Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 02 Jun 2010 10:48:38 +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/Jun/02/t12754758028ww62ssmwrd1fz6.htm/, Retrieved Thu, 25 Apr 2024 00:59:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77259, Retrieved Thu, 25 Apr 2024 00:59:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKdGP2W62
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Werkloosheid vrouwen] [2010-06-02 10:48:38] [4942f64bbdc4cce21b299a740a533758] [Current]
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Dataseries X:
43657
42811
45419
50846
54500
51035
38675
36214
38763
39486
40540
40719
40471
39947
42683
47090
51520
48823
36122
33812
36928
37737
40123
41713
42025
42169
46352
50939
56139
52713
38532
37860
40880
41988
44576
46728
46913
49357
54709
60819
63695
60109
45544
43596
44431
45575
47980
49211
51374
52954
57529
62960
64530
61008
44964
43480
45429
47616
49364
51010
53188
55317
60106
65845
67028
63617
47605
45844
47925
50156
52258
53476
54327
55214
59347
64718
66208
62744
45587
43684
45676
47088
48907
50964
51798




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server184.73.236.201 @ 184.73.236.201

\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 & 184.73.236.201 @ 184.73.236.201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77259&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]184.73.236.201 @ 184.73.236.201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77259&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77259&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 Server184.73.236.201 @ 184.73.236.201







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.670544711383677
beta0.0178522796328237
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.670544711383677 \tabularnewline
beta & 0.0178522796328237 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77259&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]0.670544711383677[/C][/ROW]
[ROW][C]beta[/C][C]0.0178522796328237[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77259&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77259&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
alpha0.670544711383677
beta0.0178522796328237
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134047141770.7616436247-1299.76164362465
143994740363.3639934426-416.363993442552
154268342785.1307600934-102.130760093416
164709047045.091506843744.908493156312
175152051340.6599528949179.340047105114
184882348479.7124150463343.287584953723
193612236571.43196847-449.431968469959
203381233974.1874547103-162.187454710329
213692836243.6064262329684.393573767105
223773737424.9263177328312.073682267161
234012338692.60506821751430.39493178254
244171339844.4915812121868.50841878798
254202540448.30265192171576.69734807833
264216941320.5907170226848.409282977416
274635244924.08620513351427.91379486646
285093950717.4047142186221.595285781448
295613955668.6199794515470.380020548502
305271352947.2538120532-234.253812053248
313853239483.6273427048-951.62734270483
323786036568.02017691451291.97982308552
334088040495.9716757207384.02832427925
344198841535.0457224968452.954277503159
354457643535.958442921040.04155707997
364672844705.74404759162022.25595240844
374691345343.43131142961569.56868857041
384935746038.70354980393318.29645019605
395470952106.14740201822602.85259798176
406081959200.57867426221618.42132573779
416369566298.6953543585-2603.69535435853
426010960973.395887549-864.395887548992
434554444999.7936439552544.206356044837
444359643687.6035908299-91.6035908299382
454443146941.5469237097-2510.54692370973
464557546242.6361075631-667.636107563114
474798047934.591765982545.4082340175082
484921148870.8720799706340.127920029357
495137448220.78347529083153.2165247092
505295450580.68265492882373.31734507121
515752956008.15758278321520.84241721684
526296062297.4002375433662.599762456652
536453067517.7939917282-2987.79399172822
546100862445.9883563443-1437.98835634426
554496446224.5442533472-1260.54425334724
564348043493.5268955971-13.5268955970678
574542945960.4182033567-531.418203356683
584761647254.3992047989361.600795201099
594936450004.9036476862-640.903647686166
605101050636.319514932373.680485068042
615318850917.77158229932270.22841770069
625531752417.34561466582899.65438533419
636010658021.70737394852084.29262605146
646584564595.59020096591249.4097990341
656702869151.2906448299-2123.29064482992
666361765079.4026750192-1462.40267501917
674760548155.3565773381-550.356577338142
684584446259.8592872908-415.859287290848
694792548455.7095054046-530.709505404608
705015650198.2509360205-42.2509360204567
715225852499.2838760528-241.283876052825
725347653859.4154956275-383.415495627538
735432754302.727957592724.2720424072904
745521454479.1556037366734.844396263397
755934758305.98733700971041.01266299035
766471863776.1518573086941.84814269143
776620866904.63716325-696.637163250009
786274463998.5568481841-1254.55684818411
794558747610.4973492564-2023.49734925642
804368444781.6865246547-1097.68652465472
814567646344.726801493-668.726801493023
824708848015.2875560134-927.287556013362
834890749475.1608830378-568.160883037788
845096450416.6699681876547.330031812446
855179851523.3285137023274.671486297681

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 40471 & 41770.7616436247 & -1299.76164362465 \tabularnewline
14 & 39947 & 40363.3639934426 & -416.363993442552 \tabularnewline
15 & 42683 & 42785.1307600934 & -102.130760093416 \tabularnewline
16 & 47090 & 47045.0915068437 & 44.908493156312 \tabularnewline
17 & 51520 & 51340.6599528949 & 179.340047105114 \tabularnewline
18 & 48823 & 48479.7124150463 & 343.287584953723 \tabularnewline
19 & 36122 & 36571.43196847 & -449.431968469959 \tabularnewline
20 & 33812 & 33974.1874547103 & -162.187454710329 \tabularnewline
21 & 36928 & 36243.6064262329 & 684.393573767105 \tabularnewline
22 & 37737 & 37424.9263177328 & 312.073682267161 \tabularnewline
23 & 40123 & 38692.6050682175 & 1430.39493178254 \tabularnewline
24 & 41713 & 39844.491581212 & 1868.50841878798 \tabularnewline
25 & 42025 & 40448.3026519217 & 1576.69734807833 \tabularnewline
26 & 42169 & 41320.5907170226 & 848.409282977416 \tabularnewline
27 & 46352 & 44924.0862051335 & 1427.91379486646 \tabularnewline
28 & 50939 & 50717.4047142186 & 221.595285781448 \tabularnewline
29 & 56139 & 55668.6199794515 & 470.380020548502 \tabularnewline
30 & 52713 & 52947.2538120532 & -234.253812053248 \tabularnewline
31 & 38532 & 39483.6273427048 & -951.62734270483 \tabularnewline
32 & 37860 & 36568.0201769145 & 1291.97982308552 \tabularnewline
33 & 40880 & 40495.9716757207 & 384.02832427925 \tabularnewline
34 & 41988 & 41535.0457224968 & 452.954277503159 \tabularnewline
35 & 44576 & 43535.95844292 & 1040.04155707997 \tabularnewline
36 & 46728 & 44705.7440475916 & 2022.25595240844 \tabularnewline
37 & 46913 & 45343.4313114296 & 1569.56868857041 \tabularnewline
38 & 49357 & 46038.7035498039 & 3318.29645019605 \tabularnewline
39 & 54709 & 52106.1474020182 & 2602.85259798176 \tabularnewline
40 & 60819 & 59200.5786742622 & 1618.42132573779 \tabularnewline
41 & 63695 & 66298.6953543585 & -2603.69535435853 \tabularnewline
42 & 60109 & 60973.395887549 & -864.395887548992 \tabularnewline
43 & 45544 & 44999.7936439552 & 544.206356044837 \tabularnewline
44 & 43596 & 43687.6035908299 & -91.6035908299382 \tabularnewline
45 & 44431 & 46941.5469237097 & -2510.54692370973 \tabularnewline
46 & 45575 & 46242.6361075631 & -667.636107563114 \tabularnewline
47 & 47980 & 47934.5917659825 & 45.4082340175082 \tabularnewline
48 & 49211 & 48870.8720799706 & 340.127920029357 \tabularnewline
49 & 51374 & 48220.7834752908 & 3153.2165247092 \tabularnewline
50 & 52954 & 50580.6826549288 & 2373.31734507121 \tabularnewline
51 & 57529 & 56008.1575827832 & 1520.84241721684 \tabularnewline
52 & 62960 & 62297.4002375433 & 662.599762456652 \tabularnewline
53 & 64530 & 67517.7939917282 & -2987.79399172822 \tabularnewline
54 & 61008 & 62445.9883563443 & -1437.98835634426 \tabularnewline
55 & 44964 & 46224.5442533472 & -1260.54425334724 \tabularnewline
56 & 43480 & 43493.5268955971 & -13.5268955970678 \tabularnewline
57 & 45429 & 45960.4182033567 & -531.418203356683 \tabularnewline
58 & 47616 & 47254.3992047989 & 361.600795201099 \tabularnewline
59 & 49364 & 50004.9036476862 & -640.903647686166 \tabularnewline
60 & 51010 & 50636.319514932 & 373.680485068042 \tabularnewline
61 & 53188 & 50917.7715822993 & 2270.22841770069 \tabularnewline
62 & 55317 & 52417.3456146658 & 2899.65438533419 \tabularnewline
63 & 60106 & 58021.7073739485 & 2084.29262605146 \tabularnewline
64 & 65845 & 64595.5902009659 & 1249.4097990341 \tabularnewline
65 & 67028 & 69151.2906448299 & -2123.29064482992 \tabularnewline
66 & 63617 & 65079.4026750192 & -1462.40267501917 \tabularnewline
67 & 47605 & 48155.3565773381 & -550.356577338142 \tabularnewline
68 & 45844 & 46259.8592872908 & -415.859287290848 \tabularnewline
69 & 47925 & 48455.7095054046 & -530.709505404608 \tabularnewline
70 & 50156 & 50198.2509360205 & -42.2509360204567 \tabularnewline
71 & 52258 & 52499.2838760528 & -241.283876052825 \tabularnewline
72 & 53476 & 53859.4154956275 & -383.415495627538 \tabularnewline
73 & 54327 & 54302.7279575927 & 24.2720424072904 \tabularnewline
74 & 55214 & 54479.1556037366 & 734.844396263397 \tabularnewline
75 & 59347 & 58305.9873370097 & 1041.01266299035 \tabularnewline
76 & 64718 & 63776.1518573086 & 941.84814269143 \tabularnewline
77 & 66208 & 66904.63716325 & -696.637163250009 \tabularnewline
78 & 62744 & 63998.5568481841 & -1254.55684818411 \tabularnewline
79 & 45587 & 47610.4973492564 & -2023.49734925642 \tabularnewline
80 & 43684 & 44781.6865246547 & -1097.68652465472 \tabularnewline
81 & 45676 & 46344.726801493 & -668.726801493023 \tabularnewline
82 & 47088 & 48015.2875560134 & -927.287556013362 \tabularnewline
83 & 48907 & 49475.1608830378 & -568.160883037788 \tabularnewline
84 & 50964 & 50416.6699681876 & 547.330031812446 \tabularnewline
85 & 51798 & 51523.3285137023 & 274.671486297681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77259&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]40471[/C][C]41770.7616436247[/C][C]-1299.76164362465[/C][/ROW]
[ROW][C]14[/C][C]39947[/C][C]40363.3639934426[/C][C]-416.363993442552[/C][/ROW]
[ROW][C]15[/C][C]42683[/C][C]42785.1307600934[/C][C]-102.130760093416[/C][/ROW]
[ROW][C]16[/C][C]47090[/C][C]47045.0915068437[/C][C]44.908493156312[/C][/ROW]
[ROW][C]17[/C][C]51520[/C][C]51340.6599528949[/C][C]179.340047105114[/C][/ROW]
[ROW][C]18[/C][C]48823[/C][C]48479.7124150463[/C][C]343.287584953723[/C][/ROW]
[ROW][C]19[/C][C]36122[/C][C]36571.43196847[/C][C]-449.431968469959[/C][/ROW]
[ROW][C]20[/C][C]33812[/C][C]33974.1874547103[/C][C]-162.187454710329[/C][/ROW]
[ROW][C]21[/C][C]36928[/C][C]36243.6064262329[/C][C]684.393573767105[/C][/ROW]
[ROW][C]22[/C][C]37737[/C][C]37424.9263177328[/C][C]312.073682267161[/C][/ROW]
[ROW][C]23[/C][C]40123[/C][C]38692.6050682175[/C][C]1430.39493178254[/C][/ROW]
[ROW][C]24[/C][C]41713[/C][C]39844.491581212[/C][C]1868.50841878798[/C][/ROW]
[ROW][C]25[/C][C]42025[/C][C]40448.3026519217[/C][C]1576.69734807833[/C][/ROW]
[ROW][C]26[/C][C]42169[/C][C]41320.5907170226[/C][C]848.409282977416[/C][/ROW]
[ROW][C]27[/C][C]46352[/C][C]44924.0862051335[/C][C]1427.91379486646[/C][/ROW]
[ROW][C]28[/C][C]50939[/C][C]50717.4047142186[/C][C]221.595285781448[/C][/ROW]
[ROW][C]29[/C][C]56139[/C][C]55668.6199794515[/C][C]470.380020548502[/C][/ROW]
[ROW][C]30[/C][C]52713[/C][C]52947.2538120532[/C][C]-234.253812053248[/C][/ROW]
[ROW][C]31[/C][C]38532[/C][C]39483.6273427048[/C][C]-951.62734270483[/C][/ROW]
[ROW][C]32[/C][C]37860[/C][C]36568.0201769145[/C][C]1291.97982308552[/C][/ROW]
[ROW][C]33[/C][C]40880[/C][C]40495.9716757207[/C][C]384.02832427925[/C][/ROW]
[ROW][C]34[/C][C]41988[/C][C]41535.0457224968[/C][C]452.954277503159[/C][/ROW]
[ROW][C]35[/C][C]44576[/C][C]43535.95844292[/C][C]1040.04155707997[/C][/ROW]
[ROW][C]36[/C][C]46728[/C][C]44705.7440475916[/C][C]2022.25595240844[/C][/ROW]
[ROW][C]37[/C][C]46913[/C][C]45343.4313114296[/C][C]1569.56868857041[/C][/ROW]
[ROW][C]38[/C][C]49357[/C][C]46038.7035498039[/C][C]3318.29645019605[/C][/ROW]
[ROW][C]39[/C][C]54709[/C][C]52106.1474020182[/C][C]2602.85259798176[/C][/ROW]
[ROW][C]40[/C][C]60819[/C][C]59200.5786742622[/C][C]1618.42132573779[/C][/ROW]
[ROW][C]41[/C][C]63695[/C][C]66298.6953543585[/C][C]-2603.69535435853[/C][/ROW]
[ROW][C]42[/C][C]60109[/C][C]60973.395887549[/C][C]-864.395887548992[/C][/ROW]
[ROW][C]43[/C][C]45544[/C][C]44999.7936439552[/C][C]544.206356044837[/C][/ROW]
[ROW][C]44[/C][C]43596[/C][C]43687.6035908299[/C][C]-91.6035908299382[/C][/ROW]
[ROW][C]45[/C][C]44431[/C][C]46941.5469237097[/C][C]-2510.54692370973[/C][/ROW]
[ROW][C]46[/C][C]45575[/C][C]46242.6361075631[/C][C]-667.636107563114[/C][/ROW]
[ROW][C]47[/C][C]47980[/C][C]47934.5917659825[/C][C]45.4082340175082[/C][/ROW]
[ROW][C]48[/C][C]49211[/C][C]48870.8720799706[/C][C]340.127920029357[/C][/ROW]
[ROW][C]49[/C][C]51374[/C][C]48220.7834752908[/C][C]3153.2165247092[/C][/ROW]
[ROW][C]50[/C][C]52954[/C][C]50580.6826549288[/C][C]2373.31734507121[/C][/ROW]
[ROW][C]51[/C][C]57529[/C][C]56008.1575827832[/C][C]1520.84241721684[/C][/ROW]
[ROW][C]52[/C][C]62960[/C][C]62297.4002375433[/C][C]662.599762456652[/C][/ROW]
[ROW][C]53[/C][C]64530[/C][C]67517.7939917282[/C][C]-2987.79399172822[/C][/ROW]
[ROW][C]54[/C][C]61008[/C][C]62445.9883563443[/C][C]-1437.98835634426[/C][/ROW]
[ROW][C]55[/C][C]44964[/C][C]46224.5442533472[/C][C]-1260.54425334724[/C][/ROW]
[ROW][C]56[/C][C]43480[/C][C]43493.5268955971[/C][C]-13.5268955970678[/C][/ROW]
[ROW][C]57[/C][C]45429[/C][C]45960.4182033567[/C][C]-531.418203356683[/C][/ROW]
[ROW][C]58[/C][C]47616[/C][C]47254.3992047989[/C][C]361.600795201099[/C][/ROW]
[ROW][C]59[/C][C]49364[/C][C]50004.9036476862[/C][C]-640.903647686166[/C][/ROW]
[ROW][C]60[/C][C]51010[/C][C]50636.319514932[/C][C]373.680485068042[/C][/ROW]
[ROW][C]61[/C][C]53188[/C][C]50917.7715822993[/C][C]2270.22841770069[/C][/ROW]
[ROW][C]62[/C][C]55317[/C][C]52417.3456146658[/C][C]2899.65438533419[/C][/ROW]
[ROW][C]63[/C][C]60106[/C][C]58021.7073739485[/C][C]2084.29262605146[/C][/ROW]
[ROW][C]64[/C][C]65845[/C][C]64595.5902009659[/C][C]1249.4097990341[/C][/ROW]
[ROW][C]65[/C][C]67028[/C][C]69151.2906448299[/C][C]-2123.29064482992[/C][/ROW]
[ROW][C]66[/C][C]63617[/C][C]65079.4026750192[/C][C]-1462.40267501917[/C][/ROW]
[ROW][C]67[/C][C]47605[/C][C]48155.3565773381[/C][C]-550.356577338142[/C][/ROW]
[ROW][C]68[/C][C]45844[/C][C]46259.8592872908[/C][C]-415.859287290848[/C][/ROW]
[ROW][C]69[/C][C]47925[/C][C]48455.7095054046[/C][C]-530.709505404608[/C][/ROW]
[ROW][C]70[/C][C]50156[/C][C]50198.2509360205[/C][C]-42.2509360204567[/C][/ROW]
[ROW][C]71[/C][C]52258[/C][C]52499.2838760528[/C][C]-241.283876052825[/C][/ROW]
[ROW][C]72[/C][C]53476[/C][C]53859.4154956275[/C][C]-383.415495627538[/C][/ROW]
[ROW][C]73[/C][C]54327[/C][C]54302.7279575927[/C][C]24.2720424072904[/C][/ROW]
[ROW][C]74[/C][C]55214[/C][C]54479.1556037366[/C][C]734.844396263397[/C][/ROW]
[ROW][C]75[/C][C]59347[/C][C]58305.9873370097[/C][C]1041.01266299035[/C][/ROW]
[ROW][C]76[/C][C]64718[/C][C]63776.1518573086[/C][C]941.84814269143[/C][/ROW]
[ROW][C]77[/C][C]66208[/C][C]66904.63716325[/C][C]-696.637163250009[/C][/ROW]
[ROW][C]78[/C][C]62744[/C][C]63998.5568481841[/C][C]-1254.55684818411[/C][/ROW]
[ROW][C]79[/C][C]45587[/C][C]47610.4973492564[/C][C]-2023.49734925642[/C][/ROW]
[ROW][C]80[/C][C]43684[/C][C]44781.6865246547[/C][C]-1097.68652465472[/C][/ROW]
[ROW][C]81[/C][C]45676[/C][C]46344.726801493[/C][C]-668.726801493023[/C][/ROW]
[ROW][C]82[/C][C]47088[/C][C]48015.2875560134[/C][C]-927.287556013362[/C][/ROW]
[ROW][C]83[/C][C]48907[/C][C]49475.1608830378[/C][C]-568.160883037788[/C][/ROW]
[ROW][C]84[/C][C]50964[/C][C]50416.6699681876[/C][C]547.330031812446[/C][/ROW]
[ROW][C]85[/C][C]51798[/C][C]51523.3285137023[/C][C]274.671486297681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77259&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77259&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
134047141770.7616436247-1299.76164362465
143994740363.3639934426-416.363993442552
154268342785.1307600934-102.130760093416
164709047045.091506843744.908493156312
175152051340.6599528949179.340047105114
184882348479.7124150463343.287584953723
193612236571.43196847-449.431968469959
203381233974.1874547103-162.187454710329
213692836243.6064262329684.393573767105
223773737424.9263177328312.073682267161
234012338692.60506821751430.39493178254
244171339844.4915812121868.50841878798
254202540448.30265192171576.69734807833
264216941320.5907170226848.409282977416
274635244924.08620513351427.91379486646
285093950717.4047142186221.595285781448
295613955668.6199794515470.380020548502
305271352947.2538120532-234.253812053248
313853239483.6273427048-951.62734270483
323786036568.02017691451291.97982308552
334088040495.9716757207384.02832427925
344198841535.0457224968452.954277503159
354457643535.958442921040.04155707997
364672844705.74404759162022.25595240844
374691345343.43131142961569.56868857041
384935746038.70354980393318.29645019605
395470952106.14740201822602.85259798176
406081959200.57867426221618.42132573779
416369566298.6953543585-2603.69535435853
426010960973.395887549-864.395887548992
434554444999.7936439552544.206356044837
444359643687.6035908299-91.6035908299382
454443146941.5469237097-2510.54692370973
464557546242.6361075631-667.636107563114
474798047934.591765982545.4082340175082
484921148870.8720799706340.127920029357
495137448220.78347529083153.2165247092
505295450580.68265492882373.31734507121
515752956008.15758278321520.84241721684
526296062297.4002375433662.599762456652
536453067517.7939917282-2987.79399172822
546100862445.9883563443-1437.98835634426
554496446224.5442533472-1260.54425334724
564348043493.5268955971-13.5268955970678
574542945960.4182033567-531.418203356683
584761647254.3992047989361.600795201099
594936450004.9036476862-640.903647686166
605101050636.319514932373.680485068042
615318850917.77158229932270.22841770069
625531752417.34561466582899.65438533419
636010658021.70737394852084.29262605146
646584564595.59020096591249.4097990341
656702869151.2906448299-2123.29064482992
666361765079.4026750192-1462.40267501917
674760548155.3565773381-550.356577338142
684584446259.8592872908-415.859287290848
694792548455.7095054046-530.709505404608
705015650198.2509360205-42.2509360204567
715225852499.2838760528-241.283876052825
725347653859.4154956275-383.415495627538
735432754302.727957592724.2720424072904
745521454479.1556037366734.844396263397
755934758305.98733700971041.01266299035
766471863776.1518573086941.84814269143
776620866904.63716325-696.637163250009
786274463998.5568481841-1254.55684818411
794558747610.4973492564-2023.49734925642
804368444781.6865246547-1097.68652465472
814567646344.726801493-668.726801493023
824708848015.2875560134-927.287556013362
834890749475.1608830378-568.160883037788
845096450416.6699681876547.330031812446
855179851523.3285137023274.671486297681







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8652030.24288067549423.472104570554637.0136567794
8755201.331146767351982.622041614358420.0402519204
8859528.119195060355684.59576391963371.6426262016
8961235.782357019856889.675646613365581.8890674262
9058724.547206180854117.855275435663331.239136926
9143868.078972962139757.86352985547978.2944160691
9242711.74114191738273.047356988947150.4349268451
9345079.794004639240060.19698123850099.3910280404
9447074.600343503941506.617766676852642.582920331
9549275.213938320143135.875209251755414.5526673885
9650986.613935645344324.592178837557648.6356924532
9751639.701386451545071.862818827758207.5399540754

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 52030.242880675 & 49423.4721045705 & 54637.0136567794 \tabularnewline
87 & 55201.3311467673 & 51982.6220416143 & 58420.0402519204 \tabularnewline
88 & 59528.1191950603 & 55684.595763919 & 63371.6426262016 \tabularnewline
89 & 61235.7823570198 & 56889.6756466133 & 65581.8890674262 \tabularnewline
90 & 58724.5472061808 & 54117.8552754356 & 63331.239136926 \tabularnewline
91 & 43868.0789729621 & 39757.863529855 & 47978.2944160691 \tabularnewline
92 & 42711.741141917 & 38273.0473569889 & 47150.4349268451 \tabularnewline
93 & 45079.7940046392 & 40060.196981238 & 50099.3910280404 \tabularnewline
94 & 47074.6003435039 & 41506.6177666768 & 52642.582920331 \tabularnewline
95 & 49275.2139383201 & 43135.8752092517 & 55414.5526673885 \tabularnewline
96 & 50986.6139356453 & 44324.5921788375 & 57648.6356924532 \tabularnewline
97 & 51639.7013864515 & 45071.8628188277 & 58207.5399540754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77259&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]86[/C][C]52030.242880675[/C][C]49423.4721045705[/C][C]54637.0136567794[/C][/ROW]
[ROW][C]87[/C][C]55201.3311467673[/C][C]51982.6220416143[/C][C]58420.0402519204[/C][/ROW]
[ROW][C]88[/C][C]59528.1191950603[/C][C]55684.595763919[/C][C]63371.6426262016[/C][/ROW]
[ROW][C]89[/C][C]61235.7823570198[/C][C]56889.6756466133[/C][C]65581.8890674262[/C][/ROW]
[ROW][C]90[/C][C]58724.5472061808[/C][C]54117.8552754356[/C][C]63331.239136926[/C][/ROW]
[ROW][C]91[/C][C]43868.0789729621[/C][C]39757.863529855[/C][C]47978.2944160691[/C][/ROW]
[ROW][C]92[/C][C]42711.741141917[/C][C]38273.0473569889[/C][C]47150.4349268451[/C][/ROW]
[ROW][C]93[/C][C]45079.7940046392[/C][C]40060.196981238[/C][C]50099.3910280404[/C][/ROW]
[ROW][C]94[/C][C]47074.6003435039[/C][C]41506.6177666768[/C][C]52642.582920331[/C][/ROW]
[ROW][C]95[/C][C]49275.2139383201[/C][C]43135.8752092517[/C][C]55414.5526673885[/C][/ROW]
[ROW][C]96[/C][C]50986.6139356453[/C][C]44324.5921788375[/C][C]57648.6356924532[/C][/ROW]
[ROW][C]97[/C][C]51639.7013864515[/C][C]45071.8628188277[/C][C]58207.5399540754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77259&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77259&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
8652030.24288067549423.472104570554637.0136567794
8755201.331146767351982.622041614358420.0402519204
8859528.119195060355684.59576391963371.6426262016
8961235.782357019856889.675646613365581.8890674262
9058724.547206180854117.855275435663331.239136926
9143868.078972962139757.86352985547978.2944160691
9242711.74114191738273.047356988947150.4349268451
9345079.794004639240060.19698123850099.3910280404
9447074.600343503941506.617766676852642.582920331
9549275.213938320143135.875209251755414.5526673885
9650986.613935645344324.592178837557648.6356924532
9751639.701386451545071.862818827758207.5399540754



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=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')