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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 09 Dec 2010 12:09:50 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/09/t12918965103d3moa3y9ni1ir9.htm/, Retrieved Mon, 29 Apr 2024 03:23:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107183, Retrieved Mon, 29 Apr 2024 03:23:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Structural Time Series Models] [HPC Retail Sales] [2008-03-06 16:52:55] [74be16979710d4c4e7c6647856088456]
- R  D    [Structural Time Series Models] [HPC Retail Sales] [2008-03-08 11:33:35] [74be16979710d4c4e7c6647856088456]
-  M D      [Structural Time Series Models] [workshop 8- struc...] [2010-12-09 12:02:42] [1df589bc3feb749f1946d8c1ee38b85f]
- RMP           [Exponential Smoothing] [workshop 8- expon...] [2010-12-09 12:09:50] [36a5183bc8f6439b2481209b0fbe6bda] [Current]
-                 [Exponential Smoothing] [workshop 8- multi...] [2010-12-09 12:13:47] [1df589bc3feb749f1946d8c1ee38b85f]
-    D            [Exponential Smoothing] [workshop- exponen...] [2010-12-09 16:15:55] [1df589bc3feb749f1946d8c1ee38b85f]
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Post a new message
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 time47 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 47 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107183&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]47 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107183&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107183&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 time47 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.158806071444759
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.158806071444759 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107183&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]0.158806071444759[/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=107183&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107183&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
alpha0.158806071444759
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
290819700-619
390849601.6990417757-517.699041775693
497439519.48529076058223.51470923942
585879554.980783645-967.980783645009
697319401.25955816033329.740441839675
795639453.62434232534109.375657674656
899989470.99386083234527.006139167657
994379554.68563542083-117.685635420828
10100389535.99644199417502.003558005834
1199189615.71765489236302.282345107637
1292529663.72192658602-411.721926586017
1397379598.33798489722138.662015102776
1490359620.3583547743-585.358354774309
1591339527.39989406523-394.399894065233
1694879464.766796310522.2332036894968
1787009468.29756404406-768.297564044064
1896279346.28724619765280.712753802352
1989479390.86613583344-443.866135833439
2092839320.37749855436-37.3774985543641
2188299314.44172484851-485.441724848513
2299479237.35063160995709.649368390048
2396289350.04725990723277.952740092771
2493189394.18784260867-76.1878426086678
2596059382.08875063213222.911249367866
2686409417.48841042509-777.488410425089
2792149294.01853037165-80.0185303716498
2895679281.31110192054285.688898079456
2985479326.68023347992-779.680233479925
3091859202.86227861785-17.8622786178457
3194709200.02564032349269.974359676507
3291239242.89920777453-119.899207774533
3392789223.8584856185254.1415143814793
34101709232.45648681951937.543513180486
3594349381.3440889562252.6559110437756
3696559389.70616732743265.293832672569
3794299431.83643867268-2.83643867268438
3887399431.38599499018-692.385994990182
3995529321.43089520242230.569104797580
4096879358.04666893186328.953331068142
4190199410.28645512746-391.286455127456
4296729348.14779037912323.852209620882
4392069399.57748751772-193.577487517716
4490699368.83620720488-299.83620720488
4597889321.22039706178466.779602938224
46103129395.34783203494916.65216796506
47101059540.9177617108564.082238289207
4898639630.49744594527232.502554054732
4996569667.42026315557-11.4202631555727
5092959665.60665602897-370.606656028971
5199469606.75206893373339.247931066269
5297019660.6267001121340.3732998878731
5390499667.03822525858-618.03822525858
54101909568.89000270257621.109997297426
5597069667.5260413084438.4739586915566
5697659673.6359395411891.3640604588218
5798939688.14510705388204.854892946116
5899949720.6773078189273.322692181107
59104339764.08261080088668.917389199121
60100739870.31075350068202.689246499323
61101129902.49903646133209.500963538667
6292669935.7690614448-669.7690614448
6398209829.4056680215-9.40566802150715
64100979827.9119908337269.088009166302
6591159870.64480044229-755.644800442289
66104119750.64381827639660.356181723611
6796789855.51238925018-177.512389250178
68104089827.32234408059580.677655919415
69101539919.5374813929233.462518607103
70103689956.6127468025411.38725319751
711058110021.9435403252559.056459674764
721059710110.725100402486.274899598
731068010187.9485068494492.051493150648
74973810266.0892714251-528.089271425135
75955610182.2254888580-626.225488857985

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 9081 & 9700 & -619 \tabularnewline
3 & 9084 & 9601.6990417757 & -517.699041775693 \tabularnewline
4 & 9743 & 9519.48529076058 & 223.51470923942 \tabularnewline
5 & 8587 & 9554.980783645 & -967.980783645009 \tabularnewline
6 & 9731 & 9401.25955816033 & 329.740441839675 \tabularnewline
7 & 9563 & 9453.62434232534 & 109.375657674656 \tabularnewline
8 & 9998 & 9470.99386083234 & 527.006139167657 \tabularnewline
9 & 9437 & 9554.68563542083 & -117.685635420828 \tabularnewline
10 & 10038 & 9535.99644199417 & 502.003558005834 \tabularnewline
11 & 9918 & 9615.71765489236 & 302.282345107637 \tabularnewline
12 & 9252 & 9663.72192658602 & -411.721926586017 \tabularnewline
13 & 9737 & 9598.33798489722 & 138.662015102776 \tabularnewline
14 & 9035 & 9620.3583547743 & -585.358354774309 \tabularnewline
15 & 9133 & 9527.39989406523 & -394.399894065233 \tabularnewline
16 & 9487 & 9464.7667963105 & 22.2332036894968 \tabularnewline
17 & 8700 & 9468.29756404406 & -768.297564044064 \tabularnewline
18 & 9627 & 9346.28724619765 & 280.712753802352 \tabularnewline
19 & 8947 & 9390.86613583344 & -443.866135833439 \tabularnewline
20 & 9283 & 9320.37749855436 & -37.3774985543641 \tabularnewline
21 & 8829 & 9314.44172484851 & -485.441724848513 \tabularnewline
22 & 9947 & 9237.35063160995 & 709.649368390048 \tabularnewline
23 & 9628 & 9350.04725990723 & 277.952740092771 \tabularnewline
24 & 9318 & 9394.18784260867 & -76.1878426086678 \tabularnewline
25 & 9605 & 9382.08875063213 & 222.911249367866 \tabularnewline
26 & 8640 & 9417.48841042509 & -777.488410425089 \tabularnewline
27 & 9214 & 9294.01853037165 & -80.0185303716498 \tabularnewline
28 & 9567 & 9281.31110192054 & 285.688898079456 \tabularnewline
29 & 8547 & 9326.68023347992 & -779.680233479925 \tabularnewline
30 & 9185 & 9202.86227861785 & -17.8622786178457 \tabularnewline
31 & 9470 & 9200.02564032349 & 269.974359676507 \tabularnewline
32 & 9123 & 9242.89920777453 & -119.899207774533 \tabularnewline
33 & 9278 & 9223.85848561852 & 54.1415143814793 \tabularnewline
34 & 10170 & 9232.45648681951 & 937.543513180486 \tabularnewline
35 & 9434 & 9381.34408895622 & 52.6559110437756 \tabularnewline
36 & 9655 & 9389.70616732743 & 265.293832672569 \tabularnewline
37 & 9429 & 9431.83643867268 & -2.83643867268438 \tabularnewline
38 & 8739 & 9431.38599499018 & -692.385994990182 \tabularnewline
39 & 9552 & 9321.43089520242 & 230.569104797580 \tabularnewline
40 & 9687 & 9358.04666893186 & 328.953331068142 \tabularnewline
41 & 9019 & 9410.28645512746 & -391.286455127456 \tabularnewline
42 & 9672 & 9348.14779037912 & 323.852209620882 \tabularnewline
43 & 9206 & 9399.57748751772 & -193.577487517716 \tabularnewline
44 & 9069 & 9368.83620720488 & -299.83620720488 \tabularnewline
45 & 9788 & 9321.22039706178 & 466.779602938224 \tabularnewline
46 & 10312 & 9395.34783203494 & 916.65216796506 \tabularnewline
47 & 10105 & 9540.9177617108 & 564.082238289207 \tabularnewline
48 & 9863 & 9630.49744594527 & 232.502554054732 \tabularnewline
49 & 9656 & 9667.42026315557 & -11.4202631555727 \tabularnewline
50 & 9295 & 9665.60665602897 & -370.606656028971 \tabularnewline
51 & 9946 & 9606.75206893373 & 339.247931066269 \tabularnewline
52 & 9701 & 9660.62670011213 & 40.3732998878731 \tabularnewline
53 & 9049 & 9667.03822525858 & -618.03822525858 \tabularnewline
54 & 10190 & 9568.89000270257 & 621.109997297426 \tabularnewline
55 & 9706 & 9667.52604130844 & 38.4739586915566 \tabularnewline
56 & 9765 & 9673.63593954118 & 91.3640604588218 \tabularnewline
57 & 9893 & 9688.14510705388 & 204.854892946116 \tabularnewline
58 & 9994 & 9720.6773078189 & 273.322692181107 \tabularnewline
59 & 10433 & 9764.08261080088 & 668.917389199121 \tabularnewline
60 & 10073 & 9870.31075350068 & 202.689246499323 \tabularnewline
61 & 10112 & 9902.49903646133 & 209.500963538667 \tabularnewline
62 & 9266 & 9935.7690614448 & -669.7690614448 \tabularnewline
63 & 9820 & 9829.4056680215 & -9.40566802150715 \tabularnewline
64 & 10097 & 9827.9119908337 & 269.088009166302 \tabularnewline
65 & 9115 & 9870.64480044229 & -755.644800442289 \tabularnewline
66 & 10411 & 9750.64381827639 & 660.356181723611 \tabularnewline
67 & 9678 & 9855.51238925018 & -177.512389250178 \tabularnewline
68 & 10408 & 9827.32234408059 & 580.677655919415 \tabularnewline
69 & 10153 & 9919.5374813929 & 233.462518607103 \tabularnewline
70 & 10368 & 9956.6127468025 & 411.38725319751 \tabularnewline
71 & 10581 & 10021.9435403252 & 559.056459674764 \tabularnewline
72 & 10597 & 10110.725100402 & 486.274899598 \tabularnewline
73 & 10680 & 10187.9485068494 & 492.051493150648 \tabularnewline
74 & 9738 & 10266.0892714251 & -528.089271425135 \tabularnewline
75 & 9556 & 10182.2254888580 & -626.225488857985 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107183&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]9081[/C][C]9700[/C][C]-619[/C][/ROW]
[ROW][C]3[/C][C]9084[/C][C]9601.6990417757[/C][C]-517.699041775693[/C][/ROW]
[ROW][C]4[/C][C]9743[/C][C]9519.48529076058[/C][C]223.51470923942[/C][/ROW]
[ROW][C]5[/C][C]8587[/C][C]9554.980783645[/C][C]-967.980783645009[/C][/ROW]
[ROW][C]6[/C][C]9731[/C][C]9401.25955816033[/C][C]329.740441839675[/C][/ROW]
[ROW][C]7[/C][C]9563[/C][C]9453.62434232534[/C][C]109.375657674656[/C][/ROW]
[ROW][C]8[/C][C]9998[/C][C]9470.99386083234[/C][C]527.006139167657[/C][/ROW]
[ROW][C]9[/C][C]9437[/C][C]9554.68563542083[/C][C]-117.685635420828[/C][/ROW]
[ROW][C]10[/C][C]10038[/C][C]9535.99644199417[/C][C]502.003558005834[/C][/ROW]
[ROW][C]11[/C][C]9918[/C][C]9615.71765489236[/C][C]302.282345107637[/C][/ROW]
[ROW][C]12[/C][C]9252[/C][C]9663.72192658602[/C][C]-411.721926586017[/C][/ROW]
[ROW][C]13[/C][C]9737[/C][C]9598.33798489722[/C][C]138.662015102776[/C][/ROW]
[ROW][C]14[/C][C]9035[/C][C]9620.3583547743[/C][C]-585.358354774309[/C][/ROW]
[ROW][C]15[/C][C]9133[/C][C]9527.39989406523[/C][C]-394.399894065233[/C][/ROW]
[ROW][C]16[/C][C]9487[/C][C]9464.7667963105[/C][C]22.2332036894968[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]9468.29756404406[/C][C]-768.297564044064[/C][/ROW]
[ROW][C]18[/C][C]9627[/C][C]9346.28724619765[/C][C]280.712753802352[/C][/ROW]
[ROW][C]19[/C][C]8947[/C][C]9390.86613583344[/C][C]-443.866135833439[/C][/ROW]
[ROW][C]20[/C][C]9283[/C][C]9320.37749855436[/C][C]-37.3774985543641[/C][/ROW]
[ROW][C]21[/C][C]8829[/C][C]9314.44172484851[/C][C]-485.441724848513[/C][/ROW]
[ROW][C]22[/C][C]9947[/C][C]9237.35063160995[/C][C]709.649368390048[/C][/ROW]
[ROW][C]23[/C][C]9628[/C][C]9350.04725990723[/C][C]277.952740092771[/C][/ROW]
[ROW][C]24[/C][C]9318[/C][C]9394.18784260867[/C][C]-76.1878426086678[/C][/ROW]
[ROW][C]25[/C][C]9605[/C][C]9382.08875063213[/C][C]222.911249367866[/C][/ROW]
[ROW][C]26[/C][C]8640[/C][C]9417.48841042509[/C][C]-777.488410425089[/C][/ROW]
[ROW][C]27[/C][C]9214[/C][C]9294.01853037165[/C][C]-80.0185303716498[/C][/ROW]
[ROW][C]28[/C][C]9567[/C][C]9281.31110192054[/C][C]285.688898079456[/C][/ROW]
[ROW][C]29[/C][C]8547[/C][C]9326.68023347992[/C][C]-779.680233479925[/C][/ROW]
[ROW][C]30[/C][C]9185[/C][C]9202.86227861785[/C][C]-17.8622786178457[/C][/ROW]
[ROW][C]31[/C][C]9470[/C][C]9200.02564032349[/C][C]269.974359676507[/C][/ROW]
[ROW][C]32[/C][C]9123[/C][C]9242.89920777453[/C][C]-119.899207774533[/C][/ROW]
[ROW][C]33[/C][C]9278[/C][C]9223.85848561852[/C][C]54.1415143814793[/C][/ROW]
[ROW][C]34[/C][C]10170[/C][C]9232.45648681951[/C][C]937.543513180486[/C][/ROW]
[ROW][C]35[/C][C]9434[/C][C]9381.34408895622[/C][C]52.6559110437756[/C][/ROW]
[ROW][C]36[/C][C]9655[/C][C]9389.70616732743[/C][C]265.293832672569[/C][/ROW]
[ROW][C]37[/C][C]9429[/C][C]9431.83643867268[/C][C]-2.83643867268438[/C][/ROW]
[ROW][C]38[/C][C]8739[/C][C]9431.38599499018[/C][C]-692.385994990182[/C][/ROW]
[ROW][C]39[/C][C]9552[/C][C]9321.43089520242[/C][C]230.569104797580[/C][/ROW]
[ROW][C]40[/C][C]9687[/C][C]9358.04666893186[/C][C]328.953331068142[/C][/ROW]
[ROW][C]41[/C][C]9019[/C][C]9410.28645512746[/C][C]-391.286455127456[/C][/ROW]
[ROW][C]42[/C][C]9672[/C][C]9348.14779037912[/C][C]323.852209620882[/C][/ROW]
[ROW][C]43[/C][C]9206[/C][C]9399.57748751772[/C][C]-193.577487517716[/C][/ROW]
[ROW][C]44[/C][C]9069[/C][C]9368.83620720488[/C][C]-299.83620720488[/C][/ROW]
[ROW][C]45[/C][C]9788[/C][C]9321.22039706178[/C][C]466.779602938224[/C][/ROW]
[ROW][C]46[/C][C]10312[/C][C]9395.34783203494[/C][C]916.65216796506[/C][/ROW]
[ROW][C]47[/C][C]10105[/C][C]9540.9177617108[/C][C]564.082238289207[/C][/ROW]
[ROW][C]48[/C][C]9863[/C][C]9630.49744594527[/C][C]232.502554054732[/C][/ROW]
[ROW][C]49[/C][C]9656[/C][C]9667.42026315557[/C][C]-11.4202631555727[/C][/ROW]
[ROW][C]50[/C][C]9295[/C][C]9665.60665602897[/C][C]-370.606656028971[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]9606.75206893373[/C][C]339.247931066269[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]9660.62670011213[/C][C]40.3732998878731[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]9667.03822525858[/C][C]-618.03822525858[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]9568.89000270257[/C][C]621.109997297426[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]9667.52604130844[/C][C]38.4739586915566[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]9673.63593954118[/C][C]91.3640604588218[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]9688.14510705388[/C][C]204.854892946116[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]9720.6773078189[/C][C]273.322692181107[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]9764.08261080088[/C][C]668.917389199121[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]9870.31075350068[/C][C]202.689246499323[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]9902.49903646133[/C][C]209.500963538667[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]9935.7690614448[/C][C]-669.7690614448[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]9829.4056680215[/C][C]-9.40566802150715[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9827.9119908337[/C][C]269.088009166302[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9870.64480044229[/C][C]-755.644800442289[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]9750.64381827639[/C][C]660.356181723611[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9855.51238925018[/C][C]-177.512389250178[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]9827.32234408059[/C][C]580.677655919415[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]9919.5374813929[/C][C]233.462518607103[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]9956.6127468025[/C][C]411.38725319751[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10021.9435403252[/C][C]559.056459674764[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10110.725100402[/C][C]486.274899598[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10187.9485068494[/C][C]492.051493150648[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]10266.0892714251[/C][C]-528.089271425135[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]10182.2254888580[/C][C]-626.225488857985[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107183&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107183&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
290819700-619
390849601.6990417757-517.699041775693
497439519.48529076058223.51470923942
585879554.980783645-967.980783645009
697319401.25955816033329.740441839675
795639453.62434232534109.375657674656
899989470.99386083234527.006139167657
994379554.68563542083-117.685635420828
10100389535.99644199417502.003558005834
1199189615.71765489236302.282345107637
1292529663.72192658602-411.721926586017
1397379598.33798489722138.662015102776
1490359620.3583547743-585.358354774309
1591339527.39989406523-394.399894065233
1694879464.766796310522.2332036894968
1787009468.29756404406-768.297564044064
1896279346.28724619765280.712753802352
1989479390.86613583344-443.866135833439
2092839320.37749855436-37.3774985543641
2188299314.44172484851-485.441724848513
2299479237.35063160995709.649368390048
2396289350.04725990723277.952740092771
2493189394.18784260867-76.1878426086678
2596059382.08875063213222.911249367866
2686409417.48841042509-777.488410425089
2792149294.01853037165-80.0185303716498
2895679281.31110192054285.688898079456
2985479326.68023347992-779.680233479925
3091859202.86227861785-17.8622786178457
3194709200.02564032349269.974359676507
3291239242.89920777453-119.899207774533
3392789223.8584856185254.1415143814793
34101709232.45648681951937.543513180486
3594349381.3440889562252.6559110437756
3696559389.70616732743265.293832672569
3794299431.83643867268-2.83643867268438
3887399431.38599499018-692.385994990182
3995529321.43089520242230.569104797580
4096879358.04666893186328.953331068142
4190199410.28645512746-391.286455127456
4296729348.14779037912323.852209620882
4392069399.57748751772-193.577487517716
4490699368.83620720488-299.83620720488
4597889321.22039706178466.779602938224
46103129395.34783203494916.65216796506
47101059540.9177617108564.082238289207
4898639630.49744594527232.502554054732
4996569667.42026315557-11.4202631555727
5092959665.60665602897-370.606656028971
5199469606.75206893373339.247931066269
5297019660.6267001121340.3732998878731
5390499667.03822525858-618.03822525858
54101909568.89000270257621.109997297426
5597069667.5260413084438.4739586915566
5697659673.6359395411891.3640604588218
5798939688.14510705388204.854892946116
5899949720.6773078189273.322692181107
59104339764.08261080088668.917389199121
60100739870.31075350068202.689246499323
61101129902.49903646133209.500963538667
6292669935.7690614448-669.7690614448
6398209829.4056680215-9.40566802150715
64100979827.9119908337269.088009166302
6591159870.64480044229-755.644800442289
66104119750.64381827639660.356181723611
6796789855.51238925018-177.512389250178
68104089827.32234408059580.677655919415
69101539919.5374813929233.462518607103
70103689956.6127468025411.38725319751
711058110021.9435403252559.056459674764
721059710110.725100402486.274899598
731068010187.9485068494492.051493150648
74973810266.0892714251-528.089271425135
75955610182.2254888580-626.225488857985







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7610082.77707913399200.1100086337510965.444149634
7710082.77707913399189.0491583453910976.5049999224
7810082.77707913399178.1235347045410987.4306235632
7910082.77707913399167.3282960224510998.2258622453
8010082.77707913399156.6588828155911008.8952754522
8110082.77707913399146.1109953006511019.4431629671
8210082.77707913399135.6805731456411029.8735851221
8310082.77707913399125.3637772068811040.1903810609
8410082.77707913399115.1569730186711050.3971852491
8510082.77707913399105.056715834611060.4974424331
8610082.77707913399095.0597370457211070.4944212220
8710082.77707913399085.1629318237411080.391226444

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 10082.7770791339 & 9200.11000863375 & 10965.444149634 \tabularnewline
77 & 10082.7770791339 & 9189.04915834539 & 10976.5049999224 \tabularnewline
78 & 10082.7770791339 & 9178.12353470454 & 10987.4306235632 \tabularnewline
79 & 10082.7770791339 & 9167.32829602245 & 10998.2258622453 \tabularnewline
80 & 10082.7770791339 & 9156.65888281559 & 11008.8952754522 \tabularnewline
81 & 10082.7770791339 & 9146.11099530065 & 11019.4431629671 \tabularnewline
82 & 10082.7770791339 & 9135.68057314564 & 11029.8735851221 \tabularnewline
83 & 10082.7770791339 & 9125.36377720688 & 11040.1903810609 \tabularnewline
84 & 10082.7770791339 & 9115.15697301867 & 11050.3971852491 \tabularnewline
85 & 10082.7770791339 & 9105.0567158346 & 11060.4974424331 \tabularnewline
86 & 10082.7770791339 & 9095.05973704572 & 11070.4944212220 \tabularnewline
87 & 10082.7770791339 & 9085.16293182374 & 11080.391226444 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107183&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]10082.7770791339[/C][C]9200.11000863375[/C][C]10965.444149634[/C][/ROW]
[ROW][C]77[/C][C]10082.7770791339[/C][C]9189.04915834539[/C][C]10976.5049999224[/C][/ROW]
[ROW][C]78[/C][C]10082.7770791339[/C][C]9178.12353470454[/C][C]10987.4306235632[/C][/ROW]
[ROW][C]79[/C][C]10082.7770791339[/C][C]9167.32829602245[/C][C]10998.2258622453[/C][/ROW]
[ROW][C]80[/C][C]10082.7770791339[/C][C]9156.65888281559[/C][C]11008.8952754522[/C][/ROW]
[ROW][C]81[/C][C]10082.7770791339[/C][C]9146.11099530065[/C][C]11019.4431629671[/C][/ROW]
[ROW][C]82[/C][C]10082.7770791339[/C][C]9135.68057314564[/C][C]11029.8735851221[/C][/ROW]
[ROW][C]83[/C][C]10082.7770791339[/C][C]9125.36377720688[/C][C]11040.1903810609[/C][/ROW]
[ROW][C]84[/C][C]10082.7770791339[/C][C]9115.15697301867[/C][C]11050.3971852491[/C][/ROW]
[ROW][C]85[/C][C]10082.7770791339[/C][C]9105.0567158346[/C][C]11060.4974424331[/C][/ROW]
[ROW][C]86[/C][C]10082.7770791339[/C][C]9095.05973704572[/C][C]11070.4944212220[/C][/ROW]
[ROW][C]87[/C][C]10082.7770791339[/C][C]9085.16293182374[/C][C]11080.391226444[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107183&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107183&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
7610082.77707913399200.1100086337510965.444149634
7710082.77707913399189.0491583453910976.5049999224
7810082.77707913399178.1235347045410987.4306235632
7910082.77707913399167.3282960224510998.2258622453
8010082.77707913399156.6588828155911008.8952754522
8110082.77707913399146.1109953006511019.4431629671
8210082.77707913399135.6805731456411029.8735851221
8310082.77707913399125.3637772068811040.1903810609
8410082.77707913399115.1569730186711050.3971852491
8510082.77707913399105.056715834611060.4974424331
8610082.77707913399095.0597370457211070.4944212220
8710082.77707913399085.1629318237411080.391226444



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')