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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 computationFri, 28 Nov 2014 17:26:54 +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/28/t14171956498aop6nsbxxc4les.htm/, Retrieved Sun, 19 May 2024 15:35:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260994, Retrieved Sun, 19 May 2024 15:35:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-28 17:26:54] [9c8c71143ae36c30e98dcd90d9bfe9d4] [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
577537
572399
565430
560619
551227
553397
610893
621668
613148
598778
590623
595902




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=260994&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=260994&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260994&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
alpha1
beta0.0544821117855046
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0544821117855046 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260994&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0544821117855046[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260994&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260994&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
alpha1
beta0.0544821117855046
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3531673537132-5459
4525919519653.5821517636265.41784823709
5511038514240.935347353-3202.93534735346
6498662499185.432665717-523.432665717206
7555362486780.91494871168581.0850512886
8564591547217.35729084717373.642709153
9541657557392.910035048-15735.9100350484
10527070533601.584425472-6531.58442547231
11509846518658.729912667-8812.72991266724
12514258500954.5937764313303.4062235702
13516922506091.3914414310830.6085585696
14507561509345.465867623-1784.4658676234
15492622499887.244398746-7265.24439874612
16490243484552.4185412655690.5814587354
17469357482483.453436424-13126.453436424
18477580460882.29653295416697.7034670465
19528379470015.02267980658363.9773201937
20533590523993.8154164129596.18458358821
21517945529727.635817609-11782.6358176091
22506174513440.692935866-7266.6929358663
23501866501273.788159024592.211840976495
24516141496998.05311074419142.9468892557
25528222512316.00128306915905.9987169313
26532638525263.5936832257374.40631677536
27536322530081.3669125276240.63308747311
28536535534105.3697820112429.63021798909
29523597534450.741167145-10853.7411671448
30536214520921.40642758615292.5935724145
31586570534371.57922008852198.4207799119
32596594587571.4594160469022.54058395396
33580523598087.02648073-17564.0264807303
34564478581059.101226604-16581.1012266036
35557560564110.727816049-6550.72781604901
36575093556835.83033089918257.1696691014
37580112575363.5194896984748.48051030247
38574761580641.226735671-5880.22673567117
39563250574969.859565334-11719.8595653342
40551531562820.336866385-11289.3368663852
41537034550486.269953247-13452.2699532466
42544686535256.3618778859429.63812211493
43600991543422.10847615157568.891523849
44604378602863.5832595211514.41674047906
45586111606333.091881666-20222.0918816655
46563668586964.349611232-23296.3496112318
47548604563252.115287518-14648.1152875185
48551174547390.0550329773783.94496702298
49555654550166.2123456615487.78765433945
50547970554945.198606099-6975.19860609935
51540324546881.175055916-6557.17505591572
52530577538877.926311522-8300.92631152226
53520579528678.674316295-8099.67431629461
54518654518239.386954768414.613045231905
55572273516336.97594904655936.0240509539
56581302573003.4886642278298.51133577304
57563280582484.609086476-19204.6090864758
58547612563416.301427429-15804.3014274294
59538712546887.249710368-8175.24971036846
60540735537541.8448417743193.15515822626
61561649539738.81467805321910.1853219473
62558685561846.527844004-3161.5278440041
63545732558710.281130594-12978.2811305941
64536352545050.196967253-8698.19696725335
65527676535196.300827751-7520.30082775117
66530455526110.5789573934344.42104260705
67581744529126.2721902852617.7278097204
68598714583281.99711870815432.0028812919
69583775601092.765224761-17317.7652247609
70571477585210.25680391-13733.2568039102
71563278572164.039971541-8886.03997154057
72564872563480.9097484811391.09025151934
73577537565150.69928306812386.3007169323
74572399578490.531103336-6091.53110333649
75565430573020.65162482-7590.65162481961
76560619565638.096894471-5019.09689447132
77551227560553.645896405-9326.64589640452
78553397550653.5105320932743.48946790723
79610893552972.98163196657920.0183680344
80621668613624.5865473118043.4134526886
81613148624837.808698178-11689.8086981778
82598778615680.923233932-16902.9232339325
83590623600390.0162808-9767.01628079952
84595902591702.8886079784199.11139202176

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 531673 & 537132 & -5459 \tabularnewline
4 & 525919 & 519653.582151763 & 6265.41784823709 \tabularnewline
5 & 511038 & 514240.935347353 & -3202.93534735346 \tabularnewline
6 & 498662 & 499185.432665717 & -523.432665717206 \tabularnewline
7 & 555362 & 486780.914948711 & 68581.0850512886 \tabularnewline
8 & 564591 & 547217.357290847 & 17373.642709153 \tabularnewline
9 & 541657 & 557392.910035048 & -15735.9100350484 \tabularnewline
10 & 527070 & 533601.584425472 & -6531.58442547231 \tabularnewline
11 & 509846 & 518658.729912667 & -8812.72991266724 \tabularnewline
12 & 514258 & 500954.59377643 & 13303.4062235702 \tabularnewline
13 & 516922 & 506091.39144143 & 10830.6085585696 \tabularnewline
14 & 507561 & 509345.465867623 & -1784.4658676234 \tabularnewline
15 & 492622 & 499887.244398746 & -7265.24439874612 \tabularnewline
16 & 490243 & 484552.418541265 & 5690.5814587354 \tabularnewline
17 & 469357 & 482483.453436424 & -13126.453436424 \tabularnewline
18 & 477580 & 460882.296532954 & 16697.7034670465 \tabularnewline
19 & 528379 & 470015.022679806 & 58363.9773201937 \tabularnewline
20 & 533590 & 523993.815416412 & 9596.18458358821 \tabularnewline
21 & 517945 & 529727.635817609 & -11782.6358176091 \tabularnewline
22 & 506174 & 513440.692935866 & -7266.6929358663 \tabularnewline
23 & 501866 & 501273.788159024 & 592.211840976495 \tabularnewline
24 & 516141 & 496998.053110744 & 19142.9468892557 \tabularnewline
25 & 528222 & 512316.001283069 & 15905.9987169313 \tabularnewline
26 & 532638 & 525263.593683225 & 7374.40631677536 \tabularnewline
27 & 536322 & 530081.366912527 & 6240.63308747311 \tabularnewline
28 & 536535 & 534105.369782011 & 2429.63021798909 \tabularnewline
29 & 523597 & 534450.741167145 & -10853.7411671448 \tabularnewline
30 & 536214 & 520921.406427586 & 15292.5935724145 \tabularnewline
31 & 586570 & 534371.579220088 & 52198.4207799119 \tabularnewline
32 & 596594 & 587571.459416046 & 9022.54058395396 \tabularnewline
33 & 580523 & 598087.02648073 & -17564.0264807303 \tabularnewline
34 & 564478 & 581059.101226604 & -16581.1012266036 \tabularnewline
35 & 557560 & 564110.727816049 & -6550.72781604901 \tabularnewline
36 & 575093 & 556835.830330899 & 18257.1696691014 \tabularnewline
37 & 580112 & 575363.519489698 & 4748.48051030247 \tabularnewline
38 & 574761 & 580641.226735671 & -5880.22673567117 \tabularnewline
39 & 563250 & 574969.859565334 & -11719.8595653342 \tabularnewline
40 & 551531 & 562820.336866385 & -11289.3368663852 \tabularnewline
41 & 537034 & 550486.269953247 & -13452.2699532466 \tabularnewline
42 & 544686 & 535256.361877885 & 9429.63812211493 \tabularnewline
43 & 600991 & 543422.108476151 & 57568.891523849 \tabularnewline
44 & 604378 & 602863.583259521 & 1514.41674047906 \tabularnewline
45 & 586111 & 606333.091881666 & -20222.0918816655 \tabularnewline
46 & 563668 & 586964.349611232 & -23296.3496112318 \tabularnewline
47 & 548604 & 563252.115287518 & -14648.1152875185 \tabularnewline
48 & 551174 & 547390.055032977 & 3783.94496702298 \tabularnewline
49 & 555654 & 550166.212345661 & 5487.78765433945 \tabularnewline
50 & 547970 & 554945.198606099 & -6975.19860609935 \tabularnewline
51 & 540324 & 546881.175055916 & -6557.17505591572 \tabularnewline
52 & 530577 & 538877.926311522 & -8300.92631152226 \tabularnewline
53 & 520579 & 528678.674316295 & -8099.67431629461 \tabularnewline
54 & 518654 & 518239.386954768 & 414.613045231905 \tabularnewline
55 & 572273 & 516336.975949046 & 55936.0240509539 \tabularnewline
56 & 581302 & 573003.488664227 & 8298.51133577304 \tabularnewline
57 & 563280 & 582484.609086476 & -19204.6090864758 \tabularnewline
58 & 547612 & 563416.301427429 & -15804.3014274294 \tabularnewline
59 & 538712 & 546887.249710368 & -8175.24971036846 \tabularnewline
60 & 540735 & 537541.844841774 & 3193.15515822626 \tabularnewline
61 & 561649 & 539738.814678053 & 21910.1853219473 \tabularnewline
62 & 558685 & 561846.527844004 & -3161.5278440041 \tabularnewline
63 & 545732 & 558710.281130594 & -12978.2811305941 \tabularnewline
64 & 536352 & 545050.196967253 & -8698.19696725335 \tabularnewline
65 & 527676 & 535196.300827751 & -7520.30082775117 \tabularnewline
66 & 530455 & 526110.578957393 & 4344.42104260705 \tabularnewline
67 & 581744 & 529126.27219028 & 52617.7278097204 \tabularnewline
68 & 598714 & 583281.997118708 & 15432.0028812919 \tabularnewline
69 & 583775 & 601092.765224761 & -17317.7652247609 \tabularnewline
70 & 571477 & 585210.25680391 & -13733.2568039102 \tabularnewline
71 & 563278 & 572164.039971541 & -8886.03997154057 \tabularnewline
72 & 564872 & 563480.909748481 & 1391.09025151934 \tabularnewline
73 & 577537 & 565150.699283068 & 12386.3007169323 \tabularnewline
74 & 572399 & 578490.531103336 & -6091.53110333649 \tabularnewline
75 & 565430 & 573020.65162482 & -7590.65162481961 \tabularnewline
76 & 560619 & 565638.096894471 & -5019.09689447132 \tabularnewline
77 & 551227 & 560553.645896405 & -9326.64589640452 \tabularnewline
78 & 553397 & 550653.510532093 & 2743.48946790723 \tabularnewline
79 & 610893 & 552972.981631966 & 57920.0183680344 \tabularnewline
80 & 621668 & 613624.586547311 & 8043.4134526886 \tabularnewline
81 & 613148 & 624837.808698178 & -11689.8086981778 \tabularnewline
82 & 598778 & 615680.923233932 & -16902.9232339325 \tabularnewline
83 & 590623 & 600390.0162808 & -9767.01628079952 \tabularnewline
84 & 595902 & 591702.888607978 & 4199.11139202176 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260994&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]3[/C][C]531673[/C][C]537132[/C][C]-5459[/C][/ROW]
[ROW][C]4[/C][C]525919[/C][C]519653.582151763[/C][C]6265.41784823709[/C][/ROW]
[ROW][C]5[/C][C]511038[/C][C]514240.935347353[/C][C]-3202.93534735346[/C][/ROW]
[ROW][C]6[/C][C]498662[/C][C]499185.432665717[/C][C]-523.432665717206[/C][/ROW]
[ROW][C]7[/C][C]555362[/C][C]486780.914948711[/C][C]68581.0850512886[/C][/ROW]
[ROW][C]8[/C][C]564591[/C][C]547217.357290847[/C][C]17373.642709153[/C][/ROW]
[ROW][C]9[/C][C]541657[/C][C]557392.910035048[/C][C]-15735.9100350484[/C][/ROW]
[ROW][C]10[/C][C]527070[/C][C]533601.584425472[/C][C]-6531.58442547231[/C][/ROW]
[ROW][C]11[/C][C]509846[/C][C]518658.729912667[/C][C]-8812.72991266724[/C][/ROW]
[ROW][C]12[/C][C]514258[/C][C]500954.59377643[/C][C]13303.4062235702[/C][/ROW]
[ROW][C]13[/C][C]516922[/C][C]506091.39144143[/C][C]10830.6085585696[/C][/ROW]
[ROW][C]14[/C][C]507561[/C][C]509345.465867623[/C][C]-1784.4658676234[/C][/ROW]
[ROW][C]15[/C][C]492622[/C][C]499887.244398746[/C][C]-7265.24439874612[/C][/ROW]
[ROW][C]16[/C][C]490243[/C][C]484552.418541265[/C][C]5690.5814587354[/C][/ROW]
[ROW][C]17[/C][C]469357[/C][C]482483.453436424[/C][C]-13126.453436424[/C][/ROW]
[ROW][C]18[/C][C]477580[/C][C]460882.296532954[/C][C]16697.7034670465[/C][/ROW]
[ROW][C]19[/C][C]528379[/C][C]470015.022679806[/C][C]58363.9773201937[/C][/ROW]
[ROW][C]20[/C][C]533590[/C][C]523993.815416412[/C][C]9596.18458358821[/C][/ROW]
[ROW][C]21[/C][C]517945[/C][C]529727.635817609[/C][C]-11782.6358176091[/C][/ROW]
[ROW][C]22[/C][C]506174[/C][C]513440.692935866[/C][C]-7266.6929358663[/C][/ROW]
[ROW][C]23[/C][C]501866[/C][C]501273.788159024[/C][C]592.211840976495[/C][/ROW]
[ROW][C]24[/C][C]516141[/C][C]496998.053110744[/C][C]19142.9468892557[/C][/ROW]
[ROW][C]25[/C][C]528222[/C][C]512316.001283069[/C][C]15905.9987169313[/C][/ROW]
[ROW][C]26[/C][C]532638[/C][C]525263.593683225[/C][C]7374.40631677536[/C][/ROW]
[ROW][C]27[/C][C]536322[/C][C]530081.366912527[/C][C]6240.63308747311[/C][/ROW]
[ROW][C]28[/C][C]536535[/C][C]534105.369782011[/C][C]2429.63021798909[/C][/ROW]
[ROW][C]29[/C][C]523597[/C][C]534450.741167145[/C][C]-10853.7411671448[/C][/ROW]
[ROW][C]30[/C][C]536214[/C][C]520921.406427586[/C][C]15292.5935724145[/C][/ROW]
[ROW][C]31[/C][C]586570[/C][C]534371.579220088[/C][C]52198.4207799119[/C][/ROW]
[ROW][C]32[/C][C]596594[/C][C]587571.459416046[/C][C]9022.54058395396[/C][/ROW]
[ROW][C]33[/C][C]580523[/C][C]598087.02648073[/C][C]-17564.0264807303[/C][/ROW]
[ROW][C]34[/C][C]564478[/C][C]581059.101226604[/C][C]-16581.1012266036[/C][/ROW]
[ROW][C]35[/C][C]557560[/C][C]564110.727816049[/C][C]-6550.72781604901[/C][/ROW]
[ROW][C]36[/C][C]575093[/C][C]556835.830330899[/C][C]18257.1696691014[/C][/ROW]
[ROW][C]37[/C][C]580112[/C][C]575363.519489698[/C][C]4748.48051030247[/C][/ROW]
[ROW][C]38[/C][C]574761[/C][C]580641.226735671[/C][C]-5880.22673567117[/C][/ROW]
[ROW][C]39[/C][C]563250[/C][C]574969.859565334[/C][C]-11719.8595653342[/C][/ROW]
[ROW][C]40[/C][C]551531[/C][C]562820.336866385[/C][C]-11289.3368663852[/C][/ROW]
[ROW][C]41[/C][C]537034[/C][C]550486.269953247[/C][C]-13452.2699532466[/C][/ROW]
[ROW][C]42[/C][C]544686[/C][C]535256.361877885[/C][C]9429.63812211493[/C][/ROW]
[ROW][C]43[/C][C]600991[/C][C]543422.108476151[/C][C]57568.891523849[/C][/ROW]
[ROW][C]44[/C][C]604378[/C][C]602863.583259521[/C][C]1514.41674047906[/C][/ROW]
[ROW][C]45[/C][C]586111[/C][C]606333.091881666[/C][C]-20222.0918816655[/C][/ROW]
[ROW][C]46[/C][C]563668[/C][C]586964.349611232[/C][C]-23296.3496112318[/C][/ROW]
[ROW][C]47[/C][C]548604[/C][C]563252.115287518[/C][C]-14648.1152875185[/C][/ROW]
[ROW][C]48[/C][C]551174[/C][C]547390.055032977[/C][C]3783.94496702298[/C][/ROW]
[ROW][C]49[/C][C]555654[/C][C]550166.212345661[/C][C]5487.78765433945[/C][/ROW]
[ROW][C]50[/C][C]547970[/C][C]554945.198606099[/C][C]-6975.19860609935[/C][/ROW]
[ROW][C]51[/C][C]540324[/C][C]546881.175055916[/C][C]-6557.17505591572[/C][/ROW]
[ROW][C]52[/C][C]530577[/C][C]538877.926311522[/C][C]-8300.92631152226[/C][/ROW]
[ROW][C]53[/C][C]520579[/C][C]528678.674316295[/C][C]-8099.67431629461[/C][/ROW]
[ROW][C]54[/C][C]518654[/C][C]518239.386954768[/C][C]414.613045231905[/C][/ROW]
[ROW][C]55[/C][C]572273[/C][C]516336.975949046[/C][C]55936.0240509539[/C][/ROW]
[ROW][C]56[/C][C]581302[/C][C]573003.488664227[/C][C]8298.51133577304[/C][/ROW]
[ROW][C]57[/C][C]563280[/C][C]582484.609086476[/C][C]-19204.6090864758[/C][/ROW]
[ROW][C]58[/C][C]547612[/C][C]563416.301427429[/C][C]-15804.3014274294[/C][/ROW]
[ROW][C]59[/C][C]538712[/C][C]546887.249710368[/C][C]-8175.24971036846[/C][/ROW]
[ROW][C]60[/C][C]540735[/C][C]537541.844841774[/C][C]3193.15515822626[/C][/ROW]
[ROW][C]61[/C][C]561649[/C][C]539738.814678053[/C][C]21910.1853219473[/C][/ROW]
[ROW][C]62[/C][C]558685[/C][C]561846.527844004[/C][C]-3161.5278440041[/C][/ROW]
[ROW][C]63[/C][C]545732[/C][C]558710.281130594[/C][C]-12978.2811305941[/C][/ROW]
[ROW][C]64[/C][C]536352[/C][C]545050.196967253[/C][C]-8698.19696725335[/C][/ROW]
[ROW][C]65[/C][C]527676[/C][C]535196.300827751[/C][C]-7520.30082775117[/C][/ROW]
[ROW][C]66[/C][C]530455[/C][C]526110.578957393[/C][C]4344.42104260705[/C][/ROW]
[ROW][C]67[/C][C]581744[/C][C]529126.27219028[/C][C]52617.7278097204[/C][/ROW]
[ROW][C]68[/C][C]598714[/C][C]583281.997118708[/C][C]15432.0028812919[/C][/ROW]
[ROW][C]69[/C][C]583775[/C][C]601092.765224761[/C][C]-17317.7652247609[/C][/ROW]
[ROW][C]70[/C][C]571477[/C][C]585210.25680391[/C][C]-13733.2568039102[/C][/ROW]
[ROW][C]71[/C][C]563278[/C][C]572164.039971541[/C][C]-8886.03997154057[/C][/ROW]
[ROW][C]72[/C][C]564872[/C][C]563480.909748481[/C][C]1391.09025151934[/C][/ROW]
[ROW][C]73[/C][C]577537[/C][C]565150.699283068[/C][C]12386.3007169323[/C][/ROW]
[ROW][C]74[/C][C]572399[/C][C]578490.531103336[/C][C]-6091.53110333649[/C][/ROW]
[ROW][C]75[/C][C]565430[/C][C]573020.65162482[/C][C]-7590.65162481961[/C][/ROW]
[ROW][C]76[/C][C]560619[/C][C]565638.096894471[/C][C]-5019.09689447132[/C][/ROW]
[ROW][C]77[/C][C]551227[/C][C]560553.645896405[/C][C]-9326.64589640452[/C][/ROW]
[ROW][C]78[/C][C]553397[/C][C]550653.510532093[/C][C]2743.48946790723[/C][/ROW]
[ROW][C]79[/C][C]610893[/C][C]552972.981631966[/C][C]57920.0183680344[/C][/ROW]
[ROW][C]80[/C][C]621668[/C][C]613624.586547311[/C][C]8043.4134526886[/C][/ROW]
[ROW][C]81[/C][C]613148[/C][C]624837.808698178[/C][C]-11689.8086981778[/C][/ROW]
[ROW][C]82[/C][C]598778[/C][C]615680.923233932[/C][C]-16902.9232339325[/C][/ROW]
[ROW][C]83[/C][C]590623[/C][C]600390.0162808[/C][C]-9767.01628079952[/C][/ROW]
[ROW][C]84[/C][C]595902[/C][C]591702.888607978[/C][C]4199.11139202176[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260994&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260994&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
3531673537132-5459
4525919519653.5821517636265.41784823709
5511038514240.935347353-3202.93534735346
6498662499185.432665717-523.432665717206
7555362486780.91494871168581.0850512886
8564591547217.35729084717373.642709153
9541657557392.910035048-15735.9100350484
10527070533601.584425472-6531.58442547231
11509846518658.729912667-8812.72991266724
12514258500954.5937764313303.4062235702
13516922506091.3914414310830.6085585696
14507561509345.465867623-1784.4658676234
15492622499887.244398746-7265.24439874612
16490243484552.4185412655690.5814587354
17469357482483.453436424-13126.453436424
18477580460882.29653295416697.7034670465
19528379470015.02267980658363.9773201937
20533590523993.8154164129596.18458358821
21517945529727.635817609-11782.6358176091
22506174513440.692935866-7266.6929358663
23501866501273.788159024592.211840976495
24516141496998.05311074419142.9468892557
25528222512316.00128306915905.9987169313
26532638525263.5936832257374.40631677536
27536322530081.3669125276240.63308747311
28536535534105.3697820112429.63021798909
29523597534450.741167145-10853.7411671448
30536214520921.40642758615292.5935724145
31586570534371.57922008852198.4207799119
32596594587571.4594160469022.54058395396
33580523598087.02648073-17564.0264807303
34564478581059.101226604-16581.1012266036
35557560564110.727816049-6550.72781604901
36575093556835.83033089918257.1696691014
37580112575363.5194896984748.48051030247
38574761580641.226735671-5880.22673567117
39563250574969.859565334-11719.8595653342
40551531562820.336866385-11289.3368663852
41537034550486.269953247-13452.2699532466
42544686535256.3618778859429.63812211493
43600991543422.10847615157568.891523849
44604378602863.5832595211514.41674047906
45586111606333.091881666-20222.0918816655
46563668586964.349611232-23296.3496112318
47548604563252.115287518-14648.1152875185
48551174547390.0550329773783.94496702298
49555654550166.2123456615487.78765433945
50547970554945.198606099-6975.19860609935
51540324546881.175055916-6557.17505591572
52530577538877.926311522-8300.92631152226
53520579528678.674316295-8099.67431629461
54518654518239.386954768414.613045231905
55572273516336.97594904655936.0240509539
56581302573003.4886642278298.51133577304
57563280582484.609086476-19204.6090864758
58547612563416.301427429-15804.3014274294
59538712546887.249710368-8175.24971036846
60540735537541.8448417743193.15515822626
61561649539738.81467805321910.1853219473
62558685561846.527844004-3161.5278440041
63545732558710.281130594-12978.2811305941
64536352545050.196967253-8698.19696725335
65527676535196.300827751-7520.30082775117
66530455526110.5789573934344.42104260705
67581744529126.2721902852617.7278097204
68598714583281.99711870815432.0028812919
69583775601092.765224761-17317.7652247609
70571477585210.25680391-13733.2568039102
71563278572164.039971541-8886.03997154057
72564872563480.9097484811391.09025151934
73577537565150.69928306812386.3007169323
74572399578490.531103336-6091.53110333649
75565430573020.65162482-7590.65162481961
76560619565638.096894471-5019.09689447132
77551227560553.645896405-9326.64589640452
78553397550653.5105320932743.48946790723
79610893552972.98163196657920.0183680344
80621668613624.5865473118043.4134526886
81613148624837.808698178-11689.8086981778
82598778615680.923233932-16902.9232339325
83590623600390.0162808-9767.01628079952
84595902591702.8886079784199.11139202176







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85597210.665064238558216.133224017636205.196904459
86598519.330128476541850.567496161655188.092760792
87599827.995192714528544.389274008671111.601111421
88601136.660256953516640.435517738685632.884996167
89602445.325321191505516.721370905699373.929271476
90603753.990385429494864.108776796712643.871994062
91605062.655449667484504.80546715725620.505432184
92606371.320513905474326.828281172738415.812746638
93607679.985578143464255.121747716751104.84940857
94608988.650642381454237.065390436763740.235894327
95610297.315706619444234.497210439776360.1342028
96611605.980770858434219.007602738788992.953938977

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 597210.665064238 & 558216.133224017 & 636205.196904459 \tabularnewline
86 & 598519.330128476 & 541850.567496161 & 655188.092760792 \tabularnewline
87 & 599827.995192714 & 528544.389274008 & 671111.601111421 \tabularnewline
88 & 601136.660256953 & 516640.435517738 & 685632.884996167 \tabularnewline
89 & 602445.325321191 & 505516.721370905 & 699373.929271476 \tabularnewline
90 & 603753.990385429 & 494864.108776796 & 712643.871994062 \tabularnewline
91 & 605062.655449667 & 484504.80546715 & 725620.505432184 \tabularnewline
92 & 606371.320513905 & 474326.828281172 & 738415.812746638 \tabularnewline
93 & 607679.985578143 & 464255.121747716 & 751104.84940857 \tabularnewline
94 & 608988.650642381 & 454237.065390436 & 763740.235894327 \tabularnewline
95 & 610297.315706619 & 444234.497210439 & 776360.1342028 \tabularnewline
96 & 611605.980770858 & 434219.007602738 & 788992.953938977 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260994&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]597210.665064238[/C][C]558216.133224017[/C][C]636205.196904459[/C][/ROW]
[ROW][C]86[/C][C]598519.330128476[/C][C]541850.567496161[/C][C]655188.092760792[/C][/ROW]
[ROW][C]87[/C][C]599827.995192714[/C][C]528544.389274008[/C][C]671111.601111421[/C][/ROW]
[ROW][C]88[/C][C]601136.660256953[/C][C]516640.435517738[/C][C]685632.884996167[/C][/ROW]
[ROW][C]89[/C][C]602445.325321191[/C][C]505516.721370905[/C][C]699373.929271476[/C][/ROW]
[ROW][C]90[/C][C]603753.990385429[/C][C]494864.108776796[/C][C]712643.871994062[/C][/ROW]
[ROW][C]91[/C][C]605062.655449667[/C][C]484504.80546715[/C][C]725620.505432184[/C][/ROW]
[ROW][C]92[/C][C]606371.320513905[/C][C]474326.828281172[/C][C]738415.812746638[/C][/ROW]
[ROW][C]93[/C][C]607679.985578143[/C][C]464255.121747716[/C][C]751104.84940857[/C][/ROW]
[ROW][C]94[/C][C]608988.650642381[/C][C]454237.065390436[/C][C]763740.235894327[/C][/ROW]
[ROW][C]95[/C][C]610297.315706619[/C][C]444234.497210439[/C][C]776360.1342028[/C][/ROW]
[ROW][C]96[/C][C]611605.980770858[/C][C]434219.007602738[/C][C]788992.953938977[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260994&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260994&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
85597210.665064238558216.133224017636205.196904459
86598519.330128476541850.567496161655188.092760792
87599827.995192714528544.389274008671111.601111421
88601136.660256953516640.435517738685632.884996167
89602445.325321191505516.721370905699373.929271476
90603753.990385429494864.108776796712643.871994062
91605062.655449667484504.80546715725620.505432184
92606371.320513905474326.828281172738415.812746638
93607679.985578143464255.121747716751104.84940857
94608988.650642381454237.065390436763740.235894327
95610297.315706619444234.497210439776360.1342028
96611605.980770858434219.007602738788992.953938977



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