Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 May 2015 21:43:05 +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/May/26/t1432673126kuarhr46gkdosh3.htm/, Retrieved Tue, 30 Apr 2024 10:12:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279437, Retrieved Tue, 30 Apr 2024 10:12:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [] [2015-04-02 18:52:13] [1f4ce71c1a7ae502d60225fda197c28f]
-   PD  [Classical Decomposition] [] [2015-05-26 20:23:00] [1f4ce71c1a7ae502d60225fda197c28f]
- RM D      [Exponential Smoothing] [] [2015-05-26 20:43:05] [c6da619eabbd864125b02146bc2bbd84] [Current]
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Dataseries X:
1.5469
1.5501
1.5494
1.5475
1.5449
1.5391
1.5578
1.5528
1.5496
1.549
1.5449
1.5479
1.5494
1.558
1.5691
1.5748
1.5564
1.5601
1.5687
1.5775
1.5841
1.5898
1.5922
1.5969
1.6155
1.6212
1.6124
1.6375
1.6506
1.6543
1.6567
1.6383
1.6475
1.6706
1.6485
1.6592
1.6203
1.608
1.572
1.5964
1.6247
1.6139
1.6193
1.6212
1.5942
1.5194
1.5162
1.5393
1.4935
1.4904
1.5083
1.5147
1.5118
1.5148
1.5202
1.5236
1.5148
1.5138
1.5105
1.502
1.4765
1.4671
1.4482
1.4337
1.4181
1.3767
1.346
1.3413
1.3089
1.3452
1.3442
1.2811
1.2779
1.2974
1.2867
1.2977
1.2537
1.2092
1.1766
1.1203
1.2005
1.2295
1.2307
1.2276
1.2108
1.2071
1.2061
1.2023
1.2012
1.2011
1.2011
1.2011
1.2089
1.2098
1.2052
1.2091
1.2288
1.2298
1.2266
1.2199
1.2418
1.2322
1.2366
1.2338
1.2338
1.2316
1.2316
1.2245




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279437&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279437&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279437&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.916698954658846
beta0.0425789585757162
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.916698954658846 \tabularnewline
beta & 0.0425789585757162 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279437&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]0.916698954658846[/C][/ROW]
[ROW][C]beta[/C][C]0.0425789585757162[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279437&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279437&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
alpha0.916698954658846
beta0.0425789585757162
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131.54941.540442280982910.0089577190170933
141.5581.5580807384044-8.07384043970405e-05
151.56911.568947166634140.000152833365864913
161.57481.573962841933380.000837158066617549
171.55641.555005179663460.00139482033654081
181.56011.558371501895230.00172849810477005
191.56871.58273617307642-0.0140361730764174
201.57751.566355692205840.0111443077941582
211.58411.57457645074980.00952354925020171
221.58981.583474852298560.0063251477014401
231.59221.586529832871870.00567016712812807
241.59691.596568211893920.000331788106082032
251.61551.600997042187040.014502957812961
261.62121.62442938266906-0.00322938266906059
271.61241.63376949201363-0.0213694920136274
281.63751.619613201074090.0178867989259066
291.65061.617497385644940.0331026143550621
301.65431.652361631621540.00193836837845662
311.65671.67801729515574-0.0213172951557417
321.63831.65918739835725-0.0208873983572542
331.64751.638787070832160.00871292916784161
341.67061.647521663769780.0230783362302243
351.64851.66737934226072-0.018879342260719
361.65921.655009928626410.00419007137359095
371.62031.66484812274614-0.044548122746136
381.6081.63105839634486-0.0230583963448636
391.5721.61832333116182-0.0463233311618181
401.59641.581201123267760.0151988767322355
411.62471.574423021727890.0502769782721149
421.61391.61963956217395-0.00573956217394955
431.61931.6332245553493-0.0139245553493037
441.62121.618400841953080.00279915804692443
451.59421.62029768557133-0.0260976855713282
461.51941.59507733827781-0.0756773382778078
471.51621.513815295127420.00238470487258269
481.53931.516594918102140.0227050818978569
491.49351.53380314055392-0.0403031405539223
501.49041.50031787213475-0.00991787213475503
511.50831.492826591021160.0154734089788375
521.51471.51502618282323-0.000326182823232601
531.51181.493880270850880.0179197291491211
541.51481.500447700423970.0143522995760308
551.52021.52823227301646-0.00803227301646259
561.52361.516896308800160.00670369119983949
571.51481.51681089599163-0.00201089599162896
581.51381.507326603684790.00647339631521393
591.51051.508866974516850.00163302548315003
601.5021.51361317447447-0.0116131744744705
611.47651.49373665527207-0.01723665527207
621.46711.48445128636017-0.0173512863601666
631.44821.47249453272596-0.0242945327259634
641.43371.45560415594214-0.0219041559421411
651.41811.414036793305330.00406320669467242
661.37671.40490309482598-0.0282030948259773
671.3461.38744979991914-0.0414497999191408
681.34131.341040465496480.000259534503515235
691.30891.32840315842366-0.0195031584236638
701.34521.296989110008680.0482108899913183
711.34421.331414723350030.0127852766499719
721.28111.34074378726331-0.0596437872633135
731.27791.269957507920830.00794249207916509
741.29741.27831537706490.0190846229350961
751.28671.2951742621776-0.00847426217760439
761.29771.289596188390470.00810381160953266
771.25371.27548223692452-0.0217822369245153
781.20921.23674145928404-0.0275414592840415
791.17661.21559027425443-0.0389902742544328
801.12031.17180506966389-0.0515050696638917
811.20051.104943524627420.0955564753725811
821.22951.184010764414110.0454892355858907
831.23071.212249808692810.0184501913071899
841.22761.220218949963190.007381050036811
851.21081.21860086864789-0.00780086864789165
861.20711.21493706241362-0.00783706241362081
871.20611.205252469006730.000847530993269618
881.20231.21039577942698-0.00809577942698203
891.20121.179104972140110.0220950278598899
901.20111.18198214065840.0191178593416041
911.20111.20634646919898-0.00524646919897576
921.20111.197465434233520.0036345657664838
931.20891.20056668516890.00833331483110133
941.20981.199267358860440.010532641139559
951.20521.195606387475910.00959361252409074
961.20911.196585989020750.0125140109792512
971.22881.200660315941740.0281396840582635
981.22981.23359469460078-0.00379469460077564
991.22661.23215148607908-0.00555148607907707
1001.21991.23424638496919-0.0143463849691898
1011.24181.203059153582040.0387408464179573
1021.23221.224915820016880.00728417998312292
1031.23661.23990905451788-0.00330905451787822
1041.23381.23712586789426-0.0033258678942627
1051.23381.23754824985942-0.00374824985942346
1061.23161.228195745908850.00340425409114564
1071.23161.220482505581020.011117494418978
1081.22451.22572233867813-0.00122233867813315

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.5494 & 1.54044228098291 & 0.0089577190170933 \tabularnewline
14 & 1.558 & 1.5580807384044 & -8.07384043970405e-05 \tabularnewline
15 & 1.5691 & 1.56894716663414 & 0.000152833365864913 \tabularnewline
16 & 1.5748 & 1.57396284193338 & 0.000837158066617549 \tabularnewline
17 & 1.5564 & 1.55500517966346 & 0.00139482033654081 \tabularnewline
18 & 1.5601 & 1.55837150189523 & 0.00172849810477005 \tabularnewline
19 & 1.5687 & 1.58273617307642 & -0.0140361730764174 \tabularnewline
20 & 1.5775 & 1.56635569220584 & 0.0111443077941582 \tabularnewline
21 & 1.5841 & 1.5745764507498 & 0.00952354925020171 \tabularnewline
22 & 1.5898 & 1.58347485229856 & 0.0063251477014401 \tabularnewline
23 & 1.5922 & 1.58652983287187 & 0.00567016712812807 \tabularnewline
24 & 1.5969 & 1.59656821189392 & 0.000331788106082032 \tabularnewline
25 & 1.6155 & 1.60099704218704 & 0.014502957812961 \tabularnewline
26 & 1.6212 & 1.62442938266906 & -0.00322938266906059 \tabularnewline
27 & 1.6124 & 1.63376949201363 & -0.0213694920136274 \tabularnewline
28 & 1.6375 & 1.61961320107409 & 0.0178867989259066 \tabularnewline
29 & 1.6506 & 1.61749738564494 & 0.0331026143550621 \tabularnewline
30 & 1.6543 & 1.65236163162154 & 0.00193836837845662 \tabularnewline
31 & 1.6567 & 1.67801729515574 & -0.0213172951557417 \tabularnewline
32 & 1.6383 & 1.65918739835725 & -0.0208873983572542 \tabularnewline
33 & 1.6475 & 1.63878707083216 & 0.00871292916784161 \tabularnewline
34 & 1.6706 & 1.64752166376978 & 0.0230783362302243 \tabularnewline
35 & 1.6485 & 1.66737934226072 & -0.018879342260719 \tabularnewline
36 & 1.6592 & 1.65500992862641 & 0.00419007137359095 \tabularnewline
37 & 1.6203 & 1.66484812274614 & -0.044548122746136 \tabularnewline
38 & 1.608 & 1.63105839634486 & -0.0230583963448636 \tabularnewline
39 & 1.572 & 1.61832333116182 & -0.0463233311618181 \tabularnewline
40 & 1.5964 & 1.58120112326776 & 0.0151988767322355 \tabularnewline
41 & 1.6247 & 1.57442302172789 & 0.0502769782721149 \tabularnewline
42 & 1.6139 & 1.61963956217395 & -0.00573956217394955 \tabularnewline
43 & 1.6193 & 1.6332245553493 & -0.0139245553493037 \tabularnewline
44 & 1.6212 & 1.61840084195308 & 0.00279915804692443 \tabularnewline
45 & 1.5942 & 1.62029768557133 & -0.0260976855713282 \tabularnewline
46 & 1.5194 & 1.59507733827781 & -0.0756773382778078 \tabularnewline
47 & 1.5162 & 1.51381529512742 & 0.00238470487258269 \tabularnewline
48 & 1.5393 & 1.51659491810214 & 0.0227050818978569 \tabularnewline
49 & 1.4935 & 1.53380314055392 & -0.0403031405539223 \tabularnewline
50 & 1.4904 & 1.50031787213475 & -0.00991787213475503 \tabularnewline
51 & 1.5083 & 1.49282659102116 & 0.0154734089788375 \tabularnewline
52 & 1.5147 & 1.51502618282323 & -0.000326182823232601 \tabularnewline
53 & 1.5118 & 1.49388027085088 & 0.0179197291491211 \tabularnewline
54 & 1.5148 & 1.50044770042397 & 0.0143522995760308 \tabularnewline
55 & 1.5202 & 1.52823227301646 & -0.00803227301646259 \tabularnewline
56 & 1.5236 & 1.51689630880016 & 0.00670369119983949 \tabularnewline
57 & 1.5148 & 1.51681089599163 & -0.00201089599162896 \tabularnewline
58 & 1.5138 & 1.50732660368479 & 0.00647339631521393 \tabularnewline
59 & 1.5105 & 1.50886697451685 & 0.00163302548315003 \tabularnewline
60 & 1.502 & 1.51361317447447 & -0.0116131744744705 \tabularnewline
61 & 1.4765 & 1.49373665527207 & -0.01723665527207 \tabularnewline
62 & 1.4671 & 1.48445128636017 & -0.0173512863601666 \tabularnewline
63 & 1.4482 & 1.47249453272596 & -0.0242945327259634 \tabularnewline
64 & 1.4337 & 1.45560415594214 & -0.0219041559421411 \tabularnewline
65 & 1.4181 & 1.41403679330533 & 0.00406320669467242 \tabularnewline
66 & 1.3767 & 1.40490309482598 & -0.0282030948259773 \tabularnewline
67 & 1.346 & 1.38744979991914 & -0.0414497999191408 \tabularnewline
68 & 1.3413 & 1.34104046549648 & 0.000259534503515235 \tabularnewline
69 & 1.3089 & 1.32840315842366 & -0.0195031584236638 \tabularnewline
70 & 1.3452 & 1.29698911000868 & 0.0482108899913183 \tabularnewline
71 & 1.3442 & 1.33141472335003 & 0.0127852766499719 \tabularnewline
72 & 1.2811 & 1.34074378726331 & -0.0596437872633135 \tabularnewline
73 & 1.2779 & 1.26995750792083 & 0.00794249207916509 \tabularnewline
74 & 1.2974 & 1.2783153770649 & 0.0190846229350961 \tabularnewline
75 & 1.2867 & 1.2951742621776 & -0.00847426217760439 \tabularnewline
76 & 1.2977 & 1.28959618839047 & 0.00810381160953266 \tabularnewline
77 & 1.2537 & 1.27548223692452 & -0.0217822369245153 \tabularnewline
78 & 1.2092 & 1.23674145928404 & -0.0275414592840415 \tabularnewline
79 & 1.1766 & 1.21559027425443 & -0.0389902742544328 \tabularnewline
80 & 1.1203 & 1.17180506966389 & -0.0515050696638917 \tabularnewline
81 & 1.2005 & 1.10494352462742 & 0.0955564753725811 \tabularnewline
82 & 1.2295 & 1.18401076441411 & 0.0454892355858907 \tabularnewline
83 & 1.2307 & 1.21224980869281 & 0.0184501913071899 \tabularnewline
84 & 1.2276 & 1.22021894996319 & 0.007381050036811 \tabularnewline
85 & 1.2108 & 1.21860086864789 & -0.00780086864789165 \tabularnewline
86 & 1.2071 & 1.21493706241362 & -0.00783706241362081 \tabularnewline
87 & 1.2061 & 1.20525246900673 & 0.000847530993269618 \tabularnewline
88 & 1.2023 & 1.21039577942698 & -0.00809577942698203 \tabularnewline
89 & 1.2012 & 1.17910497214011 & 0.0220950278598899 \tabularnewline
90 & 1.2011 & 1.1819821406584 & 0.0191178593416041 \tabularnewline
91 & 1.2011 & 1.20634646919898 & -0.00524646919897576 \tabularnewline
92 & 1.2011 & 1.19746543423352 & 0.0036345657664838 \tabularnewline
93 & 1.2089 & 1.2005666851689 & 0.00833331483110133 \tabularnewline
94 & 1.2098 & 1.19926735886044 & 0.010532641139559 \tabularnewline
95 & 1.2052 & 1.19560638747591 & 0.00959361252409074 \tabularnewline
96 & 1.2091 & 1.19658598902075 & 0.0125140109792512 \tabularnewline
97 & 1.2288 & 1.20066031594174 & 0.0281396840582635 \tabularnewline
98 & 1.2298 & 1.23359469460078 & -0.00379469460077564 \tabularnewline
99 & 1.2266 & 1.23215148607908 & -0.00555148607907707 \tabularnewline
100 & 1.2199 & 1.23424638496919 & -0.0143463849691898 \tabularnewline
101 & 1.2418 & 1.20305915358204 & 0.0387408464179573 \tabularnewline
102 & 1.2322 & 1.22491582001688 & 0.00728417998312292 \tabularnewline
103 & 1.2366 & 1.23990905451788 & -0.00330905451787822 \tabularnewline
104 & 1.2338 & 1.23712586789426 & -0.0033258678942627 \tabularnewline
105 & 1.2338 & 1.23754824985942 & -0.00374824985942346 \tabularnewline
106 & 1.2316 & 1.22819574590885 & 0.00340425409114564 \tabularnewline
107 & 1.2316 & 1.22048250558102 & 0.011117494418978 \tabularnewline
108 & 1.2245 & 1.22572233867813 & -0.00122233867813315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279437&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]1.5494[/C][C]1.54044228098291[/C][C]0.0089577190170933[/C][/ROW]
[ROW][C]14[/C][C]1.558[/C][C]1.5580807384044[/C][C]-8.07384043970405e-05[/C][/ROW]
[ROW][C]15[/C][C]1.5691[/C][C]1.56894716663414[/C][C]0.000152833365864913[/C][/ROW]
[ROW][C]16[/C][C]1.5748[/C][C]1.57396284193338[/C][C]0.000837158066617549[/C][/ROW]
[ROW][C]17[/C][C]1.5564[/C][C]1.55500517966346[/C][C]0.00139482033654081[/C][/ROW]
[ROW][C]18[/C][C]1.5601[/C][C]1.55837150189523[/C][C]0.00172849810477005[/C][/ROW]
[ROW][C]19[/C][C]1.5687[/C][C]1.58273617307642[/C][C]-0.0140361730764174[/C][/ROW]
[ROW][C]20[/C][C]1.5775[/C][C]1.56635569220584[/C][C]0.0111443077941582[/C][/ROW]
[ROW][C]21[/C][C]1.5841[/C][C]1.5745764507498[/C][C]0.00952354925020171[/C][/ROW]
[ROW][C]22[/C][C]1.5898[/C][C]1.58347485229856[/C][C]0.0063251477014401[/C][/ROW]
[ROW][C]23[/C][C]1.5922[/C][C]1.58652983287187[/C][C]0.00567016712812807[/C][/ROW]
[ROW][C]24[/C][C]1.5969[/C][C]1.59656821189392[/C][C]0.000331788106082032[/C][/ROW]
[ROW][C]25[/C][C]1.6155[/C][C]1.60099704218704[/C][C]0.014502957812961[/C][/ROW]
[ROW][C]26[/C][C]1.6212[/C][C]1.62442938266906[/C][C]-0.00322938266906059[/C][/ROW]
[ROW][C]27[/C][C]1.6124[/C][C]1.63376949201363[/C][C]-0.0213694920136274[/C][/ROW]
[ROW][C]28[/C][C]1.6375[/C][C]1.61961320107409[/C][C]0.0178867989259066[/C][/ROW]
[ROW][C]29[/C][C]1.6506[/C][C]1.61749738564494[/C][C]0.0331026143550621[/C][/ROW]
[ROW][C]30[/C][C]1.6543[/C][C]1.65236163162154[/C][C]0.00193836837845662[/C][/ROW]
[ROW][C]31[/C][C]1.6567[/C][C]1.67801729515574[/C][C]-0.0213172951557417[/C][/ROW]
[ROW][C]32[/C][C]1.6383[/C][C]1.65918739835725[/C][C]-0.0208873983572542[/C][/ROW]
[ROW][C]33[/C][C]1.6475[/C][C]1.63878707083216[/C][C]0.00871292916784161[/C][/ROW]
[ROW][C]34[/C][C]1.6706[/C][C]1.64752166376978[/C][C]0.0230783362302243[/C][/ROW]
[ROW][C]35[/C][C]1.6485[/C][C]1.66737934226072[/C][C]-0.018879342260719[/C][/ROW]
[ROW][C]36[/C][C]1.6592[/C][C]1.65500992862641[/C][C]0.00419007137359095[/C][/ROW]
[ROW][C]37[/C][C]1.6203[/C][C]1.66484812274614[/C][C]-0.044548122746136[/C][/ROW]
[ROW][C]38[/C][C]1.608[/C][C]1.63105839634486[/C][C]-0.0230583963448636[/C][/ROW]
[ROW][C]39[/C][C]1.572[/C][C]1.61832333116182[/C][C]-0.0463233311618181[/C][/ROW]
[ROW][C]40[/C][C]1.5964[/C][C]1.58120112326776[/C][C]0.0151988767322355[/C][/ROW]
[ROW][C]41[/C][C]1.6247[/C][C]1.57442302172789[/C][C]0.0502769782721149[/C][/ROW]
[ROW][C]42[/C][C]1.6139[/C][C]1.61963956217395[/C][C]-0.00573956217394955[/C][/ROW]
[ROW][C]43[/C][C]1.6193[/C][C]1.6332245553493[/C][C]-0.0139245553493037[/C][/ROW]
[ROW][C]44[/C][C]1.6212[/C][C]1.61840084195308[/C][C]0.00279915804692443[/C][/ROW]
[ROW][C]45[/C][C]1.5942[/C][C]1.62029768557133[/C][C]-0.0260976855713282[/C][/ROW]
[ROW][C]46[/C][C]1.5194[/C][C]1.59507733827781[/C][C]-0.0756773382778078[/C][/ROW]
[ROW][C]47[/C][C]1.5162[/C][C]1.51381529512742[/C][C]0.00238470487258269[/C][/ROW]
[ROW][C]48[/C][C]1.5393[/C][C]1.51659491810214[/C][C]0.0227050818978569[/C][/ROW]
[ROW][C]49[/C][C]1.4935[/C][C]1.53380314055392[/C][C]-0.0403031405539223[/C][/ROW]
[ROW][C]50[/C][C]1.4904[/C][C]1.50031787213475[/C][C]-0.00991787213475503[/C][/ROW]
[ROW][C]51[/C][C]1.5083[/C][C]1.49282659102116[/C][C]0.0154734089788375[/C][/ROW]
[ROW][C]52[/C][C]1.5147[/C][C]1.51502618282323[/C][C]-0.000326182823232601[/C][/ROW]
[ROW][C]53[/C][C]1.5118[/C][C]1.49388027085088[/C][C]0.0179197291491211[/C][/ROW]
[ROW][C]54[/C][C]1.5148[/C][C]1.50044770042397[/C][C]0.0143522995760308[/C][/ROW]
[ROW][C]55[/C][C]1.5202[/C][C]1.52823227301646[/C][C]-0.00803227301646259[/C][/ROW]
[ROW][C]56[/C][C]1.5236[/C][C]1.51689630880016[/C][C]0.00670369119983949[/C][/ROW]
[ROW][C]57[/C][C]1.5148[/C][C]1.51681089599163[/C][C]-0.00201089599162896[/C][/ROW]
[ROW][C]58[/C][C]1.5138[/C][C]1.50732660368479[/C][C]0.00647339631521393[/C][/ROW]
[ROW][C]59[/C][C]1.5105[/C][C]1.50886697451685[/C][C]0.00163302548315003[/C][/ROW]
[ROW][C]60[/C][C]1.502[/C][C]1.51361317447447[/C][C]-0.0116131744744705[/C][/ROW]
[ROW][C]61[/C][C]1.4765[/C][C]1.49373665527207[/C][C]-0.01723665527207[/C][/ROW]
[ROW][C]62[/C][C]1.4671[/C][C]1.48445128636017[/C][C]-0.0173512863601666[/C][/ROW]
[ROW][C]63[/C][C]1.4482[/C][C]1.47249453272596[/C][C]-0.0242945327259634[/C][/ROW]
[ROW][C]64[/C][C]1.4337[/C][C]1.45560415594214[/C][C]-0.0219041559421411[/C][/ROW]
[ROW][C]65[/C][C]1.4181[/C][C]1.41403679330533[/C][C]0.00406320669467242[/C][/ROW]
[ROW][C]66[/C][C]1.3767[/C][C]1.40490309482598[/C][C]-0.0282030948259773[/C][/ROW]
[ROW][C]67[/C][C]1.346[/C][C]1.38744979991914[/C][C]-0.0414497999191408[/C][/ROW]
[ROW][C]68[/C][C]1.3413[/C][C]1.34104046549648[/C][C]0.000259534503515235[/C][/ROW]
[ROW][C]69[/C][C]1.3089[/C][C]1.32840315842366[/C][C]-0.0195031584236638[/C][/ROW]
[ROW][C]70[/C][C]1.3452[/C][C]1.29698911000868[/C][C]0.0482108899913183[/C][/ROW]
[ROW][C]71[/C][C]1.3442[/C][C]1.33141472335003[/C][C]0.0127852766499719[/C][/ROW]
[ROW][C]72[/C][C]1.2811[/C][C]1.34074378726331[/C][C]-0.0596437872633135[/C][/ROW]
[ROW][C]73[/C][C]1.2779[/C][C]1.26995750792083[/C][C]0.00794249207916509[/C][/ROW]
[ROW][C]74[/C][C]1.2974[/C][C]1.2783153770649[/C][C]0.0190846229350961[/C][/ROW]
[ROW][C]75[/C][C]1.2867[/C][C]1.2951742621776[/C][C]-0.00847426217760439[/C][/ROW]
[ROW][C]76[/C][C]1.2977[/C][C]1.28959618839047[/C][C]0.00810381160953266[/C][/ROW]
[ROW][C]77[/C][C]1.2537[/C][C]1.27548223692452[/C][C]-0.0217822369245153[/C][/ROW]
[ROW][C]78[/C][C]1.2092[/C][C]1.23674145928404[/C][C]-0.0275414592840415[/C][/ROW]
[ROW][C]79[/C][C]1.1766[/C][C]1.21559027425443[/C][C]-0.0389902742544328[/C][/ROW]
[ROW][C]80[/C][C]1.1203[/C][C]1.17180506966389[/C][C]-0.0515050696638917[/C][/ROW]
[ROW][C]81[/C][C]1.2005[/C][C]1.10494352462742[/C][C]0.0955564753725811[/C][/ROW]
[ROW][C]82[/C][C]1.2295[/C][C]1.18401076441411[/C][C]0.0454892355858907[/C][/ROW]
[ROW][C]83[/C][C]1.2307[/C][C]1.21224980869281[/C][C]0.0184501913071899[/C][/ROW]
[ROW][C]84[/C][C]1.2276[/C][C]1.22021894996319[/C][C]0.007381050036811[/C][/ROW]
[ROW][C]85[/C][C]1.2108[/C][C]1.21860086864789[/C][C]-0.00780086864789165[/C][/ROW]
[ROW][C]86[/C][C]1.2071[/C][C]1.21493706241362[/C][C]-0.00783706241362081[/C][/ROW]
[ROW][C]87[/C][C]1.2061[/C][C]1.20525246900673[/C][C]0.000847530993269618[/C][/ROW]
[ROW][C]88[/C][C]1.2023[/C][C]1.21039577942698[/C][C]-0.00809577942698203[/C][/ROW]
[ROW][C]89[/C][C]1.2012[/C][C]1.17910497214011[/C][C]0.0220950278598899[/C][/ROW]
[ROW][C]90[/C][C]1.2011[/C][C]1.1819821406584[/C][C]0.0191178593416041[/C][/ROW]
[ROW][C]91[/C][C]1.2011[/C][C]1.20634646919898[/C][C]-0.00524646919897576[/C][/ROW]
[ROW][C]92[/C][C]1.2011[/C][C]1.19746543423352[/C][C]0.0036345657664838[/C][/ROW]
[ROW][C]93[/C][C]1.2089[/C][C]1.2005666851689[/C][C]0.00833331483110133[/C][/ROW]
[ROW][C]94[/C][C]1.2098[/C][C]1.19926735886044[/C][C]0.010532641139559[/C][/ROW]
[ROW][C]95[/C][C]1.2052[/C][C]1.19560638747591[/C][C]0.00959361252409074[/C][/ROW]
[ROW][C]96[/C][C]1.2091[/C][C]1.19658598902075[/C][C]0.0125140109792512[/C][/ROW]
[ROW][C]97[/C][C]1.2288[/C][C]1.20066031594174[/C][C]0.0281396840582635[/C][/ROW]
[ROW][C]98[/C][C]1.2298[/C][C]1.23359469460078[/C][C]-0.00379469460077564[/C][/ROW]
[ROW][C]99[/C][C]1.2266[/C][C]1.23215148607908[/C][C]-0.00555148607907707[/C][/ROW]
[ROW][C]100[/C][C]1.2199[/C][C]1.23424638496919[/C][C]-0.0143463849691898[/C][/ROW]
[ROW][C]101[/C][C]1.2418[/C][C]1.20305915358204[/C][C]0.0387408464179573[/C][/ROW]
[ROW][C]102[/C][C]1.2322[/C][C]1.22491582001688[/C][C]0.00728417998312292[/C][/ROW]
[ROW][C]103[/C][C]1.2366[/C][C]1.23990905451788[/C][C]-0.00330905451787822[/C][/ROW]
[ROW][C]104[/C][C]1.2338[/C][C]1.23712586789426[/C][C]-0.0033258678942627[/C][/ROW]
[ROW][C]105[/C][C]1.2338[/C][C]1.23754824985942[/C][C]-0.00374824985942346[/C][/ROW]
[ROW][C]106[/C][C]1.2316[/C][C]1.22819574590885[/C][C]0.00340425409114564[/C][/ROW]
[ROW][C]107[/C][C]1.2316[/C][C]1.22048250558102[/C][C]0.011117494418978[/C][/ROW]
[ROW][C]108[/C][C]1.2245[/C][C]1.22572233867813[/C][C]-0.00122233867813315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279437&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279437&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
131.54941.540442280982910.0089577190170933
141.5581.5580807384044-8.07384043970405e-05
151.56911.568947166634140.000152833365864913
161.57481.573962841933380.000837158066617549
171.55641.555005179663460.00139482033654081
181.56011.558371501895230.00172849810477005
191.56871.58273617307642-0.0140361730764174
201.57751.566355692205840.0111443077941582
211.58411.57457645074980.00952354925020171
221.58981.583474852298560.0063251477014401
231.59221.586529832871870.00567016712812807
241.59691.596568211893920.000331788106082032
251.61551.600997042187040.014502957812961
261.62121.62442938266906-0.00322938266906059
271.61241.63376949201363-0.0213694920136274
281.63751.619613201074090.0178867989259066
291.65061.617497385644940.0331026143550621
301.65431.652361631621540.00193836837845662
311.65671.67801729515574-0.0213172951557417
321.63831.65918739835725-0.0208873983572542
331.64751.638787070832160.00871292916784161
341.67061.647521663769780.0230783362302243
351.64851.66737934226072-0.018879342260719
361.65921.655009928626410.00419007137359095
371.62031.66484812274614-0.044548122746136
381.6081.63105839634486-0.0230583963448636
391.5721.61832333116182-0.0463233311618181
401.59641.581201123267760.0151988767322355
411.62471.574423021727890.0502769782721149
421.61391.61963956217395-0.00573956217394955
431.61931.6332245553493-0.0139245553493037
441.62121.618400841953080.00279915804692443
451.59421.62029768557133-0.0260976855713282
461.51941.59507733827781-0.0756773382778078
471.51621.513815295127420.00238470487258269
481.53931.516594918102140.0227050818978569
491.49351.53380314055392-0.0403031405539223
501.49041.50031787213475-0.00991787213475503
511.50831.492826591021160.0154734089788375
521.51471.51502618282323-0.000326182823232601
531.51181.493880270850880.0179197291491211
541.51481.500447700423970.0143522995760308
551.52021.52823227301646-0.00803227301646259
561.52361.516896308800160.00670369119983949
571.51481.51681089599163-0.00201089599162896
581.51381.507326603684790.00647339631521393
591.51051.508866974516850.00163302548315003
601.5021.51361317447447-0.0116131744744705
611.47651.49373665527207-0.01723665527207
621.46711.48445128636017-0.0173512863601666
631.44821.47249453272596-0.0242945327259634
641.43371.45560415594214-0.0219041559421411
651.41811.414036793305330.00406320669467242
661.37671.40490309482598-0.0282030948259773
671.3461.38744979991914-0.0414497999191408
681.34131.341040465496480.000259534503515235
691.30891.32840315842366-0.0195031584236638
701.34521.296989110008680.0482108899913183
711.34421.331414723350030.0127852766499719
721.28111.34074378726331-0.0596437872633135
731.27791.269957507920830.00794249207916509
741.29741.27831537706490.0190846229350961
751.28671.2951742621776-0.00847426217760439
761.29771.289596188390470.00810381160953266
771.25371.27548223692452-0.0217822369245153
781.20921.23674145928404-0.0275414592840415
791.17661.21559027425443-0.0389902742544328
801.12031.17180506966389-0.0515050696638917
811.20051.104943524627420.0955564753725811
821.22951.184010764414110.0454892355858907
831.23071.212249808692810.0184501913071899
841.22761.220218949963190.007381050036811
851.21081.21860086864789-0.00780086864789165
861.20711.21493706241362-0.00783706241362081
871.20611.205252469006730.000847530993269618
881.20231.21039577942698-0.00809577942698203
891.20121.179104972140110.0220950278598899
901.20111.18198214065840.0191178593416041
911.20111.20634646919898-0.00524646919897576
921.20111.197465434233520.0036345657664838
931.20891.20056668516890.00833331483110133
941.20981.199267358860440.010532641139559
951.20521.195606387475910.00959361252409074
961.20911.196585989020750.0125140109792512
971.22881.200660315941740.0281396840582635
981.22981.23359469460078-0.00379469460077564
991.22661.23215148607908-0.00555148607907707
1001.21991.23424638496919-0.0143463849691898
1011.24181.203059153582040.0387408464179573
1021.23221.224915820016880.00728417998312292
1031.23661.23990905451788-0.00330905451787822
1041.23381.23712586789426-0.0033258678942627
1051.23381.23754824985942-0.00374824985942346
1061.23161.228195745908850.00340425409114564
1071.23161.220482505581020.011117494418978
1081.22451.22572233867813-0.00122233867813315







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091.220590063104711.173744125021191.26743600118824
1101.226054165063041.161253822526041.29085450760003
1111.229076830782171.149260156936191.30889350462816
1121.236878457206811.143518509726131.33023840468749
1131.225175043456741.119147187267471.33120289964601
1141.209295786863791.091165063962331.32742650976525
1151.216843020518881.086990601231111.34669543980664
1161.217334826281741.076023317978351.35864633458514
1171.221143644714931.068554558501631.37373273092822
1181.216342072267351.052598986495581.38008515803913
1191.206536905332991.031720613515421.38135319715057
1201.200509711492071.014668571650371.38635085133377

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1.22059006310471 & 1.17374412502119 & 1.26743600118824 \tabularnewline
110 & 1.22605416506304 & 1.16125382252604 & 1.29085450760003 \tabularnewline
111 & 1.22907683078217 & 1.14926015693619 & 1.30889350462816 \tabularnewline
112 & 1.23687845720681 & 1.14351850972613 & 1.33023840468749 \tabularnewline
113 & 1.22517504345674 & 1.11914718726747 & 1.33120289964601 \tabularnewline
114 & 1.20929578686379 & 1.09116506396233 & 1.32742650976525 \tabularnewline
115 & 1.21684302051888 & 1.08699060123111 & 1.34669543980664 \tabularnewline
116 & 1.21733482628174 & 1.07602331797835 & 1.35864633458514 \tabularnewline
117 & 1.22114364471493 & 1.06855455850163 & 1.37373273092822 \tabularnewline
118 & 1.21634207226735 & 1.05259898649558 & 1.38008515803913 \tabularnewline
119 & 1.20653690533299 & 1.03172061351542 & 1.38135319715057 \tabularnewline
120 & 1.20050971149207 & 1.01466857165037 & 1.38635085133377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279437&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]109[/C][C]1.22059006310471[/C][C]1.17374412502119[/C][C]1.26743600118824[/C][/ROW]
[ROW][C]110[/C][C]1.22605416506304[/C][C]1.16125382252604[/C][C]1.29085450760003[/C][/ROW]
[ROW][C]111[/C][C]1.22907683078217[/C][C]1.14926015693619[/C][C]1.30889350462816[/C][/ROW]
[ROW][C]112[/C][C]1.23687845720681[/C][C]1.14351850972613[/C][C]1.33023840468749[/C][/ROW]
[ROW][C]113[/C][C]1.22517504345674[/C][C]1.11914718726747[/C][C]1.33120289964601[/C][/ROW]
[ROW][C]114[/C][C]1.20929578686379[/C][C]1.09116506396233[/C][C]1.32742650976525[/C][/ROW]
[ROW][C]115[/C][C]1.21684302051888[/C][C]1.08699060123111[/C][C]1.34669543980664[/C][/ROW]
[ROW][C]116[/C][C]1.21733482628174[/C][C]1.07602331797835[/C][C]1.35864633458514[/C][/ROW]
[ROW][C]117[/C][C]1.22114364471493[/C][C]1.06855455850163[/C][C]1.37373273092822[/C][/ROW]
[ROW][C]118[/C][C]1.21634207226735[/C][C]1.05259898649558[/C][C]1.38008515803913[/C][/ROW]
[ROW][C]119[/C][C]1.20653690533299[/C][C]1.03172061351542[/C][C]1.38135319715057[/C][/ROW]
[ROW][C]120[/C][C]1.20050971149207[/C][C]1.01466857165037[/C][C]1.38635085133377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279437&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279437&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
1091.220590063104711.173744125021191.26743600118824
1101.226054165063041.161253822526041.29085450760003
1111.229076830782171.149260156936191.30889350462816
1121.236878457206811.143518509726131.33023840468749
1131.225175043456741.119147187267471.33120289964601
1141.209295786863791.091165063962331.32742650976525
1151.216843020518881.086990601231111.34669543980664
1161.217334826281741.076023317978351.35864633458514
1171.221143644714931.068554558501631.37373273092822
1181.216342072267351.052598986495581.38008515803913
1191.206536905332991.031720613515421.38135319715057
1201.200509711492071.014668571650371.38635085133377



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