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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 17 Dec 2013 07:51:44 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/17/t1387284748pfcvf83o6hfzco7.htm/, Retrieved Thu, 18 Apr 2024 22:11:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232406, Retrieved Thu, 18 Apr 2024 22:11:17 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

141

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

-       [Exponential Smoothing] [] [2013-12-17 12:51:44] [7cfa17a50f4a533c9a90677dc09cc88d] [Current]

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Dataseries X:

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1,93
2,02
1,85
1,77
1,81
1,67
1,55
1,62
1,79
1,73
1,77
1,95
2,08
2,26
2,02
1,9
1,97
1,76
1,93
1,91
1,96
1,99
1,98
1,96
1,95
2,26
2,07
2,02
2,07
1,88
1,75
1,78
1,87
1,94
2,03
2,13
2,04
2,18
2,02
1,99
2,09
1,88
1,8
1,77
1,85
1,9
2,03
2,02
2,09
2,3
2,16
2,02
2,31
1,98
1,74
1,82
2,07
2,04
2,07
2,13
2,14
2,43
2,26
2,11
2,19
2,04
2,04
2,05
2,08
1,98
2,07
2,12
2,15
2,35
2,19
2,17
2,3
2,09
1,95
1,89
1,95
1,98
1,95
2,06

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232406&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232406&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232406&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.384205206240921
beta	0.0384392621248429
gamma	0.530909552576392

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.384205206240921 \tabularnewline
beta & 0.0384392621248429 \tabularnewline
gamma & 0.530909552576392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232406&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]0.384205206240921[/C][/ROW]
[ROW][C]beta[/C][C]0.0384392621248429[/C][/ROW]
[ROW][C]gamma[/C][C]0.530909552576392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232406&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232406&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	0.384205206240921
beta	0.0384392621248429
gamma	0.530909552576392

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2.08	2.00405448717949	0.0759455128205131
14	2.26	2.20350393895958	0.0564960610404186
15	2.02	1.98506517583618	0.0349348241638157
16	1.9	1.88010841046039	0.0198915895396115
17	1.97	1.95799905958236	0.0120009404176395
18	1.76	1.76345198356192	-0.00345198356192489
19	1.93	1.75375016618788	0.176249833812116
20	1.91	1.89777701301535	0.0122229869846529
21	1.96	2.07813107396837	-0.118131073968367
22	1.99	1.98124113298092	0.00875886701907569
23	1.98	2.03364899050081	-0.0536489905008053
24	1.96	2.2029537723342	-0.242953772334197
25	1.95	2.26160089441925	-0.311600894419252
26	2.26	2.29975060006699	-0.0397506000669945
27	2.07	2.02981913608865	0.0401808639113512
28	2.02	1.91457210959919	0.105427890400808
29	2.07	2.01662208667701	0.0533779133229926
30	1.88	1.82740682876553	0.0525931712344687
31	1.75	1.8933023286324	-0.1433023286324
32	1.78	1.85152504895684	-0.0715250489568413
33	1.87	1.94644400713547	-0.0764440071354691
34	1.94	1.89702856690417	0.0429714330958346
35	2.03	1.93265707094046	0.0973429290595447
36	2.13	2.09079308749419	0.0392069125058097
37	2.04	2.23228104532079	-0.192281045320792
38	2.18	2.4037887488219	-0.223788748821899
39	2.02	2.08520130118738	-0.0652013011873795
40	1.99	1.9451611833457	0.044838816654299
41	2.09	2.00038492795031	0.0896150720496891
42	1.88	1.81883996289344	0.0611600371065635
43	1.8	1.81811338417104	-0.0181133841710381
44	1.77	1.84388031675841	-0.0738803167584114
45	1.85	1.93223114920342	-0.0822311492034171
46	1.9	1.915492382782	-0.0154923827820015
47	2.03	1.94143057790312	0.0885694220968831
48	2.02	2.07205575717082	-0.0520557571708231
49	2.09	2.0963181111222	-0.00631811112220326
50	2.3	2.32523794888009	-0.0252379488800858
51	2.16	2.1339793315686	0.0260206684314013
52	2.02	2.06550732270776	-0.0455073227077616
53	2.31	2.09986867883609	0.210131321163909
54	1.98	1.95631400100464	0.0236859989953635
55	1.74	1.91570945780491	-0.175709457804908
56	1.82	1.86080445449298	-0.0408044544929753
57	2.07	1.95773079358771	0.112269206412295
58	2.04	2.03900929870877	0.000990701291234242
59	2.07	2.10701510525472	-0.0370151052547181
60	2.13	2.1432742335663	-0.0132742335662992
61	2.14	2.19782142442097	-0.0578214244209709
62	2.43	2.40043900696745	0.0295609930325513
63	2.26	2.24747285229238	0.0125271477076194
64	2.11	2.15071291620063	-0.0407129162006261
65	2.19	2.27084449432876	-0.0808444943287636
66	2.04	1.95059518149866	0.0894048185013379
67	2.04	1.86707670689037	0.172923293109631
68	2.05	1.99239687971341	0.0576031202865908
69	2.08	2.18080382171249	-0.100803821712486
70	1.98	2.14431867021491	-0.164318670214911
71	2.07	2.13442562496257	-0.0644256249625723
72	2.12	2.16554946839848	-0.045549468398483
73	2.15	2.19029015892195	-0.0402901589219486
74	2.35	2.42562799291993	-0.0756279929199262
75	2.19	2.22254189129545	-0.0325418912954536
76	2.17	2.08625785235469	0.0837421476453128
77	2.3	2.23812096798689	0.0618790320131066
78	2.09	2.02750995894697	0.0624900410530276
79	1.95	1.95970134698116	-0.00970134698116443
80	1.89	1.9732031536187	-0.0832031536187001
81	1.95	2.04969264176491	-0.0996926417649149
82	1.98	1.9868550707077	-0.00685507070769509
83	1.95	2.06642969226131	-0.116429692261312
84	2.06	2.07928764909357	-0.0192876490935747

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.08 & 2.00405448717949 & 0.0759455128205131 \tabularnewline
14 & 2.26 & 2.20350393895958 & 0.0564960610404186 \tabularnewline
15 & 2.02 & 1.98506517583618 & 0.0349348241638157 \tabularnewline
16 & 1.9 & 1.88010841046039 & 0.0198915895396115 \tabularnewline
17 & 1.97 & 1.95799905958236 & 0.0120009404176395 \tabularnewline
18 & 1.76 & 1.76345198356192 & -0.00345198356192489 \tabularnewline
19 & 1.93 & 1.75375016618788 & 0.176249833812116 \tabularnewline
20 & 1.91 & 1.89777701301535 & 0.0122229869846529 \tabularnewline
21 & 1.96 & 2.07813107396837 & -0.118131073968367 \tabularnewline
22 & 1.99 & 1.98124113298092 & 0.00875886701907569 \tabularnewline
23 & 1.98 & 2.03364899050081 & -0.0536489905008053 \tabularnewline
24 & 1.96 & 2.2029537723342 & -0.242953772334197 \tabularnewline
25 & 1.95 & 2.26160089441925 & -0.311600894419252 \tabularnewline
26 & 2.26 & 2.29975060006699 & -0.0397506000669945 \tabularnewline
27 & 2.07 & 2.02981913608865 & 0.0401808639113512 \tabularnewline
28 & 2.02 & 1.91457210959919 & 0.105427890400808 \tabularnewline
29 & 2.07 & 2.01662208667701 & 0.0533779133229926 \tabularnewline
30 & 1.88 & 1.82740682876553 & 0.0525931712344687 \tabularnewline
31 & 1.75 & 1.8933023286324 & -0.1433023286324 \tabularnewline
32 & 1.78 & 1.85152504895684 & -0.0715250489568413 \tabularnewline
33 & 1.87 & 1.94644400713547 & -0.0764440071354691 \tabularnewline
34 & 1.94 & 1.89702856690417 & 0.0429714330958346 \tabularnewline
35 & 2.03 & 1.93265707094046 & 0.0973429290595447 \tabularnewline
36 & 2.13 & 2.09079308749419 & 0.0392069125058097 \tabularnewline
37 & 2.04 & 2.23228104532079 & -0.192281045320792 \tabularnewline
38 & 2.18 & 2.4037887488219 & -0.223788748821899 \tabularnewline
39 & 2.02 & 2.08520130118738 & -0.0652013011873795 \tabularnewline
40 & 1.99 & 1.9451611833457 & 0.044838816654299 \tabularnewline
41 & 2.09 & 2.00038492795031 & 0.0896150720496891 \tabularnewline
42 & 1.88 & 1.81883996289344 & 0.0611600371065635 \tabularnewline
43 & 1.8 & 1.81811338417104 & -0.0181133841710381 \tabularnewline
44 & 1.77 & 1.84388031675841 & -0.0738803167584114 \tabularnewline
45 & 1.85 & 1.93223114920342 & -0.0822311492034171 \tabularnewline
46 & 1.9 & 1.915492382782 & -0.0154923827820015 \tabularnewline
47 & 2.03 & 1.94143057790312 & 0.0885694220968831 \tabularnewline
48 & 2.02 & 2.07205575717082 & -0.0520557571708231 \tabularnewline
49 & 2.09 & 2.0963181111222 & -0.00631811112220326 \tabularnewline
50 & 2.3 & 2.32523794888009 & -0.0252379488800858 \tabularnewline
51 & 2.16 & 2.1339793315686 & 0.0260206684314013 \tabularnewline
52 & 2.02 & 2.06550732270776 & -0.0455073227077616 \tabularnewline
53 & 2.31 & 2.09986867883609 & 0.210131321163909 \tabularnewline
54 & 1.98 & 1.95631400100464 & 0.0236859989953635 \tabularnewline
55 & 1.74 & 1.91570945780491 & -0.175709457804908 \tabularnewline
56 & 1.82 & 1.86080445449298 & -0.0408044544929753 \tabularnewline
57 & 2.07 & 1.95773079358771 & 0.112269206412295 \tabularnewline
58 & 2.04 & 2.03900929870877 & 0.000990701291234242 \tabularnewline
59 & 2.07 & 2.10701510525472 & -0.0370151052547181 \tabularnewline
60 & 2.13 & 2.1432742335663 & -0.0132742335662992 \tabularnewline
61 & 2.14 & 2.19782142442097 & -0.0578214244209709 \tabularnewline
62 & 2.43 & 2.40043900696745 & 0.0295609930325513 \tabularnewline
63 & 2.26 & 2.24747285229238 & 0.0125271477076194 \tabularnewline
64 & 2.11 & 2.15071291620063 & -0.0407129162006261 \tabularnewline
65 & 2.19 & 2.27084449432876 & -0.0808444943287636 \tabularnewline
66 & 2.04 & 1.95059518149866 & 0.0894048185013379 \tabularnewline
67 & 2.04 & 1.86707670689037 & 0.172923293109631 \tabularnewline
68 & 2.05 & 1.99239687971341 & 0.0576031202865908 \tabularnewline
69 & 2.08 & 2.18080382171249 & -0.100803821712486 \tabularnewline
70 & 1.98 & 2.14431867021491 & -0.164318670214911 \tabularnewline
71 & 2.07 & 2.13442562496257 & -0.0644256249625723 \tabularnewline
72 & 2.12 & 2.16554946839848 & -0.045549468398483 \tabularnewline
73 & 2.15 & 2.19029015892195 & -0.0402901589219486 \tabularnewline
74 & 2.35 & 2.42562799291993 & -0.0756279929199262 \tabularnewline
75 & 2.19 & 2.22254189129545 & -0.0325418912954536 \tabularnewline
76 & 2.17 & 2.08625785235469 & 0.0837421476453128 \tabularnewline
77 & 2.3 & 2.23812096798689 & 0.0618790320131066 \tabularnewline
78 & 2.09 & 2.02750995894697 & 0.0624900410530276 \tabularnewline
79 & 1.95 & 1.95970134698116 & -0.00970134698116443 \tabularnewline
80 & 1.89 & 1.9732031536187 & -0.0832031536187001 \tabularnewline
81 & 1.95 & 2.04969264176491 & -0.0996926417649149 \tabularnewline
82 & 1.98 & 1.9868550707077 & -0.00685507070769509 \tabularnewline
83 & 1.95 & 2.06642969226131 & -0.116429692261312 \tabularnewline
84 & 2.06 & 2.07928764909357 & -0.0192876490935747 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232406&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]13[/C][C]2.08[/C][C]2.00405448717949[/C][C]0.0759455128205131[/C][/ROW]
[ROW][C]14[/C][C]2.26[/C][C]2.20350393895958[/C][C]0.0564960610404186[/C][/ROW]
[ROW][C]15[/C][C]2.02[/C][C]1.98506517583618[/C][C]0.0349348241638157[/C][/ROW]
[ROW][C]16[/C][C]1.9[/C][C]1.88010841046039[/C][C]0.0198915895396115[/C][/ROW]
[ROW][C]17[/C][C]1.97[/C][C]1.95799905958236[/C][C]0.0120009404176395[/C][/ROW]
[ROW][C]18[/C][C]1.76[/C][C]1.76345198356192[/C][C]-0.00345198356192489[/C][/ROW]
[ROW][C]19[/C][C]1.93[/C][C]1.75375016618788[/C][C]0.176249833812116[/C][/ROW]
[ROW][C]20[/C][C]1.91[/C][C]1.89777701301535[/C][C]0.0122229869846529[/C][/ROW]
[ROW][C]21[/C][C]1.96[/C][C]2.07813107396837[/C][C]-0.118131073968367[/C][/ROW]
[ROW][C]22[/C][C]1.99[/C][C]1.98124113298092[/C][C]0.00875886701907569[/C][/ROW]
[ROW][C]23[/C][C]1.98[/C][C]2.03364899050081[/C][C]-0.0536489905008053[/C][/ROW]
[ROW][C]24[/C][C]1.96[/C][C]2.2029537723342[/C][C]-0.242953772334197[/C][/ROW]
[ROW][C]25[/C][C]1.95[/C][C]2.26160089441925[/C][C]-0.311600894419252[/C][/ROW]
[ROW][C]26[/C][C]2.26[/C][C]2.29975060006699[/C][C]-0.0397506000669945[/C][/ROW]
[ROW][C]27[/C][C]2.07[/C][C]2.02981913608865[/C][C]0.0401808639113512[/C][/ROW]
[ROW][C]28[/C][C]2.02[/C][C]1.91457210959919[/C][C]0.105427890400808[/C][/ROW]
[ROW][C]29[/C][C]2.07[/C][C]2.01662208667701[/C][C]0.0533779133229926[/C][/ROW]
[ROW][C]30[/C][C]1.88[/C][C]1.82740682876553[/C][C]0.0525931712344687[/C][/ROW]
[ROW][C]31[/C][C]1.75[/C][C]1.8933023286324[/C][C]-0.1433023286324[/C][/ROW]
[ROW][C]32[/C][C]1.78[/C][C]1.85152504895684[/C][C]-0.0715250489568413[/C][/ROW]
[ROW][C]33[/C][C]1.87[/C][C]1.94644400713547[/C][C]-0.0764440071354691[/C][/ROW]
[ROW][C]34[/C][C]1.94[/C][C]1.89702856690417[/C][C]0.0429714330958346[/C][/ROW]
[ROW][C]35[/C][C]2.03[/C][C]1.93265707094046[/C][C]0.0973429290595447[/C][/ROW]
[ROW][C]36[/C][C]2.13[/C][C]2.09079308749419[/C][C]0.0392069125058097[/C][/ROW]
[ROW][C]37[/C][C]2.04[/C][C]2.23228104532079[/C][C]-0.192281045320792[/C][/ROW]
[ROW][C]38[/C][C]2.18[/C][C]2.4037887488219[/C][C]-0.223788748821899[/C][/ROW]
[ROW][C]39[/C][C]2.02[/C][C]2.08520130118738[/C][C]-0.0652013011873795[/C][/ROW]
[ROW][C]40[/C][C]1.99[/C][C]1.9451611833457[/C][C]0.044838816654299[/C][/ROW]
[ROW][C]41[/C][C]2.09[/C][C]2.00038492795031[/C][C]0.0896150720496891[/C][/ROW]
[ROW][C]42[/C][C]1.88[/C][C]1.81883996289344[/C][C]0.0611600371065635[/C][/ROW]
[ROW][C]43[/C][C]1.8[/C][C]1.81811338417104[/C][C]-0.0181133841710381[/C][/ROW]
[ROW][C]44[/C][C]1.77[/C][C]1.84388031675841[/C][C]-0.0738803167584114[/C][/ROW]
[ROW][C]45[/C][C]1.85[/C][C]1.93223114920342[/C][C]-0.0822311492034171[/C][/ROW]
[ROW][C]46[/C][C]1.9[/C][C]1.915492382782[/C][C]-0.0154923827820015[/C][/ROW]
[ROW][C]47[/C][C]2.03[/C][C]1.94143057790312[/C][C]0.0885694220968831[/C][/ROW]
[ROW][C]48[/C][C]2.02[/C][C]2.07205575717082[/C][C]-0.0520557571708231[/C][/ROW]
[ROW][C]49[/C][C]2.09[/C][C]2.0963181111222[/C][C]-0.00631811112220326[/C][/ROW]
[ROW][C]50[/C][C]2.3[/C][C]2.32523794888009[/C][C]-0.0252379488800858[/C][/ROW]
[ROW][C]51[/C][C]2.16[/C][C]2.1339793315686[/C][C]0.0260206684314013[/C][/ROW]
[ROW][C]52[/C][C]2.02[/C][C]2.06550732270776[/C][C]-0.0455073227077616[/C][/ROW]
[ROW][C]53[/C][C]2.31[/C][C]2.09986867883609[/C][C]0.210131321163909[/C][/ROW]
[ROW][C]54[/C][C]1.98[/C][C]1.95631400100464[/C][C]0.0236859989953635[/C][/ROW]
[ROW][C]55[/C][C]1.74[/C][C]1.91570945780491[/C][C]-0.175709457804908[/C][/ROW]
[ROW][C]56[/C][C]1.82[/C][C]1.86080445449298[/C][C]-0.0408044544929753[/C][/ROW]
[ROW][C]57[/C][C]2.07[/C][C]1.95773079358771[/C][C]0.112269206412295[/C][/ROW]
[ROW][C]58[/C][C]2.04[/C][C]2.03900929870877[/C][C]0.000990701291234242[/C][/ROW]
[ROW][C]59[/C][C]2.07[/C][C]2.10701510525472[/C][C]-0.0370151052547181[/C][/ROW]
[ROW][C]60[/C][C]2.13[/C][C]2.1432742335663[/C][C]-0.0132742335662992[/C][/ROW]
[ROW][C]61[/C][C]2.14[/C][C]2.19782142442097[/C][C]-0.0578214244209709[/C][/ROW]
[ROW][C]62[/C][C]2.43[/C][C]2.40043900696745[/C][C]0.0295609930325513[/C][/ROW]
[ROW][C]63[/C][C]2.26[/C][C]2.24747285229238[/C][C]0.0125271477076194[/C][/ROW]
[ROW][C]64[/C][C]2.11[/C][C]2.15071291620063[/C][C]-0.0407129162006261[/C][/ROW]
[ROW][C]65[/C][C]2.19[/C][C]2.27084449432876[/C][C]-0.0808444943287636[/C][/ROW]
[ROW][C]66[/C][C]2.04[/C][C]1.95059518149866[/C][C]0.0894048185013379[/C][/ROW]
[ROW][C]67[/C][C]2.04[/C][C]1.86707670689037[/C][C]0.172923293109631[/C][/ROW]
[ROW][C]68[/C][C]2.05[/C][C]1.99239687971341[/C][C]0.0576031202865908[/C][/ROW]
[ROW][C]69[/C][C]2.08[/C][C]2.18080382171249[/C][C]-0.100803821712486[/C][/ROW]
[ROW][C]70[/C][C]1.98[/C][C]2.14431867021491[/C][C]-0.164318670214911[/C][/ROW]
[ROW][C]71[/C][C]2.07[/C][C]2.13442562496257[/C][C]-0.0644256249625723[/C][/ROW]
[ROW][C]72[/C][C]2.12[/C][C]2.16554946839848[/C][C]-0.045549468398483[/C][/ROW]
[ROW][C]73[/C][C]2.15[/C][C]2.19029015892195[/C][C]-0.0402901589219486[/C][/ROW]
[ROW][C]74[/C][C]2.35[/C][C]2.42562799291993[/C][C]-0.0756279929199262[/C][/ROW]
[ROW][C]75[/C][C]2.19[/C][C]2.22254189129545[/C][C]-0.0325418912954536[/C][/ROW]
[ROW][C]76[/C][C]2.17[/C][C]2.08625785235469[/C][C]0.0837421476453128[/C][/ROW]
[ROW][C]77[/C][C]2.3[/C][C]2.23812096798689[/C][C]0.0618790320131066[/C][/ROW]
[ROW][C]78[/C][C]2.09[/C][C]2.02750995894697[/C][C]0.0624900410530276[/C][/ROW]
[ROW][C]79[/C][C]1.95[/C][C]1.95970134698116[/C][C]-0.00970134698116443[/C][/ROW]
[ROW][C]80[/C][C]1.89[/C][C]1.9732031536187[/C][C]-0.0832031536187001[/C][/ROW]
[ROW][C]81[/C][C]1.95[/C][C]2.04969264176491[/C][C]-0.0996926417649149[/C][/ROW]
[ROW][C]82[/C][C]1.98[/C][C]1.9868550707077[/C][C]-0.00685507070769509[/C][/ROW]
[ROW][C]83[/C][C]1.95[/C][C]2.06642969226131[/C][C]-0.116429692261312[/C][/ROW]
[ROW][C]84[/C][C]2.06[/C][C]2.07928764909357[/C][C]-0.0192876490935747[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232406&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232406&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
13	2.08	2.00405448717949	0.0759455128205131
14	2.26	2.20350393895958	0.0564960610404186
15	2.02	1.98506517583618	0.0349348241638157
16	1.9	1.88010841046039	0.0198915895396115
17	1.97	1.95799905958236	0.0120009404176395
18	1.76	1.76345198356192	-0.00345198356192489
19	1.93	1.75375016618788	0.176249833812116
20	1.91	1.89777701301535	0.0122229869846529
21	1.96	2.07813107396837	-0.118131073968367
22	1.99	1.98124113298092	0.00875886701907569
23	1.98	2.03364899050081	-0.0536489905008053
24	1.96	2.2029537723342	-0.242953772334197
25	1.95	2.26160089441925	-0.311600894419252
26	2.26	2.29975060006699	-0.0397506000669945
27	2.07	2.02981913608865	0.0401808639113512
28	2.02	1.91457210959919	0.105427890400808
29	2.07	2.01662208667701	0.0533779133229926
30	1.88	1.82740682876553	0.0525931712344687
31	1.75	1.8933023286324	-0.1433023286324
32	1.78	1.85152504895684	-0.0715250489568413
33	1.87	1.94644400713547	-0.0764440071354691
34	1.94	1.89702856690417	0.0429714330958346
35	2.03	1.93265707094046	0.0973429290595447
36	2.13	2.09079308749419	0.0392069125058097
37	2.04	2.23228104532079	-0.192281045320792
38	2.18	2.4037887488219	-0.223788748821899
39	2.02	2.08520130118738	-0.0652013011873795
40	1.99	1.9451611833457	0.044838816654299
41	2.09	2.00038492795031	0.0896150720496891
42	1.88	1.81883996289344	0.0611600371065635
43	1.8	1.81811338417104	-0.0181133841710381
44	1.77	1.84388031675841	-0.0738803167584114
45	1.85	1.93223114920342	-0.0822311492034171
46	1.9	1.915492382782	-0.0154923827820015
47	2.03	1.94143057790312	0.0885694220968831
48	2.02	2.07205575717082	-0.0520557571708231
49	2.09	2.0963181111222	-0.00631811112220326
50	2.3	2.32523794888009	-0.0252379488800858
51	2.16	2.1339793315686	0.0260206684314013
52	2.02	2.06550732270776	-0.0455073227077616
53	2.31	2.09986867883609	0.210131321163909
54	1.98	1.95631400100464	0.0236859989953635
55	1.74	1.91570945780491	-0.175709457804908
56	1.82	1.86080445449298	-0.0408044544929753
57	2.07	1.95773079358771	0.112269206412295
58	2.04	2.03900929870877	0.000990701291234242
59	2.07	2.10701510525472	-0.0370151052547181
60	2.13	2.1432742335663	-0.0132742335662992
61	2.14	2.19782142442097	-0.0578214244209709
62	2.43	2.40043900696745	0.0295609930325513
63	2.26	2.24747285229238	0.0125271477076194
64	2.11	2.15071291620063	-0.0407129162006261
65	2.19	2.27084449432876	-0.0808444943287636
66	2.04	1.95059518149866	0.0894048185013379
67	2.04	1.86707670689037	0.172923293109631
68	2.05	1.99239687971341	0.0576031202865908
69	2.08	2.18080382171249	-0.100803821712486
70	1.98	2.14431867021491	-0.164318670214911
71	2.07	2.13442562496257	-0.0644256249625723
72	2.12	2.16554946839848	-0.045549468398483
73	2.15	2.19029015892195	-0.0402901589219486
74	2.35	2.42562799291993	-0.0756279929199262
75	2.19	2.22254189129545	-0.0325418912954536
76	2.17	2.08625785235469	0.0837421476453128
77	2.3	2.23812096798689	0.0618790320131066
78	2.09	2.02750995894697	0.0624900410530276
79	1.95	1.95970134698116	-0.00970134698116443
80	1.89	1.9732031536187	-0.0832031536187001
81	1.95	2.04969264176491	-0.0996926417649149
82	1.98	1.9868550707077	-0.00685507070769509
83	1.95	2.06642969226131	-0.116429692261312
84	2.06	2.07928764909357	-0.0192876490935747

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	2.11176868944977	1.92617576904072	2.29736160985881
86	2.34755918375964	2.14774014820904	2.54737821931025
87	2.1852588813861	1.97119349439773	2.39932426837446
88	2.09761803377776	1.86925694594568	2.32597912160983
89	2.20704602211335	1.96431765114683	2.44977439307986
90	1.96883343980285	1.71164898784147	2.22601789176423
91	1.84846422838549	1.57672142217476	2.12020703459622
92	1.83685660076198	1.55044253201282	2.12327066951113
93	1.93634433616881	1.63513765298142	2.23755101935619
94	1.94005511858188	1.62392773934885	2.25618249781492
95	1.98443576598014	1.65325423569043	2.31561729626984
96	2.07350054403897	1.72712711863632	2.41987396944163

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 2.11176868944977 & 1.92617576904072 & 2.29736160985881 \tabularnewline
86 & 2.34755918375964 & 2.14774014820904 & 2.54737821931025 \tabularnewline
87 & 2.1852588813861 & 1.97119349439773 & 2.39932426837446 \tabularnewline
88 & 2.09761803377776 & 1.86925694594568 & 2.32597912160983 \tabularnewline
89 & 2.20704602211335 & 1.96431765114683 & 2.44977439307986 \tabularnewline
90 & 1.96883343980285 & 1.71164898784147 & 2.22601789176423 \tabularnewline
91 & 1.84846422838549 & 1.57672142217476 & 2.12020703459622 \tabularnewline
92 & 1.83685660076198 & 1.55044253201282 & 2.12327066951113 \tabularnewline
93 & 1.93634433616881 & 1.63513765298142 & 2.23755101935619 \tabularnewline
94 & 1.94005511858188 & 1.62392773934885 & 2.25618249781492 \tabularnewline
95 & 1.98443576598014 & 1.65325423569043 & 2.31561729626984 \tabularnewline
96 & 2.07350054403897 & 1.72712711863632 & 2.41987396944163 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232406&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]85[/C][C]2.11176868944977[/C][C]1.92617576904072[/C][C]2.29736160985881[/C][/ROW]
[ROW][C]86[/C][C]2.34755918375964[/C][C]2.14774014820904[/C][C]2.54737821931025[/C][/ROW]
[ROW][C]87[/C][C]2.1852588813861[/C][C]1.97119349439773[/C][C]2.39932426837446[/C][/ROW]
[ROW][C]88[/C][C]2.09761803377776[/C][C]1.86925694594568[/C][C]2.32597912160983[/C][/ROW]
[ROW][C]89[/C][C]2.20704602211335[/C][C]1.96431765114683[/C][C]2.44977439307986[/C][/ROW]
[ROW][C]90[/C][C]1.96883343980285[/C][C]1.71164898784147[/C][C]2.22601789176423[/C][/ROW]
[ROW][C]91[/C][C]1.84846422838549[/C][C]1.57672142217476[/C][C]2.12020703459622[/C][/ROW]
[ROW][C]92[/C][C]1.83685660076198[/C][C]1.55044253201282[/C][C]2.12327066951113[/C][/ROW]
[ROW][C]93[/C][C]1.93634433616881[/C][C]1.63513765298142[/C][C]2.23755101935619[/C][/ROW]
[ROW][C]94[/C][C]1.94005511858188[/C][C]1.62392773934885[/C][C]2.25618249781492[/C][/ROW]
[ROW][C]95[/C][C]1.98443576598014[/C][C]1.65325423569043[/C][C]2.31561729626984[/C][/ROW]
[ROW][C]96[/C][C]2.07350054403897[/C][C]1.72712711863632[/C][C]2.41987396944163[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232406&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232406&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
85	2.11176868944977	1.92617576904072	2.29736160985881
86	2.34755918375964	2.14774014820904	2.54737821931025
87	2.1852588813861	1.97119349439773	2.39932426837446
88	2.09761803377776	1.86925694594568	2.32597912160983
89	2.20704602211335	1.96431765114683	2.44977439307986
90	1.96883343980285	1.71164898784147	2.22601789176423
91	1.84846422838549	1.57672142217476	2.12020703459622
92	1.83685660076198	1.55044253201282	2.12327066951113
93	1.93634433616881	1.63513765298142	2.23755101935619
94	1.94005511858188	1.62392773934885	2.25618249781492
95	1.98443576598014	1.65325423569043	2.31561729626984
96	2.07350054403897	1.72712711863632	2.41987396944163

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 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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