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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 computationThu, 11 Aug 2016 16:02:54 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/11/t1470927800yad0ge3o2eae0vp.htm/, Retrieved Sun, 05 May 2024 15:47:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296323, Retrieved Sun, 05 May 2024 15:47:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [Reeks A Stap 11] [2016-08-11 12:06:14] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [Reeks A Stap 32] [2016-08-11 15:02:54] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
193
223
254
284
294
304
314
314
314
314
324
335
335
335
345
365
365
385
385
385
395
395
405
405
416
416
426
436
446
446
466
476
476
476
476
486
497
507
517
527
527
547
547
557
557
557
567
567
598
598
618
628
638
669
679
689
689
689
689
709
719
729
790
831
942
952
962
1013
1033
1033
1043
1043
1053
1114
1155
1215
1236
1296
1317
1327
1347
1367
1367
1387
1408
1468
1479
1499
1499
1509
1519
1529
1539
1590
1620
1620
1651
1671
1691
1711
1721
1732
1732
1742
1762
1782
1813
1883
1904
1924
1934
1964
1985
1995
1995
2035
2066
2086
2157
2157




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296323&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296323&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296323&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.495629629160832
beta0.565014116024567
gamma0.601978987121485

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.495629629160832 \tabularnewline
beta & 0.565014116024567 \tabularnewline
gamma & 0.601978987121485 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296323&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]0.495629629160832[/C][/ROW]
[ROW][C]beta[/C][C]0.565014116024567[/C][/ROW]
[ROW][C]gamma[/C][C]0.601978987121485[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296323&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296323&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
alpha0.495629629160832
beta0.565014116024567
gamma0.601978987121485







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13335293.30288328717741.697116712823
14335326.5776467605738.42235323942737
15345355.068751440251-10.0687514402514
16365381.833109535174-16.8331095351745
17365380.054529244819-15.0545292448188
18385395.945763056085-10.9457630560845
19385408.661984616487-23.6619846164872
20385383.2584426841151.74155731588473
21395374.32135914204120.6786408579592
22395382.18580248669212.8141975133077
23405403.05986859011.94013140990018
24405420.408261033876-15.4082610338757
25416427.832456553373-11.8324565533732
26416404.71077987495711.2892201250428
27426414.26054393623711.7394560637634
28436443.575970804391-7.57597080439081
29446439.752820075856.24717992414963
30446470.515914377362-24.515914377362
31466469.961275828591-3.96127582859123
32476462.34652761245213.6534723875484
33476468.6471529988567.35284700114431
34476466.0896237282539.91037627174745
35476482.579754163414-6.5797541634139
36486488.162096861504-2.16209686150444
37497506.473252808133-9.47325280813334
38507490.81998894017616.1800110598239
39517505.74641418558911.2535858144106
40527533.780286606176-6.78028660617565
41527537.201634198006-10.2016341980059
42547550.728897493444-3.72889749344449
43547574.590002872427-27.5900028724271
44557558.138772257289-1.13877225728936
45557547.7025859084439.29741409155702
46557539.36522493585917.6347750641406
47567550.89315144463316.106848555367
48567572.525069634385-5.52506963438475
49598590.7587798982767.2412201017238
50598596.2962390092951.70376099070495
51618604.40458174787913.5954182521208
52628632.212000496731-4.21200049673132
53638638.851804350461-0.851804350461293
54669668.2882799030080.711720096992167
55679697.485117391437-18.4851173914366
56689705.655095484764-16.6550954847644
57689695.434787885905-6.43478788590528
58689680.506755716848.49324428315981
59689685.1059269837123.89407301628751
60709688.97813826306520.0218617369349
61719730.169438709828-11.169438709828
62729720.3183914326948.68160856730617
63790734.9973245932155.0026754067904
64831789.22962993199941.7703700680014
65942842.32561997826699.6743800217336
66952981.709733354863-29.7097333548633
679621038.8609010221-76.860901022095
6810131051.57646416504-38.576464165038
6910331054.52846305375-21.5284630537456
7010331049.62951028903-16.6295102890326
7110431048.17816591915-5.17816591914925
7210431061.05498849761-18.0549884976087
7310531076.37521539643-23.3752153964313
7411141057.4396961586756.5603038413283
7511551123.279179112331.7208208877032
7612151160.6295890006354.3704109993716
7712361244.30645282976-8.30645282975956
7812961258.9509469260437.0490530739594
7913171325.86432254932-8.86432254932197
8013271403.35723267363-76.3572326736275
8113471393.11736941427-46.1173694142658
8213671366.708685362430.291314637572214
8313671373.58936557819-6.58936557819084
8413871378.794353986788.20564601322144
8514081414.91318335843-6.91318335843448
8614681442.3926910967325.6073089032743
8714791489.72867642672-10.7286764267199
8814991501.66036291447-2.66036291446903
8914991509.82175117553-10.8217511755283
9015091507.77110646861.22889353140431
9115191503.4615317758615.5384682241429
9215291543.52505000318-14.5250500031811
9315391560.8717239913-21.8717239913017
9415901553.3548940207136.6451059792889
9516201578.1800970708341.8199029291691
9616201628.91682232236-8.91682232235712
9716511666.3833907354-15.3833907353967
9816711714.39737436384-43.3973743638376
9916911707.7122457398-16.7122457398007
10017111708.518905987922.48109401207603
10117211705.9800343019315.0199656980685
10217321717.3011074443714.6988925556288
10317321723.523569852238.47643014777236
10417421751.24679563685-9.24679563684526
10517621771.14110172388-9.14110172387564
10617821794.06573868885-12.0657386888497
10718131785.8421451979327.1578548020732
10818831799.108535237983.8914647621016
10919041895.282593997658.7174060023533
11019241970.04314949782-46.0431494978181
11119341991.18555746365-57.1855574636493
11219641986.96451930408-22.9645193040817
11319851975.243927146449.75607285355591
11419951981.9607319654413.0392680345644
11519951981.5496471114413.4503528885648
11620352006.6345506977828.3654493022161
11720662057.45040522878.54959477129887
11820862106.39094191851-20.3909419185088
11921572119.3833628814237.6166371185759
12021572170.69598132164-13.6959813216404

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 335 & 293.302883287177 & 41.697116712823 \tabularnewline
14 & 335 & 326.577646760573 & 8.42235323942737 \tabularnewline
15 & 345 & 355.068751440251 & -10.0687514402514 \tabularnewline
16 & 365 & 381.833109535174 & -16.8331095351745 \tabularnewline
17 & 365 & 380.054529244819 & -15.0545292448188 \tabularnewline
18 & 385 & 395.945763056085 & -10.9457630560845 \tabularnewline
19 & 385 & 408.661984616487 & -23.6619846164872 \tabularnewline
20 & 385 & 383.258442684115 & 1.74155731588473 \tabularnewline
21 & 395 & 374.321359142041 & 20.6786408579592 \tabularnewline
22 & 395 & 382.185802486692 & 12.8141975133077 \tabularnewline
23 & 405 & 403.0598685901 & 1.94013140990018 \tabularnewline
24 & 405 & 420.408261033876 & -15.4082610338757 \tabularnewline
25 & 416 & 427.832456553373 & -11.8324565533732 \tabularnewline
26 & 416 & 404.710779874957 & 11.2892201250428 \tabularnewline
27 & 426 & 414.260543936237 & 11.7394560637634 \tabularnewline
28 & 436 & 443.575970804391 & -7.57597080439081 \tabularnewline
29 & 446 & 439.75282007585 & 6.24717992414963 \tabularnewline
30 & 446 & 470.515914377362 & -24.515914377362 \tabularnewline
31 & 466 & 469.961275828591 & -3.96127582859123 \tabularnewline
32 & 476 & 462.346527612452 & 13.6534723875484 \tabularnewline
33 & 476 & 468.647152998856 & 7.35284700114431 \tabularnewline
34 & 476 & 466.089623728253 & 9.91037627174745 \tabularnewline
35 & 476 & 482.579754163414 & -6.5797541634139 \tabularnewline
36 & 486 & 488.162096861504 & -2.16209686150444 \tabularnewline
37 & 497 & 506.473252808133 & -9.47325280813334 \tabularnewline
38 & 507 & 490.819988940176 & 16.1800110598239 \tabularnewline
39 & 517 & 505.746414185589 & 11.2535858144106 \tabularnewline
40 & 527 & 533.780286606176 & -6.78028660617565 \tabularnewline
41 & 527 & 537.201634198006 & -10.2016341980059 \tabularnewline
42 & 547 & 550.728897493444 & -3.72889749344449 \tabularnewline
43 & 547 & 574.590002872427 & -27.5900028724271 \tabularnewline
44 & 557 & 558.138772257289 & -1.13877225728936 \tabularnewline
45 & 557 & 547.702585908443 & 9.29741409155702 \tabularnewline
46 & 557 & 539.365224935859 & 17.6347750641406 \tabularnewline
47 & 567 & 550.893151444633 & 16.106848555367 \tabularnewline
48 & 567 & 572.525069634385 & -5.52506963438475 \tabularnewline
49 & 598 & 590.758779898276 & 7.2412201017238 \tabularnewline
50 & 598 & 596.296239009295 & 1.70376099070495 \tabularnewline
51 & 618 & 604.404581747879 & 13.5954182521208 \tabularnewline
52 & 628 & 632.212000496731 & -4.21200049673132 \tabularnewline
53 & 638 & 638.851804350461 & -0.851804350461293 \tabularnewline
54 & 669 & 668.288279903008 & 0.711720096992167 \tabularnewline
55 & 679 & 697.485117391437 & -18.4851173914366 \tabularnewline
56 & 689 & 705.655095484764 & -16.6550954847644 \tabularnewline
57 & 689 & 695.434787885905 & -6.43478788590528 \tabularnewline
58 & 689 & 680.50675571684 & 8.49324428315981 \tabularnewline
59 & 689 & 685.105926983712 & 3.89407301628751 \tabularnewline
60 & 709 & 688.978138263065 & 20.0218617369349 \tabularnewline
61 & 719 & 730.169438709828 & -11.169438709828 \tabularnewline
62 & 729 & 720.318391432694 & 8.68160856730617 \tabularnewline
63 & 790 & 734.99732459321 & 55.0026754067904 \tabularnewline
64 & 831 & 789.229629931999 & 41.7703700680014 \tabularnewline
65 & 942 & 842.325619978266 & 99.6743800217336 \tabularnewline
66 & 952 & 981.709733354863 & -29.7097333548633 \tabularnewline
67 & 962 & 1038.8609010221 & -76.860901022095 \tabularnewline
68 & 1013 & 1051.57646416504 & -38.576464165038 \tabularnewline
69 & 1033 & 1054.52846305375 & -21.5284630537456 \tabularnewline
70 & 1033 & 1049.62951028903 & -16.6295102890326 \tabularnewline
71 & 1043 & 1048.17816591915 & -5.17816591914925 \tabularnewline
72 & 1043 & 1061.05498849761 & -18.0549884976087 \tabularnewline
73 & 1053 & 1076.37521539643 & -23.3752153964313 \tabularnewline
74 & 1114 & 1057.43969615867 & 56.5603038413283 \tabularnewline
75 & 1155 & 1123.2791791123 & 31.7208208877032 \tabularnewline
76 & 1215 & 1160.62958900063 & 54.3704109993716 \tabularnewline
77 & 1236 & 1244.30645282976 & -8.30645282975956 \tabularnewline
78 & 1296 & 1258.95094692604 & 37.0490530739594 \tabularnewline
79 & 1317 & 1325.86432254932 & -8.86432254932197 \tabularnewline
80 & 1327 & 1403.35723267363 & -76.3572326736275 \tabularnewline
81 & 1347 & 1393.11736941427 & -46.1173694142658 \tabularnewline
82 & 1367 & 1366.70868536243 & 0.291314637572214 \tabularnewline
83 & 1367 & 1373.58936557819 & -6.58936557819084 \tabularnewline
84 & 1387 & 1378.79435398678 & 8.20564601322144 \tabularnewline
85 & 1408 & 1414.91318335843 & -6.91318335843448 \tabularnewline
86 & 1468 & 1442.39269109673 & 25.6073089032743 \tabularnewline
87 & 1479 & 1489.72867642672 & -10.7286764267199 \tabularnewline
88 & 1499 & 1501.66036291447 & -2.66036291446903 \tabularnewline
89 & 1499 & 1509.82175117553 & -10.8217511755283 \tabularnewline
90 & 1509 & 1507.7711064686 & 1.22889353140431 \tabularnewline
91 & 1519 & 1503.46153177586 & 15.5384682241429 \tabularnewline
92 & 1529 & 1543.52505000318 & -14.5250500031811 \tabularnewline
93 & 1539 & 1560.8717239913 & -21.8717239913017 \tabularnewline
94 & 1590 & 1553.35489402071 & 36.6451059792889 \tabularnewline
95 & 1620 & 1578.18009707083 & 41.8199029291691 \tabularnewline
96 & 1620 & 1628.91682232236 & -8.91682232235712 \tabularnewline
97 & 1651 & 1666.3833907354 & -15.3833907353967 \tabularnewline
98 & 1671 & 1714.39737436384 & -43.3973743638376 \tabularnewline
99 & 1691 & 1707.7122457398 & -16.7122457398007 \tabularnewline
100 & 1711 & 1708.51890598792 & 2.48109401207603 \tabularnewline
101 & 1721 & 1705.98003430193 & 15.0199656980685 \tabularnewline
102 & 1732 & 1717.30110744437 & 14.6988925556288 \tabularnewline
103 & 1732 & 1723.52356985223 & 8.47643014777236 \tabularnewline
104 & 1742 & 1751.24679563685 & -9.24679563684526 \tabularnewline
105 & 1762 & 1771.14110172388 & -9.14110172387564 \tabularnewline
106 & 1782 & 1794.06573868885 & -12.0657386888497 \tabularnewline
107 & 1813 & 1785.84214519793 & 27.1578548020732 \tabularnewline
108 & 1883 & 1799.1085352379 & 83.8914647621016 \tabularnewline
109 & 1904 & 1895.28259399765 & 8.7174060023533 \tabularnewline
110 & 1924 & 1970.04314949782 & -46.0431494978181 \tabularnewline
111 & 1934 & 1991.18555746365 & -57.1855574636493 \tabularnewline
112 & 1964 & 1986.96451930408 & -22.9645193040817 \tabularnewline
113 & 1985 & 1975.24392714644 & 9.75607285355591 \tabularnewline
114 & 1995 & 1981.96073196544 & 13.0392680345644 \tabularnewline
115 & 1995 & 1981.54964711144 & 13.4503528885648 \tabularnewline
116 & 2035 & 2006.63455069778 & 28.3654493022161 \tabularnewline
117 & 2066 & 2057.4504052287 & 8.54959477129887 \tabularnewline
118 & 2086 & 2106.39094191851 & -20.3909419185088 \tabularnewline
119 & 2157 & 2119.38336288142 & 37.6166371185759 \tabularnewline
120 & 2157 & 2170.69598132164 & -13.6959813216404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296323&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]335[/C][C]293.302883287177[/C][C]41.697116712823[/C][/ROW]
[ROW][C]14[/C][C]335[/C][C]326.577646760573[/C][C]8.42235323942737[/C][/ROW]
[ROW][C]15[/C][C]345[/C][C]355.068751440251[/C][C]-10.0687514402514[/C][/ROW]
[ROW][C]16[/C][C]365[/C][C]381.833109535174[/C][C]-16.8331095351745[/C][/ROW]
[ROW][C]17[/C][C]365[/C][C]380.054529244819[/C][C]-15.0545292448188[/C][/ROW]
[ROW][C]18[/C][C]385[/C][C]395.945763056085[/C][C]-10.9457630560845[/C][/ROW]
[ROW][C]19[/C][C]385[/C][C]408.661984616487[/C][C]-23.6619846164872[/C][/ROW]
[ROW][C]20[/C][C]385[/C][C]383.258442684115[/C][C]1.74155731588473[/C][/ROW]
[ROW][C]21[/C][C]395[/C][C]374.321359142041[/C][C]20.6786408579592[/C][/ROW]
[ROW][C]22[/C][C]395[/C][C]382.185802486692[/C][C]12.8141975133077[/C][/ROW]
[ROW][C]23[/C][C]405[/C][C]403.0598685901[/C][C]1.94013140990018[/C][/ROW]
[ROW][C]24[/C][C]405[/C][C]420.408261033876[/C][C]-15.4082610338757[/C][/ROW]
[ROW][C]25[/C][C]416[/C][C]427.832456553373[/C][C]-11.8324565533732[/C][/ROW]
[ROW][C]26[/C][C]416[/C][C]404.710779874957[/C][C]11.2892201250428[/C][/ROW]
[ROW][C]27[/C][C]426[/C][C]414.260543936237[/C][C]11.7394560637634[/C][/ROW]
[ROW][C]28[/C][C]436[/C][C]443.575970804391[/C][C]-7.57597080439081[/C][/ROW]
[ROW][C]29[/C][C]446[/C][C]439.75282007585[/C][C]6.24717992414963[/C][/ROW]
[ROW][C]30[/C][C]446[/C][C]470.515914377362[/C][C]-24.515914377362[/C][/ROW]
[ROW][C]31[/C][C]466[/C][C]469.961275828591[/C][C]-3.96127582859123[/C][/ROW]
[ROW][C]32[/C][C]476[/C][C]462.346527612452[/C][C]13.6534723875484[/C][/ROW]
[ROW][C]33[/C][C]476[/C][C]468.647152998856[/C][C]7.35284700114431[/C][/ROW]
[ROW][C]34[/C][C]476[/C][C]466.089623728253[/C][C]9.91037627174745[/C][/ROW]
[ROW][C]35[/C][C]476[/C][C]482.579754163414[/C][C]-6.5797541634139[/C][/ROW]
[ROW][C]36[/C][C]486[/C][C]488.162096861504[/C][C]-2.16209686150444[/C][/ROW]
[ROW][C]37[/C][C]497[/C][C]506.473252808133[/C][C]-9.47325280813334[/C][/ROW]
[ROW][C]38[/C][C]507[/C][C]490.819988940176[/C][C]16.1800110598239[/C][/ROW]
[ROW][C]39[/C][C]517[/C][C]505.746414185589[/C][C]11.2535858144106[/C][/ROW]
[ROW][C]40[/C][C]527[/C][C]533.780286606176[/C][C]-6.78028660617565[/C][/ROW]
[ROW][C]41[/C][C]527[/C][C]537.201634198006[/C][C]-10.2016341980059[/C][/ROW]
[ROW][C]42[/C][C]547[/C][C]550.728897493444[/C][C]-3.72889749344449[/C][/ROW]
[ROW][C]43[/C][C]547[/C][C]574.590002872427[/C][C]-27.5900028724271[/C][/ROW]
[ROW][C]44[/C][C]557[/C][C]558.138772257289[/C][C]-1.13877225728936[/C][/ROW]
[ROW][C]45[/C][C]557[/C][C]547.702585908443[/C][C]9.29741409155702[/C][/ROW]
[ROW][C]46[/C][C]557[/C][C]539.365224935859[/C][C]17.6347750641406[/C][/ROW]
[ROW][C]47[/C][C]567[/C][C]550.893151444633[/C][C]16.106848555367[/C][/ROW]
[ROW][C]48[/C][C]567[/C][C]572.525069634385[/C][C]-5.52506963438475[/C][/ROW]
[ROW][C]49[/C][C]598[/C][C]590.758779898276[/C][C]7.2412201017238[/C][/ROW]
[ROW][C]50[/C][C]598[/C][C]596.296239009295[/C][C]1.70376099070495[/C][/ROW]
[ROW][C]51[/C][C]618[/C][C]604.404581747879[/C][C]13.5954182521208[/C][/ROW]
[ROW][C]52[/C][C]628[/C][C]632.212000496731[/C][C]-4.21200049673132[/C][/ROW]
[ROW][C]53[/C][C]638[/C][C]638.851804350461[/C][C]-0.851804350461293[/C][/ROW]
[ROW][C]54[/C][C]669[/C][C]668.288279903008[/C][C]0.711720096992167[/C][/ROW]
[ROW][C]55[/C][C]679[/C][C]697.485117391437[/C][C]-18.4851173914366[/C][/ROW]
[ROW][C]56[/C][C]689[/C][C]705.655095484764[/C][C]-16.6550954847644[/C][/ROW]
[ROW][C]57[/C][C]689[/C][C]695.434787885905[/C][C]-6.43478788590528[/C][/ROW]
[ROW][C]58[/C][C]689[/C][C]680.50675571684[/C][C]8.49324428315981[/C][/ROW]
[ROW][C]59[/C][C]689[/C][C]685.105926983712[/C][C]3.89407301628751[/C][/ROW]
[ROW][C]60[/C][C]709[/C][C]688.978138263065[/C][C]20.0218617369349[/C][/ROW]
[ROW][C]61[/C][C]719[/C][C]730.169438709828[/C][C]-11.169438709828[/C][/ROW]
[ROW][C]62[/C][C]729[/C][C]720.318391432694[/C][C]8.68160856730617[/C][/ROW]
[ROW][C]63[/C][C]790[/C][C]734.99732459321[/C][C]55.0026754067904[/C][/ROW]
[ROW][C]64[/C][C]831[/C][C]789.229629931999[/C][C]41.7703700680014[/C][/ROW]
[ROW][C]65[/C][C]942[/C][C]842.325619978266[/C][C]99.6743800217336[/C][/ROW]
[ROW][C]66[/C][C]952[/C][C]981.709733354863[/C][C]-29.7097333548633[/C][/ROW]
[ROW][C]67[/C][C]962[/C][C]1038.8609010221[/C][C]-76.860901022095[/C][/ROW]
[ROW][C]68[/C][C]1013[/C][C]1051.57646416504[/C][C]-38.576464165038[/C][/ROW]
[ROW][C]69[/C][C]1033[/C][C]1054.52846305375[/C][C]-21.5284630537456[/C][/ROW]
[ROW][C]70[/C][C]1033[/C][C]1049.62951028903[/C][C]-16.6295102890326[/C][/ROW]
[ROW][C]71[/C][C]1043[/C][C]1048.17816591915[/C][C]-5.17816591914925[/C][/ROW]
[ROW][C]72[/C][C]1043[/C][C]1061.05498849761[/C][C]-18.0549884976087[/C][/ROW]
[ROW][C]73[/C][C]1053[/C][C]1076.37521539643[/C][C]-23.3752153964313[/C][/ROW]
[ROW][C]74[/C][C]1114[/C][C]1057.43969615867[/C][C]56.5603038413283[/C][/ROW]
[ROW][C]75[/C][C]1155[/C][C]1123.2791791123[/C][C]31.7208208877032[/C][/ROW]
[ROW][C]76[/C][C]1215[/C][C]1160.62958900063[/C][C]54.3704109993716[/C][/ROW]
[ROW][C]77[/C][C]1236[/C][C]1244.30645282976[/C][C]-8.30645282975956[/C][/ROW]
[ROW][C]78[/C][C]1296[/C][C]1258.95094692604[/C][C]37.0490530739594[/C][/ROW]
[ROW][C]79[/C][C]1317[/C][C]1325.86432254932[/C][C]-8.86432254932197[/C][/ROW]
[ROW][C]80[/C][C]1327[/C][C]1403.35723267363[/C][C]-76.3572326736275[/C][/ROW]
[ROW][C]81[/C][C]1347[/C][C]1393.11736941427[/C][C]-46.1173694142658[/C][/ROW]
[ROW][C]82[/C][C]1367[/C][C]1366.70868536243[/C][C]0.291314637572214[/C][/ROW]
[ROW][C]83[/C][C]1367[/C][C]1373.58936557819[/C][C]-6.58936557819084[/C][/ROW]
[ROW][C]84[/C][C]1387[/C][C]1378.79435398678[/C][C]8.20564601322144[/C][/ROW]
[ROW][C]85[/C][C]1408[/C][C]1414.91318335843[/C][C]-6.91318335843448[/C][/ROW]
[ROW][C]86[/C][C]1468[/C][C]1442.39269109673[/C][C]25.6073089032743[/C][/ROW]
[ROW][C]87[/C][C]1479[/C][C]1489.72867642672[/C][C]-10.7286764267199[/C][/ROW]
[ROW][C]88[/C][C]1499[/C][C]1501.66036291447[/C][C]-2.66036291446903[/C][/ROW]
[ROW][C]89[/C][C]1499[/C][C]1509.82175117553[/C][C]-10.8217511755283[/C][/ROW]
[ROW][C]90[/C][C]1509[/C][C]1507.7711064686[/C][C]1.22889353140431[/C][/ROW]
[ROW][C]91[/C][C]1519[/C][C]1503.46153177586[/C][C]15.5384682241429[/C][/ROW]
[ROW][C]92[/C][C]1529[/C][C]1543.52505000318[/C][C]-14.5250500031811[/C][/ROW]
[ROW][C]93[/C][C]1539[/C][C]1560.8717239913[/C][C]-21.8717239913017[/C][/ROW]
[ROW][C]94[/C][C]1590[/C][C]1553.35489402071[/C][C]36.6451059792889[/C][/ROW]
[ROW][C]95[/C][C]1620[/C][C]1578.18009707083[/C][C]41.8199029291691[/C][/ROW]
[ROW][C]96[/C][C]1620[/C][C]1628.91682232236[/C][C]-8.91682232235712[/C][/ROW]
[ROW][C]97[/C][C]1651[/C][C]1666.3833907354[/C][C]-15.3833907353967[/C][/ROW]
[ROW][C]98[/C][C]1671[/C][C]1714.39737436384[/C][C]-43.3973743638376[/C][/ROW]
[ROW][C]99[/C][C]1691[/C][C]1707.7122457398[/C][C]-16.7122457398007[/C][/ROW]
[ROW][C]100[/C][C]1711[/C][C]1708.51890598792[/C][C]2.48109401207603[/C][/ROW]
[ROW][C]101[/C][C]1721[/C][C]1705.98003430193[/C][C]15.0199656980685[/C][/ROW]
[ROW][C]102[/C][C]1732[/C][C]1717.30110744437[/C][C]14.6988925556288[/C][/ROW]
[ROW][C]103[/C][C]1732[/C][C]1723.52356985223[/C][C]8.47643014777236[/C][/ROW]
[ROW][C]104[/C][C]1742[/C][C]1751.24679563685[/C][C]-9.24679563684526[/C][/ROW]
[ROW][C]105[/C][C]1762[/C][C]1771.14110172388[/C][C]-9.14110172387564[/C][/ROW]
[ROW][C]106[/C][C]1782[/C][C]1794.06573868885[/C][C]-12.0657386888497[/C][/ROW]
[ROW][C]107[/C][C]1813[/C][C]1785.84214519793[/C][C]27.1578548020732[/C][/ROW]
[ROW][C]108[/C][C]1883[/C][C]1799.1085352379[/C][C]83.8914647621016[/C][/ROW]
[ROW][C]109[/C][C]1904[/C][C]1895.28259399765[/C][C]8.7174060023533[/C][/ROW]
[ROW][C]110[/C][C]1924[/C][C]1970.04314949782[/C][C]-46.0431494978181[/C][/ROW]
[ROW][C]111[/C][C]1934[/C][C]1991.18555746365[/C][C]-57.1855574636493[/C][/ROW]
[ROW][C]112[/C][C]1964[/C][C]1986.96451930408[/C][C]-22.9645193040817[/C][/ROW]
[ROW][C]113[/C][C]1985[/C][C]1975.24392714644[/C][C]9.75607285355591[/C][/ROW]
[ROW][C]114[/C][C]1995[/C][C]1981.96073196544[/C][C]13.0392680345644[/C][/ROW]
[ROW][C]115[/C][C]1995[/C][C]1981.54964711144[/C][C]13.4503528885648[/C][/ROW]
[ROW][C]116[/C][C]2035[/C][C]2006.63455069778[/C][C]28.3654493022161[/C][/ROW]
[ROW][C]117[/C][C]2066[/C][C]2057.4504052287[/C][C]8.54959477129887[/C][/ROW]
[ROW][C]118[/C][C]2086[/C][C]2106.39094191851[/C][C]-20.3909419185088[/C][/ROW]
[ROW][C]119[/C][C]2157[/C][C]2119.38336288142[/C][C]37.6166371185759[/C][/ROW]
[ROW][C]120[/C][C]2157[/C][C]2170.69598132164[/C][C]-13.6959813216404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296323&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296323&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
13335293.30288328717741.697116712823
14335326.5776467605738.42235323942737
15345355.068751440251-10.0687514402514
16365381.833109535174-16.8331095351745
17365380.054529244819-15.0545292448188
18385395.945763056085-10.9457630560845
19385408.661984616487-23.6619846164872
20385383.2584426841151.74155731588473
21395374.32135914204120.6786408579592
22395382.18580248669212.8141975133077
23405403.05986859011.94013140990018
24405420.408261033876-15.4082610338757
25416427.832456553373-11.8324565533732
26416404.71077987495711.2892201250428
27426414.26054393623711.7394560637634
28436443.575970804391-7.57597080439081
29446439.752820075856.24717992414963
30446470.515914377362-24.515914377362
31466469.961275828591-3.96127582859123
32476462.34652761245213.6534723875484
33476468.6471529988567.35284700114431
34476466.0896237282539.91037627174745
35476482.579754163414-6.5797541634139
36486488.162096861504-2.16209686150444
37497506.473252808133-9.47325280813334
38507490.81998894017616.1800110598239
39517505.74641418558911.2535858144106
40527533.780286606176-6.78028660617565
41527537.201634198006-10.2016341980059
42547550.728897493444-3.72889749344449
43547574.590002872427-27.5900028724271
44557558.138772257289-1.13877225728936
45557547.7025859084439.29741409155702
46557539.36522493585917.6347750641406
47567550.89315144463316.106848555367
48567572.525069634385-5.52506963438475
49598590.7587798982767.2412201017238
50598596.2962390092951.70376099070495
51618604.40458174787913.5954182521208
52628632.212000496731-4.21200049673132
53638638.851804350461-0.851804350461293
54669668.2882799030080.711720096992167
55679697.485117391437-18.4851173914366
56689705.655095484764-16.6550954847644
57689695.434787885905-6.43478788590528
58689680.506755716848.49324428315981
59689685.1059269837123.89407301628751
60709688.97813826306520.0218617369349
61719730.169438709828-11.169438709828
62729720.3183914326948.68160856730617
63790734.9973245932155.0026754067904
64831789.22962993199941.7703700680014
65942842.32561997826699.6743800217336
66952981.709733354863-29.7097333548633
679621038.8609010221-76.860901022095
6810131051.57646416504-38.576464165038
6910331054.52846305375-21.5284630537456
7010331049.62951028903-16.6295102890326
7110431048.17816591915-5.17816591914925
7210431061.05498849761-18.0549884976087
7310531076.37521539643-23.3752153964313
7411141057.4396961586756.5603038413283
7511551123.279179112331.7208208877032
7612151160.6295890006354.3704109993716
7712361244.30645282976-8.30645282975956
7812961258.9509469260437.0490530739594
7913171325.86432254932-8.86432254932197
8013271403.35723267363-76.3572326736275
8113471393.11736941427-46.1173694142658
8213671366.708685362430.291314637572214
8313671373.58936557819-6.58936557819084
8413871378.794353986788.20564601322144
8514081414.91318335843-6.91318335843448
8614681442.3926910967325.6073089032743
8714791489.72867642672-10.7286764267199
8814991501.66036291447-2.66036291446903
8914991509.82175117553-10.8217511755283
9015091507.77110646861.22889353140431
9115191503.4615317758615.5384682241429
9215291543.52505000318-14.5250500031811
9315391560.8717239913-21.8717239913017
9415901553.3548940207136.6451059792889
9516201578.1800970708341.8199029291691
9616201628.91682232236-8.91682232235712
9716511666.3833907354-15.3833907353967
9816711714.39737436384-43.3973743638376
9916911707.7122457398-16.7122457398007
10017111708.518905987922.48109401207603
10117211705.9800343019315.0199656980685
10217321717.3011074443714.6988925556288
10317321723.523569852238.47643014777236
10417421751.24679563685-9.24679563684526
10517621771.14110172388-9.14110172387564
10617821794.06573868885-12.0657386888497
10718131785.8421451979327.1578548020732
10818831799.108535237983.8914647621016
10919041895.282593997658.7174060023533
11019241970.04314949782-46.0431494978181
11119341991.18555746365-57.1855574636493
11219641986.96451930408-22.9645193040817
11319851975.243927146449.75607285355591
11419951981.9607319654413.0392680345644
11519951981.5496471114413.4503528885648
11620352006.6345506977828.3654493022161
11720662057.45040522878.54959477129887
11820862106.39094191851-20.3909419185088
11921572119.3833628814237.6166371185759
12021572170.69598132164-13.6959813216404







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1212183.034933556332141.324286436872224.74558067579
1222224.511619424232166.261872686092282.76136616238
1232265.394218812072184.901925351112345.88651227304
1242318.160578649282210.657369330672425.66378796789
1252349.395726524062212.25368515362486.53776789452
1262369.33285349432200.508323574772538.15738341382
1272373.282421148162171.862052919472574.70278937684
1282408.017854546342169.476867347842646.55884174483
1292442.585937609272164.684892692162720.48698252638
1302480.392928789122160.59430493252800.19155264575
1312530.596304530612165.013984814582896.17862424664
1322540.566261636982135.314170731042945.81835254292

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 2183.03493355633 & 2141.32428643687 & 2224.74558067579 \tabularnewline
122 & 2224.51161942423 & 2166.26187268609 & 2282.76136616238 \tabularnewline
123 & 2265.39421881207 & 2184.90192535111 & 2345.88651227304 \tabularnewline
124 & 2318.16057864928 & 2210.65736933067 & 2425.66378796789 \tabularnewline
125 & 2349.39572652406 & 2212.2536851536 & 2486.53776789452 \tabularnewline
126 & 2369.3328534943 & 2200.50832357477 & 2538.15738341382 \tabularnewline
127 & 2373.28242114816 & 2171.86205291947 & 2574.70278937684 \tabularnewline
128 & 2408.01785454634 & 2169.47686734784 & 2646.55884174483 \tabularnewline
129 & 2442.58593760927 & 2164.68489269216 & 2720.48698252638 \tabularnewline
130 & 2480.39292878912 & 2160.5943049325 & 2800.19155264575 \tabularnewline
131 & 2530.59630453061 & 2165.01398481458 & 2896.17862424664 \tabularnewline
132 & 2540.56626163698 & 2135.31417073104 & 2945.81835254292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296323&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]121[/C][C]2183.03493355633[/C][C]2141.32428643687[/C][C]2224.74558067579[/C][/ROW]
[ROW][C]122[/C][C]2224.51161942423[/C][C]2166.26187268609[/C][C]2282.76136616238[/C][/ROW]
[ROW][C]123[/C][C]2265.39421881207[/C][C]2184.90192535111[/C][C]2345.88651227304[/C][/ROW]
[ROW][C]124[/C][C]2318.16057864928[/C][C]2210.65736933067[/C][C]2425.66378796789[/C][/ROW]
[ROW][C]125[/C][C]2349.39572652406[/C][C]2212.2536851536[/C][C]2486.53776789452[/C][/ROW]
[ROW][C]126[/C][C]2369.3328534943[/C][C]2200.50832357477[/C][C]2538.15738341382[/C][/ROW]
[ROW][C]127[/C][C]2373.28242114816[/C][C]2171.86205291947[/C][C]2574.70278937684[/C][/ROW]
[ROW][C]128[/C][C]2408.01785454634[/C][C]2169.47686734784[/C][C]2646.55884174483[/C][/ROW]
[ROW][C]129[/C][C]2442.58593760927[/C][C]2164.68489269216[/C][C]2720.48698252638[/C][/ROW]
[ROW][C]130[/C][C]2480.39292878912[/C][C]2160.5943049325[/C][C]2800.19155264575[/C][/ROW]
[ROW][C]131[/C][C]2530.59630453061[/C][C]2165.01398481458[/C][C]2896.17862424664[/C][/ROW]
[ROW][C]132[/C][C]2540.56626163698[/C][C]2135.31417073104[/C][C]2945.81835254292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296323&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296323&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
1212183.034933556332141.324286436872224.74558067579
1222224.511619424232166.261872686092282.76136616238
1232265.394218812072184.901925351112345.88651227304
1242318.160578649282210.657369330672425.66378796789
1252349.395726524062212.25368515362486.53776789452
1262369.33285349432200.508323574772538.15738341382
1272373.282421148162171.862052919472574.70278937684
1282408.017854546342169.476867347842646.55884174483
1292442.585937609272164.684892692162720.48698252638
1302480.392928789122160.59430493252800.19155264575
1312530.596304530612165.013984814582896.17862424664
1322540.566261636982135.314170731042945.81835254292



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')