Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 17:07:59 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/19/t1282237651oyetacw3gcqyhk5.htm/, Retrieved Fri, 03 May 2024 12:13:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79337, Retrieved Fri, 03 May 2024 12:13:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsgilian keirsebelik
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks A-Stap 32] [2010-08-19 17:07:59] [46199ea7e385a69efb178ac615a86e3a] [Current]
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Dataseries X:
668
667
666
664
684
683
668
658
659
659
660
662
659
655
655
655
674
674
665
644
638
648
641
637
651
649
652
650
661
666
652
624
613
623
615
613
621
612
611
609
631
632
624
596
584
587
581
574
593
582
571
572
594
588
571
546
535
537
527
515
545
538
520
523
541
529
504
473
455
458
450
442
469
455
439
443
461
451
425
393
366
359
351
343
366
355
344
351
367
364
353
313
278
274
261
255
274
262
265
274
291
289
277
238
203
198
190
187
201
181
181
196
207
202
186
154
120
107
99
100




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=79337&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=79337&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79337&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
alpha0.410159378916772
beta0.0621038460609066
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.410159378916772 \tabularnewline
beta & 0.0621038460609066 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79337&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]0.410159378916772[/C][/ROW]
[ROW][C]beta[/C][C]0.0621038460609066[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79337&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79337&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
alpha0.410159378916772
beta0.0621038460609066
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13659663.780715811966-4.78071581196593
14655657.445024279532-2.44502427953159
15655656.755057715721-1.75505771572114
16655656.178381745534-1.17838174553435
17674674.724885200313-0.724885200312883
18674675.022263229662-1.02226322966226
19665656.0049626300368.9950373699644
20644649.533811019997-5.53381101999696
21638648.045889448822-10.0458894488220
22648643.3264029245354.67359707546484
23641645.721633268688-4.72163326868827
24637645.143050085044-8.14305008504437
25651634.84219001543516.1578099845648
26649638.3260144900910.6739855099097
27652643.6117743147978.38822568520277
28650647.9818537838062.01814621619417
29661668.63460303119-7.63460303119052
30666666.274151416039-0.274151416038649
31652653.843024530955-1.84302453095540
32624634.451480795414-10.4514807954143
33613628.25450405094-15.2545040509395
34623629.917510515415-6.91751051541473
35615621.558300715687-6.55830071568744
36613617.702965915233-4.70296591523311
37621622.72901586869-1.72901586868954
38612614.768479643678-2.76847964367835
39611611.976710575761-0.976710575761217
40609607.2940521304461.70594786955371
41631620.66292437849710.3370756215032
42632629.0107594955282.98924050447249
43624616.0714258158657.92857418413473
44596594.9377520486621.06224795133801
45584590.251078380621-6.25107838062115
46587600.374618770544-13.3746187705436
47581589.26456046195-8.26456046194949
48574585.445994867391-11.4459948673914
49593588.9309789730864.06902102691436
50582582.353628527687-0.353628527687079
51571581.288888234256-10.2888882342560
52572573.811586256488-1.81158625648811
53594590.1815908948843.81840910511585
54588590.708527852677-2.70852785267698
55571577.387330105693-6.38733010569263
56546545.0088637014340.991136298566403
57535534.6545624912430.345437508756618
58537542.125238354085-5.12523835408547
59527536.466258996523-9.46625899652327
60515529.3010542324-14.3010542324005
61545539.7164581459535.2835418540468
62538530.009595872467.9904041275397
63520525.700561661114-5.70056166111408
64523524.415880544631-1.41588054463057
65541543.589485776745-2.58948577674505
66529536.795585282875-7.79558528287532
67504518.245669553395-14.2456695533951
68473485.823672713266-12.8236727132661
69455467.897863252303-12.8978632523032
70458464.848133213476-6.84813321347644
71450454.016380624446-4.01638062444562
72442444.467956419912-2.46795641991201
73469469.823245445614-0.823245445613793
74455457.587328167737-2.58732816773681
75439438.9738928201470.0261071798527723
76443440.8208527744472.17914722555275
77461459.1238417445161.87615825548397
78451449.5516384924671.44836150753252
79425429.684999153194-4.6849991531945
80393400.962993010947-7.96299301094672
81366384.050730431177-18.050730431177
82359381.388277941086-22.3882779410861
83351364.389423828184-13.3894238281839
84343350.207678811148-7.20767881114836
85366372.766108399427-6.76610839942651
86355355.077827879593-0.0778278795927463
87344337.1248065079626.87519349203808
88351341.3150056751599.6849943248414
89367360.9731372766556.02686272334518
90364351.41204545642212.5879545435781
91353331.34145538579521.6585446142055
92313311.0067880878811.99321191211931
93278291.997389437932-13.9973894379323
94274288.311630089255-14.3116300892552
95261280.011749786204-19.0117497862039
96255267.105356053602-12.1053560536021
97274287.725814278332-13.7258142783319
98262270.761084446498-8.76108444649827
99265252.75965415639612.2403458436038
100274260.35635501474813.6436449852524
101291279.12988579283611.8701142071636
102289275.63373501941513.3662649805847
103277261.05068242130315.9493175786973
104238226.44758557729711.5524144227035
105203201.8432493302031.15675066979736
106198204.489936299126-6.48993629912613
107190197.127298964809-7.12729896480883
108187193.973245567061-6.97324556706093
109201216.677752309969-15.6777523099687
110181202.725972776541-21.7259727765409
111181192.349277495900-11.3492774958997
112196191.0522187133094.94778128669063
113207204.9454765515422.05452344845781
114202197.7883498902964.21165010970421
115186180.2233350135395.7766649864605
116154137.84453409613516.1554659038653
117120108.10382581868211.8961741813175
118107110.026049167775-3.02604916777503
11999103.177436709157-4.17743670915672
120100100.868525698083-0.868525698082635

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 659 & 663.780715811966 & -4.78071581196593 \tabularnewline
14 & 655 & 657.445024279532 & -2.44502427953159 \tabularnewline
15 & 655 & 656.755057715721 & -1.75505771572114 \tabularnewline
16 & 655 & 656.178381745534 & -1.17838174553435 \tabularnewline
17 & 674 & 674.724885200313 & -0.724885200312883 \tabularnewline
18 & 674 & 675.022263229662 & -1.02226322966226 \tabularnewline
19 & 665 & 656.004962630036 & 8.9950373699644 \tabularnewline
20 & 644 & 649.533811019997 & -5.53381101999696 \tabularnewline
21 & 638 & 648.045889448822 & -10.0458894488220 \tabularnewline
22 & 648 & 643.326402924535 & 4.67359707546484 \tabularnewline
23 & 641 & 645.721633268688 & -4.72163326868827 \tabularnewline
24 & 637 & 645.143050085044 & -8.14305008504437 \tabularnewline
25 & 651 & 634.842190015435 & 16.1578099845648 \tabularnewline
26 & 649 & 638.32601449009 & 10.6739855099097 \tabularnewline
27 & 652 & 643.611774314797 & 8.38822568520277 \tabularnewline
28 & 650 & 647.981853783806 & 2.01814621619417 \tabularnewline
29 & 661 & 668.63460303119 & -7.63460303119052 \tabularnewline
30 & 666 & 666.274151416039 & -0.274151416038649 \tabularnewline
31 & 652 & 653.843024530955 & -1.84302453095540 \tabularnewline
32 & 624 & 634.451480795414 & -10.4514807954143 \tabularnewline
33 & 613 & 628.25450405094 & -15.2545040509395 \tabularnewline
34 & 623 & 629.917510515415 & -6.91751051541473 \tabularnewline
35 & 615 & 621.558300715687 & -6.55830071568744 \tabularnewline
36 & 613 & 617.702965915233 & -4.70296591523311 \tabularnewline
37 & 621 & 622.72901586869 & -1.72901586868954 \tabularnewline
38 & 612 & 614.768479643678 & -2.76847964367835 \tabularnewline
39 & 611 & 611.976710575761 & -0.976710575761217 \tabularnewline
40 & 609 & 607.294052130446 & 1.70594786955371 \tabularnewline
41 & 631 & 620.662924378497 & 10.3370756215032 \tabularnewline
42 & 632 & 629.010759495528 & 2.98924050447249 \tabularnewline
43 & 624 & 616.071425815865 & 7.92857418413473 \tabularnewline
44 & 596 & 594.937752048662 & 1.06224795133801 \tabularnewline
45 & 584 & 590.251078380621 & -6.25107838062115 \tabularnewline
46 & 587 & 600.374618770544 & -13.3746187705436 \tabularnewline
47 & 581 & 589.26456046195 & -8.26456046194949 \tabularnewline
48 & 574 & 585.445994867391 & -11.4459948673914 \tabularnewline
49 & 593 & 588.930978973086 & 4.06902102691436 \tabularnewline
50 & 582 & 582.353628527687 & -0.353628527687079 \tabularnewline
51 & 571 & 581.288888234256 & -10.2888882342560 \tabularnewline
52 & 572 & 573.811586256488 & -1.81158625648811 \tabularnewline
53 & 594 & 590.181590894884 & 3.81840910511585 \tabularnewline
54 & 588 & 590.708527852677 & -2.70852785267698 \tabularnewline
55 & 571 & 577.387330105693 & -6.38733010569263 \tabularnewline
56 & 546 & 545.008863701434 & 0.991136298566403 \tabularnewline
57 & 535 & 534.654562491243 & 0.345437508756618 \tabularnewline
58 & 537 & 542.125238354085 & -5.12523835408547 \tabularnewline
59 & 527 & 536.466258996523 & -9.46625899652327 \tabularnewline
60 & 515 & 529.3010542324 & -14.3010542324005 \tabularnewline
61 & 545 & 539.716458145953 & 5.2835418540468 \tabularnewline
62 & 538 & 530.00959587246 & 7.9904041275397 \tabularnewline
63 & 520 & 525.700561661114 & -5.70056166111408 \tabularnewline
64 & 523 & 524.415880544631 & -1.41588054463057 \tabularnewline
65 & 541 & 543.589485776745 & -2.58948577674505 \tabularnewline
66 & 529 & 536.795585282875 & -7.79558528287532 \tabularnewline
67 & 504 & 518.245669553395 & -14.2456695533951 \tabularnewline
68 & 473 & 485.823672713266 & -12.8236727132661 \tabularnewline
69 & 455 & 467.897863252303 & -12.8978632523032 \tabularnewline
70 & 458 & 464.848133213476 & -6.84813321347644 \tabularnewline
71 & 450 & 454.016380624446 & -4.01638062444562 \tabularnewline
72 & 442 & 444.467956419912 & -2.46795641991201 \tabularnewline
73 & 469 & 469.823245445614 & -0.823245445613793 \tabularnewline
74 & 455 & 457.587328167737 & -2.58732816773681 \tabularnewline
75 & 439 & 438.973892820147 & 0.0261071798527723 \tabularnewline
76 & 443 & 440.820852774447 & 2.17914722555275 \tabularnewline
77 & 461 & 459.123841744516 & 1.87615825548397 \tabularnewline
78 & 451 & 449.551638492467 & 1.44836150753252 \tabularnewline
79 & 425 & 429.684999153194 & -4.6849991531945 \tabularnewline
80 & 393 & 400.962993010947 & -7.96299301094672 \tabularnewline
81 & 366 & 384.050730431177 & -18.050730431177 \tabularnewline
82 & 359 & 381.388277941086 & -22.3882779410861 \tabularnewline
83 & 351 & 364.389423828184 & -13.3894238281839 \tabularnewline
84 & 343 & 350.207678811148 & -7.20767881114836 \tabularnewline
85 & 366 & 372.766108399427 & -6.76610839942651 \tabularnewline
86 & 355 & 355.077827879593 & -0.0778278795927463 \tabularnewline
87 & 344 & 337.124806507962 & 6.87519349203808 \tabularnewline
88 & 351 & 341.315005675159 & 9.6849943248414 \tabularnewline
89 & 367 & 360.973137276655 & 6.02686272334518 \tabularnewline
90 & 364 & 351.412045456422 & 12.5879545435781 \tabularnewline
91 & 353 & 331.341455385795 & 21.6585446142055 \tabularnewline
92 & 313 & 311.006788087881 & 1.99321191211931 \tabularnewline
93 & 278 & 291.997389437932 & -13.9973894379323 \tabularnewline
94 & 274 & 288.311630089255 & -14.3116300892552 \tabularnewline
95 & 261 & 280.011749786204 & -19.0117497862039 \tabularnewline
96 & 255 & 267.105356053602 & -12.1053560536021 \tabularnewline
97 & 274 & 287.725814278332 & -13.7258142783319 \tabularnewline
98 & 262 & 270.761084446498 & -8.76108444649827 \tabularnewline
99 & 265 & 252.759654156396 & 12.2403458436038 \tabularnewline
100 & 274 & 260.356355014748 & 13.6436449852524 \tabularnewline
101 & 291 & 279.129885792836 & 11.8701142071636 \tabularnewline
102 & 289 & 275.633735019415 & 13.3662649805847 \tabularnewline
103 & 277 & 261.050682421303 & 15.9493175786973 \tabularnewline
104 & 238 & 226.447585577297 & 11.5524144227035 \tabularnewline
105 & 203 & 201.843249330203 & 1.15675066979736 \tabularnewline
106 & 198 & 204.489936299126 & -6.48993629912613 \tabularnewline
107 & 190 & 197.127298964809 & -7.12729896480883 \tabularnewline
108 & 187 & 193.973245567061 & -6.97324556706093 \tabularnewline
109 & 201 & 216.677752309969 & -15.6777523099687 \tabularnewline
110 & 181 & 202.725972776541 & -21.7259727765409 \tabularnewline
111 & 181 & 192.349277495900 & -11.3492774958997 \tabularnewline
112 & 196 & 191.052218713309 & 4.94778128669063 \tabularnewline
113 & 207 & 204.945476551542 & 2.05452344845781 \tabularnewline
114 & 202 & 197.788349890296 & 4.21165010970421 \tabularnewline
115 & 186 & 180.223335013539 & 5.7766649864605 \tabularnewline
116 & 154 & 137.844534096135 & 16.1554659038653 \tabularnewline
117 & 120 & 108.103825818682 & 11.8961741813175 \tabularnewline
118 & 107 & 110.026049167775 & -3.02604916777503 \tabularnewline
119 & 99 & 103.177436709157 & -4.17743670915672 \tabularnewline
120 & 100 & 100.868525698083 & -0.868525698082635 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79337&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]659[/C][C]663.780715811966[/C][C]-4.78071581196593[/C][/ROW]
[ROW][C]14[/C][C]655[/C][C]657.445024279532[/C][C]-2.44502427953159[/C][/ROW]
[ROW][C]15[/C][C]655[/C][C]656.755057715721[/C][C]-1.75505771572114[/C][/ROW]
[ROW][C]16[/C][C]655[/C][C]656.178381745534[/C][C]-1.17838174553435[/C][/ROW]
[ROW][C]17[/C][C]674[/C][C]674.724885200313[/C][C]-0.724885200312883[/C][/ROW]
[ROW][C]18[/C][C]674[/C][C]675.022263229662[/C][C]-1.02226322966226[/C][/ROW]
[ROW][C]19[/C][C]665[/C][C]656.004962630036[/C][C]8.9950373699644[/C][/ROW]
[ROW][C]20[/C][C]644[/C][C]649.533811019997[/C][C]-5.53381101999696[/C][/ROW]
[ROW][C]21[/C][C]638[/C][C]648.045889448822[/C][C]-10.0458894488220[/C][/ROW]
[ROW][C]22[/C][C]648[/C][C]643.326402924535[/C][C]4.67359707546484[/C][/ROW]
[ROW][C]23[/C][C]641[/C][C]645.721633268688[/C][C]-4.72163326868827[/C][/ROW]
[ROW][C]24[/C][C]637[/C][C]645.143050085044[/C][C]-8.14305008504437[/C][/ROW]
[ROW][C]25[/C][C]651[/C][C]634.842190015435[/C][C]16.1578099845648[/C][/ROW]
[ROW][C]26[/C][C]649[/C][C]638.32601449009[/C][C]10.6739855099097[/C][/ROW]
[ROW][C]27[/C][C]652[/C][C]643.611774314797[/C][C]8.38822568520277[/C][/ROW]
[ROW][C]28[/C][C]650[/C][C]647.981853783806[/C][C]2.01814621619417[/C][/ROW]
[ROW][C]29[/C][C]661[/C][C]668.63460303119[/C][C]-7.63460303119052[/C][/ROW]
[ROW][C]30[/C][C]666[/C][C]666.274151416039[/C][C]-0.274151416038649[/C][/ROW]
[ROW][C]31[/C][C]652[/C][C]653.843024530955[/C][C]-1.84302453095540[/C][/ROW]
[ROW][C]32[/C][C]624[/C][C]634.451480795414[/C][C]-10.4514807954143[/C][/ROW]
[ROW][C]33[/C][C]613[/C][C]628.25450405094[/C][C]-15.2545040509395[/C][/ROW]
[ROW][C]34[/C][C]623[/C][C]629.917510515415[/C][C]-6.91751051541473[/C][/ROW]
[ROW][C]35[/C][C]615[/C][C]621.558300715687[/C][C]-6.55830071568744[/C][/ROW]
[ROW][C]36[/C][C]613[/C][C]617.702965915233[/C][C]-4.70296591523311[/C][/ROW]
[ROW][C]37[/C][C]621[/C][C]622.72901586869[/C][C]-1.72901586868954[/C][/ROW]
[ROW][C]38[/C][C]612[/C][C]614.768479643678[/C][C]-2.76847964367835[/C][/ROW]
[ROW][C]39[/C][C]611[/C][C]611.976710575761[/C][C]-0.976710575761217[/C][/ROW]
[ROW][C]40[/C][C]609[/C][C]607.294052130446[/C][C]1.70594786955371[/C][/ROW]
[ROW][C]41[/C][C]631[/C][C]620.662924378497[/C][C]10.3370756215032[/C][/ROW]
[ROW][C]42[/C][C]632[/C][C]629.010759495528[/C][C]2.98924050447249[/C][/ROW]
[ROW][C]43[/C][C]624[/C][C]616.071425815865[/C][C]7.92857418413473[/C][/ROW]
[ROW][C]44[/C][C]596[/C][C]594.937752048662[/C][C]1.06224795133801[/C][/ROW]
[ROW][C]45[/C][C]584[/C][C]590.251078380621[/C][C]-6.25107838062115[/C][/ROW]
[ROW][C]46[/C][C]587[/C][C]600.374618770544[/C][C]-13.3746187705436[/C][/ROW]
[ROW][C]47[/C][C]581[/C][C]589.26456046195[/C][C]-8.26456046194949[/C][/ROW]
[ROW][C]48[/C][C]574[/C][C]585.445994867391[/C][C]-11.4459948673914[/C][/ROW]
[ROW][C]49[/C][C]593[/C][C]588.930978973086[/C][C]4.06902102691436[/C][/ROW]
[ROW][C]50[/C][C]582[/C][C]582.353628527687[/C][C]-0.353628527687079[/C][/ROW]
[ROW][C]51[/C][C]571[/C][C]581.288888234256[/C][C]-10.2888882342560[/C][/ROW]
[ROW][C]52[/C][C]572[/C][C]573.811586256488[/C][C]-1.81158625648811[/C][/ROW]
[ROW][C]53[/C][C]594[/C][C]590.181590894884[/C][C]3.81840910511585[/C][/ROW]
[ROW][C]54[/C][C]588[/C][C]590.708527852677[/C][C]-2.70852785267698[/C][/ROW]
[ROW][C]55[/C][C]571[/C][C]577.387330105693[/C][C]-6.38733010569263[/C][/ROW]
[ROW][C]56[/C][C]546[/C][C]545.008863701434[/C][C]0.991136298566403[/C][/ROW]
[ROW][C]57[/C][C]535[/C][C]534.654562491243[/C][C]0.345437508756618[/C][/ROW]
[ROW][C]58[/C][C]537[/C][C]542.125238354085[/C][C]-5.12523835408547[/C][/ROW]
[ROW][C]59[/C][C]527[/C][C]536.466258996523[/C][C]-9.46625899652327[/C][/ROW]
[ROW][C]60[/C][C]515[/C][C]529.3010542324[/C][C]-14.3010542324005[/C][/ROW]
[ROW][C]61[/C][C]545[/C][C]539.716458145953[/C][C]5.2835418540468[/C][/ROW]
[ROW][C]62[/C][C]538[/C][C]530.00959587246[/C][C]7.9904041275397[/C][/ROW]
[ROW][C]63[/C][C]520[/C][C]525.700561661114[/C][C]-5.70056166111408[/C][/ROW]
[ROW][C]64[/C][C]523[/C][C]524.415880544631[/C][C]-1.41588054463057[/C][/ROW]
[ROW][C]65[/C][C]541[/C][C]543.589485776745[/C][C]-2.58948577674505[/C][/ROW]
[ROW][C]66[/C][C]529[/C][C]536.795585282875[/C][C]-7.79558528287532[/C][/ROW]
[ROW][C]67[/C][C]504[/C][C]518.245669553395[/C][C]-14.2456695533951[/C][/ROW]
[ROW][C]68[/C][C]473[/C][C]485.823672713266[/C][C]-12.8236727132661[/C][/ROW]
[ROW][C]69[/C][C]455[/C][C]467.897863252303[/C][C]-12.8978632523032[/C][/ROW]
[ROW][C]70[/C][C]458[/C][C]464.848133213476[/C][C]-6.84813321347644[/C][/ROW]
[ROW][C]71[/C][C]450[/C][C]454.016380624446[/C][C]-4.01638062444562[/C][/ROW]
[ROW][C]72[/C][C]442[/C][C]444.467956419912[/C][C]-2.46795641991201[/C][/ROW]
[ROW][C]73[/C][C]469[/C][C]469.823245445614[/C][C]-0.823245445613793[/C][/ROW]
[ROW][C]74[/C][C]455[/C][C]457.587328167737[/C][C]-2.58732816773681[/C][/ROW]
[ROW][C]75[/C][C]439[/C][C]438.973892820147[/C][C]0.0261071798527723[/C][/ROW]
[ROW][C]76[/C][C]443[/C][C]440.820852774447[/C][C]2.17914722555275[/C][/ROW]
[ROW][C]77[/C][C]461[/C][C]459.123841744516[/C][C]1.87615825548397[/C][/ROW]
[ROW][C]78[/C][C]451[/C][C]449.551638492467[/C][C]1.44836150753252[/C][/ROW]
[ROW][C]79[/C][C]425[/C][C]429.684999153194[/C][C]-4.6849991531945[/C][/ROW]
[ROW][C]80[/C][C]393[/C][C]400.962993010947[/C][C]-7.96299301094672[/C][/ROW]
[ROW][C]81[/C][C]366[/C][C]384.050730431177[/C][C]-18.050730431177[/C][/ROW]
[ROW][C]82[/C][C]359[/C][C]381.388277941086[/C][C]-22.3882779410861[/C][/ROW]
[ROW][C]83[/C][C]351[/C][C]364.389423828184[/C][C]-13.3894238281839[/C][/ROW]
[ROW][C]84[/C][C]343[/C][C]350.207678811148[/C][C]-7.20767881114836[/C][/ROW]
[ROW][C]85[/C][C]366[/C][C]372.766108399427[/C][C]-6.76610839942651[/C][/ROW]
[ROW][C]86[/C][C]355[/C][C]355.077827879593[/C][C]-0.0778278795927463[/C][/ROW]
[ROW][C]87[/C][C]344[/C][C]337.124806507962[/C][C]6.87519349203808[/C][/ROW]
[ROW][C]88[/C][C]351[/C][C]341.315005675159[/C][C]9.6849943248414[/C][/ROW]
[ROW][C]89[/C][C]367[/C][C]360.973137276655[/C][C]6.02686272334518[/C][/ROW]
[ROW][C]90[/C][C]364[/C][C]351.412045456422[/C][C]12.5879545435781[/C][/ROW]
[ROW][C]91[/C][C]353[/C][C]331.341455385795[/C][C]21.6585446142055[/C][/ROW]
[ROW][C]92[/C][C]313[/C][C]311.006788087881[/C][C]1.99321191211931[/C][/ROW]
[ROW][C]93[/C][C]278[/C][C]291.997389437932[/C][C]-13.9973894379323[/C][/ROW]
[ROW][C]94[/C][C]274[/C][C]288.311630089255[/C][C]-14.3116300892552[/C][/ROW]
[ROW][C]95[/C][C]261[/C][C]280.011749786204[/C][C]-19.0117497862039[/C][/ROW]
[ROW][C]96[/C][C]255[/C][C]267.105356053602[/C][C]-12.1053560536021[/C][/ROW]
[ROW][C]97[/C][C]274[/C][C]287.725814278332[/C][C]-13.7258142783319[/C][/ROW]
[ROW][C]98[/C][C]262[/C][C]270.761084446498[/C][C]-8.76108444649827[/C][/ROW]
[ROW][C]99[/C][C]265[/C][C]252.759654156396[/C][C]12.2403458436038[/C][/ROW]
[ROW][C]100[/C][C]274[/C][C]260.356355014748[/C][C]13.6436449852524[/C][/ROW]
[ROW][C]101[/C][C]291[/C][C]279.129885792836[/C][C]11.8701142071636[/C][/ROW]
[ROW][C]102[/C][C]289[/C][C]275.633735019415[/C][C]13.3662649805847[/C][/ROW]
[ROW][C]103[/C][C]277[/C][C]261.050682421303[/C][C]15.9493175786973[/C][/ROW]
[ROW][C]104[/C][C]238[/C][C]226.447585577297[/C][C]11.5524144227035[/C][/ROW]
[ROW][C]105[/C][C]203[/C][C]201.843249330203[/C][C]1.15675066979736[/C][/ROW]
[ROW][C]106[/C][C]198[/C][C]204.489936299126[/C][C]-6.48993629912613[/C][/ROW]
[ROW][C]107[/C][C]190[/C][C]197.127298964809[/C][C]-7.12729896480883[/C][/ROW]
[ROW][C]108[/C][C]187[/C][C]193.973245567061[/C][C]-6.97324556706093[/C][/ROW]
[ROW][C]109[/C][C]201[/C][C]216.677752309969[/C][C]-15.6777523099687[/C][/ROW]
[ROW][C]110[/C][C]181[/C][C]202.725972776541[/C][C]-21.7259727765409[/C][/ROW]
[ROW][C]111[/C][C]181[/C][C]192.349277495900[/C][C]-11.3492774958997[/C][/ROW]
[ROW][C]112[/C][C]196[/C][C]191.052218713309[/C][C]4.94778128669063[/C][/ROW]
[ROW][C]113[/C][C]207[/C][C]204.945476551542[/C][C]2.05452344845781[/C][/ROW]
[ROW][C]114[/C][C]202[/C][C]197.788349890296[/C][C]4.21165010970421[/C][/ROW]
[ROW][C]115[/C][C]186[/C][C]180.223335013539[/C][C]5.7766649864605[/C][/ROW]
[ROW][C]116[/C][C]154[/C][C]137.844534096135[/C][C]16.1554659038653[/C][/ROW]
[ROW][C]117[/C][C]120[/C][C]108.103825818682[/C][C]11.8961741813175[/C][/ROW]
[ROW][C]118[/C][C]107[/C][C]110.026049167775[/C][C]-3.02604916777503[/C][/ROW]
[ROW][C]119[/C][C]99[/C][C]103.177436709157[/C][C]-4.17743670915672[/C][/ROW]
[ROW][C]120[/C][C]100[/C][C]100.868525698083[/C][C]-0.868525698082635[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79337&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79337&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
13659663.780715811966-4.78071581196593
14655657.445024279532-2.44502427953159
15655656.755057715721-1.75505771572114
16655656.178381745534-1.17838174553435
17674674.724885200313-0.724885200312883
18674675.022263229662-1.02226322966226
19665656.0049626300368.9950373699644
20644649.533811019997-5.53381101999696
21638648.045889448822-10.0458894488220
22648643.3264029245354.67359707546484
23641645.721633268688-4.72163326868827
24637645.143050085044-8.14305008504437
25651634.84219001543516.1578099845648
26649638.3260144900910.6739855099097
27652643.6117743147978.38822568520277
28650647.9818537838062.01814621619417
29661668.63460303119-7.63460303119052
30666666.274151416039-0.274151416038649
31652653.843024530955-1.84302453095540
32624634.451480795414-10.4514807954143
33613628.25450405094-15.2545040509395
34623629.917510515415-6.91751051541473
35615621.558300715687-6.55830071568744
36613617.702965915233-4.70296591523311
37621622.72901586869-1.72901586868954
38612614.768479643678-2.76847964367835
39611611.976710575761-0.976710575761217
40609607.2940521304461.70594786955371
41631620.66292437849710.3370756215032
42632629.0107594955282.98924050447249
43624616.0714258158657.92857418413473
44596594.9377520486621.06224795133801
45584590.251078380621-6.25107838062115
46587600.374618770544-13.3746187705436
47581589.26456046195-8.26456046194949
48574585.445994867391-11.4459948673914
49593588.9309789730864.06902102691436
50582582.353628527687-0.353628527687079
51571581.288888234256-10.2888882342560
52572573.811586256488-1.81158625648811
53594590.1815908948843.81840910511585
54588590.708527852677-2.70852785267698
55571577.387330105693-6.38733010569263
56546545.0088637014340.991136298566403
57535534.6545624912430.345437508756618
58537542.125238354085-5.12523835408547
59527536.466258996523-9.46625899652327
60515529.3010542324-14.3010542324005
61545539.7164581459535.2835418540468
62538530.009595872467.9904041275397
63520525.700561661114-5.70056166111408
64523524.415880544631-1.41588054463057
65541543.589485776745-2.58948577674505
66529536.795585282875-7.79558528287532
67504518.245669553395-14.2456695533951
68473485.823672713266-12.8236727132661
69455467.897863252303-12.8978632523032
70458464.848133213476-6.84813321347644
71450454.016380624446-4.01638062444562
72442444.467956419912-2.46795641991201
73469469.823245445614-0.823245445613793
74455457.587328167737-2.58732816773681
75439438.9738928201470.0261071798527723
76443440.8208527744472.17914722555275
77461459.1238417445161.87615825548397
78451449.5516384924671.44836150753252
79425429.684999153194-4.6849991531945
80393400.962993010947-7.96299301094672
81366384.050730431177-18.050730431177
82359381.388277941086-22.3882779410861
83351364.389423828184-13.3894238281839
84343350.207678811148-7.20767881114836
85366372.766108399427-6.76610839942651
86355355.077827879593-0.0778278795927463
87344337.1248065079626.87519349203808
88351341.3150056751599.6849943248414
89367360.9731372766556.02686272334518
90364351.41204545642212.5879545435781
91353331.34145538579521.6585446142055
92313311.0067880878811.99321191211931
93278291.997389437932-13.9973894379323
94274288.311630089255-14.3116300892552
95261280.011749786204-19.0117497862039
96255267.105356053602-12.1053560536021
97274287.725814278332-13.7258142783319
98262270.761084446498-8.76108444649827
99265252.75965415639612.2403458436038
100274260.35635501474813.6436449852524
101291279.12988579283611.8701142071636
102289275.63373501941513.3662649805847
103277261.05068242130315.9493175786973
104238226.44758557729711.5524144227035
105203201.8432493302031.15675066979736
106198204.489936299126-6.48993629912613
107190197.127298964809-7.12729896480883
108187193.973245567061-6.97324556706093
109201216.677752309969-15.6777523099687
110181202.725972776541-21.7259727765409
111181192.349277495900-11.3492774958997
112196191.0522187133094.94778128669063
113207204.9454765515422.05452344845781
114202197.7883498902964.21165010970421
115186180.2233350135395.7766649864605
116154137.84453409613516.1554659038653
117120108.10382581868211.8961741813175
118107110.026049167775-3.02604916777503
11999103.177436709157-4.17743670915672
120100100.868525698083-0.868525698082635







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121120.642532975459103.13276033637138.152305614547
122109.65285971650890.5537577689906128.751961664026
123114.96050186289394.224965754181135.696037971606
124128.872846687314106.455213266732151.290480107895
125139.845856114932115.701766789424163.989945440441
126133.881766013898107.968051420728159.795480607068
127116.16848923119088.4430710211985143.893907441181
12878.051103956258848.4729102177818107.629297694736
12939.26918742867617.7980791463627270.7402957109895
13027.3047357634337-6.098557678118260.7080292049856
13120.8896174586161-14.484320352599756.2635552698318
13222.2237279204456-15.158552773353459.6060086142446

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 120.642532975459 & 103.13276033637 & 138.152305614547 \tabularnewline
122 & 109.652859716508 & 90.5537577689906 & 128.751961664026 \tabularnewline
123 & 114.960501862893 & 94.224965754181 & 135.696037971606 \tabularnewline
124 & 128.872846687314 & 106.455213266732 & 151.290480107895 \tabularnewline
125 & 139.845856114932 & 115.701766789424 & 163.989945440441 \tabularnewline
126 & 133.881766013898 & 107.968051420728 & 159.795480607068 \tabularnewline
127 & 116.168489231190 & 88.4430710211985 & 143.893907441181 \tabularnewline
128 & 78.0511039562588 & 48.4729102177818 & 107.629297694736 \tabularnewline
129 & 39.2691874286761 & 7.79807914636272 & 70.7402957109895 \tabularnewline
130 & 27.3047357634337 & -6.0985576781182 & 60.7080292049856 \tabularnewline
131 & 20.8896174586161 & -14.4843203525997 & 56.2635552698318 \tabularnewline
132 & 22.2237279204456 & -15.1585527733534 & 59.6060086142446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79337&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]121[/C][C]120.642532975459[/C][C]103.13276033637[/C][C]138.152305614547[/C][/ROW]
[ROW][C]122[/C][C]109.652859716508[/C][C]90.5537577689906[/C][C]128.751961664026[/C][/ROW]
[ROW][C]123[/C][C]114.960501862893[/C][C]94.224965754181[/C][C]135.696037971606[/C][/ROW]
[ROW][C]124[/C][C]128.872846687314[/C][C]106.455213266732[/C][C]151.290480107895[/C][/ROW]
[ROW][C]125[/C][C]139.845856114932[/C][C]115.701766789424[/C][C]163.989945440441[/C][/ROW]
[ROW][C]126[/C][C]133.881766013898[/C][C]107.968051420728[/C][C]159.795480607068[/C][/ROW]
[ROW][C]127[/C][C]116.168489231190[/C][C]88.4430710211985[/C][C]143.893907441181[/C][/ROW]
[ROW][C]128[/C][C]78.0511039562588[/C][C]48.4729102177818[/C][C]107.629297694736[/C][/ROW]
[ROW][C]129[/C][C]39.2691874286761[/C][C]7.79807914636272[/C][C]70.7402957109895[/C][/ROW]
[ROW][C]130[/C][C]27.3047357634337[/C][C]-6.0985576781182[/C][C]60.7080292049856[/C][/ROW]
[ROW][C]131[/C][C]20.8896174586161[/C][C]-14.4843203525997[/C][C]56.2635552698318[/C][/ROW]
[ROW][C]132[/C][C]22.2237279204456[/C][C]-15.1585527733534[/C][C]59.6060086142446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79337&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79337&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
121120.642532975459103.13276033637138.152305614547
122109.65285971650890.5537577689906128.751961664026
123114.96050186289394.224965754181135.696037971606
124128.872846687314106.455213266732151.290480107895
125139.845856114932115.701766789424163.989945440441
126133.881766013898107.968051420728159.795480607068
127116.16848923119088.4430710211985143.893907441181
12878.051103956258848.4729102177818107.629297694736
12939.26918742867617.7980791463627270.7402957109895
13027.3047357634337-6.098557678118260.7080292049856
13120.8896174586161-14.484320352599756.2635552698318
13222.2237279204456-15.158552773353459.6060086142446



Parameters (Session):
par1 = additive ; par2 = 12 ;
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=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')