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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 computationThu, 08 May 2008 16:00:10 -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/09/t1210285050xiixa3vy427ubar.htm/, Retrieved Mon, 29 Apr 2024 22:13:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12063, Retrieved Mon, 29 Apr 2024 22:13:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmultiplicative, holts-winters, tijdreeks, registratie, auto's
Estimated Impact297
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:56:43] [74be16979710d4c4e7c6647856088456]
-   PD    [Exponential Smoothing] [multiplicative ho...] [2008-05-08 22:00:10] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-  MPD      [Exponential Smoothing] [Workshop 8 - Expo...] [2010-11-30 08:26:52] [1429a1a14191a86916b95357f6de790b]
- RM          [Exponential Smoothing] [] [2011-11-29 20:31:39] [74be16979710d4c4e7c6647856088456]
- R           [Exponential Smoothing] [Exponential Smoot...] [2011-12-01 20:56:13] [3dd791303389e75e672968b227170a72]
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Dataseries X:
56421
53152
53536
52408
41454
38271
35306
26414
31917
38030
27534
18387
50556
43901
48572
43899
37532
40357
35489
29027
34485
42598
30306
26451
47460
50104
61465
53726
39477
43895
31481
29896
33842
39120
33702
25094
51442
45594
52518
48564
41745
49585
32747
33379
35645
37034
35681
20972
58552
54955
65540
51570
51145
46641
35704
33253
35193
41668
34865
21210
56126
49231
59723
48103
47472
50497
40059
34149
36860
46356
36577




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12063&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]1 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=12063&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12063&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0839511832014079
beta0.000901008505166857
gamma0.332107274688902

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0839511832014079 \tabularnewline
beta & 0.000901008505166857 \tabularnewline
gamma & 0.332107274688902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12063&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]0.0839511832014079[/C][/ROW]
[ROW][C]beta[/C][C]0.000901008505166857[/C][/ROW]
[ROW][C]gamma[/C][C]0.332107274688902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12063&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12063&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
alpha0.0839511832014079
beta0.000901008505166857
gamma0.332107274688902







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135055650171.6294214468384.3705785532
144390143678.138856552222.861143448012
154857248307.8467109056264.153289094429
164389943551.2092739331347.790726066887
173753237142.4550482428389.544951757176
184035739697.3815437588659.618456241224
193548934940.8176738392548.182326160771
202902728659.9527614384367.047238561579
213448533559.6925869967925.307413003276
224259840772.11083390231825.88916609770
233030628904.29254600861401.70745399144
242645125309.24638424491141.75361575508
254746054449.3897326998-6989.38973269978
265010446809.77945058013294.22054941986
276146552043.02758986119421.97241013893
285372647627.53892028836098.46107971165
293947741041.7339863003-1564.7339863003
304389543749.2787984640145.721201535962
313148138438.2903889479-6957.29038894793
322989630971.5037701096-1075.50377010957
333384236271.5255148524-2429.52551485235
343912043930.9885469839-4810.9885469839
353370230768.64861416442933.35138583565
362509427013.4599955897-1919.45999558971
375144254522.4051628419-3080.40516284193
384559450130.2407638437-4536.24076384374
395251856751.5887668554-4233.58876685536
404856450076.2193714957-1512.21937149567
414174540525.36205481611219.63794518391
424958544000.18689369885584.81310630123
433274736834.6941442789-4087.6941442789
443337931285.93095631462093.06904368541
453564536578.0412183693-933.041218369319
463703443854.0936960822-6820.09369608221
473568132565.70119906523115.29880093484
482097227183.8757485128-6211.87574851281
495855254378.99409539384173.00590460616
505495550014.6683357364940.33166426398
516554057806.1348095967733.86519040394
525157052615.2593318077-1045.25933180771
535114543395.1634936547749.83650634602
544664149061.9837464375-2420.98374643749
553570437643.9982540233-1939.99825402327
563325333932.7830177759-679.783017775873
573519338294.4481858341-3101.44818583415
584166843838.7008424369-2170.70084243691
593486535489.3063727399-624.306372739928
602121026494.3984978382-5284.39849783824
615612658498.6109940148-2372.61099401478
624923153611.4973649141-4380.49736491407
635972361643.2913694242-1920.29136942422
644810352871.902105855-4768.90210585498
654747245944.63866989311527.36133010690
665049747977.06676212692519.93323787311
674005937100.53653912262958.4634608774
683414934141.42281039237.57718960772036
693686037865.8761038096-1005.87610380958
704635643975.25005222982380.74994777018
713657736262.3319912097314.668008790264

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 50556 & 50171.6294214468 & 384.3705785532 \tabularnewline
14 & 43901 & 43678.138856552 & 222.861143448012 \tabularnewline
15 & 48572 & 48307.8467109056 & 264.153289094429 \tabularnewline
16 & 43899 & 43551.2092739331 & 347.790726066887 \tabularnewline
17 & 37532 & 37142.4550482428 & 389.544951757176 \tabularnewline
18 & 40357 & 39697.3815437588 & 659.618456241224 \tabularnewline
19 & 35489 & 34940.8176738392 & 548.182326160771 \tabularnewline
20 & 29027 & 28659.9527614384 & 367.047238561579 \tabularnewline
21 & 34485 & 33559.6925869967 & 925.307413003276 \tabularnewline
22 & 42598 & 40772.1108339023 & 1825.88916609770 \tabularnewline
23 & 30306 & 28904.2925460086 & 1401.70745399144 \tabularnewline
24 & 26451 & 25309.2463842449 & 1141.75361575508 \tabularnewline
25 & 47460 & 54449.3897326998 & -6989.38973269978 \tabularnewline
26 & 50104 & 46809.7794505801 & 3294.22054941986 \tabularnewline
27 & 61465 & 52043.0275898611 & 9421.97241013893 \tabularnewline
28 & 53726 & 47627.5389202883 & 6098.46107971165 \tabularnewline
29 & 39477 & 41041.7339863003 & -1564.7339863003 \tabularnewline
30 & 43895 & 43749.2787984640 & 145.721201535962 \tabularnewline
31 & 31481 & 38438.2903889479 & -6957.29038894793 \tabularnewline
32 & 29896 & 30971.5037701096 & -1075.50377010957 \tabularnewline
33 & 33842 & 36271.5255148524 & -2429.52551485235 \tabularnewline
34 & 39120 & 43930.9885469839 & -4810.9885469839 \tabularnewline
35 & 33702 & 30768.6486141644 & 2933.35138583565 \tabularnewline
36 & 25094 & 27013.4599955897 & -1919.45999558971 \tabularnewline
37 & 51442 & 54522.4051628419 & -3080.40516284193 \tabularnewline
38 & 45594 & 50130.2407638437 & -4536.24076384374 \tabularnewline
39 & 52518 & 56751.5887668554 & -4233.58876685536 \tabularnewline
40 & 48564 & 50076.2193714957 & -1512.21937149567 \tabularnewline
41 & 41745 & 40525.3620548161 & 1219.63794518391 \tabularnewline
42 & 49585 & 44000.1868936988 & 5584.81310630123 \tabularnewline
43 & 32747 & 36834.6941442789 & -4087.6941442789 \tabularnewline
44 & 33379 & 31285.9309563146 & 2093.06904368541 \tabularnewline
45 & 35645 & 36578.0412183693 & -933.041218369319 \tabularnewline
46 & 37034 & 43854.0936960822 & -6820.09369608221 \tabularnewline
47 & 35681 & 32565.7011990652 & 3115.29880093484 \tabularnewline
48 & 20972 & 27183.8757485128 & -6211.87574851281 \tabularnewline
49 & 58552 & 54378.9940953938 & 4173.00590460616 \tabularnewline
50 & 54955 & 50014.668335736 & 4940.33166426398 \tabularnewline
51 & 65540 & 57806.134809596 & 7733.86519040394 \tabularnewline
52 & 51570 & 52615.2593318077 & -1045.25933180771 \tabularnewline
53 & 51145 & 43395.163493654 & 7749.83650634602 \tabularnewline
54 & 46641 & 49061.9837464375 & -2420.98374643749 \tabularnewline
55 & 35704 & 37643.9982540233 & -1939.99825402327 \tabularnewline
56 & 33253 & 33932.7830177759 & -679.783017775873 \tabularnewline
57 & 35193 & 38294.4481858341 & -3101.44818583415 \tabularnewline
58 & 41668 & 43838.7008424369 & -2170.70084243691 \tabularnewline
59 & 34865 & 35489.3063727399 & -624.306372739928 \tabularnewline
60 & 21210 & 26494.3984978382 & -5284.39849783824 \tabularnewline
61 & 56126 & 58498.6109940148 & -2372.61099401478 \tabularnewline
62 & 49231 & 53611.4973649141 & -4380.49736491407 \tabularnewline
63 & 59723 & 61643.2913694242 & -1920.29136942422 \tabularnewline
64 & 48103 & 52871.902105855 & -4768.90210585498 \tabularnewline
65 & 47472 & 45944.6386698931 & 1527.36133010690 \tabularnewline
66 & 50497 & 47977.0667621269 & 2519.93323787311 \tabularnewline
67 & 40059 & 37100.5365391226 & 2958.4634608774 \tabularnewline
68 & 34149 & 34141.4228103923 & 7.57718960772036 \tabularnewline
69 & 36860 & 37865.8761038096 & -1005.87610380958 \tabularnewline
70 & 46356 & 43975.2500522298 & 2380.74994777018 \tabularnewline
71 & 36577 & 36262.3319912097 & 314.668008790264 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12063&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]50556[/C][C]50171.6294214468[/C][C]384.3705785532[/C][/ROW]
[ROW][C]14[/C][C]43901[/C][C]43678.138856552[/C][C]222.861143448012[/C][/ROW]
[ROW][C]15[/C][C]48572[/C][C]48307.8467109056[/C][C]264.153289094429[/C][/ROW]
[ROW][C]16[/C][C]43899[/C][C]43551.2092739331[/C][C]347.790726066887[/C][/ROW]
[ROW][C]17[/C][C]37532[/C][C]37142.4550482428[/C][C]389.544951757176[/C][/ROW]
[ROW][C]18[/C][C]40357[/C][C]39697.3815437588[/C][C]659.618456241224[/C][/ROW]
[ROW][C]19[/C][C]35489[/C][C]34940.8176738392[/C][C]548.182326160771[/C][/ROW]
[ROW][C]20[/C][C]29027[/C][C]28659.9527614384[/C][C]367.047238561579[/C][/ROW]
[ROW][C]21[/C][C]34485[/C][C]33559.6925869967[/C][C]925.307413003276[/C][/ROW]
[ROW][C]22[/C][C]42598[/C][C]40772.1108339023[/C][C]1825.88916609770[/C][/ROW]
[ROW][C]23[/C][C]30306[/C][C]28904.2925460086[/C][C]1401.70745399144[/C][/ROW]
[ROW][C]24[/C][C]26451[/C][C]25309.2463842449[/C][C]1141.75361575508[/C][/ROW]
[ROW][C]25[/C][C]47460[/C][C]54449.3897326998[/C][C]-6989.38973269978[/C][/ROW]
[ROW][C]26[/C][C]50104[/C][C]46809.7794505801[/C][C]3294.22054941986[/C][/ROW]
[ROW][C]27[/C][C]61465[/C][C]52043.0275898611[/C][C]9421.97241013893[/C][/ROW]
[ROW][C]28[/C][C]53726[/C][C]47627.5389202883[/C][C]6098.46107971165[/C][/ROW]
[ROW][C]29[/C][C]39477[/C][C]41041.7339863003[/C][C]-1564.7339863003[/C][/ROW]
[ROW][C]30[/C][C]43895[/C][C]43749.2787984640[/C][C]145.721201535962[/C][/ROW]
[ROW][C]31[/C][C]31481[/C][C]38438.2903889479[/C][C]-6957.29038894793[/C][/ROW]
[ROW][C]32[/C][C]29896[/C][C]30971.5037701096[/C][C]-1075.50377010957[/C][/ROW]
[ROW][C]33[/C][C]33842[/C][C]36271.5255148524[/C][C]-2429.52551485235[/C][/ROW]
[ROW][C]34[/C][C]39120[/C][C]43930.9885469839[/C][C]-4810.9885469839[/C][/ROW]
[ROW][C]35[/C][C]33702[/C][C]30768.6486141644[/C][C]2933.35138583565[/C][/ROW]
[ROW][C]36[/C][C]25094[/C][C]27013.4599955897[/C][C]-1919.45999558971[/C][/ROW]
[ROW][C]37[/C][C]51442[/C][C]54522.4051628419[/C][C]-3080.40516284193[/C][/ROW]
[ROW][C]38[/C][C]45594[/C][C]50130.2407638437[/C][C]-4536.24076384374[/C][/ROW]
[ROW][C]39[/C][C]52518[/C][C]56751.5887668554[/C][C]-4233.58876685536[/C][/ROW]
[ROW][C]40[/C][C]48564[/C][C]50076.2193714957[/C][C]-1512.21937149567[/C][/ROW]
[ROW][C]41[/C][C]41745[/C][C]40525.3620548161[/C][C]1219.63794518391[/C][/ROW]
[ROW][C]42[/C][C]49585[/C][C]44000.1868936988[/C][C]5584.81310630123[/C][/ROW]
[ROW][C]43[/C][C]32747[/C][C]36834.6941442789[/C][C]-4087.6941442789[/C][/ROW]
[ROW][C]44[/C][C]33379[/C][C]31285.9309563146[/C][C]2093.06904368541[/C][/ROW]
[ROW][C]45[/C][C]35645[/C][C]36578.0412183693[/C][C]-933.041218369319[/C][/ROW]
[ROW][C]46[/C][C]37034[/C][C]43854.0936960822[/C][C]-6820.09369608221[/C][/ROW]
[ROW][C]47[/C][C]35681[/C][C]32565.7011990652[/C][C]3115.29880093484[/C][/ROW]
[ROW][C]48[/C][C]20972[/C][C]27183.8757485128[/C][C]-6211.87574851281[/C][/ROW]
[ROW][C]49[/C][C]58552[/C][C]54378.9940953938[/C][C]4173.00590460616[/C][/ROW]
[ROW][C]50[/C][C]54955[/C][C]50014.668335736[/C][C]4940.33166426398[/C][/ROW]
[ROW][C]51[/C][C]65540[/C][C]57806.134809596[/C][C]7733.86519040394[/C][/ROW]
[ROW][C]52[/C][C]51570[/C][C]52615.2593318077[/C][C]-1045.25933180771[/C][/ROW]
[ROW][C]53[/C][C]51145[/C][C]43395.163493654[/C][C]7749.83650634602[/C][/ROW]
[ROW][C]54[/C][C]46641[/C][C]49061.9837464375[/C][C]-2420.98374643749[/C][/ROW]
[ROW][C]55[/C][C]35704[/C][C]37643.9982540233[/C][C]-1939.99825402327[/C][/ROW]
[ROW][C]56[/C][C]33253[/C][C]33932.7830177759[/C][C]-679.783017775873[/C][/ROW]
[ROW][C]57[/C][C]35193[/C][C]38294.4481858341[/C][C]-3101.44818583415[/C][/ROW]
[ROW][C]58[/C][C]41668[/C][C]43838.7008424369[/C][C]-2170.70084243691[/C][/ROW]
[ROW][C]59[/C][C]34865[/C][C]35489.3063727399[/C][C]-624.306372739928[/C][/ROW]
[ROW][C]60[/C][C]21210[/C][C]26494.3984978382[/C][C]-5284.39849783824[/C][/ROW]
[ROW][C]61[/C][C]56126[/C][C]58498.6109940148[/C][C]-2372.61099401478[/C][/ROW]
[ROW][C]62[/C][C]49231[/C][C]53611.4973649141[/C][C]-4380.49736491407[/C][/ROW]
[ROW][C]63[/C][C]59723[/C][C]61643.2913694242[/C][C]-1920.29136942422[/C][/ROW]
[ROW][C]64[/C][C]48103[/C][C]52871.902105855[/C][C]-4768.90210585498[/C][/ROW]
[ROW][C]65[/C][C]47472[/C][C]45944.6386698931[/C][C]1527.36133010690[/C][/ROW]
[ROW][C]66[/C][C]50497[/C][C]47977.0667621269[/C][C]2519.93323787311[/C][/ROW]
[ROW][C]67[/C][C]40059[/C][C]37100.5365391226[/C][C]2958.4634608774[/C][/ROW]
[ROW][C]68[/C][C]34149[/C][C]34141.4228103923[/C][C]7.57718960772036[/C][/ROW]
[ROW][C]69[/C][C]36860[/C][C]37865.8761038096[/C][C]-1005.87610380958[/C][/ROW]
[ROW][C]70[/C][C]46356[/C][C]43975.2500522298[/C][C]2380.74994777018[/C][/ROW]
[ROW][C]71[/C][C]36577[/C][C]36262.3319912097[/C][C]314.668008790264[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12063&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12063&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
135055650171.6294214468384.3705785532
144390143678.138856552222.861143448012
154857248307.8467109056264.153289094429
164389943551.2092739331347.790726066887
173753237142.4550482428389.544951757176
184035739697.3815437588659.618456241224
193548934940.8176738392548.182326160771
202902728659.9527614384367.047238561579
213448533559.6925869967925.307413003276
224259840772.11083390231825.88916609770
233030628904.29254600861401.70745399144
242645125309.24638424491141.75361575508
254746054449.3897326998-6989.38973269978
265010446809.77945058013294.22054941986
276146552043.02758986119421.97241013893
285372647627.53892028836098.46107971165
293947741041.7339863003-1564.7339863003
304389543749.2787984640145.721201535962
313148138438.2903889479-6957.29038894793
322989630971.5037701096-1075.50377010957
333384236271.5255148524-2429.52551485235
343912043930.9885469839-4810.9885469839
353370230768.64861416442933.35138583565
362509427013.4599955897-1919.45999558971
375144254522.4051628419-3080.40516284193
384559450130.2407638437-4536.24076384374
395251856751.5887668554-4233.58876685536
404856450076.2193714957-1512.21937149567
414174540525.36205481611219.63794518391
424958544000.18689369885584.81310630123
433274736834.6941442789-4087.6941442789
443337931285.93095631462093.06904368541
453564536578.0412183693-933.041218369319
463703443854.0936960822-6820.09369608221
473568132565.70119906523115.29880093484
482097227183.8757485128-6211.87574851281
495855254378.99409539384173.00590460616
505495550014.6683357364940.33166426398
516554057806.1348095967733.86519040394
525157052615.2593318077-1045.25933180771
535114543395.1634936547749.83650634602
544664149061.9837464375-2420.98374643749
553570437643.9982540233-1939.99825402327
563325333932.7830177759-679.783017775873
573519338294.4481858341-3101.44818583415
584166843838.7008424369-2170.70084243691
593486535489.3063727399-624.306372739928
602121026494.3984978382-5284.39849783824
615612658498.6109940148-2372.61099401478
624923153611.4973649141-4380.49736491407
635972361643.2913694242-1920.29136942422
644810352871.902105855-4768.90210585498
654747245944.63866989311527.36133010690
665049747977.06676212692519.93323787311
674005937100.53653912262958.4634608774
683414934141.42281039237.57718960772036
693686037865.8761038096-1005.87610380958
704635643975.25005222982380.74994777018
713657736262.3319912097314.668008790264







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7225590.636177466722807.590503727228373.6818512062
7360475.137683927957351.680880127863598.594487728
7454889.059197793751776.485591344858001.6328042426
7564545.979868492961242.449018134367849.5107188514
7654477.337021496451276.585963560157678.0880794326
7749539.703291817946362.046774505752717.35980913
7851872.190857154848600.576043778255143.8056705314
7940249.468711130837129.776004113443369.1614181481
8035922.343303852932823.055864218939021.6307434868
8139507.128551621536279.496745250442734.7603579926
8247109.831663688343640.726858965750578.9364684108
8338140.740800240636399.699059412939881.7825410684

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
72 & 25590.6361774667 & 22807.5905037272 & 28373.6818512062 \tabularnewline
73 & 60475.1376839279 & 57351.6808801278 & 63598.594487728 \tabularnewline
74 & 54889.0591977937 & 51776.4855913448 & 58001.6328042426 \tabularnewline
75 & 64545.9798684929 & 61242.4490181343 & 67849.5107188514 \tabularnewline
76 & 54477.3370214964 & 51276.5859635601 & 57678.0880794326 \tabularnewline
77 & 49539.7032918179 & 46362.0467745057 & 52717.35980913 \tabularnewline
78 & 51872.1908571548 & 48600.5760437782 & 55143.8056705314 \tabularnewline
79 & 40249.4687111308 & 37129.7760041134 & 43369.1614181481 \tabularnewline
80 & 35922.3433038529 & 32823.0558642189 & 39021.6307434868 \tabularnewline
81 & 39507.1285516215 & 36279.4967452504 & 42734.7603579926 \tabularnewline
82 & 47109.8316636883 & 43640.7268589657 & 50578.9364684108 \tabularnewline
83 & 38140.7408002406 & 36399.6990594129 & 39881.7825410684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12063&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]72[/C][C]25590.6361774667[/C][C]22807.5905037272[/C][C]28373.6818512062[/C][/ROW]
[ROW][C]73[/C][C]60475.1376839279[/C][C]57351.6808801278[/C][C]63598.594487728[/C][/ROW]
[ROW][C]74[/C][C]54889.0591977937[/C][C]51776.4855913448[/C][C]58001.6328042426[/C][/ROW]
[ROW][C]75[/C][C]64545.9798684929[/C][C]61242.4490181343[/C][C]67849.5107188514[/C][/ROW]
[ROW][C]76[/C][C]54477.3370214964[/C][C]51276.5859635601[/C][C]57678.0880794326[/C][/ROW]
[ROW][C]77[/C][C]49539.7032918179[/C][C]46362.0467745057[/C][C]52717.35980913[/C][/ROW]
[ROW][C]78[/C][C]51872.1908571548[/C][C]48600.5760437782[/C][C]55143.8056705314[/C][/ROW]
[ROW][C]79[/C][C]40249.4687111308[/C][C]37129.7760041134[/C][C]43369.1614181481[/C][/ROW]
[ROW][C]80[/C][C]35922.3433038529[/C][C]32823.0558642189[/C][C]39021.6307434868[/C][/ROW]
[ROW][C]81[/C][C]39507.1285516215[/C][C]36279.4967452504[/C][C]42734.7603579926[/C][/ROW]
[ROW][C]82[/C][C]47109.8316636883[/C][C]43640.7268589657[/C][C]50578.9364684108[/C][/ROW]
[ROW][C]83[/C][C]38140.7408002406[/C][C]36399.6990594129[/C][C]39881.7825410684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12063&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12063&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
7225590.636177466722807.590503727228373.6818512062
7360475.137683927957351.680880127863598.594487728
7454889.059197793751776.485591344858001.6328042426
7564545.979868492961242.449018134367849.5107188514
7654477.337021496451276.585963560157678.0880794326
7749539.703291817946362.046774505752717.35980913
7851872.190857154848600.576043778255143.8056705314
7940249.468711130837129.776004113443369.1614181481
8035922.343303852932823.055864218939021.6307434868
8139507.128551621536279.496745250442734.7603579926
8247109.831663688343640.726858965750578.9364684108
8338140.740800240636399.699059412939881.7825410684



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=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')