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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 29 Nov 2014 14:07:38 +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/2014/Nov/29/t1417270067y2woq4197l3za4k.htm/, Retrieved Sun, 19 May 2024 13:02:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261124, Retrieved Sun, 19 May 2024 13:02:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-29 14:07:38] [dfd11b28041a8e54be4091fbe3743b64] [Current]
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Dataseries X:
376
376
377
380
380
381
385
385
386
386
385
384
382
379
376
375
370
367
369
366
363
359
355
350
349
351
351
352
352
354
355
356
354
349
350
349
350
352
370
370
371
372
373
373
375
381
383
386
390
394
397
401
403
405
407
406
406
407
406
404
405
404
402
401
401
398
401
399
390
391
390
387




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261124&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261124&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261124&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999957857792944
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999957857792944 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261124&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]0.999957857792944[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261124&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261124&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
alpha0.999957857792944
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23763760
33773761
4380376.9999578577933.00004214220706
5380379.9998735716030.000126428397152267
6381379.9999999946721.00000000532799
7385380.9999578577934.00004214220723
8385384.9998314293960.000168570604216711
9386384.9999999928961.00000000710395
10386385.9999578577934.2142207348661e-05
11385385.999999998224-0.999999998224041
12384385.000042142207-1.00004214220695
13382384.000042143983-2.00004214398302
14379382.00008428619-3.00008428619014
15376379.000126430173-3.00012643017317
16375376.000126431949-1.00012643194924
17370375.000042147535-5.00004214753517
18367370.000210712811-3.00021071281145
19369367.0001264355011.9998735644989
20366368.999915720914-2.99991572091415
21363366.000126423069-3.00012642306945
22359363.000126431949-4.0001264319489
23355359.000168574156-4.00016857415631
24350355.000168575932-5.00016857593232
25349350.000210718139-1.00021071813944
26351349.0000421510871.9999578489128
27351350.9999157173628.42826377720485e-05
28352350.9999999964481.00000000355186
29352351.9999578577934.21422071781308e-05
30354351.9999999982242.00000000177596
31355353.9999157155861.00008428441419
32356354.9999578542411.00004214575898
33354355.999957856017-1.99995785601681
34349354.000084282638-5.00008428263811
35350349.0002107145870.999789285412874
36349349.999957866673-0.999957866672901
37350349.0000421404310.999957859568553
38352349.9999578595692.00004214043116
39370351.9999157138118.00008428619
40370369.9992414367210.000758563279021018
41371369.9999999680321.00000003196755
42372370.9999578577921.00004214220843
43373371.9999578560171.00004214398302
44373372.9999578560174.21439831370662e-05
45375372.9999999982242.00000000177607
46381374.9999157155866.00008428441419
47383380.9997471432062.00025285679425
48386382.999915704933.00008429507005
49390385.9998735698264.00012643017357
50394389.9998314258444.00016857415625
51397393.9998314240683.00016857593232
52401396.9998735662754.00012643372531
53403400.9998314258442.00016857415642
54405402.9999157084822.00008429151819
55407404.9999157120342.00008428796633
56406406.999915712034-0.999915712033783
57406406.000042138655-4.21386549760427e-05
58407406.0000000017760.999999998224212
59406406.999957857793-0.999957857792992
60404406.000042140431-2.00004214043111
61405404.000084286190.999915713809969
62404404.999957861345-0.999957861344967
63402404.000042140431-2.00004214043128
64401402.00008428619-1.00008428619003
65401401.000042145759-4.21457590391583e-05
66398401.000000001776-3.00000000177607
67401398.0001264266212.99987357337875
68399400.999873578707-1.99987357870668
69390399.000084279086-9.00008427908642
70391390.0003792834150.999620716584786
71390390.999957873777-0.999957873776793
72387390.000042140432-3.00004214043179

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 376 & 376 & 0 \tabularnewline
3 & 377 & 376 & 1 \tabularnewline
4 & 380 & 376.999957857793 & 3.00004214220706 \tabularnewline
5 & 380 & 379.999873571603 & 0.000126428397152267 \tabularnewline
6 & 381 & 379.999999994672 & 1.00000000532799 \tabularnewline
7 & 385 & 380.999957857793 & 4.00004214220723 \tabularnewline
8 & 385 & 384.999831429396 & 0.000168570604216711 \tabularnewline
9 & 386 & 384.999999992896 & 1.00000000710395 \tabularnewline
10 & 386 & 385.999957857793 & 4.2142207348661e-05 \tabularnewline
11 & 385 & 385.999999998224 & -0.999999998224041 \tabularnewline
12 & 384 & 385.000042142207 & -1.00004214220695 \tabularnewline
13 & 382 & 384.000042143983 & -2.00004214398302 \tabularnewline
14 & 379 & 382.00008428619 & -3.00008428619014 \tabularnewline
15 & 376 & 379.000126430173 & -3.00012643017317 \tabularnewline
16 & 375 & 376.000126431949 & -1.00012643194924 \tabularnewline
17 & 370 & 375.000042147535 & -5.00004214753517 \tabularnewline
18 & 367 & 370.000210712811 & -3.00021071281145 \tabularnewline
19 & 369 & 367.000126435501 & 1.9998735644989 \tabularnewline
20 & 366 & 368.999915720914 & -2.99991572091415 \tabularnewline
21 & 363 & 366.000126423069 & -3.00012642306945 \tabularnewline
22 & 359 & 363.000126431949 & -4.0001264319489 \tabularnewline
23 & 355 & 359.000168574156 & -4.00016857415631 \tabularnewline
24 & 350 & 355.000168575932 & -5.00016857593232 \tabularnewline
25 & 349 & 350.000210718139 & -1.00021071813944 \tabularnewline
26 & 351 & 349.000042151087 & 1.9999578489128 \tabularnewline
27 & 351 & 350.999915717362 & 8.42826377720485e-05 \tabularnewline
28 & 352 & 350.999999996448 & 1.00000000355186 \tabularnewline
29 & 352 & 351.999957857793 & 4.21422071781308e-05 \tabularnewline
30 & 354 & 351.999999998224 & 2.00000000177596 \tabularnewline
31 & 355 & 353.999915715586 & 1.00008428441419 \tabularnewline
32 & 356 & 354.999957854241 & 1.00004214575898 \tabularnewline
33 & 354 & 355.999957856017 & -1.99995785601681 \tabularnewline
34 & 349 & 354.000084282638 & -5.00008428263811 \tabularnewline
35 & 350 & 349.000210714587 & 0.999789285412874 \tabularnewline
36 & 349 & 349.999957866673 & -0.999957866672901 \tabularnewline
37 & 350 & 349.000042140431 & 0.999957859568553 \tabularnewline
38 & 352 & 349.999957859569 & 2.00004214043116 \tabularnewline
39 & 370 & 351.99991571381 & 18.00008428619 \tabularnewline
40 & 370 & 369.999241436721 & 0.000758563279021018 \tabularnewline
41 & 371 & 369.999999968032 & 1.00000003196755 \tabularnewline
42 & 372 & 370.999957857792 & 1.00004214220843 \tabularnewline
43 & 373 & 371.999957856017 & 1.00004214398302 \tabularnewline
44 & 373 & 372.999957856017 & 4.21439831370662e-05 \tabularnewline
45 & 375 & 372.999999998224 & 2.00000000177607 \tabularnewline
46 & 381 & 374.999915715586 & 6.00008428441419 \tabularnewline
47 & 383 & 380.999747143206 & 2.00025285679425 \tabularnewline
48 & 386 & 382.99991570493 & 3.00008429507005 \tabularnewline
49 & 390 & 385.999873569826 & 4.00012643017357 \tabularnewline
50 & 394 & 389.999831425844 & 4.00016857415625 \tabularnewline
51 & 397 & 393.999831424068 & 3.00016857593232 \tabularnewline
52 & 401 & 396.999873566275 & 4.00012643372531 \tabularnewline
53 & 403 & 400.999831425844 & 2.00016857415642 \tabularnewline
54 & 405 & 402.999915708482 & 2.00008429151819 \tabularnewline
55 & 407 & 404.999915712034 & 2.00008428796633 \tabularnewline
56 & 406 & 406.999915712034 & -0.999915712033783 \tabularnewline
57 & 406 & 406.000042138655 & -4.21386549760427e-05 \tabularnewline
58 & 407 & 406.000000001776 & 0.999999998224212 \tabularnewline
59 & 406 & 406.999957857793 & -0.999957857792992 \tabularnewline
60 & 404 & 406.000042140431 & -2.00004214043111 \tabularnewline
61 & 405 & 404.00008428619 & 0.999915713809969 \tabularnewline
62 & 404 & 404.999957861345 & -0.999957861344967 \tabularnewline
63 & 402 & 404.000042140431 & -2.00004214043128 \tabularnewline
64 & 401 & 402.00008428619 & -1.00008428619003 \tabularnewline
65 & 401 & 401.000042145759 & -4.21457590391583e-05 \tabularnewline
66 & 398 & 401.000000001776 & -3.00000000177607 \tabularnewline
67 & 401 & 398.000126426621 & 2.99987357337875 \tabularnewline
68 & 399 & 400.999873578707 & -1.99987357870668 \tabularnewline
69 & 390 & 399.000084279086 & -9.00008427908642 \tabularnewline
70 & 391 & 390.000379283415 & 0.999620716584786 \tabularnewline
71 & 390 & 390.999957873777 & -0.999957873776793 \tabularnewline
72 & 387 & 390.000042140432 & -3.00004214043179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261124&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]2[/C][C]376[/C][C]376[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]377[/C][C]376[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]380[/C][C]376.999957857793[/C][C]3.00004214220706[/C][/ROW]
[ROW][C]5[/C][C]380[/C][C]379.999873571603[/C][C]0.000126428397152267[/C][/ROW]
[ROW][C]6[/C][C]381[/C][C]379.999999994672[/C][C]1.00000000532799[/C][/ROW]
[ROW][C]7[/C][C]385[/C][C]380.999957857793[/C][C]4.00004214220723[/C][/ROW]
[ROW][C]8[/C][C]385[/C][C]384.999831429396[/C][C]0.000168570604216711[/C][/ROW]
[ROW][C]9[/C][C]386[/C][C]384.999999992896[/C][C]1.00000000710395[/C][/ROW]
[ROW][C]10[/C][C]386[/C][C]385.999957857793[/C][C]4.2142207348661e-05[/C][/ROW]
[ROW][C]11[/C][C]385[/C][C]385.999999998224[/C][C]-0.999999998224041[/C][/ROW]
[ROW][C]12[/C][C]384[/C][C]385.000042142207[/C][C]-1.00004214220695[/C][/ROW]
[ROW][C]13[/C][C]382[/C][C]384.000042143983[/C][C]-2.00004214398302[/C][/ROW]
[ROW][C]14[/C][C]379[/C][C]382.00008428619[/C][C]-3.00008428619014[/C][/ROW]
[ROW][C]15[/C][C]376[/C][C]379.000126430173[/C][C]-3.00012643017317[/C][/ROW]
[ROW][C]16[/C][C]375[/C][C]376.000126431949[/C][C]-1.00012643194924[/C][/ROW]
[ROW][C]17[/C][C]370[/C][C]375.000042147535[/C][C]-5.00004214753517[/C][/ROW]
[ROW][C]18[/C][C]367[/C][C]370.000210712811[/C][C]-3.00021071281145[/C][/ROW]
[ROW][C]19[/C][C]369[/C][C]367.000126435501[/C][C]1.9998735644989[/C][/ROW]
[ROW][C]20[/C][C]366[/C][C]368.999915720914[/C][C]-2.99991572091415[/C][/ROW]
[ROW][C]21[/C][C]363[/C][C]366.000126423069[/C][C]-3.00012642306945[/C][/ROW]
[ROW][C]22[/C][C]359[/C][C]363.000126431949[/C][C]-4.0001264319489[/C][/ROW]
[ROW][C]23[/C][C]355[/C][C]359.000168574156[/C][C]-4.00016857415631[/C][/ROW]
[ROW][C]24[/C][C]350[/C][C]355.000168575932[/C][C]-5.00016857593232[/C][/ROW]
[ROW][C]25[/C][C]349[/C][C]350.000210718139[/C][C]-1.00021071813944[/C][/ROW]
[ROW][C]26[/C][C]351[/C][C]349.000042151087[/C][C]1.9999578489128[/C][/ROW]
[ROW][C]27[/C][C]351[/C][C]350.999915717362[/C][C]8.42826377720485e-05[/C][/ROW]
[ROW][C]28[/C][C]352[/C][C]350.999999996448[/C][C]1.00000000355186[/C][/ROW]
[ROW][C]29[/C][C]352[/C][C]351.999957857793[/C][C]4.21422071781308e-05[/C][/ROW]
[ROW][C]30[/C][C]354[/C][C]351.999999998224[/C][C]2.00000000177596[/C][/ROW]
[ROW][C]31[/C][C]355[/C][C]353.999915715586[/C][C]1.00008428441419[/C][/ROW]
[ROW][C]32[/C][C]356[/C][C]354.999957854241[/C][C]1.00004214575898[/C][/ROW]
[ROW][C]33[/C][C]354[/C][C]355.999957856017[/C][C]-1.99995785601681[/C][/ROW]
[ROW][C]34[/C][C]349[/C][C]354.000084282638[/C][C]-5.00008428263811[/C][/ROW]
[ROW][C]35[/C][C]350[/C][C]349.000210714587[/C][C]0.999789285412874[/C][/ROW]
[ROW][C]36[/C][C]349[/C][C]349.999957866673[/C][C]-0.999957866672901[/C][/ROW]
[ROW][C]37[/C][C]350[/C][C]349.000042140431[/C][C]0.999957859568553[/C][/ROW]
[ROW][C]38[/C][C]352[/C][C]349.999957859569[/C][C]2.00004214043116[/C][/ROW]
[ROW][C]39[/C][C]370[/C][C]351.99991571381[/C][C]18.00008428619[/C][/ROW]
[ROW][C]40[/C][C]370[/C][C]369.999241436721[/C][C]0.000758563279021018[/C][/ROW]
[ROW][C]41[/C][C]371[/C][C]369.999999968032[/C][C]1.00000003196755[/C][/ROW]
[ROW][C]42[/C][C]372[/C][C]370.999957857792[/C][C]1.00004214220843[/C][/ROW]
[ROW][C]43[/C][C]373[/C][C]371.999957856017[/C][C]1.00004214398302[/C][/ROW]
[ROW][C]44[/C][C]373[/C][C]372.999957856017[/C][C]4.21439831370662e-05[/C][/ROW]
[ROW][C]45[/C][C]375[/C][C]372.999999998224[/C][C]2.00000000177607[/C][/ROW]
[ROW][C]46[/C][C]381[/C][C]374.999915715586[/C][C]6.00008428441419[/C][/ROW]
[ROW][C]47[/C][C]383[/C][C]380.999747143206[/C][C]2.00025285679425[/C][/ROW]
[ROW][C]48[/C][C]386[/C][C]382.99991570493[/C][C]3.00008429507005[/C][/ROW]
[ROW][C]49[/C][C]390[/C][C]385.999873569826[/C][C]4.00012643017357[/C][/ROW]
[ROW][C]50[/C][C]394[/C][C]389.999831425844[/C][C]4.00016857415625[/C][/ROW]
[ROW][C]51[/C][C]397[/C][C]393.999831424068[/C][C]3.00016857593232[/C][/ROW]
[ROW][C]52[/C][C]401[/C][C]396.999873566275[/C][C]4.00012643372531[/C][/ROW]
[ROW][C]53[/C][C]403[/C][C]400.999831425844[/C][C]2.00016857415642[/C][/ROW]
[ROW][C]54[/C][C]405[/C][C]402.999915708482[/C][C]2.00008429151819[/C][/ROW]
[ROW][C]55[/C][C]407[/C][C]404.999915712034[/C][C]2.00008428796633[/C][/ROW]
[ROW][C]56[/C][C]406[/C][C]406.999915712034[/C][C]-0.999915712033783[/C][/ROW]
[ROW][C]57[/C][C]406[/C][C]406.000042138655[/C][C]-4.21386549760427e-05[/C][/ROW]
[ROW][C]58[/C][C]407[/C][C]406.000000001776[/C][C]0.999999998224212[/C][/ROW]
[ROW][C]59[/C][C]406[/C][C]406.999957857793[/C][C]-0.999957857792992[/C][/ROW]
[ROW][C]60[/C][C]404[/C][C]406.000042140431[/C][C]-2.00004214043111[/C][/ROW]
[ROW][C]61[/C][C]405[/C][C]404.00008428619[/C][C]0.999915713809969[/C][/ROW]
[ROW][C]62[/C][C]404[/C][C]404.999957861345[/C][C]-0.999957861344967[/C][/ROW]
[ROW][C]63[/C][C]402[/C][C]404.000042140431[/C][C]-2.00004214043128[/C][/ROW]
[ROW][C]64[/C][C]401[/C][C]402.00008428619[/C][C]-1.00008428619003[/C][/ROW]
[ROW][C]65[/C][C]401[/C][C]401.000042145759[/C][C]-4.21457590391583e-05[/C][/ROW]
[ROW][C]66[/C][C]398[/C][C]401.000000001776[/C][C]-3.00000000177607[/C][/ROW]
[ROW][C]67[/C][C]401[/C][C]398.000126426621[/C][C]2.99987357337875[/C][/ROW]
[ROW][C]68[/C][C]399[/C][C]400.999873578707[/C][C]-1.99987357870668[/C][/ROW]
[ROW][C]69[/C][C]390[/C][C]399.000084279086[/C][C]-9.00008427908642[/C][/ROW]
[ROW][C]70[/C][C]391[/C][C]390.000379283415[/C][C]0.999620716584786[/C][/ROW]
[ROW][C]71[/C][C]390[/C][C]390.999957873777[/C][C]-0.999957873776793[/C][/ROW]
[ROW][C]72[/C][C]387[/C][C]390.000042140432[/C][C]-3.00004214043179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261124&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261124&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
23763760
33773761
4380376.9999578577933.00004214220706
5380379.9998735716030.000126428397152267
6381379.9999999946721.00000000532799
7385380.9999578577934.00004214220723
8385384.9998314293960.000168570604216711
9386384.9999999928961.00000000710395
10386385.9999578577934.2142207348661e-05
11385385.999999998224-0.999999998224041
12384385.000042142207-1.00004214220695
13382384.000042143983-2.00004214398302
14379382.00008428619-3.00008428619014
15376379.000126430173-3.00012643017317
16375376.000126431949-1.00012643194924
17370375.000042147535-5.00004214753517
18367370.000210712811-3.00021071281145
19369367.0001264355011.9998735644989
20366368.999915720914-2.99991572091415
21363366.000126423069-3.00012642306945
22359363.000126431949-4.0001264319489
23355359.000168574156-4.00016857415631
24350355.000168575932-5.00016857593232
25349350.000210718139-1.00021071813944
26351349.0000421510871.9999578489128
27351350.9999157173628.42826377720485e-05
28352350.9999999964481.00000000355186
29352351.9999578577934.21422071781308e-05
30354351.9999999982242.00000000177596
31355353.9999157155861.00008428441419
32356354.9999578542411.00004214575898
33354355.999957856017-1.99995785601681
34349354.000084282638-5.00008428263811
35350349.0002107145870.999789285412874
36349349.999957866673-0.999957866672901
37350349.0000421404310.999957859568553
38352349.9999578595692.00004214043116
39370351.9999157138118.00008428619
40370369.9992414367210.000758563279021018
41371369.9999999680321.00000003196755
42372370.9999578577921.00004214220843
43373371.9999578560171.00004214398302
44373372.9999578560174.21439831370662e-05
45375372.9999999982242.00000000177607
46381374.9999157155866.00008428441419
47383380.9997471432062.00025285679425
48386382.999915704933.00008429507005
49390385.9998735698264.00012643017357
50394389.9998314258444.00016857415625
51397393.9998314240683.00016857593232
52401396.9998735662754.00012643372531
53403400.9998314258442.00016857415642
54405402.9999157084822.00008429151819
55407404.9999157120342.00008428796633
56406406.999915712034-0.999915712033783
57406406.000042138655-4.21386549760427e-05
58407406.0000000017760.999999998224212
59406406.999957857793-0.999957857792992
60404406.000042140431-2.00004214043111
61405404.000084286190.999915713809969
62404404.999957861345-0.999957861344967
63402404.000042140431-2.00004214043128
64401402.00008428619-1.00008428619003
65401401.000042145759-4.21457590391583e-05
66398401.000000001776-3.00000000177607
67401398.0001264266212.99987357337875
68399400.999873578707-1.99987357870668
69390399.000084279086-9.00008427908642
70391390.0003792834150.999620716584786
71390390.999957873777-0.999957873776793
72387390.000042140432-3.00004214043179







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73387.000126428397380.418634755886393.581618100908
74387.000126428397377.692687764556396.307565092238
75387.000126428397375.600968725874398.39928413092
76387.000126428397373.83755911906400.162693737734
77387.000126428397372.283959807342401.716293049452
78387.000126428397370.87939623822403.120856618574
79387.000126428397369.587765195345404.412487661449
80387.000126428397368.385543286244405.61470957055
81387.000126428397367.256391032025406.743861824769
82387.000126428397366.188411716539407.811841140255
83387.000126428397365.172624255826408.827628600968
84387.000126428397364.202051225884409.79820163091

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 387.000126428397 & 380.418634755886 & 393.581618100908 \tabularnewline
74 & 387.000126428397 & 377.692687764556 & 396.307565092238 \tabularnewline
75 & 387.000126428397 & 375.600968725874 & 398.39928413092 \tabularnewline
76 & 387.000126428397 & 373.83755911906 & 400.162693737734 \tabularnewline
77 & 387.000126428397 & 372.283959807342 & 401.716293049452 \tabularnewline
78 & 387.000126428397 & 370.87939623822 & 403.120856618574 \tabularnewline
79 & 387.000126428397 & 369.587765195345 & 404.412487661449 \tabularnewline
80 & 387.000126428397 & 368.385543286244 & 405.61470957055 \tabularnewline
81 & 387.000126428397 & 367.256391032025 & 406.743861824769 \tabularnewline
82 & 387.000126428397 & 366.188411716539 & 407.811841140255 \tabularnewline
83 & 387.000126428397 & 365.172624255826 & 408.827628600968 \tabularnewline
84 & 387.000126428397 & 364.202051225884 & 409.79820163091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261124&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]73[/C][C]387.000126428397[/C][C]380.418634755886[/C][C]393.581618100908[/C][/ROW]
[ROW][C]74[/C][C]387.000126428397[/C][C]377.692687764556[/C][C]396.307565092238[/C][/ROW]
[ROW][C]75[/C][C]387.000126428397[/C][C]375.600968725874[/C][C]398.39928413092[/C][/ROW]
[ROW][C]76[/C][C]387.000126428397[/C][C]373.83755911906[/C][C]400.162693737734[/C][/ROW]
[ROW][C]77[/C][C]387.000126428397[/C][C]372.283959807342[/C][C]401.716293049452[/C][/ROW]
[ROW][C]78[/C][C]387.000126428397[/C][C]370.87939623822[/C][C]403.120856618574[/C][/ROW]
[ROW][C]79[/C][C]387.000126428397[/C][C]369.587765195345[/C][C]404.412487661449[/C][/ROW]
[ROW][C]80[/C][C]387.000126428397[/C][C]368.385543286244[/C][C]405.61470957055[/C][/ROW]
[ROW][C]81[/C][C]387.000126428397[/C][C]367.256391032025[/C][C]406.743861824769[/C][/ROW]
[ROW][C]82[/C][C]387.000126428397[/C][C]366.188411716539[/C][C]407.811841140255[/C][/ROW]
[ROW][C]83[/C][C]387.000126428397[/C][C]365.172624255826[/C][C]408.827628600968[/C][/ROW]
[ROW][C]84[/C][C]387.000126428397[/C][C]364.202051225884[/C][C]409.79820163091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261124&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261124&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
73387.000126428397380.418634755886393.581618100908
74387.000126428397377.692687764556396.307565092238
75387.000126428397375.600968725874398.39928413092
76387.000126428397373.83755911906400.162693737734
77387.000126428397372.283959807342401.716293049452
78387.000126428397370.87939623822403.120856618574
79387.000126428397369.587765195345404.412487661449
80387.000126428397368.385543286244405.61470957055
81387.000126428397367.256391032025406.743861824769
82387.000126428397366.188411716539407.811841140255
83387.000126428397365.172624255826408.827628600968
84387.000126428397364.202051225884409.79820163091



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')