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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 Dec 2011 16:38:17 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/28/t13251084294v9q5hzd7vn60t8.htm/, Retrieved Fri, 03 May 2024 03:54:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160892, Retrieved Fri, 03 May 2024 03:54:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-28 21:38:17] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
562325
560854
555332
543599
536662
542722
593530
610763
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590
517945
506174
501866
516141
528222
532638
536322
536535
523597
536214
586570
596594
580523
564478
557560
575093
580112
574761
563250
551531
537034
544686
600991
604378
586111
563668
548604
551174




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160892&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160892&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160892&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.628942599884498
beta0.697828962197878
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.628942599884498 \tabularnewline
beta & 0.697828962197878 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160892&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]0.628942599884498[/C][/ROW]
[ROW][C]beta[/C][C]0.697828962197878[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160892&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160892&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
alpha0.628942599884498
beta0.697828962197878
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13590865576660.77777777814204.2222222224
14589379590260.306126556-881.306126555661
15584428591002.852765093-6574.85276509286
16573100579623.819570227-6523.81957022694
17567456571696.865699112-4240.86569911207
18569028570523.216726793-1495.21672679321
19620735611997.889499838737.1105001698
20628884635570.193965123-6686.19396512269
21628232631101.425721615-2869.42572161485
22612117624594.144182965-12477.1441829646
23595404590629.2609835124774.73901648796
24597141588187.5530896368953.44691036385
25593408591847.7534050711560.24659492902
26590072584118.7014958785953.2985041223
27579799582268.210538545-2469.21053854469
28574205570513.291120743691.70887925988
29572775571364.9272750061410.07272499404
30572942578750.854664387-5808.85466438683
31619567623402.713234637-3835.71323463658
32625809629919.796266263-4110.79626626277
33619916626192.667247883-6276.66724788328
34587625610187.614036317-22562.6140363168
35565742568064.734983354-2322.73498335388
36557274551378.3693551125895.63064488769
37560576537698.72428154122877.2757184589
38548854541689.5056134417164.494386559
39531673534689.711181672-3016.71118167241
40525919521850.363228224068.63677177951
41511038519231.74213937-8193.74213937018
42498662510823.019342676-12161.0193426763
43555362542348.18494423713013.8150557631
44564591556892.0507460717698.94925392873
45541657562503.610281283-20846.6102812834
46527070527611.911253444-541.911253443803
47509846512833.742562511-2987.742562511
48514258504471.5380471289786.46195287246
49516922506940.758851859981.24114815047
50507561498730.9252703928830.07472960826
51492622491472.481810421149.51818958012
52490243488182.6665695122060.33343048819
53469357483169.601294187-13812.6012941867
54477580470707.4752214686872.52477853181
55528379532851.295520745-4472.29552074533
56533590536057.065220084-2467.06522008404
57517945521852.721673113-3907.72167311289
58506174509753.180419189-3579.18041918887
59501866495428.5199460896437.48005391052
60516141505142.19961841510998.8003815851
61528222516386.27152395911835.7284760414
62532638517669.66479348914968.3352065106
63536322522869.96499766513452.0350023345
64536535544503.254168159-7968.25416815933
65523597539739.085257562-16142.0852575619
66536214544910.89142213-8696.8914221304
67586570597643.208942092-11073.2089420923
68596594599134.680701142-2540.68070114183
69580523586010.403751176-5487.40375117643
70564478574006.859997136-9528.85999713605
71557560558013.286943295-453.286943294574
72575093560417.60095231314675.399047687
73580112571230.2487546968881.75124530401
74574761567467.310872627293.68912738003
75563250559558.8799733093691.120026691
76551531555101.761710292-3570.76171029196
77537034539997.241889586-2963.24188958644
78544686551931.337645612-7245.33764561161
79600991601042.887051348-51.887051348458
80604378613817.429517514-9439.42951751396
81586111593418.244316011-7307.2443160112
82563668576129.207454023-12461.207454023
83548604557730.618338833-9126.61833883275
84551174552558.54302412-1384.5430241198

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 590865 & 576660.777777778 & 14204.2222222224 \tabularnewline
14 & 589379 & 590260.306126556 & -881.306126555661 \tabularnewline
15 & 584428 & 591002.852765093 & -6574.85276509286 \tabularnewline
16 & 573100 & 579623.819570227 & -6523.81957022694 \tabularnewline
17 & 567456 & 571696.865699112 & -4240.86569911207 \tabularnewline
18 & 569028 & 570523.216726793 & -1495.21672679321 \tabularnewline
19 & 620735 & 611997.88949983 & 8737.1105001698 \tabularnewline
20 & 628884 & 635570.193965123 & -6686.19396512269 \tabularnewline
21 & 628232 & 631101.425721615 & -2869.42572161485 \tabularnewline
22 & 612117 & 624594.144182965 & -12477.1441829646 \tabularnewline
23 & 595404 & 590629.260983512 & 4774.73901648796 \tabularnewline
24 & 597141 & 588187.553089636 & 8953.44691036385 \tabularnewline
25 & 593408 & 591847.753405071 & 1560.24659492902 \tabularnewline
26 & 590072 & 584118.701495878 & 5953.2985041223 \tabularnewline
27 & 579799 & 582268.210538545 & -2469.21053854469 \tabularnewline
28 & 574205 & 570513.29112074 & 3691.70887925988 \tabularnewline
29 & 572775 & 571364.927275006 & 1410.07272499404 \tabularnewline
30 & 572942 & 578750.854664387 & -5808.85466438683 \tabularnewline
31 & 619567 & 623402.713234637 & -3835.71323463658 \tabularnewline
32 & 625809 & 629919.796266263 & -4110.79626626277 \tabularnewline
33 & 619916 & 626192.667247883 & -6276.66724788328 \tabularnewline
34 & 587625 & 610187.614036317 & -22562.6140363168 \tabularnewline
35 & 565742 & 568064.734983354 & -2322.73498335388 \tabularnewline
36 & 557274 & 551378.369355112 & 5895.63064488769 \tabularnewline
37 & 560576 & 537698.724281541 & 22877.2757184589 \tabularnewline
38 & 548854 & 541689.505613441 & 7164.494386559 \tabularnewline
39 & 531673 & 534689.711181672 & -3016.71118167241 \tabularnewline
40 & 525919 & 521850.36322822 & 4068.63677177951 \tabularnewline
41 & 511038 & 519231.74213937 & -8193.74213937018 \tabularnewline
42 & 498662 & 510823.019342676 & -12161.0193426763 \tabularnewline
43 & 555362 & 542348.184944237 & 13013.8150557631 \tabularnewline
44 & 564591 & 556892.050746071 & 7698.94925392873 \tabularnewline
45 & 541657 & 562503.610281283 & -20846.6102812834 \tabularnewline
46 & 527070 & 527611.911253444 & -541.911253443803 \tabularnewline
47 & 509846 & 512833.742562511 & -2987.742562511 \tabularnewline
48 & 514258 & 504471.538047128 & 9786.46195287246 \tabularnewline
49 & 516922 & 506940.75885185 & 9981.24114815047 \tabularnewline
50 & 507561 & 498730.925270392 & 8830.07472960826 \tabularnewline
51 & 492622 & 491472.48181042 & 1149.51818958012 \tabularnewline
52 & 490243 & 488182.666569512 & 2060.33343048819 \tabularnewline
53 & 469357 & 483169.601294187 & -13812.6012941867 \tabularnewline
54 & 477580 & 470707.475221468 & 6872.52477853181 \tabularnewline
55 & 528379 & 532851.295520745 & -4472.29552074533 \tabularnewline
56 & 533590 & 536057.065220084 & -2467.06522008404 \tabularnewline
57 & 517945 & 521852.721673113 & -3907.72167311289 \tabularnewline
58 & 506174 & 509753.180419189 & -3579.18041918887 \tabularnewline
59 & 501866 & 495428.519946089 & 6437.48005391052 \tabularnewline
60 & 516141 & 505142.199618415 & 10998.8003815851 \tabularnewline
61 & 528222 & 516386.271523959 & 11835.7284760414 \tabularnewline
62 & 532638 & 517669.664793489 & 14968.3352065106 \tabularnewline
63 & 536322 & 522869.964997665 & 13452.0350023345 \tabularnewline
64 & 536535 & 544503.254168159 & -7968.25416815933 \tabularnewline
65 & 523597 & 539739.085257562 & -16142.0852575619 \tabularnewline
66 & 536214 & 544910.89142213 & -8696.8914221304 \tabularnewline
67 & 586570 & 597643.208942092 & -11073.2089420923 \tabularnewline
68 & 596594 & 599134.680701142 & -2540.68070114183 \tabularnewline
69 & 580523 & 586010.403751176 & -5487.40375117643 \tabularnewline
70 & 564478 & 574006.859997136 & -9528.85999713605 \tabularnewline
71 & 557560 & 558013.286943295 & -453.286943294574 \tabularnewline
72 & 575093 & 560417.600952313 & 14675.399047687 \tabularnewline
73 & 580112 & 571230.248754696 & 8881.75124530401 \tabularnewline
74 & 574761 & 567467.31087262 & 7293.68912738003 \tabularnewline
75 & 563250 & 559558.879973309 & 3691.120026691 \tabularnewline
76 & 551531 & 555101.761710292 & -3570.76171029196 \tabularnewline
77 & 537034 & 539997.241889586 & -2963.24188958644 \tabularnewline
78 & 544686 & 551931.337645612 & -7245.33764561161 \tabularnewline
79 & 600991 & 601042.887051348 & -51.887051348458 \tabularnewline
80 & 604378 & 613817.429517514 & -9439.42951751396 \tabularnewline
81 & 586111 & 593418.244316011 & -7307.2443160112 \tabularnewline
82 & 563668 & 576129.207454023 & -12461.207454023 \tabularnewline
83 & 548604 & 557730.618338833 & -9126.61833883275 \tabularnewline
84 & 551174 & 552558.54302412 & -1384.5430241198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160892&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]590865[/C][C]576660.777777778[/C][C]14204.2222222224[/C][/ROW]
[ROW][C]14[/C][C]589379[/C][C]590260.306126556[/C][C]-881.306126555661[/C][/ROW]
[ROW][C]15[/C][C]584428[/C][C]591002.852765093[/C][C]-6574.85276509286[/C][/ROW]
[ROW][C]16[/C][C]573100[/C][C]579623.819570227[/C][C]-6523.81957022694[/C][/ROW]
[ROW][C]17[/C][C]567456[/C][C]571696.865699112[/C][C]-4240.86569911207[/C][/ROW]
[ROW][C]18[/C][C]569028[/C][C]570523.216726793[/C][C]-1495.21672679321[/C][/ROW]
[ROW][C]19[/C][C]620735[/C][C]611997.88949983[/C][C]8737.1105001698[/C][/ROW]
[ROW][C]20[/C][C]628884[/C][C]635570.193965123[/C][C]-6686.19396512269[/C][/ROW]
[ROW][C]21[/C][C]628232[/C][C]631101.425721615[/C][C]-2869.42572161485[/C][/ROW]
[ROW][C]22[/C][C]612117[/C][C]624594.144182965[/C][C]-12477.1441829646[/C][/ROW]
[ROW][C]23[/C][C]595404[/C][C]590629.260983512[/C][C]4774.73901648796[/C][/ROW]
[ROW][C]24[/C][C]597141[/C][C]588187.553089636[/C][C]8953.44691036385[/C][/ROW]
[ROW][C]25[/C][C]593408[/C][C]591847.753405071[/C][C]1560.24659492902[/C][/ROW]
[ROW][C]26[/C][C]590072[/C][C]584118.701495878[/C][C]5953.2985041223[/C][/ROW]
[ROW][C]27[/C][C]579799[/C][C]582268.210538545[/C][C]-2469.21053854469[/C][/ROW]
[ROW][C]28[/C][C]574205[/C][C]570513.29112074[/C][C]3691.70887925988[/C][/ROW]
[ROW][C]29[/C][C]572775[/C][C]571364.927275006[/C][C]1410.07272499404[/C][/ROW]
[ROW][C]30[/C][C]572942[/C][C]578750.854664387[/C][C]-5808.85466438683[/C][/ROW]
[ROW][C]31[/C][C]619567[/C][C]623402.713234637[/C][C]-3835.71323463658[/C][/ROW]
[ROW][C]32[/C][C]625809[/C][C]629919.796266263[/C][C]-4110.79626626277[/C][/ROW]
[ROW][C]33[/C][C]619916[/C][C]626192.667247883[/C][C]-6276.66724788328[/C][/ROW]
[ROW][C]34[/C][C]587625[/C][C]610187.614036317[/C][C]-22562.6140363168[/C][/ROW]
[ROW][C]35[/C][C]565742[/C][C]568064.734983354[/C][C]-2322.73498335388[/C][/ROW]
[ROW][C]36[/C][C]557274[/C][C]551378.369355112[/C][C]5895.63064488769[/C][/ROW]
[ROW][C]37[/C][C]560576[/C][C]537698.724281541[/C][C]22877.2757184589[/C][/ROW]
[ROW][C]38[/C][C]548854[/C][C]541689.505613441[/C][C]7164.494386559[/C][/ROW]
[ROW][C]39[/C][C]531673[/C][C]534689.711181672[/C][C]-3016.71118167241[/C][/ROW]
[ROW][C]40[/C][C]525919[/C][C]521850.36322822[/C][C]4068.63677177951[/C][/ROW]
[ROW][C]41[/C][C]511038[/C][C]519231.74213937[/C][C]-8193.74213937018[/C][/ROW]
[ROW][C]42[/C][C]498662[/C][C]510823.019342676[/C][C]-12161.0193426763[/C][/ROW]
[ROW][C]43[/C][C]555362[/C][C]542348.184944237[/C][C]13013.8150557631[/C][/ROW]
[ROW][C]44[/C][C]564591[/C][C]556892.050746071[/C][C]7698.94925392873[/C][/ROW]
[ROW][C]45[/C][C]541657[/C][C]562503.610281283[/C][C]-20846.6102812834[/C][/ROW]
[ROW][C]46[/C][C]527070[/C][C]527611.911253444[/C][C]-541.911253443803[/C][/ROW]
[ROW][C]47[/C][C]509846[/C][C]512833.742562511[/C][C]-2987.742562511[/C][/ROW]
[ROW][C]48[/C][C]514258[/C][C]504471.538047128[/C][C]9786.46195287246[/C][/ROW]
[ROW][C]49[/C][C]516922[/C][C]506940.75885185[/C][C]9981.24114815047[/C][/ROW]
[ROW][C]50[/C][C]507561[/C][C]498730.925270392[/C][C]8830.07472960826[/C][/ROW]
[ROW][C]51[/C][C]492622[/C][C]491472.48181042[/C][C]1149.51818958012[/C][/ROW]
[ROW][C]52[/C][C]490243[/C][C]488182.666569512[/C][C]2060.33343048819[/C][/ROW]
[ROW][C]53[/C][C]469357[/C][C]483169.601294187[/C][C]-13812.6012941867[/C][/ROW]
[ROW][C]54[/C][C]477580[/C][C]470707.475221468[/C][C]6872.52477853181[/C][/ROW]
[ROW][C]55[/C][C]528379[/C][C]532851.295520745[/C][C]-4472.29552074533[/C][/ROW]
[ROW][C]56[/C][C]533590[/C][C]536057.065220084[/C][C]-2467.06522008404[/C][/ROW]
[ROW][C]57[/C][C]517945[/C][C]521852.721673113[/C][C]-3907.72167311289[/C][/ROW]
[ROW][C]58[/C][C]506174[/C][C]509753.180419189[/C][C]-3579.18041918887[/C][/ROW]
[ROW][C]59[/C][C]501866[/C][C]495428.519946089[/C][C]6437.48005391052[/C][/ROW]
[ROW][C]60[/C][C]516141[/C][C]505142.199618415[/C][C]10998.8003815851[/C][/ROW]
[ROW][C]61[/C][C]528222[/C][C]516386.271523959[/C][C]11835.7284760414[/C][/ROW]
[ROW][C]62[/C][C]532638[/C][C]517669.664793489[/C][C]14968.3352065106[/C][/ROW]
[ROW][C]63[/C][C]536322[/C][C]522869.964997665[/C][C]13452.0350023345[/C][/ROW]
[ROW][C]64[/C][C]536535[/C][C]544503.254168159[/C][C]-7968.25416815933[/C][/ROW]
[ROW][C]65[/C][C]523597[/C][C]539739.085257562[/C][C]-16142.0852575619[/C][/ROW]
[ROW][C]66[/C][C]536214[/C][C]544910.89142213[/C][C]-8696.8914221304[/C][/ROW]
[ROW][C]67[/C][C]586570[/C][C]597643.208942092[/C][C]-11073.2089420923[/C][/ROW]
[ROW][C]68[/C][C]596594[/C][C]599134.680701142[/C][C]-2540.68070114183[/C][/ROW]
[ROW][C]69[/C][C]580523[/C][C]586010.403751176[/C][C]-5487.40375117643[/C][/ROW]
[ROW][C]70[/C][C]564478[/C][C]574006.859997136[/C][C]-9528.85999713605[/C][/ROW]
[ROW][C]71[/C][C]557560[/C][C]558013.286943295[/C][C]-453.286943294574[/C][/ROW]
[ROW][C]72[/C][C]575093[/C][C]560417.600952313[/C][C]14675.399047687[/C][/ROW]
[ROW][C]73[/C][C]580112[/C][C]571230.248754696[/C][C]8881.75124530401[/C][/ROW]
[ROW][C]74[/C][C]574761[/C][C]567467.31087262[/C][C]7293.68912738003[/C][/ROW]
[ROW][C]75[/C][C]563250[/C][C]559558.879973309[/C][C]3691.120026691[/C][/ROW]
[ROW][C]76[/C][C]551531[/C][C]555101.761710292[/C][C]-3570.76171029196[/C][/ROW]
[ROW][C]77[/C][C]537034[/C][C]539997.241889586[/C][C]-2963.24188958644[/C][/ROW]
[ROW][C]78[/C][C]544686[/C][C]551931.337645612[/C][C]-7245.33764561161[/C][/ROW]
[ROW][C]79[/C][C]600991[/C][C]601042.887051348[/C][C]-51.887051348458[/C][/ROW]
[ROW][C]80[/C][C]604378[/C][C]613817.429517514[/C][C]-9439.42951751396[/C][/ROW]
[ROW][C]81[/C][C]586111[/C][C]593418.244316011[/C][C]-7307.2443160112[/C][/ROW]
[ROW][C]82[/C][C]563668[/C][C]576129.207454023[/C][C]-12461.207454023[/C][/ROW]
[ROW][C]83[/C][C]548604[/C][C]557730.618338833[/C][C]-9126.61833883275[/C][/ROW]
[ROW][C]84[/C][C]551174[/C][C]552558.54302412[/C][C]-1384.5430241198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160892&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160892&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
13590865576660.77777777814204.2222222224
14589379590260.306126556-881.306126555661
15584428591002.852765093-6574.85276509286
16573100579623.819570227-6523.81957022694
17567456571696.865699112-4240.86569911207
18569028570523.216726793-1495.21672679321
19620735611997.889499838737.1105001698
20628884635570.193965123-6686.19396512269
21628232631101.425721615-2869.42572161485
22612117624594.144182965-12477.1441829646
23595404590629.2609835124774.73901648796
24597141588187.5530896368953.44691036385
25593408591847.7534050711560.24659492902
26590072584118.7014958785953.2985041223
27579799582268.210538545-2469.21053854469
28574205570513.291120743691.70887925988
29572775571364.9272750061410.07272499404
30572942578750.854664387-5808.85466438683
31619567623402.713234637-3835.71323463658
32625809629919.796266263-4110.79626626277
33619916626192.667247883-6276.66724788328
34587625610187.614036317-22562.6140363168
35565742568064.734983354-2322.73498335388
36557274551378.3693551125895.63064488769
37560576537698.72428154122877.2757184589
38548854541689.5056134417164.494386559
39531673534689.711181672-3016.71118167241
40525919521850.363228224068.63677177951
41511038519231.74213937-8193.74213937018
42498662510823.019342676-12161.0193426763
43555362542348.18494423713013.8150557631
44564591556892.0507460717698.94925392873
45541657562503.610281283-20846.6102812834
46527070527611.911253444-541.911253443803
47509846512833.742562511-2987.742562511
48514258504471.5380471289786.46195287246
49516922506940.758851859981.24114815047
50507561498730.9252703928830.07472960826
51492622491472.481810421149.51818958012
52490243488182.6665695122060.33343048819
53469357483169.601294187-13812.6012941867
54477580470707.4752214686872.52477853181
55528379532851.295520745-4472.29552074533
56533590536057.065220084-2467.06522008404
57517945521852.721673113-3907.72167311289
58506174509753.180419189-3579.18041918887
59501866495428.5199460896437.48005391052
60516141505142.19961841510998.8003815851
61528222516386.27152395911835.7284760414
62532638517669.66479348914968.3352065106
63536322522869.96499766513452.0350023345
64536535544503.254168159-7968.25416815933
65523597539739.085257562-16142.0852575619
66536214544910.89142213-8696.8914221304
67586570597643.208942092-11073.2089420923
68596594599134.680701142-2540.68070114183
69580523586010.403751176-5487.40375117643
70564478574006.859997136-9528.85999713605
71557560558013.286943295-453.286943294574
72575093560417.60095231314675.399047687
73580112571230.2487546968881.75124530401
74574761567467.310872627293.68912738003
75563250559558.8799733093691.120026691
76551531555101.761710292-3570.76171029196
77537034539997.241889586-2963.24188958644
78544686551931.337645612-7245.33764561161
79600991601042.887051348-51.887051348458
80604378613817.429517514-9439.42951751396
81586111593418.244316011-7307.2443160112
82563668576129.207454023-12461.207454023
83548604557730.618338833-9126.61833883275
84551174552558.54302412-1384.5430241198







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85536337.042572491518895.350657847553778.734487134
86507716.989583215482200.350016331533233.629150099
87472001.586735957435371.894854896508631.278617019
88439025.478900119389092.335508439488958.622291799
89404456.463150598339471.447690209469441.478610988
90396030.189996695314494.096773365477566.283220026
91434912.587165599335485.400266005534339.774065192
92426803.982633983308258.020581708545349.944686258
93399843.268391761261035.944142986538650.592640537
94375155.209455566215011.680619818535298.738291313
95361218.039064001178719.341254768543716.736873235
96364051.169026344158225.64149881569876.696553878

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 536337.042572491 & 518895.350657847 & 553778.734487134 \tabularnewline
86 & 507716.989583215 & 482200.350016331 & 533233.629150099 \tabularnewline
87 & 472001.586735957 & 435371.894854896 & 508631.278617019 \tabularnewline
88 & 439025.478900119 & 389092.335508439 & 488958.622291799 \tabularnewline
89 & 404456.463150598 & 339471.447690209 & 469441.478610988 \tabularnewline
90 & 396030.189996695 & 314494.096773365 & 477566.283220026 \tabularnewline
91 & 434912.587165599 & 335485.400266005 & 534339.774065192 \tabularnewline
92 & 426803.982633983 & 308258.020581708 & 545349.944686258 \tabularnewline
93 & 399843.268391761 & 261035.944142986 & 538650.592640537 \tabularnewline
94 & 375155.209455566 & 215011.680619818 & 535298.738291313 \tabularnewline
95 & 361218.039064001 & 178719.341254768 & 543716.736873235 \tabularnewline
96 & 364051.169026344 & 158225.64149881 & 569876.696553878 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160892&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]85[/C][C]536337.042572491[/C][C]518895.350657847[/C][C]553778.734487134[/C][/ROW]
[ROW][C]86[/C][C]507716.989583215[/C][C]482200.350016331[/C][C]533233.629150099[/C][/ROW]
[ROW][C]87[/C][C]472001.586735957[/C][C]435371.894854896[/C][C]508631.278617019[/C][/ROW]
[ROW][C]88[/C][C]439025.478900119[/C][C]389092.335508439[/C][C]488958.622291799[/C][/ROW]
[ROW][C]89[/C][C]404456.463150598[/C][C]339471.447690209[/C][C]469441.478610988[/C][/ROW]
[ROW][C]90[/C][C]396030.189996695[/C][C]314494.096773365[/C][C]477566.283220026[/C][/ROW]
[ROW][C]91[/C][C]434912.587165599[/C][C]335485.400266005[/C][C]534339.774065192[/C][/ROW]
[ROW][C]92[/C][C]426803.982633983[/C][C]308258.020581708[/C][C]545349.944686258[/C][/ROW]
[ROW][C]93[/C][C]399843.268391761[/C][C]261035.944142986[/C][C]538650.592640537[/C][/ROW]
[ROW][C]94[/C][C]375155.209455566[/C][C]215011.680619818[/C][C]535298.738291313[/C][/ROW]
[ROW][C]95[/C][C]361218.039064001[/C][C]178719.341254768[/C][C]543716.736873235[/C][/ROW]
[ROW][C]96[/C][C]364051.169026344[/C][C]158225.64149881[/C][C]569876.696553878[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160892&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160892&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
85536337.042572491518895.350657847553778.734487134
86507716.989583215482200.350016331533233.629150099
87472001.586735957435371.894854896508631.278617019
88439025.478900119389092.335508439488958.622291799
89404456.463150598339471.447690209469441.478610988
90396030.189996695314494.096773365477566.283220026
91434912.587165599335485.400266005534339.774065192
92426803.982633983308258.020581708545349.944686258
93399843.268391761261035.944142986538650.592640537
94375155.209455566215011.680619818535298.738291313
95361218.039064001178719.341254768543716.736873235
96364051.169026344158225.64149881569876.696553878



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=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')