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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 22 Dec 2011 16:24:50 -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/2011/Dec/22/t1324589243rgvnc7n5ga50psj.htm/, Retrieved Fri, 03 May 2024 23:23:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160000, Retrieved Fri, 03 May 2024 23:23:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Multiple regression] [2011-11-27 20:39:56] [e51846b5e808727784baa8d5c183dcd5]
-       [Multiple Regression] [Deel 2: multiple ...] [2011-12-21 23:11:23] [e51846b5e808727784baa8d5c183dcd5]
- RMPD      [Exponential Smoothing] [controle smoothin...] [2011-12-22 21:24:50] [5e0d67387daac495c180286b1f543191] [Current]
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Post a new message
Dataseries X:
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160000&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160000&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160000&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.459247049592553
beta0.0710317391145745
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.459247049592553 \tabularnewline
beta & 0.0710317391145745 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160000&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]0.459247049592553[/C][/ROW]
[ROW][C]beta[/C][C]0.0710317391145745[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160000&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160000&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
alpha0.459247049592553
beta0.0710317391145745
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3472324
43527.80483598900047.19516401099963
53025.12681491543824.87318508456182
64321.541400609627221.4585993903728
78226.27279236315555.727207636845
84048.5598250865124-8.55982508651243
94741.04399665225015.95600334774988
101940.3888110785855-21.3888110785855
115226.477873257502725.5221267424973
1213634.943205497122101.056794502878
138081.3941965259468-1.39419652594678
144280.7493919494925-38.7493919494925
155461.685275654246-7.68527565424596
166656.63656084244979.36343915755034
178159.72286384799921.277136152001
186368.9745809876541-5.97458098765411
1913765.51612993146371.483870068537
207299.962127650491-27.962127650491
2110787.825688496355219.1743115036448
225897.9620074036432-39.9620074036432
233679.6365410252793-43.6365410252793
245258.2000832290547-6.20008322905474
257953.753954584899825.2460454151002
267764.572921933254612.4270780667454
275469.910201510863-15.910201510863
288461.714660510108822.2853394898912
294871.7872816798647-23.7872816798647
309659.925219820763236.0747801792368
318376.7314328640976.26856713590298
326680.0537181673069-14.0537181673069
336173.5846059248184-12.5846059248184
345367.3796552477756-14.3796552477756
353059.881253054559-29.881253054559
367444.289027964087929.7109720359121
376957.03356150862311.966438491377
385962.0193289619373-3.01932896193731
394260.0244330442681-18.0244330442681
406550.550510215688614.4494897843114
417056.461499126123313.5385008738767
4210062.395760083039137.6042399169609
436380.6088329873352-17.6088329873352
4410572.891045267046832.1089547329532
458289.0534348263247-7.05343482632475
468187.0005216054986-6.00052160549862
477585.2354119597653-10.2354119597653
4810281.191550846336920.8084491536631
4912192.083286203646928.9167137963531
5098107.642013668324-9.64201366832437
5176105.17822605652-29.1782260565199
527792.7906642303913-15.7906642303913
536386.0361915748497-23.0361915748497
543775.2027655718764-38.2027655718764
553556.1579183375754-21.1579183375754
562344.2506719849453-21.2506719849453
574031.60760814443678.39239185556327
582932.8518031069712-3.8518031069712
593728.34723753999218.65276246000789
605129.867619589341521.1323804106585
612037.8085912083149-17.8085912083149
622827.28510037243790.714899627562051
631325.2917888752115-12.2917888752115
642216.92422217980195.07577782019815
652516.69823678804958.30176321195046
661318.2245884553419-5.22458845534192
671613.36857111840772.63142888159229
681312.20624671342110.793753286578925
691610.2258683318425.77413166815802
701710.72107265035966.27892734964044
71911.6529285175397-2.65292851753974
72178.396314439787458.60368556021255
732510.589928995630214.4100710043698
741415.9201815421748-1.92018154217481
75813.6881753216067-5.68817532160674

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 47 & 23 & 24 \tabularnewline
4 & 35 & 27.8048359890004 & 7.19516401099963 \tabularnewline
5 & 30 & 25.1268149154382 & 4.87318508456182 \tabularnewline
6 & 43 & 21.5414006096272 & 21.4585993903728 \tabularnewline
7 & 82 & 26.272792363155 & 55.727207636845 \tabularnewline
8 & 40 & 48.5598250865124 & -8.55982508651243 \tabularnewline
9 & 47 & 41.0439966522501 & 5.95600334774988 \tabularnewline
10 & 19 & 40.3888110785855 & -21.3888110785855 \tabularnewline
11 & 52 & 26.4778732575027 & 25.5221267424973 \tabularnewline
12 & 136 & 34.943205497122 & 101.056794502878 \tabularnewline
13 & 80 & 81.3941965259468 & -1.39419652594678 \tabularnewline
14 & 42 & 80.7493919494925 & -38.7493919494925 \tabularnewline
15 & 54 & 61.685275654246 & -7.68527565424596 \tabularnewline
16 & 66 & 56.6365608424497 & 9.36343915755034 \tabularnewline
17 & 81 & 59.722863847999 & 21.277136152001 \tabularnewline
18 & 63 & 68.9745809876541 & -5.97458098765411 \tabularnewline
19 & 137 & 65.516129931463 & 71.483870068537 \tabularnewline
20 & 72 & 99.962127650491 & -27.962127650491 \tabularnewline
21 & 107 & 87.8256884963552 & 19.1743115036448 \tabularnewline
22 & 58 & 97.9620074036432 & -39.9620074036432 \tabularnewline
23 & 36 & 79.6365410252793 & -43.6365410252793 \tabularnewline
24 & 52 & 58.2000832290547 & -6.20008322905474 \tabularnewline
25 & 79 & 53.7539545848998 & 25.2460454151002 \tabularnewline
26 & 77 & 64.5729219332546 & 12.4270780667454 \tabularnewline
27 & 54 & 69.910201510863 & -15.910201510863 \tabularnewline
28 & 84 & 61.7146605101088 & 22.2853394898912 \tabularnewline
29 & 48 & 71.7872816798647 & -23.7872816798647 \tabularnewline
30 & 96 & 59.9252198207632 & 36.0747801792368 \tabularnewline
31 & 83 & 76.731432864097 & 6.26856713590298 \tabularnewline
32 & 66 & 80.0537181673069 & -14.0537181673069 \tabularnewline
33 & 61 & 73.5846059248184 & -12.5846059248184 \tabularnewline
34 & 53 & 67.3796552477756 & -14.3796552477756 \tabularnewline
35 & 30 & 59.881253054559 & -29.881253054559 \tabularnewline
36 & 74 & 44.2890279640879 & 29.7109720359121 \tabularnewline
37 & 69 & 57.033561508623 & 11.966438491377 \tabularnewline
38 & 59 & 62.0193289619373 & -3.01932896193731 \tabularnewline
39 & 42 & 60.0244330442681 & -18.0244330442681 \tabularnewline
40 & 65 & 50.5505102156886 & 14.4494897843114 \tabularnewline
41 & 70 & 56.4614991261233 & 13.5385008738767 \tabularnewline
42 & 100 & 62.3957600830391 & 37.6042399169609 \tabularnewline
43 & 63 & 80.6088329873352 & -17.6088329873352 \tabularnewline
44 & 105 & 72.8910452670468 & 32.1089547329532 \tabularnewline
45 & 82 & 89.0534348263247 & -7.05343482632475 \tabularnewline
46 & 81 & 87.0005216054986 & -6.00052160549862 \tabularnewline
47 & 75 & 85.2354119597653 & -10.2354119597653 \tabularnewline
48 & 102 & 81.1915508463369 & 20.8084491536631 \tabularnewline
49 & 121 & 92.0832862036469 & 28.9167137963531 \tabularnewline
50 & 98 & 107.642013668324 & -9.64201366832437 \tabularnewline
51 & 76 & 105.17822605652 & -29.1782260565199 \tabularnewline
52 & 77 & 92.7906642303913 & -15.7906642303913 \tabularnewline
53 & 63 & 86.0361915748497 & -23.0361915748497 \tabularnewline
54 & 37 & 75.2027655718764 & -38.2027655718764 \tabularnewline
55 & 35 & 56.1579183375754 & -21.1579183375754 \tabularnewline
56 & 23 & 44.2506719849453 & -21.2506719849453 \tabularnewline
57 & 40 & 31.6076081444367 & 8.39239185556327 \tabularnewline
58 & 29 & 32.8518031069712 & -3.8518031069712 \tabularnewline
59 & 37 & 28.3472375399921 & 8.65276246000789 \tabularnewline
60 & 51 & 29.8676195893415 & 21.1323804106585 \tabularnewline
61 & 20 & 37.8085912083149 & -17.8085912083149 \tabularnewline
62 & 28 & 27.2851003724379 & 0.714899627562051 \tabularnewline
63 & 13 & 25.2917888752115 & -12.2917888752115 \tabularnewline
64 & 22 & 16.9242221798019 & 5.07577782019815 \tabularnewline
65 & 25 & 16.6982367880495 & 8.30176321195046 \tabularnewline
66 & 13 & 18.2245884553419 & -5.22458845534192 \tabularnewline
67 & 16 & 13.3685711184077 & 2.63142888159229 \tabularnewline
68 & 13 & 12.2062467134211 & 0.793753286578925 \tabularnewline
69 & 16 & 10.225868331842 & 5.77413166815802 \tabularnewline
70 & 17 & 10.7210726503596 & 6.27892734964044 \tabularnewline
71 & 9 & 11.6529285175397 & -2.65292851753974 \tabularnewline
72 & 17 & 8.39631443978745 & 8.60368556021255 \tabularnewline
73 & 25 & 10.5899289956302 & 14.4100710043698 \tabularnewline
74 & 14 & 15.9201815421748 & -1.92018154217481 \tabularnewline
75 & 8 & 13.6881753216067 & -5.68817532160674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160000&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]47[/C][C]23[/C][C]24[/C][/ROW]
[ROW][C]4[/C][C]35[/C][C]27.8048359890004[/C][C]7.19516401099963[/C][/ROW]
[ROW][C]5[/C][C]30[/C][C]25.1268149154382[/C][C]4.87318508456182[/C][/ROW]
[ROW][C]6[/C][C]43[/C][C]21.5414006096272[/C][C]21.4585993903728[/C][/ROW]
[ROW][C]7[/C][C]82[/C][C]26.272792363155[/C][C]55.727207636845[/C][/ROW]
[ROW][C]8[/C][C]40[/C][C]48.5598250865124[/C][C]-8.55982508651243[/C][/ROW]
[ROW][C]9[/C][C]47[/C][C]41.0439966522501[/C][C]5.95600334774988[/C][/ROW]
[ROW][C]10[/C][C]19[/C][C]40.3888110785855[/C][C]-21.3888110785855[/C][/ROW]
[ROW][C]11[/C][C]52[/C][C]26.4778732575027[/C][C]25.5221267424973[/C][/ROW]
[ROW][C]12[/C][C]136[/C][C]34.943205497122[/C][C]101.056794502878[/C][/ROW]
[ROW][C]13[/C][C]80[/C][C]81.3941965259468[/C][C]-1.39419652594678[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]80.7493919494925[/C][C]-38.7493919494925[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]61.685275654246[/C][C]-7.68527565424596[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]56.6365608424497[/C][C]9.36343915755034[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]59.722863847999[/C][C]21.277136152001[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]68.9745809876541[/C][C]-5.97458098765411[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]65.516129931463[/C][C]71.483870068537[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]99.962127650491[/C][C]-27.962127650491[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]87.8256884963552[/C][C]19.1743115036448[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]97.9620074036432[/C][C]-39.9620074036432[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]79.6365410252793[/C][C]-43.6365410252793[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]58.2000832290547[/C][C]-6.20008322905474[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]53.7539545848998[/C][C]25.2460454151002[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]64.5729219332546[/C][C]12.4270780667454[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]69.910201510863[/C][C]-15.910201510863[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]61.7146605101088[/C][C]22.2853394898912[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]71.7872816798647[/C][C]-23.7872816798647[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]59.9252198207632[/C][C]36.0747801792368[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]76.731432864097[/C][C]6.26856713590298[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]80.0537181673069[/C][C]-14.0537181673069[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]73.5846059248184[/C][C]-12.5846059248184[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]67.3796552477756[/C][C]-14.3796552477756[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]59.881253054559[/C][C]-29.881253054559[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]44.2890279640879[/C][C]29.7109720359121[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]57.033561508623[/C][C]11.966438491377[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]62.0193289619373[/C][C]-3.01932896193731[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]60.0244330442681[/C][C]-18.0244330442681[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]50.5505102156886[/C][C]14.4494897843114[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]56.4614991261233[/C][C]13.5385008738767[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]62.3957600830391[/C][C]37.6042399169609[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]80.6088329873352[/C][C]-17.6088329873352[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]72.8910452670468[/C][C]32.1089547329532[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]89.0534348263247[/C][C]-7.05343482632475[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]87.0005216054986[/C][C]-6.00052160549862[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]85.2354119597653[/C][C]-10.2354119597653[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]81.1915508463369[/C][C]20.8084491536631[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]92.0832862036469[/C][C]28.9167137963531[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]107.642013668324[/C][C]-9.64201366832437[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]105.17822605652[/C][C]-29.1782260565199[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]92.7906642303913[/C][C]-15.7906642303913[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]86.0361915748497[/C][C]-23.0361915748497[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]75.2027655718764[/C][C]-38.2027655718764[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]56.1579183375754[/C][C]-21.1579183375754[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]44.2506719849453[/C][C]-21.2506719849453[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]31.6076081444367[/C][C]8.39239185556327[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]32.8518031069712[/C][C]-3.8518031069712[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]28.3472375399921[/C][C]8.65276246000789[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]29.8676195893415[/C][C]21.1323804106585[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]37.8085912083149[/C][C]-17.8085912083149[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]27.2851003724379[/C][C]0.714899627562051[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]25.2917888752115[/C][C]-12.2917888752115[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]16.9242221798019[/C][C]5.07577782019815[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]16.6982367880495[/C][C]8.30176321195046[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]18.2245884553419[/C][C]-5.22458845534192[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]13.3685711184077[/C][C]2.63142888159229[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]12.2062467134211[/C][C]0.793753286578925[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]10.225868331842[/C][C]5.77413166815802[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]10.7210726503596[/C][C]6.27892734964044[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]11.6529285175397[/C][C]-2.65292851753974[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]8.39631443978745[/C][C]8.60368556021255[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]10.5899289956302[/C][C]14.4100710043698[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]15.9201815421748[/C][C]-1.92018154217481[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]13.6881753216067[/C][C]-5.68817532160674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160000&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160000&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
3472324
43527.80483598900047.19516401099963
53025.12681491543824.87318508456182
64321.541400609627221.4585993903728
78226.27279236315555.727207636845
84048.5598250865124-8.55982508651243
94741.04399665225015.95600334774988
101940.3888110785855-21.3888110785855
115226.477873257502725.5221267424973
1213634.943205497122101.056794502878
138081.3941965259468-1.39419652594678
144280.7493919494925-38.7493919494925
155461.685275654246-7.68527565424596
166656.63656084244979.36343915755034
178159.72286384799921.277136152001
186368.9745809876541-5.97458098765411
1913765.51612993146371.483870068537
207299.962127650491-27.962127650491
2110787.825688496355219.1743115036448
225897.9620074036432-39.9620074036432
233679.6365410252793-43.6365410252793
245258.2000832290547-6.20008322905474
257953.753954584899825.2460454151002
267764.572921933254612.4270780667454
275469.910201510863-15.910201510863
288461.714660510108822.2853394898912
294871.7872816798647-23.7872816798647
309659.925219820763236.0747801792368
318376.7314328640976.26856713590298
326680.0537181673069-14.0537181673069
336173.5846059248184-12.5846059248184
345367.3796552477756-14.3796552477756
353059.881253054559-29.881253054559
367444.289027964087929.7109720359121
376957.03356150862311.966438491377
385962.0193289619373-3.01932896193731
394260.0244330442681-18.0244330442681
406550.550510215688614.4494897843114
417056.461499126123313.5385008738767
4210062.395760083039137.6042399169609
436380.6088329873352-17.6088329873352
4410572.891045267046832.1089547329532
458289.0534348263247-7.05343482632475
468187.0005216054986-6.00052160549862
477585.2354119597653-10.2354119597653
4810281.191550846336920.8084491536631
4912192.083286203646928.9167137963531
5098107.642013668324-9.64201366832437
5176105.17822605652-29.1782260565199
527792.7906642303913-15.7906642303913
536386.0361915748497-23.0361915748497
543775.2027655718764-38.2027655718764
553556.1579183375754-21.1579183375754
562344.2506719849453-21.2506719849453
574031.60760814443678.39239185556327
582932.8518031069712-3.8518031069712
593728.34723753999218.65276246000789
605129.867619589341521.1323804106585
612037.8085912083149-17.8085912083149
622827.28510037243790.714899627562051
631325.2917888752115-12.2917888752115
642216.92422217980195.07577782019815
652516.69823678804958.30176321195046
661318.2245884553419-5.22458845534192
671613.36857111840772.63142888159229
681312.20624671342110.793753286578925
691610.2258683318425.77413166815802
701710.72107265035966.27892734964044
71911.6529285175397-2.65292851753974
72178.396314439787458.60368556021255
732510.589928995630214.4100710043698
741415.9201815421748-1.92018154217481
75813.6881753216067-5.68817532160674







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
769.54017444445423-38.777394602192557.8577434911009
778.00445130131479-45.841665081284261.8505676839137
786.46872815817535-53.042813601272265.9802699176229
794.93300501503591-60.383257744455670.2492677745274
803.39728187189646-67.86381991108974.6583836548819
811.86155872875702-75.484311134836379.2074285923504
820.325835585617581-83.243893962556183.8955651337913
83-1.20988755752186-91.141314799155188.7215396841114
84-2.7456107006613-99.175056176812293.6838347754896
85-4.28133384380074-107.34343835905298.7807706714502
86-5.81705698694019-115.644688052788104.010574078908
87-7.35278013007963-124.076985302373109.371425042214

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 9.54017444445423 & -38.7773946021925 & 57.8577434911009 \tabularnewline
77 & 8.00445130131479 & -45.8416650812842 & 61.8505676839137 \tabularnewline
78 & 6.46872815817535 & -53.0428136012722 & 65.9802699176229 \tabularnewline
79 & 4.93300501503591 & -60.3832577444556 & 70.2492677745274 \tabularnewline
80 & 3.39728187189646 & -67.863819911089 & 74.6583836548819 \tabularnewline
81 & 1.86155872875702 & -75.4843111348363 & 79.2074285923504 \tabularnewline
82 & 0.325835585617581 & -83.2438939625561 & 83.8955651337913 \tabularnewline
83 & -1.20988755752186 & -91.1413147991551 & 88.7215396841114 \tabularnewline
84 & -2.7456107006613 & -99.1750561768122 & 93.6838347754896 \tabularnewline
85 & -4.28133384380074 & -107.343438359052 & 98.7807706714502 \tabularnewline
86 & -5.81705698694019 & -115.644688052788 & 104.010574078908 \tabularnewline
87 & -7.35278013007963 & -124.076985302373 & 109.371425042214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160000&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]76[/C][C]9.54017444445423[/C][C]-38.7773946021925[/C][C]57.8577434911009[/C][/ROW]
[ROW][C]77[/C][C]8.00445130131479[/C][C]-45.8416650812842[/C][C]61.8505676839137[/C][/ROW]
[ROW][C]78[/C][C]6.46872815817535[/C][C]-53.0428136012722[/C][C]65.9802699176229[/C][/ROW]
[ROW][C]79[/C][C]4.93300501503591[/C][C]-60.3832577444556[/C][C]70.2492677745274[/C][/ROW]
[ROW][C]80[/C][C]3.39728187189646[/C][C]-67.863819911089[/C][C]74.6583836548819[/C][/ROW]
[ROW][C]81[/C][C]1.86155872875702[/C][C]-75.4843111348363[/C][C]79.2074285923504[/C][/ROW]
[ROW][C]82[/C][C]0.325835585617581[/C][C]-83.2438939625561[/C][C]83.8955651337913[/C][/ROW]
[ROW][C]83[/C][C]-1.20988755752186[/C][C]-91.1413147991551[/C][C]88.7215396841114[/C][/ROW]
[ROW][C]84[/C][C]-2.7456107006613[/C][C]-99.1750561768122[/C][C]93.6838347754896[/C][/ROW]
[ROW][C]85[/C][C]-4.28133384380074[/C][C]-107.343438359052[/C][C]98.7807706714502[/C][/ROW]
[ROW][C]86[/C][C]-5.81705698694019[/C][C]-115.644688052788[/C][C]104.010574078908[/C][/ROW]
[ROW][C]87[/C][C]-7.35278013007963[/C][C]-124.076985302373[/C][C]109.371425042214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160000&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160000&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
769.54017444445423-38.777394602192557.8577434911009
778.00445130131479-45.841665081284261.8505676839137
786.46872815817535-53.042813601272265.9802699176229
794.93300501503591-60.383257744455670.2492677745274
803.39728187189646-67.86381991108974.6583836548819
811.86155872875702-75.484311134836379.2074285923504
820.325835585617581-83.243893962556183.8955651337913
83-1.20988755752186-91.141314799155188.7215396841114
84-2.7456107006613-99.175056176812293.6838347754896
85-4.28133384380074-107.34343835905298.7807706714502
86-5.81705698694019-115.644688052788104.010574078908
87-7.35278013007963-124.076985302373109.371425042214



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