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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 18 May 2012 08:22:47 -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/18/t1337343781o2qyck1o9fg3nbs.htm/, Retrieved Sat, 04 May 2024 02:14:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166671, Retrieved Sat, 04 May 2024 02:14:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-18 12:22:47] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
7,72
7,67
7,84
7,79
7,83
7,94
8,02
8,06
8,12
8,13
7,97
8,01
8
7,9
7,99
8,02
8,08
8,02
8,07
8,11
8,19
8,16
8,08
8,22
8,15
8,19
8,31
8,3
8,34
8,31
8,38
8,34
8,44
8,64
8,6
8,61
8,54
8,69
8,73
8,91
9,01
9,08
8,94
9,03
9,02
8,96
9,03
8,94
8,95
8,95
8,99
8,93
8,98
8,95
9,02
8,92
9,1
9,06
8,97
8,89




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166671&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166671&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166671&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.821375270652587
beta0.142888673652822
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.821375270652587 \tabularnewline
beta & 0.142888673652822 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166671&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]0.821375270652587[/C][/ROW]
[ROW][C]beta[/C][C]0.142888673652822[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166671&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166671&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
alpha0.821375270652587
beta0.142888673652822
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
37.847.620.22
47.797.776522908602420.0134770913975801
57.837.764994749092770.0650052509072347
67.947.803419901315140.136580098684858
78.027.916664617241580.103335382758421
88.068.014730925866860.0452690741331381
98.128.070416019509660.0495839804903397
108.138.13546470545666-0.00546470545666189
117.978.15465639571035-0.184656395710355
128.018.004992223823270.00500777617673087
1388.01170125122073-0.0117012512207264
147.98.00331257675842-0.103312576758418
157.997.907551321378330.0824486786216703
168.027.974046374964880.0459536250351178
178.088.015958651483960.064041348516037
188.028.08024396392215-0.0602439639221455
198.078.035373847958460.0346261520415396
208.118.07249160522710.0375083947729014
218.198.116378946515990.0736210534840076
228.168.19856888398697-0.0385688839869651
238.088.18408213553343-0.104082135533432
248.228.103568799312940.116431200687066
258.158.21784463814524-0.0678446381452389
268.198.172798258897010.0172017411029852
278.318.199625758602270.11037424139773
288.38.31593694340902-0.0159369434090237
298.348.326628801691630.0133711983083717
308.318.36296295648085-0.0529629564808491
318.388.338595867728730.041404132271273
328.348.396598977258-0.056598977258
338.448.36746200458570.072537995414292
348.648.452908385800770.187091614199232
358.68.65440432567049-0.0544043256704878
368.618.65115629675402-0.0411562967540178
378.548.65395955322825-0.113959553228254
388.698.583589126834550.106410873165446
398.738.706714454921940.023285545078064
408.918.76429560734410.145704392655897
419.018.939529202363870.0704707976361316
429.089.061238603791290.0187613962087099
438.949.1426771170757-0.202677117075709
449.039.01844426653670.0115557334632967
459.029.07153322282664-0.0515332228266363
468.969.06675426238005-0.106754262380047
479.039.004088867814680.0259111321853176
488.949.05343261342365-0.113432613423653
498.958.97500980829996-0.0250098082999628
508.958.96628002693842-0.0162800269384231
518.998.962809963113470.0271900368865339
528.938.99823629947044-0.0682362994704437
538.988.947273234471140.0327267655288637
548.958.98307971844574-0.0330797184457445
559.028.960951975303020.0590480246969776
568.929.02142586670473-0.101425866704728
579.18.938186602660440.161813397339555
589.069.09015682582922-0.0301568258292217
598.979.08090809239725-0.110908092397246
608.898.9923155125363-0.102315512536292

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 7.84 & 7.62 & 0.22 \tabularnewline
4 & 7.79 & 7.77652290860242 & 0.0134770913975801 \tabularnewline
5 & 7.83 & 7.76499474909277 & 0.0650052509072347 \tabularnewline
6 & 7.94 & 7.80341990131514 & 0.136580098684858 \tabularnewline
7 & 8.02 & 7.91666461724158 & 0.103335382758421 \tabularnewline
8 & 8.06 & 8.01473092586686 & 0.0452690741331381 \tabularnewline
9 & 8.12 & 8.07041601950966 & 0.0495839804903397 \tabularnewline
10 & 8.13 & 8.13546470545666 & -0.00546470545666189 \tabularnewline
11 & 7.97 & 8.15465639571035 & -0.184656395710355 \tabularnewline
12 & 8.01 & 8.00499222382327 & 0.00500777617673087 \tabularnewline
13 & 8 & 8.01170125122073 & -0.0117012512207264 \tabularnewline
14 & 7.9 & 8.00331257675842 & -0.103312576758418 \tabularnewline
15 & 7.99 & 7.90755132137833 & 0.0824486786216703 \tabularnewline
16 & 8.02 & 7.97404637496488 & 0.0459536250351178 \tabularnewline
17 & 8.08 & 8.01595865148396 & 0.064041348516037 \tabularnewline
18 & 8.02 & 8.08024396392215 & -0.0602439639221455 \tabularnewline
19 & 8.07 & 8.03537384795846 & 0.0346261520415396 \tabularnewline
20 & 8.11 & 8.0724916052271 & 0.0375083947729014 \tabularnewline
21 & 8.19 & 8.11637894651599 & 0.0736210534840076 \tabularnewline
22 & 8.16 & 8.19856888398697 & -0.0385688839869651 \tabularnewline
23 & 8.08 & 8.18408213553343 & -0.104082135533432 \tabularnewline
24 & 8.22 & 8.10356879931294 & 0.116431200687066 \tabularnewline
25 & 8.15 & 8.21784463814524 & -0.0678446381452389 \tabularnewline
26 & 8.19 & 8.17279825889701 & 0.0172017411029852 \tabularnewline
27 & 8.31 & 8.19962575860227 & 0.11037424139773 \tabularnewline
28 & 8.3 & 8.31593694340902 & -0.0159369434090237 \tabularnewline
29 & 8.34 & 8.32662880169163 & 0.0133711983083717 \tabularnewline
30 & 8.31 & 8.36296295648085 & -0.0529629564808491 \tabularnewline
31 & 8.38 & 8.33859586772873 & 0.041404132271273 \tabularnewline
32 & 8.34 & 8.396598977258 & -0.056598977258 \tabularnewline
33 & 8.44 & 8.3674620045857 & 0.072537995414292 \tabularnewline
34 & 8.64 & 8.45290838580077 & 0.187091614199232 \tabularnewline
35 & 8.6 & 8.65440432567049 & -0.0544043256704878 \tabularnewline
36 & 8.61 & 8.65115629675402 & -0.0411562967540178 \tabularnewline
37 & 8.54 & 8.65395955322825 & -0.113959553228254 \tabularnewline
38 & 8.69 & 8.58358912683455 & 0.106410873165446 \tabularnewline
39 & 8.73 & 8.70671445492194 & 0.023285545078064 \tabularnewline
40 & 8.91 & 8.7642956073441 & 0.145704392655897 \tabularnewline
41 & 9.01 & 8.93952920236387 & 0.0704707976361316 \tabularnewline
42 & 9.08 & 9.06123860379129 & 0.0187613962087099 \tabularnewline
43 & 8.94 & 9.1426771170757 & -0.202677117075709 \tabularnewline
44 & 9.03 & 9.0184442665367 & 0.0115557334632967 \tabularnewline
45 & 9.02 & 9.07153322282664 & -0.0515332228266363 \tabularnewline
46 & 8.96 & 9.06675426238005 & -0.106754262380047 \tabularnewline
47 & 9.03 & 9.00408886781468 & 0.0259111321853176 \tabularnewline
48 & 8.94 & 9.05343261342365 & -0.113432613423653 \tabularnewline
49 & 8.95 & 8.97500980829996 & -0.0250098082999628 \tabularnewline
50 & 8.95 & 8.96628002693842 & -0.0162800269384231 \tabularnewline
51 & 8.99 & 8.96280996311347 & 0.0271900368865339 \tabularnewline
52 & 8.93 & 8.99823629947044 & -0.0682362994704437 \tabularnewline
53 & 8.98 & 8.94727323447114 & 0.0327267655288637 \tabularnewline
54 & 8.95 & 8.98307971844574 & -0.0330797184457445 \tabularnewline
55 & 9.02 & 8.96095197530302 & 0.0590480246969776 \tabularnewline
56 & 8.92 & 9.02142586670473 & -0.101425866704728 \tabularnewline
57 & 9.1 & 8.93818660266044 & 0.161813397339555 \tabularnewline
58 & 9.06 & 9.09015682582922 & -0.0301568258292217 \tabularnewline
59 & 8.97 & 9.08090809239725 & -0.110908092397246 \tabularnewline
60 & 8.89 & 8.9923155125363 & -0.102315512536292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166671&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]7.84[/C][C]7.62[/C][C]0.22[/C][/ROW]
[ROW][C]4[/C][C]7.79[/C][C]7.77652290860242[/C][C]0.0134770913975801[/C][/ROW]
[ROW][C]5[/C][C]7.83[/C][C]7.76499474909277[/C][C]0.0650052509072347[/C][/ROW]
[ROW][C]6[/C][C]7.94[/C][C]7.80341990131514[/C][C]0.136580098684858[/C][/ROW]
[ROW][C]7[/C][C]8.02[/C][C]7.91666461724158[/C][C]0.103335382758421[/C][/ROW]
[ROW][C]8[/C][C]8.06[/C][C]8.01473092586686[/C][C]0.0452690741331381[/C][/ROW]
[ROW][C]9[/C][C]8.12[/C][C]8.07041601950966[/C][C]0.0495839804903397[/C][/ROW]
[ROW][C]10[/C][C]8.13[/C][C]8.13546470545666[/C][C]-0.00546470545666189[/C][/ROW]
[ROW][C]11[/C][C]7.97[/C][C]8.15465639571035[/C][C]-0.184656395710355[/C][/ROW]
[ROW][C]12[/C][C]8.01[/C][C]8.00499222382327[/C][C]0.00500777617673087[/C][/ROW]
[ROW][C]13[/C][C]8[/C][C]8.01170125122073[/C][C]-0.0117012512207264[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]8.00331257675842[/C][C]-0.103312576758418[/C][/ROW]
[ROW][C]15[/C][C]7.99[/C][C]7.90755132137833[/C][C]0.0824486786216703[/C][/ROW]
[ROW][C]16[/C][C]8.02[/C][C]7.97404637496488[/C][C]0.0459536250351178[/C][/ROW]
[ROW][C]17[/C][C]8.08[/C][C]8.01595865148396[/C][C]0.064041348516037[/C][/ROW]
[ROW][C]18[/C][C]8.02[/C][C]8.08024396392215[/C][C]-0.0602439639221455[/C][/ROW]
[ROW][C]19[/C][C]8.07[/C][C]8.03537384795846[/C][C]0.0346261520415396[/C][/ROW]
[ROW][C]20[/C][C]8.11[/C][C]8.0724916052271[/C][C]0.0375083947729014[/C][/ROW]
[ROW][C]21[/C][C]8.19[/C][C]8.11637894651599[/C][C]0.0736210534840076[/C][/ROW]
[ROW][C]22[/C][C]8.16[/C][C]8.19856888398697[/C][C]-0.0385688839869651[/C][/ROW]
[ROW][C]23[/C][C]8.08[/C][C]8.18408213553343[/C][C]-0.104082135533432[/C][/ROW]
[ROW][C]24[/C][C]8.22[/C][C]8.10356879931294[/C][C]0.116431200687066[/C][/ROW]
[ROW][C]25[/C][C]8.15[/C][C]8.21784463814524[/C][C]-0.0678446381452389[/C][/ROW]
[ROW][C]26[/C][C]8.19[/C][C]8.17279825889701[/C][C]0.0172017411029852[/C][/ROW]
[ROW][C]27[/C][C]8.31[/C][C]8.19962575860227[/C][C]0.11037424139773[/C][/ROW]
[ROW][C]28[/C][C]8.3[/C][C]8.31593694340902[/C][C]-0.0159369434090237[/C][/ROW]
[ROW][C]29[/C][C]8.34[/C][C]8.32662880169163[/C][C]0.0133711983083717[/C][/ROW]
[ROW][C]30[/C][C]8.31[/C][C]8.36296295648085[/C][C]-0.0529629564808491[/C][/ROW]
[ROW][C]31[/C][C]8.38[/C][C]8.33859586772873[/C][C]0.041404132271273[/C][/ROW]
[ROW][C]32[/C][C]8.34[/C][C]8.396598977258[/C][C]-0.056598977258[/C][/ROW]
[ROW][C]33[/C][C]8.44[/C][C]8.3674620045857[/C][C]0.072537995414292[/C][/ROW]
[ROW][C]34[/C][C]8.64[/C][C]8.45290838580077[/C][C]0.187091614199232[/C][/ROW]
[ROW][C]35[/C][C]8.6[/C][C]8.65440432567049[/C][C]-0.0544043256704878[/C][/ROW]
[ROW][C]36[/C][C]8.61[/C][C]8.65115629675402[/C][C]-0.0411562967540178[/C][/ROW]
[ROW][C]37[/C][C]8.54[/C][C]8.65395955322825[/C][C]-0.113959553228254[/C][/ROW]
[ROW][C]38[/C][C]8.69[/C][C]8.58358912683455[/C][C]0.106410873165446[/C][/ROW]
[ROW][C]39[/C][C]8.73[/C][C]8.70671445492194[/C][C]0.023285545078064[/C][/ROW]
[ROW][C]40[/C][C]8.91[/C][C]8.7642956073441[/C][C]0.145704392655897[/C][/ROW]
[ROW][C]41[/C][C]9.01[/C][C]8.93952920236387[/C][C]0.0704707976361316[/C][/ROW]
[ROW][C]42[/C][C]9.08[/C][C]9.06123860379129[/C][C]0.0187613962087099[/C][/ROW]
[ROW][C]43[/C][C]8.94[/C][C]9.1426771170757[/C][C]-0.202677117075709[/C][/ROW]
[ROW][C]44[/C][C]9.03[/C][C]9.0184442665367[/C][C]0.0115557334632967[/C][/ROW]
[ROW][C]45[/C][C]9.02[/C][C]9.07153322282664[/C][C]-0.0515332228266363[/C][/ROW]
[ROW][C]46[/C][C]8.96[/C][C]9.06675426238005[/C][C]-0.106754262380047[/C][/ROW]
[ROW][C]47[/C][C]9.03[/C][C]9.00408886781468[/C][C]0.0259111321853176[/C][/ROW]
[ROW][C]48[/C][C]8.94[/C][C]9.05343261342365[/C][C]-0.113432613423653[/C][/ROW]
[ROW][C]49[/C][C]8.95[/C][C]8.97500980829996[/C][C]-0.0250098082999628[/C][/ROW]
[ROW][C]50[/C][C]8.95[/C][C]8.96628002693842[/C][C]-0.0162800269384231[/C][/ROW]
[ROW][C]51[/C][C]8.99[/C][C]8.96280996311347[/C][C]0.0271900368865339[/C][/ROW]
[ROW][C]52[/C][C]8.93[/C][C]8.99823629947044[/C][C]-0.0682362994704437[/C][/ROW]
[ROW][C]53[/C][C]8.98[/C][C]8.94727323447114[/C][C]0.0327267655288637[/C][/ROW]
[ROW][C]54[/C][C]8.95[/C][C]8.98307971844574[/C][C]-0.0330797184457445[/C][/ROW]
[ROW][C]55[/C][C]9.02[/C][C]8.96095197530302[/C][C]0.0590480246969776[/C][/ROW]
[ROW][C]56[/C][C]8.92[/C][C]9.02142586670473[/C][C]-0.101425866704728[/C][/ROW]
[ROW][C]57[/C][C]9.1[/C][C]8.93818660266044[/C][C]0.161813397339555[/C][/ROW]
[ROW][C]58[/C][C]9.06[/C][C]9.09015682582922[/C][C]-0.0301568258292217[/C][/ROW]
[ROW][C]59[/C][C]8.97[/C][C]9.08090809239725[/C][C]-0.110908092397246[/C][/ROW]
[ROW][C]60[/C][C]8.89[/C][C]8.9923155125363[/C][C]-0.102315512536292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166671&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166671&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
37.847.620.22
47.797.776522908602420.0134770913975801
57.837.764994749092770.0650052509072347
67.947.803419901315140.136580098684858
78.027.916664617241580.103335382758421
88.068.014730925866860.0452690741331381
98.128.070416019509660.0495839804903397
108.138.13546470545666-0.00546470545666189
117.978.15465639571035-0.184656395710355
128.018.004992223823270.00500777617673087
1388.01170125122073-0.0117012512207264
147.98.00331257675842-0.103312576758418
157.997.907551321378330.0824486786216703
168.027.974046374964880.0459536250351178
178.088.015958651483960.064041348516037
188.028.08024396392215-0.0602439639221455
198.078.035373847958460.0346261520415396
208.118.07249160522710.0375083947729014
218.198.116378946515990.0736210534840076
228.168.19856888398697-0.0385688839869651
238.088.18408213553343-0.104082135533432
248.228.103568799312940.116431200687066
258.158.21784463814524-0.0678446381452389
268.198.172798258897010.0172017411029852
278.318.199625758602270.11037424139773
288.38.31593694340902-0.0159369434090237
298.348.326628801691630.0133711983083717
308.318.36296295648085-0.0529629564808491
318.388.338595867728730.041404132271273
328.348.396598977258-0.056598977258
338.448.36746200458570.072537995414292
348.648.452908385800770.187091614199232
358.68.65440432567049-0.0544043256704878
368.618.65115629675402-0.0411562967540178
378.548.65395955322825-0.113959553228254
388.698.583589126834550.106410873165446
398.738.706714454921940.023285545078064
408.918.76429560734410.145704392655897
419.018.939529202363870.0704707976361316
429.089.061238603791290.0187613962087099
438.949.1426771170757-0.202677117075709
449.039.01844426653670.0115557334632967
459.029.07153322282664-0.0515332228266363
468.969.06675426238005-0.106754262380047
479.039.004088867814680.0259111321853176
488.949.05343261342365-0.113432613423653
498.958.97500980829996-0.0250098082999628
508.958.96628002693842-0.0162800269384231
518.998.962809963113470.0271900368865339
528.938.99823629947044-0.0682362994704437
538.988.947273234471140.0327267655288637
548.958.98307971844574-0.0330797184457445
559.028.960951975303020.0590480246969776
568.929.02142586670473-0.101425866704728
579.18.938186602660440.161813397339555
589.069.09015682582922-0.0301568258292217
598.979.08090809239725-0.110908092397246
608.898.9923155125363-0.102315512536292







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
618.898772382339598.726073337249089.0714714274301
628.889268683944348.65239800063269.12613936725608
638.879764985549098.580811365633759.17871860546442
648.870261287153848.509092002126129.23143057218155
658.860757588758598.436329348767489.28518582874969
668.851253890363338.362088115035029.34041966569165
678.841750191968098.286145673872919.39735471006326
688.832246493572838.208387007184969.4561059799607
698.822742795177588.128756020111829.51672957024335
708.813239096782338.047230617921689.57924757564298
718.803735398387087.96380900313259.64366179364167
728.794231699991837.878501730638669.709961669345

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 8.89877238233959 & 8.72607333724908 & 9.0714714274301 \tabularnewline
62 & 8.88926868394434 & 8.6523980006326 & 9.12613936725608 \tabularnewline
63 & 8.87976498554909 & 8.58081136563375 & 9.17871860546442 \tabularnewline
64 & 8.87026128715384 & 8.50909200212612 & 9.23143057218155 \tabularnewline
65 & 8.86075758875859 & 8.43632934876748 & 9.28518582874969 \tabularnewline
66 & 8.85125389036333 & 8.36208811503502 & 9.34041966569165 \tabularnewline
67 & 8.84175019196809 & 8.28614567387291 & 9.39735471006326 \tabularnewline
68 & 8.83224649357283 & 8.20838700718496 & 9.4561059799607 \tabularnewline
69 & 8.82274279517758 & 8.12875602011182 & 9.51672957024335 \tabularnewline
70 & 8.81323909678233 & 8.04723061792168 & 9.57924757564298 \tabularnewline
71 & 8.80373539838708 & 7.9638090031325 & 9.64366179364167 \tabularnewline
72 & 8.79423169999183 & 7.87850173063866 & 9.709961669345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166671&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]8.89877238233959[/C][C]8.72607333724908[/C][C]9.0714714274301[/C][/ROW]
[ROW][C]62[/C][C]8.88926868394434[/C][C]8.6523980006326[/C][C]9.12613936725608[/C][/ROW]
[ROW][C]63[/C][C]8.87976498554909[/C][C]8.58081136563375[/C][C]9.17871860546442[/C][/ROW]
[ROW][C]64[/C][C]8.87026128715384[/C][C]8.50909200212612[/C][C]9.23143057218155[/C][/ROW]
[ROW][C]65[/C][C]8.86075758875859[/C][C]8.43632934876748[/C][C]9.28518582874969[/C][/ROW]
[ROW][C]66[/C][C]8.85125389036333[/C][C]8.36208811503502[/C][C]9.34041966569165[/C][/ROW]
[ROW][C]67[/C][C]8.84175019196809[/C][C]8.28614567387291[/C][C]9.39735471006326[/C][/ROW]
[ROW][C]68[/C][C]8.83224649357283[/C][C]8.20838700718496[/C][C]9.4561059799607[/C][/ROW]
[ROW][C]69[/C][C]8.82274279517758[/C][C]8.12875602011182[/C][C]9.51672957024335[/C][/ROW]
[ROW][C]70[/C][C]8.81323909678233[/C][C]8.04723061792168[/C][C]9.57924757564298[/C][/ROW]
[ROW][C]71[/C][C]8.80373539838708[/C][C]7.9638090031325[/C][C]9.64366179364167[/C][/ROW]
[ROW][C]72[/C][C]8.79423169999183[/C][C]7.87850173063866[/C][C]9.709961669345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166671&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166671&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
618.898772382339598.726073337249089.0714714274301
628.889268683944348.65239800063269.12613936725608
638.879764985549098.580811365633759.17871860546442
648.870261287153848.509092002126129.23143057218155
658.860757588758598.436329348767489.28518582874969
668.851253890363338.362088115035029.34041966569165
678.841750191968098.286145673872919.39735471006326
688.832246493572838.208387007184969.4561059799607
698.822742795177588.128756020111829.51672957024335
708.813239096782338.047230617921689.57924757564298
718.803735398387087.96380900313259.64366179364167
728.794231699991837.878501730638669.709961669345



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')