Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 13 Dec 2016 16:58:34 +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/13/t14816451432sa3wnrdnmeztgg.htm/, Retrieved Sun, 05 May 2024 07:05:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299167, Retrieved Sun, 05 May 2024 07:05:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [ezkuhfzejlk] [2016-12-13 15:58:34] [4c05fa0998bf98e29c2e453b139976f4] [Current]
Feedback Forum

Post a new message
Dataseries X:
3281
3397
3498.5
3538
3449.5
3673
3350.5
3604
3673.5
3747
3616
3580.5
3710
3994.5
4091
3954.5
4004
4287
3831
4046.5
4079.5
4029.5
3880
3855
3841.5
4123.5
4133
3958.5
4003
4151.5
3723
3957
3965.5
3861.5
3917.5
3704
3950
4140.5
4090
4162
4066
4358.5
4022.5
4285.5
4373.5
4284.5
4077.5
4122
4181.5
4535.5
4497
4420.5
4370
4712
4475
4578.5
4751.5
4746
4581.5
4645.5
4751
4952.5
4996.5
4998
4986.5
5348
4933
5263
5330.5
5301
5159
5258.5
5411.5
5536.5
5613
5505.5
5476
5782.5
5283
5451.5
5578
5548.5
5379.5
5117.5
5316.5
5505.5
5620.5
5383.5
5461.5
5658.5
5357.5
5622
5608
5604.5
5399
5185
5221
5379.5
5333
5214
5206.5
5630
5285.5
5512.5
5592.5
5554.5
5284.5
5198.5
5241.5
5455
5548.5
5375
5346
5730.5
5457
5603




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299167&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299167&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299167&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.764947855118018
beta0.0290671609450932
gamma0.565899063690908

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.764947855118018 \tabularnewline
beta & 0.0290671609450932 \tabularnewline
gamma & 0.565899063690908 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299167&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]0.764947855118018[/C][/ROW]
[ROW][C]beta[/C][C]0.0290671609450932[/C][/ROW]
[ROW][C]gamma[/C][C]0.565899063690908[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299167&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299167&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
alpha0.764947855118018
beta0.0290671609450932
gamma0.565899063690908







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1337103438.25694444445271.743055555554
143994.53937.3426238128157.1573761871909
1540914088.656501071742.34349892826231
163954.53971.75939453366-17.2593945336635
1740044031.40000309155-27.4000030915513
1842874316.5076729178-29.5076729177954
1938313819.1386528501811.8613471498188
204046.54084.05351137361-37.5535113736087
214079.54119.52108269982-40.0210826998236
224029.54163.75289403167-134.252894031665
2338803930.00052210647-50.0005221064725
2438553846.855899977468.14410002253726
253841.54012.59941496999-171.099414969992
264123.54134.88304875972-11.3830487597152
2741334215.44461272358-82.4446127235815
283958.54018.16492457842-59.664924578417
2940034030.15916858704-27.1591685870426
304151.54301.31658155766-149.816581557664
3137233700.8910713462922.1089286537062
3239573950.770511185356.229488814653
333965.54004.07374983998-38.5737498399785
343861.54021.58273906992-160.082739069917
353917.53763.40881767297154.091182327033
3637043832.78585022452-128.785850224524
3739503855.5662477071394.4337522928718
384140.54193.74117187042-53.2411718704188
3940904223.42789994779-133.427899947793
4041623979.64186298535182.358137014647
4140664175.93940630285-109.939406302849
424358.54360.46277294632-1.96277294631727
434022.53892.29792442233130.202075577674
444285.54221.4456057691764.0543942308332
454373.54313.0029093141260.4970906858753
464284.54392.31670362657-107.816703626572
474077.54219.25918614564-141.759186145644
4841224021.46633032869100.533669671309
494181.54251.22215017358-69.7221501735776
504535.54442.3995044211793.1004955788294
5144974574.83399518196-77.8339951819617
524420.54418.285166953682.21483304631602
5343704436.60306820227-66.6030682022729
5447124668.3034284648543.6965715351471
5544754253.32519606908221.674803930919
564578.54646.35952923131-67.8595292313139
574751.54636.31676495291115.183235047088
5847464736.07053742049.92946257960375
594581.54652.18220237232-70.6822023723216
604645.54546.1830863390699.3169136609386
6147514757.52916290586-6.52916290586381
624952.55025.27665102523-72.776651025235
634996.55010.97134379776-14.4713437977625
6449984917.8328133237880.1671866762226
654986.54992.65300819091-6.15300819091044
6653485292.6368798620355.3631201379658
6749334917.8870419418515.1129580581455
6852635117.43700043742145.562999562585
695330.55302.7816439826627.7183560173398
7053015327.4668862585-26.4668862585004
7151595210.04330521052-51.0433052105191
725258.55147.14484328374111.355156716262
735411.55359.3533727240852.1466272759226
745536.55670.2104909554-133.710490955405
7556135622.73231659551-9.73231659551402
765505.55551.59550180576-46.0955018057593
7754765521.33012984589-45.330129845891
785782.55801.63781946558-19.1378194655799
7952835364.99787919491-81.9978791949125
805451.55505.90891873505-54.4089187350546
8155785516.4578185499361.5421814500687
825548.55554.40864337114-5.9086433711409
835379.55444.49871664285-64.9987166428546
845117.55387.27307778697-269.773077786967
855316.55286.3348042344630.1651957655431
865505.55541.4386800627-35.9386800627017
875620.55573.1991777964447.3008222035551
885383.55530.07826685087-146.578266850866
895461.55410.0418098018551.4581901981483
905658.55757.01476699652-98.5147669965218
915357.55238.67254396906118.827456030938
9256225528.7179074037293.2820925962842
9356085662.79359304179-54.7935930417898
945604.55595.322418531629.17758146837878
9553995481.96902107109-82.9690210710914
9651855376.23551262175-191.235512621746
9752215369.49387845419-148.493878454188
985379.55469.39053089109-89.8905308910853
9953335460.00374352942-127.003743529423
10052145242.93521033645-28.9352103364454
1015206.55227.02257113275-20.5225711327539
10256305485.17578439447144.824215605526
1035285.55173.48630643274112.013693567256
1045512.55446.3712221918266.1287778081842
1055592.55530.825545562761.6744544372996
1065554.55554.391093158220.108906841784119
1075284.55415.07760151195-130.577601511952
1085198.55250.70021060102-52.2002106010232
1095241.55351.26542728724-109.76542728724
11054555484.71040026464-29.7104002646392
1115548.55513.8876328120234.6123671879814
11253755434.55117345758-59.5511734575775
11353465396.71670434567-50.7167043456739
1145730.55653.4741225942577.0258774057529
11554575283.75805623411173.241943765891
11656035596.937296570036.06270342996868

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3710 & 3438.25694444445 & 271.743055555554 \tabularnewline
14 & 3994.5 & 3937.34262381281 & 57.1573761871909 \tabularnewline
15 & 4091 & 4088.65650107174 & 2.34349892826231 \tabularnewline
16 & 3954.5 & 3971.75939453366 & -17.2593945336635 \tabularnewline
17 & 4004 & 4031.40000309155 & -27.4000030915513 \tabularnewline
18 & 4287 & 4316.5076729178 & -29.5076729177954 \tabularnewline
19 & 3831 & 3819.13865285018 & 11.8613471498188 \tabularnewline
20 & 4046.5 & 4084.05351137361 & -37.5535113736087 \tabularnewline
21 & 4079.5 & 4119.52108269982 & -40.0210826998236 \tabularnewline
22 & 4029.5 & 4163.75289403167 & -134.252894031665 \tabularnewline
23 & 3880 & 3930.00052210647 & -50.0005221064725 \tabularnewline
24 & 3855 & 3846.85589997746 & 8.14410002253726 \tabularnewline
25 & 3841.5 & 4012.59941496999 & -171.099414969992 \tabularnewline
26 & 4123.5 & 4134.88304875972 & -11.3830487597152 \tabularnewline
27 & 4133 & 4215.44461272358 & -82.4446127235815 \tabularnewline
28 & 3958.5 & 4018.16492457842 & -59.664924578417 \tabularnewline
29 & 4003 & 4030.15916858704 & -27.1591685870426 \tabularnewline
30 & 4151.5 & 4301.31658155766 & -149.816581557664 \tabularnewline
31 & 3723 & 3700.89107134629 & 22.1089286537062 \tabularnewline
32 & 3957 & 3950.77051118535 & 6.229488814653 \tabularnewline
33 & 3965.5 & 4004.07374983998 & -38.5737498399785 \tabularnewline
34 & 3861.5 & 4021.58273906992 & -160.082739069917 \tabularnewline
35 & 3917.5 & 3763.40881767297 & 154.091182327033 \tabularnewline
36 & 3704 & 3832.78585022452 & -128.785850224524 \tabularnewline
37 & 3950 & 3855.56624770713 & 94.4337522928718 \tabularnewline
38 & 4140.5 & 4193.74117187042 & -53.2411718704188 \tabularnewline
39 & 4090 & 4223.42789994779 & -133.427899947793 \tabularnewline
40 & 4162 & 3979.64186298535 & 182.358137014647 \tabularnewline
41 & 4066 & 4175.93940630285 & -109.939406302849 \tabularnewline
42 & 4358.5 & 4360.46277294632 & -1.96277294631727 \tabularnewline
43 & 4022.5 & 3892.29792442233 & 130.202075577674 \tabularnewline
44 & 4285.5 & 4221.44560576917 & 64.0543942308332 \tabularnewline
45 & 4373.5 & 4313.00290931412 & 60.4970906858753 \tabularnewline
46 & 4284.5 & 4392.31670362657 & -107.816703626572 \tabularnewline
47 & 4077.5 & 4219.25918614564 & -141.759186145644 \tabularnewline
48 & 4122 & 4021.46633032869 & 100.533669671309 \tabularnewline
49 & 4181.5 & 4251.22215017358 & -69.7221501735776 \tabularnewline
50 & 4535.5 & 4442.39950442117 & 93.1004955788294 \tabularnewline
51 & 4497 & 4574.83399518196 & -77.8339951819617 \tabularnewline
52 & 4420.5 & 4418.28516695368 & 2.21483304631602 \tabularnewline
53 & 4370 & 4436.60306820227 & -66.6030682022729 \tabularnewline
54 & 4712 & 4668.30342846485 & 43.6965715351471 \tabularnewline
55 & 4475 & 4253.32519606908 & 221.674803930919 \tabularnewline
56 & 4578.5 & 4646.35952923131 & -67.8595292313139 \tabularnewline
57 & 4751.5 & 4636.31676495291 & 115.183235047088 \tabularnewline
58 & 4746 & 4736.0705374204 & 9.92946257960375 \tabularnewline
59 & 4581.5 & 4652.18220237232 & -70.6822023723216 \tabularnewline
60 & 4645.5 & 4546.18308633906 & 99.3169136609386 \tabularnewline
61 & 4751 & 4757.52916290586 & -6.52916290586381 \tabularnewline
62 & 4952.5 & 5025.27665102523 & -72.776651025235 \tabularnewline
63 & 4996.5 & 5010.97134379776 & -14.4713437977625 \tabularnewline
64 & 4998 & 4917.83281332378 & 80.1671866762226 \tabularnewline
65 & 4986.5 & 4992.65300819091 & -6.15300819091044 \tabularnewline
66 & 5348 & 5292.63687986203 & 55.3631201379658 \tabularnewline
67 & 4933 & 4917.88704194185 & 15.1129580581455 \tabularnewline
68 & 5263 & 5117.43700043742 & 145.562999562585 \tabularnewline
69 & 5330.5 & 5302.78164398266 & 27.7183560173398 \tabularnewline
70 & 5301 & 5327.4668862585 & -26.4668862585004 \tabularnewline
71 & 5159 & 5210.04330521052 & -51.0433052105191 \tabularnewline
72 & 5258.5 & 5147.14484328374 & 111.355156716262 \tabularnewline
73 & 5411.5 & 5359.35337272408 & 52.1466272759226 \tabularnewline
74 & 5536.5 & 5670.2104909554 & -133.710490955405 \tabularnewline
75 & 5613 & 5622.73231659551 & -9.73231659551402 \tabularnewline
76 & 5505.5 & 5551.59550180576 & -46.0955018057593 \tabularnewline
77 & 5476 & 5521.33012984589 & -45.330129845891 \tabularnewline
78 & 5782.5 & 5801.63781946558 & -19.1378194655799 \tabularnewline
79 & 5283 & 5364.99787919491 & -81.9978791949125 \tabularnewline
80 & 5451.5 & 5505.90891873505 & -54.4089187350546 \tabularnewline
81 & 5578 & 5516.45781854993 & 61.5421814500687 \tabularnewline
82 & 5548.5 & 5554.40864337114 & -5.9086433711409 \tabularnewline
83 & 5379.5 & 5444.49871664285 & -64.9987166428546 \tabularnewline
84 & 5117.5 & 5387.27307778697 & -269.773077786967 \tabularnewline
85 & 5316.5 & 5286.33480423446 & 30.1651957655431 \tabularnewline
86 & 5505.5 & 5541.4386800627 & -35.9386800627017 \tabularnewline
87 & 5620.5 & 5573.19917779644 & 47.3008222035551 \tabularnewline
88 & 5383.5 & 5530.07826685087 & -146.578266850866 \tabularnewline
89 & 5461.5 & 5410.04180980185 & 51.4581901981483 \tabularnewline
90 & 5658.5 & 5757.01476699652 & -98.5147669965218 \tabularnewline
91 & 5357.5 & 5238.67254396906 & 118.827456030938 \tabularnewline
92 & 5622 & 5528.71790740372 & 93.2820925962842 \tabularnewline
93 & 5608 & 5662.79359304179 & -54.7935930417898 \tabularnewline
94 & 5604.5 & 5595.32241853162 & 9.17758146837878 \tabularnewline
95 & 5399 & 5481.96902107109 & -82.9690210710914 \tabularnewline
96 & 5185 & 5376.23551262175 & -191.235512621746 \tabularnewline
97 & 5221 & 5369.49387845419 & -148.493878454188 \tabularnewline
98 & 5379.5 & 5469.39053089109 & -89.8905308910853 \tabularnewline
99 & 5333 & 5460.00374352942 & -127.003743529423 \tabularnewline
100 & 5214 & 5242.93521033645 & -28.9352103364454 \tabularnewline
101 & 5206.5 & 5227.02257113275 & -20.5225711327539 \tabularnewline
102 & 5630 & 5485.17578439447 & 144.824215605526 \tabularnewline
103 & 5285.5 & 5173.48630643274 & 112.013693567256 \tabularnewline
104 & 5512.5 & 5446.37122219182 & 66.1287778081842 \tabularnewline
105 & 5592.5 & 5530.8255455627 & 61.6744544372996 \tabularnewline
106 & 5554.5 & 5554.39109315822 & 0.108906841784119 \tabularnewline
107 & 5284.5 & 5415.07760151195 & -130.577601511952 \tabularnewline
108 & 5198.5 & 5250.70021060102 & -52.2002106010232 \tabularnewline
109 & 5241.5 & 5351.26542728724 & -109.76542728724 \tabularnewline
110 & 5455 & 5484.71040026464 & -29.7104002646392 \tabularnewline
111 & 5548.5 & 5513.88763281202 & 34.6123671879814 \tabularnewline
112 & 5375 & 5434.55117345758 & -59.5511734575775 \tabularnewline
113 & 5346 & 5396.71670434567 & -50.7167043456739 \tabularnewline
114 & 5730.5 & 5653.47412259425 & 77.0258774057529 \tabularnewline
115 & 5457 & 5283.75805623411 & 173.241943765891 \tabularnewline
116 & 5603 & 5596.93729657003 & 6.06270342996868 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299167&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]3710[/C][C]3438.25694444445[/C][C]271.743055555554[/C][/ROW]
[ROW][C]14[/C][C]3994.5[/C][C]3937.34262381281[/C][C]57.1573761871909[/C][/ROW]
[ROW][C]15[/C][C]4091[/C][C]4088.65650107174[/C][C]2.34349892826231[/C][/ROW]
[ROW][C]16[/C][C]3954.5[/C][C]3971.75939453366[/C][C]-17.2593945336635[/C][/ROW]
[ROW][C]17[/C][C]4004[/C][C]4031.40000309155[/C][C]-27.4000030915513[/C][/ROW]
[ROW][C]18[/C][C]4287[/C][C]4316.5076729178[/C][C]-29.5076729177954[/C][/ROW]
[ROW][C]19[/C][C]3831[/C][C]3819.13865285018[/C][C]11.8613471498188[/C][/ROW]
[ROW][C]20[/C][C]4046.5[/C][C]4084.05351137361[/C][C]-37.5535113736087[/C][/ROW]
[ROW][C]21[/C][C]4079.5[/C][C]4119.52108269982[/C][C]-40.0210826998236[/C][/ROW]
[ROW][C]22[/C][C]4029.5[/C][C]4163.75289403167[/C][C]-134.252894031665[/C][/ROW]
[ROW][C]23[/C][C]3880[/C][C]3930.00052210647[/C][C]-50.0005221064725[/C][/ROW]
[ROW][C]24[/C][C]3855[/C][C]3846.85589997746[/C][C]8.14410002253726[/C][/ROW]
[ROW][C]25[/C][C]3841.5[/C][C]4012.59941496999[/C][C]-171.099414969992[/C][/ROW]
[ROW][C]26[/C][C]4123.5[/C][C]4134.88304875972[/C][C]-11.3830487597152[/C][/ROW]
[ROW][C]27[/C][C]4133[/C][C]4215.44461272358[/C][C]-82.4446127235815[/C][/ROW]
[ROW][C]28[/C][C]3958.5[/C][C]4018.16492457842[/C][C]-59.664924578417[/C][/ROW]
[ROW][C]29[/C][C]4003[/C][C]4030.15916858704[/C][C]-27.1591685870426[/C][/ROW]
[ROW][C]30[/C][C]4151.5[/C][C]4301.31658155766[/C][C]-149.816581557664[/C][/ROW]
[ROW][C]31[/C][C]3723[/C][C]3700.89107134629[/C][C]22.1089286537062[/C][/ROW]
[ROW][C]32[/C][C]3957[/C][C]3950.77051118535[/C][C]6.229488814653[/C][/ROW]
[ROW][C]33[/C][C]3965.5[/C][C]4004.07374983998[/C][C]-38.5737498399785[/C][/ROW]
[ROW][C]34[/C][C]3861.5[/C][C]4021.58273906992[/C][C]-160.082739069917[/C][/ROW]
[ROW][C]35[/C][C]3917.5[/C][C]3763.40881767297[/C][C]154.091182327033[/C][/ROW]
[ROW][C]36[/C][C]3704[/C][C]3832.78585022452[/C][C]-128.785850224524[/C][/ROW]
[ROW][C]37[/C][C]3950[/C][C]3855.56624770713[/C][C]94.4337522928718[/C][/ROW]
[ROW][C]38[/C][C]4140.5[/C][C]4193.74117187042[/C][C]-53.2411718704188[/C][/ROW]
[ROW][C]39[/C][C]4090[/C][C]4223.42789994779[/C][C]-133.427899947793[/C][/ROW]
[ROW][C]40[/C][C]4162[/C][C]3979.64186298535[/C][C]182.358137014647[/C][/ROW]
[ROW][C]41[/C][C]4066[/C][C]4175.93940630285[/C][C]-109.939406302849[/C][/ROW]
[ROW][C]42[/C][C]4358.5[/C][C]4360.46277294632[/C][C]-1.96277294631727[/C][/ROW]
[ROW][C]43[/C][C]4022.5[/C][C]3892.29792442233[/C][C]130.202075577674[/C][/ROW]
[ROW][C]44[/C][C]4285.5[/C][C]4221.44560576917[/C][C]64.0543942308332[/C][/ROW]
[ROW][C]45[/C][C]4373.5[/C][C]4313.00290931412[/C][C]60.4970906858753[/C][/ROW]
[ROW][C]46[/C][C]4284.5[/C][C]4392.31670362657[/C][C]-107.816703626572[/C][/ROW]
[ROW][C]47[/C][C]4077.5[/C][C]4219.25918614564[/C][C]-141.759186145644[/C][/ROW]
[ROW][C]48[/C][C]4122[/C][C]4021.46633032869[/C][C]100.533669671309[/C][/ROW]
[ROW][C]49[/C][C]4181.5[/C][C]4251.22215017358[/C][C]-69.7221501735776[/C][/ROW]
[ROW][C]50[/C][C]4535.5[/C][C]4442.39950442117[/C][C]93.1004955788294[/C][/ROW]
[ROW][C]51[/C][C]4497[/C][C]4574.83399518196[/C][C]-77.8339951819617[/C][/ROW]
[ROW][C]52[/C][C]4420.5[/C][C]4418.28516695368[/C][C]2.21483304631602[/C][/ROW]
[ROW][C]53[/C][C]4370[/C][C]4436.60306820227[/C][C]-66.6030682022729[/C][/ROW]
[ROW][C]54[/C][C]4712[/C][C]4668.30342846485[/C][C]43.6965715351471[/C][/ROW]
[ROW][C]55[/C][C]4475[/C][C]4253.32519606908[/C][C]221.674803930919[/C][/ROW]
[ROW][C]56[/C][C]4578.5[/C][C]4646.35952923131[/C][C]-67.8595292313139[/C][/ROW]
[ROW][C]57[/C][C]4751.5[/C][C]4636.31676495291[/C][C]115.183235047088[/C][/ROW]
[ROW][C]58[/C][C]4746[/C][C]4736.0705374204[/C][C]9.92946257960375[/C][/ROW]
[ROW][C]59[/C][C]4581.5[/C][C]4652.18220237232[/C][C]-70.6822023723216[/C][/ROW]
[ROW][C]60[/C][C]4645.5[/C][C]4546.18308633906[/C][C]99.3169136609386[/C][/ROW]
[ROW][C]61[/C][C]4751[/C][C]4757.52916290586[/C][C]-6.52916290586381[/C][/ROW]
[ROW][C]62[/C][C]4952.5[/C][C]5025.27665102523[/C][C]-72.776651025235[/C][/ROW]
[ROW][C]63[/C][C]4996.5[/C][C]5010.97134379776[/C][C]-14.4713437977625[/C][/ROW]
[ROW][C]64[/C][C]4998[/C][C]4917.83281332378[/C][C]80.1671866762226[/C][/ROW]
[ROW][C]65[/C][C]4986.5[/C][C]4992.65300819091[/C][C]-6.15300819091044[/C][/ROW]
[ROW][C]66[/C][C]5348[/C][C]5292.63687986203[/C][C]55.3631201379658[/C][/ROW]
[ROW][C]67[/C][C]4933[/C][C]4917.88704194185[/C][C]15.1129580581455[/C][/ROW]
[ROW][C]68[/C][C]5263[/C][C]5117.43700043742[/C][C]145.562999562585[/C][/ROW]
[ROW][C]69[/C][C]5330.5[/C][C]5302.78164398266[/C][C]27.7183560173398[/C][/ROW]
[ROW][C]70[/C][C]5301[/C][C]5327.4668862585[/C][C]-26.4668862585004[/C][/ROW]
[ROW][C]71[/C][C]5159[/C][C]5210.04330521052[/C][C]-51.0433052105191[/C][/ROW]
[ROW][C]72[/C][C]5258.5[/C][C]5147.14484328374[/C][C]111.355156716262[/C][/ROW]
[ROW][C]73[/C][C]5411.5[/C][C]5359.35337272408[/C][C]52.1466272759226[/C][/ROW]
[ROW][C]74[/C][C]5536.5[/C][C]5670.2104909554[/C][C]-133.710490955405[/C][/ROW]
[ROW][C]75[/C][C]5613[/C][C]5622.73231659551[/C][C]-9.73231659551402[/C][/ROW]
[ROW][C]76[/C][C]5505.5[/C][C]5551.59550180576[/C][C]-46.0955018057593[/C][/ROW]
[ROW][C]77[/C][C]5476[/C][C]5521.33012984589[/C][C]-45.330129845891[/C][/ROW]
[ROW][C]78[/C][C]5782.5[/C][C]5801.63781946558[/C][C]-19.1378194655799[/C][/ROW]
[ROW][C]79[/C][C]5283[/C][C]5364.99787919491[/C][C]-81.9978791949125[/C][/ROW]
[ROW][C]80[/C][C]5451.5[/C][C]5505.90891873505[/C][C]-54.4089187350546[/C][/ROW]
[ROW][C]81[/C][C]5578[/C][C]5516.45781854993[/C][C]61.5421814500687[/C][/ROW]
[ROW][C]82[/C][C]5548.5[/C][C]5554.40864337114[/C][C]-5.9086433711409[/C][/ROW]
[ROW][C]83[/C][C]5379.5[/C][C]5444.49871664285[/C][C]-64.9987166428546[/C][/ROW]
[ROW][C]84[/C][C]5117.5[/C][C]5387.27307778697[/C][C]-269.773077786967[/C][/ROW]
[ROW][C]85[/C][C]5316.5[/C][C]5286.33480423446[/C][C]30.1651957655431[/C][/ROW]
[ROW][C]86[/C][C]5505.5[/C][C]5541.4386800627[/C][C]-35.9386800627017[/C][/ROW]
[ROW][C]87[/C][C]5620.5[/C][C]5573.19917779644[/C][C]47.3008222035551[/C][/ROW]
[ROW][C]88[/C][C]5383.5[/C][C]5530.07826685087[/C][C]-146.578266850866[/C][/ROW]
[ROW][C]89[/C][C]5461.5[/C][C]5410.04180980185[/C][C]51.4581901981483[/C][/ROW]
[ROW][C]90[/C][C]5658.5[/C][C]5757.01476699652[/C][C]-98.5147669965218[/C][/ROW]
[ROW][C]91[/C][C]5357.5[/C][C]5238.67254396906[/C][C]118.827456030938[/C][/ROW]
[ROW][C]92[/C][C]5622[/C][C]5528.71790740372[/C][C]93.2820925962842[/C][/ROW]
[ROW][C]93[/C][C]5608[/C][C]5662.79359304179[/C][C]-54.7935930417898[/C][/ROW]
[ROW][C]94[/C][C]5604.5[/C][C]5595.32241853162[/C][C]9.17758146837878[/C][/ROW]
[ROW][C]95[/C][C]5399[/C][C]5481.96902107109[/C][C]-82.9690210710914[/C][/ROW]
[ROW][C]96[/C][C]5185[/C][C]5376.23551262175[/C][C]-191.235512621746[/C][/ROW]
[ROW][C]97[/C][C]5221[/C][C]5369.49387845419[/C][C]-148.493878454188[/C][/ROW]
[ROW][C]98[/C][C]5379.5[/C][C]5469.39053089109[/C][C]-89.8905308910853[/C][/ROW]
[ROW][C]99[/C][C]5333[/C][C]5460.00374352942[/C][C]-127.003743529423[/C][/ROW]
[ROW][C]100[/C][C]5214[/C][C]5242.93521033645[/C][C]-28.9352103364454[/C][/ROW]
[ROW][C]101[/C][C]5206.5[/C][C]5227.02257113275[/C][C]-20.5225711327539[/C][/ROW]
[ROW][C]102[/C][C]5630[/C][C]5485.17578439447[/C][C]144.824215605526[/C][/ROW]
[ROW][C]103[/C][C]5285.5[/C][C]5173.48630643274[/C][C]112.013693567256[/C][/ROW]
[ROW][C]104[/C][C]5512.5[/C][C]5446.37122219182[/C][C]66.1287778081842[/C][/ROW]
[ROW][C]105[/C][C]5592.5[/C][C]5530.8255455627[/C][C]61.6744544372996[/C][/ROW]
[ROW][C]106[/C][C]5554.5[/C][C]5554.39109315822[/C][C]0.108906841784119[/C][/ROW]
[ROW][C]107[/C][C]5284.5[/C][C]5415.07760151195[/C][C]-130.577601511952[/C][/ROW]
[ROW][C]108[/C][C]5198.5[/C][C]5250.70021060102[/C][C]-52.2002106010232[/C][/ROW]
[ROW][C]109[/C][C]5241.5[/C][C]5351.26542728724[/C][C]-109.76542728724[/C][/ROW]
[ROW][C]110[/C][C]5455[/C][C]5484.71040026464[/C][C]-29.7104002646392[/C][/ROW]
[ROW][C]111[/C][C]5548.5[/C][C]5513.88763281202[/C][C]34.6123671879814[/C][/ROW]
[ROW][C]112[/C][C]5375[/C][C]5434.55117345758[/C][C]-59.5511734575775[/C][/ROW]
[ROW][C]113[/C][C]5346[/C][C]5396.71670434567[/C][C]-50.7167043456739[/C][/ROW]
[ROW][C]114[/C][C]5730.5[/C][C]5653.47412259425[/C][C]77.0258774057529[/C][/ROW]
[ROW][C]115[/C][C]5457[/C][C]5283.75805623411[/C][C]173.241943765891[/C][/ROW]
[ROW][C]116[/C][C]5603[/C][C]5596.93729657003[/C][C]6.06270342996868[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299167&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299167&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
1337103438.25694444445271.743055555554
143994.53937.3426238128157.1573761871909
1540914088.656501071742.34349892826231
163954.53971.75939453366-17.2593945336635
1740044031.40000309155-27.4000030915513
1842874316.5076729178-29.5076729177954
1938313819.1386528501811.8613471498188
204046.54084.05351137361-37.5535113736087
214079.54119.52108269982-40.0210826998236
224029.54163.75289403167-134.252894031665
2338803930.00052210647-50.0005221064725
2438553846.855899977468.14410002253726
253841.54012.59941496999-171.099414969992
264123.54134.88304875972-11.3830487597152
2741334215.44461272358-82.4446127235815
283958.54018.16492457842-59.664924578417
2940034030.15916858704-27.1591685870426
304151.54301.31658155766-149.816581557664
3137233700.8910713462922.1089286537062
3239573950.770511185356.229488814653
333965.54004.07374983998-38.5737498399785
343861.54021.58273906992-160.082739069917
353917.53763.40881767297154.091182327033
3637043832.78585022452-128.785850224524
3739503855.5662477071394.4337522928718
384140.54193.74117187042-53.2411718704188
3940904223.42789994779-133.427899947793
4041623979.64186298535182.358137014647
4140664175.93940630285-109.939406302849
424358.54360.46277294632-1.96277294631727
434022.53892.29792442233130.202075577674
444285.54221.4456057691764.0543942308332
454373.54313.0029093141260.4970906858753
464284.54392.31670362657-107.816703626572
474077.54219.25918614564-141.759186145644
4841224021.46633032869100.533669671309
494181.54251.22215017358-69.7221501735776
504535.54442.3995044211793.1004955788294
5144974574.83399518196-77.8339951819617
524420.54418.285166953682.21483304631602
5343704436.60306820227-66.6030682022729
5447124668.3034284648543.6965715351471
5544754253.32519606908221.674803930919
564578.54646.35952923131-67.8595292313139
574751.54636.31676495291115.183235047088
5847464736.07053742049.92946257960375
594581.54652.18220237232-70.6822023723216
604645.54546.1830863390699.3169136609386
6147514757.52916290586-6.52916290586381
624952.55025.27665102523-72.776651025235
634996.55010.97134379776-14.4713437977625
6449984917.8328133237880.1671866762226
654986.54992.65300819091-6.15300819091044
6653485292.6368798620355.3631201379658
6749334917.8870419418515.1129580581455
6852635117.43700043742145.562999562585
695330.55302.7816439826627.7183560173398
7053015327.4668862585-26.4668862585004
7151595210.04330521052-51.0433052105191
725258.55147.14484328374111.355156716262
735411.55359.3533727240852.1466272759226
745536.55670.2104909554-133.710490955405
7556135622.73231659551-9.73231659551402
765505.55551.59550180576-46.0955018057593
7754765521.33012984589-45.330129845891
785782.55801.63781946558-19.1378194655799
7952835364.99787919491-81.9978791949125
805451.55505.90891873505-54.4089187350546
8155785516.4578185499361.5421814500687
825548.55554.40864337114-5.9086433711409
835379.55444.49871664285-64.9987166428546
845117.55387.27307778697-269.773077786967
855316.55286.3348042344630.1651957655431
865505.55541.4386800627-35.9386800627017
875620.55573.1991777964447.3008222035551
885383.55530.07826685087-146.578266850866
895461.55410.0418098018551.4581901981483
905658.55757.01476699652-98.5147669965218
915357.55238.67254396906118.827456030938
9256225528.7179074037293.2820925962842
9356085662.79359304179-54.7935930417898
945604.55595.322418531629.17758146837878
9553995481.96902107109-82.9690210710914
9651855376.23551262175-191.235512621746
9752215369.49387845419-148.493878454188
985379.55469.39053089109-89.8905308910853
9953335460.00374352942-127.003743529423
10052145242.93521033645-28.9352103364454
1015206.55227.02257113275-20.5225711327539
10256305485.17578439447144.824215605526
1035285.55173.48630643274112.013693567256
1045512.55446.3712221918266.1287778081842
1055592.55530.825545562761.6744544372996
1065554.55554.391093158220.108906841784119
1075284.55415.07760151195-130.577601511952
1085198.55250.70021060102-52.2002106010232
1095241.55351.26542728724-109.76542728724
11054555484.71040026464-29.7104002646392
1115548.55513.8876328120234.6123671879814
11253755434.55117345758-59.5511734575775
11353465396.71670434567-50.7167043456739
1145730.55653.4741225942577.0258774057529
11554575283.75805623411173.241943765891
11656035596.937296570036.06270342996868







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1175633.077473117975448.562314182875817.59263205308
1185598.130529470655363.305963494355832.95509544696
1195438.202379523815159.907673228975716.49708581865
1205383.890869025935066.092807416275701.68893063558
1215517.645500390645162.935430322125872.35557045916
1225749.060561513215359.24972934476138.87139368172
1235813.537928740865389.947295044586237.12856243714
1245698.447258575145242.067462972146154.82705417814
1255711.9132507515223.500896993596200.32560450842
1266030.157557419015510.296982698686550.01813213935
1275618.305781463515067.4506724196169.16089050802
1285776.861293367135195.363835825666358.35875090859
1295807.557382651665187.613940563216427.50082474011
1305772.610439004345122.878170580636422.34270742806
1315612.68228905754933.280516028836292.08406208618
1325558.370778559624849.380100999176267.36145612006
1335692.125409924334953.593948550456430.65687129821
1345923.54047104695155.488878575766691.59206351804

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 5633.07747311797 & 5448.56231418287 & 5817.59263205308 \tabularnewline
118 & 5598.13052947065 & 5363.30596349435 & 5832.95509544696 \tabularnewline
119 & 5438.20237952381 & 5159.90767322897 & 5716.49708581865 \tabularnewline
120 & 5383.89086902593 & 5066.09280741627 & 5701.68893063558 \tabularnewline
121 & 5517.64550039064 & 5162.93543032212 & 5872.35557045916 \tabularnewline
122 & 5749.06056151321 & 5359.2497293447 & 6138.87139368172 \tabularnewline
123 & 5813.53792874086 & 5389.94729504458 & 6237.12856243714 \tabularnewline
124 & 5698.44725857514 & 5242.06746297214 & 6154.82705417814 \tabularnewline
125 & 5711.913250751 & 5223.50089699359 & 6200.32560450842 \tabularnewline
126 & 6030.15755741901 & 5510.29698269868 & 6550.01813213935 \tabularnewline
127 & 5618.30578146351 & 5067.450672419 & 6169.16089050802 \tabularnewline
128 & 5776.86129336713 & 5195.36383582566 & 6358.35875090859 \tabularnewline
129 & 5807.55738265166 & 5187.61394056321 & 6427.50082474011 \tabularnewline
130 & 5772.61043900434 & 5122.87817058063 & 6422.34270742806 \tabularnewline
131 & 5612.6822890575 & 4933.28051602883 & 6292.08406208618 \tabularnewline
132 & 5558.37077855962 & 4849.38010099917 & 6267.36145612006 \tabularnewline
133 & 5692.12540992433 & 4953.59394855045 & 6430.65687129821 \tabularnewline
134 & 5923.5404710469 & 5155.48887857576 & 6691.59206351804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299167&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]117[/C][C]5633.07747311797[/C][C]5448.56231418287[/C][C]5817.59263205308[/C][/ROW]
[ROW][C]118[/C][C]5598.13052947065[/C][C]5363.30596349435[/C][C]5832.95509544696[/C][/ROW]
[ROW][C]119[/C][C]5438.20237952381[/C][C]5159.90767322897[/C][C]5716.49708581865[/C][/ROW]
[ROW][C]120[/C][C]5383.89086902593[/C][C]5066.09280741627[/C][C]5701.68893063558[/C][/ROW]
[ROW][C]121[/C][C]5517.64550039064[/C][C]5162.93543032212[/C][C]5872.35557045916[/C][/ROW]
[ROW][C]122[/C][C]5749.06056151321[/C][C]5359.2497293447[/C][C]6138.87139368172[/C][/ROW]
[ROW][C]123[/C][C]5813.53792874086[/C][C]5389.94729504458[/C][C]6237.12856243714[/C][/ROW]
[ROW][C]124[/C][C]5698.44725857514[/C][C]5242.06746297214[/C][C]6154.82705417814[/C][/ROW]
[ROW][C]125[/C][C]5711.913250751[/C][C]5223.50089699359[/C][C]6200.32560450842[/C][/ROW]
[ROW][C]126[/C][C]6030.15755741901[/C][C]5510.29698269868[/C][C]6550.01813213935[/C][/ROW]
[ROW][C]127[/C][C]5618.30578146351[/C][C]5067.450672419[/C][C]6169.16089050802[/C][/ROW]
[ROW][C]128[/C][C]5776.86129336713[/C][C]5195.36383582566[/C][C]6358.35875090859[/C][/ROW]
[ROW][C]129[/C][C]5807.55738265166[/C][C]5187.61394056321[/C][C]6427.50082474011[/C][/ROW]
[ROW][C]130[/C][C]5772.61043900434[/C][C]5122.87817058063[/C][C]6422.34270742806[/C][/ROW]
[ROW][C]131[/C][C]5612.6822890575[/C][C]4933.28051602883[/C][C]6292.08406208618[/C][/ROW]
[ROW][C]132[/C][C]5558.37077855962[/C][C]4849.38010099917[/C][C]6267.36145612006[/C][/ROW]
[ROW][C]133[/C][C]5692.12540992433[/C][C]4953.59394855045[/C][C]6430.65687129821[/C][/ROW]
[ROW][C]134[/C][C]5923.5404710469[/C][C]5155.48887857576[/C][C]6691.59206351804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299167&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299167&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
1175633.077473117975448.562314182875817.59263205308
1185598.130529470655363.305963494355832.95509544696
1195438.202379523815159.907673228975716.49708581865
1205383.890869025935066.092807416275701.68893063558
1215517.645500390645162.935430322125872.35557045916
1225749.060561513215359.24972934476138.87139368172
1235813.537928740865389.947295044586237.12856243714
1245698.447258575145242.067462972146154.82705417814
1255711.9132507515223.500896993596200.32560450842
1266030.157557419015510.296982698686550.01813213935
1275618.305781463515067.4506724196169.16089050802
1285776.861293367135195.363835825666358.35875090859
1295807.557382651665187.613940563216427.50082474011
1305772.610439004345122.878170580636422.34270742806
1315612.68228905754933.280516028836292.08406208618
1325558.370778559624849.380100999176267.36145612006
1335692.125409924334953.593948550456430.65687129821
1345923.54047104695155.488878575766691.59206351804



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '18'
par3 <- 'multiplicative'
par2 <- 'Triple'
par1 <- '12'
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')