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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Aug 2017 23:32:39 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/16/t1502919175exyxmyb7yalvk0j.htm/, Retrieved Sat, 11 May 2024 23:22:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307516, Retrieved Sat, 11 May 2024 23:22:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-16 21:32:39] [b4406e95441bfa154caa3f19e1e15192] [Current]
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Dataseries X:
5947968
5925816
5903352
5856864
6316752
6292416
5947968
5718960
5741112
5741112
5765760
5810064
5879016
5879016
5834712
5718960
6316752
6407856
6270264
5947968
6085872
5879016
5972304
6016920
6063408
5947968
5972304
5810064
6316752
6476808
6339216
6085872
6361368
6063408
6339216
6316752
6385704
6132360
6407856
6385704
6799104
6705816
6339216
6154512
6407856
6063408
6316752
6361368
6454656
6248112
6361368
6430320
6683664
6476808
6201312
5903352
6179160
5421000
5787912
5994456
6201312
5903352
5903352
5903352
6063408
5834712
5534568
5283408
5465616
4754256
5190120
5443464
5489952
5236608
5258760
5190120
5421000
5258760
4938960
4707768
5098704
4249752
4801056
5052216
5052216
4754256
4478760
4456608
4707768
4478760
4043208
3743064
4065360
3307512
3996408
4363008
4478760
4225416
3905304
4134312
4225416
4156464
3467256
3147456
3376152
2687256
3398616
3651960
3858504
3514056
3191760
3376152
3467256
3285048
2596152
2296008
2571504
1813656
2640456
3147456




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307516&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307516&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307516&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405343002238376
beta0.0645195510983717
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238376 \tabularnewline
beta & 0.0645195510983717 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307516&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]0.405343002238376[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510983717[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307516&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307516&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
alpha0.405343002238376
beta0.0645195510983717
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1358790165878760.33333334255.666666664183
1458790165865857.6523624813158.3476375155
1558347125813289.1071586521422.8928413512
1657189605696978.8007648821981.1992351161
1763167526300772.6643410215979.3356589833
1864078566392990.6148677214865.385132282
1962702646049008.8010499221255.198950103
2059479685932545.0413278515422.95867215
2160858725984198.97304947101673.026950527
2258790166055116.77516339-176100.775163388
2359723046030623.42631396-58319.4263139572
2460169206061446.72138703-44526.7213870315
2560634086108067.33961396-44659.3396139629
2659479686087302.88198016-139334.881980159
2759723045976520.29360963-4216.29360963311
2858100645848162.24384929-38098.2438492896
2963167526420475.96550625-103723.965506249
3064768086456821.745778819986.2542212
3163392166231091.85493635108124.145063649
3260858725936858.03423191149013.96576809
3363613686087931.49989187273436.500108135
3460634086061764.48862941643.51137059648
3563392166182478.71185664156737.288143359
3663167526317420.6169302-668.616930204444
3763857046391631.89694737-5927.89694736991
3861323606341172.35912859-208812.359128593
3964078566291664.63693951116191.363060489
4063857046204201.67775932181502.322240679
4167991046844484.10035803-45380.1003580298
4267058166997550.08951918-291734.089519177
4363392166709231.85439308-370015.854393085
4461545126244351.67143992-89839.6714399206
4564078566365198.5086828842657.4913171204
4660634086070430.07047742-7022.07047741953
4763167526266199.5653887650552.4346112395
4863613686248060.86064092113307.139359078
4964546566351887.90517126102768.094828735
5062481126214227.4959606133884.5040393863
5163613686452094.76225947-90726.7622594675
5264303206309918.94717352120401.052826477
5366836646779241.56292729-95577.5629272871
5464768086752875.83215542-276067.832155419
5562013126412178.31193054-210866.311930543
5659033526170400.48264541-267048.482645413
5761791606285556.34383274-106396.343832738
5854210005884278.55035048-463278.550350476
5957879125900863.35934885-112951.359348851
6059944565821009.62237761173446.377622389
6162013125911761.92624338289550.073756618
6259033525782550.35713798120801.642862018
6359033525957521.20191753-54169.2019175291
6459033525932641.73011852-29289.7301185234
6560634086185869.6031738-122461.603173801
6658347126013588.29091678-178876.290916783
6755345685725912.50630166-191344.506301661
6852834085434002.41254911-150594.412549114
6954656165670304.43459886-204688.434598864
7047542564992800.9397078-238544.939707795
7151901205290520.62868633-100400.628686328
7254434645368107.0624911975356.937508815
7354899525467620.4862373222331.513762678
7452366085102236.97476663134371.025233373
7552587605151505.97670311107254.023296892
7651901205183920.20060366199.799396405
7754210005374123.5103912846876.4896087227
7852587605219358.7535028839401.2464971188
7949389605000878.37687939-61918.3768793894
8047077684777179.85772039-69411.8577203946
8150987045007861.6725470790842.327452925
8242497524431385.77994051-181633.779940511
8348010564837180.14602186-36124.1460218551
8450522165049874.718255952341.28174405266
8550522165090888.92143732-38672.9214373231
8647542564768436.45096485-14180.4509648466
8744787604738514.51928981-259754.519289806
8844566084549622.27126619-93014.271266195
8947077684708754.30343929-986.303439285606
9044787604513847.53184785-35087.5318478504
9140432084186679.19488662-143471.194886621
9237430643905090.91454503-162026.914545033
9340653604170729.17077936-105369.170779362
9433075123324760.09964814-17248.0996481385
9539964083860084.08066651136323.919333492
9643630084146431.66934643216576.330653571
9744787604236376.62413636242383.375863638
9842254164036244.77105622189171.22894378
9939053043941867.64139534-36563.6413953402
10041343123947584.47922245186727.520777551
10142254164287135.89512573-61719.8951257262
10241564644058047.2456666498416.7543333624
10334672563734748.90316278-267492.903162776
10431474563402817.58891009-255361.588910087
10533761523672836.85843736-296684.85843736
10626872562805239.3774904-117983.3774904
10733986163391937.463857116678.53614289034
10836519603670950.0740418-18990.0740418038
10938585043672088.72569216186415.274307837
11035140563407496.4608135106559.539186496
11131917603133106.7763411758653.2236588276
11233761523300399.2557438875752.7442561202
11334672563434523.0543926532732.9456073465
11432850483328712.99094381-43664.9909438128
11525961522716282.67790525-120130.677905248
11622960082441202.08815502-145194.088155023
11725715042724089.47949192-152585.479491921
11818136562017721.99328533-204065.993285334
11926404562637961.126935572494.8730644295
12031474562894207.44036077253248.559639227

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5879016 & 5878760.33333334 & 255.666666664183 \tabularnewline
14 & 5879016 & 5865857.65236248 & 13158.3476375155 \tabularnewline
15 & 5834712 & 5813289.10715865 & 21422.8928413512 \tabularnewline
16 & 5718960 & 5696978.80076488 & 21981.1992351161 \tabularnewline
17 & 6316752 & 6300772.66434102 & 15979.3356589833 \tabularnewline
18 & 6407856 & 6392990.61486772 & 14865.385132282 \tabularnewline
19 & 6270264 & 6049008.8010499 & 221255.198950103 \tabularnewline
20 & 5947968 & 5932545.04132785 & 15422.95867215 \tabularnewline
21 & 6085872 & 5984198.97304947 & 101673.026950527 \tabularnewline
22 & 5879016 & 6055116.77516339 & -176100.775163388 \tabularnewline
23 & 5972304 & 6030623.42631396 & -58319.4263139572 \tabularnewline
24 & 6016920 & 6061446.72138703 & -44526.7213870315 \tabularnewline
25 & 6063408 & 6108067.33961396 & -44659.3396139629 \tabularnewline
26 & 5947968 & 6087302.88198016 & -139334.881980159 \tabularnewline
27 & 5972304 & 5976520.29360963 & -4216.29360963311 \tabularnewline
28 & 5810064 & 5848162.24384929 & -38098.2438492896 \tabularnewline
29 & 6316752 & 6420475.96550625 & -103723.965506249 \tabularnewline
30 & 6476808 & 6456821.7457788 & 19986.2542212 \tabularnewline
31 & 6339216 & 6231091.85493635 & 108124.145063649 \tabularnewline
32 & 6085872 & 5936858.03423191 & 149013.96576809 \tabularnewline
33 & 6361368 & 6087931.49989187 & 273436.500108135 \tabularnewline
34 & 6063408 & 6061764.4886294 & 1643.51137059648 \tabularnewline
35 & 6339216 & 6182478.71185664 & 156737.288143359 \tabularnewline
36 & 6316752 & 6317420.6169302 & -668.616930204444 \tabularnewline
37 & 6385704 & 6391631.89694737 & -5927.89694736991 \tabularnewline
38 & 6132360 & 6341172.35912859 & -208812.359128593 \tabularnewline
39 & 6407856 & 6291664.63693951 & 116191.363060489 \tabularnewline
40 & 6385704 & 6204201.67775932 & 181502.322240679 \tabularnewline
41 & 6799104 & 6844484.10035803 & -45380.1003580298 \tabularnewline
42 & 6705816 & 6997550.08951918 & -291734.089519177 \tabularnewline
43 & 6339216 & 6709231.85439308 & -370015.854393085 \tabularnewline
44 & 6154512 & 6244351.67143992 & -89839.6714399206 \tabularnewline
45 & 6407856 & 6365198.50868288 & 42657.4913171204 \tabularnewline
46 & 6063408 & 6070430.07047742 & -7022.07047741953 \tabularnewline
47 & 6316752 & 6266199.56538876 & 50552.4346112395 \tabularnewline
48 & 6361368 & 6248060.86064092 & 113307.139359078 \tabularnewline
49 & 6454656 & 6351887.90517126 & 102768.094828735 \tabularnewline
50 & 6248112 & 6214227.49596061 & 33884.5040393863 \tabularnewline
51 & 6361368 & 6452094.76225947 & -90726.7622594675 \tabularnewline
52 & 6430320 & 6309918.94717352 & 120401.052826477 \tabularnewline
53 & 6683664 & 6779241.56292729 & -95577.5629272871 \tabularnewline
54 & 6476808 & 6752875.83215542 & -276067.832155419 \tabularnewline
55 & 6201312 & 6412178.31193054 & -210866.311930543 \tabularnewline
56 & 5903352 & 6170400.48264541 & -267048.482645413 \tabularnewline
57 & 6179160 & 6285556.34383274 & -106396.343832738 \tabularnewline
58 & 5421000 & 5884278.55035048 & -463278.550350476 \tabularnewline
59 & 5787912 & 5900863.35934885 & -112951.359348851 \tabularnewline
60 & 5994456 & 5821009.62237761 & 173446.377622389 \tabularnewline
61 & 6201312 & 5911761.92624338 & 289550.073756618 \tabularnewline
62 & 5903352 & 5782550.35713798 & 120801.642862018 \tabularnewline
63 & 5903352 & 5957521.20191753 & -54169.2019175291 \tabularnewline
64 & 5903352 & 5932641.73011852 & -29289.7301185234 \tabularnewline
65 & 6063408 & 6185869.6031738 & -122461.603173801 \tabularnewline
66 & 5834712 & 6013588.29091678 & -178876.290916783 \tabularnewline
67 & 5534568 & 5725912.50630166 & -191344.506301661 \tabularnewline
68 & 5283408 & 5434002.41254911 & -150594.412549114 \tabularnewline
69 & 5465616 & 5670304.43459886 & -204688.434598864 \tabularnewline
70 & 4754256 & 4992800.9397078 & -238544.939707795 \tabularnewline
71 & 5190120 & 5290520.62868633 & -100400.628686328 \tabularnewline
72 & 5443464 & 5368107.06249119 & 75356.937508815 \tabularnewline
73 & 5489952 & 5467620.48623732 & 22331.513762678 \tabularnewline
74 & 5236608 & 5102236.97476663 & 134371.025233373 \tabularnewline
75 & 5258760 & 5151505.97670311 & 107254.023296892 \tabularnewline
76 & 5190120 & 5183920.2006036 & 6199.799396405 \tabularnewline
77 & 5421000 & 5374123.51039128 & 46876.4896087227 \tabularnewline
78 & 5258760 & 5219358.75350288 & 39401.2464971188 \tabularnewline
79 & 4938960 & 5000878.37687939 & -61918.3768793894 \tabularnewline
80 & 4707768 & 4777179.85772039 & -69411.8577203946 \tabularnewline
81 & 5098704 & 5007861.67254707 & 90842.327452925 \tabularnewline
82 & 4249752 & 4431385.77994051 & -181633.779940511 \tabularnewline
83 & 4801056 & 4837180.14602186 & -36124.1460218551 \tabularnewline
84 & 5052216 & 5049874.71825595 & 2341.28174405266 \tabularnewline
85 & 5052216 & 5090888.92143732 & -38672.9214373231 \tabularnewline
86 & 4754256 & 4768436.45096485 & -14180.4509648466 \tabularnewline
87 & 4478760 & 4738514.51928981 & -259754.519289806 \tabularnewline
88 & 4456608 & 4549622.27126619 & -93014.271266195 \tabularnewline
89 & 4707768 & 4708754.30343929 & -986.303439285606 \tabularnewline
90 & 4478760 & 4513847.53184785 & -35087.5318478504 \tabularnewline
91 & 4043208 & 4186679.19488662 & -143471.194886621 \tabularnewline
92 & 3743064 & 3905090.91454503 & -162026.914545033 \tabularnewline
93 & 4065360 & 4170729.17077936 & -105369.170779362 \tabularnewline
94 & 3307512 & 3324760.09964814 & -17248.0996481385 \tabularnewline
95 & 3996408 & 3860084.08066651 & 136323.919333492 \tabularnewline
96 & 4363008 & 4146431.66934643 & 216576.330653571 \tabularnewline
97 & 4478760 & 4236376.62413636 & 242383.375863638 \tabularnewline
98 & 4225416 & 4036244.77105622 & 189171.22894378 \tabularnewline
99 & 3905304 & 3941867.64139534 & -36563.6413953402 \tabularnewline
100 & 4134312 & 3947584.47922245 & 186727.520777551 \tabularnewline
101 & 4225416 & 4287135.89512573 & -61719.8951257262 \tabularnewline
102 & 4156464 & 4058047.24566664 & 98416.7543333624 \tabularnewline
103 & 3467256 & 3734748.90316278 & -267492.903162776 \tabularnewline
104 & 3147456 & 3402817.58891009 & -255361.588910087 \tabularnewline
105 & 3376152 & 3672836.85843736 & -296684.85843736 \tabularnewline
106 & 2687256 & 2805239.3774904 & -117983.3774904 \tabularnewline
107 & 3398616 & 3391937.46385711 & 6678.53614289034 \tabularnewline
108 & 3651960 & 3670950.0740418 & -18990.0740418038 \tabularnewline
109 & 3858504 & 3672088.72569216 & 186415.274307837 \tabularnewline
110 & 3514056 & 3407496.4608135 & 106559.539186496 \tabularnewline
111 & 3191760 & 3133106.77634117 & 58653.2236588276 \tabularnewline
112 & 3376152 & 3300399.25574388 & 75752.7442561202 \tabularnewline
113 & 3467256 & 3434523.05439265 & 32732.9456073465 \tabularnewline
114 & 3285048 & 3328712.99094381 & -43664.9909438128 \tabularnewline
115 & 2596152 & 2716282.67790525 & -120130.677905248 \tabularnewline
116 & 2296008 & 2441202.08815502 & -145194.088155023 \tabularnewline
117 & 2571504 & 2724089.47949192 & -152585.479491921 \tabularnewline
118 & 1813656 & 2017721.99328533 & -204065.993285334 \tabularnewline
119 & 2640456 & 2637961.12693557 & 2494.8730644295 \tabularnewline
120 & 3147456 & 2894207.44036077 & 253248.559639227 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307516&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]5879016[/C][C]5878760.33333334[/C][C]255.666666664183[/C][/ROW]
[ROW][C]14[/C][C]5879016[/C][C]5865857.65236248[/C][C]13158.3476375155[/C][/ROW]
[ROW][C]15[/C][C]5834712[/C][C]5813289.10715865[/C][C]21422.8928413512[/C][/ROW]
[ROW][C]16[/C][C]5718960[/C][C]5696978.80076488[/C][C]21981.1992351161[/C][/ROW]
[ROW][C]17[/C][C]6316752[/C][C]6300772.66434102[/C][C]15979.3356589833[/C][/ROW]
[ROW][C]18[/C][C]6407856[/C][C]6392990.61486772[/C][C]14865.385132282[/C][/ROW]
[ROW][C]19[/C][C]6270264[/C][C]6049008.8010499[/C][C]221255.198950103[/C][/ROW]
[ROW][C]20[/C][C]5947968[/C][C]5932545.04132785[/C][C]15422.95867215[/C][/ROW]
[ROW][C]21[/C][C]6085872[/C][C]5984198.97304947[/C][C]101673.026950527[/C][/ROW]
[ROW][C]22[/C][C]5879016[/C][C]6055116.77516339[/C][C]-176100.775163388[/C][/ROW]
[ROW][C]23[/C][C]5972304[/C][C]6030623.42631396[/C][C]-58319.4263139572[/C][/ROW]
[ROW][C]24[/C][C]6016920[/C][C]6061446.72138703[/C][C]-44526.7213870315[/C][/ROW]
[ROW][C]25[/C][C]6063408[/C][C]6108067.33961396[/C][C]-44659.3396139629[/C][/ROW]
[ROW][C]26[/C][C]5947968[/C][C]6087302.88198016[/C][C]-139334.881980159[/C][/ROW]
[ROW][C]27[/C][C]5972304[/C][C]5976520.29360963[/C][C]-4216.29360963311[/C][/ROW]
[ROW][C]28[/C][C]5810064[/C][C]5848162.24384929[/C][C]-38098.2438492896[/C][/ROW]
[ROW][C]29[/C][C]6316752[/C][C]6420475.96550625[/C][C]-103723.965506249[/C][/ROW]
[ROW][C]30[/C][C]6476808[/C][C]6456821.7457788[/C][C]19986.2542212[/C][/ROW]
[ROW][C]31[/C][C]6339216[/C][C]6231091.85493635[/C][C]108124.145063649[/C][/ROW]
[ROW][C]32[/C][C]6085872[/C][C]5936858.03423191[/C][C]149013.96576809[/C][/ROW]
[ROW][C]33[/C][C]6361368[/C][C]6087931.49989187[/C][C]273436.500108135[/C][/ROW]
[ROW][C]34[/C][C]6063408[/C][C]6061764.4886294[/C][C]1643.51137059648[/C][/ROW]
[ROW][C]35[/C][C]6339216[/C][C]6182478.71185664[/C][C]156737.288143359[/C][/ROW]
[ROW][C]36[/C][C]6316752[/C][C]6317420.6169302[/C][C]-668.616930204444[/C][/ROW]
[ROW][C]37[/C][C]6385704[/C][C]6391631.89694737[/C][C]-5927.89694736991[/C][/ROW]
[ROW][C]38[/C][C]6132360[/C][C]6341172.35912859[/C][C]-208812.359128593[/C][/ROW]
[ROW][C]39[/C][C]6407856[/C][C]6291664.63693951[/C][C]116191.363060489[/C][/ROW]
[ROW][C]40[/C][C]6385704[/C][C]6204201.67775932[/C][C]181502.322240679[/C][/ROW]
[ROW][C]41[/C][C]6799104[/C][C]6844484.10035803[/C][C]-45380.1003580298[/C][/ROW]
[ROW][C]42[/C][C]6705816[/C][C]6997550.08951918[/C][C]-291734.089519177[/C][/ROW]
[ROW][C]43[/C][C]6339216[/C][C]6709231.85439308[/C][C]-370015.854393085[/C][/ROW]
[ROW][C]44[/C][C]6154512[/C][C]6244351.67143992[/C][C]-89839.6714399206[/C][/ROW]
[ROW][C]45[/C][C]6407856[/C][C]6365198.50868288[/C][C]42657.4913171204[/C][/ROW]
[ROW][C]46[/C][C]6063408[/C][C]6070430.07047742[/C][C]-7022.07047741953[/C][/ROW]
[ROW][C]47[/C][C]6316752[/C][C]6266199.56538876[/C][C]50552.4346112395[/C][/ROW]
[ROW][C]48[/C][C]6361368[/C][C]6248060.86064092[/C][C]113307.139359078[/C][/ROW]
[ROW][C]49[/C][C]6454656[/C][C]6351887.90517126[/C][C]102768.094828735[/C][/ROW]
[ROW][C]50[/C][C]6248112[/C][C]6214227.49596061[/C][C]33884.5040393863[/C][/ROW]
[ROW][C]51[/C][C]6361368[/C][C]6452094.76225947[/C][C]-90726.7622594675[/C][/ROW]
[ROW][C]52[/C][C]6430320[/C][C]6309918.94717352[/C][C]120401.052826477[/C][/ROW]
[ROW][C]53[/C][C]6683664[/C][C]6779241.56292729[/C][C]-95577.5629272871[/C][/ROW]
[ROW][C]54[/C][C]6476808[/C][C]6752875.83215542[/C][C]-276067.832155419[/C][/ROW]
[ROW][C]55[/C][C]6201312[/C][C]6412178.31193054[/C][C]-210866.311930543[/C][/ROW]
[ROW][C]56[/C][C]5903352[/C][C]6170400.48264541[/C][C]-267048.482645413[/C][/ROW]
[ROW][C]57[/C][C]6179160[/C][C]6285556.34383274[/C][C]-106396.343832738[/C][/ROW]
[ROW][C]58[/C][C]5421000[/C][C]5884278.55035048[/C][C]-463278.550350476[/C][/ROW]
[ROW][C]59[/C][C]5787912[/C][C]5900863.35934885[/C][C]-112951.359348851[/C][/ROW]
[ROW][C]60[/C][C]5994456[/C][C]5821009.62237761[/C][C]173446.377622389[/C][/ROW]
[ROW][C]61[/C][C]6201312[/C][C]5911761.92624338[/C][C]289550.073756618[/C][/ROW]
[ROW][C]62[/C][C]5903352[/C][C]5782550.35713798[/C][C]120801.642862018[/C][/ROW]
[ROW][C]63[/C][C]5903352[/C][C]5957521.20191753[/C][C]-54169.2019175291[/C][/ROW]
[ROW][C]64[/C][C]5903352[/C][C]5932641.73011852[/C][C]-29289.7301185234[/C][/ROW]
[ROW][C]65[/C][C]6063408[/C][C]6185869.6031738[/C][C]-122461.603173801[/C][/ROW]
[ROW][C]66[/C][C]5834712[/C][C]6013588.29091678[/C][C]-178876.290916783[/C][/ROW]
[ROW][C]67[/C][C]5534568[/C][C]5725912.50630166[/C][C]-191344.506301661[/C][/ROW]
[ROW][C]68[/C][C]5283408[/C][C]5434002.41254911[/C][C]-150594.412549114[/C][/ROW]
[ROW][C]69[/C][C]5465616[/C][C]5670304.43459886[/C][C]-204688.434598864[/C][/ROW]
[ROW][C]70[/C][C]4754256[/C][C]4992800.9397078[/C][C]-238544.939707795[/C][/ROW]
[ROW][C]71[/C][C]5190120[/C][C]5290520.62868633[/C][C]-100400.628686328[/C][/ROW]
[ROW][C]72[/C][C]5443464[/C][C]5368107.06249119[/C][C]75356.937508815[/C][/ROW]
[ROW][C]73[/C][C]5489952[/C][C]5467620.48623732[/C][C]22331.513762678[/C][/ROW]
[ROW][C]74[/C][C]5236608[/C][C]5102236.97476663[/C][C]134371.025233373[/C][/ROW]
[ROW][C]75[/C][C]5258760[/C][C]5151505.97670311[/C][C]107254.023296892[/C][/ROW]
[ROW][C]76[/C][C]5190120[/C][C]5183920.2006036[/C][C]6199.799396405[/C][/ROW]
[ROW][C]77[/C][C]5421000[/C][C]5374123.51039128[/C][C]46876.4896087227[/C][/ROW]
[ROW][C]78[/C][C]5258760[/C][C]5219358.75350288[/C][C]39401.2464971188[/C][/ROW]
[ROW][C]79[/C][C]4938960[/C][C]5000878.37687939[/C][C]-61918.3768793894[/C][/ROW]
[ROW][C]80[/C][C]4707768[/C][C]4777179.85772039[/C][C]-69411.8577203946[/C][/ROW]
[ROW][C]81[/C][C]5098704[/C][C]5007861.67254707[/C][C]90842.327452925[/C][/ROW]
[ROW][C]82[/C][C]4249752[/C][C]4431385.77994051[/C][C]-181633.779940511[/C][/ROW]
[ROW][C]83[/C][C]4801056[/C][C]4837180.14602186[/C][C]-36124.1460218551[/C][/ROW]
[ROW][C]84[/C][C]5052216[/C][C]5049874.71825595[/C][C]2341.28174405266[/C][/ROW]
[ROW][C]85[/C][C]5052216[/C][C]5090888.92143732[/C][C]-38672.9214373231[/C][/ROW]
[ROW][C]86[/C][C]4754256[/C][C]4768436.45096485[/C][C]-14180.4509648466[/C][/ROW]
[ROW][C]87[/C][C]4478760[/C][C]4738514.51928981[/C][C]-259754.519289806[/C][/ROW]
[ROW][C]88[/C][C]4456608[/C][C]4549622.27126619[/C][C]-93014.271266195[/C][/ROW]
[ROW][C]89[/C][C]4707768[/C][C]4708754.30343929[/C][C]-986.303439285606[/C][/ROW]
[ROW][C]90[/C][C]4478760[/C][C]4513847.53184785[/C][C]-35087.5318478504[/C][/ROW]
[ROW][C]91[/C][C]4043208[/C][C]4186679.19488662[/C][C]-143471.194886621[/C][/ROW]
[ROW][C]92[/C][C]3743064[/C][C]3905090.91454503[/C][C]-162026.914545033[/C][/ROW]
[ROW][C]93[/C][C]4065360[/C][C]4170729.17077936[/C][C]-105369.170779362[/C][/ROW]
[ROW][C]94[/C][C]3307512[/C][C]3324760.09964814[/C][C]-17248.0996481385[/C][/ROW]
[ROW][C]95[/C][C]3996408[/C][C]3860084.08066651[/C][C]136323.919333492[/C][/ROW]
[ROW][C]96[/C][C]4363008[/C][C]4146431.66934643[/C][C]216576.330653571[/C][/ROW]
[ROW][C]97[/C][C]4478760[/C][C]4236376.62413636[/C][C]242383.375863638[/C][/ROW]
[ROW][C]98[/C][C]4225416[/C][C]4036244.77105622[/C][C]189171.22894378[/C][/ROW]
[ROW][C]99[/C][C]3905304[/C][C]3941867.64139534[/C][C]-36563.6413953402[/C][/ROW]
[ROW][C]100[/C][C]4134312[/C][C]3947584.47922245[/C][C]186727.520777551[/C][/ROW]
[ROW][C]101[/C][C]4225416[/C][C]4287135.89512573[/C][C]-61719.8951257262[/C][/ROW]
[ROW][C]102[/C][C]4156464[/C][C]4058047.24566664[/C][C]98416.7543333624[/C][/ROW]
[ROW][C]103[/C][C]3467256[/C][C]3734748.90316278[/C][C]-267492.903162776[/C][/ROW]
[ROW][C]104[/C][C]3147456[/C][C]3402817.58891009[/C][C]-255361.588910087[/C][/ROW]
[ROW][C]105[/C][C]3376152[/C][C]3672836.85843736[/C][C]-296684.85843736[/C][/ROW]
[ROW][C]106[/C][C]2687256[/C][C]2805239.3774904[/C][C]-117983.3774904[/C][/ROW]
[ROW][C]107[/C][C]3398616[/C][C]3391937.46385711[/C][C]6678.53614289034[/C][/ROW]
[ROW][C]108[/C][C]3651960[/C][C]3670950.0740418[/C][C]-18990.0740418038[/C][/ROW]
[ROW][C]109[/C][C]3858504[/C][C]3672088.72569216[/C][C]186415.274307837[/C][/ROW]
[ROW][C]110[/C][C]3514056[/C][C]3407496.4608135[/C][C]106559.539186496[/C][/ROW]
[ROW][C]111[/C][C]3191760[/C][C]3133106.77634117[/C][C]58653.2236588276[/C][/ROW]
[ROW][C]112[/C][C]3376152[/C][C]3300399.25574388[/C][C]75752.7442561202[/C][/ROW]
[ROW][C]113[/C][C]3467256[/C][C]3434523.05439265[/C][C]32732.9456073465[/C][/ROW]
[ROW][C]114[/C][C]3285048[/C][C]3328712.99094381[/C][C]-43664.9909438128[/C][/ROW]
[ROW][C]115[/C][C]2596152[/C][C]2716282.67790525[/C][C]-120130.677905248[/C][/ROW]
[ROW][C]116[/C][C]2296008[/C][C]2441202.08815502[/C][C]-145194.088155023[/C][/ROW]
[ROW][C]117[/C][C]2571504[/C][C]2724089.47949192[/C][C]-152585.479491921[/C][/ROW]
[ROW][C]118[/C][C]1813656[/C][C]2017721.99328533[/C][C]-204065.993285334[/C][/ROW]
[ROW][C]119[/C][C]2640456[/C][C]2637961.12693557[/C][C]2494.8730644295[/C][/ROW]
[ROW][C]120[/C][C]3147456[/C][C]2894207.44036077[/C][C]253248.559639227[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307516&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307516&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
1358790165878760.33333334255.666666664183
1458790165865857.6523624813158.3476375155
1558347125813289.1071586521422.8928413512
1657189605696978.8007648821981.1992351161
1763167526300772.6643410215979.3356589833
1864078566392990.6148677214865.385132282
1962702646049008.8010499221255.198950103
2059479685932545.0413278515422.95867215
2160858725984198.97304947101673.026950527
2258790166055116.77516339-176100.775163388
2359723046030623.42631396-58319.4263139572
2460169206061446.72138703-44526.7213870315
2560634086108067.33961396-44659.3396139629
2659479686087302.88198016-139334.881980159
2759723045976520.29360963-4216.29360963311
2858100645848162.24384929-38098.2438492896
2963167526420475.96550625-103723.965506249
3064768086456821.745778819986.2542212
3163392166231091.85493635108124.145063649
3260858725936858.03423191149013.96576809
3363613686087931.49989187273436.500108135
3460634086061764.48862941643.51137059648
3563392166182478.71185664156737.288143359
3663167526317420.6169302-668.616930204444
3763857046391631.89694737-5927.89694736991
3861323606341172.35912859-208812.359128593
3964078566291664.63693951116191.363060489
4063857046204201.67775932181502.322240679
4167991046844484.10035803-45380.1003580298
4267058166997550.08951918-291734.089519177
4363392166709231.85439308-370015.854393085
4461545126244351.67143992-89839.6714399206
4564078566365198.5086828842657.4913171204
4660634086070430.07047742-7022.07047741953
4763167526266199.5653887650552.4346112395
4863613686248060.86064092113307.139359078
4964546566351887.90517126102768.094828735
5062481126214227.4959606133884.5040393863
5163613686452094.76225947-90726.7622594675
5264303206309918.94717352120401.052826477
5366836646779241.56292729-95577.5629272871
5464768086752875.83215542-276067.832155419
5562013126412178.31193054-210866.311930543
5659033526170400.48264541-267048.482645413
5761791606285556.34383274-106396.343832738
5854210005884278.55035048-463278.550350476
5957879125900863.35934885-112951.359348851
6059944565821009.62237761173446.377622389
6162013125911761.92624338289550.073756618
6259033525782550.35713798120801.642862018
6359033525957521.20191753-54169.2019175291
6459033525932641.73011852-29289.7301185234
6560634086185869.6031738-122461.603173801
6658347126013588.29091678-178876.290916783
6755345685725912.50630166-191344.506301661
6852834085434002.41254911-150594.412549114
6954656165670304.43459886-204688.434598864
7047542564992800.9397078-238544.939707795
7151901205290520.62868633-100400.628686328
7254434645368107.0624911975356.937508815
7354899525467620.4862373222331.513762678
7452366085102236.97476663134371.025233373
7552587605151505.97670311107254.023296892
7651901205183920.20060366199.799396405
7754210005374123.5103912846876.4896087227
7852587605219358.7535028839401.2464971188
7949389605000878.37687939-61918.3768793894
8047077684777179.85772039-69411.8577203946
8150987045007861.6725470790842.327452925
8242497524431385.77994051-181633.779940511
8348010564837180.14602186-36124.1460218551
8450522165049874.718255952341.28174405266
8550522165090888.92143732-38672.9214373231
8647542564768436.45096485-14180.4509648466
8744787604738514.51928981-259754.519289806
8844566084549622.27126619-93014.271266195
8947077684708754.30343929-986.303439285606
9044787604513847.53184785-35087.5318478504
9140432084186679.19488662-143471.194886621
9237430643905090.91454503-162026.914545033
9340653604170729.17077936-105369.170779362
9433075123324760.09964814-17248.0996481385
9539964083860084.08066651136323.919333492
9643630084146431.66934643216576.330653571
9744787604236376.62413636242383.375863638
9842254164036244.77105622189171.22894378
9939053043941867.64139534-36563.6413953402
10041343123947584.47922245186727.520777551
10142254164287135.89512573-61719.8951257262
10241564644058047.2456666498416.7543333624
10334672563734748.90316278-267492.903162776
10431474563402817.58891009-255361.588910087
10533761523672836.85843736-296684.85843736
10626872562805239.3774904-117983.3774904
10733986163391937.463857116678.53614289034
10836519603670950.0740418-18990.0740418038
10938585043672088.72569216186415.274307837
11035140563407496.4608135106559.539186496
11131917603133106.7763411758653.2236588276
11233761523300399.2557438875752.7442561202
11334672563434523.0543926532732.9456073465
11432850483328712.99094381-43664.9909438128
11525961522716282.67790525-120130.677905248
11622960082441202.08815502-145194.088155023
11725715042724089.47949192-152585.479491921
11818136562017721.99328533-204065.993285334
11926404562637961.126935572494.8730644295
12031474562894207.44036077253248.559639227







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1213129155.119431932844308.015721923414002.22314193
1222737951.995935492427718.52902693048185.46284409
1232385532.558679682049023.324543362722041.79281601
1242531336.019129052167701.801906732894970.23635138
1252599308.126596812207734.466535272990881.78665836
1262424079.553082012003782.377202192844376.72896183
1271774299.761483761324521.829869952224077.69309758
1281526572.971228191046580.954801892006564.98765448
1291861279.425166791350361.47707012372197.37326348
1301187499.64428291644963.3609192121730035.9276466
1312019976.707483691445147.400205882594806.0147615
1322430947.271256971823166.488127263038728.05438668

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 3129155.11943193 & 2844308.01572192 & 3414002.22314193 \tabularnewline
122 & 2737951.99593549 & 2427718.5290269 & 3048185.46284409 \tabularnewline
123 & 2385532.55867968 & 2049023.32454336 & 2722041.79281601 \tabularnewline
124 & 2531336.01912905 & 2167701.80190673 & 2894970.23635138 \tabularnewline
125 & 2599308.12659681 & 2207734.46653527 & 2990881.78665836 \tabularnewline
126 & 2424079.55308201 & 2003782.37720219 & 2844376.72896183 \tabularnewline
127 & 1774299.76148376 & 1324521.82986995 & 2224077.69309758 \tabularnewline
128 & 1526572.97122819 & 1046580.95480189 & 2006564.98765448 \tabularnewline
129 & 1861279.42516679 & 1350361.4770701 & 2372197.37326348 \tabularnewline
130 & 1187499.64428291 & 644963.360919212 & 1730035.9276466 \tabularnewline
131 & 2019976.70748369 & 1445147.40020588 & 2594806.0147615 \tabularnewline
132 & 2430947.27125697 & 1823166.48812726 & 3038728.05438668 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307516&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]121[/C][C]3129155.11943193[/C][C]2844308.01572192[/C][C]3414002.22314193[/C][/ROW]
[ROW][C]122[/C][C]2737951.99593549[/C][C]2427718.5290269[/C][C]3048185.46284409[/C][/ROW]
[ROW][C]123[/C][C]2385532.55867968[/C][C]2049023.32454336[/C][C]2722041.79281601[/C][/ROW]
[ROW][C]124[/C][C]2531336.01912905[/C][C]2167701.80190673[/C][C]2894970.23635138[/C][/ROW]
[ROW][C]125[/C][C]2599308.12659681[/C][C]2207734.46653527[/C][C]2990881.78665836[/C][/ROW]
[ROW][C]126[/C][C]2424079.55308201[/C][C]2003782.37720219[/C][C]2844376.72896183[/C][/ROW]
[ROW][C]127[/C][C]1774299.76148376[/C][C]1324521.82986995[/C][C]2224077.69309758[/C][/ROW]
[ROW][C]128[/C][C]1526572.97122819[/C][C]1046580.95480189[/C][C]2006564.98765448[/C][/ROW]
[ROW][C]129[/C][C]1861279.42516679[/C][C]1350361.4770701[/C][C]2372197.37326348[/C][/ROW]
[ROW][C]130[/C][C]1187499.64428291[/C][C]644963.360919212[/C][C]1730035.9276466[/C][/ROW]
[ROW][C]131[/C][C]2019976.70748369[/C][C]1445147.40020588[/C][C]2594806.0147615[/C][/ROW]
[ROW][C]132[/C][C]2430947.27125697[/C][C]1823166.48812726[/C][C]3038728.05438668[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307516&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307516&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
1213129155.119431932844308.015721923414002.22314193
1222737951.995935492427718.52902693048185.46284409
1232385532.558679682049023.324543362722041.79281601
1242531336.019129052167701.801906732894970.23635138
1252599308.126596812207734.466535272990881.78665836
1262424079.553082012003782.377202192844376.72896183
1271774299.761483761324521.829869952224077.69309758
1281526572.971228191046580.954801892006564.98765448
1291861279.425166791350361.47707012372197.37326348
1301187499.64428291644963.3609192121730035.9276466
1312019976.707483691445147.400205882594806.0147615
1322430947.271256971823166.488127263038728.05438668



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')