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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 03 Aug 2012 17:56:19 -0400
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/Aug/03/t1344031486ioqkdgfsxm4n6l4.htm/, Retrieved Mon, 29 Apr 2024 19:00:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169012, Retrieved Mon, 29 Apr 2024 19:00:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsyasmien naciri
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-08-03 21:56:19] [d06e8713ea83045a022ab0926c74dd0b] [Current]
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Dataseries X:
540
520
550
440
570
560
600
620
690
600
570
710
600
450
530
400
560
460
610
550
580
650
640
760
550
460
510
370
530
410
580
550
490
700
630
720
540
500
450
370
490
440
600
580
500
670
620
800
640
390
390
390
460
460
620
570
510
640
590
850
670
390
410
340
470
540
680
670
540
630
560
800
610
490
440
330
490
590
690
650
480
690
540
830
690
500
460
310
490
470
710
710
540
700
520
810
690
510
390
270
530
510
670
770
570
640
480
830




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169012&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169012&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169012&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0090380623970487
beta1
gamma0.930857409776195

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0090380623970487 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.930857409776195 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169012&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]0.0090380623970487[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.930857409776195[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169012&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169012&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
alpha0.0090380623970487
beta1
gamma0.930857409776195







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13600622.80622118194-22.8062211819403
14450466.75930383748-16.7593038374799
15530554.089874022441-24.0898740224409
16400417.555263048804-17.5552630488042
17560575.647261008679-15.6472610086794
18460465.596735775854-5.59673577585369
19610583.06924008450226.9307599154982
20550599.531021819852-49.5310218198521
21580666.441903176397-86.4419031763966
22650576.64788150279173.3521184972092
23640546.58776717788693.4122328221144
24760683.60286233945776.3971376605434
25550559.906075180639-9.90607518063928
26460420.03645945915239.9635405408483
27510496.27135958534713.7286404146528
28370375.490577030587-5.49057703058702
29530526.3671150872533.63288491274704
30410433.106621839214-23.106621839214
31580572.898029945877.10197005412977
32550522.78775362144427.212246378556
33490556.215890298593-66.2158902985934
34700612.96734163560187.0326583643995
35630604.12827804816525.8717219518345
36720720.933264483809-0.933264483809239
37540526.80021326126513.1997867387352
38500437.93679547556662.0632045244338
39450489.129643594794-39.1296435947936
40370356.10998933468413.8900106653165
41490510.382738079639-20.3827380796393
42440397.11027918871842.889720811282
43600561.18840769292338.8115923070766
44580532.65582344242547.3441765575749
45500483.24846731646316.7515326835372
46670680.993940656754-10.9939406567544
47620618.3595474364571.64045256354325
48800711.13523262044488.8647673795565
49640535.277427260077104.722572739923
50390495.442933326955-105.442933326955
51390453.127400325849-63.127400325849
52390369.65560099009120.3443990099092
53460493.821419598534-33.8214195985341
54460439.46950435041220.5304956495885
55620601.48133114147918.5186688585211
56570581.186619727135-11.1866197271349
57510502.5863480740557.41365192594475
58640676.038795318603-36.0387953186029
59590624.316646503993-34.3166465039925
60850797.69046182331752.3095381766826
61670634.27903022239835.7209697776022
62390398.100390155847-8.10039015584721
63410395.30962753303314.6903724669666
64340389.828845915553-49.8288459155531
65470463.132616027716.86738397229027
66540459.22832996080380.7716700391969
67680621.06733831741758.9326616825829
68670574.45941806437395.5405819356266
69540515.19451392392624.8054860760735
70630652.599848188001-22.5998481880006
71560604.064933624598-44.0649336245981
72800865.166350175554-65.1663501755544
73610683.099965422565-73.0999654225645
74490399.6672258724990.3327741275099
75440420.52519451149519.4748054885045
76330354.753176357102-24.7531763571017
77490486.4197098518193.58029014818146
78590554.81188871320835.1881112867925
79690703.261466297553-13.2614662975529
80650690.113932622793-40.1139326227926
81480559.08865522087-79.0886552208702
82690653.83359576551236.1664042344884
83540582.731111602379-42.7311116023785
84830831.461883744499-1.461883744499
85690635.77323523795154.2267647620491
86500500.000706207869-0.000706207868631736
87460452.677907135177.32209286482993
88310342.106251407872-32.1062514078719
89490503.892825713042-13.8928257130423
90470602.946757581896-132.946757581896
91710704.5752550457925.42474495420822
92710663.30715777284646.6928422271543
93540492.75329066290847.2467093370923
94700697.5951514950582.40484850494215
95520550.558804951054-30.5588049510542
96810840.418095997154-30.4180959971535
97690693.062774804205-3.06277480420533
98510503.7925659552996.20743404470136
99390461.989336724576-71.989336724576
100270312.568516371397-42.5685163713974
101530489.06347306937140.9365269306289
102510477.12515669505332.8748433049473
103670706.776411035694-36.7764110356936
104770702.49847427993367.501525720067
105570533.10162512925436.8983748707461
106640694.793458280429-54.7934582804289
107480517.330399150326-37.3303991503265
108830802.90546233452427.0945376654756

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 600 & 622.80622118194 & -22.8062211819403 \tabularnewline
14 & 450 & 466.75930383748 & -16.7593038374799 \tabularnewline
15 & 530 & 554.089874022441 & -24.0898740224409 \tabularnewline
16 & 400 & 417.555263048804 & -17.5552630488042 \tabularnewline
17 & 560 & 575.647261008679 & -15.6472610086794 \tabularnewline
18 & 460 & 465.596735775854 & -5.59673577585369 \tabularnewline
19 & 610 & 583.069240084502 & 26.9307599154982 \tabularnewline
20 & 550 & 599.531021819852 & -49.5310218198521 \tabularnewline
21 & 580 & 666.441903176397 & -86.4419031763966 \tabularnewline
22 & 650 & 576.647881502791 & 73.3521184972092 \tabularnewline
23 & 640 & 546.587767177886 & 93.4122328221144 \tabularnewline
24 & 760 & 683.602862339457 & 76.3971376605434 \tabularnewline
25 & 550 & 559.906075180639 & -9.90607518063928 \tabularnewline
26 & 460 & 420.036459459152 & 39.9635405408483 \tabularnewline
27 & 510 & 496.271359585347 & 13.7286404146528 \tabularnewline
28 & 370 & 375.490577030587 & -5.49057703058702 \tabularnewline
29 & 530 & 526.367115087253 & 3.63288491274704 \tabularnewline
30 & 410 & 433.106621839214 & -23.106621839214 \tabularnewline
31 & 580 & 572.89802994587 & 7.10197005412977 \tabularnewline
32 & 550 & 522.787753621444 & 27.212246378556 \tabularnewline
33 & 490 & 556.215890298593 & -66.2158902985934 \tabularnewline
34 & 700 & 612.967341635601 & 87.0326583643995 \tabularnewline
35 & 630 & 604.128278048165 & 25.8717219518345 \tabularnewline
36 & 720 & 720.933264483809 & -0.933264483809239 \tabularnewline
37 & 540 & 526.800213261265 & 13.1997867387352 \tabularnewline
38 & 500 & 437.936795475566 & 62.0632045244338 \tabularnewline
39 & 450 & 489.129643594794 & -39.1296435947936 \tabularnewline
40 & 370 & 356.109989334684 & 13.8900106653165 \tabularnewline
41 & 490 & 510.382738079639 & -20.3827380796393 \tabularnewline
42 & 440 & 397.110279188718 & 42.889720811282 \tabularnewline
43 & 600 & 561.188407692923 & 38.8115923070766 \tabularnewline
44 & 580 & 532.655823442425 & 47.3441765575749 \tabularnewline
45 & 500 & 483.248467316463 & 16.7515326835372 \tabularnewline
46 & 670 & 680.993940656754 & -10.9939406567544 \tabularnewline
47 & 620 & 618.359547436457 & 1.64045256354325 \tabularnewline
48 & 800 & 711.135232620444 & 88.8647673795565 \tabularnewline
49 & 640 & 535.277427260077 & 104.722572739923 \tabularnewline
50 & 390 & 495.442933326955 & -105.442933326955 \tabularnewline
51 & 390 & 453.127400325849 & -63.127400325849 \tabularnewline
52 & 390 & 369.655600990091 & 20.3443990099092 \tabularnewline
53 & 460 & 493.821419598534 & -33.8214195985341 \tabularnewline
54 & 460 & 439.469504350412 & 20.5304956495885 \tabularnewline
55 & 620 & 601.481331141479 & 18.5186688585211 \tabularnewline
56 & 570 & 581.186619727135 & -11.1866197271349 \tabularnewline
57 & 510 & 502.586348074055 & 7.41365192594475 \tabularnewline
58 & 640 & 676.038795318603 & -36.0387953186029 \tabularnewline
59 & 590 & 624.316646503993 & -34.3166465039925 \tabularnewline
60 & 850 & 797.690461823317 & 52.3095381766826 \tabularnewline
61 & 670 & 634.279030222398 & 35.7209697776022 \tabularnewline
62 & 390 & 398.100390155847 & -8.10039015584721 \tabularnewline
63 & 410 & 395.309627533033 & 14.6903724669666 \tabularnewline
64 & 340 & 389.828845915553 & -49.8288459155531 \tabularnewline
65 & 470 & 463.13261602771 & 6.86738397229027 \tabularnewline
66 & 540 & 459.228329960803 & 80.7716700391969 \tabularnewline
67 & 680 & 621.067338317417 & 58.9326616825829 \tabularnewline
68 & 670 & 574.459418064373 & 95.5405819356266 \tabularnewline
69 & 540 & 515.194513923926 & 24.8054860760735 \tabularnewline
70 & 630 & 652.599848188001 & -22.5998481880006 \tabularnewline
71 & 560 & 604.064933624598 & -44.0649336245981 \tabularnewline
72 & 800 & 865.166350175554 & -65.1663501755544 \tabularnewline
73 & 610 & 683.099965422565 & -73.0999654225645 \tabularnewline
74 & 490 & 399.66722587249 & 90.3327741275099 \tabularnewline
75 & 440 & 420.525194511495 & 19.4748054885045 \tabularnewline
76 & 330 & 354.753176357102 & -24.7531763571017 \tabularnewline
77 & 490 & 486.419709851819 & 3.58029014818146 \tabularnewline
78 & 590 & 554.811888713208 & 35.1881112867925 \tabularnewline
79 & 690 & 703.261466297553 & -13.2614662975529 \tabularnewline
80 & 650 & 690.113932622793 & -40.1139326227926 \tabularnewline
81 & 480 & 559.08865522087 & -79.0886552208702 \tabularnewline
82 & 690 & 653.833595765512 & 36.1664042344884 \tabularnewline
83 & 540 & 582.731111602379 & -42.7311116023785 \tabularnewline
84 & 830 & 831.461883744499 & -1.461883744499 \tabularnewline
85 & 690 & 635.773235237951 & 54.2267647620491 \tabularnewline
86 & 500 & 500.000706207869 & -0.000706207868631736 \tabularnewline
87 & 460 & 452.67790713517 & 7.32209286482993 \tabularnewline
88 & 310 & 342.106251407872 & -32.1062514078719 \tabularnewline
89 & 490 & 503.892825713042 & -13.8928257130423 \tabularnewline
90 & 470 & 602.946757581896 & -132.946757581896 \tabularnewline
91 & 710 & 704.575255045792 & 5.42474495420822 \tabularnewline
92 & 710 & 663.307157772846 & 46.6928422271543 \tabularnewline
93 & 540 & 492.753290662908 & 47.2467093370923 \tabularnewline
94 & 700 & 697.595151495058 & 2.40484850494215 \tabularnewline
95 & 520 & 550.558804951054 & -30.5588049510542 \tabularnewline
96 & 810 & 840.418095997154 & -30.4180959971535 \tabularnewline
97 & 690 & 693.062774804205 & -3.06277480420533 \tabularnewline
98 & 510 & 503.792565955299 & 6.20743404470136 \tabularnewline
99 & 390 & 461.989336724576 & -71.989336724576 \tabularnewline
100 & 270 & 312.568516371397 & -42.5685163713974 \tabularnewline
101 & 530 & 489.063473069371 & 40.9365269306289 \tabularnewline
102 & 510 & 477.125156695053 & 32.8748433049473 \tabularnewline
103 & 670 & 706.776411035694 & -36.7764110356936 \tabularnewline
104 & 770 & 702.498474279933 & 67.501525720067 \tabularnewline
105 & 570 & 533.101625129254 & 36.8983748707461 \tabularnewline
106 & 640 & 694.793458280429 & -54.7934582804289 \tabularnewline
107 & 480 & 517.330399150326 & -37.3303991503265 \tabularnewline
108 & 830 & 802.905462334524 & 27.0945376654756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169012&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]600[/C][C]622.80622118194[/C][C]-22.8062211819403[/C][/ROW]
[ROW][C]14[/C][C]450[/C][C]466.75930383748[/C][C]-16.7593038374799[/C][/ROW]
[ROW][C]15[/C][C]530[/C][C]554.089874022441[/C][C]-24.0898740224409[/C][/ROW]
[ROW][C]16[/C][C]400[/C][C]417.555263048804[/C][C]-17.5552630488042[/C][/ROW]
[ROW][C]17[/C][C]560[/C][C]575.647261008679[/C][C]-15.6472610086794[/C][/ROW]
[ROW][C]18[/C][C]460[/C][C]465.596735775854[/C][C]-5.59673577585369[/C][/ROW]
[ROW][C]19[/C][C]610[/C][C]583.069240084502[/C][C]26.9307599154982[/C][/ROW]
[ROW][C]20[/C][C]550[/C][C]599.531021819852[/C][C]-49.5310218198521[/C][/ROW]
[ROW][C]21[/C][C]580[/C][C]666.441903176397[/C][C]-86.4419031763966[/C][/ROW]
[ROW][C]22[/C][C]650[/C][C]576.647881502791[/C][C]73.3521184972092[/C][/ROW]
[ROW][C]23[/C][C]640[/C][C]546.587767177886[/C][C]93.4122328221144[/C][/ROW]
[ROW][C]24[/C][C]760[/C][C]683.602862339457[/C][C]76.3971376605434[/C][/ROW]
[ROW][C]25[/C][C]550[/C][C]559.906075180639[/C][C]-9.90607518063928[/C][/ROW]
[ROW][C]26[/C][C]460[/C][C]420.036459459152[/C][C]39.9635405408483[/C][/ROW]
[ROW][C]27[/C][C]510[/C][C]496.271359585347[/C][C]13.7286404146528[/C][/ROW]
[ROW][C]28[/C][C]370[/C][C]375.490577030587[/C][C]-5.49057703058702[/C][/ROW]
[ROW][C]29[/C][C]530[/C][C]526.367115087253[/C][C]3.63288491274704[/C][/ROW]
[ROW][C]30[/C][C]410[/C][C]433.106621839214[/C][C]-23.106621839214[/C][/ROW]
[ROW][C]31[/C][C]580[/C][C]572.89802994587[/C][C]7.10197005412977[/C][/ROW]
[ROW][C]32[/C][C]550[/C][C]522.787753621444[/C][C]27.212246378556[/C][/ROW]
[ROW][C]33[/C][C]490[/C][C]556.215890298593[/C][C]-66.2158902985934[/C][/ROW]
[ROW][C]34[/C][C]700[/C][C]612.967341635601[/C][C]87.0326583643995[/C][/ROW]
[ROW][C]35[/C][C]630[/C][C]604.128278048165[/C][C]25.8717219518345[/C][/ROW]
[ROW][C]36[/C][C]720[/C][C]720.933264483809[/C][C]-0.933264483809239[/C][/ROW]
[ROW][C]37[/C][C]540[/C][C]526.800213261265[/C][C]13.1997867387352[/C][/ROW]
[ROW][C]38[/C][C]500[/C][C]437.936795475566[/C][C]62.0632045244338[/C][/ROW]
[ROW][C]39[/C][C]450[/C][C]489.129643594794[/C][C]-39.1296435947936[/C][/ROW]
[ROW][C]40[/C][C]370[/C][C]356.109989334684[/C][C]13.8900106653165[/C][/ROW]
[ROW][C]41[/C][C]490[/C][C]510.382738079639[/C][C]-20.3827380796393[/C][/ROW]
[ROW][C]42[/C][C]440[/C][C]397.110279188718[/C][C]42.889720811282[/C][/ROW]
[ROW][C]43[/C][C]600[/C][C]561.188407692923[/C][C]38.8115923070766[/C][/ROW]
[ROW][C]44[/C][C]580[/C][C]532.655823442425[/C][C]47.3441765575749[/C][/ROW]
[ROW][C]45[/C][C]500[/C][C]483.248467316463[/C][C]16.7515326835372[/C][/ROW]
[ROW][C]46[/C][C]670[/C][C]680.993940656754[/C][C]-10.9939406567544[/C][/ROW]
[ROW][C]47[/C][C]620[/C][C]618.359547436457[/C][C]1.64045256354325[/C][/ROW]
[ROW][C]48[/C][C]800[/C][C]711.135232620444[/C][C]88.8647673795565[/C][/ROW]
[ROW][C]49[/C][C]640[/C][C]535.277427260077[/C][C]104.722572739923[/C][/ROW]
[ROW][C]50[/C][C]390[/C][C]495.442933326955[/C][C]-105.442933326955[/C][/ROW]
[ROW][C]51[/C][C]390[/C][C]453.127400325849[/C][C]-63.127400325849[/C][/ROW]
[ROW][C]52[/C][C]390[/C][C]369.655600990091[/C][C]20.3443990099092[/C][/ROW]
[ROW][C]53[/C][C]460[/C][C]493.821419598534[/C][C]-33.8214195985341[/C][/ROW]
[ROW][C]54[/C][C]460[/C][C]439.469504350412[/C][C]20.5304956495885[/C][/ROW]
[ROW][C]55[/C][C]620[/C][C]601.481331141479[/C][C]18.5186688585211[/C][/ROW]
[ROW][C]56[/C][C]570[/C][C]581.186619727135[/C][C]-11.1866197271349[/C][/ROW]
[ROW][C]57[/C][C]510[/C][C]502.586348074055[/C][C]7.41365192594475[/C][/ROW]
[ROW][C]58[/C][C]640[/C][C]676.038795318603[/C][C]-36.0387953186029[/C][/ROW]
[ROW][C]59[/C][C]590[/C][C]624.316646503993[/C][C]-34.3166465039925[/C][/ROW]
[ROW][C]60[/C][C]850[/C][C]797.690461823317[/C][C]52.3095381766826[/C][/ROW]
[ROW][C]61[/C][C]670[/C][C]634.279030222398[/C][C]35.7209697776022[/C][/ROW]
[ROW][C]62[/C][C]390[/C][C]398.100390155847[/C][C]-8.10039015584721[/C][/ROW]
[ROW][C]63[/C][C]410[/C][C]395.309627533033[/C][C]14.6903724669666[/C][/ROW]
[ROW][C]64[/C][C]340[/C][C]389.828845915553[/C][C]-49.8288459155531[/C][/ROW]
[ROW][C]65[/C][C]470[/C][C]463.13261602771[/C][C]6.86738397229027[/C][/ROW]
[ROW][C]66[/C][C]540[/C][C]459.228329960803[/C][C]80.7716700391969[/C][/ROW]
[ROW][C]67[/C][C]680[/C][C]621.067338317417[/C][C]58.9326616825829[/C][/ROW]
[ROW][C]68[/C][C]670[/C][C]574.459418064373[/C][C]95.5405819356266[/C][/ROW]
[ROW][C]69[/C][C]540[/C][C]515.194513923926[/C][C]24.8054860760735[/C][/ROW]
[ROW][C]70[/C][C]630[/C][C]652.599848188001[/C][C]-22.5998481880006[/C][/ROW]
[ROW][C]71[/C][C]560[/C][C]604.064933624598[/C][C]-44.0649336245981[/C][/ROW]
[ROW][C]72[/C][C]800[/C][C]865.166350175554[/C][C]-65.1663501755544[/C][/ROW]
[ROW][C]73[/C][C]610[/C][C]683.099965422565[/C][C]-73.0999654225645[/C][/ROW]
[ROW][C]74[/C][C]490[/C][C]399.66722587249[/C][C]90.3327741275099[/C][/ROW]
[ROW][C]75[/C][C]440[/C][C]420.525194511495[/C][C]19.4748054885045[/C][/ROW]
[ROW][C]76[/C][C]330[/C][C]354.753176357102[/C][C]-24.7531763571017[/C][/ROW]
[ROW][C]77[/C][C]490[/C][C]486.419709851819[/C][C]3.58029014818146[/C][/ROW]
[ROW][C]78[/C][C]590[/C][C]554.811888713208[/C][C]35.1881112867925[/C][/ROW]
[ROW][C]79[/C][C]690[/C][C]703.261466297553[/C][C]-13.2614662975529[/C][/ROW]
[ROW][C]80[/C][C]650[/C][C]690.113932622793[/C][C]-40.1139326227926[/C][/ROW]
[ROW][C]81[/C][C]480[/C][C]559.08865522087[/C][C]-79.0886552208702[/C][/ROW]
[ROW][C]82[/C][C]690[/C][C]653.833595765512[/C][C]36.1664042344884[/C][/ROW]
[ROW][C]83[/C][C]540[/C][C]582.731111602379[/C][C]-42.7311116023785[/C][/ROW]
[ROW][C]84[/C][C]830[/C][C]831.461883744499[/C][C]-1.461883744499[/C][/ROW]
[ROW][C]85[/C][C]690[/C][C]635.773235237951[/C][C]54.2267647620491[/C][/ROW]
[ROW][C]86[/C][C]500[/C][C]500.000706207869[/C][C]-0.000706207868631736[/C][/ROW]
[ROW][C]87[/C][C]460[/C][C]452.67790713517[/C][C]7.32209286482993[/C][/ROW]
[ROW][C]88[/C][C]310[/C][C]342.106251407872[/C][C]-32.1062514078719[/C][/ROW]
[ROW][C]89[/C][C]490[/C][C]503.892825713042[/C][C]-13.8928257130423[/C][/ROW]
[ROW][C]90[/C][C]470[/C][C]602.946757581896[/C][C]-132.946757581896[/C][/ROW]
[ROW][C]91[/C][C]710[/C][C]704.575255045792[/C][C]5.42474495420822[/C][/ROW]
[ROW][C]92[/C][C]710[/C][C]663.307157772846[/C][C]46.6928422271543[/C][/ROW]
[ROW][C]93[/C][C]540[/C][C]492.753290662908[/C][C]47.2467093370923[/C][/ROW]
[ROW][C]94[/C][C]700[/C][C]697.595151495058[/C][C]2.40484850494215[/C][/ROW]
[ROW][C]95[/C][C]520[/C][C]550.558804951054[/C][C]-30.5588049510542[/C][/ROW]
[ROW][C]96[/C][C]810[/C][C]840.418095997154[/C][C]-30.4180959971535[/C][/ROW]
[ROW][C]97[/C][C]690[/C][C]693.062774804205[/C][C]-3.06277480420533[/C][/ROW]
[ROW][C]98[/C][C]510[/C][C]503.792565955299[/C][C]6.20743404470136[/C][/ROW]
[ROW][C]99[/C][C]390[/C][C]461.989336724576[/C][C]-71.989336724576[/C][/ROW]
[ROW][C]100[/C][C]270[/C][C]312.568516371397[/C][C]-42.5685163713974[/C][/ROW]
[ROW][C]101[/C][C]530[/C][C]489.063473069371[/C][C]40.9365269306289[/C][/ROW]
[ROW][C]102[/C][C]510[/C][C]477.125156695053[/C][C]32.8748433049473[/C][/ROW]
[ROW][C]103[/C][C]670[/C][C]706.776411035694[/C][C]-36.7764110356936[/C][/ROW]
[ROW][C]104[/C][C]770[/C][C]702.498474279933[/C][C]67.501525720067[/C][/ROW]
[ROW][C]105[/C][C]570[/C][C]533.101625129254[/C][C]36.8983748707461[/C][/ROW]
[ROW][C]106[/C][C]640[/C][C]694.793458280429[/C][C]-54.7934582804289[/C][/ROW]
[ROW][C]107[/C][C]480[/C][C]517.330399150326[/C][C]-37.3303991503265[/C][/ROW]
[ROW][C]108[/C][C]830[/C][C]802.905462334524[/C][C]27.0945376654756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169012&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169012&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
13600622.80622118194-22.8062211819403
14450466.75930383748-16.7593038374799
15530554.089874022441-24.0898740224409
16400417.555263048804-17.5552630488042
17560575.647261008679-15.6472610086794
18460465.596735775854-5.59673577585369
19610583.06924008450226.9307599154982
20550599.531021819852-49.5310218198521
21580666.441903176397-86.4419031763966
22650576.64788150279173.3521184972092
23640546.58776717788693.4122328221144
24760683.60286233945776.3971376605434
25550559.906075180639-9.90607518063928
26460420.03645945915239.9635405408483
27510496.27135958534713.7286404146528
28370375.490577030587-5.49057703058702
29530526.3671150872533.63288491274704
30410433.106621839214-23.106621839214
31580572.898029945877.10197005412977
32550522.78775362144427.212246378556
33490556.215890298593-66.2158902985934
34700612.96734163560187.0326583643995
35630604.12827804816525.8717219518345
36720720.933264483809-0.933264483809239
37540526.80021326126513.1997867387352
38500437.93679547556662.0632045244338
39450489.129643594794-39.1296435947936
40370356.10998933468413.8900106653165
41490510.382738079639-20.3827380796393
42440397.11027918871842.889720811282
43600561.18840769292338.8115923070766
44580532.65582344242547.3441765575749
45500483.24846731646316.7515326835372
46670680.993940656754-10.9939406567544
47620618.3595474364571.64045256354325
48800711.13523262044488.8647673795565
49640535.277427260077104.722572739923
50390495.442933326955-105.442933326955
51390453.127400325849-63.127400325849
52390369.65560099009120.3443990099092
53460493.821419598534-33.8214195985341
54460439.46950435041220.5304956495885
55620601.48133114147918.5186688585211
56570581.186619727135-11.1866197271349
57510502.5863480740557.41365192594475
58640676.038795318603-36.0387953186029
59590624.316646503993-34.3166465039925
60850797.69046182331752.3095381766826
61670634.27903022239835.7209697776022
62390398.100390155847-8.10039015584721
63410395.30962753303314.6903724669666
64340389.828845915553-49.8288459155531
65470463.132616027716.86738397229027
66540459.22832996080380.7716700391969
67680621.06733831741758.9326616825829
68670574.45941806437395.5405819356266
69540515.19451392392624.8054860760735
70630652.599848188001-22.5998481880006
71560604.064933624598-44.0649336245981
72800865.166350175554-65.1663501755544
73610683.099965422565-73.0999654225645
74490399.6672258724990.3327741275099
75440420.52519451149519.4748054885045
76330354.753176357102-24.7531763571017
77490486.4197098518193.58029014818146
78590554.81188871320835.1881112867925
79690703.261466297553-13.2614662975529
80650690.113932622793-40.1139326227926
81480559.08865522087-79.0886552208702
82690653.83359576551236.1664042344884
83540582.731111602379-42.7311116023785
84830831.461883744499-1.461883744499
85690635.77323523795154.2267647620491
86500500.000706207869-0.000706207868631736
87460452.677907135177.32209286482993
88310342.106251407872-32.1062514078719
89490503.892825713042-13.8928257130423
90470602.946757581896-132.946757581896
91710704.5752550457925.42474495420822
92710663.30715777284646.6928422271543
93540492.75329066290847.2467093370923
94700697.5951514950582.40484850494215
95520550.558804951054-30.5588049510542
96810840.418095997154-30.4180959971535
97690693.062774804205-3.06277480420533
98510503.7925659552996.20743404470136
99390461.989336724576-71.989336724576
100270312.568516371397-42.5685163713974
101530489.06347306937140.9365269306289
102510477.12515669505332.8748433049473
103670706.776411035694-36.7764110356936
104770702.49847427993367.501525720067
105570533.10162512925436.8983748707461
106640694.793458280429-54.7934582804289
107480517.330399150326-37.3303991503265
108830802.90546233452427.0945376654756







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109681.794529837781596.06683793283767.522221742732
110502.698871308007416.962385863259588.435356752755
111389.638898930979303.889579027172475.388218834786
112269.614840916897183.858754539005355.370927294789
113521.114237660563435.131977990969607.096497330156
114501.865693232081415.708910139592588.022476324571
115665.008555412707578.062477355271751.954633470144
116756.488384306771668.420987213724844.555781399818
117560.281482315763472.741102951594647.821861679931
118635.367878078183546.51212529631724.223630860055
119476.409708257021388.371213691706564.448202822335
120817.581271559574591.1226114539451044.0399316652

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 681.794529837781 & 596.06683793283 & 767.522221742732 \tabularnewline
110 & 502.698871308007 & 416.962385863259 & 588.435356752755 \tabularnewline
111 & 389.638898930979 & 303.889579027172 & 475.388218834786 \tabularnewline
112 & 269.614840916897 & 183.858754539005 & 355.370927294789 \tabularnewline
113 & 521.114237660563 & 435.131977990969 & 607.096497330156 \tabularnewline
114 & 501.865693232081 & 415.708910139592 & 588.022476324571 \tabularnewline
115 & 665.008555412707 & 578.062477355271 & 751.954633470144 \tabularnewline
116 & 756.488384306771 & 668.420987213724 & 844.555781399818 \tabularnewline
117 & 560.281482315763 & 472.741102951594 & 647.821861679931 \tabularnewline
118 & 635.367878078183 & 546.51212529631 & 724.223630860055 \tabularnewline
119 & 476.409708257021 & 388.371213691706 & 564.448202822335 \tabularnewline
120 & 817.581271559574 & 591.122611453945 & 1044.0399316652 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169012&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]109[/C][C]681.794529837781[/C][C]596.06683793283[/C][C]767.522221742732[/C][/ROW]
[ROW][C]110[/C][C]502.698871308007[/C][C]416.962385863259[/C][C]588.435356752755[/C][/ROW]
[ROW][C]111[/C][C]389.638898930979[/C][C]303.889579027172[/C][C]475.388218834786[/C][/ROW]
[ROW][C]112[/C][C]269.614840916897[/C][C]183.858754539005[/C][C]355.370927294789[/C][/ROW]
[ROW][C]113[/C][C]521.114237660563[/C][C]435.131977990969[/C][C]607.096497330156[/C][/ROW]
[ROW][C]114[/C][C]501.865693232081[/C][C]415.708910139592[/C][C]588.022476324571[/C][/ROW]
[ROW][C]115[/C][C]665.008555412707[/C][C]578.062477355271[/C][C]751.954633470144[/C][/ROW]
[ROW][C]116[/C][C]756.488384306771[/C][C]668.420987213724[/C][C]844.555781399818[/C][/ROW]
[ROW][C]117[/C][C]560.281482315763[/C][C]472.741102951594[/C][C]647.821861679931[/C][/ROW]
[ROW][C]118[/C][C]635.367878078183[/C][C]546.51212529631[/C][C]724.223630860055[/C][/ROW]
[ROW][C]119[/C][C]476.409708257021[/C][C]388.371213691706[/C][C]564.448202822335[/C][/ROW]
[ROW][C]120[/C][C]817.581271559574[/C][C]591.122611453945[/C][C]1044.0399316652[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169012&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169012&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
109681.794529837781596.06683793283767.522221742732
110502.698871308007416.962385863259588.435356752755
111389.638898930979303.889579027172475.388218834786
112269.614840916897183.858754539005355.370927294789
113521.114237660563435.131977990969607.096497330156
114501.865693232081415.708910139592588.022476324571
115665.008555412707578.062477355271751.954633470144
116756.488384306771668.420987213724844.555781399818
117560.281482315763472.741102951594647.821861679931
118635.367878078183546.51212529631724.223630860055
119476.409708257021388.371213691706564.448202822335
120817.581271559574591.1226114539451044.0399316652



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')