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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Aug 2013 15:07:07 -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/2013/Aug/19/t1376939501fmeb78i3kmtwlm9.htm/, Retrieved Thu, 02 May 2024 16:59:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211225, Retrieved Thu, 02 May 2024 16:59:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2013-08-19 19:07:07] [084e0343a0486ff05530df6c705c8bb4] [Current]
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Dataseries X:
12960
12480
13200
10560
13680
13440
14400
14880
16560
14400
13680
17040
14400
10800
12720
9600
13440
11040
14640
13200
13920
15600
15360
18240
13200
11040
12240
8880
12720
9840
13920
13200
11760
16800
15120
17280
12960
12000
10800
8880
11760
10560
14400
13920
12000
16080
14880
19200
15360
9360
9360
9360
11040
11040
14880
13680
12240
15360
14160
20400
16080
9360
9840
8160
11280
12960
16320
16080
12960
15120
13440
19200
14640
11760
10560
7920
11760
14160
16560
15600
11520
16560
12960
19920
16560
12000
11040
7440
11760
11280
17040
17040
12960
16800
12480
19440
16560
12240
9360
6480
12720
12240
16080
18480
13680
15360
11520
19920




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211225&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211225&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211225&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0092611860578724
beta1
gamma0.929768627342331

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0092611860578724 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627342331 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211225&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]0.0092611860578724[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627342331[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211225&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211225&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
alpha0.0092611860578724
beta1
gamma0.929768627342331







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131440014892.4358974359-492.435897435898
141080011280.4476836333-480.447683633309
151272013304.12097952-584.120979520043
16960010161.4244846527-561.424484652696
171344013793.7387296374-353.738729637362
181104011184.7003508497-144.700350849747
191464013986.2578185095653.742181490536
201320014401.2642389944-1201.26423899436
211392016067.9659682586-2147.96596825861
221560013836.00740418881763.99259581119
231536013086.61487986612273.38512013393
241824016502.99417706631737.00582293368
251320013456.881498945-256.881498944966
26110409864.578270419811175.42172958019
271224011829.8831583492410.116841650839
2888808748.30511061251131.694889387491
291272012615.77250856104.227491439991
30984010245.1967760442-405.196776044213
311392013819.0848408146100.915159185372
321320012554.349318622645.650681377982
331176013417.3301965775-1657.33019657746
341680014849.22704956521950.77295043476
351512014628.3052125451491.69478745486
361728017575.1033175141-295.103317514146
371296012695.6755478661264.324452133944
381200010454.59331889531545.40668110472
391080011748.8012147798-948.801214779829
4088808416.02533615012463.974663849884
411176012282.2034677827-522.203467782738
42105609451.699814832351108.30018516765
431440013534.9641691939865.035830806137
441392012815.3199080441104.68009195599
451200011601.6213316382398.378668361782
461608016435.7057306965-355.705730696503
471488014887.5377533693-7.53775336932813
481920017138.47953966932061.52046033073
491536012851.55575463762508.44424536242
50936011887.476483419-2527.47648341904
51936010884.8264694855-1524.82646948552
5293608881.19189620205478.80810379795
531104011872.305401384-832.305401384028
541104010571.2329348773468.767065122685
551488014448.9185759128431.081424087248
561368013966.4156419149-286.415641914858
571224012096.7456229855143.254377014466
581536016239.000605114-879.000605113995
591416015007.0217500271-847.021750027063
602040019148.66133443071251.33866556926
611608015250.961585853829.038414147015
6293609601.9376577405-241.937657740504
6398409534.7068230508305.293176949197
6481609401.28758749622-1241.28758749622
651128011160.4008294721119.599170527863
661296011067.12541482641892.87458517364
671632014936.96262889421383.03737110585
681608013824.84118325922255.15881674078
691296012420.5343845873539.465615412695
701512015674.5012278712-554.501227871209
711344014527.6911390667-1087.69113906669
721920020650.5001035445-1450.50010354448
731464016364.227752255-1724.22775225499
74117609706.82807171022053.1719282898
751056010188.0026539884371.997346011603
7679208654.23789118789-734.237891187888
771176011700.016190995959.9838090041158
781416013267.4807900414892.519209958577
791656016676.9740128472-116.974012847215
801560016358.9913755562-758.991375556197
811152013323.100237639-1803.10023763904
821656015502.7155968711057.28440312898
831296013849.6671381386-889.66713813865
841992019611.9263097794308.073690220597
851656015077.90114156761482.09885843243
861200011947.578749549652.4212504503848
871104010860.8689591702179.131040829816
8874408303.78670734274-863.786707342741
891176012076.2549964315-316.25499643146
901128014399.9334921639-3119.93349216387
911704016798.0057290017241.994270998301
921704015850.91440039181189.08559960815
931296011848.28335779461111.71664220535
941680016693.7615390897106.238460910266
951248013233.6500702841-753.650070284126
961944020096.9315198885-656.931519888465
971656016622.9488977544-62.9488977543915
981224012134.5668992703105.433100729664
99936011138.7668786268-1778.7668786268
10064807558.42692139107-1078.42692139107
1011272011786.8493475204933.150652479628
1021224011504.6181134691735.381886530869
1031608017036.1159391979-956.115939197884
1041848016940.10798386371539.89201613631
1051368012862.4643511185817.535648881529
1061536016769.2970158334-1409.29701583341
1071152012479.3042348643-959.304234864338
1081992019404.1169642934515.883035706604

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 14400 & 14892.4358974359 & -492.435897435898 \tabularnewline
14 & 10800 & 11280.4476836333 & -480.447683633309 \tabularnewline
15 & 12720 & 13304.12097952 & -584.120979520043 \tabularnewline
16 & 9600 & 10161.4244846527 & -561.424484652696 \tabularnewline
17 & 13440 & 13793.7387296374 & -353.738729637362 \tabularnewline
18 & 11040 & 11184.7003508497 & -144.700350849747 \tabularnewline
19 & 14640 & 13986.2578185095 & 653.742181490536 \tabularnewline
20 & 13200 & 14401.2642389944 & -1201.26423899436 \tabularnewline
21 & 13920 & 16067.9659682586 & -2147.96596825861 \tabularnewline
22 & 15600 & 13836.0074041888 & 1763.99259581119 \tabularnewline
23 & 15360 & 13086.6148798661 & 2273.38512013393 \tabularnewline
24 & 18240 & 16502.9941770663 & 1737.00582293368 \tabularnewline
25 & 13200 & 13456.881498945 & -256.881498944966 \tabularnewline
26 & 11040 & 9864.57827041981 & 1175.42172958019 \tabularnewline
27 & 12240 & 11829.8831583492 & 410.116841650839 \tabularnewline
28 & 8880 & 8748.30511061251 & 131.694889387491 \tabularnewline
29 & 12720 & 12615.77250856 & 104.227491439991 \tabularnewline
30 & 9840 & 10245.1967760442 & -405.196776044213 \tabularnewline
31 & 13920 & 13819.0848408146 & 100.915159185372 \tabularnewline
32 & 13200 & 12554.349318622 & 645.650681377982 \tabularnewline
33 & 11760 & 13417.3301965775 & -1657.33019657746 \tabularnewline
34 & 16800 & 14849.2270495652 & 1950.77295043476 \tabularnewline
35 & 15120 & 14628.3052125451 & 491.69478745486 \tabularnewline
36 & 17280 & 17575.1033175141 & -295.103317514146 \tabularnewline
37 & 12960 & 12695.6755478661 & 264.324452133944 \tabularnewline
38 & 12000 & 10454.5933188953 & 1545.40668110472 \tabularnewline
39 & 10800 & 11748.8012147798 & -948.801214779829 \tabularnewline
40 & 8880 & 8416.02533615012 & 463.974663849884 \tabularnewline
41 & 11760 & 12282.2034677827 & -522.203467782738 \tabularnewline
42 & 10560 & 9451.69981483235 & 1108.30018516765 \tabularnewline
43 & 14400 & 13534.9641691939 & 865.035830806137 \tabularnewline
44 & 13920 & 12815.319908044 & 1104.68009195599 \tabularnewline
45 & 12000 & 11601.6213316382 & 398.378668361782 \tabularnewline
46 & 16080 & 16435.7057306965 & -355.705730696503 \tabularnewline
47 & 14880 & 14887.5377533693 & -7.53775336932813 \tabularnewline
48 & 19200 & 17138.4795396693 & 2061.52046033073 \tabularnewline
49 & 15360 & 12851.5557546376 & 2508.44424536242 \tabularnewline
50 & 9360 & 11887.476483419 & -2527.47648341904 \tabularnewline
51 & 9360 & 10884.8264694855 & -1524.82646948552 \tabularnewline
52 & 9360 & 8881.19189620205 & 478.80810379795 \tabularnewline
53 & 11040 & 11872.305401384 & -832.305401384028 \tabularnewline
54 & 11040 & 10571.2329348773 & 468.767065122685 \tabularnewline
55 & 14880 & 14448.9185759128 & 431.081424087248 \tabularnewline
56 & 13680 & 13966.4156419149 & -286.415641914858 \tabularnewline
57 & 12240 & 12096.7456229855 & 143.254377014466 \tabularnewline
58 & 15360 & 16239.000605114 & -879.000605113995 \tabularnewline
59 & 14160 & 15007.0217500271 & -847.021750027063 \tabularnewline
60 & 20400 & 19148.6613344307 & 1251.33866556926 \tabularnewline
61 & 16080 & 15250.961585853 & 829.038414147015 \tabularnewline
62 & 9360 & 9601.9376577405 & -241.937657740504 \tabularnewline
63 & 9840 & 9534.7068230508 & 305.293176949197 \tabularnewline
64 & 8160 & 9401.28758749622 & -1241.28758749622 \tabularnewline
65 & 11280 & 11160.4008294721 & 119.599170527863 \tabularnewline
66 & 12960 & 11067.1254148264 & 1892.87458517364 \tabularnewline
67 & 16320 & 14936.9626288942 & 1383.03737110585 \tabularnewline
68 & 16080 & 13824.8411832592 & 2255.15881674078 \tabularnewline
69 & 12960 & 12420.5343845873 & 539.465615412695 \tabularnewline
70 & 15120 & 15674.5012278712 & -554.501227871209 \tabularnewline
71 & 13440 & 14527.6911390667 & -1087.69113906669 \tabularnewline
72 & 19200 & 20650.5001035445 & -1450.50010354448 \tabularnewline
73 & 14640 & 16364.227752255 & -1724.22775225499 \tabularnewline
74 & 11760 & 9706.8280717102 & 2053.1719282898 \tabularnewline
75 & 10560 & 10188.0026539884 & 371.997346011603 \tabularnewline
76 & 7920 & 8654.23789118789 & -734.237891187888 \tabularnewline
77 & 11760 & 11700.0161909959 & 59.9838090041158 \tabularnewline
78 & 14160 & 13267.4807900414 & 892.519209958577 \tabularnewline
79 & 16560 & 16676.9740128472 & -116.974012847215 \tabularnewline
80 & 15600 & 16358.9913755562 & -758.991375556197 \tabularnewline
81 & 11520 & 13323.100237639 & -1803.10023763904 \tabularnewline
82 & 16560 & 15502.715596871 & 1057.28440312898 \tabularnewline
83 & 12960 & 13849.6671381386 & -889.66713813865 \tabularnewline
84 & 19920 & 19611.9263097794 & 308.073690220597 \tabularnewline
85 & 16560 & 15077.9011415676 & 1482.09885843243 \tabularnewline
86 & 12000 & 11947.5787495496 & 52.4212504503848 \tabularnewline
87 & 11040 & 10860.8689591702 & 179.131040829816 \tabularnewline
88 & 7440 & 8303.78670734274 & -863.786707342741 \tabularnewline
89 & 11760 & 12076.2549964315 & -316.25499643146 \tabularnewline
90 & 11280 & 14399.9334921639 & -3119.93349216387 \tabularnewline
91 & 17040 & 16798.0057290017 & 241.994270998301 \tabularnewline
92 & 17040 & 15850.9144003918 & 1189.08559960815 \tabularnewline
93 & 12960 & 11848.2833577946 & 1111.71664220535 \tabularnewline
94 & 16800 & 16693.7615390897 & 106.238460910266 \tabularnewline
95 & 12480 & 13233.6500702841 & -753.650070284126 \tabularnewline
96 & 19440 & 20096.9315198885 & -656.931519888465 \tabularnewline
97 & 16560 & 16622.9488977544 & -62.9488977543915 \tabularnewline
98 & 12240 & 12134.5668992703 & 105.433100729664 \tabularnewline
99 & 9360 & 11138.7668786268 & -1778.7668786268 \tabularnewline
100 & 6480 & 7558.42692139107 & -1078.42692139107 \tabularnewline
101 & 12720 & 11786.8493475204 & 933.150652479628 \tabularnewline
102 & 12240 & 11504.6181134691 & 735.381886530869 \tabularnewline
103 & 16080 & 17036.1159391979 & -956.115939197884 \tabularnewline
104 & 18480 & 16940.1079838637 & 1539.89201613631 \tabularnewline
105 & 13680 & 12862.4643511185 & 817.535648881529 \tabularnewline
106 & 15360 & 16769.2970158334 & -1409.29701583341 \tabularnewline
107 & 11520 & 12479.3042348643 & -959.304234864338 \tabularnewline
108 & 19920 & 19404.1169642934 & 515.883035706604 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211225&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]14400[/C][C]14892.4358974359[/C][C]-492.435897435898[/C][/ROW]
[ROW][C]14[/C][C]10800[/C][C]11280.4476836333[/C][C]-480.447683633309[/C][/ROW]
[ROW][C]15[/C][C]12720[/C][C]13304.12097952[/C][C]-584.120979520043[/C][/ROW]
[ROW][C]16[/C][C]9600[/C][C]10161.4244846527[/C][C]-561.424484652696[/C][/ROW]
[ROW][C]17[/C][C]13440[/C][C]13793.7387296374[/C][C]-353.738729637362[/C][/ROW]
[ROW][C]18[/C][C]11040[/C][C]11184.7003508497[/C][C]-144.700350849747[/C][/ROW]
[ROW][C]19[/C][C]14640[/C][C]13986.2578185095[/C][C]653.742181490536[/C][/ROW]
[ROW][C]20[/C][C]13200[/C][C]14401.2642389944[/C][C]-1201.26423899436[/C][/ROW]
[ROW][C]21[/C][C]13920[/C][C]16067.9659682586[/C][C]-2147.96596825861[/C][/ROW]
[ROW][C]22[/C][C]15600[/C][C]13836.0074041888[/C][C]1763.99259581119[/C][/ROW]
[ROW][C]23[/C][C]15360[/C][C]13086.6148798661[/C][C]2273.38512013393[/C][/ROW]
[ROW][C]24[/C][C]18240[/C][C]16502.9941770663[/C][C]1737.00582293368[/C][/ROW]
[ROW][C]25[/C][C]13200[/C][C]13456.881498945[/C][C]-256.881498944966[/C][/ROW]
[ROW][C]26[/C][C]11040[/C][C]9864.57827041981[/C][C]1175.42172958019[/C][/ROW]
[ROW][C]27[/C][C]12240[/C][C]11829.8831583492[/C][C]410.116841650839[/C][/ROW]
[ROW][C]28[/C][C]8880[/C][C]8748.30511061251[/C][C]131.694889387491[/C][/ROW]
[ROW][C]29[/C][C]12720[/C][C]12615.77250856[/C][C]104.227491439991[/C][/ROW]
[ROW][C]30[/C][C]9840[/C][C]10245.1967760442[/C][C]-405.196776044213[/C][/ROW]
[ROW][C]31[/C][C]13920[/C][C]13819.0848408146[/C][C]100.915159185372[/C][/ROW]
[ROW][C]32[/C][C]13200[/C][C]12554.349318622[/C][C]645.650681377982[/C][/ROW]
[ROW][C]33[/C][C]11760[/C][C]13417.3301965775[/C][C]-1657.33019657746[/C][/ROW]
[ROW][C]34[/C][C]16800[/C][C]14849.2270495652[/C][C]1950.77295043476[/C][/ROW]
[ROW][C]35[/C][C]15120[/C][C]14628.3052125451[/C][C]491.69478745486[/C][/ROW]
[ROW][C]36[/C][C]17280[/C][C]17575.1033175141[/C][C]-295.103317514146[/C][/ROW]
[ROW][C]37[/C][C]12960[/C][C]12695.6755478661[/C][C]264.324452133944[/C][/ROW]
[ROW][C]38[/C][C]12000[/C][C]10454.5933188953[/C][C]1545.40668110472[/C][/ROW]
[ROW][C]39[/C][C]10800[/C][C]11748.8012147798[/C][C]-948.801214779829[/C][/ROW]
[ROW][C]40[/C][C]8880[/C][C]8416.02533615012[/C][C]463.974663849884[/C][/ROW]
[ROW][C]41[/C][C]11760[/C][C]12282.2034677827[/C][C]-522.203467782738[/C][/ROW]
[ROW][C]42[/C][C]10560[/C][C]9451.69981483235[/C][C]1108.30018516765[/C][/ROW]
[ROW][C]43[/C][C]14400[/C][C]13534.9641691939[/C][C]865.035830806137[/C][/ROW]
[ROW][C]44[/C][C]13920[/C][C]12815.319908044[/C][C]1104.68009195599[/C][/ROW]
[ROW][C]45[/C][C]12000[/C][C]11601.6213316382[/C][C]398.378668361782[/C][/ROW]
[ROW][C]46[/C][C]16080[/C][C]16435.7057306965[/C][C]-355.705730696503[/C][/ROW]
[ROW][C]47[/C][C]14880[/C][C]14887.5377533693[/C][C]-7.53775336932813[/C][/ROW]
[ROW][C]48[/C][C]19200[/C][C]17138.4795396693[/C][C]2061.52046033073[/C][/ROW]
[ROW][C]49[/C][C]15360[/C][C]12851.5557546376[/C][C]2508.44424536242[/C][/ROW]
[ROW][C]50[/C][C]9360[/C][C]11887.476483419[/C][C]-2527.47648341904[/C][/ROW]
[ROW][C]51[/C][C]9360[/C][C]10884.8264694855[/C][C]-1524.82646948552[/C][/ROW]
[ROW][C]52[/C][C]9360[/C][C]8881.19189620205[/C][C]478.80810379795[/C][/ROW]
[ROW][C]53[/C][C]11040[/C][C]11872.305401384[/C][C]-832.305401384028[/C][/ROW]
[ROW][C]54[/C][C]11040[/C][C]10571.2329348773[/C][C]468.767065122685[/C][/ROW]
[ROW][C]55[/C][C]14880[/C][C]14448.9185759128[/C][C]431.081424087248[/C][/ROW]
[ROW][C]56[/C][C]13680[/C][C]13966.4156419149[/C][C]-286.415641914858[/C][/ROW]
[ROW][C]57[/C][C]12240[/C][C]12096.7456229855[/C][C]143.254377014466[/C][/ROW]
[ROW][C]58[/C][C]15360[/C][C]16239.000605114[/C][C]-879.000605113995[/C][/ROW]
[ROW][C]59[/C][C]14160[/C][C]15007.0217500271[/C][C]-847.021750027063[/C][/ROW]
[ROW][C]60[/C][C]20400[/C][C]19148.6613344307[/C][C]1251.33866556926[/C][/ROW]
[ROW][C]61[/C][C]16080[/C][C]15250.961585853[/C][C]829.038414147015[/C][/ROW]
[ROW][C]62[/C][C]9360[/C][C]9601.9376577405[/C][C]-241.937657740504[/C][/ROW]
[ROW][C]63[/C][C]9840[/C][C]9534.7068230508[/C][C]305.293176949197[/C][/ROW]
[ROW][C]64[/C][C]8160[/C][C]9401.28758749622[/C][C]-1241.28758749622[/C][/ROW]
[ROW][C]65[/C][C]11280[/C][C]11160.4008294721[/C][C]119.599170527863[/C][/ROW]
[ROW][C]66[/C][C]12960[/C][C]11067.1254148264[/C][C]1892.87458517364[/C][/ROW]
[ROW][C]67[/C][C]16320[/C][C]14936.9626288942[/C][C]1383.03737110585[/C][/ROW]
[ROW][C]68[/C][C]16080[/C][C]13824.8411832592[/C][C]2255.15881674078[/C][/ROW]
[ROW][C]69[/C][C]12960[/C][C]12420.5343845873[/C][C]539.465615412695[/C][/ROW]
[ROW][C]70[/C][C]15120[/C][C]15674.5012278712[/C][C]-554.501227871209[/C][/ROW]
[ROW][C]71[/C][C]13440[/C][C]14527.6911390667[/C][C]-1087.69113906669[/C][/ROW]
[ROW][C]72[/C][C]19200[/C][C]20650.5001035445[/C][C]-1450.50010354448[/C][/ROW]
[ROW][C]73[/C][C]14640[/C][C]16364.227752255[/C][C]-1724.22775225499[/C][/ROW]
[ROW][C]74[/C][C]11760[/C][C]9706.8280717102[/C][C]2053.1719282898[/C][/ROW]
[ROW][C]75[/C][C]10560[/C][C]10188.0026539884[/C][C]371.997346011603[/C][/ROW]
[ROW][C]76[/C][C]7920[/C][C]8654.23789118789[/C][C]-734.237891187888[/C][/ROW]
[ROW][C]77[/C][C]11760[/C][C]11700.0161909959[/C][C]59.9838090041158[/C][/ROW]
[ROW][C]78[/C][C]14160[/C][C]13267.4807900414[/C][C]892.519209958577[/C][/ROW]
[ROW][C]79[/C][C]16560[/C][C]16676.9740128472[/C][C]-116.974012847215[/C][/ROW]
[ROW][C]80[/C][C]15600[/C][C]16358.9913755562[/C][C]-758.991375556197[/C][/ROW]
[ROW][C]81[/C][C]11520[/C][C]13323.100237639[/C][C]-1803.10023763904[/C][/ROW]
[ROW][C]82[/C][C]16560[/C][C]15502.715596871[/C][C]1057.28440312898[/C][/ROW]
[ROW][C]83[/C][C]12960[/C][C]13849.6671381386[/C][C]-889.66713813865[/C][/ROW]
[ROW][C]84[/C][C]19920[/C][C]19611.9263097794[/C][C]308.073690220597[/C][/ROW]
[ROW][C]85[/C][C]16560[/C][C]15077.9011415676[/C][C]1482.09885843243[/C][/ROW]
[ROW][C]86[/C][C]12000[/C][C]11947.5787495496[/C][C]52.4212504503848[/C][/ROW]
[ROW][C]87[/C][C]11040[/C][C]10860.8689591702[/C][C]179.131040829816[/C][/ROW]
[ROW][C]88[/C][C]7440[/C][C]8303.78670734274[/C][C]-863.786707342741[/C][/ROW]
[ROW][C]89[/C][C]11760[/C][C]12076.2549964315[/C][C]-316.25499643146[/C][/ROW]
[ROW][C]90[/C][C]11280[/C][C]14399.9334921639[/C][C]-3119.93349216387[/C][/ROW]
[ROW][C]91[/C][C]17040[/C][C]16798.0057290017[/C][C]241.994270998301[/C][/ROW]
[ROW][C]92[/C][C]17040[/C][C]15850.9144003918[/C][C]1189.08559960815[/C][/ROW]
[ROW][C]93[/C][C]12960[/C][C]11848.2833577946[/C][C]1111.71664220535[/C][/ROW]
[ROW][C]94[/C][C]16800[/C][C]16693.7615390897[/C][C]106.238460910266[/C][/ROW]
[ROW][C]95[/C][C]12480[/C][C]13233.6500702841[/C][C]-753.650070284126[/C][/ROW]
[ROW][C]96[/C][C]19440[/C][C]20096.9315198885[/C][C]-656.931519888465[/C][/ROW]
[ROW][C]97[/C][C]16560[/C][C]16622.9488977544[/C][C]-62.9488977543915[/C][/ROW]
[ROW][C]98[/C][C]12240[/C][C]12134.5668992703[/C][C]105.433100729664[/C][/ROW]
[ROW][C]99[/C][C]9360[/C][C]11138.7668786268[/C][C]-1778.7668786268[/C][/ROW]
[ROW][C]100[/C][C]6480[/C][C]7558.42692139107[/C][C]-1078.42692139107[/C][/ROW]
[ROW][C]101[/C][C]12720[/C][C]11786.8493475204[/C][C]933.150652479628[/C][/ROW]
[ROW][C]102[/C][C]12240[/C][C]11504.6181134691[/C][C]735.381886530869[/C][/ROW]
[ROW][C]103[/C][C]16080[/C][C]17036.1159391979[/C][C]-956.115939197884[/C][/ROW]
[ROW][C]104[/C][C]18480[/C][C]16940.1079838637[/C][C]1539.89201613631[/C][/ROW]
[ROW][C]105[/C][C]13680[/C][C]12862.4643511185[/C][C]817.535648881529[/C][/ROW]
[ROW][C]106[/C][C]15360[/C][C]16769.2970158334[/C][C]-1409.29701583341[/C][/ROW]
[ROW][C]107[/C][C]11520[/C][C]12479.3042348643[/C][C]-959.304234864338[/C][/ROW]
[ROW][C]108[/C][C]19920[/C][C]19404.1169642934[/C][C]515.883035706604[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211225&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211225&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
131440014892.4358974359-492.435897435898
141080011280.4476836333-480.447683633309
151272013304.12097952-584.120979520043
16960010161.4244846527-561.424484652696
171344013793.7387296374-353.738729637362
181104011184.7003508497-144.700350849747
191464013986.2578185095653.742181490536
201320014401.2642389944-1201.26423899436
211392016067.9659682586-2147.96596825861
221560013836.00740418881763.99259581119
231536013086.61487986612273.38512013393
241824016502.99417706631737.00582293368
251320013456.881498945-256.881498944966
26110409864.578270419811175.42172958019
271224011829.8831583492410.116841650839
2888808748.30511061251131.694889387491
291272012615.77250856104.227491439991
30984010245.1967760442-405.196776044213
311392013819.0848408146100.915159185372
321320012554.349318622645.650681377982
331176013417.3301965775-1657.33019657746
341680014849.22704956521950.77295043476
351512014628.3052125451491.69478745486
361728017575.1033175141-295.103317514146
371296012695.6755478661264.324452133944
381200010454.59331889531545.40668110472
391080011748.8012147798-948.801214779829
4088808416.02533615012463.974663849884
411176012282.2034677827-522.203467782738
42105609451.699814832351108.30018516765
431440013534.9641691939865.035830806137
441392012815.3199080441104.68009195599
451200011601.6213316382398.378668361782
461608016435.7057306965-355.705730696503
471488014887.5377533693-7.53775336932813
481920017138.47953966932061.52046033073
491536012851.55575463762508.44424536242
50936011887.476483419-2527.47648341904
51936010884.8264694855-1524.82646948552
5293608881.19189620205478.80810379795
531104011872.305401384-832.305401384028
541104010571.2329348773468.767065122685
551488014448.9185759128431.081424087248
561368013966.4156419149-286.415641914858
571224012096.7456229855143.254377014466
581536016239.000605114-879.000605113995
591416015007.0217500271-847.021750027063
602040019148.66133443071251.33866556926
611608015250.961585853829.038414147015
6293609601.9376577405-241.937657740504
6398409534.7068230508305.293176949197
6481609401.28758749622-1241.28758749622
651128011160.4008294721119.599170527863
661296011067.12541482641892.87458517364
671632014936.96262889421383.03737110585
681608013824.84118325922255.15881674078
691296012420.5343845873539.465615412695
701512015674.5012278712-554.501227871209
711344014527.6911390667-1087.69113906669
721920020650.5001035445-1450.50010354448
731464016364.227752255-1724.22775225499
74117609706.82807171022053.1719282898
751056010188.0026539884371.997346011603
7679208654.23789118789-734.237891187888
771176011700.016190995959.9838090041158
781416013267.4807900414892.519209958577
791656016676.9740128472-116.974012847215
801560016358.9913755562-758.991375556197
811152013323.100237639-1803.10023763904
821656015502.7155968711057.28440312898
831296013849.6671381386-889.66713813865
841992019611.9263097794308.073690220597
851656015077.90114156761482.09885843243
861200011947.578749549652.4212504503848
871104010860.8689591702179.131040829816
8874408303.78670734274-863.786707342741
891176012076.2549964315-316.25499643146
901128014399.9334921639-3119.93349216387
911704016798.0057290017241.994270998301
921704015850.91440039181189.08559960815
931296011848.28335779461111.71664220535
941680016693.7615390897106.238460910266
951248013233.6500702841-753.650070284126
961944020096.9315198885-656.931519888465
971656016622.9488977544-62.9488977543915
981224012134.5668992703105.433100729664
99936011138.7668786268-1778.7668786268
10064807558.42692139107-1078.42692139107
1011272011786.8493475204933.150652479628
1021224011504.6181134691735.381886530869
1031608017036.1159391979-956.115939197884
1041848016940.10798386371539.89201613631
1051368012862.4643511185817.535648881529
1061536016769.2970158334-1409.29701583341
1071152012479.3042348643-959.304234864338
1081992019404.1169642934515.883035706604







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10916473.352242792214273.44826454618673.2562210384
11012126.44709132359926.1657758144414326.7284068326
1119378.836028373497177.7059405328811579.9661162141
1126461.377741836714258.739532984138664.0159506893
11312564.040218578610359.047635639614769.0328015177
11412093.62059708649885.2421250641314301.9990691087
11516055.990825514513843.01210653418268.969544495
11618272.729210292616053.756368489220491.702052096
11713505.833082186311279.297064370715732.369100002
11815336.671601242713100.833618403617572.5095840818
11911470.13836624579223.0964907512613717.1802417402
12019767.493439180717507.190377702722027.7965006587

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 16473.3522427922 & 14273.448264546 & 18673.2562210384 \tabularnewline
110 & 12126.4470913235 & 9926.16577581444 & 14326.7284068326 \tabularnewline
111 & 9378.83602837349 & 7177.70594053288 & 11579.9661162141 \tabularnewline
112 & 6461.37774183671 & 4258.73953298413 & 8664.0159506893 \tabularnewline
113 & 12564.0402185786 & 10359.0476356396 & 14769.0328015177 \tabularnewline
114 & 12093.6205970864 & 9885.24212506413 & 14301.9990691087 \tabularnewline
115 & 16055.9908255145 & 13843.012106534 & 18268.969544495 \tabularnewline
116 & 18272.7292102926 & 16053.7563684892 & 20491.702052096 \tabularnewline
117 & 13505.8330821863 & 11279.2970643707 & 15732.369100002 \tabularnewline
118 & 15336.6716012427 & 13100.8336184036 & 17572.5095840818 \tabularnewline
119 & 11470.1383662457 & 9223.09649075126 & 13717.1802417402 \tabularnewline
120 & 19767.4934391807 & 17507.1903777027 & 22027.7965006587 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211225&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]109[/C][C]16473.3522427922[/C][C]14273.448264546[/C][C]18673.2562210384[/C][/ROW]
[ROW][C]110[/C][C]12126.4470913235[/C][C]9926.16577581444[/C][C]14326.7284068326[/C][/ROW]
[ROW][C]111[/C][C]9378.83602837349[/C][C]7177.70594053288[/C][C]11579.9661162141[/C][/ROW]
[ROW][C]112[/C][C]6461.37774183671[/C][C]4258.73953298413[/C][C]8664.0159506893[/C][/ROW]
[ROW][C]113[/C][C]12564.0402185786[/C][C]10359.0476356396[/C][C]14769.0328015177[/C][/ROW]
[ROW][C]114[/C][C]12093.6205970864[/C][C]9885.24212506413[/C][C]14301.9990691087[/C][/ROW]
[ROW][C]115[/C][C]16055.9908255145[/C][C]13843.012106534[/C][C]18268.969544495[/C][/ROW]
[ROW][C]116[/C][C]18272.7292102926[/C][C]16053.7563684892[/C][C]20491.702052096[/C][/ROW]
[ROW][C]117[/C][C]13505.8330821863[/C][C]11279.2970643707[/C][C]15732.369100002[/C][/ROW]
[ROW][C]118[/C][C]15336.6716012427[/C][C]13100.8336184036[/C][C]17572.5095840818[/C][/ROW]
[ROW][C]119[/C][C]11470.1383662457[/C][C]9223.09649075126[/C][C]13717.1802417402[/C][/ROW]
[ROW][C]120[/C][C]19767.4934391807[/C][C]17507.1903777027[/C][C]22027.7965006587[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211225&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211225&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
10916473.352242792214273.44826454618673.2562210384
11012126.44709132359926.1657758144414326.7284068326
1119378.836028373497177.7059405328811579.9661162141
1126461.377741836714258.739532984138664.0159506893
11312564.040218578610359.047635639614769.0328015177
11412093.62059708649885.2421250641314301.9990691087
11516055.990825514513843.01210653418268.969544495
11618272.729210292616053.756368489220491.702052096
11713505.833082186311279.297064370715732.369100002
11815336.671601242713100.833618403617572.5095840818
11911470.13836624579223.0964907512613717.1802417402
12019767.493439180717507.190377702722027.7965006587



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