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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 05 Apr 2015 19:10:10 +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/2015/Apr/05/t1428257443p0g0yx08h60lzlk.htm/, Retrieved Thu, 09 May 2024 05:52:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278690, Retrieved Thu, 09 May 2024 05:52:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Single exponentia...] [2015-04-05 18:10:10] [d7b65c9a7c286d706dc95a87d306e880] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2
2,2
2,2
2
2,3
2,6
3,2
3,2
3,1
2,8
2,3
1,9
1,9
2
2
1,8
1,6
1,4
0,2
0,3
0,4
0,7
1
1,1
0,8
0,8
1
1,1
1
0,8
1,6
1,5
1,6
1,6
1,6
1,9
2
1,9
2
2,1
2,3
2,3
2,6
2,6
2,7
2,6
2,6
2,4
2,5
2,5
2,5
2,4
2,1
2,1
2,3
2,3
2,3
2,9
2,8
2,9
3
3
2,9
2,6
2,8
2,9
3,1
2,8
2,4
1,6
1,5
1,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278690&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278690&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278690&T=0

As an alternative you can also use a QR Code:  
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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999919076409994
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999919076409994 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278690&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]0.999919076409994[/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=278690&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278690&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999919076409994
betaFALSE
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
22.220.2
32.22.1999838152821.61847180013552e-05
422.19999999869027-0.199999998690275
52.32.00001618471790.299983815282105
62.62.299975724232720.300024275767277
73.22.599975720958520.600024279041484
83.23.199951443881254.85561187506534e-05
93.13.19999999607066-0.0999999960706646
102.83.10000809235868-0.300008092358683
112.32.80002427773186-0.500024277731864
121.92.30004046375964-0.400040463759644
131.91.90003237271047-3.23727104747373e-05
1421.900000002619720.0999999973802843
1521.999991907641218.09235878862502e-06
161.81.99999999934514-0.199999999345137
171.61.80001618471795-0.200016184717948
181.41.60001618602773-0.200016186027727
190.21.40001618602783-1.20001618602783
200.30.2000971096178380.0999028903821618
210.40.2999919154994580.100008084500542
220.70.3999919069867730.300008093013227
2310.6999757222680830.300024277731917
241.10.9999757209583570.100024279041643
250.81.09999190567625-0.299991905676252
260.80.80002427642198-2.42764219799962e-05
2710.8000000019645350.199999998035465
281.10.9999838152821580.100016184717842
2911.09999190633127-0.099991906331274
300.81.00000809170403-0.200008091704032
311.60.8000161853728110.799983814627189
321.51.59993526243777-0.0999352624377741
331.61.50000808712020.0999919128797955
341.61.599991908295448.09170456173014e-06
351.61.599999999345196.54809761968522e-10
361.91.599999999999950.300000000000053
3721.8999757229230.100024277077002
381.91.99999190567641-0.0999919056764114
3921.900008091703980.0999919082960214
402.11.999991908295810.100008091704191
412.32.099991906986190.20000809301381
422.32.299983814627081.61853729170325e-05
432.62.299999998690220.300000001309779
442.62.599975722922892.42770771077261e-05
452.72.599999998035410.100000001964589
462.62.69999190764084-0.0999919076408404
472.62.60000809170414-8.09170413784699e-06
482.42.60000000065481-0.20000000065481
492.52.400016184718050.0999838152819459
502.52.499991908950728.09104927501636e-06
512.52.499999999345246.54756693307945e-10
522.42.49999999999995-0.0999999999999472
532.12.400008092359-0.300008092359
542.12.10002427773186-2.42777318644194e-05
552.32.100000001964640.199999998035358
562.32.299983815282161.61847178423713e-05
572.32.299999998690271.3097256612582e-09
582.92.299999999999890.600000000000106
592.82.899951445846-0.0999514458459969
602.92.800008088429820.099991911570176
6132.899991908295540.100008091704456
6232.999991906986198.09301381066163e-06
632.92.99999999934508-0.0999999993450844
642.62.90000809235895-0.300008092358947
652.82.600024277731860.199975722268135
662.92.799983817246640.10001618275336
673.12.899991906331430.200008093668567
682.83.09998381462703-0.299983814627031
692.42.80002427576722-0.400024275767223
701.62.40003237140048-0.800032371400484
711.51.60006474149161-0.100064741491614
721.71.500008097598110.199991902401885

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2.2 & 2 & 0.2 \tabularnewline
3 & 2.2 & 2.199983815282 & 1.61847180013552e-05 \tabularnewline
4 & 2 & 2.19999999869027 & -0.199999998690275 \tabularnewline
5 & 2.3 & 2.0000161847179 & 0.299983815282105 \tabularnewline
6 & 2.6 & 2.29997572423272 & 0.300024275767277 \tabularnewline
7 & 3.2 & 2.59997572095852 & 0.600024279041484 \tabularnewline
8 & 3.2 & 3.19995144388125 & 4.85561187506534e-05 \tabularnewline
9 & 3.1 & 3.19999999607066 & -0.0999999960706646 \tabularnewline
10 & 2.8 & 3.10000809235868 & -0.300008092358683 \tabularnewline
11 & 2.3 & 2.80002427773186 & -0.500024277731864 \tabularnewline
12 & 1.9 & 2.30004046375964 & -0.400040463759644 \tabularnewline
13 & 1.9 & 1.90003237271047 & -3.23727104747373e-05 \tabularnewline
14 & 2 & 1.90000000261972 & 0.0999999973802843 \tabularnewline
15 & 2 & 1.99999190764121 & 8.09235878862502e-06 \tabularnewline
16 & 1.8 & 1.99999999934514 & -0.199999999345137 \tabularnewline
17 & 1.6 & 1.80001618471795 & -0.200016184717948 \tabularnewline
18 & 1.4 & 1.60001618602773 & -0.200016186027727 \tabularnewline
19 & 0.2 & 1.40001618602783 & -1.20001618602783 \tabularnewline
20 & 0.3 & 0.200097109617838 & 0.0999028903821618 \tabularnewline
21 & 0.4 & 0.299991915499458 & 0.100008084500542 \tabularnewline
22 & 0.7 & 0.399991906986773 & 0.300008093013227 \tabularnewline
23 & 1 & 0.699975722268083 & 0.300024277731917 \tabularnewline
24 & 1.1 & 0.999975720958357 & 0.100024279041643 \tabularnewline
25 & 0.8 & 1.09999190567625 & -0.299991905676252 \tabularnewline
26 & 0.8 & 0.80002427642198 & -2.42764219799962e-05 \tabularnewline
27 & 1 & 0.800000001964535 & 0.199999998035465 \tabularnewline
28 & 1.1 & 0.999983815282158 & 0.100016184717842 \tabularnewline
29 & 1 & 1.09999190633127 & -0.099991906331274 \tabularnewline
30 & 0.8 & 1.00000809170403 & -0.200008091704032 \tabularnewline
31 & 1.6 & 0.800016185372811 & 0.799983814627189 \tabularnewline
32 & 1.5 & 1.59993526243777 & -0.0999352624377741 \tabularnewline
33 & 1.6 & 1.5000080871202 & 0.0999919128797955 \tabularnewline
34 & 1.6 & 1.59999190829544 & 8.09170456173014e-06 \tabularnewline
35 & 1.6 & 1.59999999934519 & 6.54809761968522e-10 \tabularnewline
36 & 1.9 & 1.59999999999995 & 0.300000000000053 \tabularnewline
37 & 2 & 1.899975722923 & 0.100024277077002 \tabularnewline
38 & 1.9 & 1.99999190567641 & -0.0999919056764114 \tabularnewline
39 & 2 & 1.90000809170398 & 0.0999919082960214 \tabularnewline
40 & 2.1 & 1.99999190829581 & 0.100008091704191 \tabularnewline
41 & 2.3 & 2.09999190698619 & 0.20000809301381 \tabularnewline
42 & 2.3 & 2.29998381462708 & 1.61853729170325e-05 \tabularnewline
43 & 2.6 & 2.29999999869022 & 0.300000001309779 \tabularnewline
44 & 2.6 & 2.59997572292289 & 2.42770771077261e-05 \tabularnewline
45 & 2.7 & 2.59999999803541 & 0.100000001964589 \tabularnewline
46 & 2.6 & 2.69999190764084 & -0.0999919076408404 \tabularnewline
47 & 2.6 & 2.60000809170414 & -8.09170413784699e-06 \tabularnewline
48 & 2.4 & 2.60000000065481 & -0.20000000065481 \tabularnewline
49 & 2.5 & 2.40001618471805 & 0.0999838152819459 \tabularnewline
50 & 2.5 & 2.49999190895072 & 8.09104927501636e-06 \tabularnewline
51 & 2.5 & 2.49999999934524 & 6.54756693307945e-10 \tabularnewline
52 & 2.4 & 2.49999999999995 & -0.0999999999999472 \tabularnewline
53 & 2.1 & 2.400008092359 & -0.300008092359 \tabularnewline
54 & 2.1 & 2.10002427773186 & -2.42777318644194e-05 \tabularnewline
55 & 2.3 & 2.10000000196464 & 0.199999998035358 \tabularnewline
56 & 2.3 & 2.29998381528216 & 1.61847178423713e-05 \tabularnewline
57 & 2.3 & 2.29999999869027 & 1.3097256612582e-09 \tabularnewline
58 & 2.9 & 2.29999999999989 & 0.600000000000106 \tabularnewline
59 & 2.8 & 2.899951445846 & -0.0999514458459969 \tabularnewline
60 & 2.9 & 2.80000808842982 & 0.099991911570176 \tabularnewline
61 & 3 & 2.89999190829554 & 0.100008091704456 \tabularnewline
62 & 3 & 2.99999190698619 & 8.09301381066163e-06 \tabularnewline
63 & 2.9 & 2.99999999934508 & -0.0999999993450844 \tabularnewline
64 & 2.6 & 2.90000809235895 & -0.300008092358947 \tabularnewline
65 & 2.8 & 2.60002427773186 & 0.199975722268135 \tabularnewline
66 & 2.9 & 2.79998381724664 & 0.10001618275336 \tabularnewline
67 & 3.1 & 2.89999190633143 & 0.200008093668567 \tabularnewline
68 & 2.8 & 3.09998381462703 & -0.299983814627031 \tabularnewline
69 & 2.4 & 2.80002427576722 & -0.400024275767223 \tabularnewline
70 & 1.6 & 2.40003237140048 & -0.800032371400484 \tabularnewline
71 & 1.5 & 1.60006474149161 & -0.100064741491614 \tabularnewline
72 & 1.7 & 1.50000809759811 & 0.199991902401885 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278690&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]2.2[/C][C]2[/C][C]0.2[/C][/ROW]
[ROW][C]3[/C][C]2.2[/C][C]2.199983815282[/C][C]1.61847180013552e-05[/C][/ROW]
[ROW][C]4[/C][C]2[/C][C]2.19999999869027[/C][C]-0.199999998690275[/C][/ROW]
[ROW][C]5[/C][C]2.3[/C][C]2.0000161847179[/C][C]0.299983815282105[/C][/ROW]
[ROW][C]6[/C][C]2.6[/C][C]2.29997572423272[/C][C]0.300024275767277[/C][/ROW]
[ROW][C]7[/C][C]3.2[/C][C]2.59997572095852[/C][C]0.600024279041484[/C][/ROW]
[ROW][C]8[/C][C]3.2[/C][C]3.19995144388125[/C][C]4.85561187506534e-05[/C][/ROW]
[ROW][C]9[/C][C]3.1[/C][C]3.19999999607066[/C][C]-0.0999999960706646[/C][/ROW]
[ROW][C]10[/C][C]2.8[/C][C]3.10000809235868[/C][C]-0.300008092358683[/C][/ROW]
[ROW][C]11[/C][C]2.3[/C][C]2.80002427773186[/C][C]-0.500024277731864[/C][/ROW]
[ROW][C]12[/C][C]1.9[/C][C]2.30004046375964[/C][C]-0.400040463759644[/C][/ROW]
[ROW][C]13[/C][C]1.9[/C][C]1.90003237271047[/C][C]-3.23727104747373e-05[/C][/ROW]
[ROW][C]14[/C][C]2[/C][C]1.90000000261972[/C][C]0.0999999973802843[/C][/ROW]
[ROW][C]15[/C][C]2[/C][C]1.99999190764121[/C][C]8.09235878862502e-06[/C][/ROW]
[ROW][C]16[/C][C]1.8[/C][C]1.99999999934514[/C][C]-0.199999999345137[/C][/ROW]
[ROW][C]17[/C][C]1.6[/C][C]1.80001618471795[/C][C]-0.200016184717948[/C][/ROW]
[ROW][C]18[/C][C]1.4[/C][C]1.60001618602773[/C][C]-0.200016186027727[/C][/ROW]
[ROW][C]19[/C][C]0.2[/C][C]1.40001618602783[/C][C]-1.20001618602783[/C][/ROW]
[ROW][C]20[/C][C]0.3[/C][C]0.200097109617838[/C][C]0.0999028903821618[/C][/ROW]
[ROW][C]21[/C][C]0.4[/C][C]0.299991915499458[/C][C]0.100008084500542[/C][/ROW]
[ROW][C]22[/C][C]0.7[/C][C]0.399991906986773[/C][C]0.300008093013227[/C][/ROW]
[ROW][C]23[/C][C]1[/C][C]0.699975722268083[/C][C]0.300024277731917[/C][/ROW]
[ROW][C]24[/C][C]1.1[/C][C]0.999975720958357[/C][C]0.100024279041643[/C][/ROW]
[ROW][C]25[/C][C]0.8[/C][C]1.09999190567625[/C][C]-0.299991905676252[/C][/ROW]
[ROW][C]26[/C][C]0.8[/C][C]0.80002427642198[/C][C]-2.42764219799962e-05[/C][/ROW]
[ROW][C]27[/C][C]1[/C][C]0.800000001964535[/C][C]0.199999998035465[/C][/ROW]
[ROW][C]28[/C][C]1.1[/C][C]0.999983815282158[/C][C]0.100016184717842[/C][/ROW]
[ROW][C]29[/C][C]1[/C][C]1.09999190633127[/C][C]-0.099991906331274[/C][/ROW]
[ROW][C]30[/C][C]0.8[/C][C]1.00000809170403[/C][C]-0.200008091704032[/C][/ROW]
[ROW][C]31[/C][C]1.6[/C][C]0.800016185372811[/C][C]0.799983814627189[/C][/ROW]
[ROW][C]32[/C][C]1.5[/C][C]1.59993526243777[/C][C]-0.0999352624377741[/C][/ROW]
[ROW][C]33[/C][C]1.6[/C][C]1.5000080871202[/C][C]0.0999919128797955[/C][/ROW]
[ROW][C]34[/C][C]1.6[/C][C]1.59999190829544[/C][C]8.09170456173014e-06[/C][/ROW]
[ROW][C]35[/C][C]1.6[/C][C]1.59999999934519[/C][C]6.54809761968522e-10[/C][/ROW]
[ROW][C]36[/C][C]1.9[/C][C]1.59999999999995[/C][C]0.300000000000053[/C][/ROW]
[ROW][C]37[/C][C]2[/C][C]1.899975722923[/C][C]0.100024277077002[/C][/ROW]
[ROW][C]38[/C][C]1.9[/C][C]1.99999190567641[/C][C]-0.0999919056764114[/C][/ROW]
[ROW][C]39[/C][C]2[/C][C]1.90000809170398[/C][C]0.0999919082960214[/C][/ROW]
[ROW][C]40[/C][C]2.1[/C][C]1.99999190829581[/C][C]0.100008091704191[/C][/ROW]
[ROW][C]41[/C][C]2.3[/C][C]2.09999190698619[/C][C]0.20000809301381[/C][/ROW]
[ROW][C]42[/C][C]2.3[/C][C]2.29998381462708[/C][C]1.61853729170325e-05[/C][/ROW]
[ROW][C]43[/C][C]2.6[/C][C]2.29999999869022[/C][C]0.300000001309779[/C][/ROW]
[ROW][C]44[/C][C]2.6[/C][C]2.59997572292289[/C][C]2.42770771077261e-05[/C][/ROW]
[ROW][C]45[/C][C]2.7[/C][C]2.59999999803541[/C][C]0.100000001964589[/C][/ROW]
[ROW][C]46[/C][C]2.6[/C][C]2.69999190764084[/C][C]-0.0999919076408404[/C][/ROW]
[ROW][C]47[/C][C]2.6[/C][C]2.60000809170414[/C][C]-8.09170413784699e-06[/C][/ROW]
[ROW][C]48[/C][C]2.4[/C][C]2.60000000065481[/C][C]-0.20000000065481[/C][/ROW]
[ROW][C]49[/C][C]2.5[/C][C]2.40001618471805[/C][C]0.0999838152819459[/C][/ROW]
[ROW][C]50[/C][C]2.5[/C][C]2.49999190895072[/C][C]8.09104927501636e-06[/C][/ROW]
[ROW][C]51[/C][C]2.5[/C][C]2.49999999934524[/C][C]6.54756693307945e-10[/C][/ROW]
[ROW][C]52[/C][C]2.4[/C][C]2.49999999999995[/C][C]-0.0999999999999472[/C][/ROW]
[ROW][C]53[/C][C]2.1[/C][C]2.400008092359[/C][C]-0.300008092359[/C][/ROW]
[ROW][C]54[/C][C]2.1[/C][C]2.10002427773186[/C][C]-2.42777318644194e-05[/C][/ROW]
[ROW][C]55[/C][C]2.3[/C][C]2.10000000196464[/C][C]0.199999998035358[/C][/ROW]
[ROW][C]56[/C][C]2.3[/C][C]2.29998381528216[/C][C]1.61847178423713e-05[/C][/ROW]
[ROW][C]57[/C][C]2.3[/C][C]2.29999999869027[/C][C]1.3097256612582e-09[/C][/ROW]
[ROW][C]58[/C][C]2.9[/C][C]2.29999999999989[/C][C]0.600000000000106[/C][/ROW]
[ROW][C]59[/C][C]2.8[/C][C]2.899951445846[/C][C]-0.0999514458459969[/C][/ROW]
[ROW][C]60[/C][C]2.9[/C][C]2.80000808842982[/C][C]0.099991911570176[/C][/ROW]
[ROW][C]61[/C][C]3[/C][C]2.89999190829554[/C][C]0.100008091704456[/C][/ROW]
[ROW][C]62[/C][C]3[/C][C]2.99999190698619[/C][C]8.09301381066163e-06[/C][/ROW]
[ROW][C]63[/C][C]2.9[/C][C]2.99999999934508[/C][C]-0.0999999993450844[/C][/ROW]
[ROW][C]64[/C][C]2.6[/C][C]2.90000809235895[/C][C]-0.300008092358947[/C][/ROW]
[ROW][C]65[/C][C]2.8[/C][C]2.60002427773186[/C][C]0.199975722268135[/C][/ROW]
[ROW][C]66[/C][C]2.9[/C][C]2.79998381724664[/C][C]0.10001618275336[/C][/ROW]
[ROW][C]67[/C][C]3.1[/C][C]2.89999190633143[/C][C]0.200008093668567[/C][/ROW]
[ROW][C]68[/C][C]2.8[/C][C]3.09998381462703[/C][C]-0.299983814627031[/C][/ROW]
[ROW][C]69[/C][C]2.4[/C][C]2.80002427576722[/C][C]-0.400024275767223[/C][/ROW]
[ROW][C]70[/C][C]1.6[/C][C]2.40003237140048[/C][C]-0.800032371400484[/C][/ROW]
[ROW][C]71[/C][C]1.5[/C][C]1.60006474149161[/C][C]-0.100064741491614[/C][/ROW]
[ROW][C]72[/C][C]1.7[/C][C]1.50000809759811[/C][C]0.199991902401885[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278690&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278690&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
22.220.2
32.22.1999838152821.61847180013552e-05
422.19999999869027-0.199999998690275
52.32.00001618471790.299983815282105
62.62.299975724232720.300024275767277
73.22.599975720958520.600024279041484
83.23.199951443881254.85561187506534e-05
93.13.19999999607066-0.0999999960706646
102.83.10000809235868-0.300008092358683
112.32.80002427773186-0.500024277731864
121.92.30004046375964-0.400040463759644
131.91.90003237271047-3.23727104747373e-05
1421.900000002619720.0999999973802843
1521.999991907641218.09235878862502e-06
161.81.99999999934514-0.199999999345137
171.61.80001618471795-0.200016184717948
181.41.60001618602773-0.200016186027727
190.21.40001618602783-1.20001618602783
200.30.2000971096178380.0999028903821618
210.40.2999919154994580.100008084500542
220.70.3999919069867730.300008093013227
2310.6999757222680830.300024277731917
241.10.9999757209583570.100024279041643
250.81.09999190567625-0.299991905676252
260.80.80002427642198-2.42764219799962e-05
2710.8000000019645350.199999998035465
281.10.9999838152821580.100016184717842
2911.09999190633127-0.099991906331274
300.81.00000809170403-0.200008091704032
311.60.8000161853728110.799983814627189
321.51.59993526243777-0.0999352624377741
331.61.50000808712020.0999919128797955
341.61.599991908295448.09170456173014e-06
351.61.599999999345196.54809761968522e-10
361.91.599999999999950.300000000000053
3721.8999757229230.100024277077002
381.91.99999190567641-0.0999919056764114
3921.900008091703980.0999919082960214
402.11.999991908295810.100008091704191
412.32.099991906986190.20000809301381
422.32.299983814627081.61853729170325e-05
432.62.299999998690220.300000001309779
442.62.599975722922892.42770771077261e-05
452.72.599999998035410.100000001964589
462.62.69999190764084-0.0999919076408404
472.62.60000809170414-8.09170413784699e-06
482.42.60000000065481-0.20000000065481
492.52.400016184718050.0999838152819459
502.52.499991908950728.09104927501636e-06
512.52.499999999345246.54756693307945e-10
522.42.49999999999995-0.0999999999999472
532.12.400008092359-0.300008092359
542.12.10002427773186-2.42777318644194e-05
552.32.100000001964640.199999998035358
562.32.299983815282161.61847178423713e-05
572.32.299999998690271.3097256612582e-09
582.92.299999999999890.600000000000106
592.82.899951445846-0.0999514458459969
602.92.800008088429820.099991911570176
6132.899991908295540.100008091704456
6232.999991906986198.09301381066163e-06
632.92.99999999934508-0.0999999993450844
642.62.90000809235895-0.300008092358947
652.82.600024277731860.199975722268135
662.92.799983817246640.10001618275336
673.12.899991906331430.200008093668567
682.83.09998381462703-0.299983814627031
692.42.80002427576722-0.400024275767223
701.62.40003237140048-0.800032371400484
711.51.60006474149161-0.100064741491614
721.71.500008097598110.199991902401885






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731.699983815937291.138299866145312.26166776572926
741.699983815937290.9056748961890492.49429273568552
751.699983815937290.7271711615534572.67279647032111
761.699983815937290.5766840958861272.82328353598844
771.699983815937290.4441016313336852.95586600054089
781.699983815937290.3242375231411133.07573010873346
791.699983815937290.2140108475828433.18595678429173
801.699983815937290.1114141878700063.28855344400456
811.699983815937290.01505317530084853.38491445657372
821.69998381593729-0.07608742821178163.47605506008635
831.69998381593729-0.162774049387923.56274168126249
841.69998381593729-0.2456021280314243.645569759906

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.69998381593729 & 1.13829986614531 & 2.26166776572926 \tabularnewline
74 & 1.69998381593729 & 0.905674896189049 & 2.49429273568552 \tabularnewline
75 & 1.69998381593729 & 0.727171161553457 & 2.67279647032111 \tabularnewline
76 & 1.69998381593729 & 0.576684095886127 & 2.82328353598844 \tabularnewline
77 & 1.69998381593729 & 0.444101631333685 & 2.95586600054089 \tabularnewline
78 & 1.69998381593729 & 0.324237523141113 & 3.07573010873346 \tabularnewline
79 & 1.69998381593729 & 0.214010847582843 & 3.18595678429173 \tabularnewline
80 & 1.69998381593729 & 0.111414187870006 & 3.28855344400456 \tabularnewline
81 & 1.69998381593729 & 0.0150531753008485 & 3.38491445657372 \tabularnewline
82 & 1.69998381593729 & -0.0760874282117816 & 3.47605506008635 \tabularnewline
83 & 1.69998381593729 & -0.16277404938792 & 3.56274168126249 \tabularnewline
84 & 1.69998381593729 & -0.245602128031424 & 3.645569759906 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278690&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]1.69998381593729[/C][C]1.13829986614531[/C][C]2.26166776572926[/C][/ROW]
[ROW][C]74[/C][C]1.69998381593729[/C][C]0.905674896189049[/C][C]2.49429273568552[/C][/ROW]
[ROW][C]75[/C][C]1.69998381593729[/C][C]0.727171161553457[/C][C]2.67279647032111[/C][/ROW]
[ROW][C]76[/C][C]1.69998381593729[/C][C]0.576684095886127[/C][C]2.82328353598844[/C][/ROW]
[ROW][C]77[/C][C]1.69998381593729[/C][C]0.444101631333685[/C][C]2.95586600054089[/C][/ROW]
[ROW][C]78[/C][C]1.69998381593729[/C][C]0.324237523141113[/C][C]3.07573010873346[/C][/ROW]
[ROW][C]79[/C][C]1.69998381593729[/C][C]0.214010847582843[/C][C]3.18595678429173[/C][/ROW]
[ROW][C]80[/C][C]1.69998381593729[/C][C]0.111414187870006[/C][C]3.28855344400456[/C][/ROW]
[ROW][C]81[/C][C]1.69998381593729[/C][C]0.0150531753008485[/C][C]3.38491445657372[/C][/ROW]
[ROW][C]82[/C][C]1.69998381593729[/C][C]-0.0760874282117816[/C][C]3.47605506008635[/C][/ROW]
[ROW][C]83[/C][C]1.69998381593729[/C][C]-0.16277404938792[/C][C]3.56274168126249[/C][/ROW]
[ROW][C]84[/C][C]1.69998381593729[/C][C]-0.245602128031424[/C][C]3.645569759906[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278690&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278690&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731.699983815937291.138299866145312.26166776572926
741.699983815937290.9056748961890492.49429273568552
751.699983815937290.7271711615534572.67279647032111
761.699983815937290.5766840958861272.82328353598844
771.699983815937290.4441016313336852.95586600054089
781.699983815937290.3242375231411133.07573010873346
791.699983815937290.2140108475828433.18595678429173
801.699983815937290.1114141878700063.28855344400456
811.699983815937290.01505317530084853.38491445657372
821.69998381593729-0.07608742821178163.47605506008635
831.69998381593729-0.162774049387923.56274168126249
841.69998381593729-0.2456021280314243.645569759906


Figures (Output of Computation)

Input Parameters & R Code

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')