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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 13 Dec 2013 11:04:43 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/13/t1386950695lt040a489vc2i6k.htm/, Retrieved Tue, 19 Nov 2019 08:24:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232302, Retrieved Tue, 19 Nov 2019 08:24:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-13 16:04:43] [ab12ae47238ac832614ec82c15c6db51] [Current]
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Dataseries X:
5731
5040
6102
4904
5369
5578
4619
4731
5011
5227
4146
4625
4736
4219
5116
4205
4121
5103
4300
4578
3809
5657
4249
3830
4736
4840
4413
4571
4106
4801
3956
3829
4453
4027
4121
4798
3233
3554
3952
3951
3685
4312
3867
4140
4114
3818
3377
3453
3502
4017
5410
5184
5529
6434
4962
2980
2937
2969
2731
3163
3145
3173
3723
3224
4114
3446
2955
3879
4278
4177
3698
4449
4162
3961
5246
5170
3682
3495
3770
3291
3580
3898
3477
3054




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232302&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]6 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=232302&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232302&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 time6 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.543338663817181
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.543338663817181 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232302&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]0.543338663817181[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232302&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232302&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
alpha0.543338663817181
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
250405731-691
361025355.55298330233746.447016697673
449045761.12650796516-857.126507965162
553695295.4165364050873.5834635949159
655785335.39727719379242.602722806214
746195467.21271644172-848.212716441724
847315006.34595245754-275.345952457536
950114856.73985056179154.260149438211
1052274940.55535403779286.444645962215
1141465096.19180523248-950.191805232481
1246254579.9158594074345.0841405925703
1347364604.41181611634131.588183883658
1442194675.90876412182-456.908764121818
1551164427.65256673751688.34743326249
1642054801.65834136834-596.658341368337
1741214477.47079541389-356.470795413889
1851034283.78642974386819.213570256141
1943004728.89683638773-428.896836387733
2045784495.8606023894182.1393976105937
2138094540.49011293389-731.490112933894
2256574143.043252376911513.95674762309
2342494965.63448870745-716.634488707447
2438304576.25926316783-746.259263167834
2547364170.78775225703565.212247742971
2648404477.8894197188362.1105802812
2744134674.63809856285-261.638098562851
2845714532.4800036860438.5199963139567
2941064553.40940701351-447.409407013512
3048014310.31457762755490.685422372448
3139564576.92293937397-620.922939373967
3238294239.55149916108-410.551499161079
3344534016.48299617876436.517003821242
3440274253.65956176847-226.659561768471
3541214130.5066583358-9.50665833580206
3647984125.34132329826672.658676701739
3732334490.82278990242-1257.82278990242
3835543807.39903591804-253.399035918038
3939523669.71754232977282.282457670231
4039513823.09251569934127.907484300657
4136853892.58959731148-207.589597311479
4243123779.79814288591532.201857114087
4338674068.9639888113-201.963988811304
4441403959.22914499138180.770855008618
4541144057.4489398088556.551060191146
4638184088.17531729056-270.175317290556
4733773941.37862139752-564.378621397523
4834533634.72989536041-181.72989536041
4935023535.98901683965-33.9890168396487
5040173517.52146984553499.478530154466
5154103788.907467025031621.09253297497
5251844669.70971781566514.290282184339
5355294949.14351255186579.856487448139
5464345264.201961647661169.79803835234
5549625899.79846474198-937.798464741979
5629805390.25629997927-2410.25629997927
5729374080.67086249159-1143.67086249159
5829693459.27026421877-490.270264218766
5927313192.88747394885-461.887473948845
6031632941.92615101959221.073848980413
6131453062.0441207295382.9558792704743
6231733107.1172573281265.8827426718753
6337233142.91389870007580.086101299928
6432243458.09710587929-234.097105879293
6541143330.90309716737783.096902832631
6634463756.38992199182-310.389921991823
6729553587.74307651447-632.743076514467
6838793243.94929878152635.050701218476
6942783588.99689823773689.003101762265
7041773963.35892291514213.641077084863
7136984079.43838027489-381.43838027489
7244493872.18816040774576.811839592259
7341624185.59233460573-23.5923346057298
7439614172.77370704472-211.773707044725
7552464057.708864027431188.29113597257
7651704703.35338207257466.646617927432
7736824956.90053193207-1274.90053193207
7834954264.19778041228-769.197780412283
7937703846.26288619193-76.2628861919316
8032913804.82631150957-513.826311509566
8135803525.6446099798554.3553900201528
8238983555.17799496466342.822005035341
8334773741.44644510769-264.446445107688
8430543597.76246697167-543.762466971673

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 5040 & 5731 & -691 \tabularnewline
3 & 6102 & 5355.55298330233 & 746.447016697673 \tabularnewline
4 & 4904 & 5761.12650796516 & -857.126507965162 \tabularnewline
5 & 5369 & 5295.41653640508 & 73.5834635949159 \tabularnewline
6 & 5578 & 5335.39727719379 & 242.602722806214 \tabularnewline
7 & 4619 & 5467.21271644172 & -848.212716441724 \tabularnewline
8 & 4731 & 5006.34595245754 & -275.345952457536 \tabularnewline
9 & 5011 & 4856.73985056179 & 154.260149438211 \tabularnewline
10 & 5227 & 4940.55535403779 & 286.444645962215 \tabularnewline
11 & 4146 & 5096.19180523248 & -950.191805232481 \tabularnewline
12 & 4625 & 4579.91585940743 & 45.0841405925703 \tabularnewline
13 & 4736 & 4604.41181611634 & 131.588183883658 \tabularnewline
14 & 4219 & 4675.90876412182 & -456.908764121818 \tabularnewline
15 & 5116 & 4427.65256673751 & 688.34743326249 \tabularnewline
16 & 4205 & 4801.65834136834 & -596.658341368337 \tabularnewline
17 & 4121 & 4477.47079541389 & -356.470795413889 \tabularnewline
18 & 5103 & 4283.78642974386 & 819.213570256141 \tabularnewline
19 & 4300 & 4728.89683638773 & -428.896836387733 \tabularnewline
20 & 4578 & 4495.86060238941 & 82.1393976105937 \tabularnewline
21 & 3809 & 4540.49011293389 & -731.490112933894 \tabularnewline
22 & 5657 & 4143.04325237691 & 1513.95674762309 \tabularnewline
23 & 4249 & 4965.63448870745 & -716.634488707447 \tabularnewline
24 & 3830 & 4576.25926316783 & -746.259263167834 \tabularnewline
25 & 4736 & 4170.78775225703 & 565.212247742971 \tabularnewline
26 & 4840 & 4477.8894197188 & 362.1105802812 \tabularnewline
27 & 4413 & 4674.63809856285 & -261.638098562851 \tabularnewline
28 & 4571 & 4532.48000368604 & 38.5199963139567 \tabularnewline
29 & 4106 & 4553.40940701351 & -447.409407013512 \tabularnewline
30 & 4801 & 4310.31457762755 & 490.685422372448 \tabularnewline
31 & 3956 & 4576.92293937397 & -620.922939373967 \tabularnewline
32 & 3829 & 4239.55149916108 & -410.551499161079 \tabularnewline
33 & 4453 & 4016.48299617876 & 436.517003821242 \tabularnewline
34 & 4027 & 4253.65956176847 & -226.659561768471 \tabularnewline
35 & 4121 & 4130.5066583358 & -9.50665833580206 \tabularnewline
36 & 4798 & 4125.34132329826 & 672.658676701739 \tabularnewline
37 & 3233 & 4490.82278990242 & -1257.82278990242 \tabularnewline
38 & 3554 & 3807.39903591804 & -253.399035918038 \tabularnewline
39 & 3952 & 3669.71754232977 & 282.282457670231 \tabularnewline
40 & 3951 & 3823.09251569934 & 127.907484300657 \tabularnewline
41 & 3685 & 3892.58959731148 & -207.589597311479 \tabularnewline
42 & 4312 & 3779.79814288591 & 532.201857114087 \tabularnewline
43 & 3867 & 4068.9639888113 & -201.963988811304 \tabularnewline
44 & 4140 & 3959.22914499138 & 180.770855008618 \tabularnewline
45 & 4114 & 4057.44893980885 & 56.551060191146 \tabularnewline
46 & 3818 & 4088.17531729056 & -270.175317290556 \tabularnewline
47 & 3377 & 3941.37862139752 & -564.378621397523 \tabularnewline
48 & 3453 & 3634.72989536041 & -181.72989536041 \tabularnewline
49 & 3502 & 3535.98901683965 & -33.9890168396487 \tabularnewline
50 & 4017 & 3517.52146984553 & 499.478530154466 \tabularnewline
51 & 5410 & 3788.90746702503 & 1621.09253297497 \tabularnewline
52 & 5184 & 4669.70971781566 & 514.290282184339 \tabularnewline
53 & 5529 & 4949.14351255186 & 579.856487448139 \tabularnewline
54 & 6434 & 5264.20196164766 & 1169.79803835234 \tabularnewline
55 & 4962 & 5899.79846474198 & -937.798464741979 \tabularnewline
56 & 2980 & 5390.25629997927 & -2410.25629997927 \tabularnewline
57 & 2937 & 4080.67086249159 & -1143.67086249159 \tabularnewline
58 & 2969 & 3459.27026421877 & -490.270264218766 \tabularnewline
59 & 2731 & 3192.88747394885 & -461.887473948845 \tabularnewline
60 & 3163 & 2941.92615101959 & 221.073848980413 \tabularnewline
61 & 3145 & 3062.04412072953 & 82.9558792704743 \tabularnewline
62 & 3173 & 3107.11725732812 & 65.8827426718753 \tabularnewline
63 & 3723 & 3142.91389870007 & 580.086101299928 \tabularnewline
64 & 3224 & 3458.09710587929 & -234.097105879293 \tabularnewline
65 & 4114 & 3330.90309716737 & 783.096902832631 \tabularnewline
66 & 3446 & 3756.38992199182 & -310.389921991823 \tabularnewline
67 & 2955 & 3587.74307651447 & -632.743076514467 \tabularnewline
68 & 3879 & 3243.94929878152 & 635.050701218476 \tabularnewline
69 & 4278 & 3588.99689823773 & 689.003101762265 \tabularnewline
70 & 4177 & 3963.35892291514 & 213.641077084863 \tabularnewline
71 & 3698 & 4079.43838027489 & -381.43838027489 \tabularnewline
72 & 4449 & 3872.18816040774 & 576.811839592259 \tabularnewline
73 & 4162 & 4185.59233460573 & -23.5923346057298 \tabularnewline
74 & 3961 & 4172.77370704472 & -211.773707044725 \tabularnewline
75 & 5246 & 4057.70886402743 & 1188.29113597257 \tabularnewline
76 & 5170 & 4703.35338207257 & 466.646617927432 \tabularnewline
77 & 3682 & 4956.90053193207 & -1274.90053193207 \tabularnewline
78 & 3495 & 4264.19778041228 & -769.197780412283 \tabularnewline
79 & 3770 & 3846.26288619193 & -76.2628861919316 \tabularnewline
80 & 3291 & 3804.82631150957 & -513.826311509566 \tabularnewline
81 & 3580 & 3525.64460997985 & 54.3553900201528 \tabularnewline
82 & 3898 & 3555.17799496466 & 342.822005035341 \tabularnewline
83 & 3477 & 3741.44644510769 & -264.446445107688 \tabularnewline
84 & 3054 & 3597.76246697167 & -543.762466971673 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232302&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]5040[/C][C]5731[/C][C]-691[/C][/ROW]
[ROW][C]3[/C][C]6102[/C][C]5355.55298330233[/C][C]746.447016697673[/C][/ROW]
[ROW][C]4[/C][C]4904[/C][C]5761.12650796516[/C][C]-857.126507965162[/C][/ROW]
[ROW][C]5[/C][C]5369[/C][C]5295.41653640508[/C][C]73.5834635949159[/C][/ROW]
[ROW][C]6[/C][C]5578[/C][C]5335.39727719379[/C][C]242.602722806214[/C][/ROW]
[ROW][C]7[/C][C]4619[/C][C]5467.21271644172[/C][C]-848.212716441724[/C][/ROW]
[ROW][C]8[/C][C]4731[/C][C]5006.34595245754[/C][C]-275.345952457536[/C][/ROW]
[ROW][C]9[/C][C]5011[/C][C]4856.73985056179[/C][C]154.260149438211[/C][/ROW]
[ROW][C]10[/C][C]5227[/C][C]4940.55535403779[/C][C]286.444645962215[/C][/ROW]
[ROW][C]11[/C][C]4146[/C][C]5096.19180523248[/C][C]-950.191805232481[/C][/ROW]
[ROW][C]12[/C][C]4625[/C][C]4579.91585940743[/C][C]45.0841405925703[/C][/ROW]
[ROW][C]13[/C][C]4736[/C][C]4604.41181611634[/C][C]131.588183883658[/C][/ROW]
[ROW][C]14[/C][C]4219[/C][C]4675.90876412182[/C][C]-456.908764121818[/C][/ROW]
[ROW][C]15[/C][C]5116[/C][C]4427.65256673751[/C][C]688.34743326249[/C][/ROW]
[ROW][C]16[/C][C]4205[/C][C]4801.65834136834[/C][C]-596.658341368337[/C][/ROW]
[ROW][C]17[/C][C]4121[/C][C]4477.47079541389[/C][C]-356.470795413889[/C][/ROW]
[ROW][C]18[/C][C]5103[/C][C]4283.78642974386[/C][C]819.213570256141[/C][/ROW]
[ROW][C]19[/C][C]4300[/C][C]4728.89683638773[/C][C]-428.896836387733[/C][/ROW]
[ROW][C]20[/C][C]4578[/C][C]4495.86060238941[/C][C]82.1393976105937[/C][/ROW]
[ROW][C]21[/C][C]3809[/C][C]4540.49011293389[/C][C]-731.490112933894[/C][/ROW]
[ROW][C]22[/C][C]5657[/C][C]4143.04325237691[/C][C]1513.95674762309[/C][/ROW]
[ROW][C]23[/C][C]4249[/C][C]4965.63448870745[/C][C]-716.634488707447[/C][/ROW]
[ROW][C]24[/C][C]3830[/C][C]4576.25926316783[/C][C]-746.259263167834[/C][/ROW]
[ROW][C]25[/C][C]4736[/C][C]4170.78775225703[/C][C]565.212247742971[/C][/ROW]
[ROW][C]26[/C][C]4840[/C][C]4477.8894197188[/C][C]362.1105802812[/C][/ROW]
[ROW][C]27[/C][C]4413[/C][C]4674.63809856285[/C][C]-261.638098562851[/C][/ROW]
[ROW][C]28[/C][C]4571[/C][C]4532.48000368604[/C][C]38.5199963139567[/C][/ROW]
[ROW][C]29[/C][C]4106[/C][C]4553.40940701351[/C][C]-447.409407013512[/C][/ROW]
[ROW][C]30[/C][C]4801[/C][C]4310.31457762755[/C][C]490.685422372448[/C][/ROW]
[ROW][C]31[/C][C]3956[/C][C]4576.92293937397[/C][C]-620.922939373967[/C][/ROW]
[ROW][C]32[/C][C]3829[/C][C]4239.55149916108[/C][C]-410.551499161079[/C][/ROW]
[ROW][C]33[/C][C]4453[/C][C]4016.48299617876[/C][C]436.517003821242[/C][/ROW]
[ROW][C]34[/C][C]4027[/C][C]4253.65956176847[/C][C]-226.659561768471[/C][/ROW]
[ROW][C]35[/C][C]4121[/C][C]4130.5066583358[/C][C]-9.50665833580206[/C][/ROW]
[ROW][C]36[/C][C]4798[/C][C]4125.34132329826[/C][C]672.658676701739[/C][/ROW]
[ROW][C]37[/C][C]3233[/C][C]4490.82278990242[/C][C]-1257.82278990242[/C][/ROW]
[ROW][C]38[/C][C]3554[/C][C]3807.39903591804[/C][C]-253.399035918038[/C][/ROW]
[ROW][C]39[/C][C]3952[/C][C]3669.71754232977[/C][C]282.282457670231[/C][/ROW]
[ROW][C]40[/C][C]3951[/C][C]3823.09251569934[/C][C]127.907484300657[/C][/ROW]
[ROW][C]41[/C][C]3685[/C][C]3892.58959731148[/C][C]-207.589597311479[/C][/ROW]
[ROW][C]42[/C][C]4312[/C][C]3779.79814288591[/C][C]532.201857114087[/C][/ROW]
[ROW][C]43[/C][C]3867[/C][C]4068.9639888113[/C][C]-201.963988811304[/C][/ROW]
[ROW][C]44[/C][C]4140[/C][C]3959.22914499138[/C][C]180.770855008618[/C][/ROW]
[ROW][C]45[/C][C]4114[/C][C]4057.44893980885[/C][C]56.551060191146[/C][/ROW]
[ROW][C]46[/C][C]3818[/C][C]4088.17531729056[/C][C]-270.175317290556[/C][/ROW]
[ROW][C]47[/C][C]3377[/C][C]3941.37862139752[/C][C]-564.378621397523[/C][/ROW]
[ROW][C]48[/C][C]3453[/C][C]3634.72989536041[/C][C]-181.72989536041[/C][/ROW]
[ROW][C]49[/C][C]3502[/C][C]3535.98901683965[/C][C]-33.9890168396487[/C][/ROW]
[ROW][C]50[/C][C]4017[/C][C]3517.52146984553[/C][C]499.478530154466[/C][/ROW]
[ROW][C]51[/C][C]5410[/C][C]3788.90746702503[/C][C]1621.09253297497[/C][/ROW]
[ROW][C]52[/C][C]5184[/C][C]4669.70971781566[/C][C]514.290282184339[/C][/ROW]
[ROW][C]53[/C][C]5529[/C][C]4949.14351255186[/C][C]579.856487448139[/C][/ROW]
[ROW][C]54[/C][C]6434[/C][C]5264.20196164766[/C][C]1169.79803835234[/C][/ROW]
[ROW][C]55[/C][C]4962[/C][C]5899.79846474198[/C][C]-937.798464741979[/C][/ROW]
[ROW][C]56[/C][C]2980[/C][C]5390.25629997927[/C][C]-2410.25629997927[/C][/ROW]
[ROW][C]57[/C][C]2937[/C][C]4080.67086249159[/C][C]-1143.67086249159[/C][/ROW]
[ROW][C]58[/C][C]2969[/C][C]3459.27026421877[/C][C]-490.270264218766[/C][/ROW]
[ROW][C]59[/C][C]2731[/C][C]3192.88747394885[/C][C]-461.887473948845[/C][/ROW]
[ROW][C]60[/C][C]3163[/C][C]2941.92615101959[/C][C]221.073848980413[/C][/ROW]
[ROW][C]61[/C][C]3145[/C][C]3062.04412072953[/C][C]82.9558792704743[/C][/ROW]
[ROW][C]62[/C][C]3173[/C][C]3107.11725732812[/C][C]65.8827426718753[/C][/ROW]
[ROW][C]63[/C][C]3723[/C][C]3142.91389870007[/C][C]580.086101299928[/C][/ROW]
[ROW][C]64[/C][C]3224[/C][C]3458.09710587929[/C][C]-234.097105879293[/C][/ROW]
[ROW][C]65[/C][C]4114[/C][C]3330.90309716737[/C][C]783.096902832631[/C][/ROW]
[ROW][C]66[/C][C]3446[/C][C]3756.38992199182[/C][C]-310.389921991823[/C][/ROW]
[ROW][C]67[/C][C]2955[/C][C]3587.74307651447[/C][C]-632.743076514467[/C][/ROW]
[ROW][C]68[/C][C]3879[/C][C]3243.94929878152[/C][C]635.050701218476[/C][/ROW]
[ROW][C]69[/C][C]4278[/C][C]3588.99689823773[/C][C]689.003101762265[/C][/ROW]
[ROW][C]70[/C][C]4177[/C][C]3963.35892291514[/C][C]213.641077084863[/C][/ROW]
[ROW][C]71[/C][C]3698[/C][C]4079.43838027489[/C][C]-381.43838027489[/C][/ROW]
[ROW][C]72[/C][C]4449[/C][C]3872.18816040774[/C][C]576.811839592259[/C][/ROW]
[ROW][C]73[/C][C]4162[/C][C]4185.59233460573[/C][C]-23.5923346057298[/C][/ROW]
[ROW][C]74[/C][C]3961[/C][C]4172.77370704472[/C][C]-211.773707044725[/C][/ROW]
[ROW][C]75[/C][C]5246[/C][C]4057.70886402743[/C][C]1188.29113597257[/C][/ROW]
[ROW][C]76[/C][C]5170[/C][C]4703.35338207257[/C][C]466.646617927432[/C][/ROW]
[ROW][C]77[/C][C]3682[/C][C]4956.90053193207[/C][C]-1274.90053193207[/C][/ROW]
[ROW][C]78[/C][C]3495[/C][C]4264.19778041228[/C][C]-769.197780412283[/C][/ROW]
[ROW][C]79[/C][C]3770[/C][C]3846.26288619193[/C][C]-76.2628861919316[/C][/ROW]
[ROW][C]80[/C][C]3291[/C][C]3804.82631150957[/C][C]-513.826311509566[/C][/ROW]
[ROW][C]81[/C][C]3580[/C][C]3525.64460997985[/C][C]54.3553900201528[/C][/ROW]
[ROW][C]82[/C][C]3898[/C][C]3555.17799496466[/C][C]342.822005035341[/C][/ROW]
[ROW][C]83[/C][C]3477[/C][C]3741.44644510769[/C][C]-264.446445107688[/C][/ROW]
[ROW][C]84[/C][C]3054[/C][C]3597.76246697167[/C][C]-543.762466971673[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232302&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232302&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
250405731-691
361025355.55298330233746.447016697673
449045761.12650796516-857.126507965162
553695295.4165364050873.5834635949159
655785335.39727719379242.602722806214
746195467.21271644172-848.212716441724
847315006.34595245754-275.345952457536
950114856.73985056179154.260149438211
1052274940.55535403779286.444645962215
1141465096.19180523248-950.191805232481
1246254579.9158594074345.0841405925703
1347364604.41181611634131.588183883658
1442194675.90876412182-456.908764121818
1551164427.65256673751688.34743326249
1642054801.65834136834-596.658341368337
1741214477.47079541389-356.470795413889
1851034283.78642974386819.213570256141
1943004728.89683638773-428.896836387733
2045784495.8606023894182.1393976105937
2138094540.49011293389-731.490112933894
2256574143.043252376911513.95674762309
2342494965.63448870745-716.634488707447
2438304576.25926316783-746.259263167834
2547364170.78775225703565.212247742971
2648404477.8894197188362.1105802812
2744134674.63809856285-261.638098562851
2845714532.4800036860438.5199963139567
2941064553.40940701351-447.409407013512
3048014310.31457762755490.685422372448
3139564576.92293937397-620.922939373967
3238294239.55149916108-410.551499161079
3344534016.48299617876436.517003821242
3440274253.65956176847-226.659561768471
3541214130.5066583358-9.50665833580206
3647984125.34132329826672.658676701739
3732334490.82278990242-1257.82278990242
3835543807.39903591804-253.399035918038
3939523669.71754232977282.282457670231
4039513823.09251569934127.907484300657
4136853892.58959731148-207.589597311479
4243123779.79814288591532.201857114087
4338674068.9639888113-201.963988811304
4441403959.22914499138180.770855008618
4541144057.4489398088556.551060191146
4638184088.17531729056-270.175317290556
4733773941.37862139752-564.378621397523
4834533634.72989536041-181.72989536041
4935023535.98901683965-33.9890168396487
5040173517.52146984553499.478530154466
5154103788.907467025031621.09253297497
5251844669.70971781566514.290282184339
5355294949.14351255186579.856487448139
5464345264.201961647661169.79803835234
5549625899.79846474198-937.798464741979
5629805390.25629997927-2410.25629997927
5729374080.67086249159-1143.67086249159
5829693459.27026421877-490.270264218766
5927313192.88747394885-461.887473948845
6031632941.92615101959221.073848980413
6131453062.0441207295382.9558792704743
6231733107.1172573281265.8827426718753
6337233142.91389870007580.086101299928
6432243458.09710587929-234.097105879293
6541143330.90309716737783.096902832631
6634463756.38992199182-310.389921991823
6729553587.74307651447-632.743076514467
6838793243.94929878152635.050701218476
6942783588.99689823773689.003101762265
7041773963.35892291514213.641077084863
7136984079.43838027489-381.43838027489
7244493872.18816040774576.811839592259
7341624185.59233460573-23.5923346057298
7439614172.77370704472-211.773707044725
7552464057.708864027431188.29113597257
7651704703.35338207257466.646617927432
7736824956.90053193207-1274.90053193207
7834954264.19778041228-769.197780412283
7937703846.26288619193-76.2628861919316
8032913804.82631150957-513.826311509566
8135803525.6446099798554.3553900201528
8238983555.17799496466342.822005035341
8334773741.44644510769-264.446445107688
8430543597.76246697167-543.762466971673







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
853302.315294733352021.264002539374583.36658692733
863302.315294733351844.381608317754760.24898114895
873302.315294733351686.750732501644917.87985696506
883302.315294733351543.188501266645061.44208820006
893302.315294733351410.489378787075194.14121067963
903302.315294733351286.506891883645318.12369758306
913302.315294733351169.720223522445434.91036594426
923302.315294733351059.005249619975545.62533984673
933302.31529473335953.5032164137365651.12737305296
943302.31529473335852.5405295735745752.09005989313
953302.31529473335755.5772593698445849.05333009686
963302.31529473335662.1727149621935942.45787450451

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3302.31529473335 & 2021.26400253937 & 4583.36658692733 \tabularnewline
86 & 3302.31529473335 & 1844.38160831775 & 4760.24898114895 \tabularnewline
87 & 3302.31529473335 & 1686.75073250164 & 4917.87985696506 \tabularnewline
88 & 3302.31529473335 & 1543.18850126664 & 5061.44208820006 \tabularnewline
89 & 3302.31529473335 & 1410.48937878707 & 5194.14121067963 \tabularnewline
90 & 3302.31529473335 & 1286.50689188364 & 5318.12369758306 \tabularnewline
91 & 3302.31529473335 & 1169.72022352244 & 5434.91036594426 \tabularnewline
92 & 3302.31529473335 & 1059.00524961997 & 5545.62533984673 \tabularnewline
93 & 3302.31529473335 & 953.503216413736 & 5651.12737305296 \tabularnewline
94 & 3302.31529473335 & 852.540529573574 & 5752.09005989313 \tabularnewline
95 & 3302.31529473335 & 755.577259369844 & 5849.05333009686 \tabularnewline
96 & 3302.31529473335 & 662.172714962193 & 5942.45787450451 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232302&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]3302.31529473335[/C][C]2021.26400253937[/C][C]4583.36658692733[/C][/ROW]
[ROW][C]86[/C][C]3302.31529473335[/C][C]1844.38160831775[/C][C]4760.24898114895[/C][/ROW]
[ROW][C]87[/C][C]3302.31529473335[/C][C]1686.75073250164[/C][C]4917.87985696506[/C][/ROW]
[ROW][C]88[/C][C]3302.31529473335[/C][C]1543.18850126664[/C][C]5061.44208820006[/C][/ROW]
[ROW][C]89[/C][C]3302.31529473335[/C][C]1410.48937878707[/C][C]5194.14121067963[/C][/ROW]
[ROW][C]90[/C][C]3302.31529473335[/C][C]1286.50689188364[/C][C]5318.12369758306[/C][/ROW]
[ROW][C]91[/C][C]3302.31529473335[/C][C]1169.72022352244[/C][C]5434.91036594426[/C][/ROW]
[ROW][C]92[/C][C]3302.31529473335[/C][C]1059.00524961997[/C][C]5545.62533984673[/C][/ROW]
[ROW][C]93[/C][C]3302.31529473335[/C][C]953.503216413736[/C][C]5651.12737305296[/C][/ROW]
[ROW][C]94[/C][C]3302.31529473335[/C][C]852.540529573574[/C][C]5752.09005989313[/C][/ROW]
[ROW][C]95[/C][C]3302.31529473335[/C][C]755.577259369844[/C][C]5849.05333009686[/C][/ROW]
[ROW][C]96[/C][C]3302.31529473335[/C][C]662.172714962193[/C][C]5942.45787450451[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232302&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232302&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
853302.315294733352021.264002539374583.36658692733
863302.315294733351844.381608317754760.24898114895
873302.315294733351686.750732501644917.87985696506
883302.315294733351543.188501266645061.44208820006
893302.315294733351410.489378787075194.14121067963
903302.315294733351286.506891883645318.12369758306
913302.315294733351169.720223522445434.91036594426
923302.315294733351059.005249619975545.62533984673
933302.31529473335953.5032164137365651.12737305296
943302.31529473335852.5405295735745752.09005989313
953302.31529473335755.5772593698445849.05333009686
963302.31529473335662.1727149621935942.45787450451



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')