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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 computationFri, 23 Dec 2016 10:39:04 +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/23/t1482485984ve9ehqavvxpzkau.htm/, Retrieved Tue, 07 May 2024 23:27:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302820, Retrieved Tue, 07 May 2024 23:27:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [ES N2583] [2016-12-23 09:39:04] [11b61e09f442d73f657668491c17a736] [Current]
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Dataseries X:
4782
4540
4588
4740
4646
4736
4794
4730
4752
4804
4818
4948
4906
4666
4696
4872
4742
4858
4868
4782
4824
4820
4882
5062
4996
4800
4828
5002
4926
5090
5140
5116
5210
5224
5292
5538
5414
5160
5258
5492
5448
5618
5704
5684
5722
5754
5894
6280
6114
5744
5736
6020
5880
5888
5886
5812
5784
5914
5884
5972
5918
5586
5600
5842
5662
5826
5862
5782
5750
5778
5802
5978
5810
5516
5520
5664
5470
5534
5636
5542
5526
5608
5630
5830
5656
5426
5432
5600
5380
5504
5546
5534
5562
5564
5612
5798
5556
5364
5406
5558
5438
5602
5622
5580
5570
5674
5818
6058
5998
5928
6052
6276
6166
6226
6354
6396




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=302820&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=302820&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302820&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
alpha0.888051277733209
beta0.135461037003667
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.888051277733209 \tabularnewline
beta & 0.135461037003667 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302820&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]0.888051277733209[/C][/ROW]
[ROW][C]beta[/C][C]0.135461037003667[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302820&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302820&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
alpha0.888051277733209
beta0.135461037003667
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1349064848.8002136752257.1997863247834
1446664668.54158491483-2.54158491482758
1546964705.00714504407-9.00714504407279
1648724882.14742959363-10.1474295936314
1747424751.38771761382-9.38771761381577
1848584862.0900273595-4.09002735949525
1948684886.17160902077-18.1716090207728
2047824803.39537924438-21.3953792443754
2148244801.849156902822.150843097198
2248204871.38887845955-51.3888784595529
2348824831.9396619688850.060338031125
2450625005.0212942688856.9787057311205
2549965026.42123166026-30.4212316602634
2648004758.3712334345741.6287665654345
2748284835.36060905643-7.36060905643444
2850025016.05561047767-14.0556104776742
2949264883.6603042542342.3396957457726
3050905048.864920047941.1350799520997
3151405124.9453570356315.0546429643682
3251165088.7248986368827.2751013631232
3352105158.5404365662751.4595634337338
3452245272.66579262293-48.6657926229273
3552925274.110169249117.8898307509035
3655385442.6454924701695.3545075298443
3754145516.20551572753-102.205515727525
3851605211.70262777229-51.7026277722944
3952585208.3265458125849.6734541874248
4054925453.784116997838.2158830022008
4154485395.2729234199452.7270765800622
4256185591.9677384042826.0322615957202
4357045672.3001403461331.6998596538679
4456845674.815625052379.18437494762657
4557225751.6829140511-29.6829140511036
4657545793.18936414461-39.189364144614
4758945822.2887724369171.7112275630916
4862806065.5555051305214.4444948695
4961146255.34621975384-141.346219753836
5057445949.6188977593-205.618897759301
5157365830.27141780036-94.2714178003571
5260205938.6650781534181.3349218465901
5358805917.30655166861-37.3065516686129
5458886017.46396100724-129.463961007238
5558865928.04211998237-42.0421199823713
5658125821.37937077323-9.3793707732284
5757845834.00581259414-50.0058125941441
5859145810.55133554343103.448664456569
5958845950.04572452726-66.0457245272592
6059726041.69428628938-69.6942862893775
6159185859.8822794308358.1177205691656
6255865668.64610577668-82.6461057766755
6356005630.31534208275-30.3153420827484
6458425782.2032279273659.7967720726447
6556625692.88404329541-30.8840432954075
6658265753.6487541215572.3512458784453
6758625842.73424993819.2657500620026
6857825791.04602000442-9.04602000442082
6957505796.33395093704-46.3339509370417
7057785790.67455428617-12.6745542861709
7158025791.4569375285810.5430624714236
7259785943.3112162298834.6887837701233
7358105873.6614195981-63.6614195980983
7455165549.02750934267-33.0275093426744
7555205557.09461656239-37.0946165623864
7656645708.71022394885-44.7102239488468
7754705499.52018556181-29.5201855618134
7855345556.30551681838-22.3055168183773
7956365527.25362348914108.746376510859
8055425534.489027551217.51097244878656
8155265534.9275421022-8.92754210219846
8256085555.3763969356152.6236030643877
8356305613.7225204473816.2774795526238
8458305771.0386133097858.9613866902218
8556565712.52013367417-56.5201336741675
8654265399.1027297895826.8972702104156
8754325468.5847898477-36.5847898477032
8856005628.51590551971-28.51590551971
8953805446.07118857974-66.0711885797373
9055045477.4715065946226.5284934053843
9155465518.5988422326827.40115776732
9255345444.6178458412689.3821541587358
9355625528.1262004252633.8737995747379
9455645610.82856173513-46.8285617351303
9556125582.1765772669129.8234227330913
9657985763.3195147554934.6804852445111
9755565674.40838078189-118.408380781891
9853645312.02262157351.9773784270046
9954065396.340523485539.65947651447459
10055585603.47539180908-45.4753918090837
10154385404.9585227298333.0414772701661
10256025549.8582852980552.1417147019538
10356225632.02624437765-10.0262443776455
10455805545.4411851664534.5588148335546
10555705581.14916251791-11.1491625179078
10656745616.5178493865257.4821506134831
10758185703.31196647407114.688033525926
10860585984.8034230740573.1965769259532
10959985942.0324468366455.9675531633557
11059285803.62671071708124.37328928292
11160526006.2582064404745.7417935595304
11262766302.36406311062-26.3640631106227
11361666195.00823875199-29.0082387519888
11462266344.87790641069-118.877906410691
11563546305.5740006861548.4259993138503
11663966320.2823147994375.7176852005723

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4906 & 4848.80021367522 & 57.1997863247834 \tabularnewline
14 & 4666 & 4668.54158491483 & -2.54158491482758 \tabularnewline
15 & 4696 & 4705.00714504407 & -9.00714504407279 \tabularnewline
16 & 4872 & 4882.14742959363 & -10.1474295936314 \tabularnewline
17 & 4742 & 4751.38771761382 & -9.38771761381577 \tabularnewline
18 & 4858 & 4862.0900273595 & -4.09002735949525 \tabularnewline
19 & 4868 & 4886.17160902077 & -18.1716090207728 \tabularnewline
20 & 4782 & 4803.39537924438 & -21.3953792443754 \tabularnewline
21 & 4824 & 4801.8491569028 & 22.150843097198 \tabularnewline
22 & 4820 & 4871.38887845955 & -51.3888784595529 \tabularnewline
23 & 4882 & 4831.93966196888 & 50.060338031125 \tabularnewline
24 & 5062 & 5005.02129426888 & 56.9787057311205 \tabularnewline
25 & 4996 & 5026.42123166026 & -30.4212316602634 \tabularnewline
26 & 4800 & 4758.37123343457 & 41.6287665654345 \tabularnewline
27 & 4828 & 4835.36060905643 & -7.36060905643444 \tabularnewline
28 & 5002 & 5016.05561047767 & -14.0556104776742 \tabularnewline
29 & 4926 & 4883.66030425423 & 42.3396957457726 \tabularnewline
30 & 5090 & 5048.8649200479 & 41.1350799520997 \tabularnewline
31 & 5140 & 5124.94535703563 & 15.0546429643682 \tabularnewline
32 & 5116 & 5088.72489863688 & 27.2751013631232 \tabularnewline
33 & 5210 & 5158.54043656627 & 51.4595634337338 \tabularnewline
34 & 5224 & 5272.66579262293 & -48.6657926229273 \tabularnewline
35 & 5292 & 5274.1101692491 & 17.8898307509035 \tabularnewline
36 & 5538 & 5442.64549247016 & 95.3545075298443 \tabularnewline
37 & 5414 & 5516.20551572753 & -102.205515727525 \tabularnewline
38 & 5160 & 5211.70262777229 & -51.7026277722944 \tabularnewline
39 & 5258 & 5208.32654581258 & 49.6734541874248 \tabularnewline
40 & 5492 & 5453.7841169978 & 38.2158830022008 \tabularnewline
41 & 5448 & 5395.27292341994 & 52.7270765800622 \tabularnewline
42 & 5618 & 5591.96773840428 & 26.0322615957202 \tabularnewline
43 & 5704 & 5672.30014034613 & 31.6998596538679 \tabularnewline
44 & 5684 & 5674.81562505237 & 9.18437494762657 \tabularnewline
45 & 5722 & 5751.6829140511 & -29.6829140511036 \tabularnewline
46 & 5754 & 5793.18936414461 & -39.189364144614 \tabularnewline
47 & 5894 & 5822.28877243691 & 71.7112275630916 \tabularnewline
48 & 6280 & 6065.5555051305 & 214.4444948695 \tabularnewline
49 & 6114 & 6255.34621975384 & -141.346219753836 \tabularnewline
50 & 5744 & 5949.6188977593 & -205.618897759301 \tabularnewline
51 & 5736 & 5830.27141780036 & -94.2714178003571 \tabularnewline
52 & 6020 & 5938.66507815341 & 81.3349218465901 \tabularnewline
53 & 5880 & 5917.30655166861 & -37.3065516686129 \tabularnewline
54 & 5888 & 6017.46396100724 & -129.463961007238 \tabularnewline
55 & 5886 & 5928.04211998237 & -42.0421199823713 \tabularnewline
56 & 5812 & 5821.37937077323 & -9.3793707732284 \tabularnewline
57 & 5784 & 5834.00581259414 & -50.0058125941441 \tabularnewline
58 & 5914 & 5810.55133554343 & 103.448664456569 \tabularnewline
59 & 5884 & 5950.04572452726 & -66.0457245272592 \tabularnewline
60 & 5972 & 6041.69428628938 & -69.6942862893775 \tabularnewline
61 & 5918 & 5859.88227943083 & 58.1177205691656 \tabularnewline
62 & 5586 & 5668.64610577668 & -82.6461057766755 \tabularnewline
63 & 5600 & 5630.31534208275 & -30.3153420827484 \tabularnewline
64 & 5842 & 5782.20322792736 & 59.7967720726447 \tabularnewline
65 & 5662 & 5692.88404329541 & -30.8840432954075 \tabularnewline
66 & 5826 & 5753.64875412155 & 72.3512458784453 \tabularnewline
67 & 5862 & 5842.734249938 & 19.2657500620026 \tabularnewline
68 & 5782 & 5791.04602000442 & -9.04602000442082 \tabularnewline
69 & 5750 & 5796.33395093704 & -46.3339509370417 \tabularnewline
70 & 5778 & 5790.67455428617 & -12.6745542861709 \tabularnewline
71 & 5802 & 5791.45693752858 & 10.5430624714236 \tabularnewline
72 & 5978 & 5943.31121622988 & 34.6887837701233 \tabularnewline
73 & 5810 & 5873.6614195981 & -63.6614195980983 \tabularnewline
74 & 5516 & 5549.02750934267 & -33.0275093426744 \tabularnewline
75 & 5520 & 5557.09461656239 & -37.0946165623864 \tabularnewline
76 & 5664 & 5708.71022394885 & -44.7102239488468 \tabularnewline
77 & 5470 & 5499.52018556181 & -29.5201855618134 \tabularnewline
78 & 5534 & 5556.30551681838 & -22.3055168183773 \tabularnewline
79 & 5636 & 5527.25362348914 & 108.746376510859 \tabularnewline
80 & 5542 & 5534.48902755121 & 7.51097244878656 \tabularnewline
81 & 5526 & 5534.9275421022 & -8.92754210219846 \tabularnewline
82 & 5608 & 5555.37639693561 & 52.6236030643877 \tabularnewline
83 & 5630 & 5613.72252044738 & 16.2774795526238 \tabularnewline
84 & 5830 & 5771.03861330978 & 58.9613866902218 \tabularnewline
85 & 5656 & 5712.52013367417 & -56.5201336741675 \tabularnewline
86 & 5426 & 5399.10272978958 & 26.8972702104156 \tabularnewline
87 & 5432 & 5468.5847898477 & -36.5847898477032 \tabularnewline
88 & 5600 & 5628.51590551971 & -28.51590551971 \tabularnewline
89 & 5380 & 5446.07118857974 & -66.0711885797373 \tabularnewline
90 & 5504 & 5477.47150659462 & 26.5284934053843 \tabularnewline
91 & 5546 & 5518.59884223268 & 27.40115776732 \tabularnewline
92 & 5534 & 5444.61784584126 & 89.3821541587358 \tabularnewline
93 & 5562 & 5528.12620042526 & 33.8737995747379 \tabularnewline
94 & 5564 & 5610.82856173513 & -46.8285617351303 \tabularnewline
95 & 5612 & 5582.17657726691 & 29.8234227330913 \tabularnewline
96 & 5798 & 5763.31951475549 & 34.6804852445111 \tabularnewline
97 & 5556 & 5674.40838078189 & -118.408380781891 \tabularnewline
98 & 5364 & 5312.022621573 & 51.9773784270046 \tabularnewline
99 & 5406 & 5396.34052348553 & 9.65947651447459 \tabularnewline
100 & 5558 & 5603.47539180908 & -45.4753918090837 \tabularnewline
101 & 5438 & 5404.95852272983 & 33.0414772701661 \tabularnewline
102 & 5602 & 5549.85828529805 & 52.1417147019538 \tabularnewline
103 & 5622 & 5632.02624437765 & -10.0262443776455 \tabularnewline
104 & 5580 & 5545.44118516645 & 34.5588148335546 \tabularnewline
105 & 5570 & 5581.14916251791 & -11.1491625179078 \tabularnewline
106 & 5674 & 5616.51784938652 & 57.4821506134831 \tabularnewline
107 & 5818 & 5703.31196647407 & 114.688033525926 \tabularnewline
108 & 6058 & 5984.80342307405 & 73.1965769259532 \tabularnewline
109 & 5998 & 5942.03244683664 & 55.9675531633557 \tabularnewline
110 & 5928 & 5803.62671071708 & 124.37328928292 \tabularnewline
111 & 6052 & 6006.25820644047 & 45.7417935595304 \tabularnewline
112 & 6276 & 6302.36406311062 & -26.3640631106227 \tabularnewline
113 & 6166 & 6195.00823875199 & -29.0082387519888 \tabularnewline
114 & 6226 & 6344.87790641069 & -118.877906410691 \tabularnewline
115 & 6354 & 6305.57400068615 & 48.4259993138503 \tabularnewline
116 & 6396 & 6320.28231479943 & 75.7176852005723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302820&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]4906[/C][C]4848.80021367522[/C][C]57.1997863247834[/C][/ROW]
[ROW][C]14[/C][C]4666[/C][C]4668.54158491483[/C][C]-2.54158491482758[/C][/ROW]
[ROW][C]15[/C][C]4696[/C][C]4705.00714504407[/C][C]-9.00714504407279[/C][/ROW]
[ROW][C]16[/C][C]4872[/C][C]4882.14742959363[/C][C]-10.1474295936314[/C][/ROW]
[ROW][C]17[/C][C]4742[/C][C]4751.38771761382[/C][C]-9.38771761381577[/C][/ROW]
[ROW][C]18[/C][C]4858[/C][C]4862.0900273595[/C][C]-4.09002735949525[/C][/ROW]
[ROW][C]19[/C][C]4868[/C][C]4886.17160902077[/C][C]-18.1716090207728[/C][/ROW]
[ROW][C]20[/C][C]4782[/C][C]4803.39537924438[/C][C]-21.3953792443754[/C][/ROW]
[ROW][C]21[/C][C]4824[/C][C]4801.8491569028[/C][C]22.150843097198[/C][/ROW]
[ROW][C]22[/C][C]4820[/C][C]4871.38887845955[/C][C]-51.3888784595529[/C][/ROW]
[ROW][C]23[/C][C]4882[/C][C]4831.93966196888[/C][C]50.060338031125[/C][/ROW]
[ROW][C]24[/C][C]5062[/C][C]5005.02129426888[/C][C]56.9787057311205[/C][/ROW]
[ROW][C]25[/C][C]4996[/C][C]5026.42123166026[/C][C]-30.4212316602634[/C][/ROW]
[ROW][C]26[/C][C]4800[/C][C]4758.37123343457[/C][C]41.6287665654345[/C][/ROW]
[ROW][C]27[/C][C]4828[/C][C]4835.36060905643[/C][C]-7.36060905643444[/C][/ROW]
[ROW][C]28[/C][C]5002[/C][C]5016.05561047767[/C][C]-14.0556104776742[/C][/ROW]
[ROW][C]29[/C][C]4926[/C][C]4883.66030425423[/C][C]42.3396957457726[/C][/ROW]
[ROW][C]30[/C][C]5090[/C][C]5048.8649200479[/C][C]41.1350799520997[/C][/ROW]
[ROW][C]31[/C][C]5140[/C][C]5124.94535703563[/C][C]15.0546429643682[/C][/ROW]
[ROW][C]32[/C][C]5116[/C][C]5088.72489863688[/C][C]27.2751013631232[/C][/ROW]
[ROW][C]33[/C][C]5210[/C][C]5158.54043656627[/C][C]51.4595634337338[/C][/ROW]
[ROW][C]34[/C][C]5224[/C][C]5272.66579262293[/C][C]-48.6657926229273[/C][/ROW]
[ROW][C]35[/C][C]5292[/C][C]5274.1101692491[/C][C]17.8898307509035[/C][/ROW]
[ROW][C]36[/C][C]5538[/C][C]5442.64549247016[/C][C]95.3545075298443[/C][/ROW]
[ROW][C]37[/C][C]5414[/C][C]5516.20551572753[/C][C]-102.205515727525[/C][/ROW]
[ROW][C]38[/C][C]5160[/C][C]5211.70262777229[/C][C]-51.7026277722944[/C][/ROW]
[ROW][C]39[/C][C]5258[/C][C]5208.32654581258[/C][C]49.6734541874248[/C][/ROW]
[ROW][C]40[/C][C]5492[/C][C]5453.7841169978[/C][C]38.2158830022008[/C][/ROW]
[ROW][C]41[/C][C]5448[/C][C]5395.27292341994[/C][C]52.7270765800622[/C][/ROW]
[ROW][C]42[/C][C]5618[/C][C]5591.96773840428[/C][C]26.0322615957202[/C][/ROW]
[ROW][C]43[/C][C]5704[/C][C]5672.30014034613[/C][C]31.6998596538679[/C][/ROW]
[ROW][C]44[/C][C]5684[/C][C]5674.81562505237[/C][C]9.18437494762657[/C][/ROW]
[ROW][C]45[/C][C]5722[/C][C]5751.6829140511[/C][C]-29.6829140511036[/C][/ROW]
[ROW][C]46[/C][C]5754[/C][C]5793.18936414461[/C][C]-39.189364144614[/C][/ROW]
[ROW][C]47[/C][C]5894[/C][C]5822.28877243691[/C][C]71.7112275630916[/C][/ROW]
[ROW][C]48[/C][C]6280[/C][C]6065.5555051305[/C][C]214.4444948695[/C][/ROW]
[ROW][C]49[/C][C]6114[/C][C]6255.34621975384[/C][C]-141.346219753836[/C][/ROW]
[ROW][C]50[/C][C]5744[/C][C]5949.6188977593[/C][C]-205.618897759301[/C][/ROW]
[ROW][C]51[/C][C]5736[/C][C]5830.27141780036[/C][C]-94.2714178003571[/C][/ROW]
[ROW][C]52[/C][C]6020[/C][C]5938.66507815341[/C][C]81.3349218465901[/C][/ROW]
[ROW][C]53[/C][C]5880[/C][C]5917.30655166861[/C][C]-37.3065516686129[/C][/ROW]
[ROW][C]54[/C][C]5888[/C][C]6017.46396100724[/C][C]-129.463961007238[/C][/ROW]
[ROW][C]55[/C][C]5886[/C][C]5928.04211998237[/C][C]-42.0421199823713[/C][/ROW]
[ROW][C]56[/C][C]5812[/C][C]5821.37937077323[/C][C]-9.3793707732284[/C][/ROW]
[ROW][C]57[/C][C]5784[/C][C]5834.00581259414[/C][C]-50.0058125941441[/C][/ROW]
[ROW][C]58[/C][C]5914[/C][C]5810.55133554343[/C][C]103.448664456569[/C][/ROW]
[ROW][C]59[/C][C]5884[/C][C]5950.04572452726[/C][C]-66.0457245272592[/C][/ROW]
[ROW][C]60[/C][C]5972[/C][C]6041.69428628938[/C][C]-69.6942862893775[/C][/ROW]
[ROW][C]61[/C][C]5918[/C][C]5859.88227943083[/C][C]58.1177205691656[/C][/ROW]
[ROW][C]62[/C][C]5586[/C][C]5668.64610577668[/C][C]-82.6461057766755[/C][/ROW]
[ROW][C]63[/C][C]5600[/C][C]5630.31534208275[/C][C]-30.3153420827484[/C][/ROW]
[ROW][C]64[/C][C]5842[/C][C]5782.20322792736[/C][C]59.7967720726447[/C][/ROW]
[ROW][C]65[/C][C]5662[/C][C]5692.88404329541[/C][C]-30.8840432954075[/C][/ROW]
[ROW][C]66[/C][C]5826[/C][C]5753.64875412155[/C][C]72.3512458784453[/C][/ROW]
[ROW][C]67[/C][C]5862[/C][C]5842.734249938[/C][C]19.2657500620026[/C][/ROW]
[ROW][C]68[/C][C]5782[/C][C]5791.04602000442[/C][C]-9.04602000442082[/C][/ROW]
[ROW][C]69[/C][C]5750[/C][C]5796.33395093704[/C][C]-46.3339509370417[/C][/ROW]
[ROW][C]70[/C][C]5778[/C][C]5790.67455428617[/C][C]-12.6745542861709[/C][/ROW]
[ROW][C]71[/C][C]5802[/C][C]5791.45693752858[/C][C]10.5430624714236[/C][/ROW]
[ROW][C]72[/C][C]5978[/C][C]5943.31121622988[/C][C]34.6887837701233[/C][/ROW]
[ROW][C]73[/C][C]5810[/C][C]5873.6614195981[/C][C]-63.6614195980983[/C][/ROW]
[ROW][C]74[/C][C]5516[/C][C]5549.02750934267[/C][C]-33.0275093426744[/C][/ROW]
[ROW][C]75[/C][C]5520[/C][C]5557.09461656239[/C][C]-37.0946165623864[/C][/ROW]
[ROW][C]76[/C][C]5664[/C][C]5708.71022394885[/C][C]-44.7102239488468[/C][/ROW]
[ROW][C]77[/C][C]5470[/C][C]5499.52018556181[/C][C]-29.5201855618134[/C][/ROW]
[ROW][C]78[/C][C]5534[/C][C]5556.30551681838[/C][C]-22.3055168183773[/C][/ROW]
[ROW][C]79[/C][C]5636[/C][C]5527.25362348914[/C][C]108.746376510859[/C][/ROW]
[ROW][C]80[/C][C]5542[/C][C]5534.48902755121[/C][C]7.51097244878656[/C][/ROW]
[ROW][C]81[/C][C]5526[/C][C]5534.9275421022[/C][C]-8.92754210219846[/C][/ROW]
[ROW][C]82[/C][C]5608[/C][C]5555.37639693561[/C][C]52.6236030643877[/C][/ROW]
[ROW][C]83[/C][C]5630[/C][C]5613.72252044738[/C][C]16.2774795526238[/C][/ROW]
[ROW][C]84[/C][C]5830[/C][C]5771.03861330978[/C][C]58.9613866902218[/C][/ROW]
[ROW][C]85[/C][C]5656[/C][C]5712.52013367417[/C][C]-56.5201336741675[/C][/ROW]
[ROW][C]86[/C][C]5426[/C][C]5399.10272978958[/C][C]26.8972702104156[/C][/ROW]
[ROW][C]87[/C][C]5432[/C][C]5468.5847898477[/C][C]-36.5847898477032[/C][/ROW]
[ROW][C]88[/C][C]5600[/C][C]5628.51590551971[/C][C]-28.51590551971[/C][/ROW]
[ROW][C]89[/C][C]5380[/C][C]5446.07118857974[/C][C]-66.0711885797373[/C][/ROW]
[ROW][C]90[/C][C]5504[/C][C]5477.47150659462[/C][C]26.5284934053843[/C][/ROW]
[ROW][C]91[/C][C]5546[/C][C]5518.59884223268[/C][C]27.40115776732[/C][/ROW]
[ROW][C]92[/C][C]5534[/C][C]5444.61784584126[/C][C]89.3821541587358[/C][/ROW]
[ROW][C]93[/C][C]5562[/C][C]5528.12620042526[/C][C]33.8737995747379[/C][/ROW]
[ROW][C]94[/C][C]5564[/C][C]5610.82856173513[/C][C]-46.8285617351303[/C][/ROW]
[ROW][C]95[/C][C]5612[/C][C]5582.17657726691[/C][C]29.8234227330913[/C][/ROW]
[ROW][C]96[/C][C]5798[/C][C]5763.31951475549[/C][C]34.6804852445111[/C][/ROW]
[ROW][C]97[/C][C]5556[/C][C]5674.40838078189[/C][C]-118.408380781891[/C][/ROW]
[ROW][C]98[/C][C]5364[/C][C]5312.022621573[/C][C]51.9773784270046[/C][/ROW]
[ROW][C]99[/C][C]5406[/C][C]5396.34052348553[/C][C]9.65947651447459[/C][/ROW]
[ROW][C]100[/C][C]5558[/C][C]5603.47539180908[/C][C]-45.4753918090837[/C][/ROW]
[ROW][C]101[/C][C]5438[/C][C]5404.95852272983[/C][C]33.0414772701661[/C][/ROW]
[ROW][C]102[/C][C]5602[/C][C]5549.85828529805[/C][C]52.1417147019538[/C][/ROW]
[ROW][C]103[/C][C]5622[/C][C]5632.02624437765[/C][C]-10.0262443776455[/C][/ROW]
[ROW][C]104[/C][C]5580[/C][C]5545.44118516645[/C][C]34.5588148335546[/C][/ROW]
[ROW][C]105[/C][C]5570[/C][C]5581.14916251791[/C][C]-11.1491625179078[/C][/ROW]
[ROW][C]106[/C][C]5674[/C][C]5616.51784938652[/C][C]57.4821506134831[/C][/ROW]
[ROW][C]107[/C][C]5818[/C][C]5703.31196647407[/C][C]114.688033525926[/C][/ROW]
[ROW][C]108[/C][C]6058[/C][C]5984.80342307405[/C][C]73.1965769259532[/C][/ROW]
[ROW][C]109[/C][C]5998[/C][C]5942.03244683664[/C][C]55.9675531633557[/C][/ROW]
[ROW][C]110[/C][C]5928[/C][C]5803.62671071708[/C][C]124.37328928292[/C][/ROW]
[ROW][C]111[/C][C]6052[/C][C]6006.25820644047[/C][C]45.7417935595304[/C][/ROW]
[ROW][C]112[/C][C]6276[/C][C]6302.36406311062[/C][C]-26.3640631106227[/C][/ROW]
[ROW][C]113[/C][C]6166[/C][C]6195.00823875199[/C][C]-29.0082387519888[/C][/ROW]
[ROW][C]114[/C][C]6226[/C][C]6344.87790641069[/C][C]-118.877906410691[/C][/ROW]
[ROW][C]115[/C][C]6354[/C][C]6305.57400068615[/C][C]48.4259993138503[/C][/ROW]
[ROW][C]116[/C][C]6396[/C][C]6320.28231479943[/C][C]75.7176852005723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302820&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302820&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
1349064848.8002136752257.1997863247834
1446664668.54158491483-2.54158491482758
1546964705.00714504407-9.00714504407279
1648724882.14742959363-10.1474295936314
1747424751.38771761382-9.38771761381577
1848584862.0900273595-4.09002735949525
1948684886.17160902077-18.1716090207728
2047824803.39537924438-21.3953792443754
2148244801.849156902822.150843097198
2248204871.38887845955-51.3888784595529
2348824831.9396619688850.060338031125
2450625005.0212942688856.9787057311205
2549965026.42123166026-30.4212316602634
2648004758.3712334345741.6287665654345
2748284835.36060905643-7.36060905643444
2850025016.05561047767-14.0556104776742
2949264883.6603042542342.3396957457726
3050905048.864920047941.1350799520997
3151405124.9453570356315.0546429643682
3251165088.7248986368827.2751013631232
3352105158.5404365662751.4595634337338
3452245272.66579262293-48.6657926229273
3552925274.110169249117.8898307509035
3655385442.6454924701695.3545075298443
3754145516.20551572753-102.205515727525
3851605211.70262777229-51.7026277722944
3952585208.3265458125849.6734541874248
4054925453.784116997838.2158830022008
4154485395.2729234199452.7270765800622
4256185591.9677384042826.0322615957202
4357045672.3001403461331.6998596538679
4456845674.815625052379.18437494762657
4557225751.6829140511-29.6829140511036
4657545793.18936414461-39.189364144614
4758945822.2887724369171.7112275630916
4862806065.5555051305214.4444948695
4961146255.34621975384-141.346219753836
5057445949.6188977593-205.618897759301
5157365830.27141780036-94.2714178003571
5260205938.6650781534181.3349218465901
5358805917.30655166861-37.3065516686129
5458886017.46396100724-129.463961007238
5558865928.04211998237-42.0421199823713
5658125821.37937077323-9.3793707732284
5757845834.00581259414-50.0058125941441
5859145810.55133554343103.448664456569
5958845950.04572452726-66.0457245272592
6059726041.69428628938-69.6942862893775
6159185859.8822794308358.1177205691656
6255865668.64610577668-82.6461057766755
6356005630.31534208275-30.3153420827484
6458425782.2032279273659.7967720726447
6556625692.88404329541-30.8840432954075
6658265753.6487541215572.3512458784453
6758625842.73424993819.2657500620026
6857825791.04602000442-9.04602000442082
6957505796.33395093704-46.3339509370417
7057785790.67455428617-12.6745542861709
7158025791.4569375285810.5430624714236
7259785943.3112162298834.6887837701233
7358105873.6614195981-63.6614195980983
7455165549.02750934267-33.0275093426744
7555205557.09461656239-37.0946165623864
7656645708.71022394885-44.7102239488468
7754705499.52018556181-29.5201855618134
7855345556.30551681838-22.3055168183773
7956365527.25362348914108.746376510859
8055425534.489027551217.51097244878656
8155265534.9275421022-8.92754210219846
8256085555.3763969356152.6236030643877
8356305613.7225204473816.2774795526238
8458305771.0386133097858.9613866902218
8556565712.52013367417-56.5201336741675
8654265399.1027297895826.8972702104156
8754325468.5847898477-36.5847898477032
8856005628.51590551971-28.51590551971
8953805446.07118857974-66.0711885797373
9055045477.4715065946226.5284934053843
9155465518.5988422326827.40115776732
9255345444.6178458412689.3821541587358
9355625528.1262004252633.8737995747379
9455645610.82856173513-46.8285617351303
9556125582.1765772669129.8234227330913
9657985763.3195147554934.6804852445111
9755565674.40838078189-118.408380781891
9853645312.02262157351.9773784270046
9954065396.340523485539.65947651447459
10055585603.47539180908-45.4753918090837
10154385404.9585227298333.0414772701661
10256025549.8582852980552.1417147019538
10356225632.02624437765-10.0262443776455
10455805545.4411851664534.5588148335546
10555705581.14916251791-11.1491625179078
10656745616.5178493865257.4821506134831
10758185703.31196647407114.688033525926
10860585984.8034230740573.1965769259532
10959985942.0324468366455.9675531633557
11059285803.62671071708124.37328928292
11160526006.2582064404745.7417935595304
11262766302.36406311062-26.3640631106227
11361666195.00823875199-29.0082387519888
11462266344.87790641069-118.877906410691
11563546305.5740006861548.4259993138503
11663966320.2823147994375.7176852005723







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1176436.769334877036314.962648299866558.5760214542
1186540.408246069376367.427100009216713.38939212953
1196626.330507111296405.372971274056847.28804294852
1206831.302757724716563.0387998937099.56671555641
1216742.769984087936426.887336415147058.65263176071
1226576.756716890146212.475869665546941.03756411473
1236659.610597575196245.906558850757073.31463629963
1246900.995605738056436.70824856457365.28296291159
1256813.90027794196297.794566191697330.00598969212
1266980.103408494136410.904397962137549.30241902613
1277080.032669677446456.44675849677703.61858085817
1287063.900043520556384.628267482137743.17181955898
1297104.669378397586363.049127719327846.28962907584
1307208.308289589926408.810095583218007.80648359663
1317294.230550631846435.533132991768152.92796827192
1327499.202801245266580.006581896528418.399020594
1337410.670027608486429.696999970368391.6430552466
1347244.656760410696200.650130234958288.66339058643

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 6436.76933487703 & 6314.96264829986 & 6558.5760214542 \tabularnewline
118 & 6540.40824606937 & 6367.42710000921 & 6713.38939212953 \tabularnewline
119 & 6626.33050711129 & 6405.37297127405 & 6847.28804294852 \tabularnewline
120 & 6831.30275772471 & 6563.038799893 & 7099.56671555641 \tabularnewline
121 & 6742.76998408793 & 6426.88733641514 & 7058.65263176071 \tabularnewline
122 & 6576.75671689014 & 6212.47586966554 & 6941.03756411473 \tabularnewline
123 & 6659.61059757519 & 6245.90655885075 & 7073.31463629963 \tabularnewline
124 & 6900.99560573805 & 6436.7082485645 & 7365.28296291159 \tabularnewline
125 & 6813.9002779419 & 6297.79456619169 & 7330.00598969212 \tabularnewline
126 & 6980.10340849413 & 6410.90439796213 & 7549.30241902613 \tabularnewline
127 & 7080.03266967744 & 6456.4467584967 & 7703.61858085817 \tabularnewline
128 & 7063.90004352055 & 6384.62826748213 & 7743.17181955898 \tabularnewline
129 & 7104.66937839758 & 6363.04912771932 & 7846.28962907584 \tabularnewline
130 & 7208.30828958992 & 6408.81009558321 & 8007.80648359663 \tabularnewline
131 & 7294.23055063184 & 6435.53313299176 & 8152.92796827192 \tabularnewline
132 & 7499.20280124526 & 6580.00658189652 & 8418.399020594 \tabularnewline
133 & 7410.67002760848 & 6429.69699997036 & 8391.6430552466 \tabularnewline
134 & 7244.65676041069 & 6200.65013023495 & 8288.66339058643 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302820&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]6436.76933487703[/C][C]6314.96264829986[/C][C]6558.5760214542[/C][/ROW]
[ROW][C]118[/C][C]6540.40824606937[/C][C]6367.42710000921[/C][C]6713.38939212953[/C][/ROW]
[ROW][C]119[/C][C]6626.33050711129[/C][C]6405.37297127405[/C][C]6847.28804294852[/C][/ROW]
[ROW][C]120[/C][C]6831.30275772471[/C][C]6563.038799893[/C][C]7099.56671555641[/C][/ROW]
[ROW][C]121[/C][C]6742.76998408793[/C][C]6426.88733641514[/C][C]7058.65263176071[/C][/ROW]
[ROW][C]122[/C][C]6576.75671689014[/C][C]6212.47586966554[/C][C]6941.03756411473[/C][/ROW]
[ROW][C]123[/C][C]6659.61059757519[/C][C]6245.90655885075[/C][C]7073.31463629963[/C][/ROW]
[ROW][C]124[/C][C]6900.99560573805[/C][C]6436.7082485645[/C][C]7365.28296291159[/C][/ROW]
[ROW][C]125[/C][C]6813.9002779419[/C][C]6297.79456619169[/C][C]7330.00598969212[/C][/ROW]
[ROW][C]126[/C][C]6980.10340849413[/C][C]6410.90439796213[/C][C]7549.30241902613[/C][/ROW]
[ROW][C]127[/C][C]7080.03266967744[/C][C]6456.4467584967[/C][C]7703.61858085817[/C][/ROW]
[ROW][C]128[/C][C]7063.90004352055[/C][C]6384.62826748213[/C][C]7743.17181955898[/C][/ROW]
[ROW][C]129[/C][C]7104.66937839758[/C][C]6363.04912771932[/C][C]7846.28962907584[/C][/ROW]
[ROW][C]130[/C][C]7208.30828958992[/C][C]6408.81009558321[/C][C]8007.80648359663[/C][/ROW]
[ROW][C]131[/C][C]7294.23055063184[/C][C]6435.53313299176[/C][C]8152.92796827192[/C][/ROW]
[ROW][C]132[/C][C]7499.20280124526[/C][C]6580.00658189652[/C][C]8418.399020594[/C][/ROW]
[ROW][C]133[/C][C]7410.67002760848[/C][C]6429.69699997036[/C][C]8391.6430552466[/C][/ROW]
[ROW][C]134[/C][C]7244.65676041069[/C][C]6200.65013023495[/C][C]8288.66339058643[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302820&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302820&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
1176436.769334877036314.962648299866558.5760214542
1186540.408246069376367.427100009216713.38939212953
1196626.330507111296405.372971274056847.28804294852
1206831.302757724716563.0387998937099.56671555641
1216742.769984087936426.887336415147058.65263176071
1226576.756716890146212.475869665546941.03756411473
1236659.610597575196245.906558850757073.31463629963
1246900.995605738056436.70824856457365.28296291159
1256813.90027794196297.794566191697330.00598969212
1266980.103408494136410.904397962137549.30241902613
1277080.032669677446456.44675849677703.61858085817
1287063.900043520556384.628267482137743.17181955898
1297104.669378397586363.049127719327846.28962907584
1307208.308289589926408.810095583218007.80648359663
1317294.230550631846435.533132991768152.92796827192
1327499.202801245266580.006581896528418.399020594
1337410.670027608486429.696999970368391.6430552466
1347244.656760410696200.650130234958288.66339058643



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
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')