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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 11 Dec 2016 12:36:24 +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/2016/Dec/11/t14814562023yzgas9kbj3klce.htm/, Retrieved Thu, 02 May 2024 04:11:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298766, Retrieved Thu, 02 May 2024 04:11:09 +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] [Expontential Smoo...] [2016-12-11 11:36:24] [e1e79d437a44c5123ccedd8a903518e8] [Current]
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Dataseries X:
4730
4760
4815
4995
4960
5065
5075
5085
5095
5140
5140
5140
5365
5085
5105
5200
5205
5160
5140
5150
5210
5205
5200
5095
5140
5165
5190
5050
5055
4985
4995
5010
5010
5020
5170
5155
5155
5150
5130
5170
5180
5175
5185
5200
5205
5210
5195
5195
5210
5205
5235
5235
5205
5195
5200
5165
5170
5255
5240
5265
5275
5285
5320
5335
5335
5325
5355
5375
5445
5415
5415
5450
5535
5570
5590
5575
5575
5595
5650
5680
5665
5675
5700
5700
5710
5745
5745
5765
5740
5725
5765
5900
5900
5900
5890
5935
5945
6000
6000
5995
6065
6065
6065
6075
6070
6085
6095
6095
6065
6115
6190
6200
6205
6210
6230
6235
6235
6235
6225
6225
6255
6310
6305
6320
6320
6330




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=298766&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=298766&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298766&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
alpha0.439017108194885
beta0
gamma0.730635320707144

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.439017108194885 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.730635320707144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298766&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]0.439017108194885[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.730635320707144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298766&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298766&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
alpha0.439017108194885
beta0
gamma0.730635320707144







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1353655257.31303418804107.686965811962
1450855031.7194078890453.2805921109593
1551055080.1571194071224.8428805928752
1652005191.110189050868.88981094914107
1752055207.35125485944-2.35125485943718
1851605173.24063379704-13.2406337970378
1951405247.05772241675-107.057722416746
2051505182.60417075804-32.6041707580362
2152105165.2120020433744.7879979566287
2252055221.79631943475-16.7963194347494
2352005208.21906789481-8.21906789480727
2450955202.99070985552-107.990709855523
2551405430.59897236164-290.598972361639
2651655007.85125185765157.148748142351
2751905090.2329847147699.7670152852434
2850505227.54028419295-177.540284192952
2950555157.32792909928-102.327929099282
3049855074.86256524738-89.8625652473811
3149955076.58813768487-81.5881376848702
3250105053.83273817094-43.8327381709405
3350105063.23206744796-53.2320674479606
3450205051.54209390452-31.5420939045171
3551705035.00678676794134.993213232061
3651555051.75727674404103.242723255961
3751555297.25426673219-142.254266732192
3851505123.1525210741726.8474789258253
3951305124.810492026355.18950797365051
4051705106.9356192310363.0643807689703
4151805173.180410810666.81958918933742
4251755143.7419022891731.25809771083
4351855202.03298994119-17.0329899411909
4452005223.09335812241-23.0933581224126
4552055237.74509016433-32.7450901643324
4652105243.93940451751-33.939404517514
4751955294.61011534084-99.6101153408372
4851955195.35203280222-0.35203280222413
4952105294.74634013838-84.7463401383784
5052055215.20195264908-10.2019526490812
5152355191.7175519444443.2824480555619
5252355214.2875322430420.7124677569591
5352055238.88583651885-33.8858365188471
5451955201.59365688116-6.59365688116395
5552005223.47391953341-23.4739195334123
5651655239.2226225978-74.2226225977956
5751705227.47173960642-57.4717396064198
5852555222.3211135264332.678886473569
5952405275.32168246327-35.3216824632709
6052655244.9706207089220.0293792910807
6152755318.72169148612-43.7216914861156
6252855287.74162655923-2.74162655922555
6353205289.4542973524730.545702647526
6453355297.1817823262937.8182176737082
6553355306.9113827346128.0886172653936
6653255308.01340109816.9865989020009
6753555333.3270201140621.6729798859387
6853755348.0954147960126.9045852039899
6954455387.6068561260757.3931438739282
7054155469.83426908176-54.8342690817562
7154155456.54340612088-41.5434061208807
7254505446.147857622653.85214237734726
7355355486.6669436623548.333056337653
7455705512.8971475718757.102852428131
7555905554.5261764156135.473823584387
7655755567.398004998127.60199500188173
7755755559.874257297115.1257427029004
7855955550.7349242244444.2650757755582
7956505589.9450865948760.0549134051325
8056805623.7081052911356.2918947088729
8156655688.61754316439-23.6175431643942
8256755689.28078943784-14.2807894378429
8357005699.241175873850.758824126152831
8457005726.02348135837-26.0234813583693
8557105771.65822381068-61.6582238106812
8657455753.19488464076-8.19488464075675
8757455757.2919150536-12.2919150536027
8857655737.7698316873327.2301683126743
8957405741.94697579854-1.94697579853982
9057255737.25587974924-12.2558797492356
9157655758.124218240236.87578175976705
9259005766.99832513973133.00167486027
9359005832.8318747135567.168125286451
9459005877.1784744197322.8215255802706
9558905909.59175719487-19.5917571948657
9659355916.4624409143318.5375590856656
9759455967.05449107927-22.0544910792723
9860005987.8910962648512.1089037351476
9960005999.222571240430.777428759565737
10059956001.63722444189-6.63722444189079
10160655978.9870534366186.0129465633909
10260656008.6865173173856.3134826826172
10360656067.49954801838-2.49954801837703
10460756123.9534383465-48.9534383465043
10560706082.92212559255-12.9221255925495
10660856073.9312205218211.0687794781752
10760956083.8007484280611.1992515719439
10860956119.8174239174-24.8174239173959
10960656134.73827229686-69.7382722968632
11061156148.64356612901-33.6435661290052
11161906135.2444480803554.7555519196512
11262006158.317347880841.6826521191988
11362056194.855317673110.144682326898
11462106179.0742800488530.9257199511458
11562306202.6357214216727.3642785783286
11662356253.16010464312-18.160104643116
11762356240.41588742671-5.41588742670683
11862356244.55359551627-9.55359551626862
11962256245.42302509621-20.4230250962082
12062256252.79468433771-27.7946843377067
12162556247.996580463767.00341953623956
12263106310.3870684526-0.387068452603671
12363056347.82061444545-42.820614445448
12463206322.69766723708-2.69766723708472
12563206326.82532641284-6.82532641284433
12663306312.111769875817.8882301241993

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5365 & 5257.31303418804 & 107.686965811962 \tabularnewline
14 & 5085 & 5031.71940788904 & 53.2805921109593 \tabularnewline
15 & 5105 & 5080.15711940712 & 24.8428805928752 \tabularnewline
16 & 5200 & 5191.11018905086 & 8.88981094914107 \tabularnewline
17 & 5205 & 5207.35125485944 & -2.35125485943718 \tabularnewline
18 & 5160 & 5173.24063379704 & -13.2406337970378 \tabularnewline
19 & 5140 & 5247.05772241675 & -107.057722416746 \tabularnewline
20 & 5150 & 5182.60417075804 & -32.6041707580362 \tabularnewline
21 & 5210 & 5165.21200204337 & 44.7879979566287 \tabularnewline
22 & 5205 & 5221.79631943475 & -16.7963194347494 \tabularnewline
23 & 5200 & 5208.21906789481 & -8.21906789480727 \tabularnewline
24 & 5095 & 5202.99070985552 & -107.990709855523 \tabularnewline
25 & 5140 & 5430.59897236164 & -290.598972361639 \tabularnewline
26 & 5165 & 5007.85125185765 & 157.148748142351 \tabularnewline
27 & 5190 & 5090.23298471476 & 99.7670152852434 \tabularnewline
28 & 5050 & 5227.54028419295 & -177.540284192952 \tabularnewline
29 & 5055 & 5157.32792909928 & -102.327929099282 \tabularnewline
30 & 4985 & 5074.86256524738 & -89.8625652473811 \tabularnewline
31 & 4995 & 5076.58813768487 & -81.5881376848702 \tabularnewline
32 & 5010 & 5053.83273817094 & -43.8327381709405 \tabularnewline
33 & 5010 & 5063.23206744796 & -53.2320674479606 \tabularnewline
34 & 5020 & 5051.54209390452 & -31.5420939045171 \tabularnewline
35 & 5170 & 5035.00678676794 & 134.993213232061 \tabularnewline
36 & 5155 & 5051.75727674404 & 103.242723255961 \tabularnewline
37 & 5155 & 5297.25426673219 & -142.254266732192 \tabularnewline
38 & 5150 & 5123.15252107417 & 26.8474789258253 \tabularnewline
39 & 5130 & 5124.81049202635 & 5.18950797365051 \tabularnewline
40 & 5170 & 5106.93561923103 & 63.0643807689703 \tabularnewline
41 & 5180 & 5173.18041081066 & 6.81958918933742 \tabularnewline
42 & 5175 & 5143.74190228917 & 31.25809771083 \tabularnewline
43 & 5185 & 5202.03298994119 & -17.0329899411909 \tabularnewline
44 & 5200 & 5223.09335812241 & -23.0933581224126 \tabularnewline
45 & 5205 & 5237.74509016433 & -32.7450901643324 \tabularnewline
46 & 5210 & 5243.93940451751 & -33.939404517514 \tabularnewline
47 & 5195 & 5294.61011534084 & -99.6101153408372 \tabularnewline
48 & 5195 & 5195.35203280222 & -0.35203280222413 \tabularnewline
49 & 5210 & 5294.74634013838 & -84.7463401383784 \tabularnewline
50 & 5205 & 5215.20195264908 & -10.2019526490812 \tabularnewline
51 & 5235 & 5191.71755194444 & 43.2824480555619 \tabularnewline
52 & 5235 & 5214.28753224304 & 20.7124677569591 \tabularnewline
53 & 5205 & 5238.88583651885 & -33.8858365188471 \tabularnewline
54 & 5195 & 5201.59365688116 & -6.59365688116395 \tabularnewline
55 & 5200 & 5223.47391953341 & -23.4739195334123 \tabularnewline
56 & 5165 & 5239.2226225978 & -74.2226225977956 \tabularnewline
57 & 5170 & 5227.47173960642 & -57.4717396064198 \tabularnewline
58 & 5255 & 5222.32111352643 & 32.678886473569 \tabularnewline
59 & 5240 & 5275.32168246327 & -35.3216824632709 \tabularnewline
60 & 5265 & 5244.97062070892 & 20.0293792910807 \tabularnewline
61 & 5275 & 5318.72169148612 & -43.7216914861156 \tabularnewline
62 & 5285 & 5287.74162655923 & -2.74162655922555 \tabularnewline
63 & 5320 & 5289.45429735247 & 30.545702647526 \tabularnewline
64 & 5335 & 5297.18178232629 & 37.8182176737082 \tabularnewline
65 & 5335 & 5306.91138273461 & 28.0886172653936 \tabularnewline
66 & 5325 & 5308.013401098 & 16.9865989020009 \tabularnewline
67 & 5355 & 5333.32702011406 & 21.6729798859387 \tabularnewline
68 & 5375 & 5348.09541479601 & 26.9045852039899 \tabularnewline
69 & 5445 & 5387.60685612607 & 57.3931438739282 \tabularnewline
70 & 5415 & 5469.83426908176 & -54.8342690817562 \tabularnewline
71 & 5415 & 5456.54340612088 & -41.5434061208807 \tabularnewline
72 & 5450 & 5446.14785762265 & 3.85214237734726 \tabularnewline
73 & 5535 & 5486.66694366235 & 48.333056337653 \tabularnewline
74 & 5570 & 5512.89714757187 & 57.102852428131 \tabularnewline
75 & 5590 & 5554.52617641561 & 35.473823584387 \tabularnewline
76 & 5575 & 5567.39800499812 & 7.60199500188173 \tabularnewline
77 & 5575 & 5559.8742572971 & 15.1257427029004 \tabularnewline
78 & 5595 & 5550.73492422444 & 44.2650757755582 \tabularnewline
79 & 5650 & 5589.94508659487 & 60.0549134051325 \tabularnewline
80 & 5680 & 5623.70810529113 & 56.2918947088729 \tabularnewline
81 & 5665 & 5688.61754316439 & -23.6175431643942 \tabularnewline
82 & 5675 & 5689.28078943784 & -14.2807894378429 \tabularnewline
83 & 5700 & 5699.24117587385 & 0.758824126152831 \tabularnewline
84 & 5700 & 5726.02348135837 & -26.0234813583693 \tabularnewline
85 & 5710 & 5771.65822381068 & -61.6582238106812 \tabularnewline
86 & 5745 & 5753.19488464076 & -8.19488464075675 \tabularnewline
87 & 5745 & 5757.2919150536 & -12.2919150536027 \tabularnewline
88 & 5765 & 5737.76983168733 & 27.2301683126743 \tabularnewline
89 & 5740 & 5741.94697579854 & -1.94697579853982 \tabularnewline
90 & 5725 & 5737.25587974924 & -12.2558797492356 \tabularnewline
91 & 5765 & 5758.12421824023 & 6.87578175976705 \tabularnewline
92 & 5900 & 5766.99832513973 & 133.00167486027 \tabularnewline
93 & 5900 & 5832.83187471355 & 67.168125286451 \tabularnewline
94 & 5900 & 5877.17847441973 & 22.8215255802706 \tabularnewline
95 & 5890 & 5909.59175719487 & -19.5917571948657 \tabularnewline
96 & 5935 & 5916.46244091433 & 18.5375590856656 \tabularnewline
97 & 5945 & 5967.05449107927 & -22.0544910792723 \tabularnewline
98 & 6000 & 5987.89109626485 & 12.1089037351476 \tabularnewline
99 & 6000 & 5999.22257124043 & 0.777428759565737 \tabularnewline
100 & 5995 & 6001.63722444189 & -6.63722444189079 \tabularnewline
101 & 6065 & 5978.98705343661 & 86.0129465633909 \tabularnewline
102 & 6065 & 6008.68651731738 & 56.3134826826172 \tabularnewline
103 & 6065 & 6067.49954801838 & -2.49954801837703 \tabularnewline
104 & 6075 & 6123.9534383465 & -48.9534383465043 \tabularnewline
105 & 6070 & 6082.92212559255 & -12.9221255925495 \tabularnewline
106 & 6085 & 6073.93122052182 & 11.0687794781752 \tabularnewline
107 & 6095 & 6083.80074842806 & 11.1992515719439 \tabularnewline
108 & 6095 & 6119.8174239174 & -24.8174239173959 \tabularnewline
109 & 6065 & 6134.73827229686 & -69.7382722968632 \tabularnewline
110 & 6115 & 6148.64356612901 & -33.6435661290052 \tabularnewline
111 & 6190 & 6135.24444808035 & 54.7555519196512 \tabularnewline
112 & 6200 & 6158.3173478808 & 41.6826521191988 \tabularnewline
113 & 6205 & 6194.8553176731 & 10.144682326898 \tabularnewline
114 & 6210 & 6179.07428004885 & 30.9257199511458 \tabularnewline
115 & 6230 & 6202.63572142167 & 27.3642785783286 \tabularnewline
116 & 6235 & 6253.16010464312 & -18.160104643116 \tabularnewline
117 & 6235 & 6240.41588742671 & -5.41588742670683 \tabularnewline
118 & 6235 & 6244.55359551627 & -9.55359551626862 \tabularnewline
119 & 6225 & 6245.42302509621 & -20.4230250962082 \tabularnewline
120 & 6225 & 6252.79468433771 & -27.7946843377067 \tabularnewline
121 & 6255 & 6247.99658046376 & 7.00341953623956 \tabularnewline
122 & 6310 & 6310.3870684526 & -0.387068452603671 \tabularnewline
123 & 6305 & 6347.82061444545 & -42.820614445448 \tabularnewline
124 & 6320 & 6322.69766723708 & -2.69766723708472 \tabularnewline
125 & 6320 & 6326.82532641284 & -6.82532641284433 \tabularnewline
126 & 6330 & 6312.1117698758 & 17.8882301241993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298766&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]5365[/C][C]5257.31303418804[/C][C]107.686965811962[/C][/ROW]
[ROW][C]14[/C][C]5085[/C][C]5031.71940788904[/C][C]53.2805921109593[/C][/ROW]
[ROW][C]15[/C][C]5105[/C][C]5080.15711940712[/C][C]24.8428805928752[/C][/ROW]
[ROW][C]16[/C][C]5200[/C][C]5191.11018905086[/C][C]8.88981094914107[/C][/ROW]
[ROW][C]17[/C][C]5205[/C][C]5207.35125485944[/C][C]-2.35125485943718[/C][/ROW]
[ROW][C]18[/C][C]5160[/C][C]5173.24063379704[/C][C]-13.2406337970378[/C][/ROW]
[ROW][C]19[/C][C]5140[/C][C]5247.05772241675[/C][C]-107.057722416746[/C][/ROW]
[ROW][C]20[/C][C]5150[/C][C]5182.60417075804[/C][C]-32.6041707580362[/C][/ROW]
[ROW][C]21[/C][C]5210[/C][C]5165.21200204337[/C][C]44.7879979566287[/C][/ROW]
[ROW][C]22[/C][C]5205[/C][C]5221.79631943475[/C][C]-16.7963194347494[/C][/ROW]
[ROW][C]23[/C][C]5200[/C][C]5208.21906789481[/C][C]-8.21906789480727[/C][/ROW]
[ROW][C]24[/C][C]5095[/C][C]5202.99070985552[/C][C]-107.990709855523[/C][/ROW]
[ROW][C]25[/C][C]5140[/C][C]5430.59897236164[/C][C]-290.598972361639[/C][/ROW]
[ROW][C]26[/C][C]5165[/C][C]5007.85125185765[/C][C]157.148748142351[/C][/ROW]
[ROW][C]27[/C][C]5190[/C][C]5090.23298471476[/C][C]99.7670152852434[/C][/ROW]
[ROW][C]28[/C][C]5050[/C][C]5227.54028419295[/C][C]-177.540284192952[/C][/ROW]
[ROW][C]29[/C][C]5055[/C][C]5157.32792909928[/C][C]-102.327929099282[/C][/ROW]
[ROW][C]30[/C][C]4985[/C][C]5074.86256524738[/C][C]-89.8625652473811[/C][/ROW]
[ROW][C]31[/C][C]4995[/C][C]5076.58813768487[/C][C]-81.5881376848702[/C][/ROW]
[ROW][C]32[/C][C]5010[/C][C]5053.83273817094[/C][C]-43.8327381709405[/C][/ROW]
[ROW][C]33[/C][C]5010[/C][C]5063.23206744796[/C][C]-53.2320674479606[/C][/ROW]
[ROW][C]34[/C][C]5020[/C][C]5051.54209390452[/C][C]-31.5420939045171[/C][/ROW]
[ROW][C]35[/C][C]5170[/C][C]5035.00678676794[/C][C]134.993213232061[/C][/ROW]
[ROW][C]36[/C][C]5155[/C][C]5051.75727674404[/C][C]103.242723255961[/C][/ROW]
[ROW][C]37[/C][C]5155[/C][C]5297.25426673219[/C][C]-142.254266732192[/C][/ROW]
[ROW][C]38[/C][C]5150[/C][C]5123.15252107417[/C][C]26.8474789258253[/C][/ROW]
[ROW][C]39[/C][C]5130[/C][C]5124.81049202635[/C][C]5.18950797365051[/C][/ROW]
[ROW][C]40[/C][C]5170[/C][C]5106.93561923103[/C][C]63.0643807689703[/C][/ROW]
[ROW][C]41[/C][C]5180[/C][C]5173.18041081066[/C][C]6.81958918933742[/C][/ROW]
[ROW][C]42[/C][C]5175[/C][C]5143.74190228917[/C][C]31.25809771083[/C][/ROW]
[ROW][C]43[/C][C]5185[/C][C]5202.03298994119[/C][C]-17.0329899411909[/C][/ROW]
[ROW][C]44[/C][C]5200[/C][C]5223.09335812241[/C][C]-23.0933581224126[/C][/ROW]
[ROW][C]45[/C][C]5205[/C][C]5237.74509016433[/C][C]-32.7450901643324[/C][/ROW]
[ROW][C]46[/C][C]5210[/C][C]5243.93940451751[/C][C]-33.939404517514[/C][/ROW]
[ROW][C]47[/C][C]5195[/C][C]5294.61011534084[/C][C]-99.6101153408372[/C][/ROW]
[ROW][C]48[/C][C]5195[/C][C]5195.35203280222[/C][C]-0.35203280222413[/C][/ROW]
[ROW][C]49[/C][C]5210[/C][C]5294.74634013838[/C][C]-84.7463401383784[/C][/ROW]
[ROW][C]50[/C][C]5205[/C][C]5215.20195264908[/C][C]-10.2019526490812[/C][/ROW]
[ROW][C]51[/C][C]5235[/C][C]5191.71755194444[/C][C]43.2824480555619[/C][/ROW]
[ROW][C]52[/C][C]5235[/C][C]5214.28753224304[/C][C]20.7124677569591[/C][/ROW]
[ROW][C]53[/C][C]5205[/C][C]5238.88583651885[/C][C]-33.8858365188471[/C][/ROW]
[ROW][C]54[/C][C]5195[/C][C]5201.59365688116[/C][C]-6.59365688116395[/C][/ROW]
[ROW][C]55[/C][C]5200[/C][C]5223.47391953341[/C][C]-23.4739195334123[/C][/ROW]
[ROW][C]56[/C][C]5165[/C][C]5239.2226225978[/C][C]-74.2226225977956[/C][/ROW]
[ROW][C]57[/C][C]5170[/C][C]5227.47173960642[/C][C]-57.4717396064198[/C][/ROW]
[ROW][C]58[/C][C]5255[/C][C]5222.32111352643[/C][C]32.678886473569[/C][/ROW]
[ROW][C]59[/C][C]5240[/C][C]5275.32168246327[/C][C]-35.3216824632709[/C][/ROW]
[ROW][C]60[/C][C]5265[/C][C]5244.97062070892[/C][C]20.0293792910807[/C][/ROW]
[ROW][C]61[/C][C]5275[/C][C]5318.72169148612[/C][C]-43.7216914861156[/C][/ROW]
[ROW][C]62[/C][C]5285[/C][C]5287.74162655923[/C][C]-2.74162655922555[/C][/ROW]
[ROW][C]63[/C][C]5320[/C][C]5289.45429735247[/C][C]30.545702647526[/C][/ROW]
[ROW][C]64[/C][C]5335[/C][C]5297.18178232629[/C][C]37.8182176737082[/C][/ROW]
[ROW][C]65[/C][C]5335[/C][C]5306.91138273461[/C][C]28.0886172653936[/C][/ROW]
[ROW][C]66[/C][C]5325[/C][C]5308.013401098[/C][C]16.9865989020009[/C][/ROW]
[ROW][C]67[/C][C]5355[/C][C]5333.32702011406[/C][C]21.6729798859387[/C][/ROW]
[ROW][C]68[/C][C]5375[/C][C]5348.09541479601[/C][C]26.9045852039899[/C][/ROW]
[ROW][C]69[/C][C]5445[/C][C]5387.60685612607[/C][C]57.3931438739282[/C][/ROW]
[ROW][C]70[/C][C]5415[/C][C]5469.83426908176[/C][C]-54.8342690817562[/C][/ROW]
[ROW][C]71[/C][C]5415[/C][C]5456.54340612088[/C][C]-41.5434061208807[/C][/ROW]
[ROW][C]72[/C][C]5450[/C][C]5446.14785762265[/C][C]3.85214237734726[/C][/ROW]
[ROW][C]73[/C][C]5535[/C][C]5486.66694366235[/C][C]48.333056337653[/C][/ROW]
[ROW][C]74[/C][C]5570[/C][C]5512.89714757187[/C][C]57.102852428131[/C][/ROW]
[ROW][C]75[/C][C]5590[/C][C]5554.52617641561[/C][C]35.473823584387[/C][/ROW]
[ROW][C]76[/C][C]5575[/C][C]5567.39800499812[/C][C]7.60199500188173[/C][/ROW]
[ROW][C]77[/C][C]5575[/C][C]5559.8742572971[/C][C]15.1257427029004[/C][/ROW]
[ROW][C]78[/C][C]5595[/C][C]5550.73492422444[/C][C]44.2650757755582[/C][/ROW]
[ROW][C]79[/C][C]5650[/C][C]5589.94508659487[/C][C]60.0549134051325[/C][/ROW]
[ROW][C]80[/C][C]5680[/C][C]5623.70810529113[/C][C]56.2918947088729[/C][/ROW]
[ROW][C]81[/C][C]5665[/C][C]5688.61754316439[/C][C]-23.6175431643942[/C][/ROW]
[ROW][C]82[/C][C]5675[/C][C]5689.28078943784[/C][C]-14.2807894378429[/C][/ROW]
[ROW][C]83[/C][C]5700[/C][C]5699.24117587385[/C][C]0.758824126152831[/C][/ROW]
[ROW][C]84[/C][C]5700[/C][C]5726.02348135837[/C][C]-26.0234813583693[/C][/ROW]
[ROW][C]85[/C][C]5710[/C][C]5771.65822381068[/C][C]-61.6582238106812[/C][/ROW]
[ROW][C]86[/C][C]5745[/C][C]5753.19488464076[/C][C]-8.19488464075675[/C][/ROW]
[ROW][C]87[/C][C]5745[/C][C]5757.2919150536[/C][C]-12.2919150536027[/C][/ROW]
[ROW][C]88[/C][C]5765[/C][C]5737.76983168733[/C][C]27.2301683126743[/C][/ROW]
[ROW][C]89[/C][C]5740[/C][C]5741.94697579854[/C][C]-1.94697579853982[/C][/ROW]
[ROW][C]90[/C][C]5725[/C][C]5737.25587974924[/C][C]-12.2558797492356[/C][/ROW]
[ROW][C]91[/C][C]5765[/C][C]5758.12421824023[/C][C]6.87578175976705[/C][/ROW]
[ROW][C]92[/C][C]5900[/C][C]5766.99832513973[/C][C]133.00167486027[/C][/ROW]
[ROW][C]93[/C][C]5900[/C][C]5832.83187471355[/C][C]67.168125286451[/C][/ROW]
[ROW][C]94[/C][C]5900[/C][C]5877.17847441973[/C][C]22.8215255802706[/C][/ROW]
[ROW][C]95[/C][C]5890[/C][C]5909.59175719487[/C][C]-19.5917571948657[/C][/ROW]
[ROW][C]96[/C][C]5935[/C][C]5916.46244091433[/C][C]18.5375590856656[/C][/ROW]
[ROW][C]97[/C][C]5945[/C][C]5967.05449107927[/C][C]-22.0544910792723[/C][/ROW]
[ROW][C]98[/C][C]6000[/C][C]5987.89109626485[/C][C]12.1089037351476[/C][/ROW]
[ROW][C]99[/C][C]6000[/C][C]5999.22257124043[/C][C]0.777428759565737[/C][/ROW]
[ROW][C]100[/C][C]5995[/C][C]6001.63722444189[/C][C]-6.63722444189079[/C][/ROW]
[ROW][C]101[/C][C]6065[/C][C]5978.98705343661[/C][C]86.0129465633909[/C][/ROW]
[ROW][C]102[/C][C]6065[/C][C]6008.68651731738[/C][C]56.3134826826172[/C][/ROW]
[ROW][C]103[/C][C]6065[/C][C]6067.49954801838[/C][C]-2.49954801837703[/C][/ROW]
[ROW][C]104[/C][C]6075[/C][C]6123.9534383465[/C][C]-48.9534383465043[/C][/ROW]
[ROW][C]105[/C][C]6070[/C][C]6082.92212559255[/C][C]-12.9221255925495[/C][/ROW]
[ROW][C]106[/C][C]6085[/C][C]6073.93122052182[/C][C]11.0687794781752[/C][/ROW]
[ROW][C]107[/C][C]6095[/C][C]6083.80074842806[/C][C]11.1992515719439[/C][/ROW]
[ROW][C]108[/C][C]6095[/C][C]6119.8174239174[/C][C]-24.8174239173959[/C][/ROW]
[ROW][C]109[/C][C]6065[/C][C]6134.73827229686[/C][C]-69.7382722968632[/C][/ROW]
[ROW][C]110[/C][C]6115[/C][C]6148.64356612901[/C][C]-33.6435661290052[/C][/ROW]
[ROW][C]111[/C][C]6190[/C][C]6135.24444808035[/C][C]54.7555519196512[/C][/ROW]
[ROW][C]112[/C][C]6200[/C][C]6158.3173478808[/C][C]41.6826521191988[/C][/ROW]
[ROW][C]113[/C][C]6205[/C][C]6194.8553176731[/C][C]10.144682326898[/C][/ROW]
[ROW][C]114[/C][C]6210[/C][C]6179.07428004885[/C][C]30.9257199511458[/C][/ROW]
[ROW][C]115[/C][C]6230[/C][C]6202.63572142167[/C][C]27.3642785783286[/C][/ROW]
[ROW][C]116[/C][C]6235[/C][C]6253.16010464312[/C][C]-18.160104643116[/C][/ROW]
[ROW][C]117[/C][C]6235[/C][C]6240.41588742671[/C][C]-5.41588742670683[/C][/ROW]
[ROW][C]118[/C][C]6235[/C][C]6244.55359551627[/C][C]-9.55359551626862[/C][/ROW]
[ROW][C]119[/C][C]6225[/C][C]6245.42302509621[/C][C]-20.4230250962082[/C][/ROW]
[ROW][C]120[/C][C]6225[/C][C]6252.79468433771[/C][C]-27.7946843377067[/C][/ROW]
[ROW][C]121[/C][C]6255[/C][C]6247.99658046376[/C][C]7.00341953623956[/C][/ROW]
[ROW][C]122[/C][C]6310[/C][C]6310.3870684526[/C][C]-0.387068452603671[/C][/ROW]
[ROW][C]123[/C][C]6305[/C][C]6347.82061444545[/C][C]-42.820614445448[/C][/ROW]
[ROW][C]124[/C][C]6320[/C][C]6322.69766723708[/C][C]-2.69766723708472[/C][/ROW]
[ROW][C]125[/C][C]6320[/C][C]6326.82532641284[/C][C]-6.82532641284433[/C][/ROW]
[ROW][C]126[/C][C]6330[/C][C]6312.1117698758[/C][C]17.8882301241993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298766&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298766&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
1353655257.31303418804107.686965811962
1450855031.7194078890453.2805921109593
1551055080.1571194071224.8428805928752
1652005191.110189050868.88981094914107
1752055207.35125485944-2.35125485943718
1851605173.24063379704-13.2406337970378
1951405247.05772241675-107.057722416746
2051505182.60417075804-32.6041707580362
2152105165.2120020433744.7879979566287
2252055221.79631943475-16.7963194347494
2352005208.21906789481-8.21906789480727
2450955202.99070985552-107.990709855523
2551405430.59897236164-290.598972361639
2651655007.85125185765157.148748142351
2751905090.2329847147699.7670152852434
2850505227.54028419295-177.540284192952
2950555157.32792909928-102.327929099282
3049855074.86256524738-89.8625652473811
3149955076.58813768487-81.5881376848702
3250105053.83273817094-43.8327381709405
3350105063.23206744796-53.2320674479606
3450205051.54209390452-31.5420939045171
3551705035.00678676794134.993213232061
3651555051.75727674404103.242723255961
3751555297.25426673219-142.254266732192
3851505123.1525210741726.8474789258253
3951305124.810492026355.18950797365051
4051705106.9356192310363.0643807689703
4151805173.180410810666.81958918933742
4251755143.7419022891731.25809771083
4351855202.03298994119-17.0329899411909
4452005223.09335812241-23.0933581224126
4552055237.74509016433-32.7450901643324
4652105243.93940451751-33.939404517514
4751955294.61011534084-99.6101153408372
4851955195.35203280222-0.35203280222413
4952105294.74634013838-84.7463401383784
5052055215.20195264908-10.2019526490812
5152355191.7175519444443.2824480555619
5252355214.2875322430420.7124677569591
5352055238.88583651885-33.8858365188471
5451955201.59365688116-6.59365688116395
5552005223.47391953341-23.4739195334123
5651655239.2226225978-74.2226225977956
5751705227.47173960642-57.4717396064198
5852555222.3211135264332.678886473569
5952405275.32168246327-35.3216824632709
6052655244.9706207089220.0293792910807
6152755318.72169148612-43.7216914861156
6252855287.74162655923-2.74162655922555
6353205289.4542973524730.545702647526
6453355297.1817823262937.8182176737082
6553355306.9113827346128.0886172653936
6653255308.01340109816.9865989020009
6753555333.3270201140621.6729798859387
6853755348.0954147960126.9045852039899
6954455387.6068561260757.3931438739282
7054155469.83426908176-54.8342690817562
7154155456.54340612088-41.5434061208807
7254505446.147857622653.85214237734726
7355355486.6669436623548.333056337653
7455705512.8971475718757.102852428131
7555905554.5261764156135.473823584387
7655755567.398004998127.60199500188173
7755755559.874257297115.1257427029004
7855955550.7349242244444.2650757755582
7956505589.9450865948760.0549134051325
8056805623.7081052911356.2918947088729
8156655688.61754316439-23.6175431643942
8256755689.28078943784-14.2807894378429
8357005699.241175873850.758824126152831
8457005726.02348135837-26.0234813583693
8557105771.65822381068-61.6582238106812
8657455753.19488464076-8.19488464075675
8757455757.2919150536-12.2919150536027
8857655737.7698316873327.2301683126743
8957405741.94697579854-1.94697579853982
9057255737.25587974924-12.2558797492356
9157655758.124218240236.87578175976705
9259005766.99832513973133.00167486027
9359005832.8318747135567.168125286451
9459005877.1784744197322.8215255802706
9558905909.59175719487-19.5917571948657
9659355916.4624409143318.5375590856656
9759455967.05449107927-22.0544910792723
9860005987.8910962648512.1089037351476
9960005999.222571240430.777428759565737
10059956001.63722444189-6.63722444189079
10160655978.9870534366186.0129465633909
10260656008.6865173173856.3134826826172
10360656067.49954801838-2.49954801837703
10460756123.9534383465-48.9534383465043
10560706082.92212559255-12.9221255925495
10660856073.9312205218211.0687794781752
10760956083.8007484280611.1992515719439
10860956119.8174239174-24.8174239173959
10960656134.73827229686-69.7382722968632
11061156148.64356612901-33.6435661290052
11161906135.2444480803554.7555519196512
11262006158.317347880841.6826521191988
11362056194.855317673110.144682326898
11462106179.0742800488530.9257199511458
11562306202.6357214216727.3642785783286
11662356253.16010464312-18.160104643116
11762356240.41588742671-5.41588742670683
11862356244.55359551627-9.55359551626862
11962256245.42302509621-20.4230250962082
12062256252.79468433771-27.7946843377067
12162556247.996580463767.00341953623956
12263106310.3870684526-0.387068452603671
12363056347.82061444545-42.820614445448
12463206322.69766723708-2.69766723708472
12563206326.82532641284-6.82532641284433
12663306312.111769875817.8882301241993







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1276328.489788247926211.214754253816445.76482224203
1286348.341527838166220.262584724526476.4204709518
1296348.793429451626210.75358831916486.83327058415
1306353.61286616356206.284050887336500.94168143967
1316354.22139196346198.155502412016510.28728151478
1326367.537657789396203.198545122166531.87677045661
1336389.204730928236216.989383113246561.42007874322
1346445.491429678576265.7446408516625.23821850614
1356465.702501717966278.727395982976652.67760745295
1366475.823886290816281.88969065896669.75808192273
1376479.444047709456278.791974941236680.09612047767
1386477.856368409686270.704162587576685.0085742318

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 6328.48978824792 & 6211.21475425381 & 6445.76482224203 \tabularnewline
128 & 6348.34152783816 & 6220.26258472452 & 6476.4204709518 \tabularnewline
129 & 6348.79342945162 & 6210.7535883191 & 6486.83327058415 \tabularnewline
130 & 6353.6128661635 & 6206.28405088733 & 6500.94168143967 \tabularnewline
131 & 6354.2213919634 & 6198.15550241201 & 6510.28728151478 \tabularnewline
132 & 6367.53765778939 & 6203.19854512216 & 6531.87677045661 \tabularnewline
133 & 6389.20473092823 & 6216.98938311324 & 6561.42007874322 \tabularnewline
134 & 6445.49142967857 & 6265.744640851 & 6625.23821850614 \tabularnewline
135 & 6465.70250171796 & 6278.72739598297 & 6652.67760745295 \tabularnewline
136 & 6475.82388629081 & 6281.8896906589 & 6669.75808192273 \tabularnewline
137 & 6479.44404770945 & 6278.79197494123 & 6680.09612047767 \tabularnewline
138 & 6477.85636840968 & 6270.70416258757 & 6685.0085742318 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298766&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]127[/C][C]6328.48978824792[/C][C]6211.21475425381[/C][C]6445.76482224203[/C][/ROW]
[ROW][C]128[/C][C]6348.34152783816[/C][C]6220.26258472452[/C][C]6476.4204709518[/C][/ROW]
[ROW][C]129[/C][C]6348.79342945162[/C][C]6210.7535883191[/C][C]6486.83327058415[/C][/ROW]
[ROW][C]130[/C][C]6353.6128661635[/C][C]6206.28405088733[/C][C]6500.94168143967[/C][/ROW]
[ROW][C]131[/C][C]6354.2213919634[/C][C]6198.15550241201[/C][C]6510.28728151478[/C][/ROW]
[ROW][C]132[/C][C]6367.53765778939[/C][C]6203.19854512216[/C][C]6531.87677045661[/C][/ROW]
[ROW][C]133[/C][C]6389.20473092823[/C][C]6216.98938311324[/C][C]6561.42007874322[/C][/ROW]
[ROW][C]134[/C][C]6445.49142967857[/C][C]6265.744640851[/C][C]6625.23821850614[/C][/ROW]
[ROW][C]135[/C][C]6465.70250171796[/C][C]6278.72739598297[/C][C]6652.67760745295[/C][/ROW]
[ROW][C]136[/C][C]6475.82388629081[/C][C]6281.8896906589[/C][C]6669.75808192273[/C][/ROW]
[ROW][C]137[/C][C]6479.44404770945[/C][C]6278.79197494123[/C][C]6680.09612047767[/C][/ROW]
[ROW][C]138[/C][C]6477.85636840968[/C][C]6270.70416258757[/C][C]6685.0085742318[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298766&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298766&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
1276328.489788247926211.214754253816445.76482224203
1286348.341527838166220.262584724526476.4204709518
1296348.793429451626210.75358831916486.83327058415
1306353.61286616356206.284050887336500.94168143967
1316354.22139196346198.155502412016510.28728151478
1326367.537657789396203.198545122166531.87677045661
1336389.204730928236216.989383113246561.42007874322
1346445.491429678576265.7446408516625.23821850614
1356465.702501717966278.727395982976652.67760745295
1366475.823886290816281.88969065896669.75808192273
1376479.444047709456278.791974941236680.09612047767
1386477.856368409686270.704162587576685.0085742318



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
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')