Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 06 Aug 2015 14:12:14 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Aug/06/t1438866781uc2hmoui6lm0e7r.htm/, Retrieved Thu, 16 May 2024 14:50:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279872, Retrieved Thu, 16 May 2024 14:50:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-08-06 13:12:14] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
5947968.00
5925816.00
5903352.00
5856864.00
6316752.00
6292416.00
5947968.00
5718960.00
5741112.00
5741112.00
5765760.00
5810064.00
5879016.00
5879016.00
5834712.00
5718960.00
6316752.00
6407856.00
6270264.00
5947968.00
6085872.00
5879016.00
5972304.00
6016920.00
6063408.00
5947968.00
5972304.00
5810064.00
6316752.00
6476808.00
6339216.00
6085872.00
6361368.00
6063408.00
6339216.00
6316752.00
6385704.00
6132360.00
6407856.00
6385704.00
6799104.00
6705816.00
6339216.00
6154512.00
6407856.00
6063408.00
6316752.00
6361368.00
6454656.00
6248112.00
6361368.00
6430320.00
6683664.00
6476808.00
6201312.00
5903352.00
6179160.00
5421000.00
5787912.00
5994456.00
6201312.00
5903352.00
5903352.00
5903352.00
6063408.00
5834712.00
5534568.00
5283408.00
5465616.00
4754256.00
5190120.00
5443464.00
5489952.00
5236608.00
5258760.00
5190120.00
5421000.00
5258760.00
4938960.00
4707768.00
5098704.00
4249752.00
4801056.00
5052216.00
5052216.00
4754256.00
4478760.00
4456608.00
4707768.00
4478760.00
4043208.00
3743064.00
4065360.00
3307512.00
3996408.00
4363008.00
4478760.00
4225416.00
3905304.00
4134312.00
4225416.00
4156464.00
3467256.00
3147456.00
3376152.00
2687256.00
3398616.00
3651960.00
3858504.00
3514056.00
3191760.00
3376152.00
3467256.00
3285048.00
2596152.00
2296008.00
2571504.00
1813656.00
2640456.00
3147456.00




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279872&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279872&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279872&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







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=279872&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=279872&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279872&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=279872&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=279872&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279872&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=279872&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=279872&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279872&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):
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')