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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 10 Jan 2013 09:12:33 -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/2013/Jan/10/t135782716597oke70w8m416tl.htm/, Retrieved Mon, 29 Apr 2024 16:14:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205137, Retrieved Mon, 29 Apr 2024 16:14:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-10 14:12:33] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
530,3
527,76
521,41
1601,93
1577,49
1551,43
1551,43
1516,88
1485,95
1438,22
1385,06
1329,49
1329,49
1276,16
1242,34
1181,59
1160,21
1135,18
1135,18
1084,96
1077,35
1061,13
1029,98
1013,08
1013,08
996,04
975,02
951,89
944,4
932,47
932,47
920,44
900,18
886,9
867,74
859,03
859,03
844,99
834,82
825,62
816,92
813,21
813,21
811,03
804,16
788,62
778,76
765,91
765,91
753,85
742,22
732,11
729,94
731,22
731,22
729,11
726,94
720,52
709,36
703,21
703,21
695,88
681,63
672,1
665,49
658,93
658,93
656
650,66
645,93
638,74
634,67




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205137&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205137&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205137&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.562708990539238
beta0.0530547709145565
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.562708990539238 \tabularnewline
beta & 0.0530547709145565 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205137&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]0.562708990539238[/C][/ROW]
[ROW][C]beta[/C][C]0.0530547709145565[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205137&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205137&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
alpha0.562708990539238
beta0.0530547709145565
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131329.491382.81951869758-53.3295186975824
141276.161314.19332572796-38.0333257279647
151242.341272.57550737936-30.2355073793635
161181.591204.67540345956-23.0854034595648
171160.211177.74476431549-17.5347643154923
181135.181147.24127769109-12.0612776910903
191135.181374.9038275473-239.723827547298
201084.961120.93644335164-35.9764433516409
211077.35999.03331224826278.3166877517382
221061.13971.85896257455989.2710374254414
231029.98983.20921990735746.770780092643
241013.08969.81380365508343.2661963449166
251013.08979.74011028932533.3398897106747
26996.04967.44157231522128.5984276847788
27975.02965.6633585460039.35664145399676
28951.89930.01781693190421.8721830680961
29944.4931.11622775919413.2837722408058
30932.47922.9017480023079.56825199769276
31932.471029.12736272964-96.6573627296368
32920.44952.437027564243-31.9970275642431
33900.18892.3383384629287.84166153707156
34886.9840.72612326949946.173876730501
35867.74818.88553134096148.854468659039
36859.03812.07251872874846.9574812712516
37859.03823.17193412302735.8580658769731
38844.99816.36099669909628.6290033009037
39834.82811.44723888736823.3727611126317
40825.62796.13159869540729.4884013045935
41816.92802.01031897070114.9096810292987
42813.21797.81772157100715.3922784289933
43813.21854.326275953634-41.1162759536335
44811.03841.054648233559-30.024648233559
45804.16806.878513552588-2.71851355258764
46788.62774.12007335064314.499926649357
47778.76743.74405824520635.0159417547939
48765.91734.82141591275131.0885840872494
49765.91736.752297179129.1577028209005
50753.85728.84861629991425.0013837000863
51742.22724.61326469888917.6067353011108
52732.11713.82669770184218.2833022981582
53729.94711.01076997255718.9292300274427
54731.22712.88346025313418.3365397468665
55731.22745.879995345047-14.6599953450473
56729.11754.328552937699-25.2185529376993
57726.94739.05809299382-12.1180929938198
58720.52714.0449241950116.47507580498871
59709.36693.60387534076915.756124659231
60703.21677.31623086331125.8937691366892
61703.21679.25052972161223.9594702783879
62695.88671.24074215418424.6392578458161
63681.63667.84200672776313.7879932722366
64672.1659.25340322413112.8465967758688
65665.49656.9000086648458.58999133515522
66658.93655.336989287973.59301071202992
67658.93666.175342717996-7.24534271799575
68656674.609535655245-18.6095356552452
69650.66670.317901538987-19.6579015389874
70645.93651.802698446574-5.87269844657453
71638.74631.6309570332887.10904296671208
72634.67617.81071956094816.8592804390515

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1329.49 & 1382.81951869758 & -53.3295186975824 \tabularnewline
14 & 1276.16 & 1314.19332572796 & -38.0333257279647 \tabularnewline
15 & 1242.34 & 1272.57550737936 & -30.2355073793635 \tabularnewline
16 & 1181.59 & 1204.67540345956 & -23.0854034595648 \tabularnewline
17 & 1160.21 & 1177.74476431549 & -17.5347643154923 \tabularnewline
18 & 1135.18 & 1147.24127769109 & -12.0612776910903 \tabularnewline
19 & 1135.18 & 1374.9038275473 & -239.723827547298 \tabularnewline
20 & 1084.96 & 1120.93644335164 & -35.9764433516409 \tabularnewline
21 & 1077.35 & 999.033312248262 & 78.3166877517382 \tabularnewline
22 & 1061.13 & 971.858962574559 & 89.2710374254414 \tabularnewline
23 & 1029.98 & 983.209219907357 & 46.770780092643 \tabularnewline
24 & 1013.08 & 969.813803655083 & 43.2661963449166 \tabularnewline
25 & 1013.08 & 979.740110289325 & 33.3398897106747 \tabularnewline
26 & 996.04 & 967.441572315221 & 28.5984276847788 \tabularnewline
27 & 975.02 & 965.663358546003 & 9.35664145399676 \tabularnewline
28 & 951.89 & 930.017816931904 & 21.8721830680961 \tabularnewline
29 & 944.4 & 931.116227759194 & 13.2837722408058 \tabularnewline
30 & 932.47 & 922.901748002307 & 9.56825199769276 \tabularnewline
31 & 932.47 & 1029.12736272964 & -96.6573627296368 \tabularnewline
32 & 920.44 & 952.437027564243 & -31.9970275642431 \tabularnewline
33 & 900.18 & 892.338338462928 & 7.84166153707156 \tabularnewline
34 & 886.9 & 840.726123269499 & 46.173876730501 \tabularnewline
35 & 867.74 & 818.885531340961 & 48.854468659039 \tabularnewline
36 & 859.03 & 812.072518728748 & 46.9574812712516 \tabularnewline
37 & 859.03 & 823.171934123027 & 35.8580658769731 \tabularnewline
38 & 844.99 & 816.360996699096 & 28.6290033009037 \tabularnewline
39 & 834.82 & 811.447238887368 & 23.3727611126317 \tabularnewline
40 & 825.62 & 796.131598695407 & 29.4884013045935 \tabularnewline
41 & 816.92 & 802.010318970701 & 14.9096810292987 \tabularnewline
42 & 813.21 & 797.817721571007 & 15.3922784289933 \tabularnewline
43 & 813.21 & 854.326275953634 & -41.1162759536335 \tabularnewline
44 & 811.03 & 841.054648233559 & -30.024648233559 \tabularnewline
45 & 804.16 & 806.878513552588 & -2.71851355258764 \tabularnewline
46 & 788.62 & 774.120073350643 & 14.499926649357 \tabularnewline
47 & 778.76 & 743.744058245206 & 35.0159417547939 \tabularnewline
48 & 765.91 & 734.821415912751 & 31.0885840872494 \tabularnewline
49 & 765.91 & 736.7522971791 & 29.1577028209005 \tabularnewline
50 & 753.85 & 728.848616299914 & 25.0013837000863 \tabularnewline
51 & 742.22 & 724.613264698889 & 17.6067353011108 \tabularnewline
52 & 732.11 & 713.826697701842 & 18.2833022981582 \tabularnewline
53 & 729.94 & 711.010769972557 & 18.9292300274427 \tabularnewline
54 & 731.22 & 712.883460253134 & 18.3365397468665 \tabularnewline
55 & 731.22 & 745.879995345047 & -14.6599953450473 \tabularnewline
56 & 729.11 & 754.328552937699 & -25.2185529376993 \tabularnewline
57 & 726.94 & 739.05809299382 & -12.1180929938198 \tabularnewline
58 & 720.52 & 714.044924195011 & 6.47507580498871 \tabularnewline
59 & 709.36 & 693.603875340769 & 15.756124659231 \tabularnewline
60 & 703.21 & 677.316230863311 & 25.8937691366892 \tabularnewline
61 & 703.21 & 679.250529721612 & 23.9594702783879 \tabularnewline
62 & 695.88 & 671.240742154184 & 24.6392578458161 \tabularnewline
63 & 681.63 & 667.842006727763 & 13.7879932722366 \tabularnewline
64 & 672.1 & 659.253403224131 & 12.8465967758688 \tabularnewline
65 & 665.49 & 656.900008664845 & 8.58999133515522 \tabularnewline
66 & 658.93 & 655.33698928797 & 3.59301071202992 \tabularnewline
67 & 658.93 & 666.175342717996 & -7.24534271799575 \tabularnewline
68 & 656 & 674.609535655245 & -18.6095356552452 \tabularnewline
69 & 650.66 & 670.317901538987 & -19.6579015389874 \tabularnewline
70 & 645.93 & 651.802698446574 & -5.87269844657453 \tabularnewline
71 & 638.74 & 631.630957033288 & 7.10904296671208 \tabularnewline
72 & 634.67 & 617.810719560948 & 16.8592804390515 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205137&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]13[/C][C]1329.49[/C][C]1382.81951869758[/C][C]-53.3295186975824[/C][/ROW]
[ROW][C]14[/C][C]1276.16[/C][C]1314.19332572796[/C][C]-38.0333257279647[/C][/ROW]
[ROW][C]15[/C][C]1242.34[/C][C]1272.57550737936[/C][C]-30.2355073793635[/C][/ROW]
[ROW][C]16[/C][C]1181.59[/C][C]1204.67540345956[/C][C]-23.0854034595648[/C][/ROW]
[ROW][C]17[/C][C]1160.21[/C][C]1177.74476431549[/C][C]-17.5347643154923[/C][/ROW]
[ROW][C]18[/C][C]1135.18[/C][C]1147.24127769109[/C][C]-12.0612776910903[/C][/ROW]
[ROW][C]19[/C][C]1135.18[/C][C]1374.9038275473[/C][C]-239.723827547298[/C][/ROW]
[ROW][C]20[/C][C]1084.96[/C][C]1120.93644335164[/C][C]-35.9764433516409[/C][/ROW]
[ROW][C]21[/C][C]1077.35[/C][C]999.033312248262[/C][C]78.3166877517382[/C][/ROW]
[ROW][C]22[/C][C]1061.13[/C][C]971.858962574559[/C][C]89.2710374254414[/C][/ROW]
[ROW][C]23[/C][C]1029.98[/C][C]983.209219907357[/C][C]46.770780092643[/C][/ROW]
[ROW][C]24[/C][C]1013.08[/C][C]969.813803655083[/C][C]43.2661963449166[/C][/ROW]
[ROW][C]25[/C][C]1013.08[/C][C]979.740110289325[/C][C]33.3398897106747[/C][/ROW]
[ROW][C]26[/C][C]996.04[/C][C]967.441572315221[/C][C]28.5984276847788[/C][/ROW]
[ROW][C]27[/C][C]975.02[/C][C]965.663358546003[/C][C]9.35664145399676[/C][/ROW]
[ROW][C]28[/C][C]951.89[/C][C]930.017816931904[/C][C]21.8721830680961[/C][/ROW]
[ROW][C]29[/C][C]944.4[/C][C]931.116227759194[/C][C]13.2837722408058[/C][/ROW]
[ROW][C]30[/C][C]932.47[/C][C]922.901748002307[/C][C]9.56825199769276[/C][/ROW]
[ROW][C]31[/C][C]932.47[/C][C]1029.12736272964[/C][C]-96.6573627296368[/C][/ROW]
[ROW][C]32[/C][C]920.44[/C][C]952.437027564243[/C][C]-31.9970275642431[/C][/ROW]
[ROW][C]33[/C][C]900.18[/C][C]892.338338462928[/C][C]7.84166153707156[/C][/ROW]
[ROW][C]34[/C][C]886.9[/C][C]840.726123269499[/C][C]46.173876730501[/C][/ROW]
[ROW][C]35[/C][C]867.74[/C][C]818.885531340961[/C][C]48.854468659039[/C][/ROW]
[ROW][C]36[/C][C]859.03[/C][C]812.072518728748[/C][C]46.9574812712516[/C][/ROW]
[ROW][C]37[/C][C]859.03[/C][C]823.171934123027[/C][C]35.8580658769731[/C][/ROW]
[ROW][C]38[/C][C]844.99[/C][C]816.360996699096[/C][C]28.6290033009037[/C][/ROW]
[ROW][C]39[/C][C]834.82[/C][C]811.447238887368[/C][C]23.3727611126317[/C][/ROW]
[ROW][C]40[/C][C]825.62[/C][C]796.131598695407[/C][C]29.4884013045935[/C][/ROW]
[ROW][C]41[/C][C]816.92[/C][C]802.010318970701[/C][C]14.9096810292987[/C][/ROW]
[ROW][C]42[/C][C]813.21[/C][C]797.817721571007[/C][C]15.3922784289933[/C][/ROW]
[ROW][C]43[/C][C]813.21[/C][C]854.326275953634[/C][C]-41.1162759536335[/C][/ROW]
[ROW][C]44[/C][C]811.03[/C][C]841.054648233559[/C][C]-30.024648233559[/C][/ROW]
[ROW][C]45[/C][C]804.16[/C][C]806.878513552588[/C][C]-2.71851355258764[/C][/ROW]
[ROW][C]46[/C][C]788.62[/C][C]774.120073350643[/C][C]14.499926649357[/C][/ROW]
[ROW][C]47[/C][C]778.76[/C][C]743.744058245206[/C][C]35.0159417547939[/C][/ROW]
[ROW][C]48[/C][C]765.91[/C][C]734.821415912751[/C][C]31.0885840872494[/C][/ROW]
[ROW][C]49[/C][C]765.91[/C][C]736.7522971791[/C][C]29.1577028209005[/C][/ROW]
[ROW][C]50[/C][C]753.85[/C][C]728.848616299914[/C][C]25.0013837000863[/C][/ROW]
[ROW][C]51[/C][C]742.22[/C][C]724.613264698889[/C][C]17.6067353011108[/C][/ROW]
[ROW][C]52[/C][C]732.11[/C][C]713.826697701842[/C][C]18.2833022981582[/C][/ROW]
[ROW][C]53[/C][C]729.94[/C][C]711.010769972557[/C][C]18.9292300274427[/C][/ROW]
[ROW][C]54[/C][C]731.22[/C][C]712.883460253134[/C][C]18.3365397468665[/C][/ROW]
[ROW][C]55[/C][C]731.22[/C][C]745.879995345047[/C][C]-14.6599953450473[/C][/ROW]
[ROW][C]56[/C][C]729.11[/C][C]754.328552937699[/C][C]-25.2185529376993[/C][/ROW]
[ROW][C]57[/C][C]726.94[/C][C]739.05809299382[/C][C]-12.1180929938198[/C][/ROW]
[ROW][C]58[/C][C]720.52[/C][C]714.044924195011[/C][C]6.47507580498871[/C][/ROW]
[ROW][C]59[/C][C]709.36[/C][C]693.603875340769[/C][C]15.756124659231[/C][/ROW]
[ROW][C]60[/C][C]703.21[/C][C]677.316230863311[/C][C]25.8937691366892[/C][/ROW]
[ROW][C]61[/C][C]703.21[/C][C]679.250529721612[/C][C]23.9594702783879[/C][/ROW]
[ROW][C]62[/C][C]695.88[/C][C]671.240742154184[/C][C]24.6392578458161[/C][/ROW]
[ROW][C]63[/C][C]681.63[/C][C]667.842006727763[/C][C]13.7879932722366[/C][/ROW]
[ROW][C]64[/C][C]672.1[/C][C]659.253403224131[/C][C]12.8465967758688[/C][/ROW]
[ROW][C]65[/C][C]665.49[/C][C]656.900008664845[/C][C]8.58999133515522[/C][/ROW]
[ROW][C]66[/C][C]658.93[/C][C]655.33698928797[/C][C]3.59301071202992[/C][/ROW]
[ROW][C]67[/C][C]658.93[/C][C]666.175342717996[/C][C]-7.24534271799575[/C][/ROW]
[ROW][C]68[/C][C]656[/C][C]674.609535655245[/C][C]-18.6095356552452[/C][/ROW]
[ROW][C]69[/C][C]650.66[/C][C]670.317901538987[/C][C]-19.6579015389874[/C][/ROW]
[ROW][C]70[/C][C]645.93[/C][C]651.802698446574[/C][C]-5.87269844657453[/C][/ROW]
[ROW][C]71[/C][C]638.74[/C][C]631.630957033288[/C][C]7.10904296671208[/C][/ROW]
[ROW][C]72[/C][C]634.67[/C][C]617.810719560948[/C][C]16.8592804390515[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205137&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205137&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
131329.491382.81951869758-53.3295186975824
141276.161314.19332572796-38.0333257279647
151242.341272.57550737936-30.2355073793635
161181.591204.67540345956-23.0854034595648
171160.211177.74476431549-17.5347643154923
181135.181147.24127769109-12.0612776910903
191135.181374.9038275473-239.723827547298
201084.961120.93644335164-35.9764433516409
211077.35999.03331224826278.3166877517382
221061.13971.85896257455989.2710374254414
231029.98983.20921990735746.770780092643
241013.08969.81380365508343.2661963449166
251013.08979.74011028932533.3398897106747
26996.04967.44157231522128.5984276847788
27975.02965.6633585460039.35664145399676
28951.89930.01781693190421.8721830680961
29944.4931.11622775919413.2837722408058
30932.47922.9017480023079.56825199769276
31932.471029.12736272964-96.6573627296368
32920.44952.437027564243-31.9970275642431
33900.18892.3383384629287.84166153707156
34886.9840.72612326949946.173876730501
35867.74818.88553134096148.854468659039
36859.03812.07251872874846.9574812712516
37859.03823.17193412302735.8580658769731
38844.99816.36099669909628.6290033009037
39834.82811.44723888736823.3727611126317
40825.62796.13159869540729.4884013045935
41816.92802.01031897070114.9096810292987
42813.21797.81772157100715.3922784289933
43813.21854.326275953634-41.1162759536335
44811.03841.054648233559-30.024648233559
45804.16806.878513552588-2.71851355258764
46788.62774.12007335064314.499926649357
47778.76743.74405824520635.0159417547939
48765.91734.82141591275131.0885840872494
49765.91736.752297179129.1577028209005
50753.85728.84861629991425.0013837000863
51742.22724.61326469888917.6067353011108
52732.11713.82669770184218.2833022981582
53729.94711.01076997255718.9292300274427
54731.22712.88346025313418.3365397468665
55731.22745.879995345047-14.6599953450473
56729.11754.328552937699-25.2185529376993
57726.94739.05809299382-12.1180929938198
58720.52714.0449241950116.47507580498871
59709.36693.60387534076915.756124659231
60703.21677.31623086331125.8937691366892
61703.21679.25052972161223.9594702783879
62695.88671.24074215418424.6392578458161
63681.63667.84200672776313.7879932722366
64672.1659.25340322413112.8465967758688
65665.49656.9000086648458.58999133515522
66658.93655.336989287973.59301071202992
67658.93666.175342717996-7.24534271799575
68656674.609535655245-18.6095356552452
69650.66670.317901538987-19.6579015389874
70645.93651.802698446574-5.87269844657453
71638.74631.6309570332887.10904296671208
72634.67617.81071956094816.8592804390515







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73615.801403160694528.063453653615703.539352667772
74596.94947266441495.389769653371698.509175675449
75577.10602212668462.730604977621691.481439275739
76561.523655998976434.557397386714688.489914611238
77550.187150929256410.422533831119689.951768027393
78541.052772204561388.278435405064693.827109004058
79542.176485922425374.145444828995710.207527015854
80546.210800244058361.741984415197730.679616072918
81549.294222075837348.055322739588750.533121412087
82547.101384286075330.210023928694763.992744643457
83536.804991206454306.800378740363766.809603672544
84524.277796861776298.203834449847750.351759273705

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 615.801403160694 & 528.063453653615 & 703.539352667772 \tabularnewline
74 & 596.94947266441 & 495.389769653371 & 698.509175675449 \tabularnewline
75 & 577.10602212668 & 462.730604977621 & 691.481439275739 \tabularnewline
76 & 561.523655998976 & 434.557397386714 & 688.489914611238 \tabularnewline
77 & 550.187150929256 & 410.422533831119 & 689.951768027393 \tabularnewline
78 & 541.052772204561 & 388.278435405064 & 693.827109004058 \tabularnewline
79 & 542.176485922425 & 374.145444828995 & 710.207527015854 \tabularnewline
80 & 546.210800244058 & 361.741984415197 & 730.679616072918 \tabularnewline
81 & 549.294222075837 & 348.055322739588 & 750.533121412087 \tabularnewline
82 & 547.101384286075 & 330.210023928694 & 763.992744643457 \tabularnewline
83 & 536.804991206454 & 306.800378740363 & 766.809603672544 \tabularnewline
84 & 524.277796861776 & 298.203834449847 & 750.351759273705 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205137&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]615.801403160694[/C][C]528.063453653615[/C][C]703.539352667772[/C][/ROW]
[ROW][C]74[/C][C]596.94947266441[/C][C]495.389769653371[/C][C]698.509175675449[/C][/ROW]
[ROW][C]75[/C][C]577.10602212668[/C][C]462.730604977621[/C][C]691.481439275739[/C][/ROW]
[ROW][C]76[/C][C]561.523655998976[/C][C]434.557397386714[/C][C]688.489914611238[/C][/ROW]
[ROW][C]77[/C][C]550.187150929256[/C][C]410.422533831119[/C][C]689.951768027393[/C][/ROW]
[ROW][C]78[/C][C]541.052772204561[/C][C]388.278435405064[/C][C]693.827109004058[/C][/ROW]
[ROW][C]79[/C][C]542.176485922425[/C][C]374.145444828995[/C][C]710.207527015854[/C][/ROW]
[ROW][C]80[/C][C]546.210800244058[/C][C]361.741984415197[/C][C]730.679616072918[/C][/ROW]
[ROW][C]81[/C][C]549.294222075837[/C][C]348.055322739588[/C][C]750.533121412087[/C][/ROW]
[ROW][C]82[/C][C]547.101384286075[/C][C]330.210023928694[/C][C]763.992744643457[/C][/ROW]
[ROW][C]83[/C][C]536.804991206454[/C][C]306.800378740363[/C][C]766.809603672544[/C][/ROW]
[ROW][C]84[/C][C]524.277796861776[/C][C]298.203834449847[/C][C]750.351759273705[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205137&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205137&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
73615.801403160694528.063453653615703.539352667772
74596.94947266441495.389769653371698.509175675449
75577.10602212668462.730604977621691.481439275739
76561.523655998976434.557397386714688.489914611238
77550.187150929256410.422533831119689.951768027393
78541.052772204561388.278435405064693.827109004058
79542.176485922425374.145444828995710.207527015854
80546.210800244058361.741984415197730.679616072918
81549.294222075837348.055322739588750.533121412087
82547.101384286075330.210023928694763.992744643457
83536.804991206454306.800378740363766.809603672544
84524.277796861776298.203834449847750.351759273705



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')