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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 28 Dec 2010 11:57:54 +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/2010/Dec/28/t1293537374pzq8okgz5ms92gc.htm/, Retrieved Sat, 04 May 2024 21:40:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116302, Retrieved Sat, 04 May 2024 21:40:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
- R PD      [Exponential Smoothing] [Exponential smoot...] [2010-12-28 11:57:54] [062de5fc17e30860c0960288bdb996a8] [Current]
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Dataseries X:
621
587
655
517
646
657
382
345
625
654
606
510
614
647
580
614
636
388
356
639
753
611
639
630
586
695
552
619
681
421
307
754
690
644
643
608
651
691
627
634
731
475
337
803
722
590
724
627
696
825
677
656
785
412
352
839
729
696
641
695
638
762
635
721
854
418
367
824
687
601
676
740
691
683
594
729
731
386
331
706
715
657
653
642
643
718
654
632
731
392
344
792
852
649
629
685
617
715
715
629
916
531
357
917
828
708
858
775
785
1006
789
734
906
532
387
991
841
892
782
813
793
978
775
797
946
594
438
1022
868
795




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116302&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116302&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116302&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.100728105613193
beta0
gamma0.706402297696408

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.100728105613193 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.706402297696408 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116302&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]0.100728105613193[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.706402297696408[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116302&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116302&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
alpha0.100728105613193
beta0
gamma0.706402297696408







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13614651.525172725983-37.5251727259829
14647670.684799400148-23.6847994001478
15580582.366193489376-2.36619348937563
16614614.082108335153-0.0821083351529523
17636638.174882180815-2.17488218081451
18388385.9591403392022.04085966079765
19356394.926976308915-38.9269763089152
20639352.672465590974286.327534409026
21753693.55722789067159.4427721093285
22611732.547969407503-121.547969407503
23639664.801621910674-25.8016219106745
24630570.20434261314959.795657386851
25586684.778644320277-98.7786443202771
26695708.953919341885-13.9539193418846
27552629.015895313806-77.0158953138058
28619656.890366325891-37.8903663258913
29681677.188922344093.81107765590946
30421412.1320310598668.86796894013384
31307394.297058880402-87.2970588804023
32754548.078347243632205.921652756368
33690738.007640476895-48.0076404768953
34644650.364283790538-6.36428379053825
35643655.016731898568-12.0167318985677
36608615.297809380185-7.29780938018473
37651621.4578618054229.5421381945806
38691714.167953646476-23.1679536464757
39627590.36132606245236.6386739375477
40634656.629737764733-22.6297377647328
41731706.92773894495624.0722610550442
42475435.74617298177339.2538270182273
43337354.502513101708-17.5025131017079
44803720.35202868407882.647971315922
45722736.604638027393-14.6046380273928
46590676.10183672607-86.1018367260698
47724669.12301045894454.8769895410561
48627637.505502594523-10.505502594523
49696667.90337510201628.0966248979839
50825729.27138471700995.7286152829913
51677650.18827702758326.8117229724173
52656679.113810957953-23.1138109579528
53785763.60913757326621.3908624267337
54412486.525784079443-74.5257840794429
55352353.932010390557-1.93201039055725
56839799.5809690940139.4190309059899
57729748.091207851041-19.0912078510413
58696638.02523051830157.9747694816986
59641739.369895717159-98.3698957171586
60695648.51820685301446.4817931469859
61638711.124747901819-73.1247479018185
62762806.64707788869-44.64707788869
63635669.168037572516-34.1680375725161
64721660.22943633725360.7705636627469
65854782.13478503173171.8652149682692
66418444.066913202401-26.0669132024013
67367360.6645866861996.33541331380138
68824845.017958361628-21.0179583616283
69687748.612709808728-61.6127098087283
70601682.190300654261-81.1903006542611
71676669.4109014718986.58909852810211
72740680.9801840251959.0198159748098
73691668.26079833037522.7392016696249
74683793.770722055046-110.770722055046
75594654.717447856971-60.7174478569707
76729703.43579835564925.564201644351
77731828.604696928258-97.6046969282577
78386419.108486405942-33.1084864059417
79331356.880824472789-25.8808244727888
80706806.5251716464-100.525171646401
81715680.86911064199534.1308893580053
82657613.04089926046143.9591007395389
83653668.228632670744-15.2286326707435
84642710.107472507583-68.1074725075835
85643662.749894114399-19.7498941143987
86718696.89652408798921.1034759120112
87654604.37511756655849.624882433442
88632718.842688245944-86.8426882459437
89731752.99602607945-21.9960260794497
90392394.765325432344-2.76532543234441
91344340.1000456003033.8999543996967
92792747.6823816677344.3176183322699
93852721.199203322578130.800796677422
94649666.471440466248-17.4714404662477
95629678.199883454367-49.199883454367
96685682.8392993272592.16070067274075
97617672.847062803514-55.8470628035141
98715731.041817232163-16.0418172321632
99715650.77265525823264.2273447417683
100629679.867208951556-50.8672089515558
101916761.290149999896154.709850000104
102531414.330995039189116.669004960811
103357371.603349387028-14.6033493870279
104917836.96237644736180.0376235526387
105828869.245091697302-41.2450916973019
106708693.44129377671714.5587062232828
107858687.486984844789170.513015155211
108775750.86133239960224.1386676003976
109785701.0314027612883.9685972387201
1101006809.343633894797196.656366105203
111789796.57032178313-7.57032178312954
112734737.773987383306-3.77398738330567
113906984.09426384761-78.0942638476107
114532542.458664190362-10.4586641903621
115387392.075888372369-5.07588837236949
116991962.67769769466528.322302305335
117841908.330735465524-67.3307354655235
118892755.047910374334136.952089625666
119782865.880879179644-83.8808791796441
120813807.953883262625.04611673738043
121793792.7234873925030.276512607497125
122978967.74254174116210.2574582588376
123775803.9309183551-28.9309183550996
124797744.6713630173252.3286369826798
125946953.043956280599-7.04395628059876
126594550.64345039587143.3565496041286
127438403.54354264733434.4564573526662
12810221027.68207330509-5.68207330508676
129868903.510592234765-35.5105922347655
130795880.689443126828-85.6894431268275

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 614 & 651.525172725983 & -37.5251727259829 \tabularnewline
14 & 647 & 670.684799400148 & -23.6847994001478 \tabularnewline
15 & 580 & 582.366193489376 & -2.36619348937563 \tabularnewline
16 & 614 & 614.082108335153 & -0.0821083351529523 \tabularnewline
17 & 636 & 638.174882180815 & -2.17488218081451 \tabularnewline
18 & 388 & 385.959140339202 & 2.04085966079765 \tabularnewline
19 & 356 & 394.926976308915 & -38.9269763089152 \tabularnewline
20 & 639 & 352.672465590974 & 286.327534409026 \tabularnewline
21 & 753 & 693.557227890671 & 59.4427721093285 \tabularnewline
22 & 611 & 732.547969407503 & -121.547969407503 \tabularnewline
23 & 639 & 664.801621910674 & -25.8016219106745 \tabularnewline
24 & 630 & 570.204342613149 & 59.795657386851 \tabularnewline
25 & 586 & 684.778644320277 & -98.7786443202771 \tabularnewline
26 & 695 & 708.953919341885 & -13.9539193418846 \tabularnewline
27 & 552 & 629.015895313806 & -77.0158953138058 \tabularnewline
28 & 619 & 656.890366325891 & -37.8903663258913 \tabularnewline
29 & 681 & 677.18892234409 & 3.81107765590946 \tabularnewline
30 & 421 & 412.132031059866 & 8.86796894013384 \tabularnewline
31 & 307 & 394.297058880402 & -87.2970588804023 \tabularnewline
32 & 754 & 548.078347243632 & 205.921652756368 \tabularnewline
33 & 690 & 738.007640476895 & -48.0076404768953 \tabularnewline
34 & 644 & 650.364283790538 & -6.36428379053825 \tabularnewline
35 & 643 & 655.016731898568 & -12.0167318985677 \tabularnewline
36 & 608 & 615.297809380185 & -7.29780938018473 \tabularnewline
37 & 651 & 621.45786180542 & 29.5421381945806 \tabularnewline
38 & 691 & 714.167953646476 & -23.1679536464757 \tabularnewline
39 & 627 & 590.361326062452 & 36.6386739375477 \tabularnewline
40 & 634 & 656.629737764733 & -22.6297377647328 \tabularnewline
41 & 731 & 706.927738944956 & 24.0722610550442 \tabularnewline
42 & 475 & 435.746172981773 & 39.2538270182273 \tabularnewline
43 & 337 & 354.502513101708 & -17.5025131017079 \tabularnewline
44 & 803 & 720.352028684078 & 82.647971315922 \tabularnewline
45 & 722 & 736.604638027393 & -14.6046380273928 \tabularnewline
46 & 590 & 676.10183672607 & -86.1018367260698 \tabularnewline
47 & 724 & 669.123010458944 & 54.8769895410561 \tabularnewline
48 & 627 & 637.505502594523 & -10.505502594523 \tabularnewline
49 & 696 & 667.903375102016 & 28.0966248979839 \tabularnewline
50 & 825 & 729.271384717009 & 95.7286152829913 \tabularnewline
51 & 677 & 650.188277027583 & 26.8117229724173 \tabularnewline
52 & 656 & 679.113810957953 & -23.1138109579528 \tabularnewline
53 & 785 & 763.609137573266 & 21.3908624267337 \tabularnewline
54 & 412 & 486.525784079443 & -74.5257840794429 \tabularnewline
55 & 352 & 353.932010390557 & -1.93201039055725 \tabularnewline
56 & 839 & 799.58096909401 & 39.4190309059899 \tabularnewline
57 & 729 & 748.091207851041 & -19.0912078510413 \tabularnewline
58 & 696 & 638.025230518301 & 57.9747694816986 \tabularnewline
59 & 641 & 739.369895717159 & -98.3698957171586 \tabularnewline
60 & 695 & 648.518206853014 & 46.4817931469859 \tabularnewline
61 & 638 & 711.124747901819 & -73.1247479018185 \tabularnewline
62 & 762 & 806.64707788869 & -44.64707788869 \tabularnewline
63 & 635 & 669.168037572516 & -34.1680375725161 \tabularnewline
64 & 721 & 660.229436337253 & 60.7705636627469 \tabularnewline
65 & 854 & 782.134785031731 & 71.8652149682692 \tabularnewline
66 & 418 & 444.066913202401 & -26.0669132024013 \tabularnewline
67 & 367 & 360.664586686199 & 6.33541331380138 \tabularnewline
68 & 824 & 845.017958361628 & -21.0179583616283 \tabularnewline
69 & 687 & 748.612709808728 & -61.6127098087283 \tabularnewline
70 & 601 & 682.190300654261 & -81.1903006542611 \tabularnewline
71 & 676 & 669.410901471898 & 6.58909852810211 \tabularnewline
72 & 740 & 680.98018402519 & 59.0198159748098 \tabularnewline
73 & 691 & 668.260798330375 & 22.7392016696249 \tabularnewline
74 & 683 & 793.770722055046 & -110.770722055046 \tabularnewline
75 & 594 & 654.717447856971 & -60.7174478569707 \tabularnewline
76 & 729 & 703.435798355649 & 25.564201644351 \tabularnewline
77 & 731 & 828.604696928258 & -97.6046969282577 \tabularnewline
78 & 386 & 419.108486405942 & -33.1084864059417 \tabularnewline
79 & 331 & 356.880824472789 & -25.8808244727888 \tabularnewline
80 & 706 & 806.5251716464 & -100.525171646401 \tabularnewline
81 & 715 & 680.869110641995 & 34.1308893580053 \tabularnewline
82 & 657 & 613.040899260461 & 43.9591007395389 \tabularnewline
83 & 653 & 668.228632670744 & -15.2286326707435 \tabularnewline
84 & 642 & 710.107472507583 & -68.1074725075835 \tabularnewline
85 & 643 & 662.749894114399 & -19.7498941143987 \tabularnewline
86 & 718 & 696.896524087989 & 21.1034759120112 \tabularnewline
87 & 654 & 604.375117566558 & 49.624882433442 \tabularnewline
88 & 632 & 718.842688245944 & -86.8426882459437 \tabularnewline
89 & 731 & 752.99602607945 & -21.9960260794497 \tabularnewline
90 & 392 & 394.765325432344 & -2.76532543234441 \tabularnewline
91 & 344 & 340.100045600303 & 3.8999543996967 \tabularnewline
92 & 792 & 747.68238166773 & 44.3176183322699 \tabularnewline
93 & 852 & 721.199203322578 & 130.800796677422 \tabularnewline
94 & 649 & 666.471440466248 & -17.4714404662477 \tabularnewline
95 & 629 & 678.199883454367 & -49.199883454367 \tabularnewline
96 & 685 & 682.839299327259 & 2.16070067274075 \tabularnewline
97 & 617 & 672.847062803514 & -55.8470628035141 \tabularnewline
98 & 715 & 731.041817232163 & -16.0418172321632 \tabularnewline
99 & 715 & 650.772655258232 & 64.2273447417683 \tabularnewline
100 & 629 & 679.867208951556 & -50.8672089515558 \tabularnewline
101 & 916 & 761.290149999896 & 154.709850000104 \tabularnewline
102 & 531 & 414.330995039189 & 116.669004960811 \tabularnewline
103 & 357 & 371.603349387028 & -14.6033493870279 \tabularnewline
104 & 917 & 836.962376447361 & 80.0376235526387 \tabularnewline
105 & 828 & 869.245091697302 & -41.2450916973019 \tabularnewline
106 & 708 & 693.441293776717 & 14.5587062232828 \tabularnewline
107 & 858 & 687.486984844789 & 170.513015155211 \tabularnewline
108 & 775 & 750.861332399602 & 24.1386676003976 \tabularnewline
109 & 785 & 701.03140276128 & 83.9685972387201 \tabularnewline
110 & 1006 & 809.343633894797 & 196.656366105203 \tabularnewline
111 & 789 & 796.57032178313 & -7.57032178312954 \tabularnewline
112 & 734 & 737.773987383306 & -3.77398738330567 \tabularnewline
113 & 906 & 984.09426384761 & -78.0942638476107 \tabularnewline
114 & 532 & 542.458664190362 & -10.4586641903621 \tabularnewline
115 & 387 & 392.075888372369 & -5.07588837236949 \tabularnewline
116 & 991 & 962.677697694665 & 28.322302305335 \tabularnewline
117 & 841 & 908.330735465524 & -67.3307354655235 \tabularnewline
118 & 892 & 755.047910374334 & 136.952089625666 \tabularnewline
119 & 782 & 865.880879179644 & -83.8808791796441 \tabularnewline
120 & 813 & 807.95388326262 & 5.04611673738043 \tabularnewline
121 & 793 & 792.723487392503 & 0.276512607497125 \tabularnewline
122 & 978 & 967.742541741162 & 10.2574582588376 \tabularnewline
123 & 775 & 803.9309183551 & -28.9309183550996 \tabularnewline
124 & 797 & 744.67136301732 & 52.3286369826798 \tabularnewline
125 & 946 & 953.043956280599 & -7.04395628059876 \tabularnewline
126 & 594 & 550.643450395871 & 43.3565496041286 \tabularnewline
127 & 438 & 403.543542647334 & 34.4564573526662 \tabularnewline
128 & 1022 & 1027.68207330509 & -5.68207330508676 \tabularnewline
129 & 868 & 903.510592234765 & -35.5105922347655 \tabularnewline
130 & 795 & 880.689443126828 & -85.6894431268275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116302&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]614[/C][C]651.525172725983[/C][C]-37.5251727259829[/C][/ROW]
[ROW][C]14[/C][C]647[/C][C]670.684799400148[/C][C]-23.6847994001478[/C][/ROW]
[ROW][C]15[/C][C]580[/C][C]582.366193489376[/C][C]-2.36619348937563[/C][/ROW]
[ROW][C]16[/C][C]614[/C][C]614.082108335153[/C][C]-0.0821083351529523[/C][/ROW]
[ROW][C]17[/C][C]636[/C][C]638.174882180815[/C][C]-2.17488218081451[/C][/ROW]
[ROW][C]18[/C][C]388[/C][C]385.959140339202[/C][C]2.04085966079765[/C][/ROW]
[ROW][C]19[/C][C]356[/C][C]394.926976308915[/C][C]-38.9269763089152[/C][/ROW]
[ROW][C]20[/C][C]639[/C][C]352.672465590974[/C][C]286.327534409026[/C][/ROW]
[ROW][C]21[/C][C]753[/C][C]693.557227890671[/C][C]59.4427721093285[/C][/ROW]
[ROW][C]22[/C][C]611[/C][C]732.547969407503[/C][C]-121.547969407503[/C][/ROW]
[ROW][C]23[/C][C]639[/C][C]664.801621910674[/C][C]-25.8016219106745[/C][/ROW]
[ROW][C]24[/C][C]630[/C][C]570.204342613149[/C][C]59.795657386851[/C][/ROW]
[ROW][C]25[/C][C]586[/C][C]684.778644320277[/C][C]-98.7786443202771[/C][/ROW]
[ROW][C]26[/C][C]695[/C][C]708.953919341885[/C][C]-13.9539193418846[/C][/ROW]
[ROW][C]27[/C][C]552[/C][C]629.015895313806[/C][C]-77.0158953138058[/C][/ROW]
[ROW][C]28[/C][C]619[/C][C]656.890366325891[/C][C]-37.8903663258913[/C][/ROW]
[ROW][C]29[/C][C]681[/C][C]677.18892234409[/C][C]3.81107765590946[/C][/ROW]
[ROW][C]30[/C][C]421[/C][C]412.132031059866[/C][C]8.86796894013384[/C][/ROW]
[ROW][C]31[/C][C]307[/C][C]394.297058880402[/C][C]-87.2970588804023[/C][/ROW]
[ROW][C]32[/C][C]754[/C][C]548.078347243632[/C][C]205.921652756368[/C][/ROW]
[ROW][C]33[/C][C]690[/C][C]738.007640476895[/C][C]-48.0076404768953[/C][/ROW]
[ROW][C]34[/C][C]644[/C][C]650.364283790538[/C][C]-6.36428379053825[/C][/ROW]
[ROW][C]35[/C][C]643[/C][C]655.016731898568[/C][C]-12.0167318985677[/C][/ROW]
[ROW][C]36[/C][C]608[/C][C]615.297809380185[/C][C]-7.29780938018473[/C][/ROW]
[ROW][C]37[/C][C]651[/C][C]621.45786180542[/C][C]29.5421381945806[/C][/ROW]
[ROW][C]38[/C][C]691[/C][C]714.167953646476[/C][C]-23.1679536464757[/C][/ROW]
[ROW][C]39[/C][C]627[/C][C]590.361326062452[/C][C]36.6386739375477[/C][/ROW]
[ROW][C]40[/C][C]634[/C][C]656.629737764733[/C][C]-22.6297377647328[/C][/ROW]
[ROW][C]41[/C][C]731[/C][C]706.927738944956[/C][C]24.0722610550442[/C][/ROW]
[ROW][C]42[/C][C]475[/C][C]435.746172981773[/C][C]39.2538270182273[/C][/ROW]
[ROW][C]43[/C][C]337[/C][C]354.502513101708[/C][C]-17.5025131017079[/C][/ROW]
[ROW][C]44[/C][C]803[/C][C]720.352028684078[/C][C]82.647971315922[/C][/ROW]
[ROW][C]45[/C][C]722[/C][C]736.604638027393[/C][C]-14.6046380273928[/C][/ROW]
[ROW][C]46[/C][C]590[/C][C]676.10183672607[/C][C]-86.1018367260698[/C][/ROW]
[ROW][C]47[/C][C]724[/C][C]669.123010458944[/C][C]54.8769895410561[/C][/ROW]
[ROW][C]48[/C][C]627[/C][C]637.505502594523[/C][C]-10.505502594523[/C][/ROW]
[ROW][C]49[/C][C]696[/C][C]667.903375102016[/C][C]28.0966248979839[/C][/ROW]
[ROW][C]50[/C][C]825[/C][C]729.271384717009[/C][C]95.7286152829913[/C][/ROW]
[ROW][C]51[/C][C]677[/C][C]650.188277027583[/C][C]26.8117229724173[/C][/ROW]
[ROW][C]52[/C][C]656[/C][C]679.113810957953[/C][C]-23.1138109579528[/C][/ROW]
[ROW][C]53[/C][C]785[/C][C]763.609137573266[/C][C]21.3908624267337[/C][/ROW]
[ROW][C]54[/C][C]412[/C][C]486.525784079443[/C][C]-74.5257840794429[/C][/ROW]
[ROW][C]55[/C][C]352[/C][C]353.932010390557[/C][C]-1.93201039055725[/C][/ROW]
[ROW][C]56[/C][C]839[/C][C]799.58096909401[/C][C]39.4190309059899[/C][/ROW]
[ROW][C]57[/C][C]729[/C][C]748.091207851041[/C][C]-19.0912078510413[/C][/ROW]
[ROW][C]58[/C][C]696[/C][C]638.025230518301[/C][C]57.9747694816986[/C][/ROW]
[ROW][C]59[/C][C]641[/C][C]739.369895717159[/C][C]-98.3698957171586[/C][/ROW]
[ROW][C]60[/C][C]695[/C][C]648.518206853014[/C][C]46.4817931469859[/C][/ROW]
[ROW][C]61[/C][C]638[/C][C]711.124747901819[/C][C]-73.1247479018185[/C][/ROW]
[ROW][C]62[/C][C]762[/C][C]806.64707788869[/C][C]-44.64707788869[/C][/ROW]
[ROW][C]63[/C][C]635[/C][C]669.168037572516[/C][C]-34.1680375725161[/C][/ROW]
[ROW][C]64[/C][C]721[/C][C]660.229436337253[/C][C]60.7705636627469[/C][/ROW]
[ROW][C]65[/C][C]854[/C][C]782.134785031731[/C][C]71.8652149682692[/C][/ROW]
[ROW][C]66[/C][C]418[/C][C]444.066913202401[/C][C]-26.0669132024013[/C][/ROW]
[ROW][C]67[/C][C]367[/C][C]360.664586686199[/C][C]6.33541331380138[/C][/ROW]
[ROW][C]68[/C][C]824[/C][C]845.017958361628[/C][C]-21.0179583616283[/C][/ROW]
[ROW][C]69[/C][C]687[/C][C]748.612709808728[/C][C]-61.6127098087283[/C][/ROW]
[ROW][C]70[/C][C]601[/C][C]682.190300654261[/C][C]-81.1903006542611[/C][/ROW]
[ROW][C]71[/C][C]676[/C][C]669.410901471898[/C][C]6.58909852810211[/C][/ROW]
[ROW][C]72[/C][C]740[/C][C]680.98018402519[/C][C]59.0198159748098[/C][/ROW]
[ROW][C]73[/C][C]691[/C][C]668.260798330375[/C][C]22.7392016696249[/C][/ROW]
[ROW][C]74[/C][C]683[/C][C]793.770722055046[/C][C]-110.770722055046[/C][/ROW]
[ROW][C]75[/C][C]594[/C][C]654.717447856971[/C][C]-60.7174478569707[/C][/ROW]
[ROW][C]76[/C][C]729[/C][C]703.435798355649[/C][C]25.564201644351[/C][/ROW]
[ROW][C]77[/C][C]731[/C][C]828.604696928258[/C][C]-97.6046969282577[/C][/ROW]
[ROW][C]78[/C][C]386[/C][C]419.108486405942[/C][C]-33.1084864059417[/C][/ROW]
[ROW][C]79[/C][C]331[/C][C]356.880824472789[/C][C]-25.8808244727888[/C][/ROW]
[ROW][C]80[/C][C]706[/C][C]806.5251716464[/C][C]-100.525171646401[/C][/ROW]
[ROW][C]81[/C][C]715[/C][C]680.869110641995[/C][C]34.1308893580053[/C][/ROW]
[ROW][C]82[/C][C]657[/C][C]613.040899260461[/C][C]43.9591007395389[/C][/ROW]
[ROW][C]83[/C][C]653[/C][C]668.228632670744[/C][C]-15.2286326707435[/C][/ROW]
[ROW][C]84[/C][C]642[/C][C]710.107472507583[/C][C]-68.1074725075835[/C][/ROW]
[ROW][C]85[/C][C]643[/C][C]662.749894114399[/C][C]-19.7498941143987[/C][/ROW]
[ROW][C]86[/C][C]718[/C][C]696.896524087989[/C][C]21.1034759120112[/C][/ROW]
[ROW][C]87[/C][C]654[/C][C]604.375117566558[/C][C]49.624882433442[/C][/ROW]
[ROW][C]88[/C][C]632[/C][C]718.842688245944[/C][C]-86.8426882459437[/C][/ROW]
[ROW][C]89[/C][C]731[/C][C]752.99602607945[/C][C]-21.9960260794497[/C][/ROW]
[ROW][C]90[/C][C]392[/C][C]394.765325432344[/C][C]-2.76532543234441[/C][/ROW]
[ROW][C]91[/C][C]344[/C][C]340.100045600303[/C][C]3.8999543996967[/C][/ROW]
[ROW][C]92[/C][C]792[/C][C]747.68238166773[/C][C]44.3176183322699[/C][/ROW]
[ROW][C]93[/C][C]852[/C][C]721.199203322578[/C][C]130.800796677422[/C][/ROW]
[ROW][C]94[/C][C]649[/C][C]666.471440466248[/C][C]-17.4714404662477[/C][/ROW]
[ROW][C]95[/C][C]629[/C][C]678.199883454367[/C][C]-49.199883454367[/C][/ROW]
[ROW][C]96[/C][C]685[/C][C]682.839299327259[/C][C]2.16070067274075[/C][/ROW]
[ROW][C]97[/C][C]617[/C][C]672.847062803514[/C][C]-55.8470628035141[/C][/ROW]
[ROW][C]98[/C][C]715[/C][C]731.041817232163[/C][C]-16.0418172321632[/C][/ROW]
[ROW][C]99[/C][C]715[/C][C]650.772655258232[/C][C]64.2273447417683[/C][/ROW]
[ROW][C]100[/C][C]629[/C][C]679.867208951556[/C][C]-50.8672089515558[/C][/ROW]
[ROW][C]101[/C][C]916[/C][C]761.290149999896[/C][C]154.709850000104[/C][/ROW]
[ROW][C]102[/C][C]531[/C][C]414.330995039189[/C][C]116.669004960811[/C][/ROW]
[ROW][C]103[/C][C]357[/C][C]371.603349387028[/C][C]-14.6033493870279[/C][/ROW]
[ROW][C]104[/C][C]917[/C][C]836.962376447361[/C][C]80.0376235526387[/C][/ROW]
[ROW][C]105[/C][C]828[/C][C]869.245091697302[/C][C]-41.2450916973019[/C][/ROW]
[ROW][C]106[/C][C]708[/C][C]693.441293776717[/C][C]14.5587062232828[/C][/ROW]
[ROW][C]107[/C][C]858[/C][C]687.486984844789[/C][C]170.513015155211[/C][/ROW]
[ROW][C]108[/C][C]775[/C][C]750.861332399602[/C][C]24.1386676003976[/C][/ROW]
[ROW][C]109[/C][C]785[/C][C]701.03140276128[/C][C]83.9685972387201[/C][/ROW]
[ROW][C]110[/C][C]1006[/C][C]809.343633894797[/C][C]196.656366105203[/C][/ROW]
[ROW][C]111[/C][C]789[/C][C]796.57032178313[/C][C]-7.57032178312954[/C][/ROW]
[ROW][C]112[/C][C]734[/C][C]737.773987383306[/C][C]-3.77398738330567[/C][/ROW]
[ROW][C]113[/C][C]906[/C][C]984.09426384761[/C][C]-78.0942638476107[/C][/ROW]
[ROW][C]114[/C][C]532[/C][C]542.458664190362[/C][C]-10.4586641903621[/C][/ROW]
[ROW][C]115[/C][C]387[/C][C]392.075888372369[/C][C]-5.07588837236949[/C][/ROW]
[ROW][C]116[/C][C]991[/C][C]962.677697694665[/C][C]28.322302305335[/C][/ROW]
[ROW][C]117[/C][C]841[/C][C]908.330735465524[/C][C]-67.3307354655235[/C][/ROW]
[ROW][C]118[/C][C]892[/C][C]755.047910374334[/C][C]136.952089625666[/C][/ROW]
[ROW][C]119[/C][C]782[/C][C]865.880879179644[/C][C]-83.8808791796441[/C][/ROW]
[ROW][C]120[/C][C]813[/C][C]807.95388326262[/C][C]5.04611673738043[/C][/ROW]
[ROW][C]121[/C][C]793[/C][C]792.723487392503[/C][C]0.276512607497125[/C][/ROW]
[ROW][C]122[/C][C]978[/C][C]967.742541741162[/C][C]10.2574582588376[/C][/ROW]
[ROW][C]123[/C][C]775[/C][C]803.9309183551[/C][C]-28.9309183550996[/C][/ROW]
[ROW][C]124[/C][C]797[/C][C]744.67136301732[/C][C]52.3286369826798[/C][/ROW]
[ROW][C]125[/C][C]946[/C][C]953.043956280599[/C][C]-7.04395628059876[/C][/ROW]
[ROW][C]126[/C][C]594[/C][C]550.643450395871[/C][C]43.3565496041286[/C][/ROW]
[ROW][C]127[/C][C]438[/C][C]403.543542647334[/C][C]34.4564573526662[/C][/ROW]
[ROW][C]128[/C][C]1022[/C][C]1027.68207330509[/C][C]-5.68207330508676[/C][/ROW]
[ROW][C]129[/C][C]868[/C][C]903.510592234765[/C][C]-35.5105922347655[/C][/ROW]
[ROW][C]130[/C][C]795[/C][C]880.689443126828[/C][C]-85.6894431268275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116302&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116302&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
13614651.525172725983-37.5251727259829
14647670.684799400148-23.6847994001478
15580582.366193489376-2.36619348937563
16614614.082108335153-0.0821083351529523
17636638.174882180815-2.17488218081451
18388385.9591403392022.04085966079765
19356394.926976308915-38.9269763089152
20639352.672465590974286.327534409026
21753693.55722789067159.4427721093285
22611732.547969407503-121.547969407503
23639664.801621910674-25.8016219106745
24630570.20434261314959.795657386851
25586684.778644320277-98.7786443202771
26695708.953919341885-13.9539193418846
27552629.015895313806-77.0158953138058
28619656.890366325891-37.8903663258913
29681677.188922344093.81107765590946
30421412.1320310598668.86796894013384
31307394.297058880402-87.2970588804023
32754548.078347243632205.921652756368
33690738.007640476895-48.0076404768953
34644650.364283790538-6.36428379053825
35643655.016731898568-12.0167318985677
36608615.297809380185-7.29780938018473
37651621.4578618054229.5421381945806
38691714.167953646476-23.1679536464757
39627590.36132606245236.6386739375477
40634656.629737764733-22.6297377647328
41731706.92773894495624.0722610550442
42475435.74617298177339.2538270182273
43337354.502513101708-17.5025131017079
44803720.35202868407882.647971315922
45722736.604638027393-14.6046380273928
46590676.10183672607-86.1018367260698
47724669.12301045894454.8769895410561
48627637.505502594523-10.505502594523
49696667.90337510201628.0966248979839
50825729.27138471700995.7286152829913
51677650.18827702758326.8117229724173
52656679.113810957953-23.1138109579528
53785763.60913757326621.3908624267337
54412486.525784079443-74.5257840794429
55352353.932010390557-1.93201039055725
56839799.5809690940139.4190309059899
57729748.091207851041-19.0912078510413
58696638.02523051830157.9747694816986
59641739.369895717159-98.3698957171586
60695648.51820685301446.4817931469859
61638711.124747901819-73.1247479018185
62762806.64707788869-44.64707788869
63635669.168037572516-34.1680375725161
64721660.22943633725360.7705636627469
65854782.13478503173171.8652149682692
66418444.066913202401-26.0669132024013
67367360.6645866861996.33541331380138
68824845.017958361628-21.0179583616283
69687748.612709808728-61.6127098087283
70601682.190300654261-81.1903006542611
71676669.4109014718986.58909852810211
72740680.9801840251959.0198159748098
73691668.26079833037522.7392016696249
74683793.770722055046-110.770722055046
75594654.717447856971-60.7174478569707
76729703.43579835564925.564201644351
77731828.604696928258-97.6046969282577
78386419.108486405942-33.1084864059417
79331356.880824472789-25.8808244727888
80706806.5251716464-100.525171646401
81715680.86911064199534.1308893580053
82657613.04089926046143.9591007395389
83653668.228632670744-15.2286326707435
84642710.107472507583-68.1074725075835
85643662.749894114399-19.7498941143987
86718696.89652408798921.1034759120112
87654604.37511756655849.624882433442
88632718.842688245944-86.8426882459437
89731752.99602607945-21.9960260794497
90392394.765325432344-2.76532543234441
91344340.1000456003033.8999543996967
92792747.6823816677344.3176183322699
93852721.199203322578130.800796677422
94649666.471440466248-17.4714404662477
95629678.199883454367-49.199883454367
96685682.8392993272592.16070067274075
97617672.847062803514-55.8470628035141
98715731.041817232163-16.0418172321632
99715650.77265525823264.2273447417683
100629679.867208951556-50.8672089515558
101916761.290149999896154.709850000104
102531414.330995039189116.669004960811
103357371.603349387028-14.6033493870279
104917836.96237644736180.0376235526387
105828869.245091697302-41.2450916973019
106708693.44129377671714.5587062232828
107858687.486984844789170.513015155211
108775750.86133239960224.1386676003976
109785701.0314027612883.9685972387201
1101006809.343633894797196.656366105203
111789796.57032178313-7.57032178312954
112734737.773987383306-3.77398738330567
113906984.09426384761-78.0942638476107
114532542.458664190362-10.4586641903621
115387392.075888372369-5.07588837236949
116991962.67769769466528.322302305335
117841908.330735465524-67.3307354655235
118892755.047910374334136.952089625666
119782865.880879179644-83.8808791796441
120813807.953883262625.04611673738043
121793792.7234873925030.276512607497125
122978967.74254174116210.2574582588376
123775803.9309183551-28.9309183550996
124797744.6713630173252.3286369826798
125946953.043956280599-7.04395628059876
126594550.64345039587143.3565496041286
127438403.54354264733434.4564573526662
12810221027.68207330509-5.68207330508676
129868903.510592234765-35.5105922347655
130795880.689443126828-85.6894431268275







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
131827.429548585132730.229994148165924.6291030221
132834.599505198186736.481453704931932.71755669144
133815.2589480673716.331868304118914.186027830481
1341001.63937840422900.5279797856761102.75077702276
135806.666389269466706.34963912771906.983139411222
136801.510713192643700.379589898783902.641836486502
137970.7218365002866.577561635451074.86611136495
138591.883665574239491.727316897714692.040014250764
139432.044100698021332.789271702236531.298929693807
1401031.55768421552918.6570270253421144.4583414057
141887.78499969121778.181198893442997.38880048898
142835.49543354432750.709349608741920.2815174799

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
131 & 827.429548585132 & 730.229994148165 & 924.6291030221 \tabularnewline
132 & 834.599505198186 & 736.481453704931 & 932.71755669144 \tabularnewline
133 & 815.2589480673 & 716.331868304118 & 914.186027830481 \tabularnewline
134 & 1001.63937840422 & 900.527979785676 & 1102.75077702276 \tabularnewline
135 & 806.666389269466 & 706.34963912771 & 906.983139411222 \tabularnewline
136 & 801.510713192643 & 700.379589898783 & 902.641836486502 \tabularnewline
137 & 970.7218365002 & 866.57756163545 & 1074.86611136495 \tabularnewline
138 & 591.883665574239 & 491.727316897714 & 692.040014250764 \tabularnewline
139 & 432.044100698021 & 332.789271702236 & 531.298929693807 \tabularnewline
140 & 1031.55768421552 & 918.657027025342 & 1144.4583414057 \tabularnewline
141 & 887.78499969121 & 778.181198893442 & 997.38880048898 \tabularnewline
142 & 835.49543354432 & 750.709349608741 & 920.2815174799 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116302&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]131[/C][C]827.429548585132[/C][C]730.229994148165[/C][C]924.6291030221[/C][/ROW]
[ROW][C]132[/C][C]834.599505198186[/C][C]736.481453704931[/C][C]932.71755669144[/C][/ROW]
[ROW][C]133[/C][C]815.2589480673[/C][C]716.331868304118[/C][C]914.186027830481[/C][/ROW]
[ROW][C]134[/C][C]1001.63937840422[/C][C]900.527979785676[/C][C]1102.75077702276[/C][/ROW]
[ROW][C]135[/C][C]806.666389269466[/C][C]706.34963912771[/C][C]906.983139411222[/C][/ROW]
[ROW][C]136[/C][C]801.510713192643[/C][C]700.379589898783[/C][C]902.641836486502[/C][/ROW]
[ROW][C]137[/C][C]970.7218365002[/C][C]866.57756163545[/C][C]1074.86611136495[/C][/ROW]
[ROW][C]138[/C][C]591.883665574239[/C][C]491.727316897714[/C][C]692.040014250764[/C][/ROW]
[ROW][C]139[/C][C]432.044100698021[/C][C]332.789271702236[/C][C]531.298929693807[/C][/ROW]
[ROW][C]140[/C][C]1031.55768421552[/C][C]918.657027025342[/C][C]1144.4583414057[/C][/ROW]
[ROW][C]141[/C][C]887.78499969121[/C][C]778.181198893442[/C][C]997.38880048898[/C][/ROW]
[ROW][C]142[/C][C]835.49543354432[/C][C]750.709349608741[/C][C]920.2815174799[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116302&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116302&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
131827.429548585132730.229994148165924.6291030221
132834.599505198186736.481453704931932.71755669144
133815.2589480673716.331868304118914.186027830481
1341001.63937840422900.5279797856761102.75077702276
135806.666389269466706.34963912771906.983139411222
136801.510713192643700.379589898783902.641836486502
137970.7218365002866.577561635451074.86611136495
138591.883665574239491.727316897714692.040014250764
139432.044100698021332.789271702236531.298929693807
1401031.55768421552918.6570270253421144.4583414057
141887.78499969121778.181198893442997.38880048898
142835.49543354432750.709349608741920.2815174799



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=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')