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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 08:10:43 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/26/t1369570316scyltedxy8m1sx9.htm/, Retrieved Mon, 29 Apr 2024 08:51:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210595, Retrieved Mon, 29 Apr 2024 08:51:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [] [2013-05-06 14:56:49] [30fc231a08c03db7f38d4ed6e92eaa2f]
- RMP   [Exponential Smoothing] [] [2013-05-26 12:05:36] [2f0f353a58a70fd7baf0f5141860d820]
- R PD      [Exponential Smoothing] [] [2013-05-26 12:10:43] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
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
555654
547970
540324
530577
520579
518654
572273
581302
563280
547612
538712
540735
561649
558685
545732
536352
527676
530455
581744
598714
583775
571477
563278
564872




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210595&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210595&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210595&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.870022750840911
beta0.292395910563891
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.870022750840911 \tabularnewline
beta & 0.292395910563891 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210595&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]0.870022750840911[/C][/ROW]
[ROW][C]beta[/C][C]0.292395910563891[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210595&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210595&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
alpha0.870022750840911
beta0.292395910563891
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13516922533779.029380342-16857.0293803421
14507561505462.6988330422098.30116695783
15492622488457.434575274164.56542472955
16490243486448.2539206213794.74607937882
17469357465920.1716300843436.82836991618
18477580474114.8663198223465.13368017779
19528379526667.2697560841711.73024391558
20533590538969.454574871-5379.45457487088
21517945511378.8702674186566.12973258155
22506174503964.53934182209.46065819979
23501866490794.45765188711071.5423481127
24516141509179.0070937896961.99290621083
25528222521207.7770459327014.22295406827
26532638528109.42787794528.57212209981
27536322526091.04830997110230.9516900287
28536535543458.854585573-6923.85458557308
29523597524979.269111235-1382.26911123516
30536214539179.427328944-2965.42732894374
31586570594467.82530702-7897.82530702022
32596594603601.831597013-7007.83159701293
33580523581846.977930416-1323.97793041635
34564478570694.43435514-6216.43435513985
35557560552894.6570387124665.34296128759
36575093565090.99499408410002.0050059156
37580112580464.261017083-352.261017083423
38574761579452.684886652-4691.68488665228
39563250566626.960034619-3376.96003461943
40551531562937.41590427-11406.4159042704
41537034533149.4333722753884.56662772491
42544686544937.173301302-251.17330130178
43600991595847.5059103325143.49408966838
44604378613662.602621223-9284.60262122343
45586111587305.654667271-1194.65466727084
46563668572302.592569832-8634.59256983153
47548604549871.063482672-1267.06348267174
48551174552148.283558485-974.283558485447
49555654548382.4057767747271.59422322595
50547970547135.467636333834.532363667269
51540324534390.1191515815933.88084841857
52530577535227.724148924-4650.724148924
53520579512493.5671237328085.43287626759
54518654527656.007261131-9002.00726113131
55572273569685.3681336642587.63186633633
56581302580782.562522697519.437477302505
57563280563882.002457684-602.002457684255
58547612548453.444819823-841.444819823257
59538712535768.1563413592943.8436586411
60540735544826.647038901-4091.64703890134
61561649541706.96998794919942.0300120512
62558685556156.7750514692528.22494853113
63545732551488.484645132-5756.48464513232
64536352543746.230692203-7394.23069220281
65527676522549.4304158665126.56958413403
66530455534432.764440652-3977.7644406521
67581744585133.993647538-3389.99364753766
68598714592035.3182916866678.68170831387
69583775583188.154704268586.84529573191
70571477571905.707427197-428.70742719702
71563278563319.415798767-41.4157987671206
72564872571354.690247905-6482.69024790544

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 516922 & 533779.029380342 & -16857.0293803421 \tabularnewline
14 & 507561 & 505462.698833042 & 2098.30116695783 \tabularnewline
15 & 492622 & 488457.43457527 & 4164.56542472955 \tabularnewline
16 & 490243 & 486448.253920621 & 3794.74607937882 \tabularnewline
17 & 469357 & 465920.171630084 & 3436.82836991618 \tabularnewline
18 & 477580 & 474114.866319822 & 3465.13368017779 \tabularnewline
19 & 528379 & 526667.269756084 & 1711.73024391558 \tabularnewline
20 & 533590 & 538969.454574871 & -5379.45457487088 \tabularnewline
21 & 517945 & 511378.870267418 & 6566.12973258155 \tabularnewline
22 & 506174 & 503964.5393418 & 2209.46065819979 \tabularnewline
23 & 501866 & 490794.457651887 & 11071.5423481127 \tabularnewline
24 & 516141 & 509179.007093789 & 6961.99290621083 \tabularnewline
25 & 528222 & 521207.777045932 & 7014.22295406827 \tabularnewline
26 & 532638 & 528109.4278779 & 4528.57212209981 \tabularnewline
27 & 536322 & 526091.048309971 & 10230.9516900287 \tabularnewline
28 & 536535 & 543458.854585573 & -6923.85458557308 \tabularnewline
29 & 523597 & 524979.269111235 & -1382.26911123516 \tabularnewline
30 & 536214 & 539179.427328944 & -2965.42732894374 \tabularnewline
31 & 586570 & 594467.82530702 & -7897.82530702022 \tabularnewline
32 & 596594 & 603601.831597013 & -7007.83159701293 \tabularnewline
33 & 580523 & 581846.977930416 & -1323.97793041635 \tabularnewline
34 & 564478 & 570694.43435514 & -6216.43435513985 \tabularnewline
35 & 557560 & 552894.657038712 & 4665.34296128759 \tabularnewline
36 & 575093 & 565090.994994084 & 10002.0050059156 \tabularnewline
37 & 580112 & 580464.261017083 & -352.261017083423 \tabularnewline
38 & 574761 & 579452.684886652 & -4691.68488665228 \tabularnewline
39 & 563250 & 566626.960034619 & -3376.96003461943 \tabularnewline
40 & 551531 & 562937.41590427 & -11406.4159042704 \tabularnewline
41 & 537034 & 533149.433372275 & 3884.56662772491 \tabularnewline
42 & 544686 & 544937.173301302 & -251.17330130178 \tabularnewline
43 & 600991 & 595847.505910332 & 5143.49408966838 \tabularnewline
44 & 604378 & 613662.602621223 & -9284.60262122343 \tabularnewline
45 & 586111 & 587305.654667271 & -1194.65466727084 \tabularnewline
46 & 563668 & 572302.592569832 & -8634.59256983153 \tabularnewline
47 & 548604 & 549871.063482672 & -1267.06348267174 \tabularnewline
48 & 551174 & 552148.283558485 & -974.283558485447 \tabularnewline
49 & 555654 & 548382.405776774 & 7271.59422322595 \tabularnewline
50 & 547970 & 547135.467636333 & 834.532363667269 \tabularnewline
51 & 540324 & 534390.119151581 & 5933.88084841857 \tabularnewline
52 & 530577 & 535227.724148924 & -4650.724148924 \tabularnewline
53 & 520579 & 512493.567123732 & 8085.43287626759 \tabularnewline
54 & 518654 & 527656.007261131 & -9002.00726113131 \tabularnewline
55 & 572273 & 569685.368133664 & 2587.63186633633 \tabularnewline
56 & 581302 & 580782.562522697 & 519.437477302505 \tabularnewline
57 & 563280 & 563882.002457684 & -602.002457684255 \tabularnewline
58 & 547612 & 548453.444819823 & -841.444819823257 \tabularnewline
59 & 538712 & 535768.156341359 & 2943.8436586411 \tabularnewline
60 & 540735 & 544826.647038901 & -4091.64703890134 \tabularnewline
61 & 561649 & 541706.969987949 & 19942.0300120512 \tabularnewline
62 & 558685 & 556156.775051469 & 2528.22494853113 \tabularnewline
63 & 545732 & 551488.484645132 & -5756.48464513232 \tabularnewline
64 & 536352 & 543746.230692203 & -7394.23069220281 \tabularnewline
65 & 527676 & 522549.430415866 & 5126.56958413403 \tabularnewline
66 & 530455 & 534432.764440652 & -3977.7644406521 \tabularnewline
67 & 581744 & 585133.993647538 & -3389.99364753766 \tabularnewline
68 & 598714 & 592035.318291686 & 6678.68170831387 \tabularnewline
69 & 583775 & 583188.154704268 & 586.84529573191 \tabularnewline
70 & 571477 & 571905.707427197 & -428.70742719702 \tabularnewline
71 & 563278 & 563319.415798767 & -41.4157987671206 \tabularnewline
72 & 564872 & 571354.690247905 & -6482.69024790544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210595&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]516922[/C][C]533779.029380342[/C][C]-16857.0293803421[/C][/ROW]
[ROW][C]14[/C][C]507561[/C][C]505462.698833042[/C][C]2098.30116695783[/C][/ROW]
[ROW][C]15[/C][C]492622[/C][C]488457.43457527[/C][C]4164.56542472955[/C][/ROW]
[ROW][C]16[/C][C]490243[/C][C]486448.253920621[/C][C]3794.74607937882[/C][/ROW]
[ROW][C]17[/C][C]469357[/C][C]465920.171630084[/C][C]3436.82836991618[/C][/ROW]
[ROW][C]18[/C][C]477580[/C][C]474114.866319822[/C][C]3465.13368017779[/C][/ROW]
[ROW][C]19[/C][C]528379[/C][C]526667.269756084[/C][C]1711.73024391558[/C][/ROW]
[ROW][C]20[/C][C]533590[/C][C]538969.454574871[/C][C]-5379.45457487088[/C][/ROW]
[ROW][C]21[/C][C]517945[/C][C]511378.870267418[/C][C]6566.12973258155[/C][/ROW]
[ROW][C]22[/C][C]506174[/C][C]503964.5393418[/C][C]2209.46065819979[/C][/ROW]
[ROW][C]23[/C][C]501866[/C][C]490794.457651887[/C][C]11071.5423481127[/C][/ROW]
[ROW][C]24[/C][C]516141[/C][C]509179.007093789[/C][C]6961.99290621083[/C][/ROW]
[ROW][C]25[/C][C]528222[/C][C]521207.777045932[/C][C]7014.22295406827[/C][/ROW]
[ROW][C]26[/C][C]532638[/C][C]528109.4278779[/C][C]4528.57212209981[/C][/ROW]
[ROW][C]27[/C][C]536322[/C][C]526091.048309971[/C][C]10230.9516900287[/C][/ROW]
[ROW][C]28[/C][C]536535[/C][C]543458.854585573[/C][C]-6923.85458557308[/C][/ROW]
[ROW][C]29[/C][C]523597[/C][C]524979.269111235[/C][C]-1382.26911123516[/C][/ROW]
[ROW][C]30[/C][C]536214[/C][C]539179.427328944[/C][C]-2965.42732894374[/C][/ROW]
[ROW][C]31[/C][C]586570[/C][C]594467.82530702[/C][C]-7897.82530702022[/C][/ROW]
[ROW][C]32[/C][C]596594[/C][C]603601.831597013[/C][C]-7007.83159701293[/C][/ROW]
[ROW][C]33[/C][C]580523[/C][C]581846.977930416[/C][C]-1323.97793041635[/C][/ROW]
[ROW][C]34[/C][C]564478[/C][C]570694.43435514[/C][C]-6216.43435513985[/C][/ROW]
[ROW][C]35[/C][C]557560[/C][C]552894.657038712[/C][C]4665.34296128759[/C][/ROW]
[ROW][C]36[/C][C]575093[/C][C]565090.994994084[/C][C]10002.0050059156[/C][/ROW]
[ROW][C]37[/C][C]580112[/C][C]580464.261017083[/C][C]-352.261017083423[/C][/ROW]
[ROW][C]38[/C][C]574761[/C][C]579452.684886652[/C][C]-4691.68488665228[/C][/ROW]
[ROW][C]39[/C][C]563250[/C][C]566626.960034619[/C][C]-3376.96003461943[/C][/ROW]
[ROW][C]40[/C][C]551531[/C][C]562937.41590427[/C][C]-11406.4159042704[/C][/ROW]
[ROW][C]41[/C][C]537034[/C][C]533149.433372275[/C][C]3884.56662772491[/C][/ROW]
[ROW][C]42[/C][C]544686[/C][C]544937.173301302[/C][C]-251.17330130178[/C][/ROW]
[ROW][C]43[/C][C]600991[/C][C]595847.505910332[/C][C]5143.49408966838[/C][/ROW]
[ROW][C]44[/C][C]604378[/C][C]613662.602621223[/C][C]-9284.60262122343[/C][/ROW]
[ROW][C]45[/C][C]586111[/C][C]587305.654667271[/C][C]-1194.65466727084[/C][/ROW]
[ROW][C]46[/C][C]563668[/C][C]572302.592569832[/C][C]-8634.59256983153[/C][/ROW]
[ROW][C]47[/C][C]548604[/C][C]549871.063482672[/C][C]-1267.06348267174[/C][/ROW]
[ROW][C]48[/C][C]551174[/C][C]552148.283558485[/C][C]-974.283558485447[/C][/ROW]
[ROW][C]49[/C][C]555654[/C][C]548382.405776774[/C][C]7271.59422322595[/C][/ROW]
[ROW][C]50[/C][C]547970[/C][C]547135.467636333[/C][C]834.532363667269[/C][/ROW]
[ROW][C]51[/C][C]540324[/C][C]534390.119151581[/C][C]5933.88084841857[/C][/ROW]
[ROW][C]52[/C][C]530577[/C][C]535227.724148924[/C][C]-4650.724148924[/C][/ROW]
[ROW][C]53[/C][C]520579[/C][C]512493.567123732[/C][C]8085.43287626759[/C][/ROW]
[ROW][C]54[/C][C]518654[/C][C]527656.007261131[/C][C]-9002.00726113131[/C][/ROW]
[ROW][C]55[/C][C]572273[/C][C]569685.368133664[/C][C]2587.63186633633[/C][/ROW]
[ROW][C]56[/C][C]581302[/C][C]580782.562522697[/C][C]519.437477302505[/C][/ROW]
[ROW][C]57[/C][C]563280[/C][C]563882.002457684[/C][C]-602.002457684255[/C][/ROW]
[ROW][C]58[/C][C]547612[/C][C]548453.444819823[/C][C]-841.444819823257[/C][/ROW]
[ROW][C]59[/C][C]538712[/C][C]535768.156341359[/C][C]2943.8436586411[/C][/ROW]
[ROW][C]60[/C][C]540735[/C][C]544826.647038901[/C][C]-4091.64703890134[/C][/ROW]
[ROW][C]61[/C][C]561649[/C][C]541706.969987949[/C][C]19942.0300120512[/C][/ROW]
[ROW][C]62[/C][C]558685[/C][C]556156.775051469[/C][C]2528.22494853113[/C][/ROW]
[ROW][C]63[/C][C]545732[/C][C]551488.484645132[/C][C]-5756.48464513232[/C][/ROW]
[ROW][C]64[/C][C]536352[/C][C]543746.230692203[/C][C]-7394.23069220281[/C][/ROW]
[ROW][C]65[/C][C]527676[/C][C]522549.430415866[/C][C]5126.56958413403[/C][/ROW]
[ROW][C]66[/C][C]530455[/C][C]534432.764440652[/C][C]-3977.7644406521[/C][/ROW]
[ROW][C]67[/C][C]581744[/C][C]585133.993647538[/C][C]-3389.99364753766[/C][/ROW]
[ROW][C]68[/C][C]598714[/C][C]592035.318291686[/C][C]6678.68170831387[/C][/ROW]
[ROW][C]69[/C][C]583775[/C][C]583188.154704268[/C][C]586.84529573191[/C][/ROW]
[ROW][C]70[/C][C]571477[/C][C]571905.707427197[/C][C]-428.70742719702[/C][/ROW]
[ROW][C]71[/C][C]563278[/C][C]563319.415798767[/C][C]-41.4157987671206[/C][/ROW]
[ROW][C]72[/C][C]564872[/C][C]571354.690247905[/C][C]-6482.69024790544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210595&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210595&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
13516922533779.029380342-16857.0293803421
14507561505462.6988330422098.30116695783
15492622488457.434575274164.56542472955
16490243486448.2539206213794.74607937882
17469357465920.1716300843436.82836991618
18477580474114.8663198223465.13368017779
19528379526667.2697560841711.73024391558
20533590538969.454574871-5379.45457487088
21517945511378.8702674186566.12973258155
22506174503964.53934182209.46065819979
23501866490794.45765188711071.5423481127
24516141509179.0070937896961.99290621083
25528222521207.7770459327014.22295406827
26532638528109.42787794528.57212209981
27536322526091.04830997110230.9516900287
28536535543458.854585573-6923.85458557308
29523597524979.269111235-1382.26911123516
30536214539179.427328944-2965.42732894374
31586570594467.82530702-7897.82530702022
32596594603601.831597013-7007.83159701293
33580523581846.977930416-1323.97793041635
34564478570694.43435514-6216.43435513985
35557560552894.6570387124665.34296128759
36575093565090.99499408410002.0050059156
37580112580464.261017083-352.261017083423
38574761579452.684886652-4691.68488665228
39563250566626.960034619-3376.96003461943
40551531562937.41590427-11406.4159042704
41537034533149.4333722753884.56662772491
42544686544937.173301302-251.17330130178
43600991595847.5059103325143.49408966838
44604378613662.602621223-9284.60262122343
45586111587305.654667271-1194.65466727084
46563668572302.592569832-8634.59256983153
47548604549871.063482672-1267.06348267174
48551174552148.283558485-974.283558485447
49555654548382.4057767747271.59422322595
50547970547135.467636333834.532363667269
51540324534390.1191515815933.88084841857
52530577535227.724148924-4650.724148924
53520579512493.5671237328085.43287626759
54518654527656.007261131-9002.00726113131
55572273569685.3681336642587.63186633633
56581302580782.562522697519.437477302505
57563280563882.002457684-602.002457684255
58547612548453.444819823-841.444819823257
59538712535768.1563413592943.8436586411
60540735544826.647038901-4091.64703890134
61561649541706.96998794919942.0300120512
62558685556156.7750514692528.22494853113
63545732551488.484645132-5756.48464513232
64536352543746.230692203-7394.23069220281
65527676522549.4304158665126.56958413403
66530455534432.764440652-3977.7644406521
67581744585133.993647538-3389.99364753766
68598714592035.3182916866678.68170831387
69583775583188.154704268586.84529573191
70571477571905.707427197-428.70742719702
71563278563319.415798767-41.4157987671206
72564872571354.690247905-6482.69024790544







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73571158.803462391558676.510597105583641.096327677
74562802.336422991544019.465493083581585.207352899
75551021.597302532525546.067619032576497.126986032
76545703.132932146513075.033371429578331.232492862
77532076.313900968491830.405113238572322.222688697
78536521.318955361488203.727736563584838.910174159
79589976.85789696533149.67821182646804.037582101
80601215.804402291535457.797343039666973.811461543
81584146.790031752509052.734511942659240.845551562
82570453.041417789485632.64572251655273.437113068
83560630.399627483465707.121787998655553.677466968
84566215.348962713460825.260467681671605.437457744

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 571158.803462391 & 558676.510597105 & 583641.096327677 \tabularnewline
74 & 562802.336422991 & 544019.465493083 & 581585.207352899 \tabularnewline
75 & 551021.597302532 & 525546.067619032 & 576497.126986032 \tabularnewline
76 & 545703.132932146 & 513075.033371429 & 578331.232492862 \tabularnewline
77 & 532076.313900968 & 491830.405113238 & 572322.222688697 \tabularnewline
78 & 536521.318955361 & 488203.727736563 & 584838.910174159 \tabularnewline
79 & 589976.85789696 & 533149.67821182 & 646804.037582101 \tabularnewline
80 & 601215.804402291 & 535457.797343039 & 666973.811461543 \tabularnewline
81 & 584146.790031752 & 509052.734511942 & 659240.845551562 \tabularnewline
82 & 570453.041417789 & 485632.64572251 & 655273.437113068 \tabularnewline
83 & 560630.399627483 & 465707.121787998 & 655553.677466968 \tabularnewline
84 & 566215.348962713 & 460825.260467681 & 671605.437457744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210595&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]571158.803462391[/C][C]558676.510597105[/C][C]583641.096327677[/C][/ROW]
[ROW][C]74[/C][C]562802.336422991[/C][C]544019.465493083[/C][C]581585.207352899[/C][/ROW]
[ROW][C]75[/C][C]551021.597302532[/C][C]525546.067619032[/C][C]576497.126986032[/C][/ROW]
[ROW][C]76[/C][C]545703.132932146[/C][C]513075.033371429[/C][C]578331.232492862[/C][/ROW]
[ROW][C]77[/C][C]532076.313900968[/C][C]491830.405113238[/C][C]572322.222688697[/C][/ROW]
[ROW][C]78[/C][C]536521.318955361[/C][C]488203.727736563[/C][C]584838.910174159[/C][/ROW]
[ROW][C]79[/C][C]589976.85789696[/C][C]533149.67821182[/C][C]646804.037582101[/C][/ROW]
[ROW][C]80[/C][C]601215.804402291[/C][C]535457.797343039[/C][C]666973.811461543[/C][/ROW]
[ROW][C]81[/C][C]584146.790031752[/C][C]509052.734511942[/C][C]659240.845551562[/C][/ROW]
[ROW][C]82[/C][C]570453.041417789[/C][C]485632.64572251[/C][C]655273.437113068[/C][/ROW]
[ROW][C]83[/C][C]560630.399627483[/C][C]465707.121787998[/C][C]655553.677466968[/C][/ROW]
[ROW][C]84[/C][C]566215.348962713[/C][C]460825.260467681[/C][C]671605.437457744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210595&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210595&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
73571158.803462391558676.510597105583641.096327677
74562802.336422991544019.465493083581585.207352899
75551021.597302532525546.067619032576497.126986032
76545703.132932146513075.033371429578331.232492862
77532076.313900968491830.405113238572322.222688697
78536521.318955361488203.727736563584838.910174159
79589976.85789696533149.67821182646804.037582101
80601215.804402291535457.797343039666973.811461543
81584146.790031752509052.734511942659240.845551562
82570453.041417789485632.64572251655273.437113068
83560630.399627483465707.121787998655553.677466968
84566215.348962713460825.260467681671605.437457744



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')