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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 Nov 2012 07:53:26 -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/2012/Nov/22/t13535888702eu8jh8zd7sm41g.htm/, Retrieved Thu, 02 May 2024 09:56:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=191636, Retrieved Thu, 02 May 2024 09:56:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [WS 8 Exponential ...] [2012-11-22 12:53:26] [46cc0db4bd6f6541b375e62191991224] [Current]
- R P     [Exponential Smoothing] [WS 8 Exponential ...] [2012-11-22 12:55:09] [64c86865dff7d646747b84f713e71815]
-   P       [Exponential Smoothing] [WS 8 Exponential ...] [2012-11-22 12:56:26] [64c86865dff7d646747b84f713e71815]
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Dataseries X:
3.06
3.07
3.08
3.07
3.08
3.06
3.07
3.04
3.05
3.06
3.05
3.06
3.07
3.07
3.1
3.1
3.1
3.1
3.09
3.08
3.1
3.08
3.08
3.09
3.11
3.19
3.24
3.25
3.22
3.21
3.21
3.19
3.21
3.21
3.19
3.18
3.16
3.15
3.15
3.14
3.14
3.12
3.12
3.12
3.12
3.13
3.14
3.14
3.16
3.19
3.18
3.18
3.19
3.18
3.17
3.17
3.16
3.15
3.14
3.15
3.15
3.16
3.18
3.18
3.19
3.18
3.19
3.2
3.2
3.18
3.2
3.21
3.24
3.29
3.28
3.27
3.29
3.27
3.27
3.25
3.25
3.23
3.23
3.25




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191636&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191636&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191636&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999958326946269
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999958326946269 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191636&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]0.999958326946269[/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=191636&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191636&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
alpha0.999958326946269
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23.073.060.00999999999999979
33.083.069999583269460.0100004167305374
43.073.0799995832521-0.00999958325209649
53.083.070000416713170.00999958328683004
63.063.07999958328683-0.0199995832868285
73.073.060000833443710.00999916655629107
83.043.06999958330419-0.0299995833041948
93.053.040001250174250.00999874982575299
103.063.049999583321560.0100004166784391
113.053.0599995832521-0.00999958325209871
123.063.050000416713170.00999958328683004
133.073.059999583286830.0100004167131713
143.073.06999958325214.16747902853842e-07
153.13.069999999982630.0300000000173672
163.13.099998749808391.25019161245632e-06
173.13.09999999994795.20992138319798e-11
183.13.12.22044604925031e-15
193.093.1-0.0100000000000002
203.083.09000041673054-0.010000416730537
213.13.08000041674790.0199995832520963
223.083.09999916655629-0.0199991665562926
233.083.08000083342634-8.33426342605748e-07
243.093.080000000034730.00999999996526846
253.113.089999583269460.0200004167305359
263.193.109999166521560.080000833478441
273.243.189996666120970.0500033338790322
283.253.239997916208380.010002083791619
293.223.24999958318262-0.0299995831826245
303.213.22000125017424-0.0100012501742421
313.213.21000041678264-4.16782635959123e-07
323.193.21000000001737-0.0200000000173688
333.213.190000833461080.0199991665389248
343.213.209999166573668.33426341717569e-07
353.193.20999999996527-0.0199999999652687
363.183.19000083346107-0.0100008334610728
373.163.18000041676527-0.0200004167652703
383.153.16000083347844-0.0100008334784429
393.153.15000041676527-4.1676527073875e-07
403.143.15000000001737-0.0100000000173677
413.143.14000041673054-4.16730538077559e-07
423.123.14000000001737-0.0200000000173666
433.123.12000083346108-8.33461075266939e-07
443.123.12000000003473-3.47326611915832e-11
453.123.12-1.33226762955019e-15
463.133.120.00999999999999979
473.143.129999583269460.0100004167305374
483.143.13999958325214.16747903742021e-07
493.163.139999999982630.020000000017367
503.193.159999166538920.0300008334610751
513.183.18999874977366-0.00999874977365511
523.183.18000041667844-4.16678436643281e-07
533.193.180000000017360.00999999998263545
543.183.18999958326946-0.00999958326946304
553.173.18000041671317-0.0100004167131713
563.173.1700004167479-4.16747902853842e-07
573.163.17000000001737-0.0100000000173668
583.153.16000041673054-0.0100004167305383
593.143.1500004167479-0.0100004167479035
603.153.14000041674790.00999958325209516
613.153.149999583286834.16713170192651e-07
623.163.149999999982630.0100000000173659
633.183.159999583269460.0200004167305381
643.183.179999166521568.33478440931401e-07
653.193.179999999965270.0100000000347333
663.183.18999958326946-0.00999958326946082
673.193.180000416713170.00999958328682871
683.23.189999583286830.0100004167131718
693.23.19999958325214.16747902853842e-07
703.183.19999999998263-0.019999999982633
713.23.180000833461070.0199991665389261
723.213.199999166573660.0100008334263415
733.243.209999583234730.0300004167652688
743.293.239998749791020.0500012502089797
753.283.28999791629521-0.00999791629521374
763.273.2800004166437-0.0100004166437029
773.293.27000041674790.0199995832520998
783.273.28999916655629-0.0199991665562926
793.273.27000083342634-8.33426342605748e-07
803.253.27000000003473-0.0200000000347313
813.253.25000083346108-8.33461076155118e-07
823.233.25000000003473-0.0200000000347327
833.233.23000083346108-8.33461076155118e-07
843.253.230000000034730.0199999999652674

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3.07 & 3.06 & 0.00999999999999979 \tabularnewline
3 & 3.08 & 3.06999958326946 & 0.0100004167305374 \tabularnewline
4 & 3.07 & 3.0799995832521 & -0.00999958325209649 \tabularnewline
5 & 3.08 & 3.07000041671317 & 0.00999958328683004 \tabularnewline
6 & 3.06 & 3.07999958328683 & -0.0199995832868285 \tabularnewline
7 & 3.07 & 3.06000083344371 & 0.00999916655629107 \tabularnewline
8 & 3.04 & 3.06999958330419 & -0.0299995833041948 \tabularnewline
9 & 3.05 & 3.04000125017425 & 0.00999874982575299 \tabularnewline
10 & 3.06 & 3.04999958332156 & 0.0100004166784391 \tabularnewline
11 & 3.05 & 3.0599995832521 & -0.00999958325209871 \tabularnewline
12 & 3.06 & 3.05000041671317 & 0.00999958328683004 \tabularnewline
13 & 3.07 & 3.05999958328683 & 0.0100004167131713 \tabularnewline
14 & 3.07 & 3.0699995832521 & 4.16747902853842e-07 \tabularnewline
15 & 3.1 & 3.06999999998263 & 0.0300000000173672 \tabularnewline
16 & 3.1 & 3.09999874980839 & 1.25019161245632e-06 \tabularnewline
17 & 3.1 & 3.0999999999479 & 5.20992138319798e-11 \tabularnewline
18 & 3.1 & 3.1 & 2.22044604925031e-15 \tabularnewline
19 & 3.09 & 3.1 & -0.0100000000000002 \tabularnewline
20 & 3.08 & 3.09000041673054 & -0.010000416730537 \tabularnewline
21 & 3.1 & 3.0800004167479 & 0.0199995832520963 \tabularnewline
22 & 3.08 & 3.09999916655629 & -0.0199991665562926 \tabularnewline
23 & 3.08 & 3.08000083342634 & -8.33426342605748e-07 \tabularnewline
24 & 3.09 & 3.08000000003473 & 0.00999999996526846 \tabularnewline
25 & 3.11 & 3.08999958326946 & 0.0200004167305359 \tabularnewline
26 & 3.19 & 3.10999916652156 & 0.080000833478441 \tabularnewline
27 & 3.24 & 3.18999666612097 & 0.0500033338790322 \tabularnewline
28 & 3.25 & 3.23999791620838 & 0.010002083791619 \tabularnewline
29 & 3.22 & 3.24999958318262 & -0.0299995831826245 \tabularnewline
30 & 3.21 & 3.22000125017424 & -0.0100012501742421 \tabularnewline
31 & 3.21 & 3.21000041678264 & -4.16782635959123e-07 \tabularnewline
32 & 3.19 & 3.21000000001737 & -0.0200000000173688 \tabularnewline
33 & 3.21 & 3.19000083346108 & 0.0199991665389248 \tabularnewline
34 & 3.21 & 3.20999916657366 & 8.33426341717569e-07 \tabularnewline
35 & 3.19 & 3.20999999996527 & -0.0199999999652687 \tabularnewline
36 & 3.18 & 3.19000083346107 & -0.0100008334610728 \tabularnewline
37 & 3.16 & 3.18000041676527 & -0.0200004167652703 \tabularnewline
38 & 3.15 & 3.16000083347844 & -0.0100008334784429 \tabularnewline
39 & 3.15 & 3.15000041676527 & -4.1676527073875e-07 \tabularnewline
40 & 3.14 & 3.15000000001737 & -0.0100000000173677 \tabularnewline
41 & 3.14 & 3.14000041673054 & -4.16730538077559e-07 \tabularnewline
42 & 3.12 & 3.14000000001737 & -0.0200000000173666 \tabularnewline
43 & 3.12 & 3.12000083346108 & -8.33461075266939e-07 \tabularnewline
44 & 3.12 & 3.12000000003473 & -3.47326611915832e-11 \tabularnewline
45 & 3.12 & 3.12 & -1.33226762955019e-15 \tabularnewline
46 & 3.13 & 3.12 & 0.00999999999999979 \tabularnewline
47 & 3.14 & 3.12999958326946 & 0.0100004167305374 \tabularnewline
48 & 3.14 & 3.1399995832521 & 4.16747903742021e-07 \tabularnewline
49 & 3.16 & 3.13999999998263 & 0.020000000017367 \tabularnewline
50 & 3.19 & 3.15999916653892 & 0.0300008334610751 \tabularnewline
51 & 3.18 & 3.18999874977366 & -0.00999874977365511 \tabularnewline
52 & 3.18 & 3.18000041667844 & -4.16678436643281e-07 \tabularnewline
53 & 3.19 & 3.18000000001736 & 0.00999999998263545 \tabularnewline
54 & 3.18 & 3.18999958326946 & -0.00999958326946304 \tabularnewline
55 & 3.17 & 3.18000041671317 & -0.0100004167131713 \tabularnewline
56 & 3.17 & 3.1700004167479 & -4.16747902853842e-07 \tabularnewline
57 & 3.16 & 3.17000000001737 & -0.0100000000173668 \tabularnewline
58 & 3.15 & 3.16000041673054 & -0.0100004167305383 \tabularnewline
59 & 3.14 & 3.1500004167479 & -0.0100004167479035 \tabularnewline
60 & 3.15 & 3.1400004167479 & 0.00999958325209516 \tabularnewline
61 & 3.15 & 3.14999958328683 & 4.16713170192651e-07 \tabularnewline
62 & 3.16 & 3.14999999998263 & 0.0100000000173659 \tabularnewline
63 & 3.18 & 3.15999958326946 & 0.0200004167305381 \tabularnewline
64 & 3.18 & 3.17999916652156 & 8.33478440931401e-07 \tabularnewline
65 & 3.19 & 3.17999999996527 & 0.0100000000347333 \tabularnewline
66 & 3.18 & 3.18999958326946 & -0.00999958326946082 \tabularnewline
67 & 3.19 & 3.18000041671317 & 0.00999958328682871 \tabularnewline
68 & 3.2 & 3.18999958328683 & 0.0100004167131718 \tabularnewline
69 & 3.2 & 3.1999995832521 & 4.16747902853842e-07 \tabularnewline
70 & 3.18 & 3.19999999998263 & -0.019999999982633 \tabularnewline
71 & 3.2 & 3.18000083346107 & 0.0199991665389261 \tabularnewline
72 & 3.21 & 3.19999916657366 & 0.0100008334263415 \tabularnewline
73 & 3.24 & 3.20999958323473 & 0.0300004167652688 \tabularnewline
74 & 3.29 & 3.23999874979102 & 0.0500012502089797 \tabularnewline
75 & 3.28 & 3.28999791629521 & -0.00999791629521374 \tabularnewline
76 & 3.27 & 3.2800004166437 & -0.0100004166437029 \tabularnewline
77 & 3.29 & 3.2700004167479 & 0.0199995832520998 \tabularnewline
78 & 3.27 & 3.28999916655629 & -0.0199991665562926 \tabularnewline
79 & 3.27 & 3.27000083342634 & -8.33426342605748e-07 \tabularnewline
80 & 3.25 & 3.27000000003473 & -0.0200000000347313 \tabularnewline
81 & 3.25 & 3.25000083346108 & -8.33461076155118e-07 \tabularnewline
82 & 3.23 & 3.25000000003473 & -0.0200000000347327 \tabularnewline
83 & 3.23 & 3.23000083346108 & -8.33461076155118e-07 \tabularnewline
84 & 3.25 & 3.23000000003473 & 0.0199999999652674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191636&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]3.07[/C][C]3.06[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]3[/C][C]3.08[/C][C]3.06999958326946[/C][C]0.0100004167305374[/C][/ROW]
[ROW][C]4[/C][C]3.07[/C][C]3.0799995832521[/C][C]-0.00999958325209649[/C][/ROW]
[ROW][C]5[/C][C]3.08[/C][C]3.07000041671317[/C][C]0.00999958328683004[/C][/ROW]
[ROW][C]6[/C][C]3.06[/C][C]3.07999958328683[/C][C]-0.0199995832868285[/C][/ROW]
[ROW][C]7[/C][C]3.07[/C][C]3.06000083344371[/C][C]0.00999916655629107[/C][/ROW]
[ROW][C]8[/C][C]3.04[/C][C]3.06999958330419[/C][C]-0.0299995833041948[/C][/ROW]
[ROW][C]9[/C][C]3.05[/C][C]3.04000125017425[/C][C]0.00999874982575299[/C][/ROW]
[ROW][C]10[/C][C]3.06[/C][C]3.04999958332156[/C][C]0.0100004166784391[/C][/ROW]
[ROW][C]11[/C][C]3.05[/C][C]3.0599995832521[/C][C]-0.00999958325209871[/C][/ROW]
[ROW][C]12[/C][C]3.06[/C][C]3.05000041671317[/C][C]0.00999958328683004[/C][/ROW]
[ROW][C]13[/C][C]3.07[/C][C]3.05999958328683[/C][C]0.0100004167131713[/C][/ROW]
[ROW][C]14[/C][C]3.07[/C][C]3.0699995832521[/C][C]4.16747902853842e-07[/C][/ROW]
[ROW][C]15[/C][C]3.1[/C][C]3.06999999998263[/C][C]0.0300000000173672[/C][/ROW]
[ROW][C]16[/C][C]3.1[/C][C]3.09999874980839[/C][C]1.25019161245632e-06[/C][/ROW]
[ROW][C]17[/C][C]3.1[/C][C]3.0999999999479[/C][C]5.20992138319798e-11[/C][/ROW]
[ROW][C]18[/C][C]3.1[/C][C]3.1[/C][C]2.22044604925031e-15[/C][/ROW]
[ROW][C]19[/C][C]3.09[/C][C]3.1[/C][C]-0.0100000000000002[/C][/ROW]
[ROW][C]20[/C][C]3.08[/C][C]3.09000041673054[/C][C]-0.010000416730537[/C][/ROW]
[ROW][C]21[/C][C]3.1[/C][C]3.0800004167479[/C][C]0.0199995832520963[/C][/ROW]
[ROW][C]22[/C][C]3.08[/C][C]3.09999916655629[/C][C]-0.0199991665562926[/C][/ROW]
[ROW][C]23[/C][C]3.08[/C][C]3.08000083342634[/C][C]-8.33426342605748e-07[/C][/ROW]
[ROW][C]24[/C][C]3.09[/C][C]3.08000000003473[/C][C]0.00999999996526846[/C][/ROW]
[ROW][C]25[/C][C]3.11[/C][C]3.08999958326946[/C][C]0.0200004167305359[/C][/ROW]
[ROW][C]26[/C][C]3.19[/C][C]3.10999916652156[/C][C]0.080000833478441[/C][/ROW]
[ROW][C]27[/C][C]3.24[/C][C]3.18999666612097[/C][C]0.0500033338790322[/C][/ROW]
[ROW][C]28[/C][C]3.25[/C][C]3.23999791620838[/C][C]0.010002083791619[/C][/ROW]
[ROW][C]29[/C][C]3.22[/C][C]3.24999958318262[/C][C]-0.0299995831826245[/C][/ROW]
[ROW][C]30[/C][C]3.21[/C][C]3.22000125017424[/C][C]-0.0100012501742421[/C][/ROW]
[ROW][C]31[/C][C]3.21[/C][C]3.21000041678264[/C][C]-4.16782635959123e-07[/C][/ROW]
[ROW][C]32[/C][C]3.19[/C][C]3.21000000001737[/C][C]-0.0200000000173688[/C][/ROW]
[ROW][C]33[/C][C]3.21[/C][C]3.19000083346108[/C][C]0.0199991665389248[/C][/ROW]
[ROW][C]34[/C][C]3.21[/C][C]3.20999916657366[/C][C]8.33426341717569e-07[/C][/ROW]
[ROW][C]35[/C][C]3.19[/C][C]3.20999999996527[/C][C]-0.0199999999652687[/C][/ROW]
[ROW][C]36[/C][C]3.18[/C][C]3.19000083346107[/C][C]-0.0100008334610728[/C][/ROW]
[ROW][C]37[/C][C]3.16[/C][C]3.18000041676527[/C][C]-0.0200004167652703[/C][/ROW]
[ROW][C]38[/C][C]3.15[/C][C]3.16000083347844[/C][C]-0.0100008334784429[/C][/ROW]
[ROW][C]39[/C][C]3.15[/C][C]3.15000041676527[/C][C]-4.1676527073875e-07[/C][/ROW]
[ROW][C]40[/C][C]3.14[/C][C]3.15000000001737[/C][C]-0.0100000000173677[/C][/ROW]
[ROW][C]41[/C][C]3.14[/C][C]3.14000041673054[/C][C]-4.16730538077559e-07[/C][/ROW]
[ROW][C]42[/C][C]3.12[/C][C]3.14000000001737[/C][C]-0.0200000000173666[/C][/ROW]
[ROW][C]43[/C][C]3.12[/C][C]3.12000083346108[/C][C]-8.33461075266939e-07[/C][/ROW]
[ROW][C]44[/C][C]3.12[/C][C]3.12000000003473[/C][C]-3.47326611915832e-11[/C][/ROW]
[ROW][C]45[/C][C]3.12[/C][C]3.12[/C][C]-1.33226762955019e-15[/C][/ROW]
[ROW][C]46[/C][C]3.13[/C][C]3.12[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]47[/C][C]3.14[/C][C]3.12999958326946[/C][C]0.0100004167305374[/C][/ROW]
[ROW][C]48[/C][C]3.14[/C][C]3.1399995832521[/C][C]4.16747903742021e-07[/C][/ROW]
[ROW][C]49[/C][C]3.16[/C][C]3.13999999998263[/C][C]0.020000000017367[/C][/ROW]
[ROW][C]50[/C][C]3.19[/C][C]3.15999916653892[/C][C]0.0300008334610751[/C][/ROW]
[ROW][C]51[/C][C]3.18[/C][C]3.18999874977366[/C][C]-0.00999874977365511[/C][/ROW]
[ROW][C]52[/C][C]3.18[/C][C]3.18000041667844[/C][C]-4.16678436643281e-07[/C][/ROW]
[ROW][C]53[/C][C]3.19[/C][C]3.18000000001736[/C][C]0.00999999998263545[/C][/ROW]
[ROW][C]54[/C][C]3.18[/C][C]3.18999958326946[/C][C]-0.00999958326946304[/C][/ROW]
[ROW][C]55[/C][C]3.17[/C][C]3.18000041671317[/C][C]-0.0100004167131713[/C][/ROW]
[ROW][C]56[/C][C]3.17[/C][C]3.1700004167479[/C][C]-4.16747902853842e-07[/C][/ROW]
[ROW][C]57[/C][C]3.16[/C][C]3.17000000001737[/C][C]-0.0100000000173668[/C][/ROW]
[ROW][C]58[/C][C]3.15[/C][C]3.16000041673054[/C][C]-0.0100004167305383[/C][/ROW]
[ROW][C]59[/C][C]3.14[/C][C]3.1500004167479[/C][C]-0.0100004167479035[/C][/ROW]
[ROW][C]60[/C][C]3.15[/C][C]3.1400004167479[/C][C]0.00999958325209516[/C][/ROW]
[ROW][C]61[/C][C]3.15[/C][C]3.14999958328683[/C][C]4.16713170192651e-07[/C][/ROW]
[ROW][C]62[/C][C]3.16[/C][C]3.14999999998263[/C][C]0.0100000000173659[/C][/ROW]
[ROW][C]63[/C][C]3.18[/C][C]3.15999958326946[/C][C]0.0200004167305381[/C][/ROW]
[ROW][C]64[/C][C]3.18[/C][C]3.17999916652156[/C][C]8.33478440931401e-07[/C][/ROW]
[ROW][C]65[/C][C]3.19[/C][C]3.17999999996527[/C][C]0.0100000000347333[/C][/ROW]
[ROW][C]66[/C][C]3.18[/C][C]3.18999958326946[/C][C]-0.00999958326946082[/C][/ROW]
[ROW][C]67[/C][C]3.19[/C][C]3.18000041671317[/C][C]0.00999958328682871[/C][/ROW]
[ROW][C]68[/C][C]3.2[/C][C]3.18999958328683[/C][C]0.0100004167131718[/C][/ROW]
[ROW][C]69[/C][C]3.2[/C][C]3.1999995832521[/C][C]4.16747902853842e-07[/C][/ROW]
[ROW][C]70[/C][C]3.18[/C][C]3.19999999998263[/C][C]-0.019999999982633[/C][/ROW]
[ROW][C]71[/C][C]3.2[/C][C]3.18000083346107[/C][C]0.0199991665389261[/C][/ROW]
[ROW][C]72[/C][C]3.21[/C][C]3.19999916657366[/C][C]0.0100008334263415[/C][/ROW]
[ROW][C]73[/C][C]3.24[/C][C]3.20999958323473[/C][C]0.0300004167652688[/C][/ROW]
[ROW][C]74[/C][C]3.29[/C][C]3.23999874979102[/C][C]0.0500012502089797[/C][/ROW]
[ROW][C]75[/C][C]3.28[/C][C]3.28999791629521[/C][C]-0.00999791629521374[/C][/ROW]
[ROW][C]76[/C][C]3.27[/C][C]3.2800004166437[/C][C]-0.0100004166437029[/C][/ROW]
[ROW][C]77[/C][C]3.29[/C][C]3.2700004167479[/C][C]0.0199995832520998[/C][/ROW]
[ROW][C]78[/C][C]3.27[/C][C]3.28999916655629[/C][C]-0.0199991665562926[/C][/ROW]
[ROW][C]79[/C][C]3.27[/C][C]3.27000083342634[/C][C]-8.33426342605748e-07[/C][/ROW]
[ROW][C]80[/C][C]3.25[/C][C]3.27000000003473[/C][C]-0.0200000000347313[/C][/ROW]
[ROW][C]81[/C][C]3.25[/C][C]3.25000083346108[/C][C]-8.33461076155118e-07[/C][/ROW]
[ROW][C]82[/C][C]3.23[/C][C]3.25000000003473[/C][C]-0.0200000000347327[/C][/ROW]
[ROW][C]83[/C][C]3.23[/C][C]3.23000083346108[/C][C]-8.33461076155118e-07[/C][/ROW]
[ROW][C]84[/C][C]3.25[/C][C]3.23000000003473[/C][C]0.0199999999652674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191636&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191636&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
23.073.060.00999999999999979
33.083.069999583269460.0100004167305374
43.073.0799995832521-0.00999958325209649
53.083.070000416713170.00999958328683004
63.063.07999958328683-0.0199995832868285
73.073.060000833443710.00999916655629107
83.043.06999958330419-0.0299995833041948
93.053.040001250174250.00999874982575299
103.063.049999583321560.0100004166784391
113.053.0599995832521-0.00999958325209871
123.063.050000416713170.00999958328683004
133.073.059999583286830.0100004167131713
143.073.06999958325214.16747902853842e-07
153.13.069999999982630.0300000000173672
163.13.099998749808391.25019161245632e-06
173.13.09999999994795.20992138319798e-11
183.13.12.22044604925031e-15
193.093.1-0.0100000000000002
203.083.09000041673054-0.010000416730537
213.13.08000041674790.0199995832520963
223.083.09999916655629-0.0199991665562926
233.083.08000083342634-8.33426342605748e-07
243.093.080000000034730.00999999996526846
253.113.089999583269460.0200004167305359
263.193.109999166521560.080000833478441
273.243.189996666120970.0500033338790322
283.253.239997916208380.010002083791619
293.223.24999958318262-0.0299995831826245
303.213.22000125017424-0.0100012501742421
313.213.21000041678264-4.16782635959123e-07
323.193.21000000001737-0.0200000000173688
333.213.190000833461080.0199991665389248
343.213.209999166573668.33426341717569e-07
353.193.20999999996527-0.0199999999652687
363.183.19000083346107-0.0100008334610728
373.163.18000041676527-0.0200004167652703
383.153.16000083347844-0.0100008334784429
393.153.15000041676527-4.1676527073875e-07
403.143.15000000001737-0.0100000000173677
413.143.14000041673054-4.16730538077559e-07
423.123.14000000001737-0.0200000000173666
433.123.12000083346108-8.33461075266939e-07
443.123.12000000003473-3.47326611915832e-11
453.123.12-1.33226762955019e-15
463.133.120.00999999999999979
473.143.129999583269460.0100004167305374
483.143.13999958325214.16747903742021e-07
493.163.139999999982630.020000000017367
503.193.159999166538920.0300008334610751
513.183.18999874977366-0.00999874977365511
523.183.18000041667844-4.16678436643281e-07
533.193.180000000017360.00999999998263545
543.183.18999958326946-0.00999958326946304
553.173.18000041671317-0.0100004167131713
563.173.1700004167479-4.16747902853842e-07
573.163.17000000001737-0.0100000000173668
583.153.16000041673054-0.0100004167305383
593.143.1500004167479-0.0100004167479035
603.153.14000041674790.00999958325209516
613.153.149999583286834.16713170192651e-07
623.163.149999999982630.0100000000173659
633.183.159999583269460.0200004167305381
643.183.179999166521568.33478440931401e-07
653.193.179999999965270.0100000000347333
663.183.18999958326946-0.00999958326946082
673.193.180000416713170.00999958328682871
683.23.189999583286830.0100004167131718
693.23.19999958325214.16747902853842e-07
703.183.19999999998263-0.019999999982633
713.23.180000833461070.0199991665389261
723.213.199999166573660.0100008334263415
733.243.209999583234730.0300004167652688
743.293.239998749791020.0500012502089797
753.283.28999791629521-0.00999791629521374
763.273.2800004166437-0.0100004166437029
773.293.27000041674790.0199995832520998
783.273.28999916655629-0.0199991665562926
793.273.27000083342634-8.33426342605748e-07
803.253.27000000003473-0.0200000000347313
813.253.25000083346108-8.33461076155118e-07
823.233.25000000003473-0.0200000000347327
833.233.23000083346108-8.33461076155118e-07
843.253.230000000034730.0199999999652674







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
853.249999166538933.214921208761863.28507712431599
863.249999166538933.200392476552153.29960585652571
873.249999166538933.18924404937933.31075428369855
883.249999166538933.17984544368183.32015288939605
893.249999166538933.171565083384033.32843324969382
903.249999166538933.164079052654083.33591928042377
913.249999166538933.157194928814463.34280340426339
923.249999166538933.150787337056483.34921099602137
933.249999166538933.144769191347023.35522914173083
943.249999166538933.139077084659243.36092124841861
953.249999166538933.13366314968193.36633518339596
963.249999166538933.128490198195873.37150813488198

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3.24999916653893 & 3.21492120876186 & 3.28507712431599 \tabularnewline
86 & 3.24999916653893 & 3.20039247655215 & 3.29960585652571 \tabularnewline
87 & 3.24999916653893 & 3.1892440493793 & 3.31075428369855 \tabularnewline
88 & 3.24999916653893 & 3.1798454436818 & 3.32015288939605 \tabularnewline
89 & 3.24999916653893 & 3.17156508338403 & 3.32843324969382 \tabularnewline
90 & 3.24999916653893 & 3.16407905265408 & 3.33591928042377 \tabularnewline
91 & 3.24999916653893 & 3.15719492881446 & 3.34280340426339 \tabularnewline
92 & 3.24999916653893 & 3.15078733705648 & 3.34921099602137 \tabularnewline
93 & 3.24999916653893 & 3.14476919134702 & 3.35522914173083 \tabularnewline
94 & 3.24999916653893 & 3.13907708465924 & 3.36092124841861 \tabularnewline
95 & 3.24999916653893 & 3.1336631496819 & 3.36633518339596 \tabularnewline
96 & 3.24999916653893 & 3.12849019819587 & 3.37150813488198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191636&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]85[/C][C]3.24999916653893[/C][C]3.21492120876186[/C][C]3.28507712431599[/C][/ROW]
[ROW][C]86[/C][C]3.24999916653893[/C][C]3.20039247655215[/C][C]3.29960585652571[/C][/ROW]
[ROW][C]87[/C][C]3.24999916653893[/C][C]3.1892440493793[/C][C]3.31075428369855[/C][/ROW]
[ROW][C]88[/C][C]3.24999916653893[/C][C]3.1798454436818[/C][C]3.32015288939605[/C][/ROW]
[ROW][C]89[/C][C]3.24999916653893[/C][C]3.17156508338403[/C][C]3.32843324969382[/C][/ROW]
[ROW][C]90[/C][C]3.24999916653893[/C][C]3.16407905265408[/C][C]3.33591928042377[/C][/ROW]
[ROW][C]91[/C][C]3.24999916653893[/C][C]3.15719492881446[/C][C]3.34280340426339[/C][/ROW]
[ROW][C]92[/C][C]3.24999916653893[/C][C]3.15078733705648[/C][C]3.34921099602137[/C][/ROW]
[ROW][C]93[/C][C]3.24999916653893[/C][C]3.14476919134702[/C][C]3.35522914173083[/C][/ROW]
[ROW][C]94[/C][C]3.24999916653893[/C][C]3.13907708465924[/C][C]3.36092124841861[/C][/ROW]
[ROW][C]95[/C][C]3.24999916653893[/C][C]3.1336631496819[/C][C]3.36633518339596[/C][/ROW]
[ROW][C]96[/C][C]3.24999916653893[/C][C]3.12849019819587[/C][C]3.37150813488198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191636&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191636&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
853.249999166538933.214921208761863.28507712431599
863.249999166538933.200392476552153.29960585652571
873.249999166538933.18924404937933.31075428369855
883.249999166538933.17984544368183.32015288939605
893.249999166538933.171565083384033.32843324969382
903.249999166538933.164079052654083.33591928042377
913.249999166538933.157194928814463.34280340426339
923.249999166538933.150787337056483.34921099602137
933.249999166538933.144769191347023.35522914173083
943.249999166538933.139077084659243.36092124841861
953.249999166538933.13366314968193.36633518339596
963.249999166538933.128490198195873.37150813488198



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')