Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 05 Jun 2010 15:12:22 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/05/t1275750768jqlj3hiqgd3j75s.htm/, Retrieved Fri, 03 May 2024 09:06:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77565, Retrieved Fri, 03 May 2024 09:06:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Wisselkoersen] [2010-06-05 15:12:22] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1,4272
1,4614
1,4914
1,4816
1,4562
1,4268
1,4088
1,4016
1,365
1,319
1,305
1,2785
1,3239
1,3449
1,2732
1,3322
1,4369
1,4975
1,577
1,5553
1,5557
1,575
1,5527
1,4748
1,4718
1,457
1,4684
1,4227
1,3896
1,3622
1,3716
1,3419
1,3511
1,3516
1,3242
1,3074
1,2999
1,3213
1,2881
1,2611
1,2727
1,2811
1,2684
1,265
1,277
1,2271
1,202
1,1938
1,2103
1,1856
1,1786
1,2015
1,2256
1,2292
1,2037
1,2165
1,2694
1,2938
1,3201
1,3014
1,3119
1,3408
1,2991
1,249
1,2218
1,2176
1,2266
1,2138
1,2007
1,1985
1,2262
1,2646




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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77565&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77565&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77565&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 Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.356147313163450
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.356147313163450 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77565&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.356147313163450[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77565&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77565&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
alpha1
beta0.356147313163450
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31.49141.4956-0.00419999999999998
41.48161.52410418128471-0.0425041812847136
51.45621.49916643132195-0.0429664313219507
61.42681.45846405225042-0.0316640522504159
71.40881.41778698511756-0.00898698511756324
81.40161.396586294514500.00501370548549662
91.3651.39117191225216-0.0261719122521558
101.3191.3452508560232-0.0262508560232009
111.3051.289901684182300.0150983158177027
121.27851.28127890879407-0.00277890879406528
131.32391.253789207893530.0701107921064674
141.34491.324158978126010.0207410218739876
151.27321.35254583733870-0.0793458373386973
161.33221.252587030559820.0796129694401837
171.43691.339940975718900.0969590242810985
181.49751.479172671703560.0183273282964356
191.5771.546299900433800.0307000995661955
201.55531.63673365840816-0.0814336584081554
211.55571.58603127976502-0.0303312797650204
221.5751.5756288759719-0.000628875971899756
231.55271.59470490348419-0.0420049034841945
241.47481.55744496996861-0.0826449699686085
251.47181.450111185967810.0216888140321851
261.4571.454835598811080.00216440118892081
271.46841.440806444479120.0275935555208786
281.42271.46203381513851-0.0393338151385083
291.38961.40232518256046-0.0127251825604611
301.36221.36469314298204-0.00249314298203829
311.37161.336405216807650.0351947831923467
321.34191.35833974427898-0.0164397442789774
331.35111.322784773524930.0283152264750743
341.35161.342069165355640.0095308346443621
351.32421.34596354650643-0.0217635465064323
361.30741.31081251789326-0.00341251789325892
371.29991.292797158814450.0071028411855476
381.32131.287826816618510.0334731833814879
391.28811.32114820094286-0.0330482009428561
401.26111.27617817297217-0.0150781729721723
411.27271.243808122180720.0288918778192804
421.28111.265697886838300.0154021131616973
431.26841.27958330805788-0.0111833080578805
441.2651.262900402940790.00209959705921259
451.2771.260248168792150.0167518312078483
461.22711.27821428846739-0.0511142884673943
471.2021.21011007196547-0.00811007196547076
481.19381.182121691625410.0116783083745942
491.21031.178080889775310.0322191102246880
501.18561.20605563931435-0.0204556393143516
511.17861.174070418333500.00452958166649542
521.20151.168683616673780.0328163833262185
531.22561.203271083423160.0223289165768441
541.22921.23532346706785-0.00612346706784983
551.20371.23674261072439-0.0330426107243904
561.21651.199474573694990.0170254263050071
571.26941.218338133528980.0510618664710167
581.29381.289423680077750.00437631992225307
591.32011.31538229465960.00471770534039906
601.30141.34336249274088-0.041962492740881
611.31191.309717663697580.00218233630242470
621.34081.320994896908100.0198051030918969
631.29911.35694843116121-0.0578484311612073
641.2491.29464586783242-0.0456458678324223
651.22181.22828921464689-0.00648921464689156
661.21761.198778098285860.01882190171414
671.22661.201281468009980.0253185319900224
681.21381.21929859515147-0.00549859515146678
691.20071.20454028526210-0.00384028526209823
701.19851.190072577984220.00842742201577895
711.22621.190873981692030.0353260183079651
721.26461.231155248197180.0334447518028205

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.4914 & 1.4956 & -0.00419999999999998 \tabularnewline
4 & 1.4816 & 1.52410418128471 & -0.0425041812847136 \tabularnewline
5 & 1.4562 & 1.49916643132195 & -0.0429664313219507 \tabularnewline
6 & 1.4268 & 1.45846405225042 & -0.0316640522504159 \tabularnewline
7 & 1.4088 & 1.41778698511756 & -0.00898698511756324 \tabularnewline
8 & 1.4016 & 1.39658629451450 & 0.00501370548549662 \tabularnewline
9 & 1.365 & 1.39117191225216 & -0.0261719122521558 \tabularnewline
10 & 1.319 & 1.3452508560232 & -0.0262508560232009 \tabularnewline
11 & 1.305 & 1.28990168418230 & 0.0150983158177027 \tabularnewline
12 & 1.2785 & 1.28127890879407 & -0.00277890879406528 \tabularnewline
13 & 1.3239 & 1.25378920789353 & 0.0701107921064674 \tabularnewline
14 & 1.3449 & 1.32415897812601 & 0.0207410218739876 \tabularnewline
15 & 1.2732 & 1.35254583733870 & -0.0793458373386973 \tabularnewline
16 & 1.3322 & 1.25258703055982 & 0.0796129694401837 \tabularnewline
17 & 1.4369 & 1.33994097571890 & 0.0969590242810985 \tabularnewline
18 & 1.4975 & 1.47917267170356 & 0.0183273282964356 \tabularnewline
19 & 1.577 & 1.54629990043380 & 0.0307000995661955 \tabularnewline
20 & 1.5553 & 1.63673365840816 & -0.0814336584081554 \tabularnewline
21 & 1.5557 & 1.58603127976502 & -0.0303312797650204 \tabularnewline
22 & 1.575 & 1.5756288759719 & -0.000628875971899756 \tabularnewline
23 & 1.5527 & 1.59470490348419 & -0.0420049034841945 \tabularnewline
24 & 1.4748 & 1.55744496996861 & -0.0826449699686085 \tabularnewline
25 & 1.4718 & 1.45011118596781 & 0.0216888140321851 \tabularnewline
26 & 1.457 & 1.45483559881108 & 0.00216440118892081 \tabularnewline
27 & 1.4684 & 1.44080644447912 & 0.0275935555208786 \tabularnewline
28 & 1.4227 & 1.46203381513851 & -0.0393338151385083 \tabularnewline
29 & 1.3896 & 1.40232518256046 & -0.0127251825604611 \tabularnewline
30 & 1.3622 & 1.36469314298204 & -0.00249314298203829 \tabularnewline
31 & 1.3716 & 1.33640521680765 & 0.0351947831923467 \tabularnewline
32 & 1.3419 & 1.35833974427898 & -0.0164397442789774 \tabularnewline
33 & 1.3511 & 1.32278477352493 & 0.0283152264750743 \tabularnewline
34 & 1.3516 & 1.34206916535564 & 0.0095308346443621 \tabularnewline
35 & 1.3242 & 1.34596354650643 & -0.0217635465064323 \tabularnewline
36 & 1.3074 & 1.31081251789326 & -0.00341251789325892 \tabularnewline
37 & 1.2999 & 1.29279715881445 & 0.0071028411855476 \tabularnewline
38 & 1.3213 & 1.28782681661851 & 0.0334731833814879 \tabularnewline
39 & 1.2881 & 1.32114820094286 & -0.0330482009428561 \tabularnewline
40 & 1.2611 & 1.27617817297217 & -0.0150781729721723 \tabularnewline
41 & 1.2727 & 1.24380812218072 & 0.0288918778192804 \tabularnewline
42 & 1.2811 & 1.26569788683830 & 0.0154021131616973 \tabularnewline
43 & 1.2684 & 1.27958330805788 & -0.0111833080578805 \tabularnewline
44 & 1.265 & 1.26290040294079 & 0.00209959705921259 \tabularnewline
45 & 1.277 & 1.26024816879215 & 0.0167518312078483 \tabularnewline
46 & 1.2271 & 1.27821428846739 & -0.0511142884673943 \tabularnewline
47 & 1.202 & 1.21011007196547 & -0.00811007196547076 \tabularnewline
48 & 1.1938 & 1.18212169162541 & 0.0116783083745942 \tabularnewline
49 & 1.2103 & 1.17808088977531 & 0.0322191102246880 \tabularnewline
50 & 1.1856 & 1.20605563931435 & -0.0204556393143516 \tabularnewline
51 & 1.1786 & 1.17407041833350 & 0.00452958166649542 \tabularnewline
52 & 1.2015 & 1.16868361667378 & 0.0328163833262185 \tabularnewline
53 & 1.2256 & 1.20327108342316 & 0.0223289165768441 \tabularnewline
54 & 1.2292 & 1.23532346706785 & -0.00612346706784983 \tabularnewline
55 & 1.2037 & 1.23674261072439 & -0.0330426107243904 \tabularnewline
56 & 1.2165 & 1.19947457369499 & 0.0170254263050071 \tabularnewline
57 & 1.2694 & 1.21833813352898 & 0.0510618664710167 \tabularnewline
58 & 1.2938 & 1.28942368007775 & 0.00437631992225307 \tabularnewline
59 & 1.3201 & 1.3153822946596 & 0.00471770534039906 \tabularnewline
60 & 1.3014 & 1.34336249274088 & -0.041962492740881 \tabularnewline
61 & 1.3119 & 1.30971766369758 & 0.00218233630242470 \tabularnewline
62 & 1.3408 & 1.32099489690810 & 0.0198051030918969 \tabularnewline
63 & 1.2991 & 1.35694843116121 & -0.0578484311612073 \tabularnewline
64 & 1.249 & 1.29464586783242 & -0.0456458678324223 \tabularnewline
65 & 1.2218 & 1.22828921464689 & -0.00648921464689156 \tabularnewline
66 & 1.2176 & 1.19877809828586 & 0.01882190171414 \tabularnewline
67 & 1.2266 & 1.20128146800998 & 0.0253185319900224 \tabularnewline
68 & 1.2138 & 1.21929859515147 & -0.00549859515146678 \tabularnewline
69 & 1.2007 & 1.20454028526210 & -0.00384028526209823 \tabularnewline
70 & 1.1985 & 1.19007257798422 & 0.00842742201577895 \tabularnewline
71 & 1.2262 & 1.19087398169203 & 0.0353260183079651 \tabularnewline
72 & 1.2646 & 1.23115524819718 & 0.0334447518028205 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77565&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]3[/C][C]1.4914[/C][C]1.4956[/C][C]-0.00419999999999998[/C][/ROW]
[ROW][C]4[/C][C]1.4816[/C][C]1.52410418128471[/C][C]-0.0425041812847136[/C][/ROW]
[ROW][C]5[/C][C]1.4562[/C][C]1.49916643132195[/C][C]-0.0429664313219507[/C][/ROW]
[ROW][C]6[/C][C]1.4268[/C][C]1.45846405225042[/C][C]-0.0316640522504159[/C][/ROW]
[ROW][C]7[/C][C]1.4088[/C][C]1.41778698511756[/C][C]-0.00898698511756324[/C][/ROW]
[ROW][C]8[/C][C]1.4016[/C][C]1.39658629451450[/C][C]0.00501370548549662[/C][/ROW]
[ROW][C]9[/C][C]1.365[/C][C]1.39117191225216[/C][C]-0.0261719122521558[/C][/ROW]
[ROW][C]10[/C][C]1.319[/C][C]1.3452508560232[/C][C]-0.0262508560232009[/C][/ROW]
[ROW][C]11[/C][C]1.305[/C][C]1.28990168418230[/C][C]0.0150983158177027[/C][/ROW]
[ROW][C]12[/C][C]1.2785[/C][C]1.28127890879407[/C][C]-0.00277890879406528[/C][/ROW]
[ROW][C]13[/C][C]1.3239[/C][C]1.25378920789353[/C][C]0.0701107921064674[/C][/ROW]
[ROW][C]14[/C][C]1.3449[/C][C]1.32415897812601[/C][C]0.0207410218739876[/C][/ROW]
[ROW][C]15[/C][C]1.2732[/C][C]1.35254583733870[/C][C]-0.0793458373386973[/C][/ROW]
[ROW][C]16[/C][C]1.3322[/C][C]1.25258703055982[/C][C]0.0796129694401837[/C][/ROW]
[ROW][C]17[/C][C]1.4369[/C][C]1.33994097571890[/C][C]0.0969590242810985[/C][/ROW]
[ROW][C]18[/C][C]1.4975[/C][C]1.47917267170356[/C][C]0.0183273282964356[/C][/ROW]
[ROW][C]19[/C][C]1.577[/C][C]1.54629990043380[/C][C]0.0307000995661955[/C][/ROW]
[ROW][C]20[/C][C]1.5553[/C][C]1.63673365840816[/C][C]-0.0814336584081554[/C][/ROW]
[ROW][C]21[/C][C]1.5557[/C][C]1.58603127976502[/C][C]-0.0303312797650204[/C][/ROW]
[ROW][C]22[/C][C]1.575[/C][C]1.5756288759719[/C][C]-0.000628875971899756[/C][/ROW]
[ROW][C]23[/C][C]1.5527[/C][C]1.59470490348419[/C][C]-0.0420049034841945[/C][/ROW]
[ROW][C]24[/C][C]1.4748[/C][C]1.55744496996861[/C][C]-0.0826449699686085[/C][/ROW]
[ROW][C]25[/C][C]1.4718[/C][C]1.45011118596781[/C][C]0.0216888140321851[/C][/ROW]
[ROW][C]26[/C][C]1.457[/C][C]1.45483559881108[/C][C]0.00216440118892081[/C][/ROW]
[ROW][C]27[/C][C]1.4684[/C][C]1.44080644447912[/C][C]0.0275935555208786[/C][/ROW]
[ROW][C]28[/C][C]1.4227[/C][C]1.46203381513851[/C][C]-0.0393338151385083[/C][/ROW]
[ROW][C]29[/C][C]1.3896[/C][C]1.40232518256046[/C][C]-0.0127251825604611[/C][/ROW]
[ROW][C]30[/C][C]1.3622[/C][C]1.36469314298204[/C][C]-0.00249314298203829[/C][/ROW]
[ROW][C]31[/C][C]1.3716[/C][C]1.33640521680765[/C][C]0.0351947831923467[/C][/ROW]
[ROW][C]32[/C][C]1.3419[/C][C]1.35833974427898[/C][C]-0.0164397442789774[/C][/ROW]
[ROW][C]33[/C][C]1.3511[/C][C]1.32278477352493[/C][C]0.0283152264750743[/C][/ROW]
[ROW][C]34[/C][C]1.3516[/C][C]1.34206916535564[/C][C]0.0095308346443621[/C][/ROW]
[ROW][C]35[/C][C]1.3242[/C][C]1.34596354650643[/C][C]-0.0217635465064323[/C][/ROW]
[ROW][C]36[/C][C]1.3074[/C][C]1.31081251789326[/C][C]-0.00341251789325892[/C][/ROW]
[ROW][C]37[/C][C]1.2999[/C][C]1.29279715881445[/C][C]0.0071028411855476[/C][/ROW]
[ROW][C]38[/C][C]1.3213[/C][C]1.28782681661851[/C][C]0.0334731833814879[/C][/ROW]
[ROW][C]39[/C][C]1.2881[/C][C]1.32114820094286[/C][C]-0.0330482009428561[/C][/ROW]
[ROW][C]40[/C][C]1.2611[/C][C]1.27617817297217[/C][C]-0.0150781729721723[/C][/ROW]
[ROW][C]41[/C][C]1.2727[/C][C]1.24380812218072[/C][C]0.0288918778192804[/C][/ROW]
[ROW][C]42[/C][C]1.2811[/C][C]1.26569788683830[/C][C]0.0154021131616973[/C][/ROW]
[ROW][C]43[/C][C]1.2684[/C][C]1.27958330805788[/C][C]-0.0111833080578805[/C][/ROW]
[ROW][C]44[/C][C]1.265[/C][C]1.26290040294079[/C][C]0.00209959705921259[/C][/ROW]
[ROW][C]45[/C][C]1.277[/C][C]1.26024816879215[/C][C]0.0167518312078483[/C][/ROW]
[ROW][C]46[/C][C]1.2271[/C][C]1.27821428846739[/C][C]-0.0511142884673943[/C][/ROW]
[ROW][C]47[/C][C]1.202[/C][C]1.21011007196547[/C][C]-0.00811007196547076[/C][/ROW]
[ROW][C]48[/C][C]1.1938[/C][C]1.18212169162541[/C][C]0.0116783083745942[/C][/ROW]
[ROW][C]49[/C][C]1.2103[/C][C]1.17808088977531[/C][C]0.0322191102246880[/C][/ROW]
[ROW][C]50[/C][C]1.1856[/C][C]1.20605563931435[/C][C]-0.0204556393143516[/C][/ROW]
[ROW][C]51[/C][C]1.1786[/C][C]1.17407041833350[/C][C]0.00452958166649542[/C][/ROW]
[ROW][C]52[/C][C]1.2015[/C][C]1.16868361667378[/C][C]0.0328163833262185[/C][/ROW]
[ROW][C]53[/C][C]1.2256[/C][C]1.20327108342316[/C][C]0.0223289165768441[/C][/ROW]
[ROW][C]54[/C][C]1.2292[/C][C]1.23532346706785[/C][C]-0.00612346706784983[/C][/ROW]
[ROW][C]55[/C][C]1.2037[/C][C]1.23674261072439[/C][C]-0.0330426107243904[/C][/ROW]
[ROW][C]56[/C][C]1.2165[/C][C]1.19947457369499[/C][C]0.0170254263050071[/C][/ROW]
[ROW][C]57[/C][C]1.2694[/C][C]1.21833813352898[/C][C]0.0510618664710167[/C][/ROW]
[ROW][C]58[/C][C]1.2938[/C][C]1.28942368007775[/C][C]0.00437631992225307[/C][/ROW]
[ROW][C]59[/C][C]1.3201[/C][C]1.3153822946596[/C][C]0.00471770534039906[/C][/ROW]
[ROW][C]60[/C][C]1.3014[/C][C]1.34336249274088[/C][C]-0.041962492740881[/C][/ROW]
[ROW][C]61[/C][C]1.3119[/C][C]1.30971766369758[/C][C]0.00218233630242470[/C][/ROW]
[ROW][C]62[/C][C]1.3408[/C][C]1.32099489690810[/C][C]0.0198051030918969[/C][/ROW]
[ROW][C]63[/C][C]1.2991[/C][C]1.35694843116121[/C][C]-0.0578484311612073[/C][/ROW]
[ROW][C]64[/C][C]1.249[/C][C]1.29464586783242[/C][C]-0.0456458678324223[/C][/ROW]
[ROW][C]65[/C][C]1.2218[/C][C]1.22828921464689[/C][C]-0.00648921464689156[/C][/ROW]
[ROW][C]66[/C][C]1.2176[/C][C]1.19877809828586[/C][C]0.01882190171414[/C][/ROW]
[ROW][C]67[/C][C]1.2266[/C][C]1.20128146800998[/C][C]0.0253185319900224[/C][/ROW]
[ROW][C]68[/C][C]1.2138[/C][C]1.21929859515147[/C][C]-0.00549859515146678[/C][/ROW]
[ROW][C]69[/C][C]1.2007[/C][C]1.20454028526210[/C][C]-0.00384028526209823[/C][/ROW]
[ROW][C]70[/C][C]1.1985[/C][C]1.19007257798422[/C][C]0.00842742201577895[/C][/ROW]
[ROW][C]71[/C][C]1.2262[/C][C]1.19087398169203[/C][C]0.0353260183079651[/C][/ROW]
[ROW][C]72[/C][C]1.2646[/C][C]1.23115524819718[/C][C]0.0334447518028205[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77565&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77565&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
31.49141.4956-0.00419999999999998
41.48161.52410418128471-0.0425041812847136
51.45621.49916643132195-0.0429664313219507
61.42681.45846405225042-0.0316640522504159
71.40881.41778698511756-0.00898698511756324
81.40161.396586294514500.00501370548549662
91.3651.39117191225216-0.0261719122521558
101.3191.3452508560232-0.0262508560232009
111.3051.289901684182300.0150983158177027
121.27851.28127890879407-0.00277890879406528
131.32391.253789207893530.0701107921064674
141.34491.324158978126010.0207410218739876
151.27321.35254583733870-0.0793458373386973
161.33221.252587030559820.0796129694401837
171.43691.339940975718900.0969590242810985
181.49751.479172671703560.0183273282964356
191.5771.546299900433800.0307000995661955
201.55531.63673365840816-0.0814336584081554
211.55571.58603127976502-0.0303312797650204
221.5751.5756288759719-0.000628875971899756
231.55271.59470490348419-0.0420049034841945
241.47481.55744496996861-0.0826449699686085
251.47181.450111185967810.0216888140321851
261.4571.454835598811080.00216440118892081
271.46841.440806444479120.0275935555208786
281.42271.46203381513851-0.0393338151385083
291.38961.40232518256046-0.0127251825604611
301.36221.36469314298204-0.00249314298203829
311.37161.336405216807650.0351947831923467
321.34191.35833974427898-0.0164397442789774
331.35111.322784773524930.0283152264750743
341.35161.342069165355640.0095308346443621
351.32421.34596354650643-0.0217635465064323
361.30741.31081251789326-0.00341251789325892
371.29991.292797158814450.0071028411855476
381.32131.287826816618510.0334731833814879
391.28811.32114820094286-0.0330482009428561
401.26111.27617817297217-0.0150781729721723
411.27271.243808122180720.0288918778192804
421.28111.265697886838300.0154021131616973
431.26841.27958330805788-0.0111833080578805
441.2651.262900402940790.00209959705921259
451.2771.260248168792150.0167518312078483
461.22711.27821428846739-0.0511142884673943
471.2021.21011007196547-0.00811007196547076
481.19381.182121691625410.0116783083745942
491.21031.178080889775310.0322191102246880
501.18561.20605563931435-0.0204556393143516
511.17861.174070418333500.00452958166649542
521.20151.168683616673780.0328163833262185
531.22561.203271083423160.0223289165768441
541.22921.23532346706785-0.00612346706784983
551.20371.23674261072439-0.0330426107243904
561.21651.199474573694990.0170254263050071
571.26941.218338133528980.0510618664710167
581.29381.289423680077750.00437631992225307
591.32011.31538229465960.00471770534039906
601.30141.34336249274088-0.041962492740881
611.31191.309717663697580.00218233630242470
621.34081.320994896908100.0198051030918969
631.29911.35694843116121-0.0578484311612073
641.2491.29464586783242-0.0456458678324223
651.22181.22828921464689-0.00648921464689156
661.21761.198778098285860.01882190171414
671.22661.201281468009980.0253185319900224
681.21381.21929859515147-0.00549859515146678
691.20071.20454028526210-0.00384028526209823
701.19851.190072577984220.00842742201577895
711.22621.190873981692030.0353260183079651
721.26461.231155248197180.0334447518028205







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731.281466506691171.213894203833891.34903880954846
741.298333013382341.184475476956151.41219054980854
751.315199520073521.152869970303581.47752906984346
761.332066026764691.117855000527631.54627705300175
771.348932533455861.079250689488181.61861437742354
781.365799040147041.037112262793551.69448581750052
791.382665546838210.9915584247464921.77377266892992
801.399532053529380.9427214119468581.85634269511190
811.416398560220550.8907305501521961.94206657028891
821.433265066911730.8357068857652142.03082324805824
831.450131573602900.7777618489227682.12250129828303
841.466998080294070.7169974319551262.21699872863301

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.28146650669117 & 1.21389420383389 & 1.34903880954846 \tabularnewline
74 & 1.29833301338234 & 1.18447547695615 & 1.41219054980854 \tabularnewline
75 & 1.31519952007352 & 1.15286997030358 & 1.47752906984346 \tabularnewline
76 & 1.33206602676469 & 1.11785500052763 & 1.54627705300175 \tabularnewline
77 & 1.34893253345586 & 1.07925068948818 & 1.61861437742354 \tabularnewline
78 & 1.36579904014704 & 1.03711226279355 & 1.69448581750052 \tabularnewline
79 & 1.38266554683821 & 0.991558424746492 & 1.77377266892992 \tabularnewline
80 & 1.39953205352938 & 0.942721411946858 & 1.85634269511190 \tabularnewline
81 & 1.41639856022055 & 0.890730550152196 & 1.94206657028891 \tabularnewline
82 & 1.43326506691173 & 0.835706885765214 & 2.03082324805824 \tabularnewline
83 & 1.45013157360290 & 0.777761848922768 & 2.12250129828303 \tabularnewline
84 & 1.46699808029407 & 0.716997431955126 & 2.21699872863301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77565&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]1.28146650669117[/C][C]1.21389420383389[/C][C]1.34903880954846[/C][/ROW]
[ROW][C]74[/C][C]1.29833301338234[/C][C]1.18447547695615[/C][C]1.41219054980854[/C][/ROW]
[ROW][C]75[/C][C]1.31519952007352[/C][C]1.15286997030358[/C][C]1.47752906984346[/C][/ROW]
[ROW][C]76[/C][C]1.33206602676469[/C][C]1.11785500052763[/C][C]1.54627705300175[/C][/ROW]
[ROW][C]77[/C][C]1.34893253345586[/C][C]1.07925068948818[/C][C]1.61861437742354[/C][/ROW]
[ROW][C]78[/C][C]1.36579904014704[/C][C]1.03711226279355[/C][C]1.69448581750052[/C][/ROW]
[ROW][C]79[/C][C]1.38266554683821[/C][C]0.991558424746492[/C][C]1.77377266892992[/C][/ROW]
[ROW][C]80[/C][C]1.39953205352938[/C][C]0.942721411946858[/C][C]1.85634269511190[/C][/ROW]
[ROW][C]81[/C][C]1.41639856022055[/C][C]0.890730550152196[/C][C]1.94206657028891[/C][/ROW]
[ROW][C]82[/C][C]1.43326506691173[/C][C]0.835706885765214[/C][C]2.03082324805824[/C][/ROW]
[ROW][C]83[/C][C]1.45013157360290[/C][C]0.777761848922768[/C][C]2.12250129828303[/C][/ROW]
[ROW][C]84[/C][C]1.46699808029407[/C][C]0.716997431955126[/C][C]2.21699872863301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77565&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77565&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
731.281466506691171.213894203833891.34903880954846
741.298333013382341.184475476956151.41219054980854
751.315199520073521.152869970303581.47752906984346
761.332066026764691.117855000527631.54627705300175
771.348932533455861.079250689488181.61861437742354
781.365799040147041.037112262793551.69448581750052
791.382665546838210.9915584247464921.77377266892992
801.399532053529380.9427214119468581.85634269511190
811.416398560220550.8907305501521961.94206657028891
821.433265066911730.8357068857652142.03082324805824
831.450131573602900.7777618489227682.12250129828303
841.466998080294070.7169974319551262.21699872863301



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')