Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 14 Aug 2014 17:22:42 +0100
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/Aug/14/t14080334160o6wr8w0ff3imxn.htm/, Retrieved Wed, 15 May 2024 04:30:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235570, Retrieved Wed, 15 May 2024 04:30:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDaemen Wout
Estimated Impact145
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2 - Sta...] [2014-08-14 16:22:42] [a3f6f3ab25c27d7686091f6989fa462a] [Current]
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Dataseries X:
660
770
792
693
726
814
770
737
792
693
770
847
627
704
792
693
770
770
737
836
957
737
891
891
671
660
803
693
825
847
726
869
979
748
880
946
737
671
759
748
814
836
737
825
979
803
825
1034
814
704
704
825
847
858
704
803
1067
858
792
1155
869
671
583
825
803
957
737
825
1199
913
814
1111
858
704
649
847
715
968
770
869
1254
946
693
1166
924
792
627
869
627
880
869
858
1232
935
660
1155
891
825
605
814
550
825
902
891
1199
902
693
1188




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235570&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235570&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235570&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0180404889955411
beta0.239747050427764
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0180404889955411 \tabularnewline
beta & 0.239747050427764 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235570&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]0.0180404889955411[/C][/ROW]
[ROW][C]beta[/C][C]0.239747050427764[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235570&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235570&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
alpha0.0180404889955411
beta0.239747050427764
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13627631.47237392454-4.47237392454019
14704708.765602996992-4.76560299699247
15792788.3986655487023.60133445129782
16693684.4178887161268.5821112838737
17770756.4996047717713.5003952282296
18770752.73489522666417.2651047733362
19737783.791820756476-46.7918207564762
20836756.03547060174379.964529398257
21957820.09382212585136.90617787415
22737722.96613622106714.033863778933
23891805.24940769338585.7505923066154
24891891.887488557846-0.887488557846382
25671661.699151150739.30084884926976
26660744.367538841661-84.3675388416606
27803836.513819520492-33.5138195204921
28693731.882252250068-38.8822522500683
29825812.62666291918112.3733370808189
30847812.96624593219934.0337540678006
31726780.045230410334-54.0452304103342
32869882.556899063124-13.5568990631238
339791007.0528398725-28.0528398724971
34748774.300741644246-26.300741644246
35880932.817763897874-52.8177638978735
36946930.3392094997415.6607905002603
37737699.56370156698637.4362984330141
38671689.214818218031-18.2148182180306
39759837.906081573179-78.9060815731791
40748721.69918753609726.3008124639034
41814858.770662570715-44.7706625707152
42836879.189428268171-43.1894282681707
43737752.734185701642-15.7341857016422
44825899.751326641574-74.7513266415737
459791011.04661255752-32.0466125575215
46803771.30003359810731.699966401893
47825907.880175374919-82.8801753749188
481034972.71498106595561.2850189340451
49814757.04489836512956.955101634871
50704689.76621094097414.2337890590264
51704781.160366636839-77.1603666368391
52825767.27642476584557.723575234155
53847836.29291009176410.7070899082355
54858859.475763523148-1.47576352314786
55704757.778032503445-53.7780325034453
56803848.062390825867-45.0623908258672
5710671005.6551789664561.344821033549
58858825.22261952838332.7773804716165
59792849.898601667212-57.898601667212
6011551062.8696071669892.1303928330221
61869837.12552889847431.8744711015257
62671724.307682334496-53.3076823344957
63583724.424724597902-141.424724597902
64825844.201459637625-19.2014596376248
65803865.185006390986-62.1850063909856
66957874.01447796179782.9855220382035
67737718.52515230644818.4748476935521
68825820.2053745035624.79462549643824
6911991088.35399167415110.646008325846
70913875.9607533643337.0392466356695
71814810.0277765338743.9722234661258
7211111179.68141098245-68.6814109824536
73858885.578118330777-27.5781183307768
74704683.77621462416120.2237853758392
75649596.30505138288952.6949486171113
76847846.2467361940360.753263805964366
77715825.552759495096-110.552759495096
78968980.498145020575-12.4981450205752
79770754.7423254159515.2576745840496
80869845.24927872590923.7507212740908
8112541227.1637772138426.836222786156
82946934.05754879465411.9424512053463
83693832.748172982364-139.748172982364
8411661133.3023342346132.697665765394
85924875.70001069866148.2999893013389
86792718.73491901644173.2650809835594
87627662.841008780053-35.8410087800532
88869863.8032498453525.19675015464793
89627730.706578093021-103.706578093021
90880986.488422436721-106.488422436721
91869782.20042750032586.7995724996754
92858883.652739538776-25.6527395387764
9312321273.0363322915-41.0363322915
94935958.653977884843-23.6539778848435
95660703.29742169531-43.2974216953103
9611551180.61015149165-25.6101514916484
97891933.458247123746-42.4582471237458
98825796.93564176054428.0643582394561
99605630.917393533019-25.9173935330188
100814872.344780608738-58.3447806087379
101550629.103567263888-79.1035672638884
102825881.098041180462-56.0980411804622
103902865.96968664414736.0303133558526
104891854.4838258573436.5161741426597
10511991226.67649963901-27.6764996390114
106902929.567982791318-27.5679827913182
107693655.52287864694737.477121353053
10811881147.6007149185140.3992850814946

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 627 & 631.47237392454 & -4.47237392454019 \tabularnewline
14 & 704 & 708.765602996992 & -4.76560299699247 \tabularnewline
15 & 792 & 788.398665548702 & 3.60133445129782 \tabularnewline
16 & 693 & 684.417888716126 & 8.5821112838737 \tabularnewline
17 & 770 & 756.49960477177 & 13.5003952282296 \tabularnewline
18 & 770 & 752.734895226664 & 17.2651047733362 \tabularnewline
19 & 737 & 783.791820756476 & -46.7918207564762 \tabularnewline
20 & 836 & 756.035470601743 & 79.964529398257 \tabularnewline
21 & 957 & 820.09382212585 & 136.90617787415 \tabularnewline
22 & 737 & 722.966136221067 & 14.033863778933 \tabularnewline
23 & 891 & 805.249407693385 & 85.7505923066154 \tabularnewline
24 & 891 & 891.887488557846 & -0.887488557846382 \tabularnewline
25 & 671 & 661.69915115073 & 9.30084884926976 \tabularnewline
26 & 660 & 744.367538841661 & -84.3675388416606 \tabularnewline
27 & 803 & 836.513819520492 & -33.5138195204921 \tabularnewline
28 & 693 & 731.882252250068 & -38.8822522500683 \tabularnewline
29 & 825 & 812.626662919181 & 12.3733370808189 \tabularnewline
30 & 847 & 812.966245932199 & 34.0337540678006 \tabularnewline
31 & 726 & 780.045230410334 & -54.0452304103342 \tabularnewline
32 & 869 & 882.556899063124 & -13.5568990631238 \tabularnewline
33 & 979 & 1007.0528398725 & -28.0528398724971 \tabularnewline
34 & 748 & 774.300741644246 & -26.300741644246 \tabularnewline
35 & 880 & 932.817763897874 & -52.8177638978735 \tabularnewline
36 & 946 & 930.33920949974 & 15.6607905002603 \tabularnewline
37 & 737 & 699.563701566986 & 37.4362984330141 \tabularnewline
38 & 671 & 689.214818218031 & -18.2148182180306 \tabularnewline
39 & 759 & 837.906081573179 & -78.9060815731791 \tabularnewline
40 & 748 & 721.699187536097 & 26.3008124639034 \tabularnewline
41 & 814 & 858.770662570715 & -44.7706625707152 \tabularnewline
42 & 836 & 879.189428268171 & -43.1894282681707 \tabularnewline
43 & 737 & 752.734185701642 & -15.7341857016422 \tabularnewline
44 & 825 & 899.751326641574 & -74.7513266415737 \tabularnewline
45 & 979 & 1011.04661255752 & -32.0466125575215 \tabularnewline
46 & 803 & 771.300033598107 & 31.699966401893 \tabularnewline
47 & 825 & 907.880175374919 & -82.8801753749188 \tabularnewline
48 & 1034 & 972.714981065955 & 61.2850189340451 \tabularnewline
49 & 814 & 757.044898365129 & 56.955101634871 \tabularnewline
50 & 704 & 689.766210940974 & 14.2337890590264 \tabularnewline
51 & 704 & 781.160366636839 & -77.1603666368391 \tabularnewline
52 & 825 & 767.276424765845 & 57.723575234155 \tabularnewline
53 & 847 & 836.292910091764 & 10.7070899082355 \tabularnewline
54 & 858 & 859.475763523148 & -1.47576352314786 \tabularnewline
55 & 704 & 757.778032503445 & -53.7780325034453 \tabularnewline
56 & 803 & 848.062390825867 & -45.0623908258672 \tabularnewline
57 & 1067 & 1005.65517896645 & 61.344821033549 \tabularnewline
58 & 858 & 825.222619528383 & 32.7773804716165 \tabularnewline
59 & 792 & 849.898601667212 & -57.898601667212 \tabularnewline
60 & 1155 & 1062.86960716698 & 92.1303928330221 \tabularnewline
61 & 869 & 837.125528898474 & 31.8744711015257 \tabularnewline
62 & 671 & 724.307682334496 & -53.3076823344957 \tabularnewline
63 & 583 & 724.424724597902 & -141.424724597902 \tabularnewline
64 & 825 & 844.201459637625 & -19.2014596376248 \tabularnewline
65 & 803 & 865.185006390986 & -62.1850063909856 \tabularnewline
66 & 957 & 874.014477961797 & 82.9855220382035 \tabularnewline
67 & 737 & 718.525152306448 & 18.4748476935521 \tabularnewline
68 & 825 & 820.205374503562 & 4.79462549643824 \tabularnewline
69 & 1199 & 1088.35399167415 & 110.646008325846 \tabularnewline
70 & 913 & 875.96075336433 & 37.0392466356695 \tabularnewline
71 & 814 & 810.027776533874 & 3.9722234661258 \tabularnewline
72 & 1111 & 1179.68141098245 & -68.6814109824536 \tabularnewline
73 & 858 & 885.578118330777 & -27.5781183307768 \tabularnewline
74 & 704 & 683.776214624161 & 20.2237853758392 \tabularnewline
75 & 649 & 596.305051382889 & 52.6949486171113 \tabularnewline
76 & 847 & 846.246736194036 & 0.753263805964366 \tabularnewline
77 & 715 & 825.552759495096 & -110.552759495096 \tabularnewline
78 & 968 & 980.498145020575 & -12.4981450205752 \tabularnewline
79 & 770 & 754.74232541595 & 15.2576745840496 \tabularnewline
80 & 869 & 845.249278725909 & 23.7507212740908 \tabularnewline
81 & 1254 & 1227.16377721384 & 26.836222786156 \tabularnewline
82 & 946 & 934.057548794654 & 11.9424512053463 \tabularnewline
83 & 693 & 832.748172982364 & -139.748172982364 \tabularnewline
84 & 1166 & 1133.30233423461 & 32.697665765394 \tabularnewline
85 & 924 & 875.700010698661 & 48.2999893013389 \tabularnewline
86 & 792 & 718.734919016441 & 73.2650809835594 \tabularnewline
87 & 627 & 662.841008780053 & -35.8410087800532 \tabularnewline
88 & 869 & 863.803249845352 & 5.19675015464793 \tabularnewline
89 & 627 & 730.706578093021 & -103.706578093021 \tabularnewline
90 & 880 & 986.488422436721 & -106.488422436721 \tabularnewline
91 & 869 & 782.200427500325 & 86.7995724996754 \tabularnewline
92 & 858 & 883.652739538776 & -25.6527395387764 \tabularnewline
93 & 1232 & 1273.0363322915 & -41.0363322915 \tabularnewline
94 & 935 & 958.653977884843 & -23.6539778848435 \tabularnewline
95 & 660 & 703.29742169531 & -43.2974216953103 \tabularnewline
96 & 1155 & 1180.61015149165 & -25.6101514916484 \tabularnewline
97 & 891 & 933.458247123746 & -42.4582471237458 \tabularnewline
98 & 825 & 796.935641760544 & 28.0643582394561 \tabularnewline
99 & 605 & 630.917393533019 & -25.9173935330188 \tabularnewline
100 & 814 & 872.344780608738 & -58.3447806087379 \tabularnewline
101 & 550 & 629.103567263888 & -79.1035672638884 \tabularnewline
102 & 825 & 881.098041180462 & -56.0980411804622 \tabularnewline
103 & 902 & 865.969686644147 & 36.0303133558526 \tabularnewline
104 & 891 & 854.48382585734 & 36.5161741426597 \tabularnewline
105 & 1199 & 1226.67649963901 & -27.6764996390114 \tabularnewline
106 & 902 & 929.567982791318 & -27.5679827913182 \tabularnewline
107 & 693 & 655.522878646947 & 37.477121353053 \tabularnewline
108 & 1188 & 1147.60071491851 & 40.3992850814946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235570&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]627[/C][C]631.47237392454[/C][C]-4.47237392454019[/C][/ROW]
[ROW][C]14[/C][C]704[/C][C]708.765602996992[/C][C]-4.76560299699247[/C][/ROW]
[ROW][C]15[/C][C]792[/C][C]788.398665548702[/C][C]3.60133445129782[/C][/ROW]
[ROW][C]16[/C][C]693[/C][C]684.417888716126[/C][C]8.5821112838737[/C][/ROW]
[ROW][C]17[/C][C]770[/C][C]756.49960477177[/C][C]13.5003952282296[/C][/ROW]
[ROW][C]18[/C][C]770[/C][C]752.734895226664[/C][C]17.2651047733362[/C][/ROW]
[ROW][C]19[/C][C]737[/C][C]783.791820756476[/C][C]-46.7918207564762[/C][/ROW]
[ROW][C]20[/C][C]836[/C][C]756.035470601743[/C][C]79.964529398257[/C][/ROW]
[ROW][C]21[/C][C]957[/C][C]820.09382212585[/C][C]136.90617787415[/C][/ROW]
[ROW][C]22[/C][C]737[/C][C]722.966136221067[/C][C]14.033863778933[/C][/ROW]
[ROW][C]23[/C][C]891[/C][C]805.249407693385[/C][C]85.7505923066154[/C][/ROW]
[ROW][C]24[/C][C]891[/C][C]891.887488557846[/C][C]-0.887488557846382[/C][/ROW]
[ROW][C]25[/C][C]671[/C][C]661.69915115073[/C][C]9.30084884926976[/C][/ROW]
[ROW][C]26[/C][C]660[/C][C]744.367538841661[/C][C]-84.3675388416606[/C][/ROW]
[ROW][C]27[/C][C]803[/C][C]836.513819520492[/C][C]-33.5138195204921[/C][/ROW]
[ROW][C]28[/C][C]693[/C][C]731.882252250068[/C][C]-38.8822522500683[/C][/ROW]
[ROW][C]29[/C][C]825[/C][C]812.626662919181[/C][C]12.3733370808189[/C][/ROW]
[ROW][C]30[/C][C]847[/C][C]812.966245932199[/C][C]34.0337540678006[/C][/ROW]
[ROW][C]31[/C][C]726[/C][C]780.045230410334[/C][C]-54.0452304103342[/C][/ROW]
[ROW][C]32[/C][C]869[/C][C]882.556899063124[/C][C]-13.5568990631238[/C][/ROW]
[ROW][C]33[/C][C]979[/C][C]1007.0528398725[/C][C]-28.0528398724971[/C][/ROW]
[ROW][C]34[/C][C]748[/C][C]774.300741644246[/C][C]-26.300741644246[/C][/ROW]
[ROW][C]35[/C][C]880[/C][C]932.817763897874[/C][C]-52.8177638978735[/C][/ROW]
[ROW][C]36[/C][C]946[/C][C]930.33920949974[/C][C]15.6607905002603[/C][/ROW]
[ROW][C]37[/C][C]737[/C][C]699.563701566986[/C][C]37.4362984330141[/C][/ROW]
[ROW][C]38[/C][C]671[/C][C]689.214818218031[/C][C]-18.2148182180306[/C][/ROW]
[ROW][C]39[/C][C]759[/C][C]837.906081573179[/C][C]-78.9060815731791[/C][/ROW]
[ROW][C]40[/C][C]748[/C][C]721.699187536097[/C][C]26.3008124639034[/C][/ROW]
[ROW][C]41[/C][C]814[/C][C]858.770662570715[/C][C]-44.7706625707152[/C][/ROW]
[ROW][C]42[/C][C]836[/C][C]879.189428268171[/C][C]-43.1894282681707[/C][/ROW]
[ROW][C]43[/C][C]737[/C][C]752.734185701642[/C][C]-15.7341857016422[/C][/ROW]
[ROW][C]44[/C][C]825[/C][C]899.751326641574[/C][C]-74.7513266415737[/C][/ROW]
[ROW][C]45[/C][C]979[/C][C]1011.04661255752[/C][C]-32.0466125575215[/C][/ROW]
[ROW][C]46[/C][C]803[/C][C]771.300033598107[/C][C]31.699966401893[/C][/ROW]
[ROW][C]47[/C][C]825[/C][C]907.880175374919[/C][C]-82.8801753749188[/C][/ROW]
[ROW][C]48[/C][C]1034[/C][C]972.714981065955[/C][C]61.2850189340451[/C][/ROW]
[ROW][C]49[/C][C]814[/C][C]757.044898365129[/C][C]56.955101634871[/C][/ROW]
[ROW][C]50[/C][C]704[/C][C]689.766210940974[/C][C]14.2337890590264[/C][/ROW]
[ROW][C]51[/C][C]704[/C][C]781.160366636839[/C][C]-77.1603666368391[/C][/ROW]
[ROW][C]52[/C][C]825[/C][C]767.276424765845[/C][C]57.723575234155[/C][/ROW]
[ROW][C]53[/C][C]847[/C][C]836.292910091764[/C][C]10.7070899082355[/C][/ROW]
[ROW][C]54[/C][C]858[/C][C]859.475763523148[/C][C]-1.47576352314786[/C][/ROW]
[ROW][C]55[/C][C]704[/C][C]757.778032503445[/C][C]-53.7780325034453[/C][/ROW]
[ROW][C]56[/C][C]803[/C][C]848.062390825867[/C][C]-45.0623908258672[/C][/ROW]
[ROW][C]57[/C][C]1067[/C][C]1005.65517896645[/C][C]61.344821033549[/C][/ROW]
[ROW][C]58[/C][C]858[/C][C]825.222619528383[/C][C]32.7773804716165[/C][/ROW]
[ROW][C]59[/C][C]792[/C][C]849.898601667212[/C][C]-57.898601667212[/C][/ROW]
[ROW][C]60[/C][C]1155[/C][C]1062.86960716698[/C][C]92.1303928330221[/C][/ROW]
[ROW][C]61[/C][C]869[/C][C]837.125528898474[/C][C]31.8744711015257[/C][/ROW]
[ROW][C]62[/C][C]671[/C][C]724.307682334496[/C][C]-53.3076823344957[/C][/ROW]
[ROW][C]63[/C][C]583[/C][C]724.424724597902[/C][C]-141.424724597902[/C][/ROW]
[ROW][C]64[/C][C]825[/C][C]844.201459637625[/C][C]-19.2014596376248[/C][/ROW]
[ROW][C]65[/C][C]803[/C][C]865.185006390986[/C][C]-62.1850063909856[/C][/ROW]
[ROW][C]66[/C][C]957[/C][C]874.014477961797[/C][C]82.9855220382035[/C][/ROW]
[ROW][C]67[/C][C]737[/C][C]718.525152306448[/C][C]18.4748476935521[/C][/ROW]
[ROW][C]68[/C][C]825[/C][C]820.205374503562[/C][C]4.79462549643824[/C][/ROW]
[ROW][C]69[/C][C]1199[/C][C]1088.35399167415[/C][C]110.646008325846[/C][/ROW]
[ROW][C]70[/C][C]913[/C][C]875.96075336433[/C][C]37.0392466356695[/C][/ROW]
[ROW][C]71[/C][C]814[/C][C]810.027776533874[/C][C]3.9722234661258[/C][/ROW]
[ROW][C]72[/C][C]1111[/C][C]1179.68141098245[/C][C]-68.6814109824536[/C][/ROW]
[ROW][C]73[/C][C]858[/C][C]885.578118330777[/C][C]-27.5781183307768[/C][/ROW]
[ROW][C]74[/C][C]704[/C][C]683.776214624161[/C][C]20.2237853758392[/C][/ROW]
[ROW][C]75[/C][C]649[/C][C]596.305051382889[/C][C]52.6949486171113[/C][/ROW]
[ROW][C]76[/C][C]847[/C][C]846.246736194036[/C][C]0.753263805964366[/C][/ROW]
[ROW][C]77[/C][C]715[/C][C]825.552759495096[/C][C]-110.552759495096[/C][/ROW]
[ROW][C]78[/C][C]968[/C][C]980.498145020575[/C][C]-12.4981450205752[/C][/ROW]
[ROW][C]79[/C][C]770[/C][C]754.74232541595[/C][C]15.2576745840496[/C][/ROW]
[ROW][C]80[/C][C]869[/C][C]845.249278725909[/C][C]23.7507212740908[/C][/ROW]
[ROW][C]81[/C][C]1254[/C][C]1227.16377721384[/C][C]26.836222786156[/C][/ROW]
[ROW][C]82[/C][C]946[/C][C]934.057548794654[/C][C]11.9424512053463[/C][/ROW]
[ROW][C]83[/C][C]693[/C][C]832.748172982364[/C][C]-139.748172982364[/C][/ROW]
[ROW][C]84[/C][C]1166[/C][C]1133.30233423461[/C][C]32.697665765394[/C][/ROW]
[ROW][C]85[/C][C]924[/C][C]875.700010698661[/C][C]48.2999893013389[/C][/ROW]
[ROW][C]86[/C][C]792[/C][C]718.734919016441[/C][C]73.2650809835594[/C][/ROW]
[ROW][C]87[/C][C]627[/C][C]662.841008780053[/C][C]-35.8410087800532[/C][/ROW]
[ROW][C]88[/C][C]869[/C][C]863.803249845352[/C][C]5.19675015464793[/C][/ROW]
[ROW][C]89[/C][C]627[/C][C]730.706578093021[/C][C]-103.706578093021[/C][/ROW]
[ROW][C]90[/C][C]880[/C][C]986.488422436721[/C][C]-106.488422436721[/C][/ROW]
[ROW][C]91[/C][C]869[/C][C]782.200427500325[/C][C]86.7995724996754[/C][/ROW]
[ROW][C]92[/C][C]858[/C][C]883.652739538776[/C][C]-25.6527395387764[/C][/ROW]
[ROW][C]93[/C][C]1232[/C][C]1273.0363322915[/C][C]-41.0363322915[/C][/ROW]
[ROW][C]94[/C][C]935[/C][C]958.653977884843[/C][C]-23.6539778848435[/C][/ROW]
[ROW][C]95[/C][C]660[/C][C]703.29742169531[/C][C]-43.2974216953103[/C][/ROW]
[ROW][C]96[/C][C]1155[/C][C]1180.61015149165[/C][C]-25.6101514916484[/C][/ROW]
[ROW][C]97[/C][C]891[/C][C]933.458247123746[/C][C]-42.4582471237458[/C][/ROW]
[ROW][C]98[/C][C]825[/C][C]796.935641760544[/C][C]28.0643582394561[/C][/ROW]
[ROW][C]99[/C][C]605[/C][C]630.917393533019[/C][C]-25.9173935330188[/C][/ROW]
[ROW][C]100[/C][C]814[/C][C]872.344780608738[/C][C]-58.3447806087379[/C][/ROW]
[ROW][C]101[/C][C]550[/C][C]629.103567263888[/C][C]-79.1035672638884[/C][/ROW]
[ROW][C]102[/C][C]825[/C][C]881.098041180462[/C][C]-56.0980411804622[/C][/ROW]
[ROW][C]103[/C][C]902[/C][C]865.969686644147[/C][C]36.0303133558526[/C][/ROW]
[ROW][C]104[/C][C]891[/C][C]854.48382585734[/C][C]36.5161741426597[/C][/ROW]
[ROW][C]105[/C][C]1199[/C][C]1226.67649963901[/C][C]-27.6764996390114[/C][/ROW]
[ROW][C]106[/C][C]902[/C][C]929.567982791318[/C][C]-27.5679827913182[/C][/ROW]
[ROW][C]107[/C][C]693[/C][C]655.522878646947[/C][C]37.477121353053[/C][/ROW]
[ROW][C]108[/C][C]1188[/C][C]1147.60071491851[/C][C]40.3992850814946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235570&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235570&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
13627631.47237392454-4.47237392454019
14704708.765602996992-4.76560299699247
15792788.3986655487023.60133445129782
16693684.4178887161268.5821112838737
17770756.4996047717713.5003952282296
18770752.73489522666417.2651047733362
19737783.791820756476-46.7918207564762
20836756.03547060174379.964529398257
21957820.09382212585136.90617787415
22737722.96613622106714.033863778933
23891805.24940769338585.7505923066154
24891891.887488557846-0.887488557846382
25671661.699151150739.30084884926976
26660744.367538841661-84.3675388416606
27803836.513819520492-33.5138195204921
28693731.882252250068-38.8822522500683
29825812.62666291918112.3733370808189
30847812.96624593219934.0337540678006
31726780.045230410334-54.0452304103342
32869882.556899063124-13.5568990631238
339791007.0528398725-28.0528398724971
34748774.300741644246-26.300741644246
35880932.817763897874-52.8177638978735
36946930.3392094997415.6607905002603
37737699.56370156698637.4362984330141
38671689.214818218031-18.2148182180306
39759837.906081573179-78.9060815731791
40748721.69918753609726.3008124639034
41814858.770662570715-44.7706625707152
42836879.189428268171-43.1894282681707
43737752.734185701642-15.7341857016422
44825899.751326641574-74.7513266415737
459791011.04661255752-32.0466125575215
46803771.30003359810731.699966401893
47825907.880175374919-82.8801753749188
481034972.71498106595561.2850189340451
49814757.04489836512956.955101634871
50704689.76621094097414.2337890590264
51704781.160366636839-77.1603666368391
52825767.27642476584557.723575234155
53847836.29291009176410.7070899082355
54858859.475763523148-1.47576352314786
55704757.778032503445-53.7780325034453
56803848.062390825867-45.0623908258672
5710671005.6551789664561.344821033549
58858825.22261952838332.7773804716165
59792849.898601667212-57.898601667212
6011551062.8696071669892.1303928330221
61869837.12552889847431.8744711015257
62671724.307682334496-53.3076823344957
63583724.424724597902-141.424724597902
64825844.201459637625-19.2014596376248
65803865.185006390986-62.1850063909856
66957874.01447796179782.9855220382035
67737718.52515230644818.4748476935521
68825820.2053745035624.79462549643824
6911991088.35399167415110.646008325846
70913875.9607533643337.0392466356695
71814810.0277765338743.9722234661258
7211111179.68141098245-68.6814109824536
73858885.578118330777-27.5781183307768
74704683.77621462416120.2237853758392
75649596.30505138288952.6949486171113
76847846.2467361940360.753263805964366
77715825.552759495096-110.552759495096
78968980.498145020575-12.4981450205752
79770754.7423254159515.2576745840496
80869845.24927872590923.7507212740908
8112541227.1637772138426.836222786156
82946934.05754879465411.9424512053463
83693832.748172982364-139.748172982364
8411661133.3023342346132.697665765394
85924875.70001069866148.2999893013389
86792718.73491901644173.2650809835594
87627662.841008780053-35.8410087800532
88869863.8032498453525.19675015464793
89627730.706578093021-103.706578093021
90880986.488422436721-106.488422436721
91869782.20042750032586.7995724996754
92858883.652739538776-25.6527395387764
9312321273.0363322915-41.0363322915
94935958.653977884843-23.6539778848435
95660703.29742169531-43.2974216953103
9611551180.61015149165-25.6101514916484
97891933.458247123746-42.4582471237458
98825796.93564176054428.0643582394561
99605630.917393533019-25.9173935330188
100814872.344780608738-58.3447806087379
101550629.103567263888-79.1035672638884
102825881.098041180462-56.0980411804622
103902865.96968664414736.0303133558526
104891854.4838258573436.5161741426597
10511991226.67649963901-27.6764996390114
106902929.567982791318-27.5679827913182
107693655.52287864694737.477121353053
10811881147.6007149185140.3992850814946







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109885.875992007626780.294620970727991.457363044524
110819.243280754833713.639315613809924.847245895857
111600.772208261398495.159317590343706.385098932453
112808.823669443996703.115381120987914.531957767005
113547.588957823088441.916260778309653.261654867867
114822.541990121114716.628805036619928.45517520561
115899.120694634261792.9908772932661005.25051197526
116887.788458212127781.499989635298994.076926788956
1171195.370362411751088.146276155221302.59444866829
118899.99379105428793.250446145491006.73713596307
119691.021820827306584.59523746198797.448404192631
1201184.03629768968631.0577314981541737.01486388121

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 885.875992007626 & 780.294620970727 & 991.457363044524 \tabularnewline
110 & 819.243280754833 & 713.639315613809 & 924.847245895857 \tabularnewline
111 & 600.772208261398 & 495.159317590343 & 706.385098932453 \tabularnewline
112 & 808.823669443996 & 703.115381120987 & 914.531957767005 \tabularnewline
113 & 547.588957823088 & 441.916260778309 & 653.261654867867 \tabularnewline
114 & 822.541990121114 & 716.628805036619 & 928.45517520561 \tabularnewline
115 & 899.120694634261 & 792.990877293266 & 1005.25051197526 \tabularnewline
116 & 887.788458212127 & 781.499989635298 & 994.076926788956 \tabularnewline
117 & 1195.37036241175 & 1088.14627615522 & 1302.59444866829 \tabularnewline
118 & 899.99379105428 & 793.25044614549 & 1006.73713596307 \tabularnewline
119 & 691.021820827306 & 584.59523746198 & 797.448404192631 \tabularnewline
120 & 1184.03629768968 & 631.057731498154 & 1737.01486388121 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235570&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]109[/C][C]885.875992007626[/C][C]780.294620970727[/C][C]991.457363044524[/C][/ROW]
[ROW][C]110[/C][C]819.243280754833[/C][C]713.639315613809[/C][C]924.847245895857[/C][/ROW]
[ROW][C]111[/C][C]600.772208261398[/C][C]495.159317590343[/C][C]706.385098932453[/C][/ROW]
[ROW][C]112[/C][C]808.823669443996[/C][C]703.115381120987[/C][C]914.531957767005[/C][/ROW]
[ROW][C]113[/C][C]547.588957823088[/C][C]441.916260778309[/C][C]653.261654867867[/C][/ROW]
[ROW][C]114[/C][C]822.541990121114[/C][C]716.628805036619[/C][C]928.45517520561[/C][/ROW]
[ROW][C]115[/C][C]899.120694634261[/C][C]792.990877293266[/C][C]1005.25051197526[/C][/ROW]
[ROW][C]116[/C][C]887.788458212127[/C][C]781.499989635298[/C][C]994.076926788956[/C][/ROW]
[ROW][C]117[/C][C]1195.37036241175[/C][C]1088.14627615522[/C][C]1302.59444866829[/C][/ROW]
[ROW][C]118[/C][C]899.99379105428[/C][C]793.25044614549[/C][C]1006.73713596307[/C][/ROW]
[ROW][C]119[/C][C]691.021820827306[/C][C]584.59523746198[/C][C]797.448404192631[/C][/ROW]
[ROW][C]120[/C][C]1184.03629768968[/C][C]631.057731498154[/C][C]1737.01486388121[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235570&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235570&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
109885.875992007626780.294620970727991.457363044524
110819.243280754833713.639315613809924.847245895857
111600.772208261398495.159317590343706.385098932453
112808.823669443996703.115381120987914.531957767005
113547.588957823088441.916260778309653.261654867867
114822.541990121114716.628805036619928.45517520561
115899.120694634261792.9908772932661005.25051197526
116887.788458212127781.499989635298994.076926788956
1171195.370362411751088.146276155221302.59444866829
118899.99379105428793.250446145491006.73713596307
119691.021820827306584.59523746198797.448404192631
1201184.03629768968631.0577314981541737.01486388121



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')