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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 Dec 2011 05:24:51 -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/2011/Dec/26/t1324895129nutrllqg80dp922.htm/, Retrieved Sat, 04 May 2024 05:00:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160794, Retrieved Sat, 04 May 2024 05:00:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 eigen data] [2011-12-26 10:24:51] [cbc0158ed4ce90347cf58cee0539a6b2] [Current]
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Dataseries X:
106,09
106,19
106,2
106,22
106,22
106,23
106,23
106,61
106,95
107,2
107,56
107,72
107,74
107,8
107,8
108,1
108,14
108,16
108,16
108,16
108,95
110,49
110,71
110,72
110,75
110,82
110,82
110,84
110,84
110,84
110,86
110,92
111,46
112,46
113,04
113,15
113,15
113,21
113,37
113,47
113,71
113,71
113,71
113,8
115,46
117
117,94
118,08
118,08
118,45
118,47
118,49
118,54
118,55
118,55
118,55
119,04
121,37
121,73
121,83
121,83
121,91
122
122,03
122,14
122,14
122,23
122,49
123,02
125,98
126,13
126,39




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=160794&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=160794&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160794&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
alpha0.999932517899986
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999932517899986 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160794&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]0.999932517899986[/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=160794&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160794&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
alpha0.999932517899986
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2106.19106.090.0999999999999943
3106.2106.189993251790.010006748210003
4106.22106.1999993247240.0200006752763784
5106.22106.2199986503121.34968756526632e-06
6106.23106.2199999999090.0100000000910825
7106.23106.2299993251796.7482100973848e-07
8106.61106.2299999999540.380000000045527
9106.95106.6099743568020.340025643198018
10107.2106.9499770543560.25002294564446
11107.56107.1999831279270.360016872073416
12107.72107.5599757053050.160024294694566
13107.74107.7199892012250.0200107987754592
14107.8107.7399986496290.060001350370726
15107.8107.7999959509834.04901712158789e-06
16108.1107.7999999997270.300000000273229
17108.14108.099979755370.0400202446300284
18108.16108.139997299350.0200027006501529
19108.16108.1599986501761.34982424526697e-06
20108.16108.1599999999099.10915787244448e-11
21108.95108.160.790000000000006
22110.49108.9499466891411.54005331085901
23110.71110.4898960739680.220103926031555
24110.72110.7099851469250.0100148530751483
25110.75110.7199993241770.0300006758233167
26110.82110.7499979754910.0700020245085966
27110.82110.8199952761164.72388362027232e-06
28110.84110.8199999996810.0200000003187881
29110.84110.8399986503581.34964201947696e-06
30110.84110.8399999999099.10773678697296e-11
31110.86110.840.019999999999996
32110.92110.8599986503580.0600013496420075
33111.46110.9199959509830.540004049017071
34112.46111.4599635593931.00003644060725
35113.04112.4599325154410.580067484559109
36113.15113.0399608558280.110039144172006
37113.15113.1499925743277.42567253553261e-06
38113.21113.1499999994990.0600000005010912
39113.37113.2099959510740.160004048926041
40113.47113.3699892025910.100010797409226
41113.71113.4699932510610.240006748938626
42113.71113.7099838038411.61961594358218e-05
43113.71113.7099999989071.09295683614619e-09
44113.8113.710.0900000000000745
45115.46113.7999939266111.660006073389
46117115.4598879793041.54011202069587
47117.94116.9998960700070.940103929993413
48118.08117.9399365598130.140063440187433
49118.08118.0799905482259.4517750852674e-06
50118.45118.0799999993620.37000000063783
51118.47118.4499750316230.0200249683770437
52118.49118.4699986486730.0200013513269113
53118.54118.4899986502670.0500013497332077
54118.55118.5399966258040.0100033741960743
55118.55118.5499993249516.75048696052727e-07
56118.55118.5499999999544.55600002169376e-11
57119.04118.550.490000000000009
58121.37119.0399669337712.33003306622901
59121.73121.3698427644760.360157235524412
60121.83121.7299756958330.100024304166581
61121.83121.829993250156.74985010107321e-06
62121.91121.8299999995440.0800000004554988
63122121.9099946014320.0900053985680387
64122.03121.9999939262470.030006073753313
65122.14122.0299979751270.11000202487287
66122.14122.1399925768327.42316764501538e-06
67122.23122.1399999994990.090000000500936
68122.49122.2299939266110.260006073389022
69123.02122.4899824542440.530017545755854
70125.98123.0199642333032.96003576669703
71126.13125.979800250570.150199749429646
72126.39126.1299898642050.260010135794516

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 106.19 & 106.09 & 0.0999999999999943 \tabularnewline
3 & 106.2 & 106.18999325179 & 0.010006748210003 \tabularnewline
4 & 106.22 & 106.199999324724 & 0.0200006752763784 \tabularnewline
5 & 106.22 & 106.219998650312 & 1.34968756526632e-06 \tabularnewline
6 & 106.23 & 106.219999999909 & 0.0100000000910825 \tabularnewline
7 & 106.23 & 106.229999325179 & 6.7482100973848e-07 \tabularnewline
8 & 106.61 & 106.229999999954 & 0.380000000045527 \tabularnewline
9 & 106.95 & 106.609974356802 & 0.340025643198018 \tabularnewline
10 & 107.2 & 106.949977054356 & 0.25002294564446 \tabularnewline
11 & 107.56 & 107.199983127927 & 0.360016872073416 \tabularnewline
12 & 107.72 & 107.559975705305 & 0.160024294694566 \tabularnewline
13 & 107.74 & 107.719989201225 & 0.0200107987754592 \tabularnewline
14 & 107.8 & 107.739998649629 & 0.060001350370726 \tabularnewline
15 & 107.8 & 107.799995950983 & 4.04901712158789e-06 \tabularnewline
16 & 108.1 & 107.799999999727 & 0.300000000273229 \tabularnewline
17 & 108.14 & 108.09997975537 & 0.0400202446300284 \tabularnewline
18 & 108.16 & 108.13999729935 & 0.0200027006501529 \tabularnewline
19 & 108.16 & 108.159998650176 & 1.34982424526697e-06 \tabularnewline
20 & 108.16 & 108.159999999909 & 9.10915787244448e-11 \tabularnewline
21 & 108.95 & 108.16 & 0.790000000000006 \tabularnewline
22 & 110.49 & 108.949946689141 & 1.54005331085901 \tabularnewline
23 & 110.71 & 110.489896073968 & 0.220103926031555 \tabularnewline
24 & 110.72 & 110.709985146925 & 0.0100148530751483 \tabularnewline
25 & 110.75 & 110.719999324177 & 0.0300006758233167 \tabularnewline
26 & 110.82 & 110.749997975491 & 0.0700020245085966 \tabularnewline
27 & 110.82 & 110.819995276116 & 4.72388362027232e-06 \tabularnewline
28 & 110.84 & 110.819999999681 & 0.0200000003187881 \tabularnewline
29 & 110.84 & 110.839998650358 & 1.34964201947696e-06 \tabularnewline
30 & 110.84 & 110.839999999909 & 9.10773678697296e-11 \tabularnewline
31 & 110.86 & 110.84 & 0.019999999999996 \tabularnewline
32 & 110.92 & 110.859998650358 & 0.0600013496420075 \tabularnewline
33 & 111.46 & 110.919995950983 & 0.540004049017071 \tabularnewline
34 & 112.46 & 111.459963559393 & 1.00003644060725 \tabularnewline
35 & 113.04 & 112.459932515441 & 0.580067484559109 \tabularnewline
36 & 113.15 & 113.039960855828 & 0.110039144172006 \tabularnewline
37 & 113.15 & 113.149992574327 & 7.42567253553261e-06 \tabularnewline
38 & 113.21 & 113.149999999499 & 0.0600000005010912 \tabularnewline
39 & 113.37 & 113.209995951074 & 0.160004048926041 \tabularnewline
40 & 113.47 & 113.369989202591 & 0.100010797409226 \tabularnewline
41 & 113.71 & 113.469993251061 & 0.240006748938626 \tabularnewline
42 & 113.71 & 113.709983803841 & 1.61961594358218e-05 \tabularnewline
43 & 113.71 & 113.709999998907 & 1.09295683614619e-09 \tabularnewline
44 & 113.8 & 113.71 & 0.0900000000000745 \tabularnewline
45 & 115.46 & 113.799993926611 & 1.660006073389 \tabularnewline
46 & 117 & 115.459887979304 & 1.54011202069587 \tabularnewline
47 & 117.94 & 116.999896070007 & 0.940103929993413 \tabularnewline
48 & 118.08 & 117.939936559813 & 0.140063440187433 \tabularnewline
49 & 118.08 & 118.079990548225 & 9.4517750852674e-06 \tabularnewline
50 & 118.45 & 118.079999999362 & 0.37000000063783 \tabularnewline
51 & 118.47 & 118.449975031623 & 0.0200249683770437 \tabularnewline
52 & 118.49 & 118.469998648673 & 0.0200013513269113 \tabularnewline
53 & 118.54 & 118.489998650267 & 0.0500013497332077 \tabularnewline
54 & 118.55 & 118.539996625804 & 0.0100033741960743 \tabularnewline
55 & 118.55 & 118.549999324951 & 6.75048696052727e-07 \tabularnewline
56 & 118.55 & 118.549999999954 & 4.55600002169376e-11 \tabularnewline
57 & 119.04 & 118.55 & 0.490000000000009 \tabularnewline
58 & 121.37 & 119.039966933771 & 2.33003306622901 \tabularnewline
59 & 121.73 & 121.369842764476 & 0.360157235524412 \tabularnewline
60 & 121.83 & 121.729975695833 & 0.100024304166581 \tabularnewline
61 & 121.83 & 121.82999325015 & 6.74985010107321e-06 \tabularnewline
62 & 121.91 & 121.829999999544 & 0.0800000004554988 \tabularnewline
63 & 122 & 121.909994601432 & 0.0900053985680387 \tabularnewline
64 & 122.03 & 121.999993926247 & 0.030006073753313 \tabularnewline
65 & 122.14 & 122.029997975127 & 0.11000202487287 \tabularnewline
66 & 122.14 & 122.139992576832 & 7.42316764501538e-06 \tabularnewline
67 & 122.23 & 122.139999999499 & 0.090000000500936 \tabularnewline
68 & 122.49 & 122.229993926611 & 0.260006073389022 \tabularnewline
69 & 123.02 & 122.489982454244 & 0.530017545755854 \tabularnewline
70 & 125.98 & 123.019964233303 & 2.96003576669703 \tabularnewline
71 & 126.13 & 125.97980025057 & 0.150199749429646 \tabularnewline
72 & 126.39 & 126.129989864205 & 0.260010135794516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160794&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]106.19[/C][C]106.09[/C][C]0.0999999999999943[/C][/ROW]
[ROW][C]3[/C][C]106.2[/C][C]106.18999325179[/C][C]0.010006748210003[/C][/ROW]
[ROW][C]4[/C][C]106.22[/C][C]106.199999324724[/C][C]0.0200006752763784[/C][/ROW]
[ROW][C]5[/C][C]106.22[/C][C]106.219998650312[/C][C]1.34968756526632e-06[/C][/ROW]
[ROW][C]6[/C][C]106.23[/C][C]106.219999999909[/C][C]0.0100000000910825[/C][/ROW]
[ROW][C]7[/C][C]106.23[/C][C]106.229999325179[/C][C]6.7482100973848e-07[/C][/ROW]
[ROW][C]8[/C][C]106.61[/C][C]106.229999999954[/C][C]0.380000000045527[/C][/ROW]
[ROW][C]9[/C][C]106.95[/C][C]106.609974356802[/C][C]0.340025643198018[/C][/ROW]
[ROW][C]10[/C][C]107.2[/C][C]106.949977054356[/C][C]0.25002294564446[/C][/ROW]
[ROW][C]11[/C][C]107.56[/C][C]107.199983127927[/C][C]0.360016872073416[/C][/ROW]
[ROW][C]12[/C][C]107.72[/C][C]107.559975705305[/C][C]0.160024294694566[/C][/ROW]
[ROW][C]13[/C][C]107.74[/C][C]107.719989201225[/C][C]0.0200107987754592[/C][/ROW]
[ROW][C]14[/C][C]107.8[/C][C]107.739998649629[/C][C]0.060001350370726[/C][/ROW]
[ROW][C]15[/C][C]107.8[/C][C]107.799995950983[/C][C]4.04901712158789e-06[/C][/ROW]
[ROW][C]16[/C][C]108.1[/C][C]107.799999999727[/C][C]0.300000000273229[/C][/ROW]
[ROW][C]17[/C][C]108.14[/C][C]108.09997975537[/C][C]0.0400202446300284[/C][/ROW]
[ROW][C]18[/C][C]108.16[/C][C]108.13999729935[/C][C]0.0200027006501529[/C][/ROW]
[ROW][C]19[/C][C]108.16[/C][C]108.159998650176[/C][C]1.34982424526697e-06[/C][/ROW]
[ROW][C]20[/C][C]108.16[/C][C]108.159999999909[/C][C]9.10915787244448e-11[/C][/ROW]
[ROW][C]21[/C][C]108.95[/C][C]108.16[/C][C]0.790000000000006[/C][/ROW]
[ROW][C]22[/C][C]110.49[/C][C]108.949946689141[/C][C]1.54005331085901[/C][/ROW]
[ROW][C]23[/C][C]110.71[/C][C]110.489896073968[/C][C]0.220103926031555[/C][/ROW]
[ROW][C]24[/C][C]110.72[/C][C]110.709985146925[/C][C]0.0100148530751483[/C][/ROW]
[ROW][C]25[/C][C]110.75[/C][C]110.719999324177[/C][C]0.0300006758233167[/C][/ROW]
[ROW][C]26[/C][C]110.82[/C][C]110.749997975491[/C][C]0.0700020245085966[/C][/ROW]
[ROW][C]27[/C][C]110.82[/C][C]110.819995276116[/C][C]4.72388362027232e-06[/C][/ROW]
[ROW][C]28[/C][C]110.84[/C][C]110.819999999681[/C][C]0.0200000003187881[/C][/ROW]
[ROW][C]29[/C][C]110.84[/C][C]110.839998650358[/C][C]1.34964201947696e-06[/C][/ROW]
[ROW][C]30[/C][C]110.84[/C][C]110.839999999909[/C][C]9.10773678697296e-11[/C][/ROW]
[ROW][C]31[/C][C]110.86[/C][C]110.84[/C][C]0.019999999999996[/C][/ROW]
[ROW][C]32[/C][C]110.92[/C][C]110.859998650358[/C][C]0.0600013496420075[/C][/ROW]
[ROW][C]33[/C][C]111.46[/C][C]110.919995950983[/C][C]0.540004049017071[/C][/ROW]
[ROW][C]34[/C][C]112.46[/C][C]111.459963559393[/C][C]1.00003644060725[/C][/ROW]
[ROW][C]35[/C][C]113.04[/C][C]112.459932515441[/C][C]0.580067484559109[/C][/ROW]
[ROW][C]36[/C][C]113.15[/C][C]113.039960855828[/C][C]0.110039144172006[/C][/ROW]
[ROW][C]37[/C][C]113.15[/C][C]113.149992574327[/C][C]7.42567253553261e-06[/C][/ROW]
[ROW][C]38[/C][C]113.21[/C][C]113.149999999499[/C][C]0.0600000005010912[/C][/ROW]
[ROW][C]39[/C][C]113.37[/C][C]113.209995951074[/C][C]0.160004048926041[/C][/ROW]
[ROW][C]40[/C][C]113.47[/C][C]113.369989202591[/C][C]0.100010797409226[/C][/ROW]
[ROW][C]41[/C][C]113.71[/C][C]113.469993251061[/C][C]0.240006748938626[/C][/ROW]
[ROW][C]42[/C][C]113.71[/C][C]113.709983803841[/C][C]1.61961594358218e-05[/C][/ROW]
[ROW][C]43[/C][C]113.71[/C][C]113.709999998907[/C][C]1.09295683614619e-09[/C][/ROW]
[ROW][C]44[/C][C]113.8[/C][C]113.71[/C][C]0.0900000000000745[/C][/ROW]
[ROW][C]45[/C][C]115.46[/C][C]113.799993926611[/C][C]1.660006073389[/C][/ROW]
[ROW][C]46[/C][C]117[/C][C]115.459887979304[/C][C]1.54011202069587[/C][/ROW]
[ROW][C]47[/C][C]117.94[/C][C]116.999896070007[/C][C]0.940103929993413[/C][/ROW]
[ROW][C]48[/C][C]118.08[/C][C]117.939936559813[/C][C]0.140063440187433[/C][/ROW]
[ROW][C]49[/C][C]118.08[/C][C]118.079990548225[/C][C]9.4517750852674e-06[/C][/ROW]
[ROW][C]50[/C][C]118.45[/C][C]118.079999999362[/C][C]0.37000000063783[/C][/ROW]
[ROW][C]51[/C][C]118.47[/C][C]118.449975031623[/C][C]0.0200249683770437[/C][/ROW]
[ROW][C]52[/C][C]118.49[/C][C]118.469998648673[/C][C]0.0200013513269113[/C][/ROW]
[ROW][C]53[/C][C]118.54[/C][C]118.489998650267[/C][C]0.0500013497332077[/C][/ROW]
[ROW][C]54[/C][C]118.55[/C][C]118.539996625804[/C][C]0.0100033741960743[/C][/ROW]
[ROW][C]55[/C][C]118.55[/C][C]118.549999324951[/C][C]6.75048696052727e-07[/C][/ROW]
[ROW][C]56[/C][C]118.55[/C][C]118.549999999954[/C][C]4.55600002169376e-11[/C][/ROW]
[ROW][C]57[/C][C]119.04[/C][C]118.55[/C][C]0.490000000000009[/C][/ROW]
[ROW][C]58[/C][C]121.37[/C][C]119.039966933771[/C][C]2.33003306622901[/C][/ROW]
[ROW][C]59[/C][C]121.73[/C][C]121.369842764476[/C][C]0.360157235524412[/C][/ROW]
[ROW][C]60[/C][C]121.83[/C][C]121.729975695833[/C][C]0.100024304166581[/C][/ROW]
[ROW][C]61[/C][C]121.83[/C][C]121.82999325015[/C][C]6.74985010107321e-06[/C][/ROW]
[ROW][C]62[/C][C]121.91[/C][C]121.829999999544[/C][C]0.0800000004554988[/C][/ROW]
[ROW][C]63[/C][C]122[/C][C]121.909994601432[/C][C]0.0900053985680387[/C][/ROW]
[ROW][C]64[/C][C]122.03[/C][C]121.999993926247[/C][C]0.030006073753313[/C][/ROW]
[ROW][C]65[/C][C]122.14[/C][C]122.029997975127[/C][C]0.11000202487287[/C][/ROW]
[ROW][C]66[/C][C]122.14[/C][C]122.139992576832[/C][C]7.42316764501538e-06[/C][/ROW]
[ROW][C]67[/C][C]122.23[/C][C]122.139999999499[/C][C]0.090000000500936[/C][/ROW]
[ROW][C]68[/C][C]122.49[/C][C]122.229993926611[/C][C]0.260006073389022[/C][/ROW]
[ROW][C]69[/C][C]123.02[/C][C]122.489982454244[/C][C]0.530017545755854[/C][/ROW]
[ROW][C]70[/C][C]125.98[/C][C]123.019964233303[/C][C]2.96003576669703[/C][/ROW]
[ROW][C]71[/C][C]126.13[/C][C]125.97980025057[/C][C]0.150199749429646[/C][/ROW]
[ROW][C]72[/C][C]126.39[/C][C]126.129989864205[/C][C]0.260010135794516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160794&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160794&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
2106.19106.090.0999999999999943
3106.2106.189993251790.010006748210003
4106.22106.1999993247240.0200006752763784
5106.22106.2199986503121.34968756526632e-06
6106.23106.2199999999090.0100000000910825
7106.23106.2299993251796.7482100973848e-07
8106.61106.2299999999540.380000000045527
9106.95106.6099743568020.340025643198018
10107.2106.9499770543560.25002294564446
11107.56107.1999831279270.360016872073416
12107.72107.5599757053050.160024294694566
13107.74107.7199892012250.0200107987754592
14107.8107.7399986496290.060001350370726
15107.8107.7999959509834.04901712158789e-06
16108.1107.7999999997270.300000000273229
17108.14108.099979755370.0400202446300284
18108.16108.139997299350.0200027006501529
19108.16108.1599986501761.34982424526697e-06
20108.16108.1599999999099.10915787244448e-11
21108.95108.160.790000000000006
22110.49108.9499466891411.54005331085901
23110.71110.4898960739680.220103926031555
24110.72110.7099851469250.0100148530751483
25110.75110.7199993241770.0300006758233167
26110.82110.7499979754910.0700020245085966
27110.82110.8199952761164.72388362027232e-06
28110.84110.8199999996810.0200000003187881
29110.84110.8399986503581.34964201947696e-06
30110.84110.8399999999099.10773678697296e-11
31110.86110.840.019999999999996
32110.92110.8599986503580.0600013496420075
33111.46110.9199959509830.540004049017071
34112.46111.4599635593931.00003644060725
35113.04112.4599325154410.580067484559109
36113.15113.0399608558280.110039144172006
37113.15113.1499925743277.42567253553261e-06
38113.21113.1499999994990.0600000005010912
39113.37113.2099959510740.160004048926041
40113.47113.3699892025910.100010797409226
41113.71113.4699932510610.240006748938626
42113.71113.7099838038411.61961594358218e-05
43113.71113.7099999989071.09295683614619e-09
44113.8113.710.0900000000000745
45115.46113.7999939266111.660006073389
46117115.4598879793041.54011202069587
47117.94116.9998960700070.940103929993413
48118.08117.9399365598130.140063440187433
49118.08118.0799905482259.4517750852674e-06
50118.45118.0799999993620.37000000063783
51118.47118.4499750316230.0200249683770437
52118.49118.4699986486730.0200013513269113
53118.54118.4899986502670.0500013497332077
54118.55118.5399966258040.0100033741960743
55118.55118.5499993249516.75048696052727e-07
56118.55118.5499999999544.55600002169376e-11
57119.04118.550.490000000000009
58121.37119.0399669337712.33003306622901
59121.73121.3698427644760.360157235524412
60121.83121.7299756958330.100024304166581
61121.83121.829993250156.74985010107321e-06
62121.91121.8299999995440.0800000004554988
63122121.9099946014320.0900053985680387
64122.03121.9999939262470.030006073753313
65122.14122.0299979751270.11000202487287
66122.14122.1399925768327.42316764501538e-06
67122.23122.1399999994990.090000000500936
68122.49122.2299939266110.260006073389022
69123.02122.4899824542440.530017545755854
70125.98123.0199642333032.96003576669703
71126.13125.979800250570.150199749429646
72126.39126.1299898642050.260010135794516







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73126.38998245397125.321705056542127.458259851398
74126.38998245397124.879261044337127.900703863603
75126.38998245397124.539754966013128.240209941927
76126.38998245397124.253535792604128.526429115336
77126.38998245397124.001370531424128.778594376516
78126.38998245397123.773395077979129.006569829961
79126.38998245397123.563749612206129.216215295734
80126.38998245397123.368616098241129.411348809699
81126.38998245397123.185342499903129.594622408037
82126.38998245397123.011997875132129.767967032808
83126.38998245397122.847124512345129.932840395595
84126.38998245397122.689589910711130.090374997229

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 126.38998245397 & 125.321705056542 & 127.458259851398 \tabularnewline
74 & 126.38998245397 & 124.879261044337 & 127.900703863603 \tabularnewline
75 & 126.38998245397 & 124.539754966013 & 128.240209941927 \tabularnewline
76 & 126.38998245397 & 124.253535792604 & 128.526429115336 \tabularnewline
77 & 126.38998245397 & 124.001370531424 & 128.778594376516 \tabularnewline
78 & 126.38998245397 & 123.773395077979 & 129.006569829961 \tabularnewline
79 & 126.38998245397 & 123.563749612206 & 129.216215295734 \tabularnewline
80 & 126.38998245397 & 123.368616098241 & 129.411348809699 \tabularnewline
81 & 126.38998245397 & 123.185342499903 & 129.594622408037 \tabularnewline
82 & 126.38998245397 & 123.011997875132 & 129.767967032808 \tabularnewline
83 & 126.38998245397 & 122.847124512345 & 129.932840395595 \tabularnewline
84 & 126.38998245397 & 122.689589910711 & 130.090374997229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160794&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]126.38998245397[/C][C]125.321705056542[/C][C]127.458259851398[/C][/ROW]
[ROW][C]74[/C][C]126.38998245397[/C][C]124.879261044337[/C][C]127.900703863603[/C][/ROW]
[ROW][C]75[/C][C]126.38998245397[/C][C]124.539754966013[/C][C]128.240209941927[/C][/ROW]
[ROW][C]76[/C][C]126.38998245397[/C][C]124.253535792604[/C][C]128.526429115336[/C][/ROW]
[ROW][C]77[/C][C]126.38998245397[/C][C]124.001370531424[/C][C]128.778594376516[/C][/ROW]
[ROW][C]78[/C][C]126.38998245397[/C][C]123.773395077979[/C][C]129.006569829961[/C][/ROW]
[ROW][C]79[/C][C]126.38998245397[/C][C]123.563749612206[/C][C]129.216215295734[/C][/ROW]
[ROW][C]80[/C][C]126.38998245397[/C][C]123.368616098241[/C][C]129.411348809699[/C][/ROW]
[ROW][C]81[/C][C]126.38998245397[/C][C]123.185342499903[/C][C]129.594622408037[/C][/ROW]
[ROW][C]82[/C][C]126.38998245397[/C][C]123.011997875132[/C][C]129.767967032808[/C][/ROW]
[ROW][C]83[/C][C]126.38998245397[/C][C]122.847124512345[/C][C]129.932840395595[/C][/ROW]
[ROW][C]84[/C][C]126.38998245397[/C][C]122.689589910711[/C][C]130.090374997229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160794&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160794&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
73126.38998245397125.321705056542127.458259851398
74126.38998245397124.879261044337127.900703863603
75126.38998245397124.539754966013128.240209941927
76126.38998245397124.253535792604128.526429115336
77126.38998245397124.001370531424128.778594376516
78126.38998245397123.773395077979129.006569829961
79126.38998245397123.563749612206129.216215295734
80126.38998245397123.368616098241129.411348809699
81126.38998245397123.185342499903129.594622408037
82126.38998245397123.011997875132129.767967032808
83126.38998245397122.847124512345129.932840395595
84126.38998245397122.689589910711130.090374997229



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')