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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 16 Dec 2012 12:42:03 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/16/t1355679732rdd004wxrx3ohso.htm/, Retrieved Wed, 24 Apr 2024 13:49:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200516, Retrieved Wed, 24 Apr 2024 13:49:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [paper] [2012-12-09 08:56:26] [e37f7a7b9ab1c2cdf6c8d8ef0222ab12]
-   PD    [Exponential Smoothing] [paper] [2012-12-16 17:42:03] [97e5c69206415429213a02c19f23a896] [Current]
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Dataseries X:
563278
571477
583775
598714
581744
530455
527676
536352
545732
558685
561649
540735
538712
547612
563280
581302
572273
518654
520579
530577
540324
547970
555654
551174
548604
563668
586111
604378
600991
544686
537034
551531
563250
574761
580112
575093
557560
564478
580523
596594
586570
536214
523597
536535
536322
532638
528222
516141
501866
506174
517945
533590
528379
477580
469357
490243
492622
507561
516922
514258
509846
527070
541657
564591
555362
498662
511038
525919
531673
548854
560576
557274
565742
587625
619916
625809
619567
572942
572775
574205
579799
590072
593408
597141
595404
612117
628232
628884
620735
569028
567456
573100
584428
589379
590865
595454
594167
611324
612613
610763
593530
542722
536662
543599
555332
560854
562325
554788
547344
565464
577992
579714
569323
506971
500857
509127
509933
517009
519164
512238
509239




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200516&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200516&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200516&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.475080773654074
beta0.45686476384713
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.475080773654074 \tabularnewline
beta & 0.45686476384713 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200516&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]0.475080773654074[/C][/ROW]
[ROW][C]beta[/C][C]0.45686476384713[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200516&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200516&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
ParameterValue
alpha0.475080773654074
beta0.45686476384713
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13538712546150.594818376-7438.59481837589
14547612549526.817840627-1914.81784062681
15563280561809.2993608631470.7006391373
16581302578579.2210933392722.77890666062
17572273569508.4122764252764.58772357542
18518654515586.09666933067.90333069966
19520579514875.1367312675703.86326873302
20530577528751.2308865191825.76911348116
21540324541715.570993947-1391.5709939471
22547970556153.502438467-8183.50243846688
23555654555140.174404799513.82559520111
24551174534258.51268131716915.4873186833
25548604539727.8540275128876.14597248833
26563668560780.5204704282887.4795295716
27586111585190.019320966920.980679034023
28604378610305.118630191-5927.11863019061
29600991603218.514989569-2227.51498956897
30544686552071.89825581-7385.89825581003
31537034550497.365692865-13463.3656928655
32551531551790.750870123-259.750870122807
33563250560181.7587760253068.24122397474
34574761572247.5396162812513.46038371918
35580112582277.572222889-2165.5722228894
36575093569547.0152167285545.98478327179
37557560563741.683202755-6181.6832027554
38564478569575.595226241-5097.59522624081
39580523582504.640565318-1981.64056531806
40596594595361.4092084521232.59079154814
41586570587887.585026896-1317.58502689621
42536214528932.3682316247281.6317683761
43523597528786.315085992-5189.31508599175
44536535540387.63468372-3852.63468371995
45536322547485.093338285-11163.0933382852
46532638548076.181407098-15438.1814070981
47528222538802.813817501-10580.8138175013
48516141515976.967169304164.032830696378
49501866490145.24005254111720.7599474588
50506174497625.545932588548.45406742027
51517945514207.2632718733737.73672812723
52533590528243.8592655095346.14073449094
53528379519053.9529915029325.04700849811
54477580469646.9844582027933.01554179768
55469357463383.7769458665973.22305413405
56490243483532.2813866146710.71861338592
57492622496645.965314201-4023.96531420108
58507561504769.3505147832791.64948521659
59516922517047.80355179-125.803551789839
60514258517439.796255028-3181.79625502817
61509846507969.3623288931876.63767110696
62527070518855.5508789988214.44912100188
63541657542428.696117502-771.696117501822
64564591563863.812832528727.18716747174
65555362562262.185218638-6900.18521863758
66498662508588.61824025-9926.61824024975
67511038493107.91903335117930.0809666486
68525919522215.2401724533703.75982754736
69531673530504.0982191771168.90178082348
70548854548037.826072163816.173927837284
71560576560783.233191873-207.233191873413
72557274562451.608529845-5177.60852984479
73565742557174.3030088428567.69699115772
74587625578504.4343068769120.56569312373
75619916601926.03821426317989.9617857372
76625809641268.405096658-15459.4050966583
77619567632666.976793723-13099.9767937234
78572942577807.617367914-4865.6173679136
79572775583800.540002252-11025.5400022517
80574205589845.903545481-15640.9035454808
81579799581577.14490354-1778.14490354026
82590072590849.240980625-777.240980624571
83593408595278.20132796-1870.20132795954
84597141586164.30363714610976.6963628541
85595404591899.843823463504.15617654042
86612117606138.6368334465978.36316655413
87628232627065.1907340991166.80926590145
88628884631547.593001707-2663.59300170687
89620735623731.626915996-2996.6269159962
90569028573655.365478397-4627.365478397
91567456572240.544330127-4784.54433012742
92573100575895.314554992-2795.31455499178
93584428580861.3046017033566.69539829658
94589379594213.338158756-4834.33815875649
95590865596275.863170343-5410.86317034275
96595454591589.6857523013864.31424769864
97594167587846.3010366966320.69896330393
98611324603155.7733377228168.22666227759
99612613621506.152036356-8893.15203635592
100610763615924.257100628-5161.25710062834
101593530602930.419546032-9400.41954603186
102542722543749.441714617-1027.44171461731
103536662539537.332368398-2875.33236839774
104543599541132.6708793742466.32912062609
105555332549069.2889288466262.71107115445
106560854557008.8284820873845.17151791323
107562325562492.604735262-167.604735261644
108554788565904.566680793-11116.5666807932
109547344553820.340931331-6476.34093133081
110565464558729.30469836734.6953017005
111577992561840.96613619816151.0338638019
112579714569949.9795329789764.02046702232
113569323564895.0868905414427.91310945875
114506971522753.678770566-15782.6787705665
115500857513433.91458929-12576.9145892902
116509127513990.720890254-4863.72089025378
117509933519613.358904362-9680.35890436184
118517009514424.8252470982584.17475290247
119519164512644.6321710896519.36782891123
120512238510379.0067619751858.99323802546
121509239506604.1599361852634.84006381454

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 538712 & 546150.594818376 & -7438.59481837589 \tabularnewline
14 & 547612 & 549526.817840627 & -1914.81784062681 \tabularnewline
15 & 563280 & 561809.299360863 & 1470.7006391373 \tabularnewline
16 & 581302 & 578579.221093339 & 2722.77890666062 \tabularnewline
17 & 572273 & 569508.412276425 & 2764.58772357542 \tabularnewline
18 & 518654 & 515586.0966693 & 3067.90333069966 \tabularnewline
19 & 520579 & 514875.136731267 & 5703.86326873302 \tabularnewline
20 & 530577 & 528751.230886519 & 1825.76911348116 \tabularnewline
21 & 540324 & 541715.570993947 & -1391.5709939471 \tabularnewline
22 & 547970 & 556153.502438467 & -8183.50243846688 \tabularnewline
23 & 555654 & 555140.174404799 & 513.82559520111 \tabularnewline
24 & 551174 & 534258.512681317 & 16915.4873186833 \tabularnewline
25 & 548604 & 539727.854027512 & 8876.14597248833 \tabularnewline
26 & 563668 & 560780.520470428 & 2887.4795295716 \tabularnewline
27 & 586111 & 585190.019320966 & 920.980679034023 \tabularnewline
28 & 604378 & 610305.118630191 & -5927.11863019061 \tabularnewline
29 & 600991 & 603218.514989569 & -2227.51498956897 \tabularnewline
30 & 544686 & 552071.89825581 & -7385.89825581003 \tabularnewline
31 & 537034 & 550497.365692865 & -13463.3656928655 \tabularnewline
32 & 551531 & 551790.750870123 & -259.750870122807 \tabularnewline
33 & 563250 & 560181.758776025 & 3068.24122397474 \tabularnewline
34 & 574761 & 572247.539616281 & 2513.46038371918 \tabularnewline
35 & 580112 & 582277.572222889 & -2165.5722228894 \tabularnewline
36 & 575093 & 569547.015216728 & 5545.98478327179 \tabularnewline
37 & 557560 & 563741.683202755 & -6181.6832027554 \tabularnewline
38 & 564478 & 569575.595226241 & -5097.59522624081 \tabularnewline
39 & 580523 & 582504.640565318 & -1981.64056531806 \tabularnewline
40 & 596594 & 595361.409208452 & 1232.59079154814 \tabularnewline
41 & 586570 & 587887.585026896 & -1317.58502689621 \tabularnewline
42 & 536214 & 528932.368231624 & 7281.6317683761 \tabularnewline
43 & 523597 & 528786.315085992 & -5189.31508599175 \tabularnewline
44 & 536535 & 540387.63468372 & -3852.63468371995 \tabularnewline
45 & 536322 & 547485.093338285 & -11163.0933382852 \tabularnewline
46 & 532638 & 548076.181407098 & -15438.1814070981 \tabularnewline
47 & 528222 & 538802.813817501 & -10580.8138175013 \tabularnewline
48 & 516141 & 515976.967169304 & 164.032830696378 \tabularnewline
49 & 501866 & 490145.240052541 & 11720.7599474588 \tabularnewline
50 & 506174 & 497625.54593258 & 8548.45406742027 \tabularnewline
51 & 517945 & 514207.263271873 & 3737.73672812723 \tabularnewline
52 & 533590 & 528243.859265509 & 5346.14073449094 \tabularnewline
53 & 528379 & 519053.952991502 & 9325.04700849811 \tabularnewline
54 & 477580 & 469646.984458202 & 7933.01554179768 \tabularnewline
55 & 469357 & 463383.776945866 & 5973.22305413405 \tabularnewline
56 & 490243 & 483532.281386614 & 6710.71861338592 \tabularnewline
57 & 492622 & 496645.965314201 & -4023.96531420108 \tabularnewline
58 & 507561 & 504769.350514783 & 2791.64948521659 \tabularnewline
59 & 516922 & 517047.80355179 & -125.803551789839 \tabularnewline
60 & 514258 & 517439.796255028 & -3181.79625502817 \tabularnewline
61 & 509846 & 507969.362328893 & 1876.63767110696 \tabularnewline
62 & 527070 & 518855.550878998 & 8214.44912100188 \tabularnewline
63 & 541657 & 542428.696117502 & -771.696117501822 \tabularnewline
64 & 564591 & 563863.812832528 & 727.18716747174 \tabularnewline
65 & 555362 & 562262.185218638 & -6900.18521863758 \tabularnewline
66 & 498662 & 508588.61824025 & -9926.61824024975 \tabularnewline
67 & 511038 & 493107.919033351 & 17930.0809666486 \tabularnewline
68 & 525919 & 522215.240172453 & 3703.75982754736 \tabularnewline
69 & 531673 & 530504.098219177 & 1168.90178082348 \tabularnewline
70 & 548854 & 548037.826072163 & 816.173927837284 \tabularnewline
71 & 560576 & 560783.233191873 & -207.233191873413 \tabularnewline
72 & 557274 & 562451.608529845 & -5177.60852984479 \tabularnewline
73 & 565742 & 557174.303008842 & 8567.69699115772 \tabularnewline
74 & 587625 & 578504.434306876 & 9120.56569312373 \tabularnewline
75 & 619916 & 601926.038214263 & 17989.9617857372 \tabularnewline
76 & 625809 & 641268.405096658 & -15459.4050966583 \tabularnewline
77 & 619567 & 632666.976793723 & -13099.9767937234 \tabularnewline
78 & 572942 & 577807.617367914 & -4865.6173679136 \tabularnewline
79 & 572775 & 583800.540002252 & -11025.5400022517 \tabularnewline
80 & 574205 & 589845.903545481 & -15640.9035454808 \tabularnewline
81 & 579799 & 581577.14490354 & -1778.14490354026 \tabularnewline
82 & 590072 & 590849.240980625 & -777.240980624571 \tabularnewline
83 & 593408 & 595278.20132796 & -1870.20132795954 \tabularnewline
84 & 597141 & 586164.303637146 & 10976.6963628541 \tabularnewline
85 & 595404 & 591899.84382346 & 3504.15617654042 \tabularnewline
86 & 612117 & 606138.636833446 & 5978.36316655413 \tabularnewline
87 & 628232 & 627065.190734099 & 1166.80926590145 \tabularnewline
88 & 628884 & 631547.593001707 & -2663.59300170687 \tabularnewline
89 & 620735 & 623731.626915996 & -2996.6269159962 \tabularnewline
90 & 569028 & 573655.365478397 & -4627.365478397 \tabularnewline
91 & 567456 & 572240.544330127 & -4784.54433012742 \tabularnewline
92 & 573100 & 575895.314554992 & -2795.31455499178 \tabularnewline
93 & 584428 & 580861.304601703 & 3566.69539829658 \tabularnewline
94 & 589379 & 594213.338158756 & -4834.33815875649 \tabularnewline
95 & 590865 & 596275.863170343 & -5410.86317034275 \tabularnewline
96 & 595454 & 591589.685752301 & 3864.31424769864 \tabularnewline
97 & 594167 & 587846.301036696 & 6320.69896330393 \tabularnewline
98 & 611324 & 603155.773337722 & 8168.22666227759 \tabularnewline
99 & 612613 & 621506.152036356 & -8893.15203635592 \tabularnewline
100 & 610763 & 615924.257100628 & -5161.25710062834 \tabularnewline
101 & 593530 & 602930.419546032 & -9400.41954603186 \tabularnewline
102 & 542722 & 543749.441714617 & -1027.44171461731 \tabularnewline
103 & 536662 & 539537.332368398 & -2875.33236839774 \tabularnewline
104 & 543599 & 541132.670879374 & 2466.32912062609 \tabularnewline
105 & 555332 & 549069.288928846 & 6262.71107115445 \tabularnewline
106 & 560854 & 557008.828482087 & 3845.17151791323 \tabularnewline
107 & 562325 & 562492.604735262 & -167.604735261644 \tabularnewline
108 & 554788 & 565904.566680793 & -11116.5666807932 \tabularnewline
109 & 547344 & 553820.340931331 & -6476.34093133081 \tabularnewline
110 & 565464 & 558729.3046983 & 6734.6953017005 \tabularnewline
111 & 577992 & 561840.966136198 & 16151.0338638019 \tabularnewline
112 & 579714 & 569949.979532978 & 9764.02046702232 \tabularnewline
113 & 569323 & 564895.086890541 & 4427.91310945875 \tabularnewline
114 & 506971 & 522753.678770566 & -15782.6787705665 \tabularnewline
115 & 500857 & 513433.91458929 & -12576.9145892902 \tabularnewline
116 & 509127 & 513990.720890254 & -4863.72089025378 \tabularnewline
117 & 509933 & 519613.358904362 & -9680.35890436184 \tabularnewline
118 & 517009 & 514424.825247098 & 2584.17475290247 \tabularnewline
119 & 519164 & 512644.632171089 & 6519.36782891123 \tabularnewline
120 & 512238 & 510379.006761975 & 1858.99323802546 \tabularnewline
121 & 509239 & 506604.159936185 & 2634.84006381454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200516&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]538712[/C][C]546150.594818376[/C][C]-7438.59481837589[/C][/ROW]
[ROW][C]14[/C][C]547612[/C][C]549526.817840627[/C][C]-1914.81784062681[/C][/ROW]
[ROW][C]15[/C][C]563280[/C][C]561809.299360863[/C][C]1470.7006391373[/C][/ROW]
[ROW][C]16[/C][C]581302[/C][C]578579.221093339[/C][C]2722.77890666062[/C][/ROW]
[ROW][C]17[/C][C]572273[/C][C]569508.412276425[/C][C]2764.58772357542[/C][/ROW]
[ROW][C]18[/C][C]518654[/C][C]515586.0966693[/C][C]3067.90333069966[/C][/ROW]
[ROW][C]19[/C][C]520579[/C][C]514875.136731267[/C][C]5703.86326873302[/C][/ROW]
[ROW][C]20[/C][C]530577[/C][C]528751.230886519[/C][C]1825.76911348116[/C][/ROW]
[ROW][C]21[/C][C]540324[/C][C]541715.570993947[/C][C]-1391.5709939471[/C][/ROW]
[ROW][C]22[/C][C]547970[/C][C]556153.502438467[/C][C]-8183.50243846688[/C][/ROW]
[ROW][C]23[/C][C]555654[/C][C]555140.174404799[/C][C]513.82559520111[/C][/ROW]
[ROW][C]24[/C][C]551174[/C][C]534258.512681317[/C][C]16915.4873186833[/C][/ROW]
[ROW][C]25[/C][C]548604[/C][C]539727.854027512[/C][C]8876.14597248833[/C][/ROW]
[ROW][C]26[/C][C]563668[/C][C]560780.520470428[/C][C]2887.4795295716[/C][/ROW]
[ROW][C]27[/C][C]586111[/C][C]585190.019320966[/C][C]920.980679034023[/C][/ROW]
[ROW][C]28[/C][C]604378[/C][C]610305.118630191[/C][C]-5927.11863019061[/C][/ROW]
[ROW][C]29[/C][C]600991[/C][C]603218.514989569[/C][C]-2227.51498956897[/C][/ROW]
[ROW][C]30[/C][C]544686[/C][C]552071.89825581[/C][C]-7385.89825581003[/C][/ROW]
[ROW][C]31[/C][C]537034[/C][C]550497.365692865[/C][C]-13463.3656928655[/C][/ROW]
[ROW][C]32[/C][C]551531[/C][C]551790.750870123[/C][C]-259.750870122807[/C][/ROW]
[ROW][C]33[/C][C]563250[/C][C]560181.758776025[/C][C]3068.24122397474[/C][/ROW]
[ROW][C]34[/C][C]574761[/C][C]572247.539616281[/C][C]2513.46038371918[/C][/ROW]
[ROW][C]35[/C][C]580112[/C][C]582277.572222889[/C][C]-2165.5722228894[/C][/ROW]
[ROW][C]36[/C][C]575093[/C][C]569547.015216728[/C][C]5545.98478327179[/C][/ROW]
[ROW][C]37[/C][C]557560[/C][C]563741.683202755[/C][C]-6181.6832027554[/C][/ROW]
[ROW][C]38[/C][C]564478[/C][C]569575.595226241[/C][C]-5097.59522624081[/C][/ROW]
[ROW][C]39[/C][C]580523[/C][C]582504.640565318[/C][C]-1981.64056531806[/C][/ROW]
[ROW][C]40[/C][C]596594[/C][C]595361.409208452[/C][C]1232.59079154814[/C][/ROW]
[ROW][C]41[/C][C]586570[/C][C]587887.585026896[/C][C]-1317.58502689621[/C][/ROW]
[ROW][C]42[/C][C]536214[/C][C]528932.368231624[/C][C]7281.6317683761[/C][/ROW]
[ROW][C]43[/C][C]523597[/C][C]528786.315085992[/C][C]-5189.31508599175[/C][/ROW]
[ROW][C]44[/C][C]536535[/C][C]540387.63468372[/C][C]-3852.63468371995[/C][/ROW]
[ROW][C]45[/C][C]536322[/C][C]547485.093338285[/C][C]-11163.0933382852[/C][/ROW]
[ROW][C]46[/C][C]532638[/C][C]548076.181407098[/C][C]-15438.1814070981[/C][/ROW]
[ROW][C]47[/C][C]528222[/C][C]538802.813817501[/C][C]-10580.8138175013[/C][/ROW]
[ROW][C]48[/C][C]516141[/C][C]515976.967169304[/C][C]164.032830696378[/C][/ROW]
[ROW][C]49[/C][C]501866[/C][C]490145.240052541[/C][C]11720.7599474588[/C][/ROW]
[ROW][C]50[/C][C]506174[/C][C]497625.54593258[/C][C]8548.45406742027[/C][/ROW]
[ROW][C]51[/C][C]517945[/C][C]514207.263271873[/C][C]3737.73672812723[/C][/ROW]
[ROW][C]52[/C][C]533590[/C][C]528243.859265509[/C][C]5346.14073449094[/C][/ROW]
[ROW][C]53[/C][C]528379[/C][C]519053.952991502[/C][C]9325.04700849811[/C][/ROW]
[ROW][C]54[/C][C]477580[/C][C]469646.984458202[/C][C]7933.01554179768[/C][/ROW]
[ROW][C]55[/C][C]469357[/C][C]463383.776945866[/C][C]5973.22305413405[/C][/ROW]
[ROW][C]56[/C][C]490243[/C][C]483532.281386614[/C][C]6710.71861338592[/C][/ROW]
[ROW][C]57[/C][C]492622[/C][C]496645.965314201[/C][C]-4023.96531420108[/C][/ROW]
[ROW][C]58[/C][C]507561[/C][C]504769.350514783[/C][C]2791.64948521659[/C][/ROW]
[ROW][C]59[/C][C]516922[/C][C]517047.80355179[/C][C]-125.803551789839[/C][/ROW]
[ROW][C]60[/C][C]514258[/C][C]517439.796255028[/C][C]-3181.79625502817[/C][/ROW]
[ROW][C]61[/C][C]509846[/C][C]507969.362328893[/C][C]1876.63767110696[/C][/ROW]
[ROW][C]62[/C][C]527070[/C][C]518855.550878998[/C][C]8214.44912100188[/C][/ROW]
[ROW][C]63[/C][C]541657[/C][C]542428.696117502[/C][C]-771.696117501822[/C][/ROW]
[ROW][C]64[/C][C]564591[/C][C]563863.812832528[/C][C]727.18716747174[/C][/ROW]
[ROW][C]65[/C][C]555362[/C][C]562262.185218638[/C][C]-6900.18521863758[/C][/ROW]
[ROW][C]66[/C][C]498662[/C][C]508588.61824025[/C][C]-9926.61824024975[/C][/ROW]
[ROW][C]67[/C][C]511038[/C][C]493107.919033351[/C][C]17930.0809666486[/C][/ROW]
[ROW][C]68[/C][C]525919[/C][C]522215.240172453[/C][C]3703.75982754736[/C][/ROW]
[ROW][C]69[/C][C]531673[/C][C]530504.098219177[/C][C]1168.90178082348[/C][/ROW]
[ROW][C]70[/C][C]548854[/C][C]548037.826072163[/C][C]816.173927837284[/C][/ROW]
[ROW][C]71[/C][C]560576[/C][C]560783.233191873[/C][C]-207.233191873413[/C][/ROW]
[ROW][C]72[/C][C]557274[/C][C]562451.608529845[/C][C]-5177.60852984479[/C][/ROW]
[ROW][C]73[/C][C]565742[/C][C]557174.303008842[/C][C]8567.69699115772[/C][/ROW]
[ROW][C]74[/C][C]587625[/C][C]578504.434306876[/C][C]9120.56569312373[/C][/ROW]
[ROW][C]75[/C][C]619916[/C][C]601926.038214263[/C][C]17989.9617857372[/C][/ROW]
[ROW][C]76[/C][C]625809[/C][C]641268.405096658[/C][C]-15459.4050966583[/C][/ROW]
[ROW][C]77[/C][C]619567[/C][C]632666.976793723[/C][C]-13099.9767937234[/C][/ROW]
[ROW][C]78[/C][C]572942[/C][C]577807.617367914[/C][C]-4865.6173679136[/C][/ROW]
[ROW][C]79[/C][C]572775[/C][C]583800.540002252[/C][C]-11025.5400022517[/C][/ROW]
[ROW][C]80[/C][C]574205[/C][C]589845.903545481[/C][C]-15640.9035454808[/C][/ROW]
[ROW][C]81[/C][C]579799[/C][C]581577.14490354[/C][C]-1778.14490354026[/C][/ROW]
[ROW][C]82[/C][C]590072[/C][C]590849.240980625[/C][C]-777.240980624571[/C][/ROW]
[ROW][C]83[/C][C]593408[/C][C]595278.20132796[/C][C]-1870.20132795954[/C][/ROW]
[ROW][C]84[/C][C]597141[/C][C]586164.303637146[/C][C]10976.6963628541[/C][/ROW]
[ROW][C]85[/C][C]595404[/C][C]591899.84382346[/C][C]3504.15617654042[/C][/ROW]
[ROW][C]86[/C][C]612117[/C][C]606138.636833446[/C][C]5978.36316655413[/C][/ROW]
[ROW][C]87[/C][C]628232[/C][C]627065.190734099[/C][C]1166.80926590145[/C][/ROW]
[ROW][C]88[/C][C]628884[/C][C]631547.593001707[/C][C]-2663.59300170687[/C][/ROW]
[ROW][C]89[/C][C]620735[/C][C]623731.626915996[/C][C]-2996.6269159962[/C][/ROW]
[ROW][C]90[/C][C]569028[/C][C]573655.365478397[/C][C]-4627.365478397[/C][/ROW]
[ROW][C]91[/C][C]567456[/C][C]572240.544330127[/C][C]-4784.54433012742[/C][/ROW]
[ROW][C]92[/C][C]573100[/C][C]575895.314554992[/C][C]-2795.31455499178[/C][/ROW]
[ROW][C]93[/C][C]584428[/C][C]580861.304601703[/C][C]3566.69539829658[/C][/ROW]
[ROW][C]94[/C][C]589379[/C][C]594213.338158756[/C][C]-4834.33815875649[/C][/ROW]
[ROW][C]95[/C][C]590865[/C][C]596275.863170343[/C][C]-5410.86317034275[/C][/ROW]
[ROW][C]96[/C][C]595454[/C][C]591589.685752301[/C][C]3864.31424769864[/C][/ROW]
[ROW][C]97[/C][C]594167[/C][C]587846.301036696[/C][C]6320.69896330393[/C][/ROW]
[ROW][C]98[/C][C]611324[/C][C]603155.773337722[/C][C]8168.22666227759[/C][/ROW]
[ROW][C]99[/C][C]612613[/C][C]621506.152036356[/C][C]-8893.15203635592[/C][/ROW]
[ROW][C]100[/C][C]610763[/C][C]615924.257100628[/C][C]-5161.25710062834[/C][/ROW]
[ROW][C]101[/C][C]593530[/C][C]602930.419546032[/C][C]-9400.41954603186[/C][/ROW]
[ROW][C]102[/C][C]542722[/C][C]543749.441714617[/C][C]-1027.44171461731[/C][/ROW]
[ROW][C]103[/C][C]536662[/C][C]539537.332368398[/C][C]-2875.33236839774[/C][/ROW]
[ROW][C]104[/C][C]543599[/C][C]541132.670879374[/C][C]2466.32912062609[/C][/ROW]
[ROW][C]105[/C][C]555332[/C][C]549069.288928846[/C][C]6262.71107115445[/C][/ROW]
[ROW][C]106[/C][C]560854[/C][C]557008.828482087[/C][C]3845.17151791323[/C][/ROW]
[ROW][C]107[/C][C]562325[/C][C]562492.604735262[/C][C]-167.604735261644[/C][/ROW]
[ROW][C]108[/C][C]554788[/C][C]565904.566680793[/C][C]-11116.5666807932[/C][/ROW]
[ROW][C]109[/C][C]547344[/C][C]553820.340931331[/C][C]-6476.34093133081[/C][/ROW]
[ROW][C]110[/C][C]565464[/C][C]558729.3046983[/C][C]6734.6953017005[/C][/ROW]
[ROW][C]111[/C][C]577992[/C][C]561840.966136198[/C][C]16151.0338638019[/C][/ROW]
[ROW][C]112[/C][C]579714[/C][C]569949.979532978[/C][C]9764.02046702232[/C][/ROW]
[ROW][C]113[/C][C]569323[/C][C]564895.086890541[/C][C]4427.91310945875[/C][/ROW]
[ROW][C]114[/C][C]506971[/C][C]522753.678770566[/C][C]-15782.6787705665[/C][/ROW]
[ROW][C]115[/C][C]500857[/C][C]513433.91458929[/C][C]-12576.9145892902[/C][/ROW]
[ROW][C]116[/C][C]509127[/C][C]513990.720890254[/C][C]-4863.72089025378[/C][/ROW]
[ROW][C]117[/C][C]509933[/C][C]519613.358904362[/C][C]-9680.35890436184[/C][/ROW]
[ROW][C]118[/C][C]517009[/C][C]514424.825247098[/C][C]2584.17475290247[/C][/ROW]
[ROW][C]119[/C][C]519164[/C][C]512644.632171089[/C][C]6519.36782891123[/C][/ROW]
[ROW][C]120[/C][C]512238[/C][C]510379.006761975[/C][C]1858.99323802546[/C][/ROW]
[ROW][C]121[/C][C]509239[/C][C]506604.159936185[/C][C]2634.84006381454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200516&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200516&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
tObservedFittedResiduals
13538712546150.594818376-7438.59481837589
14547612549526.817840627-1914.81784062681
15563280561809.2993608631470.7006391373
16581302578579.2210933392722.77890666062
17572273569508.4122764252764.58772357542
18518654515586.09666933067.90333069966
19520579514875.1367312675703.86326873302
20530577528751.2308865191825.76911348116
21540324541715.570993947-1391.5709939471
22547970556153.502438467-8183.50243846688
23555654555140.174404799513.82559520111
24551174534258.51268131716915.4873186833
25548604539727.8540275128876.14597248833
26563668560780.5204704282887.4795295716
27586111585190.019320966920.980679034023
28604378610305.118630191-5927.11863019061
29600991603218.514989569-2227.51498956897
30544686552071.89825581-7385.89825581003
31537034550497.365692865-13463.3656928655
32551531551790.750870123-259.750870122807
33563250560181.7587760253068.24122397474
34574761572247.5396162812513.46038371918
35580112582277.572222889-2165.5722228894
36575093569547.0152167285545.98478327179
37557560563741.683202755-6181.6832027554
38564478569575.595226241-5097.59522624081
39580523582504.640565318-1981.64056531806
40596594595361.4092084521232.59079154814
41586570587887.585026896-1317.58502689621
42536214528932.3682316247281.6317683761
43523597528786.315085992-5189.31508599175
44536535540387.63468372-3852.63468371995
45536322547485.093338285-11163.0933382852
46532638548076.181407098-15438.1814070981
47528222538802.813817501-10580.8138175013
48516141515976.967169304164.032830696378
49501866490145.24005254111720.7599474588
50506174497625.545932588548.45406742027
51517945514207.2632718733737.73672812723
52533590528243.8592655095346.14073449094
53528379519053.9529915029325.04700849811
54477580469646.9844582027933.01554179768
55469357463383.7769458665973.22305413405
56490243483532.2813866146710.71861338592
57492622496645.965314201-4023.96531420108
58507561504769.3505147832791.64948521659
59516922517047.80355179-125.803551789839
60514258517439.796255028-3181.79625502817
61509846507969.3623288931876.63767110696
62527070518855.5508789988214.44912100188
63541657542428.696117502-771.696117501822
64564591563863.812832528727.18716747174
65555362562262.185218638-6900.18521863758
66498662508588.61824025-9926.61824024975
67511038493107.91903335117930.0809666486
68525919522215.2401724533703.75982754736
69531673530504.0982191771168.90178082348
70548854548037.826072163816.173927837284
71560576560783.233191873-207.233191873413
72557274562451.608529845-5177.60852984479
73565742557174.3030088428567.69699115772
74587625578504.4343068769120.56569312373
75619916601926.03821426317989.9617857372
76625809641268.405096658-15459.4050966583
77619567632666.976793723-13099.9767937234
78572942577807.617367914-4865.6173679136
79572775583800.540002252-11025.5400022517
80574205589845.903545481-15640.9035454808
81579799581577.14490354-1778.14490354026
82590072590849.240980625-777.240980624571
83593408595278.20132796-1870.20132795954
84597141586164.30363714610976.6963628541
85595404591899.843823463504.15617654042
86612117606138.6368334465978.36316655413
87628232627065.1907340991166.80926590145
88628884631547.593001707-2663.59300170687
89620735623731.626915996-2996.6269159962
90569028573655.365478397-4627.365478397
91567456572240.544330127-4784.54433012742
92573100575895.314554992-2795.31455499178
93584428580861.3046017033566.69539829658
94589379594213.338158756-4834.33815875649
95590865596275.863170343-5410.86317034275
96595454591589.6857523013864.31424769864
97594167587846.3010366966320.69896330393
98611324603155.7733377228168.22666227759
99612613621506.152036356-8893.15203635592
100610763615924.257100628-5161.25710062834
101593530602930.419546032-9400.41954603186
102542722543749.441714617-1027.44171461731
103536662539537.332368398-2875.33236839774
104543599541132.6708793742466.32912062609
105555332549069.2889288466262.71107115445
106560854557008.8284820873845.17151791323
107562325562492.604735262-167.604735261644
108554788565904.566680793-11116.5666807932
109547344553820.340931331-6476.34093133081
110565464558729.30469836734.6953017005
111577992561840.96613619816151.0338638019
112579714569949.9795329789764.02046702232
113569323564895.0868905414427.91310945875
114506971522753.678770566-15782.6787705665
115500857513433.91458929-12576.9145892902
116509127513990.720890254-4863.72089025378
117509933519613.358904362-9680.35890436184
118517009514424.8252470982584.17475290247
119519164512644.6321710896519.36782891123
120512238510379.0067619751858.99323802546
121509239506604.1599361852634.84006381454







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
122524463.154270883510126.866862014538799.441679752
123529543.115447693512107.916011836546978.31488355
124523345.879695419501577.168016897545114.591373942
125505451.468106971478348.592790034532554.343423907
126444236.651941606410988.822933857477484.480949355
127441162.432430765401090.016912804481234.847948726
128451537.612840384404050.017270127499025.208410642
129457792.744628855402361.682001649513223.807256061
130466592.331579969402735.020129306530449.643030633
131468040.494862787395308.815893622540772.173831953
132461206.698944196379179.933609132543233.46427926
133457527.822972946365807.594178319549248.051767573

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
122 & 524463.154270883 & 510126.866862014 & 538799.441679752 \tabularnewline
123 & 529543.115447693 & 512107.916011836 & 546978.31488355 \tabularnewline
124 & 523345.879695419 & 501577.168016897 & 545114.591373942 \tabularnewline
125 & 505451.468106971 & 478348.592790034 & 532554.343423907 \tabularnewline
126 & 444236.651941606 & 410988.822933857 & 477484.480949355 \tabularnewline
127 & 441162.432430765 & 401090.016912804 & 481234.847948726 \tabularnewline
128 & 451537.612840384 & 404050.017270127 & 499025.208410642 \tabularnewline
129 & 457792.744628855 & 402361.682001649 & 513223.807256061 \tabularnewline
130 & 466592.331579969 & 402735.020129306 & 530449.643030633 \tabularnewline
131 & 468040.494862787 & 395308.815893622 & 540772.173831953 \tabularnewline
132 & 461206.698944196 & 379179.933609132 & 543233.46427926 \tabularnewline
133 & 457527.822972946 & 365807.594178319 & 549248.051767573 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200516&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]122[/C][C]524463.154270883[/C][C]510126.866862014[/C][C]538799.441679752[/C][/ROW]
[ROW][C]123[/C][C]529543.115447693[/C][C]512107.916011836[/C][C]546978.31488355[/C][/ROW]
[ROW][C]124[/C][C]523345.879695419[/C][C]501577.168016897[/C][C]545114.591373942[/C][/ROW]
[ROW][C]125[/C][C]505451.468106971[/C][C]478348.592790034[/C][C]532554.343423907[/C][/ROW]
[ROW][C]126[/C][C]444236.651941606[/C][C]410988.822933857[/C][C]477484.480949355[/C][/ROW]
[ROW][C]127[/C][C]441162.432430765[/C][C]401090.016912804[/C][C]481234.847948726[/C][/ROW]
[ROW][C]128[/C][C]451537.612840384[/C][C]404050.017270127[/C][C]499025.208410642[/C][/ROW]
[ROW][C]129[/C][C]457792.744628855[/C][C]402361.682001649[/C][C]513223.807256061[/C][/ROW]
[ROW][C]130[/C][C]466592.331579969[/C][C]402735.020129306[/C][C]530449.643030633[/C][/ROW]
[ROW][C]131[/C][C]468040.494862787[/C][C]395308.815893622[/C][C]540772.173831953[/C][/ROW]
[ROW][C]132[/C][C]461206.698944196[/C][C]379179.933609132[/C][C]543233.46427926[/C][/ROW]
[ROW][C]133[/C][C]457527.822972946[/C][C]365807.594178319[/C][C]549248.051767573[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200516&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200516&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
tForecast95% Lower Bound95% Upper Bound
122524463.154270883510126.866862014538799.441679752
123529543.115447693512107.916011836546978.31488355
124523345.879695419501577.168016897545114.591373942
125505451.468106971478348.592790034532554.343423907
126444236.651941606410988.822933857477484.480949355
127441162.432430765401090.016912804481234.847948726
128451537.612840384404050.017270127499025.208410642
129457792.744628855402361.682001649513223.807256061
130466592.331579969402735.020129306530449.643030633
131468040.494862787395308.815893622540772.173831953
132461206.698944196379179.933609132543233.46427926
133457527.822972946365807.594178319549248.051767573



Parameters (Session):
par1 = additive ; par2 = 12 ;
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')