Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 07 Jun 2009 14:50:54 -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/07/t1244407957f8kzofmbecprfvk.htm/, Retrieved Mon, 13 May 2024 03:56:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42267, Retrieved Mon, 13 May 2024 03:56:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Annelies Reul ban...] [2009-06-07 20:50:54] [9202dc9f5562cf74198e3e368d8190ce] [Current]
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Dataseries X:
334053
326018
326894
330958
333913
337042
342103
344795
342060
342535
343083
354261
363049
347562
347577
349715
353818
354073
357040
359177
354845
354481
352747
360446
368285
354819
353017
354551
352682
351146
350760
347555
335363
325165
311274
297987
344276
306152
283323
285869
293660
300831
313351
322765
323613
329199
334038
350683
353929
340715
347752
358474
366179
373163
382739
391636
391693
395453
399368
416075
427623
418000
425316
436397
442533
449148
460852
462789
465097
469728
475434
495992
487101
489496
498649
505533
512839
522584
532603
531520
531623
535608
539804
559182
548414
550774
556397
569125
571988
578807
588234
588724
588550
592764
598593
619494
604560
606210
614823
620033
625236
631307
639704
639223
637312
640124
644649
668209
651667
653170
662102
667617
671420
677156
686086
684954
684331
722145
731098
753123
740228
741472
747315
757533




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42267&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42267&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42267&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.587581147577237
beta0.113062234272449
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.587581147577237 \tabularnewline
beta & 0.113062234272449 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42267&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]0.587581147577237[/C][/ROW]
[ROW][C]beta[/C][C]0.113062234272449[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42267&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42267&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
alpha0.587581147577237
beta0.113062234272449
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13363049353087.9209599309961.07904006977
14347562344405.6088840133156.39111598709
15347577347337.391404895239.608595105237
16349715350793.877166463-1078.87716646300
17353818355513.605943885-1695.60594388511
18354073356144.036570634-2071.03657063353
19357040359932.518160865-2892.51816086471
20359177360547.305711935-1370.30571193516
21354845356668.890735919-1823.89073591860
22354481355877.811354502-1396.81135450187
23352747355358.23644073-2611.23644073005
24360446364983.306173255-4537.30617325479
25368285375099.330256504-6814.3302565043
26354819351832.8749533922986.12504660804
27353017351934.0729254151082.92707458546
28354551353915.772399946635.227600054408
29352682358093.648816612-5411.64881661232
30351146354805.161015928-3659.16101592797
31350760355610.127186802-4850.12718680239
32347555353854.734323942-6299.73432394234
33335363344882.718038305-9519.71803830477
34325165337155.456479371-11990.4564793712
35311274326691.810421809-15417.8104218086
36297987322794.807369723-24807.8073697231
37344276312659.94484200031616.0551579995
38306152314480.733949943-8328.73394994321
39283323303717.173372717-20394.1733727167
40285869287563.091179627-1694.09117962723
41293660282341.08276020811318.9172397919
42300831285251.43756723615579.5624327643
43313351293432.03928625419918.9607137465
44322765304111.37096890118653.6290310990
45323613309215.30548048714397.6945195131
46329199316331.17859115112867.8214088489
47334038322299.93853218811738.0614678123
48350683335473.31105816615209.6889418335
49353929385079.064761858-31150.0647618583
50340715335538.3650526545176.63494734565
51347752331339.21785826216412.7821417376
52358474353579.2168754214894.78312457888
53366179366920.185652254-741.18565225444
54373163371988.8158861651174.18411383481
55382739380338.7778755812400.22212441912
56391636385017.9214019236618.0785980766
57391693383811.2461724957881.75382750528
58395453389511.6967566875941.30324331328
59399368393341.9676301746026.03236982564
60416075408270.8530333087804.14696669194
61427623439314.291098872-11691.2910988723
62418000415739.3630320422260.63696795801
63425316416506.3045055868809.69549441378
64436397433328.1922458583068.80775414233
65442533446993.027822810-4460.02782280958
66449148453768.896846519-4620.89684651862
67460852462310.847118031-1458.84711803065
68462789468575.403903413-5786.40390341281
69465097459960.6889107535136.31108924706
70469728463275.2265122796452.77348772087
71475434467450.8020875317983.19791246857
72495992486446.7963670379545.20363296272
73487101513778.002093938-26677.0020939382
74489496484631.6821272794864.31787272118
75498649489366.066862529282.93313748017
76505533504980.580435954552.419564045616
77512839514630.703435691-1791.70343569096
78522584523794.220730494-1210.22073049383
79532603537359.113234139-4756.1132341387
80531520540205.455461221-8685.45546122128
81531623533628.849129188-2005.84912918822
82535608532292.1110275973315.8889724029
83539804534045.9662249575758.03377504298
84559182552756.3448451556425.65515484475
85548414561998.233876658-13584.2338766580
86550774552690.89639527-1916.89639527060
87556397554464.918204391932.08179561037
88569125561191.6012778787933.39872212161
89571988573939.989918909-1951.98991890938
90578807583210.341233609-4403.34123360901
91588234593401.584171042-5167.58417104173
92588724593363.118301346-4639.11830134573
93588550590959.540717115-2409.54071711493
94592764590702.051901132061.94809887046
95598593591621.9427514116971.05724858865
96619494611769.6406783857724.35932161508
97604560612067.245640871-7507.24564087135
98606210610893.931073229-4683.93107322929
99614823612321.1039165512501.89608344855
100620033621911.352555018-1878.35255501792
101625236623794.7167639511441.28323604865
102631307633741.997700565-2434.99770056549
103639704644893.945075553-5189.9450755528
104639223644361.088129804-5138.08812980389
105637312641717.082081744-4405.0820817441
106640124641311.34241897-1187.34241897031
107644649641191.0589822153457.94101778546
108668209659234.8390715368974.16092846438
109651667651742.246322526-75.2463225261308
110653170655481.841083591-2311.84108359087
111662102661048.7276401171053.27235988271
112667617667583.26355439633.7364456035430
113671420671549.249221964-129.249221963575
114677156678682.004715812-1526.00471581169
115686086689283.670760843-3197.67076084274
116684954689495.530469153-4541.53046915319
117684331686988.240550832-2657.24055083189
118722145688775.64519153633369.3548084638
119731098712897.29051231618200.7094876842
120753123746797.906463446325.09353656066
121740228734364.623416845863.37658315944
122741472743776.558518572-2304.55851857178
123747315754619.090993971-7304.09099397098
124757533758756.52229664-1223.52229663951

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 363049 & 353087.920959930 & 9961.07904006977 \tabularnewline
14 & 347562 & 344405.608884013 & 3156.39111598709 \tabularnewline
15 & 347577 & 347337.391404895 & 239.608595105237 \tabularnewline
16 & 349715 & 350793.877166463 & -1078.87716646300 \tabularnewline
17 & 353818 & 355513.605943885 & -1695.60594388511 \tabularnewline
18 & 354073 & 356144.036570634 & -2071.03657063353 \tabularnewline
19 & 357040 & 359932.518160865 & -2892.51816086471 \tabularnewline
20 & 359177 & 360547.305711935 & -1370.30571193516 \tabularnewline
21 & 354845 & 356668.890735919 & -1823.89073591860 \tabularnewline
22 & 354481 & 355877.811354502 & -1396.81135450187 \tabularnewline
23 & 352747 & 355358.23644073 & -2611.23644073005 \tabularnewline
24 & 360446 & 364983.306173255 & -4537.30617325479 \tabularnewline
25 & 368285 & 375099.330256504 & -6814.3302565043 \tabularnewline
26 & 354819 & 351832.874953392 & 2986.12504660804 \tabularnewline
27 & 353017 & 351934.072925415 & 1082.92707458546 \tabularnewline
28 & 354551 & 353915.772399946 & 635.227600054408 \tabularnewline
29 & 352682 & 358093.648816612 & -5411.64881661232 \tabularnewline
30 & 351146 & 354805.161015928 & -3659.16101592797 \tabularnewline
31 & 350760 & 355610.127186802 & -4850.12718680239 \tabularnewline
32 & 347555 & 353854.734323942 & -6299.73432394234 \tabularnewline
33 & 335363 & 344882.718038305 & -9519.71803830477 \tabularnewline
34 & 325165 & 337155.456479371 & -11990.4564793712 \tabularnewline
35 & 311274 & 326691.810421809 & -15417.8104218086 \tabularnewline
36 & 297987 & 322794.807369723 & -24807.8073697231 \tabularnewline
37 & 344276 & 312659.944842000 & 31616.0551579995 \tabularnewline
38 & 306152 & 314480.733949943 & -8328.73394994321 \tabularnewline
39 & 283323 & 303717.173372717 & -20394.1733727167 \tabularnewline
40 & 285869 & 287563.091179627 & -1694.09117962723 \tabularnewline
41 & 293660 & 282341.082760208 & 11318.9172397919 \tabularnewline
42 & 300831 & 285251.437567236 & 15579.5624327643 \tabularnewline
43 & 313351 & 293432.039286254 & 19918.9607137465 \tabularnewline
44 & 322765 & 304111.370968901 & 18653.6290310990 \tabularnewline
45 & 323613 & 309215.305480487 & 14397.6945195131 \tabularnewline
46 & 329199 & 316331.178591151 & 12867.8214088489 \tabularnewline
47 & 334038 & 322299.938532188 & 11738.0614678123 \tabularnewline
48 & 350683 & 335473.311058166 & 15209.6889418335 \tabularnewline
49 & 353929 & 385079.064761858 & -31150.0647618583 \tabularnewline
50 & 340715 & 335538.365052654 & 5176.63494734565 \tabularnewline
51 & 347752 & 331339.217858262 & 16412.7821417376 \tabularnewline
52 & 358474 & 353579.216875421 & 4894.78312457888 \tabularnewline
53 & 366179 & 366920.185652254 & -741.18565225444 \tabularnewline
54 & 373163 & 371988.815886165 & 1174.18411383481 \tabularnewline
55 & 382739 & 380338.777875581 & 2400.22212441912 \tabularnewline
56 & 391636 & 385017.921401923 & 6618.0785980766 \tabularnewline
57 & 391693 & 383811.246172495 & 7881.75382750528 \tabularnewline
58 & 395453 & 389511.696756687 & 5941.30324331328 \tabularnewline
59 & 399368 & 393341.967630174 & 6026.03236982564 \tabularnewline
60 & 416075 & 408270.853033308 & 7804.14696669194 \tabularnewline
61 & 427623 & 439314.291098872 & -11691.2910988723 \tabularnewline
62 & 418000 & 415739.363032042 & 2260.63696795801 \tabularnewline
63 & 425316 & 416506.304505586 & 8809.69549441378 \tabularnewline
64 & 436397 & 433328.192245858 & 3068.80775414233 \tabularnewline
65 & 442533 & 446993.027822810 & -4460.02782280958 \tabularnewline
66 & 449148 & 453768.896846519 & -4620.89684651862 \tabularnewline
67 & 460852 & 462310.847118031 & -1458.84711803065 \tabularnewline
68 & 462789 & 468575.403903413 & -5786.40390341281 \tabularnewline
69 & 465097 & 459960.688910753 & 5136.31108924706 \tabularnewline
70 & 469728 & 463275.226512279 & 6452.77348772087 \tabularnewline
71 & 475434 & 467450.802087531 & 7983.19791246857 \tabularnewline
72 & 495992 & 486446.796367037 & 9545.20363296272 \tabularnewline
73 & 487101 & 513778.002093938 & -26677.0020939382 \tabularnewline
74 & 489496 & 484631.682127279 & 4864.31787272118 \tabularnewline
75 & 498649 & 489366.06686252 & 9282.93313748017 \tabularnewline
76 & 505533 & 504980.580435954 & 552.419564045616 \tabularnewline
77 & 512839 & 514630.703435691 & -1791.70343569096 \tabularnewline
78 & 522584 & 523794.220730494 & -1210.22073049383 \tabularnewline
79 & 532603 & 537359.113234139 & -4756.1132341387 \tabularnewline
80 & 531520 & 540205.455461221 & -8685.45546122128 \tabularnewline
81 & 531623 & 533628.849129188 & -2005.84912918822 \tabularnewline
82 & 535608 & 532292.111027597 & 3315.8889724029 \tabularnewline
83 & 539804 & 534045.966224957 & 5758.03377504298 \tabularnewline
84 & 559182 & 552756.344845155 & 6425.65515484475 \tabularnewline
85 & 548414 & 561998.233876658 & -13584.2338766580 \tabularnewline
86 & 550774 & 552690.89639527 & -1916.89639527060 \tabularnewline
87 & 556397 & 554464.91820439 & 1932.08179561037 \tabularnewline
88 & 569125 & 561191.601277878 & 7933.39872212161 \tabularnewline
89 & 571988 & 573939.989918909 & -1951.98991890938 \tabularnewline
90 & 578807 & 583210.341233609 & -4403.34123360901 \tabularnewline
91 & 588234 & 593401.584171042 & -5167.58417104173 \tabularnewline
92 & 588724 & 593363.118301346 & -4639.11830134573 \tabularnewline
93 & 588550 & 590959.540717115 & -2409.54071711493 \tabularnewline
94 & 592764 & 590702.05190113 & 2061.94809887046 \tabularnewline
95 & 598593 & 591621.942751411 & 6971.05724858865 \tabularnewline
96 & 619494 & 611769.640678385 & 7724.35932161508 \tabularnewline
97 & 604560 & 612067.245640871 & -7507.24564087135 \tabularnewline
98 & 606210 & 610893.931073229 & -4683.93107322929 \tabularnewline
99 & 614823 & 612321.103916551 & 2501.89608344855 \tabularnewline
100 & 620033 & 621911.352555018 & -1878.35255501792 \tabularnewline
101 & 625236 & 623794.716763951 & 1441.28323604865 \tabularnewline
102 & 631307 & 633741.997700565 & -2434.99770056549 \tabularnewline
103 & 639704 & 644893.945075553 & -5189.9450755528 \tabularnewline
104 & 639223 & 644361.088129804 & -5138.08812980389 \tabularnewline
105 & 637312 & 641717.082081744 & -4405.0820817441 \tabularnewline
106 & 640124 & 641311.34241897 & -1187.34241897031 \tabularnewline
107 & 644649 & 641191.058982215 & 3457.94101778546 \tabularnewline
108 & 668209 & 659234.839071536 & 8974.16092846438 \tabularnewline
109 & 651667 & 651742.246322526 & -75.2463225261308 \tabularnewline
110 & 653170 & 655481.841083591 & -2311.84108359087 \tabularnewline
111 & 662102 & 661048.727640117 & 1053.27235988271 \tabularnewline
112 & 667617 & 667583.263554396 & 33.7364456035430 \tabularnewline
113 & 671420 & 671549.249221964 & -129.249221963575 \tabularnewline
114 & 677156 & 678682.004715812 & -1526.00471581169 \tabularnewline
115 & 686086 & 689283.670760843 & -3197.67076084274 \tabularnewline
116 & 684954 & 689495.530469153 & -4541.53046915319 \tabularnewline
117 & 684331 & 686988.240550832 & -2657.24055083189 \tabularnewline
118 & 722145 & 688775.645191536 & 33369.3548084638 \tabularnewline
119 & 731098 & 712897.290512316 & 18200.7094876842 \tabularnewline
120 & 753123 & 746797.90646344 & 6325.09353656066 \tabularnewline
121 & 740228 & 734364.62341684 & 5863.37658315944 \tabularnewline
122 & 741472 & 743776.558518572 & -2304.55851857178 \tabularnewline
123 & 747315 & 754619.090993971 & -7304.09099397098 \tabularnewline
124 & 757533 & 758756.52229664 & -1223.52229663951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42267&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]363049[/C][C]353087.920959930[/C][C]9961.07904006977[/C][/ROW]
[ROW][C]14[/C][C]347562[/C][C]344405.608884013[/C][C]3156.39111598709[/C][/ROW]
[ROW][C]15[/C][C]347577[/C][C]347337.391404895[/C][C]239.608595105237[/C][/ROW]
[ROW][C]16[/C][C]349715[/C][C]350793.877166463[/C][C]-1078.87716646300[/C][/ROW]
[ROW][C]17[/C][C]353818[/C][C]355513.605943885[/C][C]-1695.60594388511[/C][/ROW]
[ROW][C]18[/C][C]354073[/C][C]356144.036570634[/C][C]-2071.03657063353[/C][/ROW]
[ROW][C]19[/C][C]357040[/C][C]359932.518160865[/C][C]-2892.51816086471[/C][/ROW]
[ROW][C]20[/C][C]359177[/C][C]360547.305711935[/C][C]-1370.30571193516[/C][/ROW]
[ROW][C]21[/C][C]354845[/C][C]356668.890735919[/C][C]-1823.89073591860[/C][/ROW]
[ROW][C]22[/C][C]354481[/C][C]355877.811354502[/C][C]-1396.81135450187[/C][/ROW]
[ROW][C]23[/C][C]352747[/C][C]355358.23644073[/C][C]-2611.23644073005[/C][/ROW]
[ROW][C]24[/C][C]360446[/C][C]364983.306173255[/C][C]-4537.30617325479[/C][/ROW]
[ROW][C]25[/C][C]368285[/C][C]375099.330256504[/C][C]-6814.3302565043[/C][/ROW]
[ROW][C]26[/C][C]354819[/C][C]351832.874953392[/C][C]2986.12504660804[/C][/ROW]
[ROW][C]27[/C][C]353017[/C][C]351934.072925415[/C][C]1082.92707458546[/C][/ROW]
[ROW][C]28[/C][C]354551[/C][C]353915.772399946[/C][C]635.227600054408[/C][/ROW]
[ROW][C]29[/C][C]352682[/C][C]358093.648816612[/C][C]-5411.64881661232[/C][/ROW]
[ROW][C]30[/C][C]351146[/C][C]354805.161015928[/C][C]-3659.16101592797[/C][/ROW]
[ROW][C]31[/C][C]350760[/C][C]355610.127186802[/C][C]-4850.12718680239[/C][/ROW]
[ROW][C]32[/C][C]347555[/C][C]353854.734323942[/C][C]-6299.73432394234[/C][/ROW]
[ROW][C]33[/C][C]335363[/C][C]344882.718038305[/C][C]-9519.71803830477[/C][/ROW]
[ROW][C]34[/C][C]325165[/C][C]337155.456479371[/C][C]-11990.4564793712[/C][/ROW]
[ROW][C]35[/C][C]311274[/C][C]326691.810421809[/C][C]-15417.8104218086[/C][/ROW]
[ROW][C]36[/C][C]297987[/C][C]322794.807369723[/C][C]-24807.8073697231[/C][/ROW]
[ROW][C]37[/C][C]344276[/C][C]312659.944842000[/C][C]31616.0551579995[/C][/ROW]
[ROW][C]38[/C][C]306152[/C][C]314480.733949943[/C][C]-8328.73394994321[/C][/ROW]
[ROW][C]39[/C][C]283323[/C][C]303717.173372717[/C][C]-20394.1733727167[/C][/ROW]
[ROW][C]40[/C][C]285869[/C][C]287563.091179627[/C][C]-1694.09117962723[/C][/ROW]
[ROW][C]41[/C][C]293660[/C][C]282341.082760208[/C][C]11318.9172397919[/C][/ROW]
[ROW][C]42[/C][C]300831[/C][C]285251.437567236[/C][C]15579.5624327643[/C][/ROW]
[ROW][C]43[/C][C]313351[/C][C]293432.039286254[/C][C]19918.9607137465[/C][/ROW]
[ROW][C]44[/C][C]322765[/C][C]304111.370968901[/C][C]18653.6290310990[/C][/ROW]
[ROW][C]45[/C][C]323613[/C][C]309215.305480487[/C][C]14397.6945195131[/C][/ROW]
[ROW][C]46[/C][C]329199[/C][C]316331.178591151[/C][C]12867.8214088489[/C][/ROW]
[ROW][C]47[/C][C]334038[/C][C]322299.938532188[/C][C]11738.0614678123[/C][/ROW]
[ROW][C]48[/C][C]350683[/C][C]335473.311058166[/C][C]15209.6889418335[/C][/ROW]
[ROW][C]49[/C][C]353929[/C][C]385079.064761858[/C][C]-31150.0647618583[/C][/ROW]
[ROW][C]50[/C][C]340715[/C][C]335538.365052654[/C][C]5176.63494734565[/C][/ROW]
[ROW][C]51[/C][C]347752[/C][C]331339.217858262[/C][C]16412.7821417376[/C][/ROW]
[ROW][C]52[/C][C]358474[/C][C]353579.216875421[/C][C]4894.78312457888[/C][/ROW]
[ROW][C]53[/C][C]366179[/C][C]366920.185652254[/C][C]-741.18565225444[/C][/ROW]
[ROW][C]54[/C][C]373163[/C][C]371988.815886165[/C][C]1174.18411383481[/C][/ROW]
[ROW][C]55[/C][C]382739[/C][C]380338.777875581[/C][C]2400.22212441912[/C][/ROW]
[ROW][C]56[/C][C]391636[/C][C]385017.921401923[/C][C]6618.0785980766[/C][/ROW]
[ROW][C]57[/C][C]391693[/C][C]383811.246172495[/C][C]7881.75382750528[/C][/ROW]
[ROW][C]58[/C][C]395453[/C][C]389511.696756687[/C][C]5941.30324331328[/C][/ROW]
[ROW][C]59[/C][C]399368[/C][C]393341.967630174[/C][C]6026.03236982564[/C][/ROW]
[ROW][C]60[/C][C]416075[/C][C]408270.853033308[/C][C]7804.14696669194[/C][/ROW]
[ROW][C]61[/C][C]427623[/C][C]439314.291098872[/C][C]-11691.2910988723[/C][/ROW]
[ROW][C]62[/C][C]418000[/C][C]415739.363032042[/C][C]2260.63696795801[/C][/ROW]
[ROW][C]63[/C][C]425316[/C][C]416506.304505586[/C][C]8809.69549441378[/C][/ROW]
[ROW][C]64[/C][C]436397[/C][C]433328.192245858[/C][C]3068.80775414233[/C][/ROW]
[ROW][C]65[/C][C]442533[/C][C]446993.027822810[/C][C]-4460.02782280958[/C][/ROW]
[ROW][C]66[/C][C]449148[/C][C]453768.896846519[/C][C]-4620.89684651862[/C][/ROW]
[ROW][C]67[/C][C]460852[/C][C]462310.847118031[/C][C]-1458.84711803065[/C][/ROW]
[ROW][C]68[/C][C]462789[/C][C]468575.403903413[/C][C]-5786.40390341281[/C][/ROW]
[ROW][C]69[/C][C]465097[/C][C]459960.688910753[/C][C]5136.31108924706[/C][/ROW]
[ROW][C]70[/C][C]469728[/C][C]463275.226512279[/C][C]6452.77348772087[/C][/ROW]
[ROW][C]71[/C][C]475434[/C][C]467450.802087531[/C][C]7983.19791246857[/C][/ROW]
[ROW][C]72[/C][C]495992[/C][C]486446.796367037[/C][C]9545.20363296272[/C][/ROW]
[ROW][C]73[/C][C]487101[/C][C]513778.002093938[/C][C]-26677.0020939382[/C][/ROW]
[ROW][C]74[/C][C]489496[/C][C]484631.682127279[/C][C]4864.31787272118[/C][/ROW]
[ROW][C]75[/C][C]498649[/C][C]489366.06686252[/C][C]9282.93313748017[/C][/ROW]
[ROW][C]76[/C][C]505533[/C][C]504980.580435954[/C][C]552.419564045616[/C][/ROW]
[ROW][C]77[/C][C]512839[/C][C]514630.703435691[/C][C]-1791.70343569096[/C][/ROW]
[ROW][C]78[/C][C]522584[/C][C]523794.220730494[/C][C]-1210.22073049383[/C][/ROW]
[ROW][C]79[/C][C]532603[/C][C]537359.113234139[/C][C]-4756.1132341387[/C][/ROW]
[ROW][C]80[/C][C]531520[/C][C]540205.455461221[/C][C]-8685.45546122128[/C][/ROW]
[ROW][C]81[/C][C]531623[/C][C]533628.849129188[/C][C]-2005.84912918822[/C][/ROW]
[ROW][C]82[/C][C]535608[/C][C]532292.111027597[/C][C]3315.8889724029[/C][/ROW]
[ROW][C]83[/C][C]539804[/C][C]534045.966224957[/C][C]5758.03377504298[/C][/ROW]
[ROW][C]84[/C][C]559182[/C][C]552756.344845155[/C][C]6425.65515484475[/C][/ROW]
[ROW][C]85[/C][C]548414[/C][C]561998.233876658[/C][C]-13584.2338766580[/C][/ROW]
[ROW][C]86[/C][C]550774[/C][C]552690.89639527[/C][C]-1916.89639527060[/C][/ROW]
[ROW][C]87[/C][C]556397[/C][C]554464.91820439[/C][C]1932.08179561037[/C][/ROW]
[ROW][C]88[/C][C]569125[/C][C]561191.601277878[/C][C]7933.39872212161[/C][/ROW]
[ROW][C]89[/C][C]571988[/C][C]573939.989918909[/C][C]-1951.98991890938[/C][/ROW]
[ROW][C]90[/C][C]578807[/C][C]583210.341233609[/C][C]-4403.34123360901[/C][/ROW]
[ROW][C]91[/C][C]588234[/C][C]593401.584171042[/C][C]-5167.58417104173[/C][/ROW]
[ROW][C]92[/C][C]588724[/C][C]593363.118301346[/C][C]-4639.11830134573[/C][/ROW]
[ROW][C]93[/C][C]588550[/C][C]590959.540717115[/C][C]-2409.54071711493[/C][/ROW]
[ROW][C]94[/C][C]592764[/C][C]590702.05190113[/C][C]2061.94809887046[/C][/ROW]
[ROW][C]95[/C][C]598593[/C][C]591621.942751411[/C][C]6971.05724858865[/C][/ROW]
[ROW][C]96[/C][C]619494[/C][C]611769.640678385[/C][C]7724.35932161508[/C][/ROW]
[ROW][C]97[/C][C]604560[/C][C]612067.245640871[/C][C]-7507.24564087135[/C][/ROW]
[ROW][C]98[/C][C]606210[/C][C]610893.931073229[/C][C]-4683.93107322929[/C][/ROW]
[ROW][C]99[/C][C]614823[/C][C]612321.103916551[/C][C]2501.89608344855[/C][/ROW]
[ROW][C]100[/C][C]620033[/C][C]621911.352555018[/C][C]-1878.35255501792[/C][/ROW]
[ROW][C]101[/C][C]625236[/C][C]623794.716763951[/C][C]1441.28323604865[/C][/ROW]
[ROW][C]102[/C][C]631307[/C][C]633741.997700565[/C][C]-2434.99770056549[/C][/ROW]
[ROW][C]103[/C][C]639704[/C][C]644893.945075553[/C][C]-5189.9450755528[/C][/ROW]
[ROW][C]104[/C][C]639223[/C][C]644361.088129804[/C][C]-5138.08812980389[/C][/ROW]
[ROW][C]105[/C][C]637312[/C][C]641717.082081744[/C][C]-4405.0820817441[/C][/ROW]
[ROW][C]106[/C][C]640124[/C][C]641311.34241897[/C][C]-1187.34241897031[/C][/ROW]
[ROW][C]107[/C][C]644649[/C][C]641191.058982215[/C][C]3457.94101778546[/C][/ROW]
[ROW][C]108[/C][C]668209[/C][C]659234.839071536[/C][C]8974.16092846438[/C][/ROW]
[ROW][C]109[/C][C]651667[/C][C]651742.246322526[/C][C]-75.2463225261308[/C][/ROW]
[ROW][C]110[/C][C]653170[/C][C]655481.841083591[/C][C]-2311.84108359087[/C][/ROW]
[ROW][C]111[/C][C]662102[/C][C]661048.727640117[/C][C]1053.27235988271[/C][/ROW]
[ROW][C]112[/C][C]667617[/C][C]667583.263554396[/C][C]33.7364456035430[/C][/ROW]
[ROW][C]113[/C][C]671420[/C][C]671549.249221964[/C][C]-129.249221963575[/C][/ROW]
[ROW][C]114[/C][C]677156[/C][C]678682.004715812[/C][C]-1526.00471581169[/C][/ROW]
[ROW][C]115[/C][C]686086[/C][C]689283.670760843[/C][C]-3197.67076084274[/C][/ROW]
[ROW][C]116[/C][C]684954[/C][C]689495.530469153[/C][C]-4541.53046915319[/C][/ROW]
[ROW][C]117[/C][C]684331[/C][C]686988.240550832[/C][C]-2657.24055083189[/C][/ROW]
[ROW][C]118[/C][C]722145[/C][C]688775.645191536[/C][C]33369.3548084638[/C][/ROW]
[ROW][C]119[/C][C]731098[/C][C]712897.290512316[/C][C]18200.7094876842[/C][/ROW]
[ROW][C]120[/C][C]753123[/C][C]746797.90646344[/C][C]6325.09353656066[/C][/ROW]
[ROW][C]121[/C][C]740228[/C][C]734364.62341684[/C][C]5863.37658315944[/C][/ROW]
[ROW][C]122[/C][C]741472[/C][C]743776.558518572[/C][C]-2304.55851857178[/C][/ROW]
[ROW][C]123[/C][C]747315[/C][C]754619.090993971[/C][C]-7304.09099397098[/C][/ROW]
[ROW][C]124[/C][C]757533[/C][C]758756.52229664[/C][C]-1223.52229663951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42267&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42267&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
13363049353087.9209599309961.07904006977
14347562344405.6088840133156.39111598709
15347577347337.391404895239.608595105237
16349715350793.877166463-1078.87716646300
17353818355513.605943885-1695.60594388511
18354073356144.036570634-2071.03657063353
19357040359932.518160865-2892.51816086471
20359177360547.305711935-1370.30571193516
21354845356668.890735919-1823.89073591860
22354481355877.811354502-1396.81135450187
23352747355358.23644073-2611.23644073005
24360446364983.306173255-4537.30617325479
25368285375099.330256504-6814.3302565043
26354819351832.8749533922986.12504660804
27353017351934.0729254151082.92707458546
28354551353915.772399946635.227600054408
29352682358093.648816612-5411.64881661232
30351146354805.161015928-3659.16101592797
31350760355610.127186802-4850.12718680239
32347555353854.734323942-6299.73432394234
33335363344882.718038305-9519.71803830477
34325165337155.456479371-11990.4564793712
35311274326691.810421809-15417.8104218086
36297987322794.807369723-24807.8073697231
37344276312659.94484200031616.0551579995
38306152314480.733949943-8328.73394994321
39283323303717.173372717-20394.1733727167
40285869287563.091179627-1694.09117962723
41293660282341.08276020811318.9172397919
42300831285251.43756723615579.5624327643
43313351293432.03928625419918.9607137465
44322765304111.37096890118653.6290310990
45323613309215.30548048714397.6945195131
46329199316331.17859115112867.8214088489
47334038322299.93853218811738.0614678123
48350683335473.31105816615209.6889418335
49353929385079.064761858-31150.0647618583
50340715335538.3650526545176.63494734565
51347752331339.21785826216412.7821417376
52358474353579.2168754214894.78312457888
53366179366920.185652254-741.18565225444
54373163371988.8158861651174.18411383481
55382739380338.7778755812400.22212441912
56391636385017.9214019236618.0785980766
57391693383811.2461724957881.75382750528
58395453389511.6967566875941.30324331328
59399368393341.9676301746026.03236982564
60416075408270.8530333087804.14696669194
61427623439314.291098872-11691.2910988723
62418000415739.3630320422260.63696795801
63425316416506.3045055868809.69549441378
64436397433328.1922458583068.80775414233
65442533446993.027822810-4460.02782280958
66449148453768.896846519-4620.89684651862
67460852462310.847118031-1458.84711803065
68462789468575.403903413-5786.40390341281
69465097459960.6889107535136.31108924706
70469728463275.2265122796452.77348772087
71475434467450.8020875317983.19791246857
72495992486446.7963670379545.20363296272
73487101513778.002093938-26677.0020939382
74489496484631.6821272794864.31787272118
75498649489366.066862529282.93313748017
76505533504980.580435954552.419564045616
77512839514630.703435691-1791.70343569096
78522584523794.220730494-1210.22073049383
79532603537359.113234139-4756.1132341387
80531520540205.455461221-8685.45546122128
81531623533628.849129188-2005.84912918822
82535608532292.1110275973315.8889724029
83539804534045.9662249575758.03377504298
84559182552756.3448451556425.65515484475
85548414561998.233876658-13584.2338766580
86550774552690.89639527-1916.89639527060
87556397554464.918204391932.08179561037
88569125561191.6012778787933.39872212161
89571988573939.989918909-1951.98991890938
90578807583210.341233609-4403.34123360901
91588234593401.584171042-5167.58417104173
92588724593363.118301346-4639.11830134573
93588550590959.540717115-2409.54071711493
94592764590702.051901132061.94809887046
95598593591621.9427514116971.05724858865
96619494611769.6406783857724.35932161508
97604560612067.245640871-7507.24564087135
98606210610893.931073229-4683.93107322929
99614823612321.1039165512501.89608344855
100620033621911.352555018-1878.35255501792
101625236623794.7167639511441.28323604865
102631307633741.997700565-2434.99770056549
103639704644893.945075553-5189.9450755528
104639223644361.088129804-5138.08812980389
105637312641717.082081744-4405.0820817441
106640124641311.34241897-1187.34241897031
107644649641191.0589822153457.94101778546
108668209659234.8390715368974.16092846438
109651667651742.246322526-75.2463225261308
110653170655481.841083591-2311.84108359087
111662102661048.7276401171053.27235988271
112667617667583.26355439633.7364456035430
113671420671549.249221964-129.249221963575
114677156678682.004715812-1526.00471581169
115686086689283.670760843-3197.67076084274
116684954689495.530469153-4541.53046915319
117684331686988.240550832-2657.24055083189
118722145688775.64519153633369.3548084638
119731098712897.29051231618200.7094876842
120753123746797.906463446325.09353656066
121740228734364.623416845863.37658315944
122741472743776.558518572-2304.55851857178
123747315754619.090993971-7304.09099397098
124757533758756.52229664-1223.52229663951







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
125764548.96717861745841.739600701783256.19475652
126774210.575115706751834.732221783796586.41800963
127788791.541992229762542.86547957815040.218504887
128792984.302614655762931.851261701823036.75396761
129796807.045928898762861.553924692830752.537933104
130820543.116749691781888.628161576859197.605337806
131818947.29783685776394.863554706861499.732118992
132838663.770140599791140.21015529886187.330125908
133819292.769537547768666.692545515869918.84652958
134820631.911614681765775.924215194875487.899014168
135830459.899339409770751.927646977890167.87103184
136841742.096125143779695.703355233903788.488895053

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
125 & 764548.96717861 & 745841.739600701 & 783256.19475652 \tabularnewline
126 & 774210.575115706 & 751834.732221783 & 796586.41800963 \tabularnewline
127 & 788791.541992229 & 762542.86547957 & 815040.218504887 \tabularnewline
128 & 792984.302614655 & 762931.851261701 & 823036.75396761 \tabularnewline
129 & 796807.045928898 & 762861.553924692 & 830752.537933104 \tabularnewline
130 & 820543.116749691 & 781888.628161576 & 859197.605337806 \tabularnewline
131 & 818947.29783685 & 776394.863554706 & 861499.732118992 \tabularnewline
132 & 838663.770140599 & 791140.21015529 & 886187.330125908 \tabularnewline
133 & 819292.769537547 & 768666.692545515 & 869918.84652958 \tabularnewline
134 & 820631.911614681 & 765775.924215194 & 875487.899014168 \tabularnewline
135 & 830459.899339409 & 770751.927646977 & 890167.87103184 \tabularnewline
136 & 841742.096125143 & 779695.703355233 & 903788.488895053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42267&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]125[/C][C]764548.96717861[/C][C]745841.739600701[/C][C]783256.19475652[/C][/ROW]
[ROW][C]126[/C][C]774210.575115706[/C][C]751834.732221783[/C][C]796586.41800963[/C][/ROW]
[ROW][C]127[/C][C]788791.541992229[/C][C]762542.86547957[/C][C]815040.218504887[/C][/ROW]
[ROW][C]128[/C][C]792984.302614655[/C][C]762931.851261701[/C][C]823036.75396761[/C][/ROW]
[ROW][C]129[/C][C]796807.045928898[/C][C]762861.553924692[/C][C]830752.537933104[/C][/ROW]
[ROW][C]130[/C][C]820543.116749691[/C][C]781888.628161576[/C][C]859197.605337806[/C][/ROW]
[ROW][C]131[/C][C]818947.29783685[/C][C]776394.863554706[/C][C]861499.732118992[/C][/ROW]
[ROW][C]132[/C][C]838663.770140599[/C][C]791140.21015529[/C][C]886187.330125908[/C][/ROW]
[ROW][C]133[/C][C]819292.769537547[/C][C]768666.692545515[/C][C]869918.84652958[/C][/ROW]
[ROW][C]134[/C][C]820631.911614681[/C][C]765775.924215194[/C][C]875487.899014168[/C][/ROW]
[ROW][C]135[/C][C]830459.899339409[/C][C]770751.927646977[/C][C]890167.87103184[/C][/ROW]
[ROW][C]136[/C][C]841742.096125143[/C][C]779695.703355233[/C][C]903788.488895053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42267&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42267&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
125764548.96717861745841.739600701783256.19475652
126774210.575115706751834.732221783796586.41800963
127788791.541992229762542.86547957815040.218504887
128792984.302614655762931.851261701823036.75396761
129796807.045928898762861.553924692830752.537933104
130820543.116749691781888.628161576859197.605337806
131818947.29783685776394.863554706861499.732118992
132838663.770140599791140.21015529886187.330125908
133819292.769537547768666.692545515869918.84652958
134820631.911614681765775.924215194875487.899014168
135830459.899339409770751.927646977890167.87103184
136841742.096125143779695.703355233903788.488895053



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')