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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 21:48:17 +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/Apr/26/t1461703736jnz63z3yqpzvo4o.htm/, Retrieved Fri, 03 May 2024 19:38:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294981, Retrieved Fri, 03 May 2024 19:38:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 20:48:17] [50e1ac7d003038f762f5217b1e15faa4] [Current]
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Dataseries X:
16489042
16495231
16501683
16506782
16513615
16520661
16528400
16538542
16554596
16562317
16568499
16574989
16578604
16585167
16588947
16593973
16599333
16606135
16611675
16624215
16638805
16648268
16654119
16655799
16661142
16669012
16673931
16676905
16681513
16686550
16690580
16703472
16719078
16725328
16729674
16730348
16731280
16735690
16737631
16739764
16742830
16744696
16746558
16758167
16772610
16778726
16781377
16779575
16781367
16783870
16784986
16785783
16788992
16792122
16795289
16805879
16820076
16825762
16829252
16829289
16833919
16840299
16844980
16849473
16853737
16857811
16859859
16870851
16887455
16895020
16900158
16900726
16903174
16907715
16910467
16913766
16917152
16922460
16924725
16937725
16957605
16967706
16976281
16980049
16980049




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294981&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294981&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294981&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999953627468008
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999953627468008 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294981&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]0.999953627468008[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294981&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294981&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
alpha0.999953627468008
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
216495231164890426189
31650168316495230.71300046452.28699960001
41650678216501682.70079115099.29920888506
51651361516506781.76353266833.23646741547
61652066116513614.68312557046.31687447615
71652840016520660.67324447739.32675555535
81653854216528399.641107810142.3588921782
91655459616538541.529673116054.4703268614
101656231716554595.25551367721.74448643811
111656849916562316.64192326182.35807684436
121657498916568498.71330846490.28669159859
131657860416574988.6990293615.30097102746
141658516716578603.83234936563.1676506605
151658894716585166.69564933780.30435070209
161659397316588946.82469775026.17530228384
171659933316593972.76692355360.2330764737
181660613516599332.75143246802.24856757931
191661167516606134.68456255540.31543748826
201662421516611674.743081512540.2569184545
211663880516624214.418476514590.581523465
221664826816638804.32339789463.67660220899
231665411916648267.56114545851.43885464594
241665579916654118.7286541680.27134603448
251666114216655798.92208165343.07791843638
261666901216661141.75222797870.24777205102
271667393116669011.63503674919.36496331543
281667690516673930.77187662974.22812340967
291668151316676904.86207754608.13792248815
301668655016681512.7863095037.21369102411
311669058016686549.76641164030.2335883528
321670347216690579.813107912892.1868921369
331671907816703471.402156715606.597843349
341672532816719077.27628256250.72371745855
351672967416725327.71013814346.28986188583
361673034816729673.7984515674.201548466459
371673128016730347.9687356932.031264433637
381673569016731279.95677944410.04322064854
391673763116735689.79549511941.20450486988
401673976416737630.90998142133.09001856856
411674283016739763.90108323066.09891678393
421674469616742829.85781721866.14218276925
431674655816744695.91346231862.08653773926
441675816716746557.913650311609.086349668
451677261016758166.461657314443.5383427292
461677872616772609.33021666116.66978344321
471678137716778725.71635452651.28364546597
481677957516781376.8770533-1801.87705326453
491678136716779575.08355761791.91644239798
501678387016781366.91690432503.08309570327
511678498616783869.88392571116.11607429758
521678578316784985.9482429797.051757127047
531678899216785782.96303873209.03696130589
541679212216788991.85118883130.14881116897
551679528916792121.85484713167.14515292645
561680587916795288.853131510590.1468685381
571682007616805878.508908114197.4910919257
581682576216820075.34162645686.65837360919
591682925216825761.73629533490.26370474696
601682928916829251.838147637.161852363497
611683391916829288.99827674630.00172328949
621684029916833918.78529516380.21470490471
631684498016840298.70413334681.2958667092
641684947316844979.78291654493.21708354354
651685373716849472.79163814264.20836185291
661685781116853736.80225794074.19774213806
671685985916857810.81106912048.18893086538
681687085116859858.905020310992.0949797072
691688745516870850.490268716604.5097312778
701689502016887454.23000687565.76999315619
711690015816895019.64915615138.35084391013
721690072616900157.7617217568.238278340548
731690317416900725.97364942448.02635064721
741690771516903173.88647884541.11352118105
751691046716907714.78941712752.21058293059
761691376616910466.8723733299.12762697414
771691715216913765.84701113386.1529888995
781692246016917151.84297555308.15702448785
791692472516922459.75384732265.24615268409
801693772516924724.894954813000.1050452031
811695760516937724.397152219880.6028477885
821696770616957604.078086110101.921913892
831697628116967705.53154838575.46845169738
841698004916976280.60233383768.39766618609
851698004916980048.82524990.17475014179945

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 16495231 & 16489042 & 6189 \tabularnewline
3 & 16501683 & 16495230.7130004 & 6452.28699960001 \tabularnewline
4 & 16506782 & 16501682.7007911 & 5099.29920888506 \tabularnewline
5 & 16513615 & 16506781.7635326 & 6833.23646741547 \tabularnewline
6 & 16520661 & 16513614.6831255 & 7046.31687447615 \tabularnewline
7 & 16528400 & 16520660.6732444 & 7739.32675555535 \tabularnewline
8 & 16538542 & 16528399.6411078 & 10142.3588921782 \tabularnewline
9 & 16554596 & 16538541.5296731 & 16054.4703268614 \tabularnewline
10 & 16562317 & 16554595.2555136 & 7721.74448643811 \tabularnewline
11 & 16568499 & 16562316.6419232 & 6182.35807684436 \tabularnewline
12 & 16574989 & 16568498.7133084 & 6490.28669159859 \tabularnewline
13 & 16578604 & 16574988.699029 & 3615.30097102746 \tabularnewline
14 & 16585167 & 16578603.8323493 & 6563.1676506605 \tabularnewline
15 & 16588947 & 16585166.6956493 & 3780.30435070209 \tabularnewline
16 & 16593973 & 16588946.8246977 & 5026.17530228384 \tabularnewline
17 & 16599333 & 16593972.7669235 & 5360.2330764737 \tabularnewline
18 & 16606135 & 16599332.7514324 & 6802.24856757931 \tabularnewline
19 & 16611675 & 16606134.6845625 & 5540.31543748826 \tabularnewline
20 & 16624215 & 16611674.7430815 & 12540.2569184545 \tabularnewline
21 & 16638805 & 16624214.4184765 & 14590.581523465 \tabularnewline
22 & 16648268 & 16638804.3233978 & 9463.67660220899 \tabularnewline
23 & 16654119 & 16648267.5611454 & 5851.43885464594 \tabularnewline
24 & 16655799 & 16654118.728654 & 1680.27134603448 \tabularnewline
25 & 16661142 & 16655798.9220816 & 5343.07791843638 \tabularnewline
26 & 16669012 & 16661141.7522279 & 7870.24777205102 \tabularnewline
27 & 16673931 & 16669011.6350367 & 4919.36496331543 \tabularnewline
28 & 16676905 & 16673930.7718766 & 2974.22812340967 \tabularnewline
29 & 16681513 & 16676904.8620775 & 4608.13792248815 \tabularnewline
30 & 16686550 & 16681512.786309 & 5037.21369102411 \tabularnewline
31 & 16690580 & 16686549.7664116 & 4030.2335883528 \tabularnewline
32 & 16703472 & 16690579.8131079 & 12892.1868921369 \tabularnewline
33 & 16719078 & 16703471.4021567 & 15606.597843349 \tabularnewline
34 & 16725328 & 16719077.2762825 & 6250.72371745855 \tabularnewline
35 & 16729674 & 16725327.7101381 & 4346.28986188583 \tabularnewline
36 & 16730348 & 16729673.7984515 & 674.201548466459 \tabularnewline
37 & 16731280 & 16730347.9687356 & 932.031264433637 \tabularnewline
38 & 16735690 & 16731279.9567794 & 4410.04322064854 \tabularnewline
39 & 16737631 & 16735689.7954951 & 1941.20450486988 \tabularnewline
40 & 16739764 & 16737630.9099814 & 2133.09001856856 \tabularnewline
41 & 16742830 & 16739763.9010832 & 3066.09891678393 \tabularnewline
42 & 16744696 & 16742829.8578172 & 1866.14218276925 \tabularnewline
43 & 16746558 & 16744695.9134623 & 1862.08653773926 \tabularnewline
44 & 16758167 & 16746557.9136503 & 11609.086349668 \tabularnewline
45 & 16772610 & 16758166.4616573 & 14443.5383427292 \tabularnewline
46 & 16778726 & 16772609.3302166 & 6116.66978344321 \tabularnewline
47 & 16781377 & 16778725.7163545 & 2651.28364546597 \tabularnewline
48 & 16779575 & 16781376.8770533 & -1801.87705326453 \tabularnewline
49 & 16781367 & 16779575.0835576 & 1791.91644239798 \tabularnewline
50 & 16783870 & 16781366.9169043 & 2503.08309570327 \tabularnewline
51 & 16784986 & 16783869.8839257 & 1116.11607429758 \tabularnewline
52 & 16785783 & 16784985.9482429 & 797.051757127047 \tabularnewline
53 & 16788992 & 16785782.9630387 & 3209.03696130589 \tabularnewline
54 & 16792122 & 16788991.8511888 & 3130.14881116897 \tabularnewline
55 & 16795289 & 16792121.8548471 & 3167.14515292645 \tabularnewline
56 & 16805879 & 16795288.8531315 & 10590.1468685381 \tabularnewline
57 & 16820076 & 16805878.5089081 & 14197.4910919257 \tabularnewline
58 & 16825762 & 16820075.3416264 & 5686.65837360919 \tabularnewline
59 & 16829252 & 16825761.7362953 & 3490.26370474696 \tabularnewline
60 & 16829289 & 16829251.8381476 & 37.161852363497 \tabularnewline
61 & 16833919 & 16829288.9982767 & 4630.00172328949 \tabularnewline
62 & 16840299 & 16833918.7852951 & 6380.21470490471 \tabularnewline
63 & 16844980 & 16840298.7041333 & 4681.2958667092 \tabularnewline
64 & 16849473 & 16844979.7829165 & 4493.21708354354 \tabularnewline
65 & 16853737 & 16849472.7916381 & 4264.20836185291 \tabularnewline
66 & 16857811 & 16853736.8022579 & 4074.19774213806 \tabularnewline
67 & 16859859 & 16857810.8110691 & 2048.18893086538 \tabularnewline
68 & 16870851 & 16859858.9050203 & 10992.0949797072 \tabularnewline
69 & 16887455 & 16870850.4902687 & 16604.5097312778 \tabularnewline
70 & 16895020 & 16887454.2300068 & 7565.76999315619 \tabularnewline
71 & 16900158 & 16895019.6491561 & 5138.35084391013 \tabularnewline
72 & 16900726 & 16900157.7617217 & 568.238278340548 \tabularnewline
73 & 16903174 & 16900725.9736494 & 2448.02635064721 \tabularnewline
74 & 16907715 & 16903173.8864788 & 4541.11352118105 \tabularnewline
75 & 16910467 & 16907714.7894171 & 2752.21058293059 \tabularnewline
76 & 16913766 & 16910466.872373 & 3299.12762697414 \tabularnewline
77 & 16917152 & 16913765.8470111 & 3386.1529888995 \tabularnewline
78 & 16922460 & 16917151.8429755 & 5308.15702448785 \tabularnewline
79 & 16924725 & 16922459.7538473 & 2265.24615268409 \tabularnewline
80 & 16937725 & 16924724.8949548 & 13000.1050452031 \tabularnewline
81 & 16957605 & 16937724.3971522 & 19880.6028477885 \tabularnewline
82 & 16967706 & 16957604.0780861 & 10101.921913892 \tabularnewline
83 & 16976281 & 16967705.5315483 & 8575.46845169738 \tabularnewline
84 & 16980049 & 16976280.6023338 & 3768.39766618609 \tabularnewline
85 & 16980049 & 16980048.8252499 & 0.17475014179945 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294981&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]2[/C][C]16495231[/C][C]16489042[/C][C]6189[/C][/ROW]
[ROW][C]3[/C][C]16501683[/C][C]16495230.7130004[/C][C]6452.28699960001[/C][/ROW]
[ROW][C]4[/C][C]16506782[/C][C]16501682.7007911[/C][C]5099.29920888506[/C][/ROW]
[ROW][C]5[/C][C]16513615[/C][C]16506781.7635326[/C][C]6833.23646741547[/C][/ROW]
[ROW][C]6[/C][C]16520661[/C][C]16513614.6831255[/C][C]7046.31687447615[/C][/ROW]
[ROW][C]7[/C][C]16528400[/C][C]16520660.6732444[/C][C]7739.32675555535[/C][/ROW]
[ROW][C]8[/C][C]16538542[/C][C]16528399.6411078[/C][C]10142.3588921782[/C][/ROW]
[ROW][C]9[/C][C]16554596[/C][C]16538541.5296731[/C][C]16054.4703268614[/C][/ROW]
[ROW][C]10[/C][C]16562317[/C][C]16554595.2555136[/C][C]7721.74448643811[/C][/ROW]
[ROW][C]11[/C][C]16568499[/C][C]16562316.6419232[/C][C]6182.35807684436[/C][/ROW]
[ROW][C]12[/C][C]16574989[/C][C]16568498.7133084[/C][C]6490.28669159859[/C][/ROW]
[ROW][C]13[/C][C]16578604[/C][C]16574988.699029[/C][C]3615.30097102746[/C][/ROW]
[ROW][C]14[/C][C]16585167[/C][C]16578603.8323493[/C][C]6563.1676506605[/C][/ROW]
[ROW][C]15[/C][C]16588947[/C][C]16585166.6956493[/C][C]3780.30435070209[/C][/ROW]
[ROW][C]16[/C][C]16593973[/C][C]16588946.8246977[/C][C]5026.17530228384[/C][/ROW]
[ROW][C]17[/C][C]16599333[/C][C]16593972.7669235[/C][C]5360.2330764737[/C][/ROW]
[ROW][C]18[/C][C]16606135[/C][C]16599332.7514324[/C][C]6802.24856757931[/C][/ROW]
[ROW][C]19[/C][C]16611675[/C][C]16606134.6845625[/C][C]5540.31543748826[/C][/ROW]
[ROW][C]20[/C][C]16624215[/C][C]16611674.7430815[/C][C]12540.2569184545[/C][/ROW]
[ROW][C]21[/C][C]16638805[/C][C]16624214.4184765[/C][C]14590.581523465[/C][/ROW]
[ROW][C]22[/C][C]16648268[/C][C]16638804.3233978[/C][C]9463.67660220899[/C][/ROW]
[ROW][C]23[/C][C]16654119[/C][C]16648267.5611454[/C][C]5851.43885464594[/C][/ROW]
[ROW][C]24[/C][C]16655799[/C][C]16654118.728654[/C][C]1680.27134603448[/C][/ROW]
[ROW][C]25[/C][C]16661142[/C][C]16655798.9220816[/C][C]5343.07791843638[/C][/ROW]
[ROW][C]26[/C][C]16669012[/C][C]16661141.7522279[/C][C]7870.24777205102[/C][/ROW]
[ROW][C]27[/C][C]16673931[/C][C]16669011.6350367[/C][C]4919.36496331543[/C][/ROW]
[ROW][C]28[/C][C]16676905[/C][C]16673930.7718766[/C][C]2974.22812340967[/C][/ROW]
[ROW][C]29[/C][C]16681513[/C][C]16676904.8620775[/C][C]4608.13792248815[/C][/ROW]
[ROW][C]30[/C][C]16686550[/C][C]16681512.786309[/C][C]5037.21369102411[/C][/ROW]
[ROW][C]31[/C][C]16690580[/C][C]16686549.7664116[/C][C]4030.2335883528[/C][/ROW]
[ROW][C]32[/C][C]16703472[/C][C]16690579.8131079[/C][C]12892.1868921369[/C][/ROW]
[ROW][C]33[/C][C]16719078[/C][C]16703471.4021567[/C][C]15606.597843349[/C][/ROW]
[ROW][C]34[/C][C]16725328[/C][C]16719077.2762825[/C][C]6250.72371745855[/C][/ROW]
[ROW][C]35[/C][C]16729674[/C][C]16725327.7101381[/C][C]4346.28986188583[/C][/ROW]
[ROW][C]36[/C][C]16730348[/C][C]16729673.7984515[/C][C]674.201548466459[/C][/ROW]
[ROW][C]37[/C][C]16731280[/C][C]16730347.9687356[/C][C]932.031264433637[/C][/ROW]
[ROW][C]38[/C][C]16735690[/C][C]16731279.9567794[/C][C]4410.04322064854[/C][/ROW]
[ROW][C]39[/C][C]16737631[/C][C]16735689.7954951[/C][C]1941.20450486988[/C][/ROW]
[ROW][C]40[/C][C]16739764[/C][C]16737630.9099814[/C][C]2133.09001856856[/C][/ROW]
[ROW][C]41[/C][C]16742830[/C][C]16739763.9010832[/C][C]3066.09891678393[/C][/ROW]
[ROW][C]42[/C][C]16744696[/C][C]16742829.8578172[/C][C]1866.14218276925[/C][/ROW]
[ROW][C]43[/C][C]16746558[/C][C]16744695.9134623[/C][C]1862.08653773926[/C][/ROW]
[ROW][C]44[/C][C]16758167[/C][C]16746557.9136503[/C][C]11609.086349668[/C][/ROW]
[ROW][C]45[/C][C]16772610[/C][C]16758166.4616573[/C][C]14443.5383427292[/C][/ROW]
[ROW][C]46[/C][C]16778726[/C][C]16772609.3302166[/C][C]6116.66978344321[/C][/ROW]
[ROW][C]47[/C][C]16781377[/C][C]16778725.7163545[/C][C]2651.28364546597[/C][/ROW]
[ROW][C]48[/C][C]16779575[/C][C]16781376.8770533[/C][C]-1801.87705326453[/C][/ROW]
[ROW][C]49[/C][C]16781367[/C][C]16779575.0835576[/C][C]1791.91644239798[/C][/ROW]
[ROW][C]50[/C][C]16783870[/C][C]16781366.9169043[/C][C]2503.08309570327[/C][/ROW]
[ROW][C]51[/C][C]16784986[/C][C]16783869.8839257[/C][C]1116.11607429758[/C][/ROW]
[ROW][C]52[/C][C]16785783[/C][C]16784985.9482429[/C][C]797.051757127047[/C][/ROW]
[ROW][C]53[/C][C]16788992[/C][C]16785782.9630387[/C][C]3209.03696130589[/C][/ROW]
[ROW][C]54[/C][C]16792122[/C][C]16788991.8511888[/C][C]3130.14881116897[/C][/ROW]
[ROW][C]55[/C][C]16795289[/C][C]16792121.8548471[/C][C]3167.14515292645[/C][/ROW]
[ROW][C]56[/C][C]16805879[/C][C]16795288.8531315[/C][C]10590.1468685381[/C][/ROW]
[ROW][C]57[/C][C]16820076[/C][C]16805878.5089081[/C][C]14197.4910919257[/C][/ROW]
[ROW][C]58[/C][C]16825762[/C][C]16820075.3416264[/C][C]5686.65837360919[/C][/ROW]
[ROW][C]59[/C][C]16829252[/C][C]16825761.7362953[/C][C]3490.26370474696[/C][/ROW]
[ROW][C]60[/C][C]16829289[/C][C]16829251.8381476[/C][C]37.161852363497[/C][/ROW]
[ROW][C]61[/C][C]16833919[/C][C]16829288.9982767[/C][C]4630.00172328949[/C][/ROW]
[ROW][C]62[/C][C]16840299[/C][C]16833918.7852951[/C][C]6380.21470490471[/C][/ROW]
[ROW][C]63[/C][C]16844980[/C][C]16840298.7041333[/C][C]4681.2958667092[/C][/ROW]
[ROW][C]64[/C][C]16849473[/C][C]16844979.7829165[/C][C]4493.21708354354[/C][/ROW]
[ROW][C]65[/C][C]16853737[/C][C]16849472.7916381[/C][C]4264.20836185291[/C][/ROW]
[ROW][C]66[/C][C]16857811[/C][C]16853736.8022579[/C][C]4074.19774213806[/C][/ROW]
[ROW][C]67[/C][C]16859859[/C][C]16857810.8110691[/C][C]2048.18893086538[/C][/ROW]
[ROW][C]68[/C][C]16870851[/C][C]16859858.9050203[/C][C]10992.0949797072[/C][/ROW]
[ROW][C]69[/C][C]16887455[/C][C]16870850.4902687[/C][C]16604.5097312778[/C][/ROW]
[ROW][C]70[/C][C]16895020[/C][C]16887454.2300068[/C][C]7565.76999315619[/C][/ROW]
[ROW][C]71[/C][C]16900158[/C][C]16895019.6491561[/C][C]5138.35084391013[/C][/ROW]
[ROW][C]72[/C][C]16900726[/C][C]16900157.7617217[/C][C]568.238278340548[/C][/ROW]
[ROW][C]73[/C][C]16903174[/C][C]16900725.9736494[/C][C]2448.02635064721[/C][/ROW]
[ROW][C]74[/C][C]16907715[/C][C]16903173.8864788[/C][C]4541.11352118105[/C][/ROW]
[ROW][C]75[/C][C]16910467[/C][C]16907714.7894171[/C][C]2752.21058293059[/C][/ROW]
[ROW][C]76[/C][C]16913766[/C][C]16910466.872373[/C][C]3299.12762697414[/C][/ROW]
[ROW][C]77[/C][C]16917152[/C][C]16913765.8470111[/C][C]3386.1529888995[/C][/ROW]
[ROW][C]78[/C][C]16922460[/C][C]16917151.8429755[/C][C]5308.15702448785[/C][/ROW]
[ROW][C]79[/C][C]16924725[/C][C]16922459.7538473[/C][C]2265.24615268409[/C][/ROW]
[ROW][C]80[/C][C]16937725[/C][C]16924724.8949548[/C][C]13000.1050452031[/C][/ROW]
[ROW][C]81[/C][C]16957605[/C][C]16937724.3971522[/C][C]19880.6028477885[/C][/ROW]
[ROW][C]82[/C][C]16967706[/C][C]16957604.0780861[/C][C]10101.921913892[/C][/ROW]
[ROW][C]83[/C][C]16976281[/C][C]16967705.5315483[/C][C]8575.46845169738[/C][/ROW]
[ROW][C]84[/C][C]16980049[/C][C]16976280.6023338[/C][C]3768.39766618609[/C][/ROW]
[ROW][C]85[/C][C]16980049[/C][C]16980048.8252499[/C][C]0.17475014179945[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294981&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294981&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
216495231164890426189
31650168316495230.71300046452.28699960001
41650678216501682.70079115099.29920888506
51651361516506781.76353266833.23646741547
61652066116513614.68312557046.31687447615
71652840016520660.67324447739.32675555535
81653854216528399.641107810142.3588921782
91655459616538541.529673116054.4703268614
101656231716554595.25551367721.74448643811
111656849916562316.64192326182.35807684436
121657498916568498.71330846490.28669159859
131657860416574988.6990293615.30097102746
141658516716578603.83234936563.1676506605
151658894716585166.69564933780.30435070209
161659397316588946.82469775026.17530228384
171659933316593972.76692355360.2330764737
181660613516599332.75143246802.24856757931
191661167516606134.68456255540.31543748826
201662421516611674.743081512540.2569184545
211663880516624214.418476514590.581523465
221664826816638804.32339789463.67660220899
231665411916648267.56114545851.43885464594
241665579916654118.7286541680.27134603448
251666114216655798.92208165343.07791843638
261666901216661141.75222797870.24777205102
271667393116669011.63503674919.36496331543
281667690516673930.77187662974.22812340967
291668151316676904.86207754608.13792248815
301668655016681512.7863095037.21369102411
311669058016686549.76641164030.2335883528
321670347216690579.813107912892.1868921369
331671907816703471.402156715606.597843349
341672532816719077.27628256250.72371745855
351672967416725327.71013814346.28986188583
361673034816729673.7984515674.201548466459
371673128016730347.9687356932.031264433637
381673569016731279.95677944410.04322064854
391673763116735689.79549511941.20450486988
401673976416737630.90998142133.09001856856
411674283016739763.90108323066.09891678393
421674469616742829.85781721866.14218276925
431674655816744695.91346231862.08653773926
441675816716746557.913650311609.086349668
451677261016758166.461657314443.5383427292
461677872616772609.33021666116.66978344321
471678137716778725.71635452651.28364546597
481677957516781376.8770533-1801.87705326453
491678136716779575.08355761791.91644239798
501678387016781366.91690432503.08309570327
511678498616783869.88392571116.11607429758
521678578316784985.9482429797.051757127047
531678899216785782.96303873209.03696130589
541679212216788991.85118883130.14881116897
551679528916792121.85484713167.14515292645
561680587916795288.853131510590.1468685381
571682007616805878.508908114197.4910919257
581682576216820075.34162645686.65837360919
591682925216825761.73629533490.26370474696
601682928916829251.838147637.161852363497
611683391916829288.99827674630.00172328949
621684029916833918.78529516380.21470490471
631684498016840298.70413334681.2958667092
641684947316844979.78291654493.21708354354
651685373716849472.79163814264.20836185291
661685781116853736.80225794074.19774213806
671685985916857810.81106912048.18893086538
681687085116859858.905020310992.0949797072
691688745516870850.490268716604.5097312778
701689502016887454.23000687565.76999315619
711690015816895019.64915615138.35084391013
721690072616900157.7617217568.238278340548
731690317416900725.97364942448.02635064721
741690771516903173.88647884541.11352118105
751691046716907714.78941712752.21058293059
761691376616910466.8723733299.12762697414
771691715216913765.84701113386.1529888995
781692246016917151.84297555308.15702448785
791692472516922459.75384732265.24615268409
801693772516924724.894954813000.1050452031
811695760516937724.397152219880.6028477885
821696770616957604.078086110101.921913892
831697628116967705.53154838575.46845169738
841698004916976280.60233383768.39766618609
851698004916980048.82524990.17475014179945







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8616980048.999991916971583.164564116988514.8354197
8716980048.999991916968076.778307416992021.2216764
8816980048.999991916965386.196213816994711.8037699
8916980048.999991916963117.918006216996980.0819776
9016980048.999991916961119.518758216998978.4812256
9116980048.999991916959312.824299417000785.1756844
9216980048.999991916957651.395099417002446.6048844
9316980048.999991916956104.973022917003993.0269609
9416980048.999991916954652.540591817005445.459392
9516980048.999991916953278.795049917006819.2049339
9616980048.999991916951972.184018517008125.8159653
9716980048.999991916950723.732426617009374.2675572

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 16980048.9999919 & 16971583.1645641 & 16988514.8354197 \tabularnewline
87 & 16980048.9999919 & 16968076.7783074 & 16992021.2216764 \tabularnewline
88 & 16980048.9999919 & 16965386.1962138 & 16994711.8037699 \tabularnewline
89 & 16980048.9999919 & 16963117.9180062 & 16996980.0819776 \tabularnewline
90 & 16980048.9999919 & 16961119.5187582 & 16998978.4812256 \tabularnewline
91 & 16980048.9999919 & 16959312.8242994 & 17000785.1756844 \tabularnewline
92 & 16980048.9999919 & 16957651.3950994 & 17002446.6048844 \tabularnewline
93 & 16980048.9999919 & 16956104.9730229 & 17003993.0269609 \tabularnewline
94 & 16980048.9999919 & 16954652.5405918 & 17005445.459392 \tabularnewline
95 & 16980048.9999919 & 16953278.7950499 & 17006819.2049339 \tabularnewline
96 & 16980048.9999919 & 16951972.1840185 & 17008125.8159653 \tabularnewline
97 & 16980048.9999919 & 16950723.7324266 & 17009374.2675572 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294981&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]86[/C][C]16980048.9999919[/C][C]16971583.1645641[/C][C]16988514.8354197[/C][/ROW]
[ROW][C]87[/C][C]16980048.9999919[/C][C]16968076.7783074[/C][C]16992021.2216764[/C][/ROW]
[ROW][C]88[/C][C]16980048.9999919[/C][C]16965386.1962138[/C][C]16994711.8037699[/C][/ROW]
[ROW][C]89[/C][C]16980048.9999919[/C][C]16963117.9180062[/C][C]16996980.0819776[/C][/ROW]
[ROW][C]90[/C][C]16980048.9999919[/C][C]16961119.5187582[/C][C]16998978.4812256[/C][/ROW]
[ROW][C]91[/C][C]16980048.9999919[/C][C]16959312.8242994[/C][C]17000785.1756844[/C][/ROW]
[ROW][C]92[/C][C]16980048.9999919[/C][C]16957651.3950994[/C][C]17002446.6048844[/C][/ROW]
[ROW][C]93[/C][C]16980048.9999919[/C][C]16956104.9730229[/C][C]17003993.0269609[/C][/ROW]
[ROW][C]94[/C][C]16980048.9999919[/C][C]16954652.5405918[/C][C]17005445.459392[/C][/ROW]
[ROW][C]95[/C][C]16980048.9999919[/C][C]16953278.7950499[/C][C]17006819.2049339[/C][/ROW]
[ROW][C]96[/C][C]16980048.9999919[/C][C]16951972.1840185[/C][C]17008125.8159653[/C][/ROW]
[ROW][C]97[/C][C]16980048.9999919[/C][C]16950723.7324266[/C][C]17009374.2675572[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294981&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294981&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
8616980048.999991916971583.164564116988514.8354197
8716980048.999991916968076.778307416992021.2216764
8816980048.999991916965386.196213816994711.8037699
8916980048.999991916963117.918006216996980.0819776
9016980048.999991916961119.518758216998978.4812256
9116980048.999991916959312.824299417000785.1756844
9216980048.999991916957651.395099417002446.6048844
9316980048.999991916956104.973022917003993.0269609
9416980048.999991916954652.540591817005445.459392
9516980048.999991916953278.795049917006819.2049339
9616980048.999991916951972.184018517008125.8159653
9716980048.999991916950723.732426617009374.2675572



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')