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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 17 Nov 2013 14:33:22 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/17/t1384716994c6pa62tzju2eegq.htm/, Retrieved Mon, 29 Apr 2024 03:08:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=225865, Retrieved Mon, 29 Apr 2024 03:08:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [EST: monthly births] [2013-11-17 19:33:22] [52470199905e60369cb08b2777ede3f4] [Current]
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Dataseries X:
9700
9081
9084
9743
8587
9731
9563
9998
9437
10038
9918
9252
9737
9035
9133
9487
8700
9627
8947
9283
8829
9947
9628
9318
9605
8640
9214
9567
8547
9185
9470
9123
9278
10170
9434
9655
9429
8739
9552
9687
9019
9672
9206
9069
9788
10312
10105
9863
9656
9295
9946
9701
9049
10190
9706
9765
9893
9994
10433
10073
10112
9266
9820
10097
9115
10411
9678
10408
10153
10368
10581
10597
10680
9738
9556




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225865&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225865&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225865&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.118633222491654
beta0.177842898060244
gamma0.593783465803279

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.118633222491654 \tabularnewline
beta & 0.177842898060244 \tabularnewline
gamma & 0.593783465803279 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225865&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]0.118633222491654[/C][/ROW]
[ROW][C]beta[/C][C]0.177842898060244[/C][/ROW]
[ROW][C]gamma[/C][C]0.593783465803279[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225865&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225865&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
alpha0.118633222491654
beta0.177842898060244
gamma0.593783465803279







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397379768.09802350428-31.0980235042789
1490359094.82069242711-59.820692427109
1591339216.5404637229-83.5404637228985
1694879563.68373905254-76.6837390525397
1787008755.77257036385-55.772570363848
1896279656.62380040259-29.6238004025945
1989479350.24380475761-403.243804757614
2092839699.78239553138-416.78239553138
2188299042.42155295804-213.421552958043
2299479575.43327830336371.566721696643
2396289462.01672409253165.983275907465
2493188775.37973766891542.620262331086
2596059309.97278290489295.027217095108
2686408661.11902781648-21.1190278164759
2792148776.59914227238437.400857727622
2895679201.70519948747365.294800512525
2985478479.0693673371667.9306326628412
3091859432.78885628291-247.788856282914
3194708924.90192534116545.098074658838
3291239419.7736209385-296.773620938502
3392788925.52238256567352.477617434326
34101709886.20179988817283.798200111829
3594349707.31587557311-273.315875573109
3696559208.9377754286446.062224571398
3794299643.72781956261-214.727819562615
3887398799.42061988801-60.4206198880147
3995529179.84407265274372.155927347258
4096879587.7408618328899.2591381671227
4190198700.57566008411318.42433991589
4296729546.72216589415125.277834105849
4392069533.85368355124-327.85368355124
4490699501.97079455686-432.970794556861
4597889345.86084071546442.139159284539
461031210297.645014353814.354985646165
47101059805.95946624944299.040533750564
4898639774.7634805109488.2365194890554
4996569836.5370992484-180.537099248399
5092959093.01482721567201.985172784327
5199469752.4631185881193.536881411899
52970110014.0928950338-313.092895033786
5390499201.7485726286-152.748572628605
54101909890.01737584722299.982624152781
5597069663.5188578303642.4811421696395
5697659631.15772152312133.842278476883
57989310022.8300650886-129.830065088627
58999410693.3737308995-699.373730899468
591043310261.4366175684171.563382431581
601007310097.5384434728-24.5384434728476
61101129995.63683516219116.363164837807
6292669484.15430846765-218.154308467645
63982010077.1025414272-257.102541427173
64100979998.3875218294898.6124781705221
6591159305.74224179466-190.742241794662
661041110212.5772925227198.422707477264
6796789823.26733998667-145.267339986673
68104089796.48292855588611.517071444121
691015310096.947740159856.0522598402149
701036810485.5143429535-117.514342953506
711058110584.7149952148-3.71499521481746
721059710300.0096105419296.99038945808
731068010319.3899927212360.610007278758
7497389676.3680764099361.6319235900664
75955610302.5795309444-746.579530944382

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9737 & 9768.09802350428 & -31.0980235042789 \tabularnewline
14 & 9035 & 9094.82069242711 & -59.820692427109 \tabularnewline
15 & 9133 & 9216.5404637229 & -83.5404637228985 \tabularnewline
16 & 9487 & 9563.68373905254 & -76.6837390525397 \tabularnewline
17 & 8700 & 8755.77257036385 & -55.772570363848 \tabularnewline
18 & 9627 & 9656.62380040259 & -29.6238004025945 \tabularnewline
19 & 8947 & 9350.24380475761 & -403.243804757614 \tabularnewline
20 & 9283 & 9699.78239553138 & -416.78239553138 \tabularnewline
21 & 8829 & 9042.42155295804 & -213.421552958043 \tabularnewline
22 & 9947 & 9575.43327830336 & 371.566721696643 \tabularnewline
23 & 9628 & 9462.01672409253 & 165.983275907465 \tabularnewline
24 & 9318 & 8775.37973766891 & 542.620262331086 \tabularnewline
25 & 9605 & 9309.97278290489 & 295.027217095108 \tabularnewline
26 & 8640 & 8661.11902781648 & -21.1190278164759 \tabularnewline
27 & 9214 & 8776.59914227238 & 437.400857727622 \tabularnewline
28 & 9567 & 9201.70519948747 & 365.294800512525 \tabularnewline
29 & 8547 & 8479.06936733716 & 67.9306326628412 \tabularnewline
30 & 9185 & 9432.78885628291 & -247.788856282914 \tabularnewline
31 & 9470 & 8924.90192534116 & 545.098074658838 \tabularnewline
32 & 9123 & 9419.7736209385 & -296.773620938502 \tabularnewline
33 & 9278 & 8925.52238256567 & 352.477617434326 \tabularnewline
34 & 10170 & 9886.20179988817 & 283.798200111829 \tabularnewline
35 & 9434 & 9707.31587557311 & -273.315875573109 \tabularnewline
36 & 9655 & 9208.9377754286 & 446.062224571398 \tabularnewline
37 & 9429 & 9643.72781956261 & -214.727819562615 \tabularnewline
38 & 8739 & 8799.42061988801 & -60.4206198880147 \tabularnewline
39 & 9552 & 9179.84407265274 & 372.155927347258 \tabularnewline
40 & 9687 & 9587.74086183288 & 99.2591381671227 \tabularnewline
41 & 9019 & 8700.57566008411 & 318.42433991589 \tabularnewline
42 & 9672 & 9546.72216589415 & 125.277834105849 \tabularnewline
43 & 9206 & 9533.85368355124 & -327.85368355124 \tabularnewline
44 & 9069 & 9501.97079455686 & -432.970794556861 \tabularnewline
45 & 9788 & 9345.86084071546 & 442.139159284539 \tabularnewline
46 & 10312 & 10297.6450143538 & 14.354985646165 \tabularnewline
47 & 10105 & 9805.95946624944 & 299.040533750564 \tabularnewline
48 & 9863 & 9774.76348051094 & 88.2365194890554 \tabularnewline
49 & 9656 & 9836.5370992484 & -180.537099248399 \tabularnewline
50 & 9295 & 9093.01482721567 & 201.985172784327 \tabularnewline
51 & 9946 & 9752.4631185881 & 193.536881411899 \tabularnewline
52 & 9701 & 10014.0928950338 & -313.092895033786 \tabularnewline
53 & 9049 & 9201.7485726286 & -152.748572628605 \tabularnewline
54 & 10190 & 9890.01737584722 & 299.982624152781 \tabularnewline
55 & 9706 & 9663.51885783036 & 42.4811421696395 \tabularnewline
56 & 9765 & 9631.15772152312 & 133.842278476883 \tabularnewline
57 & 9893 & 10022.8300650886 & -129.830065088627 \tabularnewline
58 & 9994 & 10693.3737308995 & -699.373730899468 \tabularnewline
59 & 10433 & 10261.4366175684 & 171.563382431581 \tabularnewline
60 & 10073 & 10097.5384434728 & -24.5384434728476 \tabularnewline
61 & 10112 & 9995.63683516219 & 116.363164837807 \tabularnewline
62 & 9266 & 9484.15430846765 & -218.154308467645 \tabularnewline
63 & 9820 & 10077.1025414272 & -257.102541427173 \tabularnewline
64 & 10097 & 9998.38752182948 & 98.6124781705221 \tabularnewline
65 & 9115 & 9305.74224179466 & -190.742241794662 \tabularnewline
66 & 10411 & 10212.5772925227 & 198.422707477264 \tabularnewline
67 & 9678 & 9823.26733998667 & -145.267339986673 \tabularnewline
68 & 10408 & 9796.48292855588 & 611.517071444121 \tabularnewline
69 & 10153 & 10096.9477401598 & 56.0522598402149 \tabularnewline
70 & 10368 & 10485.5143429535 & -117.514342953506 \tabularnewline
71 & 10581 & 10584.7149952148 & -3.71499521481746 \tabularnewline
72 & 10597 & 10300.0096105419 & 296.99038945808 \tabularnewline
73 & 10680 & 10319.3899927212 & 360.610007278758 \tabularnewline
74 & 9738 & 9676.36807640993 & 61.6319235900664 \tabularnewline
75 & 9556 & 10302.5795309444 & -746.579530944382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225865&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]9737[/C][C]9768.09802350428[/C][C]-31.0980235042789[/C][/ROW]
[ROW][C]14[/C][C]9035[/C][C]9094.82069242711[/C][C]-59.820692427109[/C][/ROW]
[ROW][C]15[/C][C]9133[/C][C]9216.5404637229[/C][C]-83.5404637228985[/C][/ROW]
[ROW][C]16[/C][C]9487[/C][C]9563.68373905254[/C][C]-76.6837390525397[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]8755.77257036385[/C][C]-55.772570363848[/C][/ROW]
[ROW][C]18[/C][C]9627[/C][C]9656.62380040259[/C][C]-29.6238004025945[/C][/ROW]
[ROW][C]19[/C][C]8947[/C][C]9350.24380475761[/C][C]-403.243804757614[/C][/ROW]
[ROW][C]20[/C][C]9283[/C][C]9699.78239553138[/C][C]-416.78239553138[/C][/ROW]
[ROW][C]21[/C][C]8829[/C][C]9042.42155295804[/C][C]-213.421552958043[/C][/ROW]
[ROW][C]22[/C][C]9947[/C][C]9575.43327830336[/C][C]371.566721696643[/C][/ROW]
[ROW][C]23[/C][C]9628[/C][C]9462.01672409253[/C][C]165.983275907465[/C][/ROW]
[ROW][C]24[/C][C]9318[/C][C]8775.37973766891[/C][C]542.620262331086[/C][/ROW]
[ROW][C]25[/C][C]9605[/C][C]9309.97278290489[/C][C]295.027217095108[/C][/ROW]
[ROW][C]26[/C][C]8640[/C][C]8661.11902781648[/C][C]-21.1190278164759[/C][/ROW]
[ROW][C]27[/C][C]9214[/C][C]8776.59914227238[/C][C]437.400857727622[/C][/ROW]
[ROW][C]28[/C][C]9567[/C][C]9201.70519948747[/C][C]365.294800512525[/C][/ROW]
[ROW][C]29[/C][C]8547[/C][C]8479.06936733716[/C][C]67.9306326628412[/C][/ROW]
[ROW][C]30[/C][C]9185[/C][C]9432.78885628291[/C][C]-247.788856282914[/C][/ROW]
[ROW][C]31[/C][C]9470[/C][C]8924.90192534116[/C][C]545.098074658838[/C][/ROW]
[ROW][C]32[/C][C]9123[/C][C]9419.7736209385[/C][C]-296.773620938502[/C][/ROW]
[ROW][C]33[/C][C]9278[/C][C]8925.52238256567[/C][C]352.477617434326[/C][/ROW]
[ROW][C]34[/C][C]10170[/C][C]9886.20179988817[/C][C]283.798200111829[/C][/ROW]
[ROW][C]35[/C][C]9434[/C][C]9707.31587557311[/C][C]-273.315875573109[/C][/ROW]
[ROW][C]36[/C][C]9655[/C][C]9208.9377754286[/C][C]446.062224571398[/C][/ROW]
[ROW][C]37[/C][C]9429[/C][C]9643.72781956261[/C][C]-214.727819562615[/C][/ROW]
[ROW][C]38[/C][C]8739[/C][C]8799.42061988801[/C][C]-60.4206198880147[/C][/ROW]
[ROW][C]39[/C][C]9552[/C][C]9179.84407265274[/C][C]372.155927347258[/C][/ROW]
[ROW][C]40[/C][C]9687[/C][C]9587.74086183288[/C][C]99.2591381671227[/C][/ROW]
[ROW][C]41[/C][C]9019[/C][C]8700.57566008411[/C][C]318.42433991589[/C][/ROW]
[ROW][C]42[/C][C]9672[/C][C]9546.72216589415[/C][C]125.277834105849[/C][/ROW]
[ROW][C]43[/C][C]9206[/C][C]9533.85368355124[/C][C]-327.85368355124[/C][/ROW]
[ROW][C]44[/C][C]9069[/C][C]9501.97079455686[/C][C]-432.970794556861[/C][/ROW]
[ROW][C]45[/C][C]9788[/C][C]9345.86084071546[/C][C]442.139159284539[/C][/ROW]
[ROW][C]46[/C][C]10312[/C][C]10297.6450143538[/C][C]14.354985646165[/C][/ROW]
[ROW][C]47[/C][C]10105[/C][C]9805.95946624944[/C][C]299.040533750564[/C][/ROW]
[ROW][C]48[/C][C]9863[/C][C]9774.76348051094[/C][C]88.2365194890554[/C][/ROW]
[ROW][C]49[/C][C]9656[/C][C]9836.5370992484[/C][C]-180.537099248399[/C][/ROW]
[ROW][C]50[/C][C]9295[/C][C]9093.01482721567[/C][C]201.985172784327[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]9752.4631185881[/C][C]193.536881411899[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]10014.0928950338[/C][C]-313.092895033786[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]9201.7485726286[/C][C]-152.748572628605[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]9890.01737584722[/C][C]299.982624152781[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]9663.51885783036[/C][C]42.4811421696395[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]9631.15772152312[/C][C]133.842278476883[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]10022.8300650886[/C][C]-129.830065088627[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]10693.3737308995[/C][C]-699.373730899468[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]10261.4366175684[/C][C]171.563382431581[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]10097.5384434728[/C][C]-24.5384434728476[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]9995.63683516219[/C][C]116.363164837807[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]9484.15430846765[/C][C]-218.154308467645[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]10077.1025414272[/C][C]-257.102541427173[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9998.38752182948[/C][C]98.6124781705221[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9305.74224179466[/C][C]-190.742241794662[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]10212.5772925227[/C][C]198.422707477264[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9823.26733998667[/C][C]-145.267339986673[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]9796.48292855588[/C][C]611.517071444121[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]10096.9477401598[/C][C]56.0522598402149[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10485.5143429535[/C][C]-117.514342953506[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10584.7149952148[/C][C]-3.71499521481746[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10300.0096105419[/C][C]296.99038945808[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10319.3899927212[/C][C]360.610007278758[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]9676.36807640993[/C][C]61.6319235900664[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]10302.5795309444[/C][C]-746.579530944382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225865&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225865&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
1397379768.09802350428-31.0980235042789
1490359094.82069242711-59.820692427109
1591339216.5404637229-83.5404637228985
1694879563.68373905254-76.6837390525397
1787008755.77257036385-55.772570363848
1896279656.62380040259-29.6238004025945
1989479350.24380475761-403.243804757614
2092839699.78239553138-416.78239553138
2188299042.42155295804-213.421552958043
2299479575.43327830336371.566721696643
2396289462.01672409253165.983275907465
2493188775.37973766891542.620262331086
2596059309.97278290489295.027217095108
2686408661.11902781648-21.1190278164759
2792148776.59914227238437.400857727622
2895679201.70519948747365.294800512525
2985478479.0693673371667.9306326628412
3091859432.78885628291-247.788856282914
3194708924.90192534116545.098074658838
3291239419.7736209385-296.773620938502
3392788925.52238256567352.477617434326
34101709886.20179988817283.798200111829
3594349707.31587557311-273.315875573109
3696559208.9377754286446.062224571398
3794299643.72781956261-214.727819562615
3887398799.42061988801-60.4206198880147
3995529179.84407265274372.155927347258
4096879587.7408618328899.2591381671227
4190198700.57566008411318.42433991589
4296729546.72216589415125.277834105849
4392069533.85368355124-327.85368355124
4490699501.97079455686-432.970794556861
4597889345.86084071546442.139159284539
461031210297.645014353814.354985646165
47101059805.95946624944299.040533750564
4898639774.7634805109488.2365194890554
4996569836.5370992484-180.537099248399
5092959093.01482721567201.985172784327
5199469752.4631185881193.536881411899
52970110014.0928950338-313.092895033786
5390499201.7485726286-152.748572628605
54101909890.01737584722299.982624152781
5597069663.5188578303642.4811421696395
5697659631.15772152312133.842278476883
57989310022.8300650886-129.830065088627
58999410693.3737308995-699.373730899468
591043310261.4366175684171.563382431581
601007310097.5384434728-24.5384434728476
61101129995.63683516219116.363164837807
6292669484.15430846765-218.154308467645
63982010077.1025414272-257.102541427173
64100979998.3875218294898.6124781705221
6591159305.74224179466-190.742241794662
661041110212.5772925227198.422707477264
6796789823.26733998667-145.267339986673
68104089796.48292855588611.517071444121
691015310096.947740159856.0522598402149
701036810485.5143429535-117.514342953506
711058110584.7149952148-3.71499521481746
721059710300.0096105419296.99038945808
731068010319.3899927212360.610007278758
7497389676.3680764099361.6319235900664
75955610302.5795309444-746.579530944382







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7610362.08400429879787.7649000433810936.4031085541
779514.355744846078934.4570012120210094.2544884801
7810659.556369008710072.347474150511246.7652638668
7910074.72467916119478.2925554015910671.1568029206
8010472.17987525479864.4569336384611079.9028168708
8110407.4488406129786.2438684114411028.6538128125
8210695.396580952810058.426994429711332.3661674758
8310867.438852322710212.362728108211522.5149765371
8410739.96867864510064.415064702211415.5222925877
8510750.567990176310052.164260744511448.9717196081
869893.847174685039170.242569131510617.4517802386
8710074.02543693729322.9103340825810825.1405397918

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 10362.0840042987 & 9787.76490004338 & 10936.4031085541 \tabularnewline
77 & 9514.35574484607 & 8934.45700121202 & 10094.2544884801 \tabularnewline
78 & 10659.5563690087 & 10072.3474741505 & 11246.7652638668 \tabularnewline
79 & 10074.7246791611 & 9478.29255540159 & 10671.1568029206 \tabularnewline
80 & 10472.1798752547 & 9864.45693363846 & 11079.9028168708 \tabularnewline
81 & 10407.448840612 & 9786.24386841144 & 11028.6538128125 \tabularnewline
82 & 10695.3965809528 & 10058.4269944297 & 11332.3661674758 \tabularnewline
83 & 10867.4388523227 & 10212.3627281082 & 11522.5149765371 \tabularnewline
84 & 10739.968678645 & 10064.4150647022 & 11415.5222925877 \tabularnewline
85 & 10750.5679901763 & 10052.1642607445 & 11448.9717196081 \tabularnewline
86 & 9893.84717468503 & 9170.2425691315 & 10617.4517802386 \tabularnewline
87 & 10074.0254369372 & 9322.91033408258 & 10825.1405397918 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225865&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]76[/C][C]10362.0840042987[/C][C]9787.76490004338[/C][C]10936.4031085541[/C][/ROW]
[ROW][C]77[/C][C]9514.35574484607[/C][C]8934.45700121202[/C][C]10094.2544884801[/C][/ROW]
[ROW][C]78[/C][C]10659.5563690087[/C][C]10072.3474741505[/C][C]11246.7652638668[/C][/ROW]
[ROW][C]79[/C][C]10074.7246791611[/C][C]9478.29255540159[/C][C]10671.1568029206[/C][/ROW]
[ROW][C]80[/C][C]10472.1798752547[/C][C]9864.45693363846[/C][C]11079.9028168708[/C][/ROW]
[ROW][C]81[/C][C]10407.448840612[/C][C]9786.24386841144[/C][C]11028.6538128125[/C][/ROW]
[ROW][C]82[/C][C]10695.3965809528[/C][C]10058.4269944297[/C][C]11332.3661674758[/C][/ROW]
[ROW][C]83[/C][C]10867.4388523227[/C][C]10212.3627281082[/C][C]11522.5149765371[/C][/ROW]
[ROW][C]84[/C][C]10739.968678645[/C][C]10064.4150647022[/C][C]11415.5222925877[/C][/ROW]
[ROW][C]85[/C][C]10750.5679901763[/C][C]10052.1642607445[/C][C]11448.9717196081[/C][/ROW]
[ROW][C]86[/C][C]9893.84717468503[/C][C]9170.2425691315[/C][C]10617.4517802386[/C][/ROW]
[ROW][C]87[/C][C]10074.0254369372[/C][C]9322.91033408258[/C][C]10825.1405397918[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225865&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225865&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
7610362.08400429879787.7649000433810936.4031085541
779514.355744846078934.4570012120210094.2544884801
7810659.556369008710072.347474150511246.7652638668
7910074.72467916119478.2925554015910671.1568029206
8010472.17987525479864.4569336384611079.9028168708
8110407.4488406129786.2438684114411028.6538128125
8210695.396580952810058.426994429711332.3661674758
8310867.438852322710212.362728108211522.5149765371
8410739.96867864510064.415064702211415.5222925877
8510750.567990176310052.164260744511448.9717196081
869893.847174685039170.242569131510617.4517802386
8710074.02543693729322.9103340825810825.1405397918



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')