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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 04:43:07 -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/2012/Dec/21/t1356083101i8u3ank5jnplrq4.htm/, Retrieved Fri, 26 Apr 2024 15:22:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203387, Retrieved Fri, 26 Apr 2024 15:22:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Gemiddelde consum...] [2012-12-21 09:43:07] [6b47280b0442613aa0037e9cfc5a696f] [Current]
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Dataseries X:
1.94
1.82
1.8
1.79
1.79
1.78
1.81
1.84
1.87
1.87
1.87
1.84
1.82
1.83
1.83
1.82
1.83
1.87
1.88
1.9
1.98
2.03
2.14
2.42
2.73
2.84
2.85
2.94
3.06
3.24
3.18
3.01
2.87
2.73
2.63
2.39
2.26
2.11
2.01
1.99
1.96
1.93
1.98
2.07
2.24
2.31
2.23
2.26
2.28
2.3
2.33
2.26
2.24
2.47
2.55
2.89
3.21
3.21
2.92
2.68
2.4
2.28
2.24
2.2
2.18
2.23
2.24
2.25
2.23
2.25
2.23
2.21




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203387&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203387&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203387&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999920025746041
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999920025746041 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203387&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]0.999920025746041[/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=203387&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203387&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
alpha0.999920025746041
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21.821.94-0.12
31.81.82000959691048-0.0200095969104752
41.791.80000160025258-0.0100016002525849
51.791.79000079987052-7.99870518708445e-07
61.781.79000000006397-0.0100000000639691
71.811.780000799742540.0299992002574554
81.841.809997600836340.03000239916366
91.871.839997600580510.0300023994194902
101.871.869997600580492.39941951063471e-06
111.871.869999999808111.91891835754632e-10
121.841.86999999999998-0.0299999999999847
131.821.84000239922762-0.0200023992276188
141.831.820001599676960.00999840032304444
151.831.829999200385397.9961460652811e-07
161.821.82999999993605-0.00999999993605138
171.831.820000799742530.00999920025746559
181.871.829999200321420.0400007996785807
191.881.869996800965890.0100031990341118
201.91.879999200001620.02000079999838
211.981.899998400450940.0800015995490586
222.031.979993601931760.0500063980682393
232.142.029996000775620.110003999224379
242.422.139991202512230.28000879748777
252.732.419977606505320.310022393494681
262.842.729975206190370.11002479380963
272.852.83999120084920.010008799150802
282.942.849999199553750.0900008004462451
293.062.939992802253130.120007197746872
303.243.059990402513890.18000959748611
313.183.23998560386674-0.0599856038667355
323.013.18000479730392-0.170004797303918
332.873.01001359600683-0.140013596006833
342.732.87001119748289-0.140011197482885
352.632.73001119729106-0.100011197291065
362.392.63000799832089-0.240007998320891
372.262.39001919446061-0.13001919446061
382.112.26001039818808-0.150010398188077
392.012.11001199696968-0.100011996969681
401.992.01000799838484-0.0200079983848445
411.961.99000160012474-0.0300016001247441
421.931.96000239935559-0.0300023993555876
431.981.930002399419510.0499976005804945
442.071.979996001479190.0900039985208061
452.242.069992801997370.170007198002635
462.312.239986403801170.070013596198828
472.232.30999440071488-0.079994400714877
482.262.230006397492520.0299936025074818
492.282.259997601284020.0200023987159841
502.32.279998400323090.0200015996769145
512.332.299998400386990.0300015996130125
522.262.32999760064445-0.0699976006444536
532.242.26000559800589-0.02000559800589
542.472.240001599932780.229998400067224
552.552.469981606049540.0800183939504566
562.892.549993600588640.340006399411359
573.212.889972808241870.320027191758134
583.213.209974406064092.55939359075086e-05
592.923.20999999795314-0.289999997953144
602.682.92002319253348-0.240023192533484
612.42.68001919567576-0.280019195675756
622.282.40002239432627-0.120022394326269
632.242.28000959870144-0.0400095987014444
642.22.24000319973781-0.0400031997378072
652.182.20000319922606-0.0200031992260552
662.232.180001599740930.049998400259065
672.242.229996001415240.01000399858476
682.252.239999199937680.0100008000623233
692.232.24999920019348-0.0199992001934759
702.252.230001599421120.0199984005788849
712.232.24999840064283-0.0199984006428333
722.212.23000159935717-0.0200015993571716

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.82 & 1.94 & -0.12 \tabularnewline
3 & 1.8 & 1.82000959691048 & -0.0200095969104752 \tabularnewline
4 & 1.79 & 1.80000160025258 & -0.0100016002525849 \tabularnewline
5 & 1.79 & 1.79000079987052 & -7.99870518708445e-07 \tabularnewline
6 & 1.78 & 1.79000000006397 & -0.0100000000639691 \tabularnewline
7 & 1.81 & 1.78000079974254 & 0.0299992002574554 \tabularnewline
8 & 1.84 & 1.80999760083634 & 0.03000239916366 \tabularnewline
9 & 1.87 & 1.83999760058051 & 0.0300023994194902 \tabularnewline
10 & 1.87 & 1.86999760058049 & 2.39941951063471e-06 \tabularnewline
11 & 1.87 & 1.86999999980811 & 1.91891835754632e-10 \tabularnewline
12 & 1.84 & 1.86999999999998 & -0.0299999999999847 \tabularnewline
13 & 1.82 & 1.84000239922762 & -0.0200023992276188 \tabularnewline
14 & 1.83 & 1.82000159967696 & 0.00999840032304444 \tabularnewline
15 & 1.83 & 1.82999920038539 & 7.9961460652811e-07 \tabularnewline
16 & 1.82 & 1.82999999993605 & -0.00999999993605138 \tabularnewline
17 & 1.83 & 1.82000079974253 & 0.00999920025746559 \tabularnewline
18 & 1.87 & 1.82999920032142 & 0.0400007996785807 \tabularnewline
19 & 1.88 & 1.86999680096589 & 0.0100031990341118 \tabularnewline
20 & 1.9 & 1.87999920000162 & 0.02000079999838 \tabularnewline
21 & 1.98 & 1.89999840045094 & 0.0800015995490586 \tabularnewline
22 & 2.03 & 1.97999360193176 & 0.0500063980682393 \tabularnewline
23 & 2.14 & 2.02999600077562 & 0.110003999224379 \tabularnewline
24 & 2.42 & 2.13999120251223 & 0.28000879748777 \tabularnewline
25 & 2.73 & 2.41997760650532 & 0.310022393494681 \tabularnewline
26 & 2.84 & 2.72997520619037 & 0.11002479380963 \tabularnewline
27 & 2.85 & 2.8399912008492 & 0.010008799150802 \tabularnewline
28 & 2.94 & 2.84999919955375 & 0.0900008004462451 \tabularnewline
29 & 3.06 & 2.93999280225313 & 0.120007197746872 \tabularnewline
30 & 3.24 & 3.05999040251389 & 0.18000959748611 \tabularnewline
31 & 3.18 & 3.23998560386674 & -0.0599856038667355 \tabularnewline
32 & 3.01 & 3.18000479730392 & -0.170004797303918 \tabularnewline
33 & 2.87 & 3.01001359600683 & -0.140013596006833 \tabularnewline
34 & 2.73 & 2.87001119748289 & -0.140011197482885 \tabularnewline
35 & 2.63 & 2.73001119729106 & -0.100011197291065 \tabularnewline
36 & 2.39 & 2.63000799832089 & -0.240007998320891 \tabularnewline
37 & 2.26 & 2.39001919446061 & -0.13001919446061 \tabularnewline
38 & 2.11 & 2.26001039818808 & -0.150010398188077 \tabularnewline
39 & 2.01 & 2.11001199696968 & -0.100011996969681 \tabularnewline
40 & 1.99 & 2.01000799838484 & -0.0200079983848445 \tabularnewline
41 & 1.96 & 1.99000160012474 & -0.0300016001247441 \tabularnewline
42 & 1.93 & 1.96000239935559 & -0.0300023993555876 \tabularnewline
43 & 1.98 & 1.93000239941951 & 0.0499976005804945 \tabularnewline
44 & 2.07 & 1.97999600147919 & 0.0900039985208061 \tabularnewline
45 & 2.24 & 2.06999280199737 & 0.170007198002635 \tabularnewline
46 & 2.31 & 2.23998640380117 & 0.070013596198828 \tabularnewline
47 & 2.23 & 2.30999440071488 & -0.079994400714877 \tabularnewline
48 & 2.26 & 2.23000639749252 & 0.0299936025074818 \tabularnewline
49 & 2.28 & 2.25999760128402 & 0.0200023987159841 \tabularnewline
50 & 2.3 & 2.27999840032309 & 0.0200015996769145 \tabularnewline
51 & 2.33 & 2.29999840038699 & 0.0300015996130125 \tabularnewline
52 & 2.26 & 2.32999760064445 & -0.0699976006444536 \tabularnewline
53 & 2.24 & 2.26000559800589 & -0.02000559800589 \tabularnewline
54 & 2.47 & 2.24000159993278 & 0.229998400067224 \tabularnewline
55 & 2.55 & 2.46998160604954 & 0.0800183939504566 \tabularnewline
56 & 2.89 & 2.54999360058864 & 0.340006399411359 \tabularnewline
57 & 3.21 & 2.88997280824187 & 0.320027191758134 \tabularnewline
58 & 3.21 & 3.20997440606409 & 2.55939359075086e-05 \tabularnewline
59 & 2.92 & 3.20999999795314 & -0.289999997953144 \tabularnewline
60 & 2.68 & 2.92002319253348 & -0.240023192533484 \tabularnewline
61 & 2.4 & 2.68001919567576 & -0.280019195675756 \tabularnewline
62 & 2.28 & 2.40002239432627 & -0.120022394326269 \tabularnewline
63 & 2.24 & 2.28000959870144 & -0.0400095987014444 \tabularnewline
64 & 2.2 & 2.24000319973781 & -0.0400031997378072 \tabularnewline
65 & 2.18 & 2.20000319922606 & -0.0200031992260552 \tabularnewline
66 & 2.23 & 2.18000159974093 & 0.049998400259065 \tabularnewline
67 & 2.24 & 2.22999600141524 & 0.01000399858476 \tabularnewline
68 & 2.25 & 2.23999919993768 & 0.0100008000623233 \tabularnewline
69 & 2.23 & 2.24999920019348 & -0.0199992001934759 \tabularnewline
70 & 2.25 & 2.23000159942112 & 0.0199984005788849 \tabularnewline
71 & 2.23 & 2.24999840064283 & -0.0199984006428333 \tabularnewline
72 & 2.21 & 2.23000159935717 & -0.0200015993571716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203387&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]1.82[/C][C]1.94[/C][C]-0.12[/C][/ROW]
[ROW][C]3[/C][C]1.8[/C][C]1.82000959691048[/C][C]-0.0200095969104752[/C][/ROW]
[ROW][C]4[/C][C]1.79[/C][C]1.80000160025258[/C][C]-0.0100016002525849[/C][/ROW]
[ROW][C]5[/C][C]1.79[/C][C]1.79000079987052[/C][C]-7.99870518708445e-07[/C][/ROW]
[ROW][C]6[/C][C]1.78[/C][C]1.79000000006397[/C][C]-0.0100000000639691[/C][/ROW]
[ROW][C]7[/C][C]1.81[/C][C]1.78000079974254[/C][C]0.0299992002574554[/C][/ROW]
[ROW][C]8[/C][C]1.84[/C][C]1.80999760083634[/C][C]0.03000239916366[/C][/ROW]
[ROW][C]9[/C][C]1.87[/C][C]1.83999760058051[/C][C]0.0300023994194902[/C][/ROW]
[ROW][C]10[/C][C]1.87[/C][C]1.86999760058049[/C][C]2.39941951063471e-06[/C][/ROW]
[ROW][C]11[/C][C]1.87[/C][C]1.86999999980811[/C][C]1.91891835754632e-10[/C][/ROW]
[ROW][C]12[/C][C]1.84[/C][C]1.86999999999998[/C][C]-0.0299999999999847[/C][/ROW]
[ROW][C]13[/C][C]1.82[/C][C]1.84000239922762[/C][C]-0.0200023992276188[/C][/ROW]
[ROW][C]14[/C][C]1.83[/C][C]1.82000159967696[/C][C]0.00999840032304444[/C][/ROW]
[ROW][C]15[/C][C]1.83[/C][C]1.82999920038539[/C][C]7.9961460652811e-07[/C][/ROW]
[ROW][C]16[/C][C]1.82[/C][C]1.82999999993605[/C][C]-0.00999999993605138[/C][/ROW]
[ROW][C]17[/C][C]1.83[/C][C]1.82000079974253[/C][C]0.00999920025746559[/C][/ROW]
[ROW][C]18[/C][C]1.87[/C][C]1.82999920032142[/C][C]0.0400007996785807[/C][/ROW]
[ROW][C]19[/C][C]1.88[/C][C]1.86999680096589[/C][C]0.0100031990341118[/C][/ROW]
[ROW][C]20[/C][C]1.9[/C][C]1.87999920000162[/C][C]0.02000079999838[/C][/ROW]
[ROW][C]21[/C][C]1.98[/C][C]1.89999840045094[/C][C]0.0800015995490586[/C][/ROW]
[ROW][C]22[/C][C]2.03[/C][C]1.97999360193176[/C][C]0.0500063980682393[/C][/ROW]
[ROW][C]23[/C][C]2.14[/C][C]2.02999600077562[/C][C]0.110003999224379[/C][/ROW]
[ROW][C]24[/C][C]2.42[/C][C]2.13999120251223[/C][C]0.28000879748777[/C][/ROW]
[ROW][C]25[/C][C]2.73[/C][C]2.41997760650532[/C][C]0.310022393494681[/C][/ROW]
[ROW][C]26[/C][C]2.84[/C][C]2.72997520619037[/C][C]0.11002479380963[/C][/ROW]
[ROW][C]27[/C][C]2.85[/C][C]2.8399912008492[/C][C]0.010008799150802[/C][/ROW]
[ROW][C]28[/C][C]2.94[/C][C]2.84999919955375[/C][C]0.0900008004462451[/C][/ROW]
[ROW][C]29[/C][C]3.06[/C][C]2.93999280225313[/C][C]0.120007197746872[/C][/ROW]
[ROW][C]30[/C][C]3.24[/C][C]3.05999040251389[/C][C]0.18000959748611[/C][/ROW]
[ROW][C]31[/C][C]3.18[/C][C]3.23998560386674[/C][C]-0.0599856038667355[/C][/ROW]
[ROW][C]32[/C][C]3.01[/C][C]3.18000479730392[/C][C]-0.170004797303918[/C][/ROW]
[ROW][C]33[/C][C]2.87[/C][C]3.01001359600683[/C][C]-0.140013596006833[/C][/ROW]
[ROW][C]34[/C][C]2.73[/C][C]2.87001119748289[/C][C]-0.140011197482885[/C][/ROW]
[ROW][C]35[/C][C]2.63[/C][C]2.73001119729106[/C][C]-0.100011197291065[/C][/ROW]
[ROW][C]36[/C][C]2.39[/C][C]2.63000799832089[/C][C]-0.240007998320891[/C][/ROW]
[ROW][C]37[/C][C]2.26[/C][C]2.39001919446061[/C][C]-0.13001919446061[/C][/ROW]
[ROW][C]38[/C][C]2.11[/C][C]2.26001039818808[/C][C]-0.150010398188077[/C][/ROW]
[ROW][C]39[/C][C]2.01[/C][C]2.11001199696968[/C][C]-0.100011996969681[/C][/ROW]
[ROW][C]40[/C][C]1.99[/C][C]2.01000799838484[/C][C]-0.0200079983848445[/C][/ROW]
[ROW][C]41[/C][C]1.96[/C][C]1.99000160012474[/C][C]-0.0300016001247441[/C][/ROW]
[ROW][C]42[/C][C]1.93[/C][C]1.96000239935559[/C][C]-0.0300023993555876[/C][/ROW]
[ROW][C]43[/C][C]1.98[/C][C]1.93000239941951[/C][C]0.0499976005804945[/C][/ROW]
[ROW][C]44[/C][C]2.07[/C][C]1.97999600147919[/C][C]0.0900039985208061[/C][/ROW]
[ROW][C]45[/C][C]2.24[/C][C]2.06999280199737[/C][C]0.170007198002635[/C][/ROW]
[ROW][C]46[/C][C]2.31[/C][C]2.23998640380117[/C][C]0.070013596198828[/C][/ROW]
[ROW][C]47[/C][C]2.23[/C][C]2.30999440071488[/C][C]-0.079994400714877[/C][/ROW]
[ROW][C]48[/C][C]2.26[/C][C]2.23000639749252[/C][C]0.0299936025074818[/C][/ROW]
[ROW][C]49[/C][C]2.28[/C][C]2.25999760128402[/C][C]0.0200023987159841[/C][/ROW]
[ROW][C]50[/C][C]2.3[/C][C]2.27999840032309[/C][C]0.0200015996769145[/C][/ROW]
[ROW][C]51[/C][C]2.33[/C][C]2.29999840038699[/C][C]0.0300015996130125[/C][/ROW]
[ROW][C]52[/C][C]2.26[/C][C]2.32999760064445[/C][C]-0.0699976006444536[/C][/ROW]
[ROW][C]53[/C][C]2.24[/C][C]2.26000559800589[/C][C]-0.02000559800589[/C][/ROW]
[ROW][C]54[/C][C]2.47[/C][C]2.24000159993278[/C][C]0.229998400067224[/C][/ROW]
[ROW][C]55[/C][C]2.55[/C][C]2.46998160604954[/C][C]0.0800183939504566[/C][/ROW]
[ROW][C]56[/C][C]2.89[/C][C]2.54999360058864[/C][C]0.340006399411359[/C][/ROW]
[ROW][C]57[/C][C]3.21[/C][C]2.88997280824187[/C][C]0.320027191758134[/C][/ROW]
[ROW][C]58[/C][C]3.21[/C][C]3.20997440606409[/C][C]2.55939359075086e-05[/C][/ROW]
[ROW][C]59[/C][C]2.92[/C][C]3.20999999795314[/C][C]-0.289999997953144[/C][/ROW]
[ROW][C]60[/C][C]2.68[/C][C]2.92002319253348[/C][C]-0.240023192533484[/C][/ROW]
[ROW][C]61[/C][C]2.4[/C][C]2.68001919567576[/C][C]-0.280019195675756[/C][/ROW]
[ROW][C]62[/C][C]2.28[/C][C]2.40002239432627[/C][C]-0.120022394326269[/C][/ROW]
[ROW][C]63[/C][C]2.24[/C][C]2.28000959870144[/C][C]-0.0400095987014444[/C][/ROW]
[ROW][C]64[/C][C]2.2[/C][C]2.24000319973781[/C][C]-0.0400031997378072[/C][/ROW]
[ROW][C]65[/C][C]2.18[/C][C]2.20000319922606[/C][C]-0.0200031992260552[/C][/ROW]
[ROW][C]66[/C][C]2.23[/C][C]2.18000159974093[/C][C]0.049998400259065[/C][/ROW]
[ROW][C]67[/C][C]2.24[/C][C]2.22999600141524[/C][C]0.01000399858476[/C][/ROW]
[ROW][C]68[/C][C]2.25[/C][C]2.23999919993768[/C][C]0.0100008000623233[/C][/ROW]
[ROW][C]69[/C][C]2.23[/C][C]2.24999920019348[/C][C]-0.0199992001934759[/C][/ROW]
[ROW][C]70[/C][C]2.25[/C][C]2.23000159942112[/C][C]0.0199984005788849[/C][/ROW]
[ROW][C]71[/C][C]2.23[/C][C]2.24999840064283[/C][C]-0.0199984006428333[/C][/ROW]
[ROW][C]72[/C][C]2.21[/C][C]2.23000159935717[/C][C]-0.0200015993571716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203387&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203387&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
21.821.94-0.12
31.81.82000959691048-0.0200095969104752
41.791.80000160025258-0.0100016002525849
51.791.79000079987052-7.99870518708445e-07
61.781.79000000006397-0.0100000000639691
71.811.780000799742540.0299992002574554
81.841.809997600836340.03000239916366
91.871.839997600580510.0300023994194902
101.871.869997600580492.39941951063471e-06
111.871.869999999808111.91891835754632e-10
121.841.86999999999998-0.0299999999999847
131.821.84000239922762-0.0200023992276188
141.831.820001599676960.00999840032304444
151.831.829999200385397.9961460652811e-07
161.821.82999999993605-0.00999999993605138
171.831.820000799742530.00999920025746559
181.871.829999200321420.0400007996785807
191.881.869996800965890.0100031990341118
201.91.879999200001620.02000079999838
211.981.899998400450940.0800015995490586
222.031.979993601931760.0500063980682393
232.142.029996000775620.110003999224379
242.422.139991202512230.28000879748777
252.732.419977606505320.310022393494681
262.842.729975206190370.11002479380963
272.852.83999120084920.010008799150802
282.942.849999199553750.0900008004462451
293.062.939992802253130.120007197746872
303.243.059990402513890.18000959748611
313.183.23998560386674-0.0599856038667355
323.013.18000479730392-0.170004797303918
332.873.01001359600683-0.140013596006833
342.732.87001119748289-0.140011197482885
352.632.73001119729106-0.100011197291065
362.392.63000799832089-0.240007998320891
372.262.39001919446061-0.13001919446061
382.112.26001039818808-0.150010398188077
392.012.11001199696968-0.100011996969681
401.992.01000799838484-0.0200079983848445
411.961.99000160012474-0.0300016001247441
421.931.96000239935559-0.0300023993555876
431.981.930002399419510.0499976005804945
442.071.979996001479190.0900039985208061
452.242.069992801997370.170007198002635
462.312.239986403801170.070013596198828
472.232.30999440071488-0.079994400714877
482.262.230006397492520.0299936025074818
492.282.259997601284020.0200023987159841
502.32.279998400323090.0200015996769145
512.332.299998400386990.0300015996130125
522.262.32999760064445-0.0699976006444536
532.242.26000559800589-0.02000559800589
542.472.240001599932780.229998400067224
552.552.469981606049540.0800183939504566
562.892.549993600588640.340006399411359
573.212.889972808241870.320027191758134
583.213.209974406064092.55939359075086e-05
592.923.20999999795314-0.289999997953144
602.682.92002319253348-0.240023192533484
612.42.68001919567576-0.280019195675756
622.282.40002239432627-0.120022394326269
632.242.28000959870144-0.0400095987014444
642.22.24000319973781-0.0400031997378072
652.182.20000319922606-0.0200031992260552
662.232.180001599740930.049998400259065
672.242.229996001415240.01000399858476
682.252.239999199937680.0100008000623233
692.232.24999920019348-0.0199992001934759
702.252.230001599421120.0199984005788849
712.232.24999840064283-0.0199984006428333
722.212.23000159935717-0.0200015993571716







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
732.210001599612991.969683504523832.45031969470215
742.210001599612991.870154080051842.54984911917413
752.210001599612991.793780641134872.62622255809111
762.210001599612991.729394238037012.69060896118897
772.210001599612991.672668382953522.74733481627245
782.210001599612991.621384121576372.7986190776496
792.210001599612991.5742232693952.84577992983097
802.210001599612991.530326945900382.88967625332559
812.210001599612991.489098565478762.93090463374721
822.210001599612991.450103754933512.96989944429246
832.210001599612991.413014595908983.00698860331699
842.210001599612991.377576327412733.04242687181324

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2.21000159961299 & 1.96968350452383 & 2.45031969470215 \tabularnewline
74 & 2.21000159961299 & 1.87015408005184 & 2.54984911917413 \tabularnewline
75 & 2.21000159961299 & 1.79378064113487 & 2.62622255809111 \tabularnewline
76 & 2.21000159961299 & 1.72939423803701 & 2.69060896118897 \tabularnewline
77 & 2.21000159961299 & 1.67266838295352 & 2.74733481627245 \tabularnewline
78 & 2.21000159961299 & 1.62138412157637 & 2.7986190776496 \tabularnewline
79 & 2.21000159961299 & 1.574223269395 & 2.84577992983097 \tabularnewline
80 & 2.21000159961299 & 1.53032694590038 & 2.88967625332559 \tabularnewline
81 & 2.21000159961299 & 1.48909856547876 & 2.93090463374721 \tabularnewline
82 & 2.21000159961299 & 1.45010375493351 & 2.96989944429246 \tabularnewline
83 & 2.21000159961299 & 1.41301459590898 & 3.00698860331699 \tabularnewline
84 & 2.21000159961299 & 1.37757632741273 & 3.04242687181324 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203387&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]73[/C][C]2.21000159961299[/C][C]1.96968350452383[/C][C]2.45031969470215[/C][/ROW]
[ROW][C]74[/C][C]2.21000159961299[/C][C]1.87015408005184[/C][C]2.54984911917413[/C][/ROW]
[ROW][C]75[/C][C]2.21000159961299[/C][C]1.79378064113487[/C][C]2.62622255809111[/C][/ROW]
[ROW][C]76[/C][C]2.21000159961299[/C][C]1.72939423803701[/C][C]2.69060896118897[/C][/ROW]
[ROW][C]77[/C][C]2.21000159961299[/C][C]1.67266838295352[/C][C]2.74733481627245[/C][/ROW]
[ROW][C]78[/C][C]2.21000159961299[/C][C]1.62138412157637[/C][C]2.7986190776496[/C][/ROW]
[ROW][C]79[/C][C]2.21000159961299[/C][C]1.574223269395[/C][C]2.84577992983097[/C][/ROW]
[ROW][C]80[/C][C]2.21000159961299[/C][C]1.53032694590038[/C][C]2.88967625332559[/C][/ROW]
[ROW][C]81[/C][C]2.21000159961299[/C][C]1.48909856547876[/C][C]2.93090463374721[/C][/ROW]
[ROW][C]82[/C][C]2.21000159961299[/C][C]1.45010375493351[/C][C]2.96989944429246[/C][/ROW]
[ROW][C]83[/C][C]2.21000159961299[/C][C]1.41301459590898[/C][C]3.00698860331699[/C][/ROW]
[ROW][C]84[/C][C]2.21000159961299[/C][C]1.37757632741273[/C][C]3.04242687181324[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203387&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203387&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
732.210001599612991.969683504523832.45031969470215
742.210001599612991.870154080051842.54984911917413
752.210001599612991.793780641134872.62622255809111
762.210001599612991.729394238037012.69060896118897
772.210001599612991.672668382953522.74733481627245
782.210001599612991.621384121576372.7986190776496
792.210001599612991.5742232693952.84577992983097
802.210001599612991.530326945900382.88967625332559
812.210001599612991.489098565478762.93090463374721
822.210001599612991.450103754933512.96989944429246
832.210001599612991.413014595908983.00698860331699
842.210001599612991.377576327412733.04242687181324



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')