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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 computationMon, 23 Nov 2015 21:32:21 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/23/t14483144614so4n33difbmcx4.htm/, Retrieved Tue, 14 May 2024 13:42:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283983, Retrieved Tue, 14 May 2024 13:42:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-23 21:32:21] [4535d628e97572fda841f25b347e529f] [Current]
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Dataseries X:
340,7
343,5
345,3
346,9
349
351,4
353
355
360,1
364,7
366,5
369
369,9
370,8
374,5
378,4
381,3
383,5
387,6
391,7
395,4
399,3
403,3
406,6
410,5
413,5
418,7
421,7
422,8
425,8
427,6
431
434,3
437,6
440,4
443,5
446,2
446,2
449,7
454,2
458,4
461,1
464
466,2
468,7
471,8
474,9
477,5
480
482,8
485,7
488,5
492
495,1
498,5
502,2
502,1
510
515
520,4
525,2
530,1
534,5
538,5
544,4
548,4
551,9
554,9
558,1
561,3
564,4
567
568,7
570,9
572,5
574,6
577,1
580,9
583,3
586,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283983&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283983&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283983&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.21927075638506
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.21927075638506 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283983&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.21927075638506[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283983&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283983&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
alpha1
beta0.21927075638506
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3345.3346.3-1
4346.9347.880729243615-0.980729243614974
5349349.265684000559-0.265684000558508
6351.4351.3074272687970.0925727312032905
7353353.727725761588-0.727725761588204
8355355.168156783404-0.168156783403901
9360.1357.1312849183162.96871508168437
10364.7362.8822373197681.81776268023162
11366.5367.880819517591-1.38081951759125
12369369.378046177538-0.378046177537783
13369.9371.795151706241-1.8951517062406
14370.8372.279600358149-1.47960035814873
15374.5372.855167268471.64483273153013
16378.4376.9158309856391.48416901436059
17381.3381.1412658480210.158734151978535
18383.5384.07607160559-0.576071605590016
19387.6386.14975594891.45024405109973
20391.7390.5677520589281.13224794107208
21395.4394.9160209213820.483979078617836
22399.3398.7221433800250.577856619974796
23403.3402.7488504381690.551149561830755
24406.6406.869701419473-0.269701419473165
25410.5410.1105637852270.389436214772843
26413.5414.095955758604-0.595955758604134
27418.7416.9652800886431.73471991135699
28421.7422.545653435722-0.845653435722454
29422.8425.360226367232-2.56022636723196
30425.8425.898843595172-0.0988435951720135
31427.6428.877170085295-1.27717008529481
32431430.397124034660.602875965340104
33434.3433.9293171035860.370682896413655
34437.6437.3105970226620.289402977338
35440.4440.674054632403-0.274054632403022
36443.5443.4139624658650.0860375341349027
37446.2446.532827981052-0.332827981052446
38446.2449.159848537901-2.95984853790094
39449.7448.510840310211.18915968978985
40454.2452.2715882548531.928411745147
41458.4457.1944325568331.20556744316679
42461.1461.65877824197-0.558778241969549
43464464.236254514201-0.236254514201448
44466.2467.084450808173-0.884450808173085
45468.7469.09051661048-0.390516610479608
46471.8471.5048877379190.295112262081204
47474.9474.6695972268440.230402773156129
48477.5477.820117817187-0.320117817186997
49480480.34992534128-0.349925341280084
50482.8482.7731969470190.0268030529807106
51485.7485.579074072720.120925927280155
52488.5488.505589592261-0.00558959226106026
53492491.3043639581380.69563604186186
54495.1494.9568965992060.143103400794132
55498.5498.0882749901390.411725009860675
56502.2501.5785542444740.621445755525883
57502.1505.414819125341-3.31481912534048
58510504.5879762284475.41202377155253
59515513.674674774411.32532522559029
60520.4518.9652798390811.43472016091891
61525.2524.6798720139670.520127986033344
62530.1529.5939208708810.506079129118689
63534.5534.604889224314-0.104889224313865
64538.5538.981890084762-0.481890084761858
65544.4542.8762256813821.52377431861828
66548.4549.110344828785-0.710344828785196
67551.9552.954586980883-1.0545869808833
68554.9556.223346895911-1.32334689591119
69558.1558.933175621085-0.83317562108482
70561.3561.950484572448-0.650484572448136
71564.4565.00785232823-0.607852328230479
72567567.974568088449-0.974568088449018
73568.7570.360873806546-1.66087380654596
74570.9571.696692750725-0.796692750724674
75572.5573.722001328667-1.22200132866669
76574.6575.054052173026-0.454052173026412
77577.1577.0544918096090.0455081903913879
78580.9579.5644704249371.33552957506254
79583.3583.657313005036-0.357313005036076
80586.5585.9789647121560.521035287844484

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 345.3 & 346.3 & -1 \tabularnewline
4 & 346.9 & 347.880729243615 & -0.980729243614974 \tabularnewline
5 & 349 & 349.265684000559 & -0.265684000558508 \tabularnewline
6 & 351.4 & 351.307427268797 & 0.0925727312032905 \tabularnewline
7 & 353 & 353.727725761588 & -0.727725761588204 \tabularnewline
8 & 355 & 355.168156783404 & -0.168156783403901 \tabularnewline
9 & 360.1 & 357.131284918316 & 2.96871508168437 \tabularnewline
10 & 364.7 & 362.882237319768 & 1.81776268023162 \tabularnewline
11 & 366.5 & 367.880819517591 & -1.38081951759125 \tabularnewline
12 & 369 & 369.378046177538 & -0.378046177537783 \tabularnewline
13 & 369.9 & 371.795151706241 & -1.8951517062406 \tabularnewline
14 & 370.8 & 372.279600358149 & -1.47960035814873 \tabularnewline
15 & 374.5 & 372.85516726847 & 1.64483273153013 \tabularnewline
16 & 378.4 & 376.915830985639 & 1.48416901436059 \tabularnewline
17 & 381.3 & 381.141265848021 & 0.158734151978535 \tabularnewline
18 & 383.5 & 384.07607160559 & -0.576071605590016 \tabularnewline
19 & 387.6 & 386.1497559489 & 1.45024405109973 \tabularnewline
20 & 391.7 & 390.567752058928 & 1.13224794107208 \tabularnewline
21 & 395.4 & 394.916020921382 & 0.483979078617836 \tabularnewline
22 & 399.3 & 398.722143380025 & 0.577856619974796 \tabularnewline
23 & 403.3 & 402.748850438169 & 0.551149561830755 \tabularnewline
24 & 406.6 & 406.869701419473 & -0.269701419473165 \tabularnewline
25 & 410.5 & 410.110563785227 & 0.389436214772843 \tabularnewline
26 & 413.5 & 414.095955758604 & -0.595955758604134 \tabularnewline
27 & 418.7 & 416.965280088643 & 1.73471991135699 \tabularnewline
28 & 421.7 & 422.545653435722 & -0.845653435722454 \tabularnewline
29 & 422.8 & 425.360226367232 & -2.56022636723196 \tabularnewline
30 & 425.8 & 425.898843595172 & -0.0988435951720135 \tabularnewline
31 & 427.6 & 428.877170085295 & -1.27717008529481 \tabularnewline
32 & 431 & 430.39712403466 & 0.602875965340104 \tabularnewline
33 & 434.3 & 433.929317103586 & 0.370682896413655 \tabularnewline
34 & 437.6 & 437.310597022662 & 0.289402977338 \tabularnewline
35 & 440.4 & 440.674054632403 & -0.274054632403022 \tabularnewline
36 & 443.5 & 443.413962465865 & 0.0860375341349027 \tabularnewline
37 & 446.2 & 446.532827981052 & -0.332827981052446 \tabularnewline
38 & 446.2 & 449.159848537901 & -2.95984853790094 \tabularnewline
39 & 449.7 & 448.51084031021 & 1.18915968978985 \tabularnewline
40 & 454.2 & 452.271588254853 & 1.928411745147 \tabularnewline
41 & 458.4 & 457.194432556833 & 1.20556744316679 \tabularnewline
42 & 461.1 & 461.65877824197 & -0.558778241969549 \tabularnewline
43 & 464 & 464.236254514201 & -0.236254514201448 \tabularnewline
44 & 466.2 & 467.084450808173 & -0.884450808173085 \tabularnewline
45 & 468.7 & 469.09051661048 & -0.390516610479608 \tabularnewline
46 & 471.8 & 471.504887737919 & 0.295112262081204 \tabularnewline
47 & 474.9 & 474.669597226844 & 0.230402773156129 \tabularnewline
48 & 477.5 & 477.820117817187 & -0.320117817186997 \tabularnewline
49 & 480 & 480.34992534128 & -0.349925341280084 \tabularnewline
50 & 482.8 & 482.773196947019 & 0.0268030529807106 \tabularnewline
51 & 485.7 & 485.57907407272 & 0.120925927280155 \tabularnewline
52 & 488.5 & 488.505589592261 & -0.00558959226106026 \tabularnewline
53 & 492 & 491.304363958138 & 0.69563604186186 \tabularnewline
54 & 495.1 & 494.956896599206 & 0.143103400794132 \tabularnewline
55 & 498.5 & 498.088274990139 & 0.411725009860675 \tabularnewline
56 & 502.2 & 501.578554244474 & 0.621445755525883 \tabularnewline
57 & 502.1 & 505.414819125341 & -3.31481912534048 \tabularnewline
58 & 510 & 504.587976228447 & 5.41202377155253 \tabularnewline
59 & 515 & 513.67467477441 & 1.32532522559029 \tabularnewline
60 & 520.4 & 518.965279839081 & 1.43472016091891 \tabularnewline
61 & 525.2 & 524.679872013967 & 0.520127986033344 \tabularnewline
62 & 530.1 & 529.593920870881 & 0.506079129118689 \tabularnewline
63 & 534.5 & 534.604889224314 & -0.104889224313865 \tabularnewline
64 & 538.5 & 538.981890084762 & -0.481890084761858 \tabularnewline
65 & 544.4 & 542.876225681382 & 1.52377431861828 \tabularnewline
66 & 548.4 & 549.110344828785 & -0.710344828785196 \tabularnewline
67 & 551.9 & 552.954586980883 & -1.0545869808833 \tabularnewline
68 & 554.9 & 556.223346895911 & -1.32334689591119 \tabularnewline
69 & 558.1 & 558.933175621085 & -0.83317562108482 \tabularnewline
70 & 561.3 & 561.950484572448 & -0.650484572448136 \tabularnewline
71 & 564.4 & 565.00785232823 & -0.607852328230479 \tabularnewline
72 & 567 & 567.974568088449 & -0.974568088449018 \tabularnewline
73 & 568.7 & 570.360873806546 & -1.66087380654596 \tabularnewline
74 & 570.9 & 571.696692750725 & -0.796692750724674 \tabularnewline
75 & 572.5 & 573.722001328667 & -1.22200132866669 \tabularnewline
76 & 574.6 & 575.054052173026 & -0.454052173026412 \tabularnewline
77 & 577.1 & 577.054491809609 & 0.0455081903913879 \tabularnewline
78 & 580.9 & 579.564470424937 & 1.33552957506254 \tabularnewline
79 & 583.3 & 583.657313005036 & -0.357313005036076 \tabularnewline
80 & 586.5 & 585.978964712156 & 0.521035287844484 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283983&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]345.3[/C][C]346.3[/C][C]-1[/C][/ROW]
[ROW][C]4[/C][C]346.9[/C][C]347.880729243615[/C][C]-0.980729243614974[/C][/ROW]
[ROW][C]5[/C][C]349[/C][C]349.265684000559[/C][C]-0.265684000558508[/C][/ROW]
[ROW][C]6[/C][C]351.4[/C][C]351.307427268797[/C][C]0.0925727312032905[/C][/ROW]
[ROW][C]7[/C][C]353[/C][C]353.727725761588[/C][C]-0.727725761588204[/C][/ROW]
[ROW][C]8[/C][C]355[/C][C]355.168156783404[/C][C]-0.168156783403901[/C][/ROW]
[ROW][C]9[/C][C]360.1[/C][C]357.131284918316[/C][C]2.96871508168437[/C][/ROW]
[ROW][C]10[/C][C]364.7[/C][C]362.882237319768[/C][C]1.81776268023162[/C][/ROW]
[ROW][C]11[/C][C]366.5[/C][C]367.880819517591[/C][C]-1.38081951759125[/C][/ROW]
[ROW][C]12[/C][C]369[/C][C]369.378046177538[/C][C]-0.378046177537783[/C][/ROW]
[ROW][C]13[/C][C]369.9[/C][C]371.795151706241[/C][C]-1.8951517062406[/C][/ROW]
[ROW][C]14[/C][C]370.8[/C][C]372.279600358149[/C][C]-1.47960035814873[/C][/ROW]
[ROW][C]15[/C][C]374.5[/C][C]372.85516726847[/C][C]1.64483273153013[/C][/ROW]
[ROW][C]16[/C][C]378.4[/C][C]376.915830985639[/C][C]1.48416901436059[/C][/ROW]
[ROW][C]17[/C][C]381.3[/C][C]381.141265848021[/C][C]0.158734151978535[/C][/ROW]
[ROW][C]18[/C][C]383.5[/C][C]384.07607160559[/C][C]-0.576071605590016[/C][/ROW]
[ROW][C]19[/C][C]387.6[/C][C]386.1497559489[/C][C]1.45024405109973[/C][/ROW]
[ROW][C]20[/C][C]391.7[/C][C]390.567752058928[/C][C]1.13224794107208[/C][/ROW]
[ROW][C]21[/C][C]395.4[/C][C]394.916020921382[/C][C]0.483979078617836[/C][/ROW]
[ROW][C]22[/C][C]399.3[/C][C]398.722143380025[/C][C]0.577856619974796[/C][/ROW]
[ROW][C]23[/C][C]403.3[/C][C]402.748850438169[/C][C]0.551149561830755[/C][/ROW]
[ROW][C]24[/C][C]406.6[/C][C]406.869701419473[/C][C]-0.269701419473165[/C][/ROW]
[ROW][C]25[/C][C]410.5[/C][C]410.110563785227[/C][C]0.389436214772843[/C][/ROW]
[ROW][C]26[/C][C]413.5[/C][C]414.095955758604[/C][C]-0.595955758604134[/C][/ROW]
[ROW][C]27[/C][C]418.7[/C][C]416.965280088643[/C][C]1.73471991135699[/C][/ROW]
[ROW][C]28[/C][C]421.7[/C][C]422.545653435722[/C][C]-0.845653435722454[/C][/ROW]
[ROW][C]29[/C][C]422.8[/C][C]425.360226367232[/C][C]-2.56022636723196[/C][/ROW]
[ROW][C]30[/C][C]425.8[/C][C]425.898843595172[/C][C]-0.0988435951720135[/C][/ROW]
[ROW][C]31[/C][C]427.6[/C][C]428.877170085295[/C][C]-1.27717008529481[/C][/ROW]
[ROW][C]32[/C][C]431[/C][C]430.39712403466[/C][C]0.602875965340104[/C][/ROW]
[ROW][C]33[/C][C]434.3[/C][C]433.929317103586[/C][C]0.370682896413655[/C][/ROW]
[ROW][C]34[/C][C]437.6[/C][C]437.310597022662[/C][C]0.289402977338[/C][/ROW]
[ROW][C]35[/C][C]440.4[/C][C]440.674054632403[/C][C]-0.274054632403022[/C][/ROW]
[ROW][C]36[/C][C]443.5[/C][C]443.413962465865[/C][C]0.0860375341349027[/C][/ROW]
[ROW][C]37[/C][C]446.2[/C][C]446.532827981052[/C][C]-0.332827981052446[/C][/ROW]
[ROW][C]38[/C][C]446.2[/C][C]449.159848537901[/C][C]-2.95984853790094[/C][/ROW]
[ROW][C]39[/C][C]449.7[/C][C]448.51084031021[/C][C]1.18915968978985[/C][/ROW]
[ROW][C]40[/C][C]454.2[/C][C]452.271588254853[/C][C]1.928411745147[/C][/ROW]
[ROW][C]41[/C][C]458.4[/C][C]457.194432556833[/C][C]1.20556744316679[/C][/ROW]
[ROW][C]42[/C][C]461.1[/C][C]461.65877824197[/C][C]-0.558778241969549[/C][/ROW]
[ROW][C]43[/C][C]464[/C][C]464.236254514201[/C][C]-0.236254514201448[/C][/ROW]
[ROW][C]44[/C][C]466.2[/C][C]467.084450808173[/C][C]-0.884450808173085[/C][/ROW]
[ROW][C]45[/C][C]468.7[/C][C]469.09051661048[/C][C]-0.390516610479608[/C][/ROW]
[ROW][C]46[/C][C]471.8[/C][C]471.504887737919[/C][C]0.295112262081204[/C][/ROW]
[ROW][C]47[/C][C]474.9[/C][C]474.669597226844[/C][C]0.230402773156129[/C][/ROW]
[ROW][C]48[/C][C]477.5[/C][C]477.820117817187[/C][C]-0.320117817186997[/C][/ROW]
[ROW][C]49[/C][C]480[/C][C]480.34992534128[/C][C]-0.349925341280084[/C][/ROW]
[ROW][C]50[/C][C]482.8[/C][C]482.773196947019[/C][C]0.0268030529807106[/C][/ROW]
[ROW][C]51[/C][C]485.7[/C][C]485.57907407272[/C][C]0.120925927280155[/C][/ROW]
[ROW][C]52[/C][C]488.5[/C][C]488.505589592261[/C][C]-0.00558959226106026[/C][/ROW]
[ROW][C]53[/C][C]492[/C][C]491.304363958138[/C][C]0.69563604186186[/C][/ROW]
[ROW][C]54[/C][C]495.1[/C][C]494.956896599206[/C][C]0.143103400794132[/C][/ROW]
[ROW][C]55[/C][C]498.5[/C][C]498.088274990139[/C][C]0.411725009860675[/C][/ROW]
[ROW][C]56[/C][C]502.2[/C][C]501.578554244474[/C][C]0.621445755525883[/C][/ROW]
[ROW][C]57[/C][C]502.1[/C][C]505.414819125341[/C][C]-3.31481912534048[/C][/ROW]
[ROW][C]58[/C][C]510[/C][C]504.587976228447[/C][C]5.41202377155253[/C][/ROW]
[ROW][C]59[/C][C]515[/C][C]513.67467477441[/C][C]1.32532522559029[/C][/ROW]
[ROW][C]60[/C][C]520.4[/C][C]518.965279839081[/C][C]1.43472016091891[/C][/ROW]
[ROW][C]61[/C][C]525.2[/C][C]524.679872013967[/C][C]0.520127986033344[/C][/ROW]
[ROW][C]62[/C][C]530.1[/C][C]529.593920870881[/C][C]0.506079129118689[/C][/ROW]
[ROW][C]63[/C][C]534.5[/C][C]534.604889224314[/C][C]-0.104889224313865[/C][/ROW]
[ROW][C]64[/C][C]538.5[/C][C]538.981890084762[/C][C]-0.481890084761858[/C][/ROW]
[ROW][C]65[/C][C]544.4[/C][C]542.876225681382[/C][C]1.52377431861828[/C][/ROW]
[ROW][C]66[/C][C]548.4[/C][C]549.110344828785[/C][C]-0.710344828785196[/C][/ROW]
[ROW][C]67[/C][C]551.9[/C][C]552.954586980883[/C][C]-1.0545869808833[/C][/ROW]
[ROW][C]68[/C][C]554.9[/C][C]556.223346895911[/C][C]-1.32334689591119[/C][/ROW]
[ROW][C]69[/C][C]558.1[/C][C]558.933175621085[/C][C]-0.83317562108482[/C][/ROW]
[ROW][C]70[/C][C]561.3[/C][C]561.950484572448[/C][C]-0.650484572448136[/C][/ROW]
[ROW][C]71[/C][C]564.4[/C][C]565.00785232823[/C][C]-0.607852328230479[/C][/ROW]
[ROW][C]72[/C][C]567[/C][C]567.974568088449[/C][C]-0.974568088449018[/C][/ROW]
[ROW][C]73[/C][C]568.7[/C][C]570.360873806546[/C][C]-1.66087380654596[/C][/ROW]
[ROW][C]74[/C][C]570.9[/C][C]571.696692750725[/C][C]-0.796692750724674[/C][/ROW]
[ROW][C]75[/C][C]572.5[/C][C]573.722001328667[/C][C]-1.22200132866669[/C][/ROW]
[ROW][C]76[/C][C]574.6[/C][C]575.054052173026[/C][C]-0.454052173026412[/C][/ROW]
[ROW][C]77[/C][C]577.1[/C][C]577.054491809609[/C][C]0.0455081903913879[/C][/ROW]
[ROW][C]78[/C][C]580.9[/C][C]579.564470424937[/C][C]1.33552957506254[/C][/ROW]
[ROW][C]79[/C][C]583.3[/C][C]583.657313005036[/C][C]-0.357313005036076[/C][/ROW]
[ROW][C]80[/C][C]586.5[/C][C]585.978964712156[/C][C]0.521035287844484[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283983&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283983&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
3345.3346.3-1
4346.9347.880729243615-0.980729243614974
5349349.265684000559-0.265684000558508
6351.4351.3074272687970.0925727312032905
7353353.727725761588-0.727725761588204
8355355.168156783404-0.168156783403901
9360.1357.1312849183162.96871508168437
10364.7362.8822373197681.81776268023162
11366.5367.880819517591-1.38081951759125
12369369.378046177538-0.378046177537783
13369.9371.795151706241-1.8951517062406
14370.8372.279600358149-1.47960035814873
15374.5372.855167268471.64483273153013
16378.4376.9158309856391.48416901436059
17381.3381.1412658480210.158734151978535
18383.5384.07607160559-0.576071605590016
19387.6386.14975594891.45024405109973
20391.7390.5677520589281.13224794107208
21395.4394.9160209213820.483979078617836
22399.3398.7221433800250.577856619974796
23403.3402.7488504381690.551149561830755
24406.6406.869701419473-0.269701419473165
25410.5410.1105637852270.389436214772843
26413.5414.095955758604-0.595955758604134
27418.7416.9652800886431.73471991135699
28421.7422.545653435722-0.845653435722454
29422.8425.360226367232-2.56022636723196
30425.8425.898843595172-0.0988435951720135
31427.6428.877170085295-1.27717008529481
32431430.397124034660.602875965340104
33434.3433.9293171035860.370682896413655
34437.6437.3105970226620.289402977338
35440.4440.674054632403-0.274054632403022
36443.5443.4139624658650.0860375341349027
37446.2446.532827981052-0.332827981052446
38446.2449.159848537901-2.95984853790094
39449.7448.510840310211.18915968978985
40454.2452.2715882548531.928411745147
41458.4457.1944325568331.20556744316679
42461.1461.65877824197-0.558778241969549
43464464.236254514201-0.236254514201448
44466.2467.084450808173-0.884450808173085
45468.7469.09051661048-0.390516610479608
46471.8471.5048877379190.295112262081204
47474.9474.6695972268440.230402773156129
48477.5477.820117817187-0.320117817186997
49480480.34992534128-0.349925341280084
50482.8482.7731969470190.0268030529807106
51485.7485.579074072720.120925927280155
52488.5488.505589592261-0.00558959226106026
53492491.3043639581380.69563604186186
54495.1494.9568965992060.143103400794132
55498.5498.0882749901390.411725009860675
56502.2501.5785542444740.621445755525883
57502.1505.414819125341-3.31481912534048
58510504.5879762284475.41202377155253
59515513.674674774411.32532522559029
60520.4518.9652798390811.43472016091891
61525.2524.6798720139670.520127986033344
62530.1529.5939208708810.506079129118689
63534.5534.604889224314-0.104889224313865
64538.5538.981890084762-0.481890084761858
65544.4542.8762256813821.52377431861828
66548.4549.110344828785-0.710344828785196
67551.9552.954586980883-1.0545869808833
68554.9556.223346895911-1.32334689591119
69558.1558.933175621085-0.83317562108482
70561.3561.950484572448-0.650484572448136
71564.4565.00785232823-0.607852328230479
72567567.974568088449-0.974568088449018
73568.7570.360873806546-1.66087380654596
74570.9571.696692750725-0.796692750724674
75572.5573.722001328667-1.22200132866669
76574.6575.054052173026-0.454052173026412
77577.1577.0544918096090.0455081903913879
78580.9579.5644704249371.33552957506254
79583.3583.657313005036-0.357313005036076
80586.5585.9789647121560.521035287844484







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
81589.293212513825586.808968021656591.777457005993
82592.086425027649588.16901392714596.003836128158
83594.879637541474589.577056888337600.18221819461
84597.672850055298590.958784912837604.38691519776

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 589.293212513825 & 586.808968021656 & 591.777457005993 \tabularnewline
82 & 592.086425027649 & 588.16901392714 & 596.003836128158 \tabularnewline
83 & 594.879637541474 & 589.577056888337 & 600.18221819461 \tabularnewline
84 & 597.672850055298 & 590.958784912837 & 604.38691519776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283983&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]81[/C][C]589.293212513825[/C][C]586.808968021656[/C][C]591.777457005993[/C][/ROW]
[ROW][C]82[/C][C]592.086425027649[/C][C]588.16901392714[/C][C]596.003836128158[/C][/ROW]
[ROW][C]83[/C][C]594.879637541474[/C][C]589.577056888337[/C][C]600.18221819461[/C][/ROW]
[ROW][C]84[/C][C]597.672850055298[/C][C]590.958784912837[/C][C]604.38691519776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283983&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283983&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
81589.293212513825586.808968021656591.777457005993
82592.086425027649588.16901392714596.003836128158
83594.879637541474589.577056888337600.18221819461
84597.672850055298590.958784912837604.38691519776



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