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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, 03 Dec 2009 18:00:44 -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/2009/Dec/04/t1259888490zjixejb2llxjy2z.htm/, Retrieved Sat, 27 Apr 2024 17:51:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63162, Retrieved Sat, 27 Apr 2024 17:51:13 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [WS9] [2009-12-04 01:00:44] [557d56ec4b06cd0135c259898de8ce95] [Current]
-   PD        [Exponential Smoothing] [Exponential smoot...] [2009-12-04 19:29:39] [4395c69e961f9a13a0559fd2f0a72538]
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Dataseries X:
10284,5
12792
12823,61538
13845,66667
15335,63636
11188,5
13633,25
12298,46667
15353,63636
12696,15385
12213,93333
13683,72727
11214,14286
13950,23077
11179,13333
11801,875
11188,82353
16456,27273
11110,0625
16530,69231
10038,41176
11681,25
11148,88235
8631
9386,444444
9764,736842
12043,75
12948,06667
10987,125
11648,3125
10633,35294
10219,3
9037,6
10296,31579
11705,41176
10681,94444
9362,947368
11306,35294
10984,45
10062,61905
8118,583333
8867,48
8346,72
8529,307692
10697,18182
8591,84
8695,607143
8125,571429
7009,758621
7883,466667
7527,645161
6763,758621
6682,333333
7855,681818
6738,88
7895,434783
6361,884615
6935,956522
8344,454545
9107,944444




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63162&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63162&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63162&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0122813786912377
beta1
gamma0.307319000739082

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0122813786912377 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.307319000739082 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63162&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]0.0122813786912377[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.307319000739082[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63162&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63162&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
alpha0.0122813786912377
beta1
gamma0.307319000739082







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311214.1428611317.8707366739-103.727876673851
1413950.2307713936.393013925713.8377560742665
1511179.1333311156.090740546123.0425894539458
1611801.87511968.9629018635-167.087901863466
1711188.8235311369.3560351760-180.532505175972
1816456.2727316980.4703000559-524.197570055858
1911110.062513168.7856608462-2058.72316084616
2016530.6923111691.67222481754839.02008518248
2110038.4117614659.1242517512-4620.71249175119
2211681.2512142.2725291783-461.022529178315
2311148.8823511832.7142237104-683.831873710384
24863113100.0922870866-4469.09228708658
259386.44444410442.0305732304-1055.5861292304
269764.73684212771.7203402321-3006.98349823212
2712043.7510077.41318736121966.33681263881
2812948.0666710681.09538692512266.97128307485
2910987.12510097.4583126012889.666687398842
3011648.312514944.1062254668-3295.79372546682
3110633.3529411025.2312092342-391.878269234188
3210219.311498.7853851808-1279.48538518083
339037.611354.2387879176-2316.6387879176
3410296.3157910169.619844963126.695945036998
3511705.411769735.93771728321969.4740427168
3610681.944449770.63335280387911.311087196129
379362.9473688435.79129498913927.156073010865
3811306.352949892.656167662431413.69677233757
3910984.458975.675488099642008.77451190036
4010062.619059598.36072023008464.258329769917
418118.5833338751.10972783345-632.526394833453
428867.4811741.3831926416-2873.90319264157
438346.729177.31323726594-830.59323726594
448529.3076929330.20333134276-800.895639342758
4510697.181828937.036598893671760.14522110633
468591.848643.8730759575-52.0330759574972
478695.6071438781.57830909206-85.9711660920602
488125.5714298528.63927066995-403.067841669952
497009.7586217384.15879524876-374.400174248764
507883.4666678704.91215291219-821.445485912192
517527.6451618015.4737319519-487.828570951894
526763.7586218042.31200932614-1278.55338832614
536682.3333336964.31746764857-281.984134648573
547855.6818188738.03916057733-882.357342577327
556738.887111.96439923036-373.084399230363
567895.4347837166.41343459764729.021348402359
576361.8846157419.61285898916-1057.72824398916
586935.9565226640.7472986639295.209223336094
598344.4545456652.045117347231692.40942765277
609107.9444446338.767529778682769.17691422132

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 11214.14286 & 11317.8707366739 & -103.727876673851 \tabularnewline
14 & 13950.23077 & 13936.3930139257 & 13.8377560742665 \tabularnewline
15 & 11179.13333 & 11156.0907405461 & 23.0425894539458 \tabularnewline
16 & 11801.875 & 11968.9629018635 & -167.087901863466 \tabularnewline
17 & 11188.82353 & 11369.3560351760 & -180.532505175972 \tabularnewline
18 & 16456.27273 & 16980.4703000559 & -524.197570055858 \tabularnewline
19 & 11110.0625 & 13168.7856608462 & -2058.72316084616 \tabularnewline
20 & 16530.69231 & 11691.6722248175 & 4839.02008518248 \tabularnewline
21 & 10038.41176 & 14659.1242517512 & -4620.71249175119 \tabularnewline
22 & 11681.25 & 12142.2725291783 & -461.022529178315 \tabularnewline
23 & 11148.88235 & 11832.7142237104 & -683.831873710384 \tabularnewline
24 & 8631 & 13100.0922870866 & -4469.09228708658 \tabularnewline
25 & 9386.444444 & 10442.0305732304 & -1055.5861292304 \tabularnewline
26 & 9764.736842 & 12771.7203402321 & -3006.98349823212 \tabularnewline
27 & 12043.75 & 10077.4131873612 & 1966.33681263881 \tabularnewline
28 & 12948.06667 & 10681.0953869251 & 2266.97128307485 \tabularnewline
29 & 10987.125 & 10097.4583126012 & 889.666687398842 \tabularnewline
30 & 11648.3125 & 14944.1062254668 & -3295.79372546682 \tabularnewline
31 & 10633.35294 & 11025.2312092342 & -391.878269234188 \tabularnewline
32 & 10219.3 & 11498.7853851808 & -1279.48538518083 \tabularnewline
33 & 9037.6 & 11354.2387879176 & -2316.6387879176 \tabularnewline
34 & 10296.31579 & 10169.619844963 & 126.695945036998 \tabularnewline
35 & 11705.41176 & 9735.9377172832 & 1969.4740427168 \tabularnewline
36 & 10681.94444 & 9770.63335280387 & 911.311087196129 \tabularnewline
37 & 9362.947368 & 8435.79129498913 & 927.156073010865 \tabularnewline
38 & 11306.35294 & 9892.65616766243 & 1413.69677233757 \tabularnewline
39 & 10984.45 & 8975.67548809964 & 2008.77451190036 \tabularnewline
40 & 10062.61905 & 9598.36072023008 & 464.258329769917 \tabularnewline
41 & 8118.583333 & 8751.10972783345 & -632.526394833453 \tabularnewline
42 & 8867.48 & 11741.3831926416 & -2873.90319264157 \tabularnewline
43 & 8346.72 & 9177.31323726594 & -830.59323726594 \tabularnewline
44 & 8529.307692 & 9330.20333134276 & -800.895639342758 \tabularnewline
45 & 10697.18182 & 8937.03659889367 & 1760.14522110633 \tabularnewline
46 & 8591.84 & 8643.8730759575 & -52.0330759574972 \tabularnewline
47 & 8695.607143 & 8781.57830909206 & -85.9711660920602 \tabularnewline
48 & 8125.571429 & 8528.63927066995 & -403.067841669952 \tabularnewline
49 & 7009.758621 & 7384.15879524876 & -374.400174248764 \tabularnewline
50 & 7883.466667 & 8704.91215291219 & -821.445485912192 \tabularnewline
51 & 7527.645161 & 8015.4737319519 & -487.828570951894 \tabularnewline
52 & 6763.758621 & 8042.31200932614 & -1278.55338832614 \tabularnewline
53 & 6682.333333 & 6964.31746764857 & -281.984134648573 \tabularnewline
54 & 7855.681818 & 8738.03916057733 & -882.357342577327 \tabularnewline
55 & 6738.88 & 7111.96439923036 & -373.084399230363 \tabularnewline
56 & 7895.434783 & 7166.41343459764 & 729.021348402359 \tabularnewline
57 & 6361.884615 & 7419.61285898916 & -1057.72824398916 \tabularnewline
58 & 6935.956522 & 6640.7472986639 & 295.209223336094 \tabularnewline
59 & 8344.454545 & 6652.04511734723 & 1692.40942765277 \tabularnewline
60 & 9107.944444 & 6338.76752977868 & 2769.17691422132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63162&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]13[/C][C]11214.14286[/C][C]11317.8707366739[/C][C]-103.727876673851[/C][/ROW]
[ROW][C]14[/C][C]13950.23077[/C][C]13936.3930139257[/C][C]13.8377560742665[/C][/ROW]
[ROW][C]15[/C][C]11179.13333[/C][C]11156.0907405461[/C][C]23.0425894539458[/C][/ROW]
[ROW][C]16[/C][C]11801.875[/C][C]11968.9629018635[/C][C]-167.087901863466[/C][/ROW]
[ROW][C]17[/C][C]11188.82353[/C][C]11369.3560351760[/C][C]-180.532505175972[/C][/ROW]
[ROW][C]18[/C][C]16456.27273[/C][C]16980.4703000559[/C][C]-524.197570055858[/C][/ROW]
[ROW][C]19[/C][C]11110.0625[/C][C]13168.7856608462[/C][C]-2058.72316084616[/C][/ROW]
[ROW][C]20[/C][C]16530.69231[/C][C]11691.6722248175[/C][C]4839.02008518248[/C][/ROW]
[ROW][C]21[/C][C]10038.41176[/C][C]14659.1242517512[/C][C]-4620.71249175119[/C][/ROW]
[ROW][C]22[/C][C]11681.25[/C][C]12142.2725291783[/C][C]-461.022529178315[/C][/ROW]
[ROW][C]23[/C][C]11148.88235[/C][C]11832.7142237104[/C][C]-683.831873710384[/C][/ROW]
[ROW][C]24[/C][C]8631[/C][C]13100.0922870866[/C][C]-4469.09228708658[/C][/ROW]
[ROW][C]25[/C][C]9386.444444[/C][C]10442.0305732304[/C][C]-1055.5861292304[/C][/ROW]
[ROW][C]26[/C][C]9764.736842[/C][C]12771.7203402321[/C][C]-3006.98349823212[/C][/ROW]
[ROW][C]27[/C][C]12043.75[/C][C]10077.4131873612[/C][C]1966.33681263881[/C][/ROW]
[ROW][C]28[/C][C]12948.06667[/C][C]10681.0953869251[/C][C]2266.97128307485[/C][/ROW]
[ROW][C]29[/C][C]10987.125[/C][C]10097.4583126012[/C][C]889.666687398842[/C][/ROW]
[ROW][C]30[/C][C]11648.3125[/C][C]14944.1062254668[/C][C]-3295.79372546682[/C][/ROW]
[ROW][C]31[/C][C]10633.35294[/C][C]11025.2312092342[/C][C]-391.878269234188[/C][/ROW]
[ROW][C]32[/C][C]10219.3[/C][C]11498.7853851808[/C][C]-1279.48538518083[/C][/ROW]
[ROW][C]33[/C][C]9037.6[/C][C]11354.2387879176[/C][C]-2316.6387879176[/C][/ROW]
[ROW][C]34[/C][C]10296.31579[/C][C]10169.619844963[/C][C]126.695945036998[/C][/ROW]
[ROW][C]35[/C][C]11705.41176[/C][C]9735.9377172832[/C][C]1969.4740427168[/C][/ROW]
[ROW][C]36[/C][C]10681.94444[/C][C]9770.63335280387[/C][C]911.311087196129[/C][/ROW]
[ROW][C]37[/C][C]9362.947368[/C][C]8435.79129498913[/C][C]927.156073010865[/C][/ROW]
[ROW][C]38[/C][C]11306.35294[/C][C]9892.65616766243[/C][C]1413.69677233757[/C][/ROW]
[ROW][C]39[/C][C]10984.45[/C][C]8975.67548809964[/C][C]2008.77451190036[/C][/ROW]
[ROW][C]40[/C][C]10062.61905[/C][C]9598.36072023008[/C][C]464.258329769917[/C][/ROW]
[ROW][C]41[/C][C]8118.583333[/C][C]8751.10972783345[/C][C]-632.526394833453[/C][/ROW]
[ROW][C]42[/C][C]8867.48[/C][C]11741.3831926416[/C][C]-2873.90319264157[/C][/ROW]
[ROW][C]43[/C][C]8346.72[/C][C]9177.31323726594[/C][C]-830.59323726594[/C][/ROW]
[ROW][C]44[/C][C]8529.307692[/C][C]9330.20333134276[/C][C]-800.895639342758[/C][/ROW]
[ROW][C]45[/C][C]10697.18182[/C][C]8937.03659889367[/C][C]1760.14522110633[/C][/ROW]
[ROW][C]46[/C][C]8591.84[/C][C]8643.8730759575[/C][C]-52.0330759574972[/C][/ROW]
[ROW][C]47[/C][C]8695.607143[/C][C]8781.57830909206[/C][C]-85.9711660920602[/C][/ROW]
[ROW][C]48[/C][C]8125.571429[/C][C]8528.63927066995[/C][C]-403.067841669952[/C][/ROW]
[ROW][C]49[/C][C]7009.758621[/C][C]7384.15879524876[/C][C]-374.400174248764[/C][/ROW]
[ROW][C]50[/C][C]7883.466667[/C][C]8704.91215291219[/C][C]-821.445485912192[/C][/ROW]
[ROW][C]51[/C][C]7527.645161[/C][C]8015.4737319519[/C][C]-487.828570951894[/C][/ROW]
[ROW][C]52[/C][C]6763.758621[/C][C]8042.31200932614[/C][C]-1278.55338832614[/C][/ROW]
[ROW][C]53[/C][C]6682.333333[/C][C]6964.31746764857[/C][C]-281.984134648573[/C][/ROW]
[ROW][C]54[/C][C]7855.681818[/C][C]8738.03916057733[/C][C]-882.357342577327[/C][/ROW]
[ROW][C]55[/C][C]6738.88[/C][C]7111.96439923036[/C][C]-373.084399230363[/C][/ROW]
[ROW][C]56[/C][C]7895.434783[/C][C]7166.41343459764[/C][C]729.021348402359[/C][/ROW]
[ROW][C]57[/C][C]6361.884615[/C][C]7419.61285898916[/C][C]-1057.72824398916[/C][/ROW]
[ROW][C]58[/C][C]6935.956522[/C][C]6640.7472986639[/C][C]295.209223336094[/C][/ROW]
[ROW][C]59[/C][C]8344.454545[/C][C]6652.04511734723[/C][C]1692.40942765277[/C][/ROW]
[ROW][C]60[/C][C]9107.944444[/C][C]6338.76752977868[/C][C]2769.17691422132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63162&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63162&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
1311214.1428611317.8707366739-103.727876673851
1413950.2307713936.393013925713.8377560742665
1511179.1333311156.090740546123.0425894539458
1611801.87511968.9629018635-167.087901863466
1711188.8235311369.3560351760-180.532505175972
1816456.2727316980.4703000559-524.197570055858
1911110.062513168.7856608462-2058.72316084616
2016530.6923111691.67222481754839.02008518248
2110038.4117614659.1242517512-4620.71249175119
2211681.2512142.2725291783-461.022529178315
2311148.8823511832.7142237104-683.831873710384
24863113100.0922870866-4469.09228708658
259386.44444410442.0305732304-1055.5861292304
269764.73684212771.7203402321-3006.98349823212
2712043.7510077.41318736121966.33681263881
2812948.0666710681.09538692512266.97128307485
2910987.12510097.4583126012889.666687398842
3011648.312514944.1062254668-3295.79372546682
3110633.3529411025.2312092342-391.878269234188
3210219.311498.7853851808-1279.48538518083
339037.611354.2387879176-2316.6387879176
3410296.3157910169.619844963126.695945036998
3511705.411769735.93771728321969.4740427168
3610681.944449770.63335280387911.311087196129
379362.9473688435.79129498913927.156073010865
3811306.352949892.656167662431413.69677233757
3910984.458975.675488099642008.77451190036
4010062.619059598.36072023008464.258329769917
418118.5833338751.10972783345-632.526394833453
428867.4811741.3831926416-2873.90319264157
438346.729177.31323726594-830.59323726594
448529.3076929330.20333134276-800.895639342758
4510697.181828937.036598893671760.14522110633
468591.848643.8730759575-52.0330759574972
478695.6071438781.57830909206-85.9711660920602
488125.5714298528.63927066995-403.067841669952
497009.7586217384.15879524876-374.400174248764
507883.4666678704.91215291219-821.445485912192
517527.6451618015.4737319519-487.828570951894
526763.7586218042.31200932614-1278.55338832614
536682.3333336964.31746764857-281.984134648573
547855.6818188738.03916057733-882.357342577327
556738.887111.96439923036-373.084399230363
567895.4347837166.41343459764729.021348402359
576361.8846157419.61285898916-1057.72824398916
586935.9565226640.7472986639295.209223336094
598344.4545456652.045117347231692.40942765277
609107.9444446338.767529778682769.17691422132







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
615487.304253885944394.047924265956580.56058350593
626356.386147002575258.505821374027454.26647263112
635900.201912415374794.645057200457005.75876763029
645727.334116577894608.055820349886846.61241280591
655152.363540683284019.049079900656285.6780014659
666343.910841948065147.93866928537539.88301461081
675252.305013909554046.76096144436457.8490663748
685555.678287778254276.902526686376834.45404887014
695332.447369070513995.475276082336669.41946205868
705075.583436090873677.555155134986473.61171704676
715408.518578653743864.336529850646952.70062745684
725391.113124178664128.193684866396654.03256349093

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 5487.30425388594 & 4394.04792426595 & 6580.56058350593 \tabularnewline
62 & 6356.38614700257 & 5258.50582137402 & 7454.26647263112 \tabularnewline
63 & 5900.20191241537 & 4794.64505720045 & 7005.75876763029 \tabularnewline
64 & 5727.33411657789 & 4608.05582034988 & 6846.61241280591 \tabularnewline
65 & 5152.36354068328 & 4019.04907990065 & 6285.6780014659 \tabularnewline
66 & 6343.91084194806 & 5147.9386692853 & 7539.88301461081 \tabularnewline
67 & 5252.30501390955 & 4046.7609614443 & 6457.8490663748 \tabularnewline
68 & 5555.67828777825 & 4276.90252668637 & 6834.45404887014 \tabularnewline
69 & 5332.44736907051 & 3995.47527608233 & 6669.41946205868 \tabularnewline
70 & 5075.58343609087 & 3677.55515513498 & 6473.61171704676 \tabularnewline
71 & 5408.51857865374 & 3864.33652985064 & 6952.70062745684 \tabularnewline
72 & 5391.11312417866 & 4128.19368486639 & 6654.03256349093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63162&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]5487.30425388594[/C][C]4394.04792426595[/C][C]6580.56058350593[/C][/ROW]
[ROW][C]62[/C][C]6356.38614700257[/C][C]5258.50582137402[/C][C]7454.26647263112[/C][/ROW]
[ROW][C]63[/C][C]5900.20191241537[/C][C]4794.64505720045[/C][C]7005.75876763029[/C][/ROW]
[ROW][C]64[/C][C]5727.33411657789[/C][C]4608.05582034988[/C][C]6846.61241280591[/C][/ROW]
[ROW][C]65[/C][C]5152.36354068328[/C][C]4019.04907990065[/C][C]6285.6780014659[/C][/ROW]
[ROW][C]66[/C][C]6343.91084194806[/C][C]5147.9386692853[/C][C]7539.88301461081[/C][/ROW]
[ROW][C]67[/C][C]5252.30501390955[/C][C]4046.7609614443[/C][C]6457.8490663748[/C][/ROW]
[ROW][C]68[/C][C]5555.67828777825[/C][C]4276.90252668637[/C][C]6834.45404887014[/C][/ROW]
[ROW][C]69[/C][C]5332.44736907051[/C][C]3995.47527608233[/C][C]6669.41946205868[/C][/ROW]
[ROW][C]70[/C][C]5075.58343609087[/C][C]3677.55515513498[/C][C]6473.61171704676[/C][/ROW]
[ROW][C]71[/C][C]5408.51857865374[/C][C]3864.33652985064[/C][C]6952.70062745684[/C][/ROW]
[ROW][C]72[/C][C]5391.11312417866[/C][C]4128.19368486639[/C][C]6654.03256349093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63162&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63162&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
615487.304253885944394.047924265956580.56058350593
626356.386147002575258.505821374027454.26647263112
635900.201912415374794.645057200457005.75876763029
645727.334116577894608.055820349886846.61241280591
655152.363540683284019.049079900656285.6780014659
666343.910841948065147.93866928537539.88301461081
675252.305013909554046.76096144436457.8490663748
685555.678287778254276.902526686376834.45404887014
695332.447369070513995.475276082336669.41946205868
705075.583436090873677.555155134986473.61171704676
715408.518578653743864.336529850646952.70062745684
725391.113124178664128.193684866396654.03256349093



Parameters (Session):
par1 = FALSE ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')