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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 May 2008 12:32:54 -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/2008/May/28/t1211999665cz381a4e8h64249.htm/, Retrieved Tue, 14 May 2024 07:51:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13464, Retrieved Tue, 14 May 2024 07:51:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Shari Van Elsen-E...] [2008-05-28 18:32:54] [1e6b76cbac3599a7b5e2d7b56a39d7dc] [Current]
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Dataseries X:
516.922
514.258
509.846
527.070
541.657
564.591
555.362
498.662
511.038
525.919
531.673
548.854
560.576
557.274
565.742
587.625
619.916
625.809
619.567
572.942
572.775
574.205
579.799
590.072
593.408
597.141
595.404
612.117
628.232
628.884
620.735
569.028
567.456
573.100
584.428
589.379
590.865
595.454
594.167
611.324
612.613
610.763
593.530
542.722
536.662
543.599
555.332
560.854
562.325
554.788
547.344
565.464
577.992
579.714
569.323
506.971
500.857
509.127
509.933
517.009
519.164
512.238
509.239
518.585
522.975
525.192
516.847
455.626
454.724
461.251
470.439
474.605
476.049
471.067
470.984
502.831
512.927
509.673
484.015
431.328
436.087
442.867
447.988
460.070
467.037
460.170
464.196
485.025
501.492
520.564
488.180
439.148
441.977
456.608
461.935
480.961
492.865




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13464&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13464&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13464&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.888914021311308
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.888914021311308 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13464&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]0.888914021311308[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13464&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13464&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
alpha0.888914021311308
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13560.576535.63162394323624.9443760567635
14557.274548.7328212396228.54117876037787
15565.742559.1258197982486.6161802017516
16587.625582.3057434804415.31925651955896
17619.916615.3079385169624.60806148303811
18625.809621.5744423136324.23455768636757
19619.567616.0111833484293.55581665157058
20572.942569.5178736272233.42412637277732
21572.775569.497585904063.27741409594034
22574.205571.5845085809182.62049141908244
23579.799578.1409001460661.65809985393400
24590.072589.4131833549620.65881664503786
25593.408600.145118468587-6.73711846858725
26597.141583.26202583999813.8789741600016
27595.404598.186025223382-2.78202522338177
28612.117612.867682291489-0.750682291488602
29628.232640.395219813697-12.1632198136972
30628.884631.712005475546-2.82800547554643
31620.735619.7953364771950.939663522805176
32569.028570.961862614428-1.93386261442754
33567.456566.1624856776491.29351432235148
34573.1566.4129171304056.68708286959463
35584.428576.4772506459627.9507493540375
36589.379593.232151873451-3.853151873451
37590.865599.131750216861-8.26675021686117
38595.454583.17910530617212.2748946938277
39594.167594.826412538341-0.659412538341257
40611.324611.620543501636-0.296543501635597
41612.613638.28399846179-25.6709984617898
42610.763618.630541707602-7.86754170760219
43593.53602.652693489727-9.12269348972688
44542.722544.555440927838-1.83344092783761
45536.662540.203846561932-3.54184656193149
46543.599536.7552077672446.84379223275607
47555.332547.0992180611468.23278193885358
48560.854562.793574087544-1.93957408754432
49562.325569.9038896642-7.57888966420023
50554.788556.844582372258-2.05658237225805
51547.344554.315618516736-6.97161851673627
52565.464565.539050742508-0.0750507425084379
53577.992589.580647558929-11.5886475589292
54579.714584.422904392901-4.70890439290088
55569.323571.113383408181-1.79038340818056
56506.971520.343657841127-13.3726578411266
57500.857505.544911854185-4.68791185418473
58509.127502.231218401696.89578159830972
59509.933512.775740052483-2.84274005248290
60517.009517.494903162678-0.485903162677914
61519.164525.270958316853-6.10695831685291
62512.238514.13352234812-1.89552234812038
63509.239511.201735405928-1.96273540592773
64518.585527.6437460408-9.05874604079986
65522.975542.420610972802-19.4456109728018
66525.192531.042945865977-5.85094586597734
67516.847517.042454962831-0.195454962831377
68455.626466.403855363012-10.7778553630118
69454.724454.876419189022-0.152419189021543
70461.251456.8811746841454.36982531585477
71470.439464.0985251696856.3404748303152
72474.605477.242588282427-2.63758828242732
73476.049482.481559951146-6.4325599511456
74471.067471.5225236106-0.455523610599926
75470.984469.8633053085531.12069469144740
76502.831488.25795290455514.5730470954454
77512.927522.887615047615-9.96061504761451
78509.673521.451472489106-11.7784724891062
79484.015502.810165800906-18.7951658009059
80431.328434.462466139456-3.13446613945638
81436.087430.9096827930065.17731720699373
82442.867438.1544736571354.71252634286515
83447.988445.8953674206682.09263257933196
84460.07454.2661270685855.80387293141496
85467.037466.5872638287280.44973617127215
86460.17462.409961941763-2.23996194176311
87464.196459.3396271396894.85637286031056
88485.025482.5493391715642.47566082843611
89501.492503.700119170681-2.20811917068079
90520.564508.95334042433211.6106595756676
91488.18510.323504931112-22.1435049311117
92439.148440.739103817559-1.59110381755869
93441.977439.4815594666962.49544053330413
94456.608444.29076080412712.3172391958732
95461.935458.5005569879633.43444301203732
96480.961468.47633751011312.4846624898867
97492.865486.1413522601786.72364773982179

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 560.576 & 535.631623943236 & 24.9443760567635 \tabularnewline
14 & 557.274 & 548.732821239622 & 8.54117876037787 \tabularnewline
15 & 565.742 & 559.125819798248 & 6.6161802017516 \tabularnewline
16 & 587.625 & 582.305743480441 & 5.31925651955896 \tabularnewline
17 & 619.916 & 615.307938516962 & 4.60806148303811 \tabularnewline
18 & 625.809 & 621.574442313632 & 4.23455768636757 \tabularnewline
19 & 619.567 & 616.011183348429 & 3.55581665157058 \tabularnewline
20 & 572.942 & 569.517873627223 & 3.42412637277732 \tabularnewline
21 & 572.775 & 569.49758590406 & 3.27741409594034 \tabularnewline
22 & 574.205 & 571.584508580918 & 2.62049141908244 \tabularnewline
23 & 579.799 & 578.140900146066 & 1.65809985393400 \tabularnewline
24 & 590.072 & 589.413183354962 & 0.65881664503786 \tabularnewline
25 & 593.408 & 600.145118468587 & -6.73711846858725 \tabularnewline
26 & 597.141 & 583.262025839998 & 13.8789741600016 \tabularnewline
27 & 595.404 & 598.186025223382 & -2.78202522338177 \tabularnewline
28 & 612.117 & 612.867682291489 & -0.750682291488602 \tabularnewline
29 & 628.232 & 640.395219813697 & -12.1632198136972 \tabularnewline
30 & 628.884 & 631.712005475546 & -2.82800547554643 \tabularnewline
31 & 620.735 & 619.795336477195 & 0.939663522805176 \tabularnewline
32 & 569.028 & 570.961862614428 & -1.93386261442754 \tabularnewline
33 & 567.456 & 566.162485677649 & 1.29351432235148 \tabularnewline
34 & 573.1 & 566.412917130405 & 6.68708286959463 \tabularnewline
35 & 584.428 & 576.477250645962 & 7.9507493540375 \tabularnewline
36 & 589.379 & 593.232151873451 & -3.853151873451 \tabularnewline
37 & 590.865 & 599.131750216861 & -8.26675021686117 \tabularnewline
38 & 595.454 & 583.179105306172 & 12.2748946938277 \tabularnewline
39 & 594.167 & 594.826412538341 & -0.659412538341257 \tabularnewline
40 & 611.324 & 611.620543501636 & -0.296543501635597 \tabularnewline
41 & 612.613 & 638.28399846179 & -25.6709984617898 \tabularnewline
42 & 610.763 & 618.630541707602 & -7.86754170760219 \tabularnewline
43 & 593.53 & 602.652693489727 & -9.12269348972688 \tabularnewline
44 & 542.722 & 544.555440927838 & -1.83344092783761 \tabularnewline
45 & 536.662 & 540.203846561932 & -3.54184656193149 \tabularnewline
46 & 543.599 & 536.755207767244 & 6.84379223275607 \tabularnewline
47 & 555.332 & 547.099218061146 & 8.23278193885358 \tabularnewline
48 & 560.854 & 562.793574087544 & -1.93957408754432 \tabularnewline
49 & 562.325 & 569.9038896642 & -7.57888966420023 \tabularnewline
50 & 554.788 & 556.844582372258 & -2.05658237225805 \tabularnewline
51 & 547.344 & 554.315618516736 & -6.97161851673627 \tabularnewline
52 & 565.464 & 565.539050742508 & -0.0750507425084379 \tabularnewline
53 & 577.992 & 589.580647558929 & -11.5886475589292 \tabularnewline
54 & 579.714 & 584.422904392901 & -4.70890439290088 \tabularnewline
55 & 569.323 & 571.113383408181 & -1.79038340818056 \tabularnewline
56 & 506.971 & 520.343657841127 & -13.3726578411266 \tabularnewline
57 & 500.857 & 505.544911854185 & -4.68791185418473 \tabularnewline
58 & 509.127 & 502.23121840169 & 6.89578159830972 \tabularnewline
59 & 509.933 & 512.775740052483 & -2.84274005248290 \tabularnewline
60 & 517.009 & 517.494903162678 & -0.485903162677914 \tabularnewline
61 & 519.164 & 525.270958316853 & -6.10695831685291 \tabularnewline
62 & 512.238 & 514.13352234812 & -1.89552234812038 \tabularnewline
63 & 509.239 & 511.201735405928 & -1.96273540592773 \tabularnewline
64 & 518.585 & 527.6437460408 & -9.05874604079986 \tabularnewline
65 & 522.975 & 542.420610972802 & -19.4456109728018 \tabularnewline
66 & 525.192 & 531.042945865977 & -5.85094586597734 \tabularnewline
67 & 516.847 & 517.042454962831 & -0.195454962831377 \tabularnewline
68 & 455.626 & 466.403855363012 & -10.7778553630118 \tabularnewline
69 & 454.724 & 454.876419189022 & -0.152419189021543 \tabularnewline
70 & 461.251 & 456.881174684145 & 4.36982531585477 \tabularnewline
71 & 470.439 & 464.098525169685 & 6.3404748303152 \tabularnewline
72 & 474.605 & 477.242588282427 & -2.63758828242732 \tabularnewline
73 & 476.049 & 482.481559951146 & -6.4325599511456 \tabularnewline
74 & 471.067 & 471.5225236106 & -0.455523610599926 \tabularnewline
75 & 470.984 & 469.863305308553 & 1.12069469144740 \tabularnewline
76 & 502.831 & 488.257952904555 & 14.5730470954454 \tabularnewline
77 & 512.927 & 522.887615047615 & -9.96061504761451 \tabularnewline
78 & 509.673 & 521.451472489106 & -11.7784724891062 \tabularnewline
79 & 484.015 & 502.810165800906 & -18.7951658009059 \tabularnewline
80 & 431.328 & 434.462466139456 & -3.13446613945638 \tabularnewline
81 & 436.087 & 430.909682793006 & 5.17731720699373 \tabularnewline
82 & 442.867 & 438.154473657135 & 4.71252634286515 \tabularnewline
83 & 447.988 & 445.895367420668 & 2.09263257933196 \tabularnewline
84 & 460.07 & 454.266127068585 & 5.80387293141496 \tabularnewline
85 & 467.037 & 466.587263828728 & 0.44973617127215 \tabularnewline
86 & 460.17 & 462.409961941763 & -2.23996194176311 \tabularnewline
87 & 464.196 & 459.339627139689 & 4.85637286031056 \tabularnewline
88 & 485.025 & 482.549339171564 & 2.47566082843611 \tabularnewline
89 & 501.492 & 503.700119170681 & -2.20811917068079 \tabularnewline
90 & 520.564 & 508.953340424332 & 11.6106595756676 \tabularnewline
91 & 488.18 & 510.323504931112 & -22.1435049311117 \tabularnewline
92 & 439.148 & 440.739103817559 & -1.59110381755869 \tabularnewline
93 & 441.977 & 439.481559466696 & 2.49544053330413 \tabularnewline
94 & 456.608 & 444.290760804127 & 12.3172391958732 \tabularnewline
95 & 461.935 & 458.500556987963 & 3.43444301203732 \tabularnewline
96 & 480.961 & 468.476337510113 & 12.4846624898867 \tabularnewline
97 & 492.865 & 486.141352260178 & 6.72364773982179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13464&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]560.576[/C][C]535.631623943236[/C][C]24.9443760567635[/C][/ROW]
[ROW][C]14[/C][C]557.274[/C][C]548.732821239622[/C][C]8.54117876037787[/C][/ROW]
[ROW][C]15[/C][C]565.742[/C][C]559.125819798248[/C][C]6.6161802017516[/C][/ROW]
[ROW][C]16[/C][C]587.625[/C][C]582.305743480441[/C][C]5.31925651955896[/C][/ROW]
[ROW][C]17[/C][C]619.916[/C][C]615.307938516962[/C][C]4.60806148303811[/C][/ROW]
[ROW][C]18[/C][C]625.809[/C][C]621.574442313632[/C][C]4.23455768636757[/C][/ROW]
[ROW][C]19[/C][C]619.567[/C][C]616.011183348429[/C][C]3.55581665157058[/C][/ROW]
[ROW][C]20[/C][C]572.942[/C][C]569.517873627223[/C][C]3.42412637277732[/C][/ROW]
[ROW][C]21[/C][C]572.775[/C][C]569.49758590406[/C][C]3.27741409594034[/C][/ROW]
[ROW][C]22[/C][C]574.205[/C][C]571.584508580918[/C][C]2.62049141908244[/C][/ROW]
[ROW][C]23[/C][C]579.799[/C][C]578.140900146066[/C][C]1.65809985393400[/C][/ROW]
[ROW][C]24[/C][C]590.072[/C][C]589.413183354962[/C][C]0.65881664503786[/C][/ROW]
[ROW][C]25[/C][C]593.408[/C][C]600.145118468587[/C][C]-6.73711846858725[/C][/ROW]
[ROW][C]26[/C][C]597.141[/C][C]583.262025839998[/C][C]13.8789741600016[/C][/ROW]
[ROW][C]27[/C][C]595.404[/C][C]598.186025223382[/C][C]-2.78202522338177[/C][/ROW]
[ROW][C]28[/C][C]612.117[/C][C]612.867682291489[/C][C]-0.750682291488602[/C][/ROW]
[ROW][C]29[/C][C]628.232[/C][C]640.395219813697[/C][C]-12.1632198136972[/C][/ROW]
[ROW][C]30[/C][C]628.884[/C][C]631.712005475546[/C][C]-2.82800547554643[/C][/ROW]
[ROW][C]31[/C][C]620.735[/C][C]619.795336477195[/C][C]0.939663522805176[/C][/ROW]
[ROW][C]32[/C][C]569.028[/C][C]570.961862614428[/C][C]-1.93386261442754[/C][/ROW]
[ROW][C]33[/C][C]567.456[/C][C]566.162485677649[/C][C]1.29351432235148[/C][/ROW]
[ROW][C]34[/C][C]573.1[/C][C]566.412917130405[/C][C]6.68708286959463[/C][/ROW]
[ROW][C]35[/C][C]584.428[/C][C]576.477250645962[/C][C]7.9507493540375[/C][/ROW]
[ROW][C]36[/C][C]589.379[/C][C]593.232151873451[/C][C]-3.853151873451[/C][/ROW]
[ROW][C]37[/C][C]590.865[/C][C]599.131750216861[/C][C]-8.26675021686117[/C][/ROW]
[ROW][C]38[/C][C]595.454[/C][C]583.179105306172[/C][C]12.2748946938277[/C][/ROW]
[ROW][C]39[/C][C]594.167[/C][C]594.826412538341[/C][C]-0.659412538341257[/C][/ROW]
[ROW][C]40[/C][C]611.324[/C][C]611.620543501636[/C][C]-0.296543501635597[/C][/ROW]
[ROW][C]41[/C][C]612.613[/C][C]638.28399846179[/C][C]-25.6709984617898[/C][/ROW]
[ROW][C]42[/C][C]610.763[/C][C]618.630541707602[/C][C]-7.86754170760219[/C][/ROW]
[ROW][C]43[/C][C]593.53[/C][C]602.652693489727[/C][C]-9.12269348972688[/C][/ROW]
[ROW][C]44[/C][C]542.722[/C][C]544.555440927838[/C][C]-1.83344092783761[/C][/ROW]
[ROW][C]45[/C][C]536.662[/C][C]540.203846561932[/C][C]-3.54184656193149[/C][/ROW]
[ROW][C]46[/C][C]543.599[/C][C]536.755207767244[/C][C]6.84379223275607[/C][/ROW]
[ROW][C]47[/C][C]555.332[/C][C]547.099218061146[/C][C]8.23278193885358[/C][/ROW]
[ROW][C]48[/C][C]560.854[/C][C]562.793574087544[/C][C]-1.93957408754432[/C][/ROW]
[ROW][C]49[/C][C]562.325[/C][C]569.9038896642[/C][C]-7.57888966420023[/C][/ROW]
[ROW][C]50[/C][C]554.788[/C][C]556.844582372258[/C][C]-2.05658237225805[/C][/ROW]
[ROW][C]51[/C][C]547.344[/C][C]554.315618516736[/C][C]-6.97161851673627[/C][/ROW]
[ROW][C]52[/C][C]565.464[/C][C]565.539050742508[/C][C]-0.0750507425084379[/C][/ROW]
[ROW][C]53[/C][C]577.992[/C][C]589.580647558929[/C][C]-11.5886475589292[/C][/ROW]
[ROW][C]54[/C][C]579.714[/C][C]584.422904392901[/C][C]-4.70890439290088[/C][/ROW]
[ROW][C]55[/C][C]569.323[/C][C]571.113383408181[/C][C]-1.79038340818056[/C][/ROW]
[ROW][C]56[/C][C]506.971[/C][C]520.343657841127[/C][C]-13.3726578411266[/C][/ROW]
[ROW][C]57[/C][C]500.857[/C][C]505.544911854185[/C][C]-4.68791185418473[/C][/ROW]
[ROW][C]58[/C][C]509.127[/C][C]502.23121840169[/C][C]6.89578159830972[/C][/ROW]
[ROW][C]59[/C][C]509.933[/C][C]512.775740052483[/C][C]-2.84274005248290[/C][/ROW]
[ROW][C]60[/C][C]517.009[/C][C]517.494903162678[/C][C]-0.485903162677914[/C][/ROW]
[ROW][C]61[/C][C]519.164[/C][C]525.270958316853[/C][C]-6.10695831685291[/C][/ROW]
[ROW][C]62[/C][C]512.238[/C][C]514.13352234812[/C][C]-1.89552234812038[/C][/ROW]
[ROW][C]63[/C][C]509.239[/C][C]511.201735405928[/C][C]-1.96273540592773[/C][/ROW]
[ROW][C]64[/C][C]518.585[/C][C]527.6437460408[/C][C]-9.05874604079986[/C][/ROW]
[ROW][C]65[/C][C]522.975[/C][C]542.420610972802[/C][C]-19.4456109728018[/C][/ROW]
[ROW][C]66[/C][C]525.192[/C][C]531.042945865977[/C][C]-5.85094586597734[/C][/ROW]
[ROW][C]67[/C][C]516.847[/C][C]517.042454962831[/C][C]-0.195454962831377[/C][/ROW]
[ROW][C]68[/C][C]455.626[/C][C]466.403855363012[/C][C]-10.7778553630118[/C][/ROW]
[ROW][C]69[/C][C]454.724[/C][C]454.876419189022[/C][C]-0.152419189021543[/C][/ROW]
[ROW][C]70[/C][C]461.251[/C][C]456.881174684145[/C][C]4.36982531585477[/C][/ROW]
[ROW][C]71[/C][C]470.439[/C][C]464.098525169685[/C][C]6.3404748303152[/C][/ROW]
[ROW][C]72[/C][C]474.605[/C][C]477.242588282427[/C][C]-2.63758828242732[/C][/ROW]
[ROW][C]73[/C][C]476.049[/C][C]482.481559951146[/C][C]-6.4325599511456[/C][/ROW]
[ROW][C]74[/C][C]471.067[/C][C]471.5225236106[/C][C]-0.455523610599926[/C][/ROW]
[ROW][C]75[/C][C]470.984[/C][C]469.863305308553[/C][C]1.12069469144740[/C][/ROW]
[ROW][C]76[/C][C]502.831[/C][C]488.257952904555[/C][C]14.5730470954454[/C][/ROW]
[ROW][C]77[/C][C]512.927[/C][C]522.887615047615[/C][C]-9.96061504761451[/C][/ROW]
[ROW][C]78[/C][C]509.673[/C][C]521.451472489106[/C][C]-11.7784724891062[/C][/ROW]
[ROW][C]79[/C][C]484.015[/C][C]502.810165800906[/C][C]-18.7951658009059[/C][/ROW]
[ROW][C]80[/C][C]431.328[/C][C]434.462466139456[/C][C]-3.13446613945638[/C][/ROW]
[ROW][C]81[/C][C]436.087[/C][C]430.909682793006[/C][C]5.17731720699373[/C][/ROW]
[ROW][C]82[/C][C]442.867[/C][C]438.154473657135[/C][C]4.71252634286515[/C][/ROW]
[ROW][C]83[/C][C]447.988[/C][C]445.895367420668[/C][C]2.09263257933196[/C][/ROW]
[ROW][C]84[/C][C]460.07[/C][C]454.266127068585[/C][C]5.80387293141496[/C][/ROW]
[ROW][C]85[/C][C]467.037[/C][C]466.587263828728[/C][C]0.44973617127215[/C][/ROW]
[ROW][C]86[/C][C]460.17[/C][C]462.409961941763[/C][C]-2.23996194176311[/C][/ROW]
[ROW][C]87[/C][C]464.196[/C][C]459.339627139689[/C][C]4.85637286031056[/C][/ROW]
[ROW][C]88[/C][C]485.025[/C][C]482.549339171564[/C][C]2.47566082843611[/C][/ROW]
[ROW][C]89[/C][C]501.492[/C][C]503.700119170681[/C][C]-2.20811917068079[/C][/ROW]
[ROW][C]90[/C][C]520.564[/C][C]508.953340424332[/C][C]11.6106595756676[/C][/ROW]
[ROW][C]91[/C][C]488.18[/C][C]510.323504931112[/C][C]-22.1435049311117[/C][/ROW]
[ROW][C]92[/C][C]439.148[/C][C]440.739103817559[/C][C]-1.59110381755869[/C][/ROW]
[ROW][C]93[/C][C]441.977[/C][C]439.481559466696[/C][C]2.49544053330413[/C][/ROW]
[ROW][C]94[/C][C]456.608[/C][C]444.290760804127[/C][C]12.3172391958732[/C][/ROW]
[ROW][C]95[/C][C]461.935[/C][C]458.500556987963[/C][C]3.43444301203732[/C][/ROW]
[ROW][C]96[/C][C]480.961[/C][C]468.476337510113[/C][C]12.4846624898867[/C][/ROW]
[ROW][C]97[/C][C]492.865[/C][C]486.141352260178[/C][C]6.72364773982179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13464&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13464&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
13560.576535.63162394323624.9443760567635
14557.274548.7328212396228.54117876037787
15565.742559.1258197982486.6161802017516
16587.625582.3057434804415.31925651955896
17619.916615.3079385169624.60806148303811
18625.809621.5744423136324.23455768636757
19619.567616.0111833484293.55581665157058
20572.942569.5178736272233.42412637277732
21572.775569.497585904063.27741409594034
22574.205571.5845085809182.62049141908244
23579.799578.1409001460661.65809985393400
24590.072589.4131833549620.65881664503786
25593.408600.145118468587-6.73711846858725
26597.141583.26202583999813.8789741600016
27595.404598.186025223382-2.78202522338177
28612.117612.867682291489-0.750682291488602
29628.232640.395219813697-12.1632198136972
30628.884631.712005475546-2.82800547554643
31620.735619.7953364771950.939663522805176
32569.028570.961862614428-1.93386261442754
33567.456566.1624856776491.29351432235148
34573.1566.4129171304056.68708286959463
35584.428576.4772506459627.9507493540375
36589.379593.232151873451-3.853151873451
37590.865599.131750216861-8.26675021686117
38595.454583.17910530617212.2748946938277
39594.167594.826412538341-0.659412538341257
40611.324611.620543501636-0.296543501635597
41612.613638.28399846179-25.6709984617898
42610.763618.630541707602-7.86754170760219
43593.53602.652693489727-9.12269348972688
44542.722544.555440927838-1.83344092783761
45536.662540.203846561932-3.54184656193149
46543.599536.7552077672446.84379223275607
47555.332547.0992180611468.23278193885358
48560.854562.793574087544-1.93957408754432
49562.325569.9038896642-7.57888966420023
50554.788556.844582372258-2.05658237225805
51547.344554.315618516736-6.97161851673627
52565.464565.539050742508-0.0750507425084379
53577.992589.580647558929-11.5886475589292
54579.714584.422904392901-4.70890439290088
55569.323571.113383408181-1.79038340818056
56506.971520.343657841127-13.3726578411266
57500.857505.544911854185-4.68791185418473
58509.127502.231218401696.89578159830972
59509.933512.775740052483-2.84274005248290
60517.009517.494903162678-0.485903162677914
61519.164525.270958316853-6.10695831685291
62512.238514.13352234812-1.89552234812038
63509.239511.201735405928-1.96273540592773
64518.585527.6437460408-9.05874604079986
65522.975542.420610972802-19.4456109728018
66525.192531.042945865977-5.85094586597734
67516.847517.042454962831-0.195454962831377
68455.626466.403855363012-10.7778553630118
69454.724454.876419189022-0.152419189021543
70461.251456.8811746841454.36982531585477
71470.439464.0985251696856.3404748303152
72474.605477.242588282427-2.63758828242732
73476.049482.481559951146-6.4325599511456
74471.067471.5225236106-0.455523610599926
75470.984469.8633053085531.12069469144740
76502.831488.25795290455514.5730470954454
77512.927522.887615047615-9.96061504761451
78509.673521.451472489106-11.7784724891062
79484.015502.810165800906-18.7951658009059
80431.328434.462466139456-3.13446613945638
81436.087430.9096827930065.17731720699373
82442.867438.1544736571354.71252634286515
83447.988445.8953674206682.09263257933196
84460.07454.2661270685855.80387293141496
85467.037466.5872638287280.44973617127215
86460.17462.409961941763-2.23996194176311
87464.196459.3396271396894.85637286031056
88485.025482.5493391715642.47566082843611
89501.492503.700119170681-2.20811917068079
90520.564508.95334042433211.6106595756676
91488.18510.323504931112-22.1435049311117
92439.148440.739103817559-1.59110381755869
93441.977439.4815594666962.49544053330413
94456.608444.29076080412712.3172391958732
95461.935458.5005569879633.43444301203732
96480.961468.47633751011312.4846624898867
97492.865486.1413522601786.72364773982179







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
98487.242230587701471.034855510506503.449605664895
99486.951332659455465.266324278711508.6363410402
100505.579683037047479.545087398684531.61427867541
101524.009511128592494.254498918324553.764523338859
102532.760633035108499.701272284887565.819993785329
103520.06030504935483.998109958183556.122500140516
104472.442659542139433.609136699453511.276182384826
105473.053427462737431.63358827964514.473266645833
106476.73546083768432.881570935715520.589350739645
107479.009536288885432.849767646552525.169304931219
108486.937744750286438.581929973841535.293559526731
109492.865442.408628704851543.321371295149

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
98 & 487.242230587701 & 471.034855510506 & 503.449605664895 \tabularnewline
99 & 486.951332659455 & 465.266324278711 & 508.6363410402 \tabularnewline
100 & 505.579683037047 & 479.545087398684 & 531.61427867541 \tabularnewline
101 & 524.009511128592 & 494.254498918324 & 553.764523338859 \tabularnewline
102 & 532.760633035108 & 499.701272284887 & 565.819993785329 \tabularnewline
103 & 520.06030504935 & 483.998109958183 & 556.122500140516 \tabularnewline
104 & 472.442659542139 & 433.609136699453 & 511.276182384826 \tabularnewline
105 & 473.053427462737 & 431.63358827964 & 514.473266645833 \tabularnewline
106 & 476.73546083768 & 432.881570935715 & 520.589350739645 \tabularnewline
107 & 479.009536288885 & 432.849767646552 & 525.169304931219 \tabularnewline
108 & 486.937744750286 & 438.581929973841 & 535.293559526731 \tabularnewline
109 & 492.865 & 442.408628704851 & 543.321371295149 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13464&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]98[/C][C]487.242230587701[/C][C]471.034855510506[/C][C]503.449605664895[/C][/ROW]
[ROW][C]99[/C][C]486.951332659455[/C][C]465.266324278711[/C][C]508.6363410402[/C][/ROW]
[ROW][C]100[/C][C]505.579683037047[/C][C]479.545087398684[/C][C]531.61427867541[/C][/ROW]
[ROW][C]101[/C][C]524.009511128592[/C][C]494.254498918324[/C][C]553.764523338859[/C][/ROW]
[ROW][C]102[/C][C]532.760633035108[/C][C]499.701272284887[/C][C]565.819993785329[/C][/ROW]
[ROW][C]103[/C][C]520.06030504935[/C][C]483.998109958183[/C][C]556.122500140516[/C][/ROW]
[ROW][C]104[/C][C]472.442659542139[/C][C]433.609136699453[/C][C]511.276182384826[/C][/ROW]
[ROW][C]105[/C][C]473.053427462737[/C][C]431.63358827964[/C][C]514.473266645833[/C][/ROW]
[ROW][C]106[/C][C]476.73546083768[/C][C]432.881570935715[/C][C]520.589350739645[/C][/ROW]
[ROW][C]107[/C][C]479.009536288885[/C][C]432.849767646552[/C][C]525.169304931219[/C][/ROW]
[ROW][C]108[/C][C]486.937744750286[/C][C]438.581929973841[/C][C]535.293559526731[/C][/ROW]
[ROW][C]109[/C][C]492.865[/C][C]442.408628704851[/C][C]543.321371295149[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13464&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13464&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
98487.242230587701471.034855510506503.449605664895
99486.951332659455465.266324278711508.6363410402
100505.579683037047479.545087398684531.61427867541
101524.009511128592494.254498918324553.764523338859
102532.760633035108499.701272284887565.819993785329
103520.06030504935483.998109958183556.122500140516
104472.442659542139433.609136699453511.276182384826
105473.053427462737431.63358827964514.473266645833
106476.73546083768432.881570935715520.589350739645
107479.009536288885432.849767646552525.169304931219
108486.937744750286438.581929973841535.293559526731
109492.865442.408628704851543.321371295149



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