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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 22 May 2012 13:01:28 -0400
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/May/22/t1337706140sdr0sl3tqh63ilv.htm/, Retrieved Fri, 03 May 2024 11:56:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167104, Retrieved Fri, 03 May 2024 11:56:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Double exponentia...] [2012-05-22 17:01:28] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
6,81
6,8
6,8
6,85
6,85
6,85
6,85
6,85
6,85
6,86
6,86
6,88
6,88
6,88
6,91
6,91
6,91
6,91
6,99
6,99
6,99
7,02
7,02
7,05
7,05
7,05
7,05
7,1
7,1
7,1
7,1
7,12
7,13
7,18
7,24
7,24
7,24
7,27
7,27
7,27
7,27
7,3
7,3
7,57
7,76
7,94
7,94
7,96
7,96
7,98
7,99
8
8
8,04
8,04
8,04
8,04
8,04
8,07
8,07




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167104&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167104&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167104&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.531517209785423
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.531517209785423 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167104&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.531517209785423[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167104&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167104&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
alpha1
beta0.531517209785423
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
36.86.790.00999999999999979
46.856.795315172097850.0546848279021459
56.856.874381099242-0.0243810992419986
66.856.86142212540139-0.0114221254013902
76.856.85535106917822-0.00535106917822414
86.856.85250688381925-0.00250688381924569
96.856.85117443192638-0.00117443192638422
106.866.850550201145790.00944979885421127
116.866.86557293186581-0.00557293186581287
126.886.862610822670170.0173891773298278
136.886.89185346968499-0.0118534696849855
146.886.88555314655175-0.00555314655174577
156.916.882601553591030.0273984464089674
166.916.92716429937878-0.0171642993787824
176.916.91804117886505-0.00804117886505029
186.916.91376715391131-0.00376715391131288
196.996.911764846775540.0782351532244601
206.997.03334817712454-0.0433481771245399
216.997.01030787497002-0.0203078749700198
227.026.999513889929280.0204861100707152
237.027.04040260999343-0.020402609993428
247.057.029558271657380.020441728342619
257.057.07042340206924-0.0204234020692411
267.057.05956801238707-0.0095680123870725
277.057.0544824491399-0.00448244913990337
287.17.052099950280060.0479000497199431
297.17.12755965105578-0.0275596510557836
307.17.11291122222395-0.0129112222239538
317.17.10604868541256-0.00604868541255854
327.127.102833705019210.0171662949807949
337.137.13195788622975-0.00195788622975179
347.187.140917236003840.0390827639961637
357.247.211690397673780.028309602326221
367.247.28673743851235-0.0467374385123476
377.247.26189568560175-0.0218956856017467
387.277.250257751884370.019742248115632
397.277.29075109651768-0.0207510965176798
407.277.27972153159661-0.0097215315966146
417.277.27455437024754-0.0045543702475408
427.37.272133644081240.0278663559187615
437.37.31694509182607-0.0169450918260665
447.577.307938483899120.262061516100883
457.767.71722868972920.0427713102708029
467.947.92996237722320.0100376227768004
477.948.1152975464744-0.175297546474403
487.968.0221238836901-0.0621238836900995
497.968.0091039703701-0.0491039703701022
507.987.9830043650496-0.00300436504959922
517.998.00140749332126-0.0114074933212596
5288.0053442143005-0.00534421430049825
5388.012503672427-0.0125036724270018
548.048.005857755346530.0341422446534683
558.048.06400494596055-0.024004945960554
568.048.05124590406255-0.0112459040625499
578.048.04526851251371-0.00526851251370886
588.048.0424682074427-0.00246820744270337
598.078.041156312709590.028843687290415
608.078.08648722889811-0.0164872288981108

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 6.8 & 6.79 & 0.00999999999999979 \tabularnewline
4 & 6.85 & 6.79531517209785 & 0.0546848279021459 \tabularnewline
5 & 6.85 & 6.874381099242 & -0.0243810992419986 \tabularnewline
6 & 6.85 & 6.86142212540139 & -0.0114221254013902 \tabularnewline
7 & 6.85 & 6.85535106917822 & -0.00535106917822414 \tabularnewline
8 & 6.85 & 6.85250688381925 & -0.00250688381924569 \tabularnewline
9 & 6.85 & 6.85117443192638 & -0.00117443192638422 \tabularnewline
10 & 6.86 & 6.85055020114579 & 0.00944979885421127 \tabularnewline
11 & 6.86 & 6.86557293186581 & -0.00557293186581287 \tabularnewline
12 & 6.88 & 6.86261082267017 & 0.0173891773298278 \tabularnewline
13 & 6.88 & 6.89185346968499 & -0.0118534696849855 \tabularnewline
14 & 6.88 & 6.88555314655175 & -0.00555314655174577 \tabularnewline
15 & 6.91 & 6.88260155359103 & 0.0273984464089674 \tabularnewline
16 & 6.91 & 6.92716429937878 & -0.0171642993787824 \tabularnewline
17 & 6.91 & 6.91804117886505 & -0.00804117886505029 \tabularnewline
18 & 6.91 & 6.91376715391131 & -0.00376715391131288 \tabularnewline
19 & 6.99 & 6.91176484677554 & 0.0782351532244601 \tabularnewline
20 & 6.99 & 7.03334817712454 & -0.0433481771245399 \tabularnewline
21 & 6.99 & 7.01030787497002 & -0.0203078749700198 \tabularnewline
22 & 7.02 & 6.99951388992928 & 0.0204861100707152 \tabularnewline
23 & 7.02 & 7.04040260999343 & -0.020402609993428 \tabularnewline
24 & 7.05 & 7.02955827165738 & 0.020441728342619 \tabularnewline
25 & 7.05 & 7.07042340206924 & -0.0204234020692411 \tabularnewline
26 & 7.05 & 7.05956801238707 & -0.0095680123870725 \tabularnewline
27 & 7.05 & 7.0544824491399 & -0.00448244913990337 \tabularnewline
28 & 7.1 & 7.05209995028006 & 0.0479000497199431 \tabularnewline
29 & 7.1 & 7.12755965105578 & -0.0275596510557836 \tabularnewline
30 & 7.1 & 7.11291122222395 & -0.0129112222239538 \tabularnewline
31 & 7.1 & 7.10604868541256 & -0.00604868541255854 \tabularnewline
32 & 7.12 & 7.10283370501921 & 0.0171662949807949 \tabularnewline
33 & 7.13 & 7.13195788622975 & -0.00195788622975179 \tabularnewline
34 & 7.18 & 7.14091723600384 & 0.0390827639961637 \tabularnewline
35 & 7.24 & 7.21169039767378 & 0.028309602326221 \tabularnewline
36 & 7.24 & 7.28673743851235 & -0.0467374385123476 \tabularnewline
37 & 7.24 & 7.26189568560175 & -0.0218956856017467 \tabularnewline
38 & 7.27 & 7.25025775188437 & 0.019742248115632 \tabularnewline
39 & 7.27 & 7.29075109651768 & -0.0207510965176798 \tabularnewline
40 & 7.27 & 7.27972153159661 & -0.0097215315966146 \tabularnewline
41 & 7.27 & 7.27455437024754 & -0.0045543702475408 \tabularnewline
42 & 7.3 & 7.27213364408124 & 0.0278663559187615 \tabularnewline
43 & 7.3 & 7.31694509182607 & -0.0169450918260665 \tabularnewline
44 & 7.57 & 7.30793848389912 & 0.262061516100883 \tabularnewline
45 & 7.76 & 7.7172286897292 & 0.0427713102708029 \tabularnewline
46 & 7.94 & 7.9299623772232 & 0.0100376227768004 \tabularnewline
47 & 7.94 & 8.1152975464744 & -0.175297546474403 \tabularnewline
48 & 7.96 & 8.0221238836901 & -0.0621238836900995 \tabularnewline
49 & 7.96 & 8.0091039703701 & -0.0491039703701022 \tabularnewline
50 & 7.98 & 7.9830043650496 & -0.00300436504959922 \tabularnewline
51 & 7.99 & 8.00140749332126 & -0.0114074933212596 \tabularnewline
52 & 8 & 8.0053442143005 & -0.00534421430049825 \tabularnewline
53 & 8 & 8.012503672427 & -0.0125036724270018 \tabularnewline
54 & 8.04 & 8.00585775534653 & 0.0341422446534683 \tabularnewline
55 & 8.04 & 8.06400494596055 & -0.024004945960554 \tabularnewline
56 & 8.04 & 8.05124590406255 & -0.0112459040625499 \tabularnewline
57 & 8.04 & 8.04526851251371 & -0.00526851251370886 \tabularnewline
58 & 8.04 & 8.0424682074427 & -0.00246820744270337 \tabularnewline
59 & 8.07 & 8.04115631270959 & 0.028843687290415 \tabularnewline
60 & 8.07 & 8.08648722889811 & -0.0164872288981108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167104&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]6.8[/C][C]6.79[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]6.85[/C][C]6.79531517209785[/C][C]0.0546848279021459[/C][/ROW]
[ROW][C]5[/C][C]6.85[/C][C]6.874381099242[/C][C]-0.0243810992419986[/C][/ROW]
[ROW][C]6[/C][C]6.85[/C][C]6.86142212540139[/C][C]-0.0114221254013902[/C][/ROW]
[ROW][C]7[/C][C]6.85[/C][C]6.85535106917822[/C][C]-0.00535106917822414[/C][/ROW]
[ROW][C]8[/C][C]6.85[/C][C]6.85250688381925[/C][C]-0.00250688381924569[/C][/ROW]
[ROW][C]9[/C][C]6.85[/C][C]6.85117443192638[/C][C]-0.00117443192638422[/C][/ROW]
[ROW][C]10[/C][C]6.86[/C][C]6.85055020114579[/C][C]0.00944979885421127[/C][/ROW]
[ROW][C]11[/C][C]6.86[/C][C]6.86557293186581[/C][C]-0.00557293186581287[/C][/ROW]
[ROW][C]12[/C][C]6.88[/C][C]6.86261082267017[/C][C]0.0173891773298278[/C][/ROW]
[ROW][C]13[/C][C]6.88[/C][C]6.89185346968499[/C][C]-0.0118534696849855[/C][/ROW]
[ROW][C]14[/C][C]6.88[/C][C]6.88555314655175[/C][C]-0.00555314655174577[/C][/ROW]
[ROW][C]15[/C][C]6.91[/C][C]6.88260155359103[/C][C]0.0273984464089674[/C][/ROW]
[ROW][C]16[/C][C]6.91[/C][C]6.92716429937878[/C][C]-0.0171642993787824[/C][/ROW]
[ROW][C]17[/C][C]6.91[/C][C]6.91804117886505[/C][C]-0.00804117886505029[/C][/ROW]
[ROW][C]18[/C][C]6.91[/C][C]6.91376715391131[/C][C]-0.00376715391131288[/C][/ROW]
[ROW][C]19[/C][C]6.99[/C][C]6.91176484677554[/C][C]0.0782351532244601[/C][/ROW]
[ROW][C]20[/C][C]6.99[/C][C]7.03334817712454[/C][C]-0.0433481771245399[/C][/ROW]
[ROW][C]21[/C][C]6.99[/C][C]7.01030787497002[/C][C]-0.0203078749700198[/C][/ROW]
[ROW][C]22[/C][C]7.02[/C][C]6.99951388992928[/C][C]0.0204861100707152[/C][/ROW]
[ROW][C]23[/C][C]7.02[/C][C]7.04040260999343[/C][C]-0.020402609993428[/C][/ROW]
[ROW][C]24[/C][C]7.05[/C][C]7.02955827165738[/C][C]0.020441728342619[/C][/ROW]
[ROW][C]25[/C][C]7.05[/C][C]7.07042340206924[/C][C]-0.0204234020692411[/C][/ROW]
[ROW][C]26[/C][C]7.05[/C][C]7.05956801238707[/C][C]-0.0095680123870725[/C][/ROW]
[ROW][C]27[/C][C]7.05[/C][C]7.0544824491399[/C][C]-0.00448244913990337[/C][/ROW]
[ROW][C]28[/C][C]7.1[/C][C]7.05209995028006[/C][C]0.0479000497199431[/C][/ROW]
[ROW][C]29[/C][C]7.1[/C][C]7.12755965105578[/C][C]-0.0275596510557836[/C][/ROW]
[ROW][C]30[/C][C]7.1[/C][C]7.11291122222395[/C][C]-0.0129112222239538[/C][/ROW]
[ROW][C]31[/C][C]7.1[/C][C]7.10604868541256[/C][C]-0.00604868541255854[/C][/ROW]
[ROW][C]32[/C][C]7.12[/C][C]7.10283370501921[/C][C]0.0171662949807949[/C][/ROW]
[ROW][C]33[/C][C]7.13[/C][C]7.13195788622975[/C][C]-0.00195788622975179[/C][/ROW]
[ROW][C]34[/C][C]7.18[/C][C]7.14091723600384[/C][C]0.0390827639961637[/C][/ROW]
[ROW][C]35[/C][C]7.24[/C][C]7.21169039767378[/C][C]0.028309602326221[/C][/ROW]
[ROW][C]36[/C][C]7.24[/C][C]7.28673743851235[/C][C]-0.0467374385123476[/C][/ROW]
[ROW][C]37[/C][C]7.24[/C][C]7.26189568560175[/C][C]-0.0218956856017467[/C][/ROW]
[ROW][C]38[/C][C]7.27[/C][C]7.25025775188437[/C][C]0.019742248115632[/C][/ROW]
[ROW][C]39[/C][C]7.27[/C][C]7.29075109651768[/C][C]-0.0207510965176798[/C][/ROW]
[ROW][C]40[/C][C]7.27[/C][C]7.27972153159661[/C][C]-0.0097215315966146[/C][/ROW]
[ROW][C]41[/C][C]7.27[/C][C]7.27455437024754[/C][C]-0.0045543702475408[/C][/ROW]
[ROW][C]42[/C][C]7.3[/C][C]7.27213364408124[/C][C]0.0278663559187615[/C][/ROW]
[ROW][C]43[/C][C]7.3[/C][C]7.31694509182607[/C][C]-0.0169450918260665[/C][/ROW]
[ROW][C]44[/C][C]7.57[/C][C]7.30793848389912[/C][C]0.262061516100883[/C][/ROW]
[ROW][C]45[/C][C]7.76[/C][C]7.7172286897292[/C][C]0.0427713102708029[/C][/ROW]
[ROW][C]46[/C][C]7.94[/C][C]7.9299623772232[/C][C]0.0100376227768004[/C][/ROW]
[ROW][C]47[/C][C]7.94[/C][C]8.1152975464744[/C][C]-0.175297546474403[/C][/ROW]
[ROW][C]48[/C][C]7.96[/C][C]8.0221238836901[/C][C]-0.0621238836900995[/C][/ROW]
[ROW][C]49[/C][C]7.96[/C][C]8.0091039703701[/C][C]-0.0491039703701022[/C][/ROW]
[ROW][C]50[/C][C]7.98[/C][C]7.9830043650496[/C][C]-0.00300436504959922[/C][/ROW]
[ROW][C]51[/C][C]7.99[/C][C]8.00140749332126[/C][C]-0.0114074933212596[/C][/ROW]
[ROW][C]52[/C][C]8[/C][C]8.0053442143005[/C][C]-0.00534421430049825[/C][/ROW]
[ROW][C]53[/C][C]8[/C][C]8.012503672427[/C][C]-0.0125036724270018[/C][/ROW]
[ROW][C]54[/C][C]8.04[/C][C]8.00585775534653[/C][C]0.0341422446534683[/C][/ROW]
[ROW][C]55[/C][C]8.04[/C][C]8.06400494596055[/C][C]-0.024004945960554[/C][/ROW]
[ROW][C]56[/C][C]8.04[/C][C]8.05124590406255[/C][C]-0.0112459040625499[/C][/ROW]
[ROW][C]57[/C][C]8.04[/C][C]8.04526851251371[/C][C]-0.00526851251370886[/C][/ROW]
[ROW][C]58[/C][C]8.04[/C][C]8.0424682074427[/C][C]-0.00246820744270337[/C][/ROW]
[ROW][C]59[/C][C]8.07[/C][C]8.04115631270959[/C][C]0.028843687290415[/C][/ROW]
[ROW][C]60[/C][C]8.07[/C][C]8.08648722889811[/C][C]-0.0164872288981108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167104&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167104&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
36.86.790.00999999999999979
46.856.795315172097850.0546848279021459
56.856.874381099242-0.0243810992419986
66.856.86142212540139-0.0114221254013902
76.856.85535106917822-0.00535106917822414
86.856.85250688381925-0.00250688381924569
96.856.85117443192638-0.00117443192638422
106.866.850550201145790.00944979885421127
116.866.86557293186581-0.00557293186581287
126.886.862610822670170.0173891773298278
136.886.89185346968499-0.0118534696849855
146.886.88555314655175-0.00555314655174577
156.916.882601553591030.0273984464089674
166.916.92716429937878-0.0171642993787824
176.916.91804117886505-0.00804117886505029
186.916.91376715391131-0.00376715391131288
196.996.911764846775540.0782351532244601
206.997.03334817712454-0.0433481771245399
216.997.01030787497002-0.0203078749700198
227.026.999513889929280.0204861100707152
237.027.04040260999343-0.020402609993428
247.057.029558271657380.020441728342619
257.057.07042340206924-0.0204234020692411
267.057.05956801238707-0.0095680123870725
277.057.0544824491399-0.00448244913990337
287.17.052099950280060.0479000497199431
297.17.12755965105578-0.0275596510557836
307.17.11291122222395-0.0129112222239538
317.17.10604868541256-0.00604868541255854
327.127.102833705019210.0171662949807949
337.137.13195788622975-0.00195788622975179
347.187.140917236003840.0390827639961637
357.247.211690397673780.028309602326221
367.247.28673743851235-0.0467374385123476
377.247.26189568560175-0.0218956856017467
387.277.250257751884370.019742248115632
397.277.29075109651768-0.0207510965176798
407.277.27972153159661-0.0097215315966146
417.277.27455437024754-0.0045543702475408
427.37.272133644081240.0278663559187615
437.37.31694509182607-0.0169450918260665
447.577.307938483899120.262061516100883
457.767.71722868972920.0427713102708029
467.947.92996237722320.0100376227768004
477.948.1152975464744-0.175297546474403
487.968.0221238836901-0.0621238836900995
497.968.0091039703701-0.0491039703701022
507.987.9830043650496-0.00300436504959922
517.998.00140749332126-0.0114074933212596
5288.0053442143005-0.00534421430049825
5388.012503672427-0.0125036724270018
548.048.005857755346530.0341422446534683
558.048.06400494596055-0.024004945960554
568.048.05124590406255-0.0112459040625499
578.048.04526851251371-0.00526851251370886
588.048.0424682074427-0.00246820744270337
598.078.041156312709590.028843687290415
608.078.08648722889811-0.0164872288981108







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
618.077723982997097.981555143726848.17389282226735
628.085447965994197.909547167938698.26134876404968
638.093171948991287.828023873084688.35832002489788
648.100895931988377.736806318465998.46498554551076
658.108619914985477.636454804947318.58078502502363
668.116343897982567.527561253561528.7051265424036
678.124067880979657.410652050482338.83748371147697
688.131791863976757.286181497163138.97740223079036
698.139515846973847.154541327012069.12449036693562
708.147239829970937.016071649917659.27840801002421
718.154963812968036.87107035980969.43885726612645
728.162687795965126.719800685240579.60557490668967

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 8.07772398299709 & 7.98155514372684 & 8.17389282226735 \tabularnewline
62 & 8.08544796599419 & 7.90954716793869 & 8.26134876404968 \tabularnewline
63 & 8.09317194899128 & 7.82802387308468 & 8.35832002489788 \tabularnewline
64 & 8.10089593198837 & 7.73680631846599 & 8.46498554551076 \tabularnewline
65 & 8.10861991498547 & 7.63645480494731 & 8.58078502502363 \tabularnewline
66 & 8.11634389798256 & 7.52756125356152 & 8.7051265424036 \tabularnewline
67 & 8.12406788097965 & 7.41065205048233 & 8.83748371147697 \tabularnewline
68 & 8.13179186397675 & 7.28618149716313 & 8.97740223079036 \tabularnewline
69 & 8.13951584697384 & 7.15454132701206 & 9.12449036693562 \tabularnewline
70 & 8.14723982997093 & 7.01607164991765 & 9.27840801002421 \tabularnewline
71 & 8.15496381296803 & 6.8710703598096 & 9.43885726612645 \tabularnewline
72 & 8.16268779596512 & 6.71980068524057 & 9.60557490668967 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167104&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]61[/C][C]8.07772398299709[/C][C]7.98155514372684[/C][C]8.17389282226735[/C][/ROW]
[ROW][C]62[/C][C]8.08544796599419[/C][C]7.90954716793869[/C][C]8.26134876404968[/C][/ROW]
[ROW][C]63[/C][C]8.09317194899128[/C][C]7.82802387308468[/C][C]8.35832002489788[/C][/ROW]
[ROW][C]64[/C][C]8.10089593198837[/C][C]7.73680631846599[/C][C]8.46498554551076[/C][/ROW]
[ROW][C]65[/C][C]8.10861991498547[/C][C]7.63645480494731[/C][C]8.58078502502363[/C][/ROW]
[ROW][C]66[/C][C]8.11634389798256[/C][C]7.52756125356152[/C][C]8.7051265424036[/C][/ROW]
[ROW][C]67[/C][C]8.12406788097965[/C][C]7.41065205048233[/C][C]8.83748371147697[/C][/ROW]
[ROW][C]68[/C][C]8.13179186397675[/C][C]7.28618149716313[/C][C]8.97740223079036[/C][/ROW]
[ROW][C]69[/C][C]8.13951584697384[/C][C]7.15454132701206[/C][C]9.12449036693562[/C][/ROW]
[ROW][C]70[/C][C]8.14723982997093[/C][C]7.01607164991765[/C][C]9.27840801002421[/C][/ROW]
[ROW][C]71[/C][C]8.15496381296803[/C][C]6.8710703598096[/C][C]9.43885726612645[/C][/ROW]
[ROW][C]72[/C][C]8.16268779596512[/C][C]6.71980068524057[/C][C]9.60557490668967[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167104&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167104&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
618.077723982997097.981555143726848.17389282226735
628.085447965994197.909547167938698.26134876404968
638.093171948991287.828023873084688.35832002489788
648.100895931988377.736806318465998.46498554551076
658.108619914985477.636454804947318.58078502502363
668.116343897982567.527561253561528.7051265424036
678.124067880979657.410652050482338.83748371147697
688.131791863976757.286181497163138.97740223079036
698.139515846973847.154541327012069.12449036693562
708.147239829970937.016071649917659.27840801002421
718.154963812968036.87107035980969.43885726612645
728.162687795965126.719800685240579.60557490668967



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')