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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 06 Jun 2009 12:55:18 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/06/t12443145740hg4alsf7wazivu.htm/, Retrieved Sun, 28 Apr 2024 22:03:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42055, Retrieved Sun, 28 Apr 2024 22:03:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Opgave 9: oefenin...] [2009-06-02 11:25:26] [c8528bac4a55a95c146713266fd5749f]
- RMPD    [Exponential Smoothing] [Opgave 10: oefeni...] [2009-06-06 18:55:18] [58dac46aef85915ed9cef356d57a9717] [Current]
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Dataseries X:
11310
64305
15310
37299
21302
61308
72300
26303
18301
54305
66309
50301
31298
52291
87286
81288
14293
90302
50306
15310
44310
26314
98313
76310
25313
48309
95307
10320
87327
63328
34333
90333
81332
7342
30424
13344
88347
40339
23330
1339
10341
46342
81342
2342
76350
35368
93367
88377
39376
41366
77375
56382
79397
26385
73397
28404
98413
73414
47423
52431
24441
92439
90441
441
13448
18458
18459
69477
41491
10492
73508
82515
13525
55533
19550
85558
57563
60570
49568
51570
26561
61558
78548
77537
539
18540
47542
86542
81544
16543
22538
25538
99527
63518
95508
65496
5488
96475
81465
5463
81458
74445
21434
67427
27418
81407
82395
97359




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42055&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42055&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42055&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0
beta0
gamma0.282949687340327

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.282949687340327 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42055&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.282949687340327[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42055&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42055&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
beta0
gamma0.282949687340327







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133129818421.276515151512876.7234848485
145229140788.734848484911502.2651515151
158728675158.068181818212127.9318181818
168128869242.651515151512045.3484848485
17142932080.4431818181912212.5568181818
189030275672.234848484914629.7651515151
195030669834.3598484848-19528.3598484848
201531023505.1098484849-8195.10984848486
214431013004.693181818231305.3068181818
222631444176.8181818182-17862.8181818182
239831354639.984848484943673.0151515151
247631037715.943181818238594.0568181818
252531322064.74139915733248.25860084275
264830944043.29717681164265.70282318839
279530778589.662697857616717.3373021424
281032072650.8791028447-62330.8791028447
29873275535.9823151487281791.0176848513
306332879811.7223239685-16483.7223239685
313433364308.8165350867-29975.8165350867
329033321186.306079136469146.6939208636
338133221862.519958115859469.4800418842
34734239122.5393622556-31780.5393622556
353042466997.2508308155-36573.2508308155
361334448636.1194917176-35292.1194917176
378834722983.835154666265363.1648453338
384033945250.2764569195-4911.27645691952
392333083319.8280606616-59989.8280606616
40133955014.376349047-53675.376349047
411034128678.7251963246-18337.7251963246
424634275147.6582461968-28805.6582461968
438134255827.168618712925514.8313812871
44234240751.3415046621-38409.3415046621
457635038689.390742258837660.6092577412
463536830130.24568619845237.75431380158
479336756648.860943216836718.1390567832
488837738650.225315958649726.7746840414
493937641478.3222112277-2102.32221122771
504136643860.6323189922-2494.63231899223
517737566345.724967297411029.2750327026
525638239826.945393209816555.0546067902
537939723490.071585491755906.9284145083
542638566997.1062518031-40612.1062518031
557339763046.582180589210350.4178194108
562840429883.4303349701-1479.43033497009
579841349345.448356782949067.5516432171
587341431612.26663165441801.733368346
594742367038.2469090523-19615.2469090523
605243152720.400665251-289.400665251029
612444140883.4707988722-16442.4707988722
629243943154.776884304349284.2231156957
639044169466.45488939120974.5451106089
6444144511.1929181031-44070.1929181031
651344839308.9195005349-25860.9195005349
661845855505.9234856233-37047.9234856233
671845965975.2296664333-47516.2296664333
686947729464.825984248540012.1740157515
694149163229.0967527865-21738.0967527865
701049243440.0540185113-32948.0540185113
717350861488.118929032612019.8810709674
728251552638.514837502229876.4851624978
731352536231.0788272288-22706.0788272288
745553357099.7324057013-1566.73240570134
751955075401.1958705435-55851.1958705435
768555832041.545610897953516.4543891021
775756331991.580413525225571.4195864748
786057045023.225118757815546.7748812422
794956852530.5273387248-2962.52733872478
805157040786.258111812210783.7418881878
812656157078.3090732118-30517.3090732118
826155834117.412435501327440.5875644987
837854864889.140519930813658.8594800692
847753761092.056973058916444.9430269411
8553929806.4009223396-29267.4009223396
861854056656.4259613622-38116.4259613622
874754259598.1174613898-12056.1174613898
888654247184.009647857339357.9903521427
898154439227.005590366542316.9944096335
901654349422.1802105557-32879.1802105557
912253851692.2811544954-29154.2811544954
922553843837.5145074337-18299.5145074337
939952748443.446012478451083.5539875216
946351841881.718107311121636.2818926889
959550868753.910539241826754.0894607582
966549665745.1484608614-249.148460861354
97548821525.1989820996-16037.1989820996
989647545871.39515306450603.604846936
998146556186.842795151325278.1572048487
100546358320.3407123397-52857.3407123397
1018145851200.585927754730257.4140722453
1027444540119.026449972734325.9735500273
1032143443443.0864171989-22009.0864171989
1046742738659.672599075628767.3274009244
1052741862897.5216414804-35479.5216414804
1068140748003.697304054633403.3026959454
1078239576323.97178723856071.02821276151
1089735965674.651981759331684.3480182407

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 31298 & 18421.2765151515 & 12876.7234848485 \tabularnewline
14 & 52291 & 40788.7348484849 & 11502.2651515151 \tabularnewline
15 & 87286 & 75158.0681818182 & 12127.9318181818 \tabularnewline
16 & 81288 & 69242.6515151515 & 12045.3484848485 \tabularnewline
17 & 14293 & 2080.44318181819 & 12212.5568181818 \tabularnewline
18 & 90302 & 75672.2348484849 & 14629.7651515151 \tabularnewline
19 & 50306 & 69834.3598484848 & -19528.3598484848 \tabularnewline
20 & 15310 & 23505.1098484849 & -8195.10984848486 \tabularnewline
21 & 44310 & 13004.6931818182 & 31305.3068181818 \tabularnewline
22 & 26314 & 44176.8181818182 & -17862.8181818182 \tabularnewline
23 & 98313 & 54639.9848484849 & 43673.0151515151 \tabularnewline
24 & 76310 & 37715.9431818182 & 38594.0568181818 \tabularnewline
25 & 25313 & 22064.7413991573 & 3248.25860084275 \tabularnewline
26 & 48309 & 44043.2971768116 & 4265.70282318839 \tabularnewline
27 & 95307 & 78589.6626978576 & 16717.3373021424 \tabularnewline
28 & 10320 & 72650.8791028447 & -62330.8791028447 \tabularnewline
29 & 87327 & 5535.98231514872 & 81791.0176848513 \tabularnewline
30 & 63328 & 79811.7223239685 & -16483.7223239685 \tabularnewline
31 & 34333 & 64308.8165350867 & -29975.8165350867 \tabularnewline
32 & 90333 & 21186.3060791364 & 69146.6939208636 \tabularnewline
33 & 81332 & 21862.5199581158 & 59469.4800418842 \tabularnewline
34 & 7342 & 39122.5393622556 & -31780.5393622556 \tabularnewline
35 & 30424 & 66997.2508308155 & -36573.2508308155 \tabularnewline
36 & 13344 & 48636.1194917176 & -35292.1194917176 \tabularnewline
37 & 88347 & 22983.8351546662 & 65363.1648453338 \tabularnewline
38 & 40339 & 45250.2764569195 & -4911.27645691952 \tabularnewline
39 & 23330 & 83319.8280606616 & -59989.8280606616 \tabularnewline
40 & 1339 & 55014.376349047 & -53675.376349047 \tabularnewline
41 & 10341 & 28678.7251963246 & -18337.7251963246 \tabularnewline
42 & 46342 & 75147.6582461968 & -28805.6582461968 \tabularnewline
43 & 81342 & 55827.1686187129 & 25514.8313812871 \tabularnewline
44 & 2342 & 40751.3415046621 & -38409.3415046621 \tabularnewline
45 & 76350 & 38689.3907422588 & 37660.6092577412 \tabularnewline
46 & 35368 & 30130.2456861984 & 5237.75431380158 \tabularnewline
47 & 93367 & 56648.8609432168 & 36718.1390567832 \tabularnewline
48 & 88377 & 38650.2253159586 & 49726.7746840414 \tabularnewline
49 & 39376 & 41478.3222112277 & -2102.32221122771 \tabularnewline
50 & 41366 & 43860.6323189922 & -2494.63231899223 \tabularnewline
51 & 77375 & 66345.7249672974 & 11029.2750327026 \tabularnewline
52 & 56382 & 39826.9453932098 & 16555.0546067902 \tabularnewline
53 & 79397 & 23490.0715854917 & 55906.9284145083 \tabularnewline
54 & 26385 & 66997.1062518031 & -40612.1062518031 \tabularnewline
55 & 73397 & 63046.5821805892 & 10350.4178194108 \tabularnewline
56 & 28404 & 29883.4303349701 & -1479.43033497009 \tabularnewline
57 & 98413 & 49345.4483567829 & 49067.5516432171 \tabularnewline
58 & 73414 & 31612.266631654 & 41801.733368346 \tabularnewline
59 & 47423 & 67038.2469090523 & -19615.2469090523 \tabularnewline
60 & 52431 & 52720.400665251 & -289.400665251029 \tabularnewline
61 & 24441 & 40883.4707988722 & -16442.4707988722 \tabularnewline
62 & 92439 & 43154.7768843043 & 49284.2231156957 \tabularnewline
63 & 90441 & 69466.454889391 & 20974.5451106089 \tabularnewline
64 & 441 & 44511.1929181031 & -44070.1929181031 \tabularnewline
65 & 13448 & 39308.9195005349 & -25860.9195005349 \tabularnewline
66 & 18458 & 55505.9234856233 & -37047.9234856233 \tabularnewline
67 & 18459 & 65975.2296664333 & -47516.2296664333 \tabularnewline
68 & 69477 & 29464.8259842485 & 40012.1740157515 \tabularnewline
69 & 41491 & 63229.0967527865 & -21738.0967527865 \tabularnewline
70 & 10492 & 43440.0540185113 & -32948.0540185113 \tabularnewline
71 & 73508 & 61488.1189290326 & 12019.8810709674 \tabularnewline
72 & 82515 & 52638.5148375022 & 29876.4851624978 \tabularnewline
73 & 13525 & 36231.0788272288 & -22706.0788272288 \tabularnewline
74 & 55533 & 57099.7324057013 & -1566.73240570134 \tabularnewline
75 & 19550 & 75401.1958705435 & -55851.1958705435 \tabularnewline
76 & 85558 & 32041.5456108979 & 53516.4543891021 \tabularnewline
77 & 57563 & 31991.5804135252 & 25571.4195864748 \tabularnewline
78 & 60570 & 45023.2251187578 & 15546.7748812422 \tabularnewline
79 & 49568 & 52530.5273387248 & -2962.52733872478 \tabularnewline
80 & 51570 & 40786.2581118122 & 10783.7418881878 \tabularnewline
81 & 26561 & 57078.3090732118 & -30517.3090732118 \tabularnewline
82 & 61558 & 34117.4124355013 & 27440.5875644987 \tabularnewline
83 & 78548 & 64889.1405199308 & 13658.8594800692 \tabularnewline
84 & 77537 & 61092.0569730589 & 16444.9430269411 \tabularnewline
85 & 539 & 29806.4009223396 & -29267.4009223396 \tabularnewline
86 & 18540 & 56656.4259613622 & -38116.4259613622 \tabularnewline
87 & 47542 & 59598.1174613898 & -12056.1174613898 \tabularnewline
88 & 86542 & 47184.0096478573 & 39357.9903521427 \tabularnewline
89 & 81544 & 39227.0055903665 & 42316.9944096335 \tabularnewline
90 & 16543 & 49422.1802105557 & -32879.1802105557 \tabularnewline
91 & 22538 & 51692.2811544954 & -29154.2811544954 \tabularnewline
92 & 25538 & 43837.5145074337 & -18299.5145074337 \tabularnewline
93 & 99527 & 48443.4460124784 & 51083.5539875216 \tabularnewline
94 & 63518 & 41881.7181073111 & 21636.2818926889 \tabularnewline
95 & 95508 & 68753.9105392418 & 26754.0894607582 \tabularnewline
96 & 65496 & 65745.1484608614 & -249.148460861354 \tabularnewline
97 & 5488 & 21525.1989820996 & -16037.1989820996 \tabularnewline
98 & 96475 & 45871.395153064 & 50603.604846936 \tabularnewline
99 & 81465 & 56186.8427951513 & 25278.1572048487 \tabularnewline
100 & 5463 & 58320.3407123397 & -52857.3407123397 \tabularnewline
101 & 81458 & 51200.5859277547 & 30257.4140722453 \tabularnewline
102 & 74445 & 40119.0264499727 & 34325.9735500273 \tabularnewline
103 & 21434 & 43443.0864171989 & -22009.0864171989 \tabularnewline
104 & 67427 & 38659.6725990756 & 28767.3274009244 \tabularnewline
105 & 27418 & 62897.5216414804 & -35479.5216414804 \tabularnewline
106 & 81407 & 48003.6973040546 & 33403.3026959454 \tabularnewline
107 & 82395 & 76323.9717872385 & 6071.02821276151 \tabularnewline
108 & 97359 & 65674.6519817593 & 31684.3480182407 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42055&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]31298[/C][C]18421.2765151515[/C][C]12876.7234848485[/C][/ROW]
[ROW][C]14[/C][C]52291[/C][C]40788.7348484849[/C][C]11502.2651515151[/C][/ROW]
[ROW][C]15[/C][C]87286[/C][C]75158.0681818182[/C][C]12127.9318181818[/C][/ROW]
[ROW][C]16[/C][C]81288[/C][C]69242.6515151515[/C][C]12045.3484848485[/C][/ROW]
[ROW][C]17[/C][C]14293[/C][C]2080.44318181819[/C][C]12212.5568181818[/C][/ROW]
[ROW][C]18[/C][C]90302[/C][C]75672.2348484849[/C][C]14629.7651515151[/C][/ROW]
[ROW][C]19[/C][C]50306[/C][C]69834.3598484848[/C][C]-19528.3598484848[/C][/ROW]
[ROW][C]20[/C][C]15310[/C][C]23505.1098484849[/C][C]-8195.10984848486[/C][/ROW]
[ROW][C]21[/C][C]44310[/C][C]13004.6931818182[/C][C]31305.3068181818[/C][/ROW]
[ROW][C]22[/C][C]26314[/C][C]44176.8181818182[/C][C]-17862.8181818182[/C][/ROW]
[ROW][C]23[/C][C]98313[/C][C]54639.9848484849[/C][C]43673.0151515151[/C][/ROW]
[ROW][C]24[/C][C]76310[/C][C]37715.9431818182[/C][C]38594.0568181818[/C][/ROW]
[ROW][C]25[/C][C]25313[/C][C]22064.7413991573[/C][C]3248.25860084275[/C][/ROW]
[ROW][C]26[/C][C]48309[/C][C]44043.2971768116[/C][C]4265.70282318839[/C][/ROW]
[ROW][C]27[/C][C]95307[/C][C]78589.6626978576[/C][C]16717.3373021424[/C][/ROW]
[ROW][C]28[/C][C]10320[/C][C]72650.8791028447[/C][C]-62330.8791028447[/C][/ROW]
[ROW][C]29[/C][C]87327[/C][C]5535.98231514872[/C][C]81791.0176848513[/C][/ROW]
[ROW][C]30[/C][C]63328[/C][C]79811.7223239685[/C][C]-16483.7223239685[/C][/ROW]
[ROW][C]31[/C][C]34333[/C][C]64308.8165350867[/C][C]-29975.8165350867[/C][/ROW]
[ROW][C]32[/C][C]90333[/C][C]21186.3060791364[/C][C]69146.6939208636[/C][/ROW]
[ROW][C]33[/C][C]81332[/C][C]21862.5199581158[/C][C]59469.4800418842[/C][/ROW]
[ROW][C]34[/C][C]7342[/C][C]39122.5393622556[/C][C]-31780.5393622556[/C][/ROW]
[ROW][C]35[/C][C]30424[/C][C]66997.2508308155[/C][C]-36573.2508308155[/C][/ROW]
[ROW][C]36[/C][C]13344[/C][C]48636.1194917176[/C][C]-35292.1194917176[/C][/ROW]
[ROW][C]37[/C][C]88347[/C][C]22983.8351546662[/C][C]65363.1648453338[/C][/ROW]
[ROW][C]38[/C][C]40339[/C][C]45250.2764569195[/C][C]-4911.27645691952[/C][/ROW]
[ROW][C]39[/C][C]23330[/C][C]83319.8280606616[/C][C]-59989.8280606616[/C][/ROW]
[ROW][C]40[/C][C]1339[/C][C]55014.376349047[/C][C]-53675.376349047[/C][/ROW]
[ROW][C]41[/C][C]10341[/C][C]28678.7251963246[/C][C]-18337.7251963246[/C][/ROW]
[ROW][C]42[/C][C]46342[/C][C]75147.6582461968[/C][C]-28805.6582461968[/C][/ROW]
[ROW][C]43[/C][C]81342[/C][C]55827.1686187129[/C][C]25514.8313812871[/C][/ROW]
[ROW][C]44[/C][C]2342[/C][C]40751.3415046621[/C][C]-38409.3415046621[/C][/ROW]
[ROW][C]45[/C][C]76350[/C][C]38689.3907422588[/C][C]37660.6092577412[/C][/ROW]
[ROW][C]46[/C][C]35368[/C][C]30130.2456861984[/C][C]5237.75431380158[/C][/ROW]
[ROW][C]47[/C][C]93367[/C][C]56648.8609432168[/C][C]36718.1390567832[/C][/ROW]
[ROW][C]48[/C][C]88377[/C][C]38650.2253159586[/C][C]49726.7746840414[/C][/ROW]
[ROW][C]49[/C][C]39376[/C][C]41478.3222112277[/C][C]-2102.32221122771[/C][/ROW]
[ROW][C]50[/C][C]41366[/C][C]43860.6323189922[/C][C]-2494.63231899223[/C][/ROW]
[ROW][C]51[/C][C]77375[/C][C]66345.7249672974[/C][C]11029.2750327026[/C][/ROW]
[ROW][C]52[/C][C]56382[/C][C]39826.9453932098[/C][C]16555.0546067902[/C][/ROW]
[ROW][C]53[/C][C]79397[/C][C]23490.0715854917[/C][C]55906.9284145083[/C][/ROW]
[ROW][C]54[/C][C]26385[/C][C]66997.1062518031[/C][C]-40612.1062518031[/C][/ROW]
[ROW][C]55[/C][C]73397[/C][C]63046.5821805892[/C][C]10350.4178194108[/C][/ROW]
[ROW][C]56[/C][C]28404[/C][C]29883.4303349701[/C][C]-1479.43033497009[/C][/ROW]
[ROW][C]57[/C][C]98413[/C][C]49345.4483567829[/C][C]49067.5516432171[/C][/ROW]
[ROW][C]58[/C][C]73414[/C][C]31612.266631654[/C][C]41801.733368346[/C][/ROW]
[ROW][C]59[/C][C]47423[/C][C]67038.2469090523[/C][C]-19615.2469090523[/C][/ROW]
[ROW][C]60[/C][C]52431[/C][C]52720.400665251[/C][C]-289.400665251029[/C][/ROW]
[ROW][C]61[/C][C]24441[/C][C]40883.4707988722[/C][C]-16442.4707988722[/C][/ROW]
[ROW][C]62[/C][C]92439[/C][C]43154.7768843043[/C][C]49284.2231156957[/C][/ROW]
[ROW][C]63[/C][C]90441[/C][C]69466.454889391[/C][C]20974.5451106089[/C][/ROW]
[ROW][C]64[/C][C]441[/C][C]44511.1929181031[/C][C]-44070.1929181031[/C][/ROW]
[ROW][C]65[/C][C]13448[/C][C]39308.9195005349[/C][C]-25860.9195005349[/C][/ROW]
[ROW][C]66[/C][C]18458[/C][C]55505.9234856233[/C][C]-37047.9234856233[/C][/ROW]
[ROW][C]67[/C][C]18459[/C][C]65975.2296664333[/C][C]-47516.2296664333[/C][/ROW]
[ROW][C]68[/C][C]69477[/C][C]29464.8259842485[/C][C]40012.1740157515[/C][/ROW]
[ROW][C]69[/C][C]41491[/C][C]63229.0967527865[/C][C]-21738.0967527865[/C][/ROW]
[ROW][C]70[/C][C]10492[/C][C]43440.0540185113[/C][C]-32948.0540185113[/C][/ROW]
[ROW][C]71[/C][C]73508[/C][C]61488.1189290326[/C][C]12019.8810709674[/C][/ROW]
[ROW][C]72[/C][C]82515[/C][C]52638.5148375022[/C][C]29876.4851624978[/C][/ROW]
[ROW][C]73[/C][C]13525[/C][C]36231.0788272288[/C][C]-22706.0788272288[/C][/ROW]
[ROW][C]74[/C][C]55533[/C][C]57099.7324057013[/C][C]-1566.73240570134[/C][/ROW]
[ROW][C]75[/C][C]19550[/C][C]75401.1958705435[/C][C]-55851.1958705435[/C][/ROW]
[ROW][C]76[/C][C]85558[/C][C]32041.5456108979[/C][C]53516.4543891021[/C][/ROW]
[ROW][C]77[/C][C]57563[/C][C]31991.5804135252[/C][C]25571.4195864748[/C][/ROW]
[ROW][C]78[/C][C]60570[/C][C]45023.2251187578[/C][C]15546.7748812422[/C][/ROW]
[ROW][C]79[/C][C]49568[/C][C]52530.5273387248[/C][C]-2962.52733872478[/C][/ROW]
[ROW][C]80[/C][C]51570[/C][C]40786.2581118122[/C][C]10783.7418881878[/C][/ROW]
[ROW][C]81[/C][C]26561[/C][C]57078.3090732118[/C][C]-30517.3090732118[/C][/ROW]
[ROW][C]82[/C][C]61558[/C][C]34117.4124355013[/C][C]27440.5875644987[/C][/ROW]
[ROW][C]83[/C][C]78548[/C][C]64889.1405199308[/C][C]13658.8594800692[/C][/ROW]
[ROW][C]84[/C][C]77537[/C][C]61092.0569730589[/C][C]16444.9430269411[/C][/ROW]
[ROW][C]85[/C][C]539[/C][C]29806.4009223396[/C][C]-29267.4009223396[/C][/ROW]
[ROW][C]86[/C][C]18540[/C][C]56656.4259613622[/C][C]-38116.4259613622[/C][/ROW]
[ROW][C]87[/C][C]47542[/C][C]59598.1174613898[/C][C]-12056.1174613898[/C][/ROW]
[ROW][C]88[/C][C]86542[/C][C]47184.0096478573[/C][C]39357.9903521427[/C][/ROW]
[ROW][C]89[/C][C]81544[/C][C]39227.0055903665[/C][C]42316.9944096335[/C][/ROW]
[ROW][C]90[/C][C]16543[/C][C]49422.1802105557[/C][C]-32879.1802105557[/C][/ROW]
[ROW][C]91[/C][C]22538[/C][C]51692.2811544954[/C][C]-29154.2811544954[/C][/ROW]
[ROW][C]92[/C][C]25538[/C][C]43837.5145074337[/C][C]-18299.5145074337[/C][/ROW]
[ROW][C]93[/C][C]99527[/C][C]48443.4460124784[/C][C]51083.5539875216[/C][/ROW]
[ROW][C]94[/C][C]63518[/C][C]41881.7181073111[/C][C]21636.2818926889[/C][/ROW]
[ROW][C]95[/C][C]95508[/C][C]68753.9105392418[/C][C]26754.0894607582[/C][/ROW]
[ROW][C]96[/C][C]65496[/C][C]65745.1484608614[/C][C]-249.148460861354[/C][/ROW]
[ROW][C]97[/C][C]5488[/C][C]21525.1989820996[/C][C]-16037.1989820996[/C][/ROW]
[ROW][C]98[/C][C]96475[/C][C]45871.395153064[/C][C]50603.604846936[/C][/ROW]
[ROW][C]99[/C][C]81465[/C][C]56186.8427951513[/C][C]25278.1572048487[/C][/ROW]
[ROW][C]100[/C][C]5463[/C][C]58320.3407123397[/C][C]-52857.3407123397[/C][/ROW]
[ROW][C]101[/C][C]81458[/C][C]51200.5859277547[/C][C]30257.4140722453[/C][/ROW]
[ROW][C]102[/C][C]74445[/C][C]40119.0264499727[/C][C]34325.9735500273[/C][/ROW]
[ROW][C]103[/C][C]21434[/C][C]43443.0864171989[/C][C]-22009.0864171989[/C][/ROW]
[ROW][C]104[/C][C]67427[/C][C]38659.6725990756[/C][C]28767.3274009244[/C][/ROW]
[ROW][C]105[/C][C]27418[/C][C]62897.5216414804[/C][C]-35479.5216414804[/C][/ROW]
[ROW][C]106[/C][C]81407[/C][C]48003.6973040546[/C][C]33403.3026959454[/C][/ROW]
[ROW][C]107[/C][C]82395[/C][C]76323.9717872385[/C][C]6071.02821276151[/C][/ROW]
[ROW][C]108[/C][C]97359[/C][C]65674.6519817593[/C][C]31684.3480182407[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42055&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42055&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
133129818421.276515151512876.7234848485
145229140788.734848484911502.2651515151
158728675158.068181818212127.9318181818
168128869242.651515151512045.3484848485
17142932080.4431818181912212.5568181818
189030275672.234848484914629.7651515151
195030669834.3598484848-19528.3598484848
201531023505.1098484849-8195.10984848486
214431013004.693181818231305.3068181818
222631444176.8181818182-17862.8181818182
239831354639.984848484943673.0151515151
247631037715.943181818238594.0568181818
252531322064.74139915733248.25860084275
264830944043.29717681164265.70282318839
279530778589.662697857616717.3373021424
281032072650.8791028447-62330.8791028447
29873275535.9823151487281791.0176848513
306332879811.7223239685-16483.7223239685
313433364308.8165350867-29975.8165350867
329033321186.306079136469146.6939208636
338133221862.519958115859469.4800418842
34734239122.5393622556-31780.5393622556
353042466997.2508308155-36573.2508308155
361334448636.1194917176-35292.1194917176
378834722983.835154666265363.1648453338
384033945250.2764569195-4911.27645691952
392333083319.8280606616-59989.8280606616
40133955014.376349047-53675.376349047
411034128678.7251963246-18337.7251963246
424634275147.6582461968-28805.6582461968
438134255827.168618712925514.8313812871
44234240751.3415046621-38409.3415046621
457635038689.390742258837660.6092577412
463536830130.24568619845237.75431380158
479336756648.860943216836718.1390567832
488837738650.225315958649726.7746840414
493937641478.3222112277-2102.32221122771
504136643860.6323189922-2494.63231899223
517737566345.724967297411029.2750327026
525638239826.945393209816555.0546067902
537939723490.071585491755906.9284145083
542638566997.1062518031-40612.1062518031
557339763046.582180589210350.4178194108
562840429883.4303349701-1479.43033497009
579841349345.448356782949067.5516432171
587341431612.26663165441801.733368346
594742367038.2469090523-19615.2469090523
605243152720.400665251-289.400665251029
612444140883.4707988722-16442.4707988722
629243943154.776884304349284.2231156957
639044169466.45488939120974.5451106089
6444144511.1929181031-44070.1929181031
651344839308.9195005349-25860.9195005349
661845855505.9234856233-37047.9234856233
671845965975.2296664333-47516.2296664333
686947729464.825984248540012.1740157515
694149163229.0967527865-21738.0967527865
701049243440.0540185113-32948.0540185113
717350861488.118929032612019.8810709674
728251552638.514837502229876.4851624978
731352536231.0788272288-22706.0788272288
745553357099.7324057013-1566.73240570134
751955075401.1958705435-55851.1958705435
768555832041.545610897953516.4543891021
775756331991.580413525225571.4195864748
786057045023.225118757815546.7748812422
794956852530.5273387248-2962.52733872478
805157040786.258111812210783.7418881878
812656157078.3090732118-30517.3090732118
826155834117.412435501327440.5875644987
837854864889.140519930813658.8594800692
847753761092.056973058916444.9430269411
8553929806.4009223396-29267.4009223396
861854056656.4259613622-38116.4259613622
874754259598.1174613898-12056.1174613898
888654247184.009647857339357.9903521427
898154439227.005590366542316.9944096335
901654349422.1802105557-32879.1802105557
912253851692.2811544954-29154.2811544954
922553843837.5145074337-18299.5145074337
939952748443.446012478451083.5539875216
946351841881.718107311121636.2818926889
959550868753.910539241826754.0894607582
966549665745.1484608614-249.148460861354
97548821525.1989820996-16037.1989820996
989647545871.39515306450603.604846936
998146556186.842795151325278.1572048487
100546358320.3407123397-52857.3407123397
1018145851200.585927754730257.4140722453
1027444540119.026449972734325.9735500273
1032143443443.0864171989-22009.0864171989
1046742738659.672599075628767.3274009244
1052741862897.5216414804-35479.5216414804
1068140748003.697304054633403.3026959454
1078239576323.97178723856071.02821276151
1089735965674.651981759331684.3480182407







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10916987.4785442999-48369.50594842382344.4630370228
11060189.669322798-5167.31516992491125546.653815521
11163339.2894728029-2017.69501992006128696.273965526
11243364.372684142-21992.6118085809108721.357176865
11359761.9117792233-5595.07271349959125118.896271946
11449831.5499336053-15525.4345591177115188.534426328
11537215.6222968063-28141.3621959167102572.606789529
11646799.378892784-18557.6055999390112156.363385507
11752858.6020860391-12498.3824066838118215.586578762
11857455.1513580067-7901.83313471627122812.135850730
11978041.767321873712684.7828291507143398.751814597
12074639.72834710269282.74385437971139996.712839826

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 16987.4785442999 & -48369.505948423 & 82344.4630370228 \tabularnewline
110 & 60189.669322798 & -5167.31516992491 & 125546.653815521 \tabularnewline
111 & 63339.2894728029 & -2017.69501992006 & 128696.273965526 \tabularnewline
112 & 43364.372684142 & -21992.6118085809 & 108721.357176865 \tabularnewline
113 & 59761.9117792233 & -5595.07271349959 & 125118.896271946 \tabularnewline
114 & 49831.5499336053 & -15525.4345591177 & 115188.534426328 \tabularnewline
115 & 37215.6222968063 & -28141.3621959167 & 102572.606789529 \tabularnewline
116 & 46799.378892784 & -18557.6055999390 & 112156.363385507 \tabularnewline
117 & 52858.6020860391 & -12498.3824066838 & 118215.586578762 \tabularnewline
118 & 57455.1513580067 & -7901.83313471627 & 122812.135850730 \tabularnewline
119 & 78041.7673218737 & 12684.7828291507 & 143398.751814597 \tabularnewline
120 & 74639.7283471026 & 9282.74385437971 & 139996.712839826 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42055&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]109[/C][C]16987.4785442999[/C][C]-48369.505948423[/C][C]82344.4630370228[/C][/ROW]
[ROW][C]110[/C][C]60189.669322798[/C][C]-5167.31516992491[/C][C]125546.653815521[/C][/ROW]
[ROW][C]111[/C][C]63339.2894728029[/C][C]-2017.69501992006[/C][C]128696.273965526[/C][/ROW]
[ROW][C]112[/C][C]43364.372684142[/C][C]-21992.6118085809[/C][C]108721.357176865[/C][/ROW]
[ROW][C]113[/C][C]59761.9117792233[/C][C]-5595.07271349959[/C][C]125118.896271946[/C][/ROW]
[ROW][C]114[/C][C]49831.5499336053[/C][C]-15525.4345591177[/C][C]115188.534426328[/C][/ROW]
[ROW][C]115[/C][C]37215.6222968063[/C][C]-28141.3621959167[/C][C]102572.606789529[/C][/ROW]
[ROW][C]116[/C][C]46799.378892784[/C][C]-18557.6055999390[/C][C]112156.363385507[/C][/ROW]
[ROW][C]117[/C][C]52858.6020860391[/C][C]-12498.3824066838[/C][C]118215.586578762[/C][/ROW]
[ROW][C]118[/C][C]57455.1513580067[/C][C]-7901.83313471627[/C][C]122812.135850730[/C][/ROW]
[ROW][C]119[/C][C]78041.7673218737[/C][C]12684.7828291507[/C][C]143398.751814597[/C][/ROW]
[ROW][C]120[/C][C]74639.7283471026[/C][C]9282.74385437971[/C][C]139996.712839826[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42055&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42055&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
10916987.4785442999-48369.50594842382344.4630370228
11060189.669322798-5167.31516992491125546.653815521
11163339.2894728029-2017.69501992006128696.273965526
11243364.372684142-21992.6118085809108721.357176865
11359761.9117792233-5595.07271349959125118.896271946
11449831.5499336053-15525.4345591177115188.534426328
11537215.6222968063-28141.3621959167102572.606789529
11646799.378892784-18557.6055999390112156.363385507
11752858.6020860391-12498.3824066838118215.586578762
11857455.1513580067-7901.83313471627122812.135850730
11978041.767321873712684.7828291507143398.751814597
12074639.72834710269282.74385437971139996.712839826



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')