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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 20 Jan 2010 15:23:55 -0700
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/Jan/20/t1264026272gmwaccntdouyzrr.htm/, Retrieved Mon, 06 May 2024 07:44:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72322, Retrieved Mon, 06 May 2024 07:44:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact177
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [KDGP2W62] [2010-01-20 22:23:55] [d00efe1a3b3f6588aa0a3288268f2e7e] [Current]
-   P     [Exponential Smoothing] [Exponental smooth...] [2010-01-23 15:31:48] [74be16979710d4c4e7c6647856088456]
-   P       [Exponential Smoothing] [] [2010-01-27 01:30:26] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
1
4
-3
-3
0
6
-1
0
-1
1
-4
-1
-1
0
3
0
8
8
8
8
11
13
5
12
13
9
11
7
12
11
10
13
14
10
13
12
13
17
15
6
9
6
11
12
13
11
16
16
19
14
15
12
14
16
13
13
15
12
13
12
15
10
8
11
8
13
9
8
8
6
8
6
12
16




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72322&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72322&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72322&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.472554940548756
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.472554940548756 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72322&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]0.472554940548756[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72322&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72322&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
alpha0.472554940548756
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2413
3-32.41766482164627-5.41766482164627
4-3-0.142479456059871-2.85752054394013
50-1.492814906818351.49281490681835
66-0.7873778472765076.78737784727651
7-12.42003108782519-3.42003108782519
800.803878500443058-0.803878500443058
9-10.424001743457766-1.42400174345777
101-0.2489173157632441.24891731576324
11-40.341264732137568-4.34126473213757
12-1-1.710221365264110.710221365264111
13-1-1.374602750225270.374602750225273
140-1.197582369863171.19758236986317
153-0.6316589042702413.63165890427024
1601.08449945333054-1.08449945333054
1780.572013878636777.42798612136323
1884.082145418614563.91785458138544
1985.933546957399822.06645304260018
2086.910059552092551.08994044790745
21117.425116295655143.57488370434486
22139.114445252030543.88555474796946
23510.9505833449562-5.95058334495619
24128.138605786153.86139421385
25139.96332669931123.03667330068880
26911.3983216703842-2.39832167038419
271110.2649829160190.735017083981003
28710.6123188704420-3.61231887044196
29128.905299741377113.09470025862289
301110.36771563810690.632284361893129
311010.6665047371512-0.666504737151188
321310.35154463071122.64845536928875
331411.60308530029152.39691469970847
341012.7357591837127-2.73575918371271
351311.44296266529761.55703733470236
361212.1787483504301-0.178748350430105
371312.09427993431940.90572006568058
381712.52228242611094.47771757388908
391514.63824998803420.361750011965803
40614.8091967434322-8.80919674343221
41910.6463673000573-1.64636730005731
4269.86836829845731-3.86836829845731
43118.040351747159132.95964825284087
44129.438948151325582.56105184867442
451310.64918585541822.3508141445818
461111.7600746937522-0.760074693752227
471611.40089764203354.59910235796647
481613.57422618338002.42577381661998
491914.72053758507764.27946241492240
501416.7428186921419-2.74281869214190
511515.4466861681408-0.446686168140765
521215.2356024125111-3.23560241251106
531413.70660250682750.293397493172517
541613.84524894177082.15475105822922
551314.8634871999897-1.86348719998966
561313.9828871169852-0.982887116985179
571513.51841895385211.48158104614789
581214.2185473970327-2.21854739703269
591313.1701618637233-0.170161863723312
601213.0897510343279-1.08975103432788
611512.57478379908812.42521620091188
621013.7208316967279-3.72083169672792
63811.9625342954887-3.96253429548873
641110.09001913706160.909980862938353
65810.520035089648-2.52003508964799
66139.32918005767863.67081994232140
67911.0638441572875-2.06384415728748
68810.0885644042386-2.0885644042386
6989.10160297636138-1.10160297636138
7068.5810350473586-2.58103504735860
7187.36135418399980.6386458160002
7267.66314941961149-1.66314941961149
73126.877219944503285.12278005549672
74169.298014969072896.70198503092711

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 4 & 1 & 3 \tabularnewline
3 & -3 & 2.41766482164627 & -5.41766482164627 \tabularnewline
4 & -3 & -0.142479456059871 & -2.85752054394013 \tabularnewline
5 & 0 & -1.49281490681835 & 1.49281490681835 \tabularnewline
6 & 6 & -0.787377847276507 & 6.78737784727651 \tabularnewline
7 & -1 & 2.42003108782519 & -3.42003108782519 \tabularnewline
8 & 0 & 0.803878500443058 & -0.803878500443058 \tabularnewline
9 & -1 & 0.424001743457766 & -1.42400174345777 \tabularnewline
10 & 1 & -0.248917315763244 & 1.24891731576324 \tabularnewline
11 & -4 & 0.341264732137568 & -4.34126473213757 \tabularnewline
12 & -1 & -1.71022136526411 & 0.710221365264111 \tabularnewline
13 & -1 & -1.37460275022527 & 0.374602750225273 \tabularnewline
14 & 0 & -1.19758236986317 & 1.19758236986317 \tabularnewline
15 & 3 & -0.631658904270241 & 3.63165890427024 \tabularnewline
16 & 0 & 1.08449945333054 & -1.08449945333054 \tabularnewline
17 & 8 & 0.57201387863677 & 7.42798612136323 \tabularnewline
18 & 8 & 4.08214541861456 & 3.91785458138544 \tabularnewline
19 & 8 & 5.93354695739982 & 2.06645304260018 \tabularnewline
20 & 8 & 6.91005955209255 & 1.08994044790745 \tabularnewline
21 & 11 & 7.42511629565514 & 3.57488370434486 \tabularnewline
22 & 13 & 9.11444525203054 & 3.88555474796946 \tabularnewline
23 & 5 & 10.9505833449562 & -5.95058334495619 \tabularnewline
24 & 12 & 8.13860578615 & 3.86139421385 \tabularnewline
25 & 13 & 9.9633266993112 & 3.03667330068880 \tabularnewline
26 & 9 & 11.3983216703842 & -2.39832167038419 \tabularnewline
27 & 11 & 10.264982916019 & 0.735017083981003 \tabularnewline
28 & 7 & 10.6123188704420 & -3.61231887044196 \tabularnewline
29 & 12 & 8.90529974137711 & 3.09470025862289 \tabularnewline
30 & 11 & 10.3677156381069 & 0.632284361893129 \tabularnewline
31 & 10 & 10.6665047371512 & -0.666504737151188 \tabularnewline
32 & 13 & 10.3515446307112 & 2.64845536928875 \tabularnewline
33 & 14 & 11.6030853002915 & 2.39691469970847 \tabularnewline
34 & 10 & 12.7357591837127 & -2.73575918371271 \tabularnewline
35 & 13 & 11.4429626652976 & 1.55703733470236 \tabularnewline
36 & 12 & 12.1787483504301 & -0.178748350430105 \tabularnewline
37 & 13 & 12.0942799343194 & 0.90572006568058 \tabularnewline
38 & 17 & 12.5222824261109 & 4.47771757388908 \tabularnewline
39 & 15 & 14.6382499880342 & 0.361750011965803 \tabularnewline
40 & 6 & 14.8091967434322 & -8.80919674343221 \tabularnewline
41 & 9 & 10.6463673000573 & -1.64636730005731 \tabularnewline
42 & 6 & 9.86836829845731 & -3.86836829845731 \tabularnewline
43 & 11 & 8.04035174715913 & 2.95964825284087 \tabularnewline
44 & 12 & 9.43894815132558 & 2.56105184867442 \tabularnewline
45 & 13 & 10.6491858554182 & 2.3508141445818 \tabularnewline
46 & 11 & 11.7600746937522 & -0.760074693752227 \tabularnewline
47 & 16 & 11.4008976420335 & 4.59910235796647 \tabularnewline
48 & 16 & 13.5742261833800 & 2.42577381661998 \tabularnewline
49 & 19 & 14.7205375850776 & 4.27946241492240 \tabularnewline
50 & 14 & 16.7428186921419 & -2.74281869214190 \tabularnewline
51 & 15 & 15.4466861681408 & -0.446686168140765 \tabularnewline
52 & 12 & 15.2356024125111 & -3.23560241251106 \tabularnewline
53 & 14 & 13.7066025068275 & 0.293397493172517 \tabularnewline
54 & 16 & 13.8452489417708 & 2.15475105822922 \tabularnewline
55 & 13 & 14.8634871999897 & -1.86348719998966 \tabularnewline
56 & 13 & 13.9828871169852 & -0.982887116985179 \tabularnewline
57 & 15 & 13.5184189538521 & 1.48158104614789 \tabularnewline
58 & 12 & 14.2185473970327 & -2.21854739703269 \tabularnewline
59 & 13 & 13.1701618637233 & -0.170161863723312 \tabularnewline
60 & 12 & 13.0897510343279 & -1.08975103432788 \tabularnewline
61 & 15 & 12.5747837990881 & 2.42521620091188 \tabularnewline
62 & 10 & 13.7208316967279 & -3.72083169672792 \tabularnewline
63 & 8 & 11.9625342954887 & -3.96253429548873 \tabularnewline
64 & 11 & 10.0900191370616 & 0.909980862938353 \tabularnewline
65 & 8 & 10.520035089648 & -2.52003508964799 \tabularnewline
66 & 13 & 9.3291800576786 & 3.67081994232140 \tabularnewline
67 & 9 & 11.0638441572875 & -2.06384415728748 \tabularnewline
68 & 8 & 10.0885644042386 & -2.0885644042386 \tabularnewline
69 & 8 & 9.10160297636138 & -1.10160297636138 \tabularnewline
70 & 6 & 8.5810350473586 & -2.58103504735860 \tabularnewline
71 & 8 & 7.3613541839998 & 0.6386458160002 \tabularnewline
72 & 6 & 7.66314941961149 & -1.66314941961149 \tabularnewline
73 & 12 & 6.87721994450328 & 5.12278005549672 \tabularnewline
74 & 16 & 9.29801496907289 & 6.70198503092711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72322&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]2[/C][C]4[/C][C]1[/C][C]3[/C][/ROW]
[ROW][C]3[/C][C]-3[/C][C]2.41766482164627[/C][C]-5.41766482164627[/C][/ROW]
[ROW][C]4[/C][C]-3[/C][C]-0.142479456059871[/C][C]-2.85752054394013[/C][/ROW]
[ROW][C]5[/C][C]0[/C][C]-1.49281490681835[/C][C]1.49281490681835[/C][/ROW]
[ROW][C]6[/C][C]6[/C][C]-0.787377847276507[/C][C]6.78737784727651[/C][/ROW]
[ROW][C]7[/C][C]-1[/C][C]2.42003108782519[/C][C]-3.42003108782519[/C][/ROW]
[ROW][C]8[/C][C]0[/C][C]0.803878500443058[/C][C]-0.803878500443058[/C][/ROW]
[ROW][C]9[/C][C]-1[/C][C]0.424001743457766[/C][C]-1.42400174345777[/C][/ROW]
[ROW][C]10[/C][C]1[/C][C]-0.248917315763244[/C][C]1.24891731576324[/C][/ROW]
[ROW][C]11[/C][C]-4[/C][C]0.341264732137568[/C][C]-4.34126473213757[/C][/ROW]
[ROW][C]12[/C][C]-1[/C][C]-1.71022136526411[/C][C]0.710221365264111[/C][/ROW]
[ROW][C]13[/C][C]-1[/C][C]-1.37460275022527[/C][C]0.374602750225273[/C][/ROW]
[ROW][C]14[/C][C]0[/C][C]-1.19758236986317[/C][C]1.19758236986317[/C][/ROW]
[ROW][C]15[/C][C]3[/C][C]-0.631658904270241[/C][C]3.63165890427024[/C][/ROW]
[ROW][C]16[/C][C]0[/C][C]1.08449945333054[/C][C]-1.08449945333054[/C][/ROW]
[ROW][C]17[/C][C]8[/C][C]0.57201387863677[/C][C]7.42798612136323[/C][/ROW]
[ROW][C]18[/C][C]8[/C][C]4.08214541861456[/C][C]3.91785458138544[/C][/ROW]
[ROW][C]19[/C][C]8[/C][C]5.93354695739982[/C][C]2.06645304260018[/C][/ROW]
[ROW][C]20[/C][C]8[/C][C]6.91005955209255[/C][C]1.08994044790745[/C][/ROW]
[ROW][C]21[/C][C]11[/C][C]7.42511629565514[/C][C]3.57488370434486[/C][/ROW]
[ROW][C]22[/C][C]13[/C][C]9.11444525203054[/C][C]3.88555474796946[/C][/ROW]
[ROW][C]23[/C][C]5[/C][C]10.9505833449562[/C][C]-5.95058334495619[/C][/ROW]
[ROW][C]24[/C][C]12[/C][C]8.13860578615[/C][C]3.86139421385[/C][/ROW]
[ROW][C]25[/C][C]13[/C][C]9.9633266993112[/C][C]3.03667330068880[/C][/ROW]
[ROW][C]26[/C][C]9[/C][C]11.3983216703842[/C][C]-2.39832167038419[/C][/ROW]
[ROW][C]27[/C][C]11[/C][C]10.264982916019[/C][C]0.735017083981003[/C][/ROW]
[ROW][C]28[/C][C]7[/C][C]10.6123188704420[/C][C]-3.61231887044196[/C][/ROW]
[ROW][C]29[/C][C]12[/C][C]8.90529974137711[/C][C]3.09470025862289[/C][/ROW]
[ROW][C]30[/C][C]11[/C][C]10.3677156381069[/C][C]0.632284361893129[/C][/ROW]
[ROW][C]31[/C][C]10[/C][C]10.6665047371512[/C][C]-0.666504737151188[/C][/ROW]
[ROW][C]32[/C][C]13[/C][C]10.3515446307112[/C][C]2.64845536928875[/C][/ROW]
[ROW][C]33[/C][C]14[/C][C]11.6030853002915[/C][C]2.39691469970847[/C][/ROW]
[ROW][C]34[/C][C]10[/C][C]12.7357591837127[/C][C]-2.73575918371271[/C][/ROW]
[ROW][C]35[/C][C]13[/C][C]11.4429626652976[/C][C]1.55703733470236[/C][/ROW]
[ROW][C]36[/C][C]12[/C][C]12.1787483504301[/C][C]-0.178748350430105[/C][/ROW]
[ROW][C]37[/C][C]13[/C][C]12.0942799343194[/C][C]0.90572006568058[/C][/ROW]
[ROW][C]38[/C][C]17[/C][C]12.5222824261109[/C][C]4.47771757388908[/C][/ROW]
[ROW][C]39[/C][C]15[/C][C]14.6382499880342[/C][C]0.361750011965803[/C][/ROW]
[ROW][C]40[/C][C]6[/C][C]14.8091967434322[/C][C]-8.80919674343221[/C][/ROW]
[ROW][C]41[/C][C]9[/C][C]10.6463673000573[/C][C]-1.64636730005731[/C][/ROW]
[ROW][C]42[/C][C]6[/C][C]9.86836829845731[/C][C]-3.86836829845731[/C][/ROW]
[ROW][C]43[/C][C]11[/C][C]8.04035174715913[/C][C]2.95964825284087[/C][/ROW]
[ROW][C]44[/C][C]12[/C][C]9.43894815132558[/C][C]2.56105184867442[/C][/ROW]
[ROW][C]45[/C][C]13[/C][C]10.6491858554182[/C][C]2.3508141445818[/C][/ROW]
[ROW][C]46[/C][C]11[/C][C]11.7600746937522[/C][C]-0.760074693752227[/C][/ROW]
[ROW][C]47[/C][C]16[/C][C]11.4008976420335[/C][C]4.59910235796647[/C][/ROW]
[ROW][C]48[/C][C]16[/C][C]13.5742261833800[/C][C]2.42577381661998[/C][/ROW]
[ROW][C]49[/C][C]19[/C][C]14.7205375850776[/C][C]4.27946241492240[/C][/ROW]
[ROW][C]50[/C][C]14[/C][C]16.7428186921419[/C][C]-2.74281869214190[/C][/ROW]
[ROW][C]51[/C][C]15[/C][C]15.4466861681408[/C][C]-0.446686168140765[/C][/ROW]
[ROW][C]52[/C][C]12[/C][C]15.2356024125111[/C][C]-3.23560241251106[/C][/ROW]
[ROW][C]53[/C][C]14[/C][C]13.7066025068275[/C][C]0.293397493172517[/C][/ROW]
[ROW][C]54[/C][C]16[/C][C]13.8452489417708[/C][C]2.15475105822922[/C][/ROW]
[ROW][C]55[/C][C]13[/C][C]14.8634871999897[/C][C]-1.86348719998966[/C][/ROW]
[ROW][C]56[/C][C]13[/C][C]13.9828871169852[/C][C]-0.982887116985179[/C][/ROW]
[ROW][C]57[/C][C]15[/C][C]13.5184189538521[/C][C]1.48158104614789[/C][/ROW]
[ROW][C]58[/C][C]12[/C][C]14.2185473970327[/C][C]-2.21854739703269[/C][/ROW]
[ROW][C]59[/C][C]13[/C][C]13.1701618637233[/C][C]-0.170161863723312[/C][/ROW]
[ROW][C]60[/C][C]12[/C][C]13.0897510343279[/C][C]-1.08975103432788[/C][/ROW]
[ROW][C]61[/C][C]15[/C][C]12.5747837990881[/C][C]2.42521620091188[/C][/ROW]
[ROW][C]62[/C][C]10[/C][C]13.7208316967279[/C][C]-3.72083169672792[/C][/ROW]
[ROW][C]63[/C][C]8[/C][C]11.9625342954887[/C][C]-3.96253429548873[/C][/ROW]
[ROW][C]64[/C][C]11[/C][C]10.0900191370616[/C][C]0.909980862938353[/C][/ROW]
[ROW][C]65[/C][C]8[/C][C]10.520035089648[/C][C]-2.52003508964799[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]9.3291800576786[/C][C]3.67081994232140[/C][/ROW]
[ROW][C]67[/C][C]9[/C][C]11.0638441572875[/C][C]-2.06384415728748[/C][/ROW]
[ROW][C]68[/C][C]8[/C][C]10.0885644042386[/C][C]-2.0885644042386[/C][/ROW]
[ROW][C]69[/C][C]8[/C][C]9.10160297636138[/C][C]-1.10160297636138[/C][/ROW]
[ROW][C]70[/C][C]6[/C][C]8.5810350473586[/C][C]-2.58103504735860[/C][/ROW]
[ROW][C]71[/C][C]8[/C][C]7.3613541839998[/C][C]0.6386458160002[/C][/ROW]
[ROW][C]72[/C][C]6[/C][C]7.66314941961149[/C][C]-1.66314941961149[/C][/ROW]
[ROW][C]73[/C][C]12[/C][C]6.87721994450328[/C][C]5.12278005549672[/C][/ROW]
[ROW][C]74[/C][C]16[/C][C]9.29801496907289[/C][C]6.70198503092711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72322&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72322&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
2413
3-32.41766482164627-5.41766482164627
4-3-0.142479456059871-2.85752054394013
50-1.492814906818351.49281490681835
66-0.7873778472765076.78737784727651
7-12.42003108782519-3.42003108782519
800.803878500443058-0.803878500443058
9-10.424001743457766-1.42400174345777
101-0.2489173157632441.24891731576324
11-40.341264732137568-4.34126473213757
12-1-1.710221365264110.710221365264111
13-1-1.374602750225270.374602750225273
140-1.197582369863171.19758236986317
153-0.6316589042702413.63165890427024
1601.08449945333054-1.08449945333054
1780.572013878636777.42798612136323
1884.082145418614563.91785458138544
1985.933546957399822.06645304260018
2086.910059552092551.08994044790745
21117.425116295655143.57488370434486
22139.114445252030543.88555474796946
23510.9505833449562-5.95058334495619
24128.138605786153.86139421385
25139.96332669931123.03667330068880
26911.3983216703842-2.39832167038419
271110.2649829160190.735017083981003
28710.6123188704420-3.61231887044196
29128.905299741377113.09470025862289
301110.36771563810690.632284361893129
311010.6665047371512-0.666504737151188
321310.35154463071122.64845536928875
331411.60308530029152.39691469970847
341012.7357591837127-2.73575918371271
351311.44296266529761.55703733470236
361212.1787483504301-0.178748350430105
371312.09427993431940.90572006568058
381712.52228242611094.47771757388908
391514.63824998803420.361750011965803
40614.8091967434322-8.80919674343221
41910.6463673000573-1.64636730005731
4269.86836829845731-3.86836829845731
43118.040351747159132.95964825284087
44129.438948151325582.56105184867442
451310.64918585541822.3508141445818
461111.7600746937522-0.760074693752227
471611.40089764203354.59910235796647
481613.57422618338002.42577381661998
491914.72053758507764.27946241492240
501416.7428186921419-2.74281869214190
511515.4466861681408-0.446686168140765
521215.2356024125111-3.23560241251106
531413.70660250682750.293397493172517
541613.84524894177082.15475105822922
551314.8634871999897-1.86348719998966
561313.9828871169852-0.982887116985179
571513.51841895385211.48158104614789
581214.2185473970327-2.21854739703269
591313.1701618637233-0.170161863723312
601213.0897510343279-1.08975103432788
611512.57478379908812.42521620091188
621013.7208316967279-3.72083169672792
63811.9625342954887-3.96253429548873
641110.09001913706160.909980862938353
65810.520035089648-2.52003508964799
66139.32918005767863.67081994232140
67911.0638441572875-2.06384415728748
68810.0885644042386-2.0885644042386
6989.10160297636138-1.10160297636138
7068.5810350473586-2.58103504735860
7187.36135418399980.6386458160002
7267.66314941961149-1.66314941961149
73126.877219944503285.12278005549672
74169.298014969072896.70198503092711







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7512.46507110692136.2693174069455618.6608248068970
7612.46507110692135.6123653663164519.3177768475262
7712.46507110692135.0131057269779519.9170364868647
7812.46507110692134.4585737403801820.4715684734624
7912.46507110692133.9400366708040220.9901055430386
8012.46507110692133.4512803287003521.4788618851423
8112.46507110692132.987696140713821.9424460731288
8212.46507110692132.5457541794987222.3843880343439
8312.46507110692132.1226796831156922.8074625307269
8412.46507110692131.7162445467909623.2138976670516
8512.46507110692131.3246274678053523.6055147460373
8612.46507110692130.94631698449666123.9838252293459

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
75 & 12.4650711069213 & 6.26931740694556 & 18.6608248068970 \tabularnewline
76 & 12.4650711069213 & 5.61236536631645 & 19.3177768475262 \tabularnewline
77 & 12.4650711069213 & 5.01310572697795 & 19.9170364868647 \tabularnewline
78 & 12.4650711069213 & 4.45857374038018 & 20.4715684734624 \tabularnewline
79 & 12.4650711069213 & 3.94003667080402 & 20.9901055430386 \tabularnewline
80 & 12.4650711069213 & 3.45128032870035 & 21.4788618851423 \tabularnewline
81 & 12.4650711069213 & 2.9876961407138 & 21.9424460731288 \tabularnewline
82 & 12.4650711069213 & 2.54575417949872 & 22.3843880343439 \tabularnewline
83 & 12.4650711069213 & 2.12267968311569 & 22.8074625307269 \tabularnewline
84 & 12.4650711069213 & 1.71624454679096 & 23.2138976670516 \tabularnewline
85 & 12.4650711069213 & 1.32462746780535 & 23.6055147460373 \tabularnewline
86 & 12.4650711069213 & 0.946316984496661 & 23.9838252293459 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72322&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]75[/C][C]12.4650711069213[/C][C]6.26931740694556[/C][C]18.6608248068970[/C][/ROW]
[ROW][C]76[/C][C]12.4650711069213[/C][C]5.61236536631645[/C][C]19.3177768475262[/C][/ROW]
[ROW][C]77[/C][C]12.4650711069213[/C][C]5.01310572697795[/C][C]19.9170364868647[/C][/ROW]
[ROW][C]78[/C][C]12.4650711069213[/C][C]4.45857374038018[/C][C]20.4715684734624[/C][/ROW]
[ROW][C]79[/C][C]12.4650711069213[/C][C]3.94003667080402[/C][C]20.9901055430386[/C][/ROW]
[ROW][C]80[/C][C]12.4650711069213[/C][C]3.45128032870035[/C][C]21.4788618851423[/C][/ROW]
[ROW][C]81[/C][C]12.4650711069213[/C][C]2.9876961407138[/C][C]21.9424460731288[/C][/ROW]
[ROW][C]82[/C][C]12.4650711069213[/C][C]2.54575417949872[/C][C]22.3843880343439[/C][/ROW]
[ROW][C]83[/C][C]12.4650711069213[/C][C]2.12267968311569[/C][C]22.8074625307269[/C][/ROW]
[ROW][C]84[/C][C]12.4650711069213[/C][C]1.71624454679096[/C][C]23.2138976670516[/C][/ROW]
[ROW][C]85[/C][C]12.4650711069213[/C][C]1.32462746780535[/C][C]23.6055147460373[/C][/ROW]
[ROW][C]86[/C][C]12.4650711069213[/C][C]0.946316984496661[/C][C]23.9838252293459[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72322&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72322&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
7512.46507110692136.2693174069455618.6608248068970
7612.46507110692135.6123653663164519.3177768475262
7712.46507110692135.0131057269779519.9170364868647
7812.46507110692134.4585737403801820.4715684734624
7912.46507110692133.9400366708040220.9901055430386
8012.46507110692133.4512803287003521.4788618851423
8112.46507110692132.987696140713821.9424460731288
8212.46507110692132.5457541794987222.3843880343439
8312.46507110692132.1226796831156922.8074625307269
8412.46507110692131.7162445467909623.2138976670516
8512.46507110692131.3246274678053523.6055147460373
8612.46507110692130.94631698449666123.9838252293459



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