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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 computationSun, 17 Nov 2013 11:07:01 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/17/t138470446719q6ntfbm3i5ytg.htm/, Retrieved Sun, 28 Apr 2024 22:40:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=225810, Retrieved Sun, 28 Apr 2024 22:40:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Structural Time Series Models] [] [2013-11-17 15:53:00] [22b6f4a061c8797aa483199554a73d13]
- RMP   [Exponential Smoothing] [] [2013-11-17 16:04:53] [22b6f4a061c8797aa483199554a73d13]
- R P       [Exponential Smoothing] [] [2013-11-17 16:07:01] [30e9f90970b737702ce92dadc5d0e0ae] [Current]
-   P         [Exponential Smoothing] [] [2013-11-17 16:08:50] [22b6f4a061c8797aa483199554a73d13]
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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
7
10
7
10
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225810&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225810&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225810&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.45886966836066
beta0.0711214003438525
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.45886966836066 \tabularnewline
beta & 0.0711214003438525 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225810&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]0.45886966836066[/C][/ROW]
[ROW][C]beta[/C][C]0.0711214003438525[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225810&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225810&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
alpha0.45886966836066
beta0.0711214003438525
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3472324
43527.79612292199497.20387707800505
53025.12011628362944.87988371637056
64321.536956799708321.4630432002917
78226.26376235449855.736237645502
84048.536474663787-8.53647466378699
94741.03779707007495.96220292992509
101940.3867020512737-21.3867020512737
115226.488059355781125.5119406442189
1213634.9423750302949101.057624969705
138081.3603752266386-1.36037522663862
144280.7374651764234-38.7374651764234
155461.6991275174856-7.69912751748564
166656.6520770493379.34792295066301
178159.732474679776721.2675253202233
186368.9764916278177-5.97649162781774
1913765.524010040148871.4759899598512
207299.9447743311003-27.9447743311003
2110787.832375103547119.1676248964529
225897.9639710141048-39.9639710141048
233679.6576288062729-43.6576288062729
245258.2315925623241-6.23159256232412
257953.775858309082425.2241416909176
267764.577407701101412.4225922988986
275469.910131301045-15.910131301045
288461.72259307043822.277406929562
294871.7851911187001-23.7851911187001
309659.934819580619836.0651804193802
318376.7249716960286.27502830397199
326680.0501149835549-14.0501149835549
336173.5901346386938-12.5901346386938
345367.3892102383282-14.3892102383282
353059.8931462141633-29.8931462141633
367444.307219850555329.6927801494447
376957.032505098939611.9674949010604
385962.014759205828-3.01475920582796
394260.0237233058521-18.0237233058521
406550.557316645014314.4426833549857
417056.460102760943213.5398972390568
4210062.390508396493937.6094916035061
436380.5931236258502-17.5931236258502
4410572.8907735462132.10922645379
458289.0432235276534-7.04322352765342
468186.9999429774586-5.9999429774586
477585.2395813679605-10.2395813679605
4810281.199604915785420.8003950842146
4912192.08176248838928.918237511611
5098107.632711515862-9.632711515862
5176105.179431440423-29.1794314404229
527792.8044705009666-15.8044705009666
536386.0510873917613-23.0510873917613
543775.2201689049976-38.2201689049976
553556.1812864740957-21.1812864740957
562344.2697694860509-21.2697694860509
574031.62350175699518.37649824300489
582932.8543778868762-3.8543778868762
593728.34708657340728.65291342659279
605129.861403629853621.1385963701464
612037.7948895544144-17.7948895544144
622827.28223541602970.7177645839703
631325.2879013152257-12.2879013152257
642216.92464038582495.07535961417513
652516.69448990287938.30551009712073
661318.2176115884455-5.21761158844546
671613.36510379115782.63489620884224
681312.20186467501980.798135324980176
691610.22183920944295.77816079055712
701710.7155692748386.28443072516201
71911.6467065032345-2.64670650323446
72178.393239286832088.60676071316792
732510.584532378013814.4154676219862
741415.9117202037091-1.91172020370908
75813.6844669109641-5.68446691096415
7679.54049943293749-2.54049943293749
77106.756292918060893.24370708193911
7876.732143179675890.267856820324106
79105.351207647427294.64879235257271
8036.13226599610916-3.13226599610916

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 47 & 23 & 24 \tabularnewline
4 & 35 & 27.7961229219949 & 7.20387707800505 \tabularnewline
5 & 30 & 25.1201162836294 & 4.87988371637056 \tabularnewline
6 & 43 & 21.5369567997083 & 21.4630432002917 \tabularnewline
7 & 82 & 26.263762354498 & 55.736237645502 \tabularnewline
8 & 40 & 48.536474663787 & -8.53647466378699 \tabularnewline
9 & 47 & 41.0377970700749 & 5.96220292992509 \tabularnewline
10 & 19 & 40.3867020512737 & -21.3867020512737 \tabularnewline
11 & 52 & 26.4880593557811 & 25.5119406442189 \tabularnewline
12 & 136 & 34.9423750302949 & 101.057624969705 \tabularnewline
13 & 80 & 81.3603752266386 & -1.36037522663862 \tabularnewline
14 & 42 & 80.7374651764234 & -38.7374651764234 \tabularnewline
15 & 54 & 61.6991275174856 & -7.69912751748564 \tabularnewline
16 & 66 & 56.652077049337 & 9.34792295066301 \tabularnewline
17 & 81 & 59.7324746797767 & 21.2675253202233 \tabularnewline
18 & 63 & 68.9764916278177 & -5.97649162781774 \tabularnewline
19 & 137 & 65.5240100401488 & 71.4759899598512 \tabularnewline
20 & 72 & 99.9447743311003 & -27.9447743311003 \tabularnewline
21 & 107 & 87.8323751035471 & 19.1676248964529 \tabularnewline
22 & 58 & 97.9639710141048 & -39.9639710141048 \tabularnewline
23 & 36 & 79.6576288062729 & -43.6576288062729 \tabularnewline
24 & 52 & 58.2315925623241 & -6.23159256232412 \tabularnewline
25 & 79 & 53.7758583090824 & 25.2241416909176 \tabularnewline
26 & 77 & 64.5774077011014 & 12.4225922988986 \tabularnewline
27 & 54 & 69.910131301045 & -15.910131301045 \tabularnewline
28 & 84 & 61.722593070438 & 22.277406929562 \tabularnewline
29 & 48 & 71.7851911187001 & -23.7851911187001 \tabularnewline
30 & 96 & 59.9348195806198 & 36.0651804193802 \tabularnewline
31 & 83 & 76.724971696028 & 6.27502830397199 \tabularnewline
32 & 66 & 80.0501149835549 & -14.0501149835549 \tabularnewline
33 & 61 & 73.5901346386938 & -12.5901346386938 \tabularnewline
34 & 53 & 67.3892102383282 & -14.3892102383282 \tabularnewline
35 & 30 & 59.8931462141633 & -29.8931462141633 \tabularnewline
36 & 74 & 44.3072198505553 & 29.6927801494447 \tabularnewline
37 & 69 & 57.0325050989396 & 11.9674949010604 \tabularnewline
38 & 59 & 62.014759205828 & -3.01475920582796 \tabularnewline
39 & 42 & 60.0237233058521 & -18.0237233058521 \tabularnewline
40 & 65 & 50.5573166450143 & 14.4426833549857 \tabularnewline
41 & 70 & 56.4601027609432 & 13.5398972390568 \tabularnewline
42 & 100 & 62.3905083964939 & 37.6094916035061 \tabularnewline
43 & 63 & 80.5931236258502 & -17.5931236258502 \tabularnewline
44 & 105 & 72.89077354621 & 32.10922645379 \tabularnewline
45 & 82 & 89.0432235276534 & -7.04322352765342 \tabularnewline
46 & 81 & 86.9999429774586 & -5.9999429774586 \tabularnewline
47 & 75 & 85.2395813679605 & -10.2395813679605 \tabularnewline
48 & 102 & 81.1996049157854 & 20.8003950842146 \tabularnewline
49 & 121 & 92.081762488389 & 28.918237511611 \tabularnewline
50 & 98 & 107.632711515862 & -9.632711515862 \tabularnewline
51 & 76 & 105.179431440423 & -29.1794314404229 \tabularnewline
52 & 77 & 92.8044705009666 & -15.8044705009666 \tabularnewline
53 & 63 & 86.0510873917613 & -23.0510873917613 \tabularnewline
54 & 37 & 75.2201689049976 & -38.2201689049976 \tabularnewline
55 & 35 & 56.1812864740957 & -21.1812864740957 \tabularnewline
56 & 23 & 44.2697694860509 & -21.2697694860509 \tabularnewline
57 & 40 & 31.6235017569951 & 8.37649824300489 \tabularnewline
58 & 29 & 32.8543778868762 & -3.8543778868762 \tabularnewline
59 & 37 & 28.3470865734072 & 8.65291342659279 \tabularnewline
60 & 51 & 29.8614036298536 & 21.1385963701464 \tabularnewline
61 & 20 & 37.7948895544144 & -17.7948895544144 \tabularnewline
62 & 28 & 27.2822354160297 & 0.7177645839703 \tabularnewline
63 & 13 & 25.2879013152257 & -12.2879013152257 \tabularnewline
64 & 22 & 16.9246403858249 & 5.07535961417513 \tabularnewline
65 & 25 & 16.6944899028793 & 8.30551009712073 \tabularnewline
66 & 13 & 18.2176115884455 & -5.21761158844546 \tabularnewline
67 & 16 & 13.3651037911578 & 2.63489620884224 \tabularnewline
68 & 13 & 12.2018646750198 & 0.798135324980176 \tabularnewline
69 & 16 & 10.2218392094429 & 5.77816079055712 \tabularnewline
70 & 17 & 10.715569274838 & 6.28443072516201 \tabularnewline
71 & 9 & 11.6467065032345 & -2.64670650323446 \tabularnewline
72 & 17 & 8.39323928683208 & 8.60676071316792 \tabularnewline
73 & 25 & 10.5845323780138 & 14.4154676219862 \tabularnewline
74 & 14 & 15.9117202037091 & -1.91172020370908 \tabularnewline
75 & 8 & 13.6844669109641 & -5.68446691096415 \tabularnewline
76 & 7 & 9.54049943293749 & -2.54049943293749 \tabularnewline
77 & 10 & 6.75629291806089 & 3.24370708193911 \tabularnewline
78 & 7 & 6.73214317967589 & 0.267856820324106 \tabularnewline
79 & 10 & 5.35120764742729 & 4.64879235257271 \tabularnewline
80 & 3 & 6.13226599610916 & -3.13226599610916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225810&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]27.7961229219949[/C][C]7.20387707800505[/C][/ROW]
[ROW][C]5[/C][C]30[/C][C]25.1201162836294[/C][C]4.87988371637056[/C][/ROW]
[ROW][C]6[/C][C]43[/C][C]21.5369567997083[/C][C]21.4630432002917[/C][/ROW]
[ROW][C]7[/C][C]82[/C][C]26.263762354498[/C][C]55.736237645502[/C][/ROW]
[ROW][C]8[/C][C]40[/C][C]48.536474663787[/C][C]-8.53647466378699[/C][/ROW]
[ROW][C]9[/C][C]47[/C][C]41.0377970700749[/C][C]5.96220292992509[/C][/ROW]
[ROW][C]10[/C][C]19[/C][C]40.3867020512737[/C][C]-21.3867020512737[/C][/ROW]
[ROW][C]11[/C][C]52[/C][C]26.4880593557811[/C][C]25.5119406442189[/C][/ROW]
[ROW][C]12[/C][C]136[/C][C]34.9423750302949[/C][C]101.057624969705[/C][/ROW]
[ROW][C]13[/C][C]80[/C][C]81.3603752266386[/C][C]-1.36037522663862[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]80.7374651764234[/C][C]-38.7374651764234[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]61.6991275174856[/C][C]-7.69912751748564[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]56.652077049337[/C][C]9.34792295066301[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]59.7324746797767[/C][C]21.2675253202233[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]68.9764916278177[/C][C]-5.97649162781774[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]65.5240100401488[/C][C]71.4759899598512[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]99.9447743311003[/C][C]-27.9447743311003[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]87.8323751035471[/C][C]19.1676248964529[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]97.9639710141048[/C][C]-39.9639710141048[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]79.6576288062729[/C][C]-43.6576288062729[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]58.2315925623241[/C][C]-6.23159256232412[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]53.7758583090824[/C][C]25.2241416909176[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]64.5774077011014[/C][C]12.4225922988986[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]69.910131301045[/C][C]-15.910131301045[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]61.722593070438[/C][C]22.277406929562[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]71.7851911187001[/C][C]-23.7851911187001[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]59.9348195806198[/C][C]36.0651804193802[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]76.724971696028[/C][C]6.27502830397199[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]80.0501149835549[/C][C]-14.0501149835549[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]73.5901346386938[/C][C]-12.5901346386938[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]67.3892102383282[/C][C]-14.3892102383282[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]59.8931462141633[/C][C]-29.8931462141633[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]44.3072198505553[/C][C]29.6927801494447[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]57.0325050989396[/C][C]11.9674949010604[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]62.014759205828[/C][C]-3.01475920582796[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]60.0237233058521[/C][C]-18.0237233058521[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]50.5573166450143[/C][C]14.4426833549857[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]56.4601027609432[/C][C]13.5398972390568[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]62.3905083964939[/C][C]37.6094916035061[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]80.5931236258502[/C][C]-17.5931236258502[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]72.89077354621[/C][C]32.10922645379[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]89.0432235276534[/C][C]-7.04322352765342[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]86.9999429774586[/C][C]-5.9999429774586[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]85.2395813679605[/C][C]-10.2395813679605[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]81.1996049157854[/C][C]20.8003950842146[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]92.081762488389[/C][C]28.918237511611[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]107.632711515862[/C][C]-9.632711515862[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]105.179431440423[/C][C]-29.1794314404229[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]92.8044705009666[/C][C]-15.8044705009666[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]86.0510873917613[/C][C]-23.0510873917613[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]75.2201689049976[/C][C]-38.2201689049976[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]56.1812864740957[/C][C]-21.1812864740957[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]44.2697694860509[/C][C]-21.2697694860509[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]31.6235017569951[/C][C]8.37649824300489[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]32.8543778868762[/C][C]-3.8543778868762[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]28.3470865734072[/C][C]8.65291342659279[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]29.8614036298536[/C][C]21.1385963701464[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]37.7948895544144[/C][C]-17.7948895544144[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]27.2822354160297[/C][C]0.7177645839703[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]25.2879013152257[/C][C]-12.2879013152257[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]16.9246403858249[/C][C]5.07535961417513[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]16.6944899028793[/C][C]8.30551009712073[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]18.2176115884455[/C][C]-5.21761158844546[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]13.3651037911578[/C][C]2.63489620884224[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]12.2018646750198[/C][C]0.798135324980176[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]10.2218392094429[/C][C]5.77816079055712[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]10.715569274838[/C][C]6.28443072516201[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]11.6467065032345[/C][C]-2.64670650323446[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]8.39323928683208[/C][C]8.60676071316792[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]10.5845323780138[/C][C]14.4154676219862[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]15.9117202037091[/C][C]-1.91172020370908[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]13.6844669109641[/C][C]-5.68446691096415[/C][/ROW]
[ROW][C]76[/C][C]7[/C][C]9.54049943293749[/C][C]-2.54049943293749[/C][/ROW]
[ROW][C]77[/C][C]10[/C][C]6.75629291806089[/C][C]3.24370708193911[/C][/ROW]
[ROW][C]78[/C][C]7[/C][C]6.73214317967589[/C][C]0.267856820324106[/C][/ROW]
[ROW][C]79[/C][C]10[/C][C]5.35120764742729[/C][C]4.64879235257271[/C][/ROW]
[ROW][C]80[/C][C]3[/C][C]6.13226599610916[/C][C]-3.13226599610916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225810&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225810&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
43527.79612292199497.20387707800505
53025.12011628362944.87988371637056
64321.536956799708321.4630432002917
78226.26376235449855.736237645502
84048.536474663787-8.53647466378699
94741.03779707007495.96220292992509
101940.3867020512737-21.3867020512737
115226.488059355781125.5119406442189
1213634.9423750302949101.057624969705
138081.3603752266386-1.36037522663862
144280.7374651764234-38.7374651764234
155461.6991275174856-7.69912751748564
166656.6520770493379.34792295066301
178159.732474679776721.2675253202233
186368.9764916278177-5.97649162781774
1913765.524010040148871.4759899598512
207299.9447743311003-27.9447743311003
2110787.832375103547119.1676248964529
225897.9639710141048-39.9639710141048
233679.6576288062729-43.6576288062729
245258.2315925623241-6.23159256232412
257953.775858309082425.2241416909176
267764.577407701101412.4225922988986
275469.910131301045-15.910131301045
288461.72259307043822.277406929562
294871.7851911187001-23.7851911187001
309659.934819580619836.0651804193802
318376.7249716960286.27502830397199
326680.0501149835549-14.0501149835549
336173.5901346386938-12.5901346386938
345367.3892102383282-14.3892102383282
353059.8931462141633-29.8931462141633
367444.307219850555329.6927801494447
376957.032505098939611.9674949010604
385962.014759205828-3.01475920582796
394260.0237233058521-18.0237233058521
406550.557316645014314.4426833549857
417056.460102760943213.5398972390568
4210062.390508396493937.6094916035061
436380.5931236258502-17.5931236258502
4410572.8907735462132.10922645379
458289.0432235276534-7.04322352765342
468186.9999429774586-5.9999429774586
477585.2395813679605-10.2395813679605
4810281.199604915785420.8003950842146
4912192.08176248838928.918237511611
5098107.632711515862-9.632711515862
5176105.179431440423-29.1794314404229
527792.8044705009666-15.8044705009666
536386.0510873917613-23.0510873917613
543775.2201689049976-38.2201689049976
553556.1812864740957-21.1812864740957
562344.2697694860509-21.2697694860509
574031.62350175699518.37649824300489
582932.8543778868762-3.8543778868762
593728.34708657340728.65291342659279
605129.861403629853621.1385963701464
612037.7948895544144-17.7948895544144
622827.28223541602970.7177645839703
631325.2879013152257-12.2879013152257
642216.92464038582495.07535961417513
652516.69448990287938.30551009712073
661318.2176115884455-5.21761158844546
671613.36510379115782.63489620884224
681312.20186467501980.798135324980176
691610.22183920944295.77816079055712
701710.7155692748386.28443072516201
71911.6467065032345-2.64670650323446
72178.393239286832088.60676071316792
732510.584532378013814.4154676219862
741415.9117202037091-1.91172020370908
75813.6844669109641-5.68446691096415
7679.54049943293749-2.54049943293749
77106.756292918060893.24370708193911
7876.732143179675890.267856820324106
79105.351207647427294.64879235257271
8036.13226599610916-3.13226599610916







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
813.24060975991806-43.515313575403249.9965330952393
821.78625538257894-50.312040394877953.8845511600358
830.331901005239822-57.242482346645757.9062843571253
84-1.1224533720993-64.30872323731962.0638164931204
85-2.57680774943841-71.51137391580666.3577584169292
86-4.03116212677753-78.850113628273170.7877893747181
87-5.48551650411665-86.324026630369875.3529936221365
88-6.93987088145577-93.931817668105580.052075905194
89-8.39422525879489-101.67195308767484.8835025700845
90-9.848579636134-109.54275486835389.845595596085
91-11.3029340134731-117.54246409014294.9365960631956
92-12.7572883908122-125.669284131717100.154707350092

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 3.24060975991806 & -43.5153135754032 & 49.9965330952393 \tabularnewline
82 & 1.78625538257894 & -50.3120403948779 & 53.8845511600358 \tabularnewline
83 & 0.331901005239822 & -57.2424823466457 & 57.9062843571253 \tabularnewline
84 & -1.1224533720993 & -64.308723237319 & 62.0638164931204 \tabularnewline
85 & -2.57680774943841 & -71.511373915806 & 66.3577584169292 \tabularnewline
86 & -4.03116212677753 & -78.8501136282731 & 70.7877893747181 \tabularnewline
87 & -5.48551650411665 & -86.3240266303698 & 75.3529936221365 \tabularnewline
88 & -6.93987088145577 & -93.9318176681055 & 80.052075905194 \tabularnewline
89 & -8.39422525879489 & -101.671953087674 & 84.8835025700845 \tabularnewline
90 & -9.848579636134 & -109.542754868353 & 89.845595596085 \tabularnewline
91 & -11.3029340134731 & -117.542464090142 & 94.9365960631956 \tabularnewline
92 & -12.7572883908122 & -125.669284131717 & 100.154707350092 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225810&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]81[/C][C]3.24060975991806[/C][C]-43.5153135754032[/C][C]49.9965330952393[/C][/ROW]
[ROW][C]82[/C][C]1.78625538257894[/C][C]-50.3120403948779[/C][C]53.8845511600358[/C][/ROW]
[ROW][C]83[/C][C]0.331901005239822[/C][C]-57.2424823466457[/C][C]57.9062843571253[/C][/ROW]
[ROW][C]84[/C][C]-1.1224533720993[/C][C]-64.308723237319[/C][C]62.0638164931204[/C][/ROW]
[ROW][C]85[/C][C]-2.57680774943841[/C][C]-71.511373915806[/C][C]66.3577584169292[/C][/ROW]
[ROW][C]86[/C][C]-4.03116212677753[/C][C]-78.8501136282731[/C][C]70.7877893747181[/C][/ROW]
[ROW][C]87[/C][C]-5.48551650411665[/C][C]-86.3240266303698[/C][C]75.3529936221365[/C][/ROW]
[ROW][C]88[/C][C]-6.93987088145577[/C][C]-93.9318176681055[/C][C]80.052075905194[/C][/ROW]
[ROW][C]89[/C][C]-8.39422525879489[/C][C]-101.671953087674[/C][C]84.8835025700845[/C][/ROW]
[ROW][C]90[/C][C]-9.848579636134[/C][C]-109.542754868353[/C][C]89.845595596085[/C][/ROW]
[ROW][C]91[/C][C]-11.3029340134731[/C][C]-117.542464090142[/C][C]94.9365960631956[/C][/ROW]
[ROW][C]92[/C][C]-12.7572883908122[/C][C]-125.669284131717[/C][C]100.154707350092[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225810&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225810&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
813.24060975991806-43.515313575403249.9965330952393
821.78625538257894-50.312040394877953.8845511600358
830.331901005239822-57.242482346645757.9062843571253
84-1.1224533720993-64.30872323731962.0638164931204
85-2.57680774943841-71.51137391580666.3577584169292
86-4.03116212677753-78.850113628273170.7877893747181
87-5.48551650411665-86.324026630369875.3529936221365
88-6.93987088145577-93.931817668105580.052075905194
89-8.39422525879489-101.67195308767484.8835025700845
90-9.848579636134-109.54275486835389.845595596085
91-11.3029340134731-117.54246409014294.9365960631956
92-12.7572883908122-125.669284131717100.154707350092



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')