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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 11 Aug 2016 18:04:35 +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/2016/Aug/11/t14709351066bretlk351k1g2g.htm/, Retrieved Sun, 05 May 2024 12:34:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296346, Retrieved Sun, 05 May 2024 12:34:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Nagasaki Bomb Mus...] [2016-08-11 17:04:35] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
840
880
930
920
940
880
980
860
900
930
870
1000
870
860
930
980
1010
860
1140
880
800
900
900
1000
890
890
870
1000
1050
790
1160
830
730
950
980
910
840
860
880
1030
1060
770
1140
890
740
860
1050
840
810
830
920
1070
1040
740
1250
850
790
810
1080
760
840
820
900
1010
1080
780
1150
820
790
820
1130
800
890
810
950
1090
1090
850
1200
790
800
850
1230
800
930
700
1030
1040
1000
830
1190
720
810
870
1190
800
970
690
1010
1030
950
830
1150
750
840
880
1210
830




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296346&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296346&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296346&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0586850505117358
beta0.0455307064612279
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0586850505117358 \tabularnewline
beta & 0.0455307064612279 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296346&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]0.0586850505117358[/C][/ROW]
[ROW][C]beta[/C][C]0.0455307064612279[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296346&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296346&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
alpha0.0586850505117358
beta0.0455307064612279
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13870855.68376068376114.316239316239
14860840.93279186965919.0672081303412
15930917.34491427631712.6550857236834
16980975.4978883212744.50211167872646
1710101007.76776752142.23223247860108
18860858.6604032082621.33959679173756
191140996.170900556282143.829099443718
20880886.59437553045-6.59437553045018
21800929.422621292096-129.422621292096
22900951.363538318142-51.363538318142
23900884.83144797837615.1685520216237
2410001015.57765999756-15.5776599975623
25890894.203996031829-4.20399603182852
26890882.815964365327.1840356346795
27870952.440784137809-82.4407841378087
281000997.0303310451172.96966895488333
2910501026.7613080381623.2386919618421
30790877.790286708094-87.7902867080943
3111601143.7033679599916.2966320400119
32830884.211641365662-54.2116413656622
33730807.663082999909-77.6630829999093
34950905.29567439718944.7043256028106
35980906.46165489117173.5383451088293
369101011.28006672331-101.280066723307
37840894.942792767668-54.9427927676683
38860890.520944226638-30.5209442266377
39880872.6911835330517.308816466949
4010301002.3089559052827.6910440947194
4110601051.999426513848.00057348615792
42770797.00938625867-27.0093862586702
4311401164.01884351561-24.0188435156124
44890835.23386069666454.7661393033355
45740742.739813168593-2.73981316859329
46860959.890081224931-99.8900812249315
471050979.26060282327570.7393971767245
48840918.896272599194-78.8962725991939
49810847.09106914016-37.0910691401597
50830866.353708044818-36.3537080448178
51920883.42399262496436.5760073750363
5210701033.6562302894736.3437697105264
5310401065.05349517609-25.0534951760862
54740774.813900187963-34.8139001879628
5512501143.80516174557106.19483825443
56850896.795954831742-46.7959548317416
57790743.91184417101946.0881558289814
58810872.310377580901-62.3103775809012
5910801054.4345499321425.5654500678563
60760850.376392993717-90.376392993717
61840817.03016810409922.9698318959012
62820840.452881108679-20.4528811086792
63900927.089932535314-27.0899325353139
6410101073.1810035462-63.1810035461972
6510801040.4912424345539.5087575654529
66780744.57313352112835.4268664788716
6711501250.32805503336-100.328055033365
68820846.542641190853-26.5426411908535
69790781.6905356439358.3094643560654
70820805.14415748145614.855842518544
7111301074.0311424324655.9688575675414
72800762.21613671251537.7838632874846
73890843.02465534348546.9753446565152
74810826.984982682249-16.9849826822491
75950907.59055680544242.4094431945581
7610901023.9854025092966.0145974907135
7710901096.08437107122-6.08437107121745
78850794.06993045146855.9300695485322
7912001173.7163788186926.283621181306
80790847.631225957093-57.6312259570926
81800814.493160655967-14.4931606559666
82850843.441552391696.55844760831042
8312301151.1904690516378.8095309483697
84800824.307661130152-24.3076611301522
85930910.66810623170719.3318937682933
86700833.269193335945-133.269193335945
871030963.11860491998966.8813950800114
8810401103.39398258851-63.3939825885054
8910001099.90949867226-99.9094986722598
90830850.39208117407-20.3920811740699
9111901197.07702002315-7.0770200231525
92720789.378762258633-69.3787622586328
93810795.46137497706314.5386250229375
94870845.31084122546724.6891587745334
9511901221.56437833357-31.5643783335695
96800790.2731954267799.72680457322065
97970918.93513732391651.0648626760842
98690699.063197352056-9.06319735205579
9910101024.24866666884-14.2486666688446
10010301036.55826633795-6.55826633794732
1019501001.6139558763-51.6139558762997
102830829.4881106646360.511889335363776
10311501189.69573309586-39.6957330958649
104750721.11279378205828.8872062179419
105840811.89251551219928.107484487801
106880872.0670502572527.93294974274818
10712101194.3141109602415.6858890397571
108830804.71922952528525.2807704747149

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 870 & 855.683760683761 & 14.316239316239 \tabularnewline
14 & 860 & 840.932791869659 & 19.0672081303412 \tabularnewline
15 & 930 & 917.344914276317 & 12.6550857236834 \tabularnewline
16 & 980 & 975.497888321274 & 4.50211167872646 \tabularnewline
17 & 1010 & 1007.7677675214 & 2.23223247860108 \tabularnewline
18 & 860 & 858.660403208262 & 1.33959679173756 \tabularnewline
19 & 1140 & 996.170900556282 & 143.829099443718 \tabularnewline
20 & 880 & 886.59437553045 & -6.59437553045018 \tabularnewline
21 & 800 & 929.422621292096 & -129.422621292096 \tabularnewline
22 & 900 & 951.363538318142 & -51.363538318142 \tabularnewline
23 & 900 & 884.831447978376 & 15.1685520216237 \tabularnewline
24 & 1000 & 1015.57765999756 & -15.5776599975623 \tabularnewline
25 & 890 & 894.203996031829 & -4.20399603182852 \tabularnewline
26 & 890 & 882.81596436532 & 7.1840356346795 \tabularnewline
27 & 870 & 952.440784137809 & -82.4407841378087 \tabularnewline
28 & 1000 & 997.030331045117 & 2.96966895488333 \tabularnewline
29 & 1050 & 1026.76130803816 & 23.2386919618421 \tabularnewline
30 & 790 & 877.790286708094 & -87.7902867080943 \tabularnewline
31 & 1160 & 1143.70336795999 & 16.2966320400119 \tabularnewline
32 & 830 & 884.211641365662 & -54.2116413656622 \tabularnewline
33 & 730 & 807.663082999909 & -77.6630829999093 \tabularnewline
34 & 950 & 905.295674397189 & 44.7043256028106 \tabularnewline
35 & 980 & 906.461654891171 & 73.5383451088293 \tabularnewline
36 & 910 & 1011.28006672331 & -101.280066723307 \tabularnewline
37 & 840 & 894.942792767668 & -54.9427927676683 \tabularnewline
38 & 860 & 890.520944226638 & -30.5209442266377 \tabularnewline
39 & 880 & 872.691183533051 & 7.308816466949 \tabularnewline
40 & 1030 & 1002.30895590528 & 27.6910440947194 \tabularnewline
41 & 1060 & 1051.99942651384 & 8.00057348615792 \tabularnewline
42 & 770 & 797.00938625867 & -27.0093862586702 \tabularnewline
43 & 1140 & 1164.01884351561 & -24.0188435156124 \tabularnewline
44 & 890 & 835.233860696664 & 54.7661393033355 \tabularnewline
45 & 740 & 742.739813168593 & -2.73981316859329 \tabularnewline
46 & 860 & 959.890081224931 & -99.8900812249315 \tabularnewline
47 & 1050 & 979.260602823275 & 70.7393971767245 \tabularnewline
48 & 840 & 918.896272599194 & -78.8962725991939 \tabularnewline
49 & 810 & 847.09106914016 & -37.0910691401597 \tabularnewline
50 & 830 & 866.353708044818 & -36.3537080448178 \tabularnewline
51 & 920 & 883.423992624964 & 36.5760073750363 \tabularnewline
52 & 1070 & 1033.65623028947 & 36.3437697105264 \tabularnewline
53 & 1040 & 1065.05349517609 & -25.0534951760862 \tabularnewline
54 & 740 & 774.813900187963 & -34.8139001879628 \tabularnewline
55 & 1250 & 1143.80516174557 & 106.19483825443 \tabularnewline
56 & 850 & 896.795954831742 & -46.7959548317416 \tabularnewline
57 & 790 & 743.911844171019 & 46.0881558289814 \tabularnewline
58 & 810 & 872.310377580901 & -62.3103775809012 \tabularnewline
59 & 1080 & 1054.43454993214 & 25.5654500678563 \tabularnewline
60 & 760 & 850.376392993717 & -90.376392993717 \tabularnewline
61 & 840 & 817.030168104099 & 22.9698318959012 \tabularnewline
62 & 820 & 840.452881108679 & -20.4528811086792 \tabularnewline
63 & 900 & 927.089932535314 & -27.0899325353139 \tabularnewline
64 & 1010 & 1073.1810035462 & -63.1810035461972 \tabularnewline
65 & 1080 & 1040.49124243455 & 39.5087575654529 \tabularnewline
66 & 780 & 744.573133521128 & 35.4268664788716 \tabularnewline
67 & 1150 & 1250.32805503336 & -100.328055033365 \tabularnewline
68 & 820 & 846.542641190853 & -26.5426411908535 \tabularnewline
69 & 790 & 781.690535643935 & 8.3094643560654 \tabularnewline
70 & 820 & 805.144157481456 & 14.855842518544 \tabularnewline
71 & 1130 & 1074.03114243246 & 55.9688575675414 \tabularnewline
72 & 800 & 762.216136712515 & 37.7838632874846 \tabularnewline
73 & 890 & 843.024655343485 & 46.9753446565152 \tabularnewline
74 & 810 & 826.984982682249 & -16.9849826822491 \tabularnewline
75 & 950 & 907.590556805442 & 42.4094431945581 \tabularnewline
76 & 1090 & 1023.98540250929 & 66.0145974907135 \tabularnewline
77 & 1090 & 1096.08437107122 & -6.08437107121745 \tabularnewline
78 & 850 & 794.069930451468 & 55.9300695485322 \tabularnewline
79 & 1200 & 1173.71637881869 & 26.283621181306 \tabularnewline
80 & 790 & 847.631225957093 & -57.6312259570926 \tabularnewline
81 & 800 & 814.493160655967 & -14.4931606559666 \tabularnewline
82 & 850 & 843.44155239169 & 6.55844760831042 \tabularnewline
83 & 1230 & 1151.19046905163 & 78.8095309483697 \tabularnewline
84 & 800 & 824.307661130152 & -24.3076611301522 \tabularnewline
85 & 930 & 910.668106231707 & 19.3318937682933 \tabularnewline
86 & 700 & 833.269193335945 & -133.269193335945 \tabularnewline
87 & 1030 & 963.118604919989 & 66.8813950800114 \tabularnewline
88 & 1040 & 1103.39398258851 & -63.3939825885054 \tabularnewline
89 & 1000 & 1099.90949867226 & -99.9094986722598 \tabularnewline
90 & 830 & 850.39208117407 & -20.3920811740699 \tabularnewline
91 & 1190 & 1197.07702002315 & -7.0770200231525 \tabularnewline
92 & 720 & 789.378762258633 & -69.3787622586328 \tabularnewline
93 & 810 & 795.461374977063 & 14.5386250229375 \tabularnewline
94 & 870 & 845.310841225467 & 24.6891587745334 \tabularnewline
95 & 1190 & 1221.56437833357 & -31.5643783335695 \tabularnewline
96 & 800 & 790.273195426779 & 9.72680457322065 \tabularnewline
97 & 970 & 918.935137323916 & 51.0648626760842 \tabularnewline
98 & 690 & 699.063197352056 & -9.06319735205579 \tabularnewline
99 & 1010 & 1024.24866666884 & -14.2486666688446 \tabularnewline
100 & 1030 & 1036.55826633795 & -6.55826633794732 \tabularnewline
101 & 950 & 1001.6139558763 & -51.6139558762997 \tabularnewline
102 & 830 & 829.488110664636 & 0.511889335363776 \tabularnewline
103 & 1150 & 1189.69573309586 & -39.6957330958649 \tabularnewline
104 & 750 & 721.112793782058 & 28.8872062179419 \tabularnewline
105 & 840 & 811.892515512199 & 28.107484487801 \tabularnewline
106 & 880 & 872.067050257252 & 7.93294974274818 \tabularnewline
107 & 1210 & 1194.31411096024 & 15.6858890397571 \tabularnewline
108 & 830 & 804.719229525285 & 25.2807704747149 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296346&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]870[/C][C]855.683760683761[/C][C]14.316239316239[/C][/ROW]
[ROW][C]14[/C][C]860[/C][C]840.932791869659[/C][C]19.0672081303412[/C][/ROW]
[ROW][C]15[/C][C]930[/C][C]917.344914276317[/C][C]12.6550857236834[/C][/ROW]
[ROW][C]16[/C][C]980[/C][C]975.497888321274[/C][C]4.50211167872646[/C][/ROW]
[ROW][C]17[/C][C]1010[/C][C]1007.7677675214[/C][C]2.23223247860108[/C][/ROW]
[ROW][C]18[/C][C]860[/C][C]858.660403208262[/C][C]1.33959679173756[/C][/ROW]
[ROW][C]19[/C][C]1140[/C][C]996.170900556282[/C][C]143.829099443718[/C][/ROW]
[ROW][C]20[/C][C]880[/C][C]886.59437553045[/C][C]-6.59437553045018[/C][/ROW]
[ROW][C]21[/C][C]800[/C][C]929.422621292096[/C][C]-129.422621292096[/C][/ROW]
[ROW][C]22[/C][C]900[/C][C]951.363538318142[/C][C]-51.363538318142[/C][/ROW]
[ROW][C]23[/C][C]900[/C][C]884.831447978376[/C][C]15.1685520216237[/C][/ROW]
[ROW][C]24[/C][C]1000[/C][C]1015.57765999756[/C][C]-15.5776599975623[/C][/ROW]
[ROW][C]25[/C][C]890[/C][C]894.203996031829[/C][C]-4.20399603182852[/C][/ROW]
[ROW][C]26[/C][C]890[/C][C]882.81596436532[/C][C]7.1840356346795[/C][/ROW]
[ROW][C]27[/C][C]870[/C][C]952.440784137809[/C][C]-82.4407841378087[/C][/ROW]
[ROW][C]28[/C][C]1000[/C][C]997.030331045117[/C][C]2.96966895488333[/C][/ROW]
[ROW][C]29[/C][C]1050[/C][C]1026.76130803816[/C][C]23.2386919618421[/C][/ROW]
[ROW][C]30[/C][C]790[/C][C]877.790286708094[/C][C]-87.7902867080943[/C][/ROW]
[ROW][C]31[/C][C]1160[/C][C]1143.70336795999[/C][C]16.2966320400119[/C][/ROW]
[ROW][C]32[/C][C]830[/C][C]884.211641365662[/C][C]-54.2116413656622[/C][/ROW]
[ROW][C]33[/C][C]730[/C][C]807.663082999909[/C][C]-77.6630829999093[/C][/ROW]
[ROW][C]34[/C][C]950[/C][C]905.295674397189[/C][C]44.7043256028106[/C][/ROW]
[ROW][C]35[/C][C]980[/C][C]906.461654891171[/C][C]73.5383451088293[/C][/ROW]
[ROW][C]36[/C][C]910[/C][C]1011.28006672331[/C][C]-101.280066723307[/C][/ROW]
[ROW][C]37[/C][C]840[/C][C]894.942792767668[/C][C]-54.9427927676683[/C][/ROW]
[ROW][C]38[/C][C]860[/C][C]890.520944226638[/C][C]-30.5209442266377[/C][/ROW]
[ROW][C]39[/C][C]880[/C][C]872.691183533051[/C][C]7.308816466949[/C][/ROW]
[ROW][C]40[/C][C]1030[/C][C]1002.30895590528[/C][C]27.6910440947194[/C][/ROW]
[ROW][C]41[/C][C]1060[/C][C]1051.99942651384[/C][C]8.00057348615792[/C][/ROW]
[ROW][C]42[/C][C]770[/C][C]797.00938625867[/C][C]-27.0093862586702[/C][/ROW]
[ROW][C]43[/C][C]1140[/C][C]1164.01884351561[/C][C]-24.0188435156124[/C][/ROW]
[ROW][C]44[/C][C]890[/C][C]835.233860696664[/C][C]54.7661393033355[/C][/ROW]
[ROW][C]45[/C][C]740[/C][C]742.739813168593[/C][C]-2.73981316859329[/C][/ROW]
[ROW][C]46[/C][C]860[/C][C]959.890081224931[/C][C]-99.8900812249315[/C][/ROW]
[ROW][C]47[/C][C]1050[/C][C]979.260602823275[/C][C]70.7393971767245[/C][/ROW]
[ROW][C]48[/C][C]840[/C][C]918.896272599194[/C][C]-78.8962725991939[/C][/ROW]
[ROW][C]49[/C][C]810[/C][C]847.09106914016[/C][C]-37.0910691401597[/C][/ROW]
[ROW][C]50[/C][C]830[/C][C]866.353708044818[/C][C]-36.3537080448178[/C][/ROW]
[ROW][C]51[/C][C]920[/C][C]883.423992624964[/C][C]36.5760073750363[/C][/ROW]
[ROW][C]52[/C][C]1070[/C][C]1033.65623028947[/C][C]36.3437697105264[/C][/ROW]
[ROW][C]53[/C][C]1040[/C][C]1065.05349517609[/C][C]-25.0534951760862[/C][/ROW]
[ROW][C]54[/C][C]740[/C][C]774.813900187963[/C][C]-34.8139001879628[/C][/ROW]
[ROW][C]55[/C][C]1250[/C][C]1143.80516174557[/C][C]106.19483825443[/C][/ROW]
[ROW][C]56[/C][C]850[/C][C]896.795954831742[/C][C]-46.7959548317416[/C][/ROW]
[ROW][C]57[/C][C]790[/C][C]743.911844171019[/C][C]46.0881558289814[/C][/ROW]
[ROW][C]58[/C][C]810[/C][C]872.310377580901[/C][C]-62.3103775809012[/C][/ROW]
[ROW][C]59[/C][C]1080[/C][C]1054.43454993214[/C][C]25.5654500678563[/C][/ROW]
[ROW][C]60[/C][C]760[/C][C]850.376392993717[/C][C]-90.376392993717[/C][/ROW]
[ROW][C]61[/C][C]840[/C][C]817.030168104099[/C][C]22.9698318959012[/C][/ROW]
[ROW][C]62[/C][C]820[/C][C]840.452881108679[/C][C]-20.4528811086792[/C][/ROW]
[ROW][C]63[/C][C]900[/C][C]927.089932535314[/C][C]-27.0899325353139[/C][/ROW]
[ROW][C]64[/C][C]1010[/C][C]1073.1810035462[/C][C]-63.1810035461972[/C][/ROW]
[ROW][C]65[/C][C]1080[/C][C]1040.49124243455[/C][C]39.5087575654529[/C][/ROW]
[ROW][C]66[/C][C]780[/C][C]744.573133521128[/C][C]35.4268664788716[/C][/ROW]
[ROW][C]67[/C][C]1150[/C][C]1250.32805503336[/C][C]-100.328055033365[/C][/ROW]
[ROW][C]68[/C][C]820[/C][C]846.542641190853[/C][C]-26.5426411908535[/C][/ROW]
[ROW][C]69[/C][C]790[/C][C]781.690535643935[/C][C]8.3094643560654[/C][/ROW]
[ROW][C]70[/C][C]820[/C][C]805.144157481456[/C][C]14.855842518544[/C][/ROW]
[ROW][C]71[/C][C]1130[/C][C]1074.03114243246[/C][C]55.9688575675414[/C][/ROW]
[ROW][C]72[/C][C]800[/C][C]762.216136712515[/C][C]37.7838632874846[/C][/ROW]
[ROW][C]73[/C][C]890[/C][C]843.024655343485[/C][C]46.9753446565152[/C][/ROW]
[ROW][C]74[/C][C]810[/C][C]826.984982682249[/C][C]-16.9849826822491[/C][/ROW]
[ROW][C]75[/C][C]950[/C][C]907.590556805442[/C][C]42.4094431945581[/C][/ROW]
[ROW][C]76[/C][C]1090[/C][C]1023.98540250929[/C][C]66.0145974907135[/C][/ROW]
[ROW][C]77[/C][C]1090[/C][C]1096.08437107122[/C][C]-6.08437107121745[/C][/ROW]
[ROW][C]78[/C][C]850[/C][C]794.069930451468[/C][C]55.9300695485322[/C][/ROW]
[ROW][C]79[/C][C]1200[/C][C]1173.71637881869[/C][C]26.283621181306[/C][/ROW]
[ROW][C]80[/C][C]790[/C][C]847.631225957093[/C][C]-57.6312259570926[/C][/ROW]
[ROW][C]81[/C][C]800[/C][C]814.493160655967[/C][C]-14.4931606559666[/C][/ROW]
[ROW][C]82[/C][C]850[/C][C]843.44155239169[/C][C]6.55844760831042[/C][/ROW]
[ROW][C]83[/C][C]1230[/C][C]1151.19046905163[/C][C]78.8095309483697[/C][/ROW]
[ROW][C]84[/C][C]800[/C][C]824.307661130152[/C][C]-24.3076611301522[/C][/ROW]
[ROW][C]85[/C][C]930[/C][C]910.668106231707[/C][C]19.3318937682933[/C][/ROW]
[ROW][C]86[/C][C]700[/C][C]833.269193335945[/C][C]-133.269193335945[/C][/ROW]
[ROW][C]87[/C][C]1030[/C][C]963.118604919989[/C][C]66.8813950800114[/C][/ROW]
[ROW][C]88[/C][C]1040[/C][C]1103.39398258851[/C][C]-63.3939825885054[/C][/ROW]
[ROW][C]89[/C][C]1000[/C][C]1099.90949867226[/C][C]-99.9094986722598[/C][/ROW]
[ROW][C]90[/C][C]830[/C][C]850.39208117407[/C][C]-20.3920811740699[/C][/ROW]
[ROW][C]91[/C][C]1190[/C][C]1197.07702002315[/C][C]-7.0770200231525[/C][/ROW]
[ROW][C]92[/C][C]720[/C][C]789.378762258633[/C][C]-69.3787622586328[/C][/ROW]
[ROW][C]93[/C][C]810[/C][C]795.461374977063[/C][C]14.5386250229375[/C][/ROW]
[ROW][C]94[/C][C]870[/C][C]845.310841225467[/C][C]24.6891587745334[/C][/ROW]
[ROW][C]95[/C][C]1190[/C][C]1221.56437833357[/C][C]-31.5643783335695[/C][/ROW]
[ROW][C]96[/C][C]800[/C][C]790.273195426779[/C][C]9.72680457322065[/C][/ROW]
[ROW][C]97[/C][C]970[/C][C]918.935137323916[/C][C]51.0648626760842[/C][/ROW]
[ROW][C]98[/C][C]690[/C][C]699.063197352056[/C][C]-9.06319735205579[/C][/ROW]
[ROW][C]99[/C][C]1010[/C][C]1024.24866666884[/C][C]-14.2486666688446[/C][/ROW]
[ROW][C]100[/C][C]1030[/C][C]1036.55826633795[/C][C]-6.55826633794732[/C][/ROW]
[ROW][C]101[/C][C]950[/C][C]1001.6139558763[/C][C]-51.6139558762997[/C][/ROW]
[ROW][C]102[/C][C]830[/C][C]829.488110664636[/C][C]0.511889335363776[/C][/ROW]
[ROW][C]103[/C][C]1150[/C][C]1189.69573309586[/C][C]-39.6957330958649[/C][/ROW]
[ROW][C]104[/C][C]750[/C][C]721.112793782058[/C][C]28.8872062179419[/C][/ROW]
[ROW][C]105[/C][C]840[/C][C]811.892515512199[/C][C]28.107484487801[/C][/ROW]
[ROW][C]106[/C][C]880[/C][C]872.067050257252[/C][C]7.93294974274818[/C][/ROW]
[ROW][C]107[/C][C]1210[/C][C]1194.31411096024[/C][C]15.6858890397571[/C][/ROW]
[ROW][C]108[/C][C]830[/C][C]804.719229525285[/C][C]25.2807704747149[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296346&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296346&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
13870855.68376068376114.316239316239
14860840.93279186965919.0672081303412
15930917.34491427631712.6550857236834
16980975.4978883212744.50211167872646
1710101007.76776752142.23223247860108
18860858.6604032082621.33959679173756
191140996.170900556282143.829099443718
20880886.59437553045-6.59437553045018
21800929.422621292096-129.422621292096
22900951.363538318142-51.363538318142
23900884.83144797837615.1685520216237
2410001015.57765999756-15.5776599975623
25890894.203996031829-4.20399603182852
26890882.815964365327.1840356346795
27870952.440784137809-82.4407841378087
281000997.0303310451172.96966895488333
2910501026.7613080381623.2386919618421
30790877.790286708094-87.7902867080943
3111601143.7033679599916.2966320400119
32830884.211641365662-54.2116413656622
33730807.663082999909-77.6630829999093
34950905.29567439718944.7043256028106
35980906.46165489117173.5383451088293
369101011.28006672331-101.280066723307
37840894.942792767668-54.9427927676683
38860890.520944226638-30.5209442266377
39880872.6911835330517.308816466949
4010301002.3089559052827.6910440947194
4110601051.999426513848.00057348615792
42770797.00938625867-27.0093862586702
4311401164.01884351561-24.0188435156124
44890835.23386069666454.7661393033355
45740742.739813168593-2.73981316859329
46860959.890081224931-99.8900812249315
471050979.26060282327570.7393971767245
48840918.896272599194-78.8962725991939
49810847.09106914016-37.0910691401597
50830866.353708044818-36.3537080448178
51920883.42399262496436.5760073750363
5210701033.6562302894736.3437697105264
5310401065.05349517609-25.0534951760862
54740774.813900187963-34.8139001879628
5512501143.80516174557106.19483825443
56850896.795954831742-46.7959548317416
57790743.91184417101946.0881558289814
58810872.310377580901-62.3103775809012
5910801054.4345499321425.5654500678563
60760850.376392993717-90.376392993717
61840817.03016810409922.9698318959012
62820840.452881108679-20.4528811086792
63900927.089932535314-27.0899325353139
6410101073.1810035462-63.1810035461972
6510801040.4912424345539.5087575654529
66780744.57313352112835.4268664788716
6711501250.32805503336-100.328055033365
68820846.542641190853-26.5426411908535
69790781.6905356439358.3094643560654
70820805.14415748145614.855842518544
7111301074.0311424324655.9688575675414
72800762.21613671251537.7838632874846
73890843.02465534348546.9753446565152
74810826.984982682249-16.9849826822491
75950907.59055680544242.4094431945581
7610901023.9854025092966.0145974907135
7710901096.08437107122-6.08437107121745
78850794.06993045146855.9300695485322
7912001173.7163788186926.283621181306
80790847.631225957093-57.6312259570926
81800814.493160655967-14.4931606559666
82850843.441552391696.55844760831042
8312301151.1904690516378.8095309483697
84800824.307661130152-24.3076611301522
85930910.66810623170719.3318937682933
86700833.269193335945-133.269193335945
871030963.11860491998966.8813950800114
8810401103.39398258851-63.3939825885054
8910001099.90949867226-99.9094986722598
90830850.39208117407-20.3920811740699
9111901197.07702002315-7.0770200231525
92720789.378762258633-69.3787622586328
93810795.46137497706314.5386250229375
94870845.31084122546724.6891587745334
9511901221.56437833357-31.5643783335695
96800790.2731954267799.72680457322065
97970918.93513732391651.0648626760842
98690699.063197352056-9.06319735205579
9910101024.24866666884-14.2486666688446
10010301036.55826633795-6.55826633794732
1019501001.6139558763-51.6139558762997
102830829.4881106646360.511889335363776
10311501189.69573309586-39.6957330958649
104750721.11279378205828.8872062179419
105840811.89251551219928.107484487801
106880872.0670502572527.93294974274818
10712101194.3141109602415.6858890397571
108830804.71922952528525.2807704747149







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109973.303057922568873.4075897592611073.19852608588
110693.795457394014593.712128429035793.878786358993
1111014.61638300206914.3288753437621114.90389066037
1121035.02406911389934.5154554697071135.53268275807
113958.093374144876857.3461315022151058.84061678754
114838.24158235168737.237606524535939.245558178825
1151160.748009157941059.468630183981262.02738813191
116759.335708586084657.761706952849860.909710219319
117847.891980222702746.003603895947949.780356549457
118887.557093043724785.334075264957989.780110822492
1191216.746027612421114.167605427341319.32444979749
120835.329973826138732.374907300252938.285040352024

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 973.303057922568 & 873.407589759261 & 1073.19852608588 \tabularnewline
110 & 693.795457394014 & 593.712128429035 & 793.878786358993 \tabularnewline
111 & 1014.61638300206 & 914.328875343762 & 1114.90389066037 \tabularnewline
112 & 1035.02406911389 & 934.515455469707 & 1135.53268275807 \tabularnewline
113 & 958.093374144876 & 857.346131502215 & 1058.84061678754 \tabularnewline
114 & 838.24158235168 & 737.237606524535 & 939.245558178825 \tabularnewline
115 & 1160.74800915794 & 1059.46863018398 & 1262.02738813191 \tabularnewline
116 & 759.335708586084 & 657.761706952849 & 860.909710219319 \tabularnewline
117 & 847.891980222702 & 746.003603895947 & 949.780356549457 \tabularnewline
118 & 887.557093043724 & 785.334075264957 & 989.780110822492 \tabularnewline
119 & 1216.74602761242 & 1114.16760542734 & 1319.32444979749 \tabularnewline
120 & 835.329973826138 & 732.374907300252 & 938.285040352024 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296346&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]973.303057922568[/C][C]873.407589759261[/C][C]1073.19852608588[/C][/ROW]
[ROW][C]110[/C][C]693.795457394014[/C][C]593.712128429035[/C][C]793.878786358993[/C][/ROW]
[ROW][C]111[/C][C]1014.61638300206[/C][C]914.328875343762[/C][C]1114.90389066037[/C][/ROW]
[ROW][C]112[/C][C]1035.02406911389[/C][C]934.515455469707[/C][C]1135.53268275807[/C][/ROW]
[ROW][C]113[/C][C]958.093374144876[/C][C]857.346131502215[/C][C]1058.84061678754[/C][/ROW]
[ROW][C]114[/C][C]838.24158235168[/C][C]737.237606524535[/C][C]939.245558178825[/C][/ROW]
[ROW][C]115[/C][C]1160.74800915794[/C][C]1059.46863018398[/C][C]1262.02738813191[/C][/ROW]
[ROW][C]116[/C][C]759.335708586084[/C][C]657.761706952849[/C][C]860.909710219319[/C][/ROW]
[ROW][C]117[/C][C]847.891980222702[/C][C]746.003603895947[/C][C]949.780356549457[/C][/ROW]
[ROW][C]118[/C][C]887.557093043724[/C][C]785.334075264957[/C][C]989.780110822492[/C][/ROW]
[ROW][C]119[/C][C]1216.74602761242[/C][C]1114.16760542734[/C][C]1319.32444979749[/C][/ROW]
[ROW][C]120[/C][C]835.329973826138[/C][C]732.374907300252[/C][C]938.285040352024[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296346&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296346&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
109973.303057922568873.4075897592611073.19852608588
110693.795457394014593.712128429035793.878786358993
1111014.61638300206914.3288753437621114.90389066037
1121035.02406911389934.5154554697071135.53268275807
113958.093374144876857.3461315022151058.84061678754
114838.24158235168737.237606524535939.245558178825
1151160.748009157941059.468630183981262.02738813191
116759.335708586084657.761706952849860.909710219319
117847.891980222702746.003603895947949.780356549457
118887.557093043724785.334075264957989.780110822492
1191216.746027612421114.167605427341319.32444979749
120835.329973826138732.374907300252938.285040352024



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')