Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 09 May 2017 13:44:36 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/May/09/t1494333929n8gd539b2rocjzz.htm/, Retrieved Fri, 17 May 2024 07:32:58 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 07:32:58 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
79,92
80,26
80,69
84,5
85,45
86,19
86,4
85,98
85,87
86,06
86,43
86,43
86,37
86,84
86,73
90,99
92,61
93,83
94,2
94,01
93,47
93,27
94,3
94,53
94,59
94,69
94,67
96,55
97,14
97,32
97,97
98,49
99,11
99,09
98,76
99,2
99,61
99,54
99,68
100,75
100,38
100,79
100,39
100,39
100,12
100
99,17
99,17
99,59
99,96
99,68
101,03
100,99
101,38
101,84
101,52
101,37
101,22
101,45
101,99
104,05
104,61
105,06
105,4
104,71
104,8
104,83
104,81
104,49
104,59
104,5
104,61




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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999927950355013
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999927950355013 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.999927950355013[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.999927950355013
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
280.2679.920.340000000000003
380.6980.25997550312070.430024496879284
484.580.68996901688773.81003098311234
585.4584.49972548862030.950274511379732
686.1985.44993153305880.740068466941182
786.486.18994667832970.210053321670316
885.9886.3999848657328-0.419984865732758
985.8785.9800302597605-0.110030259760478
1086.0685.87000792764120.189992072358848
1186.4386.05998631113860.370013688861363
1286.4386.42997334064512.66593549156369e-05
1386.3786.4299999980792-0.0599999980792063
1486.8486.37000432297860.46999567702143
1586.7386.8399661369783-0.109966136978329
1690.9986.73000792302114.25999207697886
1792.6190.98969306908321.6203069309168
1893.8392.60988325746091.22011674253915
1994.293.82991209102190.370087908978149
2094.0194.1999733352975-0.189973335297537
2193.4794.0100136875114-0.540013687511362
2293.2793.4700389077945-0.200038907794479
2394.393.27001441273231.02998558726772
2494.5394.29992578990410.230074210095907
2594.5994.52998342323480.0600165767651646
2694.6994.5899956758270.100004324173042
2794.6794.6899927947239-0.0199927947239473
2896.5594.67000144047381.87999855952624
2997.1496.54986454677120.590135453228797
3097.3297.13995748095010.180042519049891
3197.9797.31998702800040.650012971999587
3298.4997.96995316679610.520046833203864
3399.1198.48996253081030.620037469189711
3499.0999.1099553265205-0.0199553265204599
3598.7699.0900014377742-0.330001437774186
3699.298.76002377648640.439976223513568
3799.6199.19996829986930.410031700130716
3899.5499.6099704573616-0.0699704573615776
3999.6899.54000504134660.139994958653389
40100.7599.67998991341291.07001008658706
41100.38100.749922906153-0.369922906153136
42100.79100.3800266528140.409973347185939
43100.39100.789970461566-0.399970461565886
44100.39100.39002881773-2.88177297562697e-05
45100.12100.390000002076-0.270000002076301
46100100.120019453404-0.120019453404296
4799.17100.000008647359-0.830008647358994
4899.1799.1700598018284-5.98018283852753e-05
4999.5999.17000000430870.419999995691299
5099.9699.58996973914940.370030260850584
5199.6899.9599733394511-0.279973339451061
52101.0399.68002017197971.34997982802028
53100.99101.029902734433-0.0399027344326583
54101.38100.9900028749780.389997125022148
55101.84101.3799719008460.4600280991544
56101.52101.839966855139-0.319966855138787
57101.37101.520023053498-0.150023053498302
58101.22101.370010809108-0.150010809107755
59101.45101.2200108082260.229989191774465
60101.99101.449983429360.540016570639608
61104.05101.9899610919982.06003890800221
62104.61104.0498515749280.560148425071986
63105.06104.6099596415050.450040358495158
64105.4105.0599675747520.340032425248069
65104.71105.399975500784-0.689975500784485
66104.8104.710049712490.0899502875101206
67104.83104.7999935191140.0300064808862857
68104.81104.829997838044-0.0199978380437074
69104.49104.810001440837-0.320001440837132
70104.59104.490023055990.0999769440097964
71104.5104.589992796697-0.0899927966966771
72104.61104.5000064839490.109993516050935

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 80.26 & 79.92 & 0.340000000000003 \tabularnewline
3 & 80.69 & 80.2599755031207 & 0.430024496879284 \tabularnewline
4 & 84.5 & 80.6899690168877 & 3.81003098311234 \tabularnewline
5 & 85.45 & 84.4997254886203 & 0.950274511379732 \tabularnewline
6 & 86.19 & 85.4499315330588 & 0.740068466941182 \tabularnewline
7 & 86.4 & 86.1899466783297 & 0.210053321670316 \tabularnewline
8 & 85.98 & 86.3999848657328 & -0.419984865732758 \tabularnewline
9 & 85.87 & 85.9800302597605 & -0.110030259760478 \tabularnewline
10 & 86.06 & 85.8700079276412 & 0.189992072358848 \tabularnewline
11 & 86.43 & 86.0599863111386 & 0.370013688861363 \tabularnewline
12 & 86.43 & 86.4299733406451 & 2.66593549156369e-05 \tabularnewline
13 & 86.37 & 86.4299999980792 & -0.0599999980792063 \tabularnewline
14 & 86.84 & 86.3700043229786 & 0.46999567702143 \tabularnewline
15 & 86.73 & 86.8399661369783 & -0.109966136978329 \tabularnewline
16 & 90.99 & 86.7300079230211 & 4.25999207697886 \tabularnewline
17 & 92.61 & 90.9896930690832 & 1.6203069309168 \tabularnewline
18 & 93.83 & 92.6098832574609 & 1.22011674253915 \tabularnewline
19 & 94.2 & 93.8299120910219 & 0.370087908978149 \tabularnewline
20 & 94.01 & 94.1999733352975 & -0.189973335297537 \tabularnewline
21 & 93.47 & 94.0100136875114 & -0.540013687511362 \tabularnewline
22 & 93.27 & 93.4700389077945 & -0.200038907794479 \tabularnewline
23 & 94.3 & 93.2700144127323 & 1.02998558726772 \tabularnewline
24 & 94.53 & 94.2999257899041 & 0.230074210095907 \tabularnewline
25 & 94.59 & 94.5299834232348 & 0.0600165767651646 \tabularnewline
26 & 94.69 & 94.589995675827 & 0.100004324173042 \tabularnewline
27 & 94.67 & 94.6899927947239 & -0.0199927947239473 \tabularnewline
28 & 96.55 & 94.6700014404738 & 1.87999855952624 \tabularnewline
29 & 97.14 & 96.5498645467712 & 0.590135453228797 \tabularnewline
30 & 97.32 & 97.1399574809501 & 0.180042519049891 \tabularnewline
31 & 97.97 & 97.3199870280004 & 0.650012971999587 \tabularnewline
32 & 98.49 & 97.9699531667961 & 0.520046833203864 \tabularnewline
33 & 99.11 & 98.4899625308103 & 0.620037469189711 \tabularnewline
34 & 99.09 & 99.1099553265205 & -0.0199553265204599 \tabularnewline
35 & 98.76 & 99.0900014377742 & -0.330001437774186 \tabularnewline
36 & 99.2 & 98.7600237764864 & 0.439976223513568 \tabularnewline
37 & 99.61 & 99.1999682998693 & 0.410031700130716 \tabularnewline
38 & 99.54 & 99.6099704573616 & -0.0699704573615776 \tabularnewline
39 & 99.68 & 99.5400050413466 & 0.139994958653389 \tabularnewline
40 & 100.75 & 99.6799899134129 & 1.07001008658706 \tabularnewline
41 & 100.38 & 100.749922906153 & -0.369922906153136 \tabularnewline
42 & 100.79 & 100.380026652814 & 0.409973347185939 \tabularnewline
43 & 100.39 & 100.789970461566 & -0.399970461565886 \tabularnewline
44 & 100.39 & 100.39002881773 & -2.88177297562697e-05 \tabularnewline
45 & 100.12 & 100.390000002076 & -0.270000002076301 \tabularnewline
46 & 100 & 100.120019453404 & -0.120019453404296 \tabularnewline
47 & 99.17 & 100.000008647359 & -0.830008647358994 \tabularnewline
48 & 99.17 & 99.1700598018284 & -5.98018283852753e-05 \tabularnewline
49 & 99.59 & 99.1700000043087 & 0.419999995691299 \tabularnewline
50 & 99.96 & 99.5899697391494 & 0.370030260850584 \tabularnewline
51 & 99.68 & 99.9599733394511 & -0.279973339451061 \tabularnewline
52 & 101.03 & 99.6800201719797 & 1.34997982802028 \tabularnewline
53 & 100.99 & 101.029902734433 & -0.0399027344326583 \tabularnewline
54 & 101.38 & 100.990002874978 & 0.389997125022148 \tabularnewline
55 & 101.84 & 101.379971900846 & 0.4600280991544 \tabularnewline
56 & 101.52 & 101.839966855139 & -0.319966855138787 \tabularnewline
57 & 101.37 & 101.520023053498 & -0.150023053498302 \tabularnewline
58 & 101.22 & 101.370010809108 & -0.150010809107755 \tabularnewline
59 & 101.45 & 101.220010808226 & 0.229989191774465 \tabularnewline
60 & 101.99 & 101.44998342936 & 0.540016570639608 \tabularnewline
61 & 104.05 & 101.989961091998 & 2.06003890800221 \tabularnewline
62 & 104.61 & 104.049851574928 & 0.560148425071986 \tabularnewline
63 & 105.06 & 104.609959641505 & 0.450040358495158 \tabularnewline
64 & 105.4 & 105.059967574752 & 0.340032425248069 \tabularnewline
65 & 104.71 & 105.399975500784 & -0.689975500784485 \tabularnewline
66 & 104.8 & 104.71004971249 & 0.0899502875101206 \tabularnewline
67 & 104.83 & 104.799993519114 & 0.0300064808862857 \tabularnewline
68 & 104.81 & 104.829997838044 & -0.0199978380437074 \tabularnewline
69 & 104.49 & 104.810001440837 & -0.320001440837132 \tabularnewline
70 & 104.59 & 104.49002305599 & 0.0999769440097964 \tabularnewline
71 & 104.5 & 104.589992796697 & -0.0899927966966771 \tabularnewline
72 & 104.61 & 104.500006483949 & 0.109993516050935 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]80.26[/C][C]79.92[/C][C]0.340000000000003[/C][/ROW]
[ROW][C]3[/C][C]80.69[/C][C]80.2599755031207[/C][C]0.430024496879284[/C][/ROW]
[ROW][C]4[/C][C]84.5[/C][C]80.6899690168877[/C][C]3.81003098311234[/C][/ROW]
[ROW][C]5[/C][C]85.45[/C][C]84.4997254886203[/C][C]0.950274511379732[/C][/ROW]
[ROW][C]6[/C][C]86.19[/C][C]85.4499315330588[/C][C]0.740068466941182[/C][/ROW]
[ROW][C]7[/C][C]86.4[/C][C]86.1899466783297[/C][C]0.210053321670316[/C][/ROW]
[ROW][C]8[/C][C]85.98[/C][C]86.3999848657328[/C][C]-0.419984865732758[/C][/ROW]
[ROW][C]9[/C][C]85.87[/C][C]85.9800302597605[/C][C]-0.110030259760478[/C][/ROW]
[ROW][C]10[/C][C]86.06[/C][C]85.8700079276412[/C][C]0.189992072358848[/C][/ROW]
[ROW][C]11[/C][C]86.43[/C][C]86.0599863111386[/C][C]0.370013688861363[/C][/ROW]
[ROW][C]12[/C][C]86.43[/C][C]86.4299733406451[/C][C]2.66593549156369e-05[/C][/ROW]
[ROW][C]13[/C][C]86.37[/C][C]86.4299999980792[/C][C]-0.0599999980792063[/C][/ROW]
[ROW][C]14[/C][C]86.84[/C][C]86.3700043229786[/C][C]0.46999567702143[/C][/ROW]
[ROW][C]15[/C][C]86.73[/C][C]86.8399661369783[/C][C]-0.109966136978329[/C][/ROW]
[ROW][C]16[/C][C]90.99[/C][C]86.7300079230211[/C][C]4.25999207697886[/C][/ROW]
[ROW][C]17[/C][C]92.61[/C][C]90.9896930690832[/C][C]1.6203069309168[/C][/ROW]
[ROW][C]18[/C][C]93.83[/C][C]92.6098832574609[/C][C]1.22011674253915[/C][/ROW]
[ROW][C]19[/C][C]94.2[/C][C]93.8299120910219[/C][C]0.370087908978149[/C][/ROW]
[ROW][C]20[/C][C]94.01[/C][C]94.1999733352975[/C][C]-0.189973335297537[/C][/ROW]
[ROW][C]21[/C][C]93.47[/C][C]94.0100136875114[/C][C]-0.540013687511362[/C][/ROW]
[ROW][C]22[/C][C]93.27[/C][C]93.4700389077945[/C][C]-0.200038907794479[/C][/ROW]
[ROW][C]23[/C][C]94.3[/C][C]93.2700144127323[/C][C]1.02998558726772[/C][/ROW]
[ROW][C]24[/C][C]94.53[/C][C]94.2999257899041[/C][C]0.230074210095907[/C][/ROW]
[ROW][C]25[/C][C]94.59[/C][C]94.5299834232348[/C][C]0.0600165767651646[/C][/ROW]
[ROW][C]26[/C][C]94.69[/C][C]94.589995675827[/C][C]0.100004324173042[/C][/ROW]
[ROW][C]27[/C][C]94.67[/C][C]94.6899927947239[/C][C]-0.0199927947239473[/C][/ROW]
[ROW][C]28[/C][C]96.55[/C][C]94.6700014404738[/C][C]1.87999855952624[/C][/ROW]
[ROW][C]29[/C][C]97.14[/C][C]96.5498645467712[/C][C]0.590135453228797[/C][/ROW]
[ROW][C]30[/C][C]97.32[/C][C]97.1399574809501[/C][C]0.180042519049891[/C][/ROW]
[ROW][C]31[/C][C]97.97[/C][C]97.3199870280004[/C][C]0.650012971999587[/C][/ROW]
[ROW][C]32[/C][C]98.49[/C][C]97.9699531667961[/C][C]0.520046833203864[/C][/ROW]
[ROW][C]33[/C][C]99.11[/C][C]98.4899625308103[/C][C]0.620037469189711[/C][/ROW]
[ROW][C]34[/C][C]99.09[/C][C]99.1099553265205[/C][C]-0.0199553265204599[/C][/ROW]
[ROW][C]35[/C][C]98.76[/C][C]99.0900014377742[/C][C]-0.330001437774186[/C][/ROW]
[ROW][C]36[/C][C]99.2[/C][C]98.7600237764864[/C][C]0.439976223513568[/C][/ROW]
[ROW][C]37[/C][C]99.61[/C][C]99.1999682998693[/C][C]0.410031700130716[/C][/ROW]
[ROW][C]38[/C][C]99.54[/C][C]99.6099704573616[/C][C]-0.0699704573615776[/C][/ROW]
[ROW][C]39[/C][C]99.68[/C][C]99.5400050413466[/C][C]0.139994958653389[/C][/ROW]
[ROW][C]40[/C][C]100.75[/C][C]99.6799899134129[/C][C]1.07001008658706[/C][/ROW]
[ROW][C]41[/C][C]100.38[/C][C]100.749922906153[/C][C]-0.369922906153136[/C][/ROW]
[ROW][C]42[/C][C]100.79[/C][C]100.380026652814[/C][C]0.409973347185939[/C][/ROW]
[ROW][C]43[/C][C]100.39[/C][C]100.789970461566[/C][C]-0.399970461565886[/C][/ROW]
[ROW][C]44[/C][C]100.39[/C][C]100.39002881773[/C][C]-2.88177297562697e-05[/C][/ROW]
[ROW][C]45[/C][C]100.12[/C][C]100.390000002076[/C][C]-0.270000002076301[/C][/ROW]
[ROW][C]46[/C][C]100[/C][C]100.120019453404[/C][C]-0.120019453404296[/C][/ROW]
[ROW][C]47[/C][C]99.17[/C][C]100.000008647359[/C][C]-0.830008647358994[/C][/ROW]
[ROW][C]48[/C][C]99.17[/C][C]99.1700598018284[/C][C]-5.98018283852753e-05[/C][/ROW]
[ROW][C]49[/C][C]99.59[/C][C]99.1700000043087[/C][C]0.419999995691299[/C][/ROW]
[ROW][C]50[/C][C]99.96[/C][C]99.5899697391494[/C][C]0.370030260850584[/C][/ROW]
[ROW][C]51[/C][C]99.68[/C][C]99.9599733394511[/C][C]-0.279973339451061[/C][/ROW]
[ROW][C]52[/C][C]101.03[/C][C]99.6800201719797[/C][C]1.34997982802028[/C][/ROW]
[ROW][C]53[/C][C]100.99[/C][C]101.029902734433[/C][C]-0.0399027344326583[/C][/ROW]
[ROW][C]54[/C][C]101.38[/C][C]100.990002874978[/C][C]0.389997125022148[/C][/ROW]
[ROW][C]55[/C][C]101.84[/C][C]101.379971900846[/C][C]0.4600280991544[/C][/ROW]
[ROW][C]56[/C][C]101.52[/C][C]101.839966855139[/C][C]-0.319966855138787[/C][/ROW]
[ROW][C]57[/C][C]101.37[/C][C]101.520023053498[/C][C]-0.150023053498302[/C][/ROW]
[ROW][C]58[/C][C]101.22[/C][C]101.370010809108[/C][C]-0.150010809107755[/C][/ROW]
[ROW][C]59[/C][C]101.45[/C][C]101.220010808226[/C][C]0.229989191774465[/C][/ROW]
[ROW][C]60[/C][C]101.99[/C][C]101.44998342936[/C][C]0.540016570639608[/C][/ROW]
[ROW][C]61[/C][C]104.05[/C][C]101.989961091998[/C][C]2.06003890800221[/C][/ROW]
[ROW][C]62[/C][C]104.61[/C][C]104.049851574928[/C][C]0.560148425071986[/C][/ROW]
[ROW][C]63[/C][C]105.06[/C][C]104.609959641505[/C][C]0.450040358495158[/C][/ROW]
[ROW][C]64[/C][C]105.4[/C][C]105.059967574752[/C][C]0.340032425248069[/C][/ROW]
[ROW][C]65[/C][C]104.71[/C][C]105.399975500784[/C][C]-0.689975500784485[/C][/ROW]
[ROW][C]66[/C][C]104.8[/C][C]104.71004971249[/C][C]0.0899502875101206[/C][/ROW]
[ROW][C]67[/C][C]104.83[/C][C]104.799993519114[/C][C]0.0300064808862857[/C][/ROW]
[ROW][C]68[/C][C]104.81[/C][C]104.829997838044[/C][C]-0.0199978380437074[/C][/ROW]
[ROW][C]69[/C][C]104.49[/C][C]104.810001440837[/C][C]-0.320001440837132[/C][/ROW]
[ROW][C]70[/C][C]104.59[/C][C]104.49002305599[/C][C]0.0999769440097964[/C][/ROW]
[ROW][C]71[/C][C]104.5[/C][C]104.589992796697[/C][C]-0.0899927966966771[/C][/ROW]
[ROW][C]72[/C][C]104.61[/C][C]104.500006483949[/C][C]0.109993516050935[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
280.2679.920.340000000000003
380.6980.25997550312070.430024496879284
484.580.68996901688773.81003098311234
585.4584.49972548862030.950274511379732
686.1985.44993153305880.740068466941182
786.486.18994667832970.210053321670316
885.9886.3999848657328-0.419984865732758
985.8785.9800302597605-0.110030259760478
1086.0685.87000792764120.189992072358848
1186.4386.05998631113860.370013688861363
1286.4386.42997334064512.66593549156369e-05
1386.3786.4299999980792-0.0599999980792063
1486.8486.37000432297860.46999567702143
1586.7386.8399661369783-0.109966136978329
1690.9986.73000792302114.25999207697886
1792.6190.98969306908321.6203069309168
1893.8392.60988325746091.22011674253915
1994.293.82991209102190.370087908978149
2094.0194.1999733352975-0.189973335297537
2193.4794.0100136875114-0.540013687511362
2293.2793.4700389077945-0.200038907794479
2394.393.27001441273231.02998558726772
2494.5394.29992578990410.230074210095907
2594.5994.52998342323480.0600165767651646
2694.6994.5899956758270.100004324173042
2794.6794.6899927947239-0.0199927947239473
2896.5594.67000144047381.87999855952624
2997.1496.54986454677120.590135453228797
3097.3297.13995748095010.180042519049891
3197.9797.31998702800040.650012971999587
3298.4997.96995316679610.520046833203864
3399.1198.48996253081030.620037469189711
3499.0999.1099553265205-0.0199553265204599
3598.7699.0900014377742-0.330001437774186
3699.298.76002377648640.439976223513568
3799.6199.19996829986930.410031700130716
3899.5499.6099704573616-0.0699704573615776
3999.6899.54000504134660.139994958653389
40100.7599.67998991341291.07001008658706
41100.38100.749922906153-0.369922906153136
42100.79100.3800266528140.409973347185939
43100.39100.789970461566-0.399970461565886
44100.39100.39002881773-2.88177297562697e-05
45100.12100.390000002076-0.270000002076301
46100100.120019453404-0.120019453404296
4799.17100.000008647359-0.830008647358994
4899.1799.1700598018284-5.98018283852753e-05
4999.5999.17000000430870.419999995691299
5099.9699.58996973914940.370030260850584
5199.6899.9599733394511-0.279973339451061
52101.0399.68002017197971.34997982802028
53100.99101.029902734433-0.0399027344326583
54101.38100.9900028749780.389997125022148
55101.84101.3799719008460.4600280991544
56101.52101.839966855139-0.319966855138787
57101.37101.520023053498-0.150023053498302
58101.22101.370010809108-0.150010809107755
59101.45101.2200108082260.229989191774465
60101.99101.449983429360.540016570639608
61104.05101.9899610919982.06003890800221
62104.61104.0498515749280.560148425071986
63105.06104.6099596415050.450040358495158
64105.4105.0599675747520.340032425248069
65104.71105.399975500784-0.689975500784485
66104.8104.710049712490.0899502875101206
67104.83104.7999935191140.0300064808862857
68104.81104.829997838044-0.0199978380437074
69104.49104.810001440837-0.320001440837132
70104.59104.490023055990.0999769440097964
71104.5104.589992796697-0.0899927966966771
72104.61104.5000064839490.109993516050935







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73104.609992075006102.975935997385106.244048152627
74104.609992075006102.299171056773106.92081309324
75104.609992075006101.779859871061107.440124278952
76104.609992075006101.342056517914107.877927632099
77104.609992075006100.956342212361108.263641937652
78104.609992075006100.607628794105108.612355355908
79104.609992075006100.286953057624108.933031092388
80104.60999207500699.9884749151002109.231509234912
81104.60999207500699.7081377959802109.511846354032
82104.60999207500699.4429881185238109.776996031489
83104.60999207500699.1907961568091110.029187993203
84104.60999207500698.9498296291657110.270154520847

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 104.609992075006 & 102.975935997385 & 106.244048152627 \tabularnewline
74 & 104.609992075006 & 102.299171056773 & 106.92081309324 \tabularnewline
75 & 104.609992075006 & 101.779859871061 & 107.440124278952 \tabularnewline
76 & 104.609992075006 & 101.342056517914 & 107.877927632099 \tabularnewline
77 & 104.609992075006 & 100.956342212361 & 108.263641937652 \tabularnewline
78 & 104.609992075006 & 100.607628794105 & 108.612355355908 \tabularnewline
79 & 104.609992075006 & 100.286953057624 & 108.933031092388 \tabularnewline
80 & 104.609992075006 & 99.9884749151002 & 109.231509234912 \tabularnewline
81 & 104.609992075006 & 99.7081377959802 & 109.511846354032 \tabularnewline
82 & 104.609992075006 & 99.4429881185238 & 109.776996031489 \tabularnewline
83 & 104.609992075006 & 99.1907961568091 & 110.029187993203 \tabularnewline
84 & 104.609992075006 & 98.9498296291657 & 110.270154520847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]104.609992075006[/C][C]102.975935997385[/C][C]106.244048152627[/C][/ROW]
[ROW][C]74[/C][C]104.609992075006[/C][C]102.299171056773[/C][C]106.92081309324[/C][/ROW]
[ROW][C]75[/C][C]104.609992075006[/C][C]101.779859871061[/C][C]107.440124278952[/C][/ROW]
[ROW][C]76[/C][C]104.609992075006[/C][C]101.342056517914[/C][C]107.877927632099[/C][/ROW]
[ROW][C]77[/C][C]104.609992075006[/C][C]100.956342212361[/C][C]108.263641937652[/C][/ROW]
[ROW][C]78[/C][C]104.609992075006[/C][C]100.607628794105[/C][C]108.612355355908[/C][/ROW]
[ROW][C]79[/C][C]104.609992075006[/C][C]100.286953057624[/C][C]108.933031092388[/C][/ROW]
[ROW][C]80[/C][C]104.609992075006[/C][C]99.9884749151002[/C][C]109.231509234912[/C][/ROW]
[ROW][C]81[/C][C]104.609992075006[/C][C]99.7081377959802[/C][C]109.511846354032[/C][/ROW]
[ROW][C]82[/C][C]104.609992075006[/C][C]99.4429881185238[/C][C]109.776996031489[/C][/ROW]
[ROW][C]83[/C][C]104.609992075006[/C][C]99.1907961568091[/C][C]110.029187993203[/C][/ROW]
[ROW][C]84[/C][C]104.609992075006[/C][C]98.9498296291657[/C][C]110.270154520847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
73104.609992075006102.975935997385106.244048152627
74104.609992075006102.299171056773106.92081309324
75104.609992075006101.779859871061107.440124278952
76104.609992075006101.342056517914107.877927632099
77104.609992075006100.956342212361108.263641937652
78104.609992075006100.607628794105108.612355355908
79104.609992075006100.286953057624108.933031092388
80104.60999207500699.9884749151002109.231509234912
81104.60999207500699.7081377959802109.511846354032
82104.60999207500699.4429881185238109.776996031489
83104.60999207500699.1907961568091110.029187993203
84104.60999207500698.9498296291657110.270154520847



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')