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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 03 Jun 2009 09:45:45 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/03/t12440439877sptib91c179i87.htm/, Retrieved Sat, 11 May 2024 12:43:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41502, Retrieved Sat, 11 May 2024 12:43:27 +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)
-     [Classical Decomposition] [Opgave 9 oefening...] [2009-06-03 09:11:31] [74be16979710d4c4e7c6647856088456]
- RMP     [Exponential Smoothing] [Opgave 10 oefenin...] [2009-06-03 15:45:45] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
464
675
703
887
1139
1077
1318
1260
1120
963
996
960
530
883
894
1045
1199
1287
1565
1577
1076
918
1008
1063
544
635
804
980
1018
1064
1404
1286
1104
999
996
1015
615
722
832
977
1270
1437
1520
1708
1151
934
1159
1209
699
830
996
1124
1458
1270
1753
2258
1208
1241
1265
1828
809
997
1164
1205
1538
1513
1378
2083
1357
1536
1526
1376




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41502&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41502&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41502&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.209519063877484
beta0
gamma0.465190252066663

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.209519063877484 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.465190252066663 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41502&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]0.209519063877484[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.465190252066663[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41502&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41502&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
alpha0.209519063877484
beta0
gamma0.465190252066663







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13530488.83695900046341.163040999537
14883820.16072069481462.8392793051855
15894844.40900051303749.5909994869633
1610451013.8264147347731.1735852652289
1711991185.1044040517913.8955959482057
1812871283.335635377753.6643646222476
1915651489.4444777146475.5555222853648
2015771437.15912845219139.840871547813
2110761294.77226900069-218.772269000687
229181069.44046705832-151.440467058321
2310081075.02870997955-67.028709979546
2410631022.2633361574840.7366638425229
25544581.785735147963-37.7857351479632
26635942.48289047864-307.482890478641
27804883.952871712233-79.9528717122333
289801018.44134462843-38.4413446284339
2910181165.74639585476-147.746395854757
3010641222.54495453123-158.544954531232
3114041404.70509513422-0.705095134221892
3212861364.16298139455-78.162981394548
3311041076.9927626430927.0072373569128
34999938.47376545712560.5262345428753
359961017.39665210894-21.3966521089432
3610151013.926048399611.07395160039459
37615550.70864101243764.291358987563
38722827.219571156814-105.219571156814
39832898.346982730057-66.3469827300567
409771059.47969247122-82.4796924712214
4112701160.55657930228109.443420697716
4214371272.22597311833164.774026881674
4315201620.1494184966-100.149418496598
4417081518.23450979679189.765490203213
4511511281.53135550461-130.531355504612
469341100.90437589662-166.904375896615
4711591104.4017438550954.5982561449059
4812091124.9299025004884.0700974995202
49699645.40203452606653.5979654739335
50830878.698732627998-48.6987326279976
51996988.6102514626777.38974853732338
5211241182.62029356514-58.6202935651388
5314581385.9627443851872.0372556148216
5412701522.12793662550-252.127936625497
5517531699.6978813046653.3021186953367
5622581735.53144398777522.468556012228
5712081395.37652222639-187.376522226388
5812411165.229934552275.7700654477992
5912651319.89166166391-54.8916616639074
6018281329.0833845422498.9166154578
61809810.754172821664-1.75417282166381
629971029.56191649395-32.5619164939549
6311641190.09698892522-26.0969889252178
6412051382.97132720244-177.971327202437
6515381651.98726775624-113.987267756240
6615131624.62899778875-111.628997788746
6713781997.13485081984-619.134850819837
6820832066.5273786458616.4726213541367
6913571345.6595369818311.3404630181678
7015361248.58565571582287.414344284179
7115261405.93532530904120.064674690959
7213761664.04549005685-288.045490056852

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 530 & 488.836959000463 & 41.163040999537 \tabularnewline
14 & 883 & 820.160720694814 & 62.8392793051855 \tabularnewline
15 & 894 & 844.409000513037 & 49.5909994869633 \tabularnewline
16 & 1045 & 1013.82641473477 & 31.1735852652289 \tabularnewline
17 & 1199 & 1185.10440405179 & 13.8955959482057 \tabularnewline
18 & 1287 & 1283.33563537775 & 3.6643646222476 \tabularnewline
19 & 1565 & 1489.44447771464 & 75.5555222853648 \tabularnewline
20 & 1577 & 1437.15912845219 & 139.840871547813 \tabularnewline
21 & 1076 & 1294.77226900069 & -218.772269000687 \tabularnewline
22 & 918 & 1069.44046705832 & -151.440467058321 \tabularnewline
23 & 1008 & 1075.02870997955 & -67.028709979546 \tabularnewline
24 & 1063 & 1022.26333615748 & 40.7366638425229 \tabularnewline
25 & 544 & 581.785735147963 & -37.7857351479632 \tabularnewline
26 & 635 & 942.48289047864 & -307.482890478641 \tabularnewline
27 & 804 & 883.952871712233 & -79.9528717122333 \tabularnewline
28 & 980 & 1018.44134462843 & -38.4413446284339 \tabularnewline
29 & 1018 & 1165.74639585476 & -147.746395854757 \tabularnewline
30 & 1064 & 1222.54495453123 & -158.544954531232 \tabularnewline
31 & 1404 & 1404.70509513422 & -0.705095134221892 \tabularnewline
32 & 1286 & 1364.16298139455 & -78.162981394548 \tabularnewline
33 & 1104 & 1076.99276264309 & 27.0072373569128 \tabularnewline
34 & 999 & 938.473765457125 & 60.5262345428753 \tabularnewline
35 & 996 & 1017.39665210894 & -21.3966521089432 \tabularnewline
36 & 1015 & 1013.92604839961 & 1.07395160039459 \tabularnewline
37 & 615 & 550.708641012437 & 64.291358987563 \tabularnewline
38 & 722 & 827.219571156814 & -105.219571156814 \tabularnewline
39 & 832 & 898.346982730057 & -66.3469827300567 \tabularnewline
40 & 977 & 1059.47969247122 & -82.4796924712214 \tabularnewline
41 & 1270 & 1160.55657930228 & 109.443420697716 \tabularnewline
42 & 1437 & 1272.22597311833 & 164.774026881674 \tabularnewline
43 & 1520 & 1620.1494184966 & -100.149418496598 \tabularnewline
44 & 1708 & 1518.23450979679 & 189.765490203213 \tabularnewline
45 & 1151 & 1281.53135550461 & -130.531355504612 \tabularnewline
46 & 934 & 1100.90437589662 & -166.904375896615 \tabularnewline
47 & 1159 & 1104.40174385509 & 54.5982561449059 \tabularnewline
48 & 1209 & 1124.92990250048 & 84.0700974995202 \tabularnewline
49 & 699 & 645.402034526066 & 53.5979654739335 \tabularnewline
50 & 830 & 878.698732627998 & -48.6987326279976 \tabularnewline
51 & 996 & 988.610251462677 & 7.38974853732338 \tabularnewline
52 & 1124 & 1182.62029356514 & -58.6202935651388 \tabularnewline
53 & 1458 & 1385.96274438518 & 72.0372556148216 \tabularnewline
54 & 1270 & 1522.12793662550 & -252.127936625497 \tabularnewline
55 & 1753 & 1699.69788130466 & 53.3021186953367 \tabularnewline
56 & 2258 & 1735.53144398777 & 522.468556012228 \tabularnewline
57 & 1208 & 1395.37652222639 & -187.376522226388 \tabularnewline
58 & 1241 & 1165.2299345522 & 75.7700654477992 \tabularnewline
59 & 1265 & 1319.89166166391 & -54.8916616639074 \tabularnewline
60 & 1828 & 1329.0833845422 & 498.9166154578 \tabularnewline
61 & 809 & 810.754172821664 & -1.75417282166381 \tabularnewline
62 & 997 & 1029.56191649395 & -32.5619164939549 \tabularnewline
63 & 1164 & 1190.09698892522 & -26.0969889252178 \tabularnewline
64 & 1205 & 1382.97132720244 & -177.971327202437 \tabularnewline
65 & 1538 & 1651.98726775624 & -113.987267756240 \tabularnewline
66 & 1513 & 1624.62899778875 & -111.628997788746 \tabularnewline
67 & 1378 & 1997.13485081984 & -619.134850819837 \tabularnewline
68 & 2083 & 2066.52737864586 & 16.4726213541367 \tabularnewline
69 & 1357 & 1345.65953698183 & 11.3404630181678 \tabularnewline
70 & 1536 & 1248.58565571582 & 287.414344284179 \tabularnewline
71 & 1526 & 1405.93532530904 & 120.064674690959 \tabularnewline
72 & 1376 & 1664.04549005685 & -288.045490056852 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41502&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]530[/C][C]488.836959000463[/C][C]41.163040999537[/C][/ROW]
[ROW][C]14[/C][C]883[/C][C]820.160720694814[/C][C]62.8392793051855[/C][/ROW]
[ROW][C]15[/C][C]894[/C][C]844.409000513037[/C][C]49.5909994869633[/C][/ROW]
[ROW][C]16[/C][C]1045[/C][C]1013.82641473477[/C][C]31.1735852652289[/C][/ROW]
[ROW][C]17[/C][C]1199[/C][C]1185.10440405179[/C][C]13.8955959482057[/C][/ROW]
[ROW][C]18[/C][C]1287[/C][C]1283.33563537775[/C][C]3.6643646222476[/C][/ROW]
[ROW][C]19[/C][C]1565[/C][C]1489.44447771464[/C][C]75.5555222853648[/C][/ROW]
[ROW][C]20[/C][C]1577[/C][C]1437.15912845219[/C][C]139.840871547813[/C][/ROW]
[ROW][C]21[/C][C]1076[/C][C]1294.77226900069[/C][C]-218.772269000687[/C][/ROW]
[ROW][C]22[/C][C]918[/C][C]1069.44046705832[/C][C]-151.440467058321[/C][/ROW]
[ROW][C]23[/C][C]1008[/C][C]1075.02870997955[/C][C]-67.028709979546[/C][/ROW]
[ROW][C]24[/C][C]1063[/C][C]1022.26333615748[/C][C]40.7366638425229[/C][/ROW]
[ROW][C]25[/C][C]544[/C][C]581.785735147963[/C][C]-37.7857351479632[/C][/ROW]
[ROW][C]26[/C][C]635[/C][C]942.48289047864[/C][C]-307.482890478641[/C][/ROW]
[ROW][C]27[/C][C]804[/C][C]883.952871712233[/C][C]-79.9528717122333[/C][/ROW]
[ROW][C]28[/C][C]980[/C][C]1018.44134462843[/C][C]-38.4413446284339[/C][/ROW]
[ROW][C]29[/C][C]1018[/C][C]1165.74639585476[/C][C]-147.746395854757[/C][/ROW]
[ROW][C]30[/C][C]1064[/C][C]1222.54495453123[/C][C]-158.544954531232[/C][/ROW]
[ROW][C]31[/C][C]1404[/C][C]1404.70509513422[/C][C]-0.705095134221892[/C][/ROW]
[ROW][C]32[/C][C]1286[/C][C]1364.16298139455[/C][C]-78.162981394548[/C][/ROW]
[ROW][C]33[/C][C]1104[/C][C]1076.99276264309[/C][C]27.0072373569128[/C][/ROW]
[ROW][C]34[/C][C]999[/C][C]938.473765457125[/C][C]60.5262345428753[/C][/ROW]
[ROW][C]35[/C][C]996[/C][C]1017.39665210894[/C][C]-21.3966521089432[/C][/ROW]
[ROW][C]36[/C][C]1015[/C][C]1013.92604839961[/C][C]1.07395160039459[/C][/ROW]
[ROW][C]37[/C][C]615[/C][C]550.708641012437[/C][C]64.291358987563[/C][/ROW]
[ROW][C]38[/C][C]722[/C][C]827.219571156814[/C][C]-105.219571156814[/C][/ROW]
[ROW][C]39[/C][C]832[/C][C]898.346982730057[/C][C]-66.3469827300567[/C][/ROW]
[ROW][C]40[/C][C]977[/C][C]1059.47969247122[/C][C]-82.4796924712214[/C][/ROW]
[ROW][C]41[/C][C]1270[/C][C]1160.55657930228[/C][C]109.443420697716[/C][/ROW]
[ROW][C]42[/C][C]1437[/C][C]1272.22597311833[/C][C]164.774026881674[/C][/ROW]
[ROW][C]43[/C][C]1520[/C][C]1620.1494184966[/C][C]-100.149418496598[/C][/ROW]
[ROW][C]44[/C][C]1708[/C][C]1518.23450979679[/C][C]189.765490203213[/C][/ROW]
[ROW][C]45[/C][C]1151[/C][C]1281.53135550461[/C][C]-130.531355504612[/C][/ROW]
[ROW][C]46[/C][C]934[/C][C]1100.90437589662[/C][C]-166.904375896615[/C][/ROW]
[ROW][C]47[/C][C]1159[/C][C]1104.40174385509[/C][C]54.5982561449059[/C][/ROW]
[ROW][C]48[/C][C]1209[/C][C]1124.92990250048[/C][C]84.0700974995202[/C][/ROW]
[ROW][C]49[/C][C]699[/C][C]645.402034526066[/C][C]53.5979654739335[/C][/ROW]
[ROW][C]50[/C][C]830[/C][C]878.698732627998[/C][C]-48.6987326279976[/C][/ROW]
[ROW][C]51[/C][C]996[/C][C]988.610251462677[/C][C]7.38974853732338[/C][/ROW]
[ROW][C]52[/C][C]1124[/C][C]1182.62029356514[/C][C]-58.6202935651388[/C][/ROW]
[ROW][C]53[/C][C]1458[/C][C]1385.96274438518[/C][C]72.0372556148216[/C][/ROW]
[ROW][C]54[/C][C]1270[/C][C]1522.12793662550[/C][C]-252.127936625497[/C][/ROW]
[ROW][C]55[/C][C]1753[/C][C]1699.69788130466[/C][C]53.3021186953367[/C][/ROW]
[ROW][C]56[/C][C]2258[/C][C]1735.53144398777[/C][C]522.468556012228[/C][/ROW]
[ROW][C]57[/C][C]1208[/C][C]1395.37652222639[/C][C]-187.376522226388[/C][/ROW]
[ROW][C]58[/C][C]1241[/C][C]1165.2299345522[/C][C]75.7700654477992[/C][/ROW]
[ROW][C]59[/C][C]1265[/C][C]1319.89166166391[/C][C]-54.8916616639074[/C][/ROW]
[ROW][C]60[/C][C]1828[/C][C]1329.0833845422[/C][C]498.9166154578[/C][/ROW]
[ROW][C]61[/C][C]809[/C][C]810.754172821664[/C][C]-1.75417282166381[/C][/ROW]
[ROW][C]62[/C][C]997[/C][C]1029.56191649395[/C][C]-32.5619164939549[/C][/ROW]
[ROW][C]63[/C][C]1164[/C][C]1190.09698892522[/C][C]-26.0969889252178[/C][/ROW]
[ROW][C]64[/C][C]1205[/C][C]1382.97132720244[/C][C]-177.971327202437[/C][/ROW]
[ROW][C]65[/C][C]1538[/C][C]1651.98726775624[/C][C]-113.987267756240[/C][/ROW]
[ROW][C]66[/C][C]1513[/C][C]1624.62899778875[/C][C]-111.628997788746[/C][/ROW]
[ROW][C]67[/C][C]1378[/C][C]1997.13485081984[/C][C]-619.134850819837[/C][/ROW]
[ROW][C]68[/C][C]2083[/C][C]2066.52737864586[/C][C]16.4726213541367[/C][/ROW]
[ROW][C]69[/C][C]1357[/C][C]1345.65953698183[/C][C]11.3404630181678[/C][/ROW]
[ROW][C]70[/C][C]1536[/C][C]1248.58565571582[/C][C]287.414344284179[/C][/ROW]
[ROW][C]71[/C][C]1526[/C][C]1405.93532530904[/C][C]120.064674690959[/C][/ROW]
[ROW][C]72[/C][C]1376[/C][C]1664.04549005685[/C][C]-288.045490056852[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41502&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41502&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
13530488.83695900046341.163040999537
14883820.16072069481462.8392793051855
15894844.40900051303749.5909994869633
1610451013.8264147347731.1735852652289
1711991185.1044040517913.8955959482057
1812871283.335635377753.6643646222476
1915651489.4444777146475.5555222853648
2015771437.15912845219139.840871547813
2110761294.77226900069-218.772269000687
229181069.44046705832-151.440467058321
2310081075.02870997955-67.028709979546
2410631022.2633361574840.7366638425229
25544581.785735147963-37.7857351479632
26635942.48289047864-307.482890478641
27804883.952871712233-79.9528717122333
289801018.44134462843-38.4413446284339
2910181165.74639585476-147.746395854757
3010641222.54495453123-158.544954531232
3114041404.70509513422-0.705095134221892
3212861364.16298139455-78.162981394548
3311041076.9927626430927.0072373569128
34999938.47376545712560.5262345428753
359961017.39665210894-21.3966521089432
3610151013.926048399611.07395160039459
37615550.70864101243764.291358987563
38722827.219571156814-105.219571156814
39832898.346982730057-66.3469827300567
409771059.47969247122-82.4796924712214
4112701160.55657930228109.443420697716
4214371272.22597311833164.774026881674
4315201620.1494184966-100.149418496598
4417081518.23450979679189.765490203213
4511511281.53135550461-130.531355504612
469341100.90437589662-166.904375896615
4711591104.4017438550954.5982561449059
4812091124.9299025004884.0700974995202
49699645.40203452606653.5979654739335
50830878.698732627998-48.6987326279976
51996988.6102514626777.38974853732338
5211241182.62029356514-58.6202935651388
5314581385.9627443851872.0372556148216
5412701522.12793662550-252.127936625497
5517531699.6978813046653.3021186953367
5622581735.53144398777522.468556012228
5712081395.37652222639-187.376522226388
5812411165.229934552275.7700654477992
5912651319.89166166391-54.8916616639074
6018281329.0833845422498.9166154578
61809810.754172821664-1.75417282166381
629971029.56191649395-32.5619164939549
6311641190.09698892522-26.0969889252178
6412051382.97132720244-177.971327202437
6515381651.98726775624-113.987267756240
6615131624.62899778875-111.628997788746
6713781997.13485081984-619.134850819837
6820832066.5273786458616.4726213541367
6913571345.6595369818311.3404630181678
7015361248.58565571582287.414344284179
7115261405.93532530904120.064674690959
7213761664.04549005685-288.045490056852







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73803.455573633234611.871659473103995.039487793364
741009.6704681992799.3800635350851219.96087286331
751179.18690328686948.3317567574361410.04204981628
761320.329294926191069.023417559621571.63517229275
771659.460683422541367.269606238581951.65176060649
781655.525957734191356.937133401721954.11478206667
791859.950798487221531.423212621292188.47838435315
802348.558597540721953.365828184722743.75136689671
811525.533381406761228.243928128321822.82283468519
821520.95035473581217.543294989311824.35741448229
831557.532730240241243.041191206971872.02426927352
841640.168088825581368.973030828301911.36314682286

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 803.455573633234 & 611.871659473103 & 995.039487793364 \tabularnewline
74 & 1009.6704681992 & 799.380063535085 & 1219.96087286331 \tabularnewline
75 & 1179.18690328686 & 948.331756757436 & 1410.04204981628 \tabularnewline
76 & 1320.32929492619 & 1069.02341755962 & 1571.63517229275 \tabularnewline
77 & 1659.46068342254 & 1367.26960623858 & 1951.65176060649 \tabularnewline
78 & 1655.52595773419 & 1356.93713340172 & 1954.11478206667 \tabularnewline
79 & 1859.95079848722 & 1531.42321262129 & 2188.47838435315 \tabularnewline
80 & 2348.55859754072 & 1953.36582818472 & 2743.75136689671 \tabularnewline
81 & 1525.53338140676 & 1228.24392812832 & 1822.82283468519 \tabularnewline
82 & 1520.9503547358 & 1217.54329498931 & 1824.35741448229 \tabularnewline
83 & 1557.53273024024 & 1243.04119120697 & 1872.02426927352 \tabularnewline
84 & 1640.16808882558 & 1368.97303082830 & 1911.36314682286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41502&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]803.455573633234[/C][C]611.871659473103[/C][C]995.039487793364[/C][/ROW]
[ROW][C]74[/C][C]1009.6704681992[/C][C]799.380063535085[/C][C]1219.96087286331[/C][/ROW]
[ROW][C]75[/C][C]1179.18690328686[/C][C]948.331756757436[/C][C]1410.04204981628[/C][/ROW]
[ROW][C]76[/C][C]1320.32929492619[/C][C]1069.02341755962[/C][C]1571.63517229275[/C][/ROW]
[ROW][C]77[/C][C]1659.46068342254[/C][C]1367.26960623858[/C][C]1951.65176060649[/C][/ROW]
[ROW][C]78[/C][C]1655.52595773419[/C][C]1356.93713340172[/C][C]1954.11478206667[/C][/ROW]
[ROW][C]79[/C][C]1859.95079848722[/C][C]1531.42321262129[/C][C]2188.47838435315[/C][/ROW]
[ROW][C]80[/C][C]2348.55859754072[/C][C]1953.36582818472[/C][C]2743.75136689671[/C][/ROW]
[ROW][C]81[/C][C]1525.53338140676[/C][C]1228.24392812832[/C][C]1822.82283468519[/C][/ROW]
[ROW][C]82[/C][C]1520.9503547358[/C][C]1217.54329498931[/C][C]1824.35741448229[/C][/ROW]
[ROW][C]83[/C][C]1557.53273024024[/C][C]1243.04119120697[/C][C]1872.02426927352[/C][/ROW]
[ROW][C]84[/C][C]1640.16808882558[/C][C]1368.97303082830[/C][C]1911.36314682286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41502&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41502&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
73803.455573633234611.871659473103995.039487793364
741009.6704681992799.3800635350851219.96087286331
751179.18690328686948.3317567574361410.04204981628
761320.329294926191069.023417559621571.63517229275
771659.460683422541367.269606238581951.65176060649
781655.525957734191356.937133401721954.11478206667
791859.950798487221531.423212621292188.47838435315
802348.558597540721953.365828184722743.75136689671
811525.533381406761228.243928128321822.82283468519
821520.95035473581217.543294989311824.35741448229
831557.532730240241243.041191206971872.02426927352
841640.168088825581368.973030828301911.36314682286



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')