 \tabularnewline
31 & 100.78 & 100.402056386539 & 0.377943613460658 \tabularnewline
32 & 100.68 & 100.696922562916 & -0.016922562916136 \tabularnewline
33 & 101.69 & 100.63148105429 & 1.05851894570982 \tabularnewline
34 & 98.09 & 101.547358948315 & -3.45735894831458 \tabularnewline
35 & 99.13 & 98.3425863356759 & 0.787413664324077 \tabularnewline
36 & 99.18 & 99.0110859477101 & 0.168914052289864 \tabularnewline
37 & 96.22 & 99.1152167261512 & -2.8952167261512 \tabularnewline
38 & 96.11 & 96.4233879279676 & -0.313387927967611 \tabularnewline
39 & 96 & 96.0874275555956 & -0.0874275555955819 \tabularnewline
40 & 95.96 & 95.9576516161846 & 0.00234838381541635 \tabularnewline
41 & 97.95 & 95.9097944706164 & 2.04020552938358 \tabularnewline
42 & 98.43 & 97.7214422267428 & 0.708557773257198 \tabularnewline
43 & 98.32 & 98.3179873760782 & 0.00201262392180013 \tabularnewline
44 & 97.45 & 98.2698238561553 & -0.819823856155324 \tabularnewline
45 & 96.42 & 97.4717505761601 & -1.05175057616006 \tabularnewline
46 & 95.36 & 96.4620486873486 & -1.1020486873486 \tabularnewline
47 & 95.1 & 95.4064507530246 & -0.306450753024606 \tabularnewline
48 & 95.54 & 95.0768204174947 & 0.463179582505319 \tabularnewline
49 & 94.07 & 95.4494627532966 & -1.37946275329658 \tabularnewline
50 & 93.48 & 94.1407298941074 & -0.660729894107433 \tabularnewline
51 & 92.86 & 93.4878267517253 & -0.627826751725323 \tabularnewline
52 & 90.98 & 92.8649470850681 & -1.88494708506806 \tabularnewline
53 & 91.45 & 91.0949696314268 & 0.355030368573154 \tabularnewline
54 & 91.16 & 91.3689279187131 & -0.208927918713059 \tabularnewline
55 & 90.71 & 91.1282852675377 & -0.418285267537698 \tabularnewline
56 & 90.31 & 90.6966081185852 & -0.386608118585187 \tabularnewline
57 & 89.78 & 90.2938357502632 & -0.513835750263169 \tabularnewline
58 & 91.02 & 89.7749706493123 & 1.24502935068769 \tabularnewline
59 & 90.77 & 90.8610356504299 & -0.0910356504298733 \tabularnewline
60 & 90.69 & 90.72796739485 & -0.0379673948500141 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294806&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]98.82[/C][C]98.62[/C][C]0.199999999999989[/C][/ROW]
[ROW][C]4[/C][C]99.39[/C][C]98.7524960994679[/C][C]0.637503900532138[/C][/ROW]
[ROW][C]5[/C][C]99.33[/C][C]99.2842059756812[/C][C]0.0457940243187949[/C][/ROW]
[ROW][C]6[/C][C]99.22[/C][C]99.2759921297668[/C][C]-0.0559921297667927[/C][/ROW]
[ROW][C]7[/C][C]99.05[/C][C]99.1749004033501[/C][C]-0.124900403350111[/C][/ROW]
[ROW][C]8[/C][C]98.83[/C][C]99.0109312211833[/C][C]-0.180931221183315[/C][/ROW]
[ROW][C]9[/C][C]98.84[/C][C]98.7958350104937[/C][C]0.0441649895062568[/C][/ROW]
[ROW][C]10[/C][C]98.89[/C][C]98.7861347020834[/C][C]0.103865297916599[/C][/ROW]
[ROW][C]11[/C][C]98.8[/C][C]98.8309097607826[/C][C]-0.0309097607826487[/C][/ROW]
[ROW][C]12[/C][C]99.4[/C][C]98.7527052068911[/C][C]0.647294793108941[/C][/ROW]
[ROW][C]13[/C][C]98.89[/C][C]99.2933490816323[/C][C]-0.403349081632285[/C][/ROW]
[ROW][C]14[/C][C]98.85[/C][C]98.8753009110231[/C][C]-0.0253009110231091[/C][/ROW]
[ROW][C]15[/C][C]98.69[/C][C]98.8022143231496[/C][C]-0.112214323149601[/C][/ROW]
[ROW][C]16[/C][C]98.48[/C][C]98.6498209417535[/C][C]-0.169820941753457[/C][/ROW]
[ROW][C]17[/C][C]98.39[/C][C]98.4448626443636[/C][C]-0.054862644363638[/C][/ROW]
[ROW][C]18[/C][C]98.35[/C][C]98.3448015513494[/C][C]0.00519844865063135[/C][/ROW]
[ROW][C]19[/C][C]98.26[/C][C]98.2995450343595[/C][C]-0.0395450343594774[/C][/ROW]
[ROW][C]20[/C][C]98.06[/C][C]98.2134609617399[/C][C]-0.153460961739853[/C][/ROW]
[ROW][C]21[/C][C]98.14[/C][C]98.0234308270493[/C][C]0.11656917295069[/C][/ROW]
[ROW][C]22[/C][C]98.17[/C][C]98.0797979239578[/C][C]0.0902020760422033[/C][/ROW]
[ROW][C]23[/C][C]98.41[/C][C]98.1121055591658[/C][C]0.29789444083417[/C][/ROW]
[ROW][C]24[/C][C]98.64[/C][C]98.3339284266928[/C][C]0.306071573307179[/C][/ROW]
[ROW][C]25[/C][C]99.25[/C][C]98.5632127681256[/C][C]0.686787231874419[/C][/ROW]
[ROW][C]26[/C][C]99.61[/C][C]99.1398927230326[/C][C]0.470107276967354[/C][/ROW]
[ROW][C]27[/C][C]100.28[/C][C]99.5188564449227[/C][C]0.761143555077339[/C][/ROW]
[ROW][C]28[/C][C]100.31[/C][C]100.163385094606[/C][C]0.146614905393733[/C][/ROW]
[ROW][C]29[/C][C]100.55[/C][C]100.247168336397[/C][C]0.302831663602703[/C][/ROW]
[ROW][C]30[/C][C]100.45[/C][C]100.473496323412[/C][C]-0.0234963234115924[/C][/ROW]
[ROW][C]31[/C][C]100.78[/C][C]100.402056386539[/C][C]0.377943613460658[/C][/ROW]
[ROW][C]32[/C][C]100.68[/C][C]100.696922562916[/C][C]-0.016922562916136[/C][/ROW]
[ROW][C]33[/C][C]101.69[/C][C]100.63148105429[/C][C]1.05851894570982[/C][/ROW]
[ROW][C]34[/C][C]98.09[/C][C]101.547358948315[/C][C]-3.45735894831458[/C][/ROW]
[ROW][C]35[/C][C]99.13[/C][C]98.3425863356759[/C][C]0.787413664324077[/C][/ROW]
[ROW][C]36[/C][C]99.18[/C][C]99.0110859477101[/C][C]0.168914052289864[/C][/ROW]
[ROW][C]37[/C][C]96.22[/C][C]99.1152167261512[/C][C]-2.8952167261512[/C][/ROW]
[ROW][C]38[/C][C]96.11[/C][C]96.4233879279676[/C][C]-0.313387927967611[/C][/ROW]
[ROW][C]39[/C][C]96[/C][C]96.0874275555956[/C][C]-0.0874275555955819[/C][/ROW]
[ROW][C]40[/C][C]95.96[/C][C]95.9576516161846[/C][C]0.00234838381541635[/C][/ROW]
[ROW][C]41[/C][C]97.95[/C][C]95.9097944706164[/C][C]2.04020552938358[/C][/ROW]
[ROW][C]42[/C][C]98.43[/C][C]97.7214422267428[/C][C]0.708557773257198[/C][/ROW]
[ROW][C]43[/C][C]98.32[/C][C]98.3179873760782[/C][C]0.00201262392180013[/C][/ROW]
[ROW][C]44[/C][C]97.45[/C][C]98.2698238561553[/C][C]-0.819823856155324[/C][/ROW]
[ROW][C]45[/C][C]96.42[/C][C]97.4717505761601[/C][C]-1.05175057616006[/C][/ROW]
[ROW][C]46[/C][C]95.36[/C][C]96.4620486873486[/C][C]-1.1020486873486[/C][/ROW]
[ROW][C]47[/C][C]95.1[/C][C]95.4064507530246[/C][C]-0.306450753024606[/C][/ROW]
[ROW][C]48[/C][C]95.54[/C][C]95.0768204174947[/C][C]0.463179582505319[/C][/ROW]
[ROW][C]49[/C][C]94.07[/C][C]95.4494627532966[/C][C]-1.37946275329658[/C][/ROW]
[ROW][C]50[/C][C]93.48[/C][C]94.1407298941074[/C][C]-0.660729894107433[/C][/ROW]
[ROW][C]51[/C][C]92.86[/C][C]93.4878267517253[/C][C]-0.627826751725323[/C][/ROW]
[ROW][C]52[/C][C]90.98[/C][C]92.8649470850681[/C][C]-1.88494708506806[/C][/ROW]
[ROW][C]53[/C][C]91.45[/C][C]91.0949696314268[/C][C]0.355030368573154[/C][/ROW]
[ROW][C]54[/C][C]91.16[/C][C]91.3689279187131[/C][C]-0.208927918713059[/C][/ROW]
[ROW][C]55[/C][C]90.71[/C][C]91.1282852675377[/C][C]-0.418285267537698[/C][/ROW]
[ROW][C]56[/C][C]90.31[/C][C]90.6966081185852[/C][C]-0.386608118585187[/C][/ROW]
[ROW][C]57[/C][C]89.78[/C][C]90.2938357502632[/C][C]-0.513835750263169[/C][/ROW]
[ROW][C]58[/C][C]91.02[/C][C]89.7749706493123[/C][C]1.24502935068769[/C][/ROW]
[ROW][C]59[/C][C]90.77[/C][C]90.8610356504299[/C][C]-0.0910356504298733[/C][/ROW]
[ROW][C]60[/C][C]90.69[/C][C]90.72796739485[/C][C]-0.0379673948500141[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294806&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294806&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	98.82	98.62	0.199999999999989
4	99.39	98.7524960994679	0.637503900532138
5	99.33	99.2842059756812	0.0457940243187949
6	99.22	99.2759921297668	-0.0559921297667927
7	99.05	99.1749004033501	-0.124900403350111
8	98.83	99.0109312211833	-0.180931221183315
9	98.84	98.7958350104937	0.0441649895062568
10	98.89	98.7861347020834	0.103865297916599
11	98.8	98.8309097607826	-0.0309097607826487
12	99.4	98.7527052068911	0.647294793108941
13	98.89	99.2933490816323	-0.403349081632285
14	98.85	98.8753009110231	-0.0253009110231091
15	98.69	98.8022143231496	-0.112214323149601
16	98.48	98.6498209417535	-0.169820941753457
17	98.39	98.4448626443636	-0.054862644363638
18	98.35	98.3448015513494	0.00519844865063135
19	98.26	98.2995450343595	-0.0395450343594774
20	98.06	98.2134609617399	-0.153460961739853
21	98.14	98.0234308270493	0.11656917295069
22	98.17	98.0797979239578	0.0902020760422033
23	98.41	98.1121055591658	0.29789444083417
24	98.64	98.3339284266928	0.306071573307179
25	99.25	98.5632127681256	0.686787231874419
26	99.61	99.1398927230326	0.470107276967354
27	100.28	99.5188564449227	0.761143555077339
28	100.31	100.163385094606	0.146614905393733
29	100.55	100.247168336397	0.302831663602703
30	100.45	100.473496323412	-0.0234963234115924
31	100.78	100.402056386539	0.377943613460658
32	100.68	100.696922562916	-0.016922562916136
33	101.69	100.63148105429	1.05851894570982
34	98.09	101.547358948315	-3.45735894831458
35	99.13	98.3425863356759	0.787413664324077
36	99.18	99.0110859477101	0.168914052289864
37	96.22	99.1152167261512	-2.8952167261512
38	96.11	96.4233879279676	-0.313387927967611
39	96	96.0874275555956	-0.0874275555955819
40	95.96	95.9576516161846	0.00234838381541635
41	97.95	95.9097944706164	2.04020552938358
42	98.43	97.7214422267428	0.708557773257198
43	98.32	98.3179873760782	0.00201262392180013
44	97.45	98.2698238561553	-0.819823856155324
45	96.42	97.4717505761601	-1.05175057616006
46	95.36	96.4620486873486	-1.1020486873486
47	95.1	95.4064507530246	-0.306450753024606
48	95.54	95.0768204174947	0.463179582505319
49	94.07	95.4494627532966	-1.37946275329658
50	93.48	94.1407298941074	-0.660729894107433
51	92.86	93.4878267517253	-0.627826751725323
52	90.98	92.8649470850681	-1.88494708506806
53	91.45	91.0949696314268	0.355030368573154
54	91.16	91.3689279187131	-0.208927918713059
55	90.71	91.1282852675377	-0.418285267537698
56	90.31	90.6966081185852	-0.386608118585187
57	89.78	90.2938357502632	-0.513835750263169
58	91.02	89.7749706493123	1.24502935068769
59	90.77	90.8610356504299	-0.0910356504298733
60	90.69	90.72796739485	-0.0379673948500141

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	90.6433228875146	88.9780954835408	92.3085502914883
62	90.5933228875146	88.339032608947	92.8476131660822
63	90.5433228875146	87.8247447640935	93.2619010109357
64	90.4933228875146	87.3789193545338	93.6077264204954
65	90.4433228875146	86.9780160151954	93.9086297598338
66	90.3933228875146	86.6095160646916	94.1771297103376
67	90.3433228875146	86.265819187266	94.4208265877632
68	90.2933228875146	85.9419002720197	94.6447455030095
69	90.2433228875146	85.6342317480664	94.8524140269628
70	90.1933228875146	85.3402245488407	95.0464212261885
71	90.1433228875146	85.0579118089548	95.2287339660744
72	90.0933228875146	84.7857577027017	95.4008880723275

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 90.6433228875146 & 88.9780954835408 & 92.3085502914883 \tabularnewline
62 & 90.5933228875146 & 88.339032608947 & 92.8476131660822 \tabularnewline
63 & 90.5433228875146 & 87.8247447640935 & 93.2619010109357 \tabularnewline
64 & 90.4933228875146 & 87.3789193545338 & 93.6077264204954 \tabularnewline
65 & 90.4433228875146 & 86.9780160151954 & 93.9086297598338 \tabularnewline
66 & 90.3933228875146 & 86.6095160646916 & 94.1771297103376 \tabularnewline
67 & 90.3433228875146 & 86.265819187266 & 94.4208265877632 \tabularnewline
68 & 90.2933228875146 & 85.9419002720197 & 94.6447455030095 \tabularnewline
69 & 90.2433228875146 & 85.6342317480664 & 94.8524140269628 \tabularnewline
70 & 90.1933228875146 & 85.3402245488407 & 95.0464212261885 \tabularnewline
71 & 90.1433228875146 & 85.0579118089548 & 95.2287339660744 \tabularnewline
72 & 90.0933228875146 & 84.7857577027017 & 95.4008880723275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294806&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]61[/C][C]90.6433228875146[/C][C]88.9780954835408[/C][C]92.3085502914883[/C][/ROW]
[ROW][C]62[/C][C]90.5933228875146[/C][C]88.339032608947[/C][C]92.8476131660822[/C][/ROW]
[ROW][C]63[/C][C]90.5433228875146[/C][C]87.8247447640935[/C][C]93.2619010109357[/C][/ROW]
[ROW][C]64[/C][C]90.4933228875146[/C][C]87.3789193545338[/C][C]93.6077264204954[/C][/ROW]
[ROW][C]65[/C][C]90.4433228875146[/C][C]86.9780160151954[/C][C]93.9086297598338[/C][/ROW]
[ROW][C]66[/C][C]90.3933228875146[/C][C]86.6095160646916[/C][C]94.1771297103376[/C][/ROW]
[ROW][C]67[/C][C]90.3433228875146[/C][C]86.265819187266[/C][C]94.4208265877632[/C][/ROW]
[ROW][C]68[/C][C]90.2933228875146[/C][C]85.9419002720197[/C][C]94.6447455030095[/C][/ROW]
[ROW][C]69[/C][C]90.2433228875146[/C][C]85.6342317480664[/C][C]94.8524140269628[/C][/ROW]
[ROW][C]70[/C][C]90.1933228875146[/C][C]85.3402245488407[/C][C]95.0464212261885[/C][/ROW]
[ROW][C]71[/C][C]90.1433228875146[/C][C]85.0579118089548[/C][C]95.2287339660744[/C][/ROW]
[ROW][C]72[/C][C]90.0933228875146[/C][C]84.7857577027017[/C][C]95.4008880723275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294806&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294806&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
61	90.6433228875146	88.9780954835408	92.3085502914883
62	90.5933228875146	88.339032608947	92.8476131660822
63	90.5433228875146	87.8247447640935	93.2619010109357
64	90.4933228875146	87.3789193545338	93.6077264204954
65	90.4433228875146	86.9780160151954	93.9086297598338
66	90.3933228875146	86.6095160646916	94.1771297103376
67	90.3433228875146	86.265819187266	94.4208265877632
68	90.2933228875146	85.9419002720197	94.6447455030095
69	90.2433228875146	85.6342317480664	94.8524140269628
70	90.1933228875146	85.3402245488407	95.0464212261885
71	90.1433228875146	85.0579118089548	95.2287339660744
72	90.0933228875146	84.7857577027017	95.4008880723275

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 ; par2 = Double ; par3 = additive ;

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