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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 09 Aug 2012 03:43:41 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/09/t13444982848z7pr3kfp99f7cf.htm/, Retrieved Wed, 01 May 2024 19:33:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169162, Retrieved Wed, 01 May 2024 19:33:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan der Smissen Britt
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B-Stap 27] [2012-08-09 07:43:41] [b3616d670e39c9c081ac68ec1f5d1a32] [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'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169162&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169162&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169162&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0586850505117233
beta0.0455307064612329
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0586850505117233 \tabularnewline
beta & 0.0455307064612329 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169162&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]0.0586850505117233[/C][/ROW]
[ROW][C]beta[/C][C]0.0455307064612329[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169162&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169162&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
alpha0.0586850505117233
beta0.0455307064612329
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13870855.68376068376114.3162393162395
14860840.93279186965819.0672081303418
15930917.34491427631612.6550857236841
16980975.4978883212734.50211167872737
1710101007.76776752142.23223247860187
18860858.6604032082621.33959679173836
191140996.170900556282143.829099443718
20880886.594375530448-6.59437553044779
21800929.422621292094-129.422621292094
22900951.363538318142-51.3635383181417
23900884.83144797837715.1685520216233
2410001015.57765999756-15.5776599975624
25890894.20399603183-4.20399603182966
26890882.8159643653227.18403563467814
27870952.44078413781-82.4407841378101
281000997.0303310451192.96966895488106
2910501026.7613080381623.2386919618398
30790877.790286708096-87.790286708096
3111601143.7033679599916.2966320400076
32830884.211641365666-54.2116413656661
33730807.663082999912-77.6630829999118
34950905.29567439719244.7043256028077
35980906.46165489117373.5383451088269
369101011.28006672331-101.280066723308
37840894.94279276767-54.9427927676703
38860890.52094422664-30.5209442266404
39880872.6911835330537.30881646694695
4010301002.3089559052827.6910440947174
4110601051.999426513848.0005734861561
42770797.009386258671-27.0093862586708
4311401164.01884351561-24.0188435156138
44890835.23386069666654.7661393033344
45740742.739813168593-2.73981316859283
46860959.890081224932-99.8900812249317
471050979.26060282327870.7393971767222
48840918.896272599194-78.8962725991942
49810847.09106914016-37.0910691401604
50830866.353708044819-36.3537080448189
51920883.42399262496536.5760073750348
5210701033.6562302894736.3437697105251
5310401065.05349517609-25.0534951760876
54740774.813900187964-34.8139001879641
5512501143.80516174557106.194838254428
56850896.795954831742-46.7959548317423
57790743.9118441710246.08815582898
58810872.310377580901-62.3103775809008
5910801054.4345499321425.5654500678552
60760850.376392993717-90.3763929937168
61840817.03016810409922.9698318959006
62820840.452881108679-20.452881108679
63900927.089932535315-27.0899325353146
6410101073.1810035462-63.1810035461986
6510801040.4912424345539.5087575654516
66780744.57313352112935.4268664788709
6711501250.32805503337-100.328055033366
68820846.542641190855-26.5426411908554
69790781.6905356439388.30946435606245
70820805.14415748145814.8558425185421
7111301074.0311424324655.9688575675393
72800762.21613671251537.7838632874846
73890843.02465534348446.9753446565155
74810826.984982682248-16.9849826822477
75950907.59055680544142.4094431945595
7610901023.9854025092866.014597490716
7710901096.08437107121-6.08437107121472
78850794.06993045146655.9300695485343
7912001173.7163788186926.2836211813101
80790847.631225957088-57.6312259570883
81800814.493160655963-14.4931606559635
82850843.4415523916876.55844760831292
8312301151.1904690516378.809530948371
84800824.30766113015-24.3076611301503
85930910.66810623170619.331893768294
86700833.269193335944-133.269193335944
871030963.1186049199966.8813950800104
8810401103.39398258851-63.3939825885066
8910001099.90949867226-99.9094986722614
90830850.392081174073-20.3920811740734
9111901197.07702002316-7.07702002315614
92720789.378762258636-69.3787622586356
93810795.46137497706614.5386250229344
94870845.31084122546924.6891587745309
9511901221.56437833357-31.5643783335724
96800790.2731954267829.72680457321792
97970918.93513732391851.0648626760816
98690699.063197352056-9.06319735205602
9910101024.24866666885-14.248666668846
10010301036.55826633795-6.55826633794823
1019501001.6139558763-51.6139558762993
102830829.4881106646360.511889335363549
10311501189.69573309587-39.6957330958653
104750721.11279378205828.8872062179419
105840811.89251551219928.1074844878008
106880872.0670502572527.93294974274772
10712101194.3141109602415.6858890397571
108830804.71922952528525.2807704747147

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 870 & 855.683760683761 & 14.3162393162395 \tabularnewline
14 & 860 & 840.932791869658 & 19.0672081303418 \tabularnewline
15 & 930 & 917.344914276316 & 12.6550857236841 \tabularnewline
16 & 980 & 975.497888321273 & 4.50211167872737 \tabularnewline
17 & 1010 & 1007.7677675214 & 2.23223247860187 \tabularnewline
18 & 860 & 858.660403208262 & 1.33959679173836 \tabularnewline
19 & 1140 & 996.170900556282 & 143.829099443718 \tabularnewline
20 & 880 & 886.594375530448 & -6.59437553044779 \tabularnewline
21 & 800 & 929.422621292094 & -129.422621292094 \tabularnewline
22 & 900 & 951.363538318142 & -51.3635383181417 \tabularnewline
23 & 900 & 884.831447978377 & 15.1685520216233 \tabularnewline
24 & 1000 & 1015.57765999756 & -15.5776599975624 \tabularnewline
25 & 890 & 894.20399603183 & -4.20399603182966 \tabularnewline
26 & 890 & 882.815964365322 & 7.18403563467814 \tabularnewline
27 & 870 & 952.44078413781 & -82.4407841378101 \tabularnewline
28 & 1000 & 997.030331045119 & 2.96966895488106 \tabularnewline
29 & 1050 & 1026.76130803816 & 23.2386919618398 \tabularnewline
30 & 790 & 877.790286708096 & -87.790286708096 \tabularnewline
31 & 1160 & 1143.70336795999 & 16.2966320400076 \tabularnewline
32 & 830 & 884.211641365666 & -54.2116413656661 \tabularnewline
33 & 730 & 807.663082999912 & -77.6630829999118 \tabularnewline
34 & 950 & 905.295674397192 & 44.7043256028077 \tabularnewline
35 & 980 & 906.461654891173 & 73.5383451088269 \tabularnewline
36 & 910 & 1011.28006672331 & -101.280066723308 \tabularnewline
37 & 840 & 894.94279276767 & -54.9427927676703 \tabularnewline
38 & 860 & 890.52094422664 & -30.5209442266404 \tabularnewline
39 & 880 & 872.691183533053 & 7.30881646694695 \tabularnewline
40 & 1030 & 1002.30895590528 & 27.6910440947174 \tabularnewline
41 & 1060 & 1051.99942651384 & 8.0005734861561 \tabularnewline
42 & 770 & 797.009386258671 & -27.0093862586708 \tabularnewline
43 & 1140 & 1164.01884351561 & -24.0188435156138 \tabularnewline
44 & 890 & 835.233860696666 & 54.7661393033344 \tabularnewline
45 & 740 & 742.739813168593 & -2.73981316859283 \tabularnewline
46 & 860 & 959.890081224932 & -99.8900812249317 \tabularnewline
47 & 1050 & 979.260602823278 & 70.7393971767222 \tabularnewline
48 & 840 & 918.896272599194 & -78.8962725991942 \tabularnewline
49 & 810 & 847.09106914016 & -37.0910691401604 \tabularnewline
50 & 830 & 866.353708044819 & -36.3537080448189 \tabularnewline
51 & 920 & 883.423992624965 & 36.5760073750348 \tabularnewline
52 & 1070 & 1033.65623028947 & 36.3437697105251 \tabularnewline
53 & 1040 & 1065.05349517609 & -25.0534951760876 \tabularnewline
54 & 740 & 774.813900187964 & -34.8139001879641 \tabularnewline
55 & 1250 & 1143.80516174557 & 106.194838254428 \tabularnewline
56 & 850 & 896.795954831742 & -46.7959548317423 \tabularnewline
57 & 790 & 743.91184417102 & 46.08815582898 \tabularnewline
58 & 810 & 872.310377580901 & -62.3103775809008 \tabularnewline
59 & 1080 & 1054.43454993214 & 25.5654500678552 \tabularnewline
60 & 760 & 850.376392993717 & -90.3763929937168 \tabularnewline
61 & 840 & 817.030168104099 & 22.9698318959006 \tabularnewline
62 & 820 & 840.452881108679 & -20.452881108679 \tabularnewline
63 & 900 & 927.089932535315 & -27.0899325353146 \tabularnewline
64 & 1010 & 1073.1810035462 & -63.1810035461986 \tabularnewline
65 & 1080 & 1040.49124243455 & 39.5087575654516 \tabularnewline
66 & 780 & 744.573133521129 & 35.4268664788709 \tabularnewline
67 & 1150 & 1250.32805503337 & -100.328055033366 \tabularnewline
68 & 820 & 846.542641190855 & -26.5426411908554 \tabularnewline
69 & 790 & 781.690535643938 & 8.30946435606245 \tabularnewline
70 & 820 & 805.144157481458 & 14.8558425185421 \tabularnewline
71 & 1130 & 1074.03114243246 & 55.9688575675393 \tabularnewline
72 & 800 & 762.216136712515 & 37.7838632874846 \tabularnewline
73 & 890 & 843.024655343484 & 46.9753446565155 \tabularnewline
74 & 810 & 826.984982682248 & -16.9849826822477 \tabularnewline
75 & 950 & 907.590556805441 & 42.4094431945595 \tabularnewline
76 & 1090 & 1023.98540250928 & 66.014597490716 \tabularnewline
77 & 1090 & 1096.08437107121 & -6.08437107121472 \tabularnewline
78 & 850 & 794.069930451466 & 55.9300695485343 \tabularnewline
79 & 1200 & 1173.71637881869 & 26.2836211813101 \tabularnewline
80 & 790 & 847.631225957088 & -57.6312259570883 \tabularnewline
81 & 800 & 814.493160655963 & -14.4931606559635 \tabularnewline
82 & 850 & 843.441552391687 & 6.55844760831292 \tabularnewline
83 & 1230 & 1151.19046905163 & 78.809530948371 \tabularnewline
84 & 800 & 824.30766113015 & -24.3076611301503 \tabularnewline
85 & 930 & 910.668106231706 & 19.331893768294 \tabularnewline
86 & 700 & 833.269193335944 & -133.269193335944 \tabularnewline
87 & 1030 & 963.11860491999 & 66.8813950800104 \tabularnewline
88 & 1040 & 1103.39398258851 & -63.3939825885066 \tabularnewline
89 & 1000 & 1099.90949867226 & -99.9094986722614 \tabularnewline
90 & 830 & 850.392081174073 & -20.3920811740734 \tabularnewline
91 & 1190 & 1197.07702002316 & -7.07702002315614 \tabularnewline
92 & 720 & 789.378762258636 & -69.3787622586356 \tabularnewline
93 & 810 & 795.461374977066 & 14.5386250229344 \tabularnewline
94 & 870 & 845.310841225469 & 24.6891587745309 \tabularnewline
95 & 1190 & 1221.56437833357 & -31.5643783335724 \tabularnewline
96 & 800 & 790.273195426782 & 9.72680457321792 \tabularnewline
97 & 970 & 918.935137323918 & 51.0648626760816 \tabularnewline
98 & 690 & 699.063197352056 & -9.06319735205602 \tabularnewline
99 & 1010 & 1024.24866666885 & -14.248666668846 \tabularnewline
100 & 1030 & 1036.55826633795 & -6.55826633794823 \tabularnewline
101 & 950 & 1001.6139558763 & -51.6139558762993 \tabularnewline
102 & 830 & 829.488110664636 & 0.511889335363549 \tabularnewline
103 & 1150 & 1189.69573309587 & -39.6957330958653 \tabularnewline
104 & 750 & 721.112793782058 & 28.8872062179419 \tabularnewline
105 & 840 & 811.892515512199 & 28.1074844878008 \tabularnewline
106 & 880 & 872.067050257252 & 7.93294974274772 \tabularnewline
107 & 1210 & 1194.31411096024 & 15.6858890397571 \tabularnewline
108 & 830 & 804.719229525285 & 25.2807704747147 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169162&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]14.3162393162395[/C][/ROW]
[ROW][C]14[/C][C]860[/C][C]840.932791869658[/C][C]19.0672081303418[/C][/ROW]
[ROW][C]15[/C][C]930[/C][C]917.344914276316[/C][C]12.6550857236841[/C][/ROW]
[ROW][C]16[/C][C]980[/C][C]975.497888321273[/C][C]4.50211167872737[/C][/ROW]
[ROW][C]17[/C][C]1010[/C][C]1007.7677675214[/C][C]2.23223247860187[/C][/ROW]
[ROW][C]18[/C][C]860[/C][C]858.660403208262[/C][C]1.33959679173836[/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]886.594375530448[/C][C]-6.59437553044779[/C][/ROW]
[ROW][C]21[/C][C]800[/C][C]929.422621292094[/C][C]-129.422621292094[/C][/ROW]
[ROW][C]22[/C][C]900[/C][C]951.363538318142[/C][C]-51.3635383181417[/C][/ROW]
[ROW][C]23[/C][C]900[/C][C]884.831447978377[/C][C]15.1685520216233[/C][/ROW]
[ROW][C]24[/C][C]1000[/C][C]1015.57765999756[/C][C]-15.5776599975624[/C][/ROW]
[ROW][C]25[/C][C]890[/C][C]894.20399603183[/C][C]-4.20399603182966[/C][/ROW]
[ROW][C]26[/C][C]890[/C][C]882.815964365322[/C][C]7.18403563467814[/C][/ROW]
[ROW][C]27[/C][C]870[/C][C]952.44078413781[/C][C]-82.4407841378101[/C][/ROW]
[ROW][C]28[/C][C]1000[/C][C]997.030331045119[/C][C]2.96966895488106[/C][/ROW]
[ROW][C]29[/C][C]1050[/C][C]1026.76130803816[/C][C]23.2386919618398[/C][/ROW]
[ROW][C]30[/C][C]790[/C][C]877.790286708096[/C][C]-87.790286708096[/C][/ROW]
[ROW][C]31[/C][C]1160[/C][C]1143.70336795999[/C][C]16.2966320400076[/C][/ROW]
[ROW][C]32[/C][C]830[/C][C]884.211641365666[/C][C]-54.2116413656661[/C][/ROW]
[ROW][C]33[/C][C]730[/C][C]807.663082999912[/C][C]-77.6630829999118[/C][/ROW]
[ROW][C]34[/C][C]950[/C][C]905.295674397192[/C][C]44.7043256028077[/C][/ROW]
[ROW][C]35[/C][C]980[/C][C]906.461654891173[/C][C]73.5383451088269[/C][/ROW]
[ROW][C]36[/C][C]910[/C][C]1011.28006672331[/C][C]-101.280066723308[/C][/ROW]
[ROW][C]37[/C][C]840[/C][C]894.94279276767[/C][C]-54.9427927676703[/C][/ROW]
[ROW][C]38[/C][C]860[/C][C]890.52094422664[/C][C]-30.5209442266404[/C][/ROW]
[ROW][C]39[/C][C]880[/C][C]872.691183533053[/C][C]7.30881646694695[/C][/ROW]
[ROW][C]40[/C][C]1030[/C][C]1002.30895590528[/C][C]27.6910440947174[/C][/ROW]
[ROW][C]41[/C][C]1060[/C][C]1051.99942651384[/C][C]8.0005734861561[/C][/ROW]
[ROW][C]42[/C][C]770[/C][C]797.009386258671[/C][C]-27.0093862586708[/C][/ROW]
[ROW][C]43[/C][C]1140[/C][C]1164.01884351561[/C][C]-24.0188435156138[/C][/ROW]
[ROW][C]44[/C][C]890[/C][C]835.233860696666[/C][C]54.7661393033344[/C][/ROW]
[ROW][C]45[/C][C]740[/C][C]742.739813168593[/C][C]-2.73981316859283[/C][/ROW]
[ROW][C]46[/C][C]860[/C][C]959.890081224932[/C][C]-99.8900812249317[/C][/ROW]
[ROW][C]47[/C][C]1050[/C][C]979.260602823278[/C][C]70.7393971767222[/C][/ROW]
[ROW][C]48[/C][C]840[/C][C]918.896272599194[/C][C]-78.8962725991942[/C][/ROW]
[ROW][C]49[/C][C]810[/C][C]847.09106914016[/C][C]-37.0910691401604[/C][/ROW]
[ROW][C]50[/C][C]830[/C][C]866.353708044819[/C][C]-36.3537080448189[/C][/ROW]
[ROW][C]51[/C][C]920[/C][C]883.423992624965[/C][C]36.5760073750348[/C][/ROW]
[ROW][C]52[/C][C]1070[/C][C]1033.65623028947[/C][C]36.3437697105251[/C][/ROW]
[ROW][C]53[/C][C]1040[/C][C]1065.05349517609[/C][C]-25.0534951760876[/C][/ROW]
[ROW][C]54[/C][C]740[/C][C]774.813900187964[/C][C]-34.8139001879641[/C][/ROW]
[ROW][C]55[/C][C]1250[/C][C]1143.80516174557[/C][C]106.194838254428[/C][/ROW]
[ROW][C]56[/C][C]850[/C][C]896.795954831742[/C][C]-46.7959548317423[/C][/ROW]
[ROW][C]57[/C][C]790[/C][C]743.91184417102[/C][C]46.08815582898[/C][/ROW]
[ROW][C]58[/C][C]810[/C][C]872.310377580901[/C][C]-62.3103775809008[/C][/ROW]
[ROW][C]59[/C][C]1080[/C][C]1054.43454993214[/C][C]25.5654500678552[/C][/ROW]
[ROW][C]60[/C][C]760[/C][C]850.376392993717[/C][C]-90.3763929937168[/C][/ROW]
[ROW][C]61[/C][C]840[/C][C]817.030168104099[/C][C]22.9698318959006[/C][/ROW]
[ROW][C]62[/C][C]820[/C][C]840.452881108679[/C][C]-20.452881108679[/C][/ROW]
[ROW][C]63[/C][C]900[/C][C]927.089932535315[/C][C]-27.0899325353146[/C][/ROW]
[ROW][C]64[/C][C]1010[/C][C]1073.1810035462[/C][C]-63.1810035461986[/C][/ROW]
[ROW][C]65[/C][C]1080[/C][C]1040.49124243455[/C][C]39.5087575654516[/C][/ROW]
[ROW][C]66[/C][C]780[/C][C]744.573133521129[/C][C]35.4268664788709[/C][/ROW]
[ROW][C]67[/C][C]1150[/C][C]1250.32805503337[/C][C]-100.328055033366[/C][/ROW]
[ROW][C]68[/C][C]820[/C][C]846.542641190855[/C][C]-26.5426411908554[/C][/ROW]
[ROW][C]69[/C][C]790[/C][C]781.690535643938[/C][C]8.30946435606245[/C][/ROW]
[ROW][C]70[/C][C]820[/C][C]805.144157481458[/C][C]14.8558425185421[/C][/ROW]
[ROW][C]71[/C][C]1130[/C][C]1074.03114243246[/C][C]55.9688575675393[/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]843.024655343484[/C][C]46.9753446565155[/C][/ROW]
[ROW][C]74[/C][C]810[/C][C]826.984982682248[/C][C]-16.9849826822477[/C][/ROW]
[ROW][C]75[/C][C]950[/C][C]907.590556805441[/C][C]42.4094431945595[/C][/ROW]
[ROW][C]76[/C][C]1090[/C][C]1023.98540250928[/C][C]66.014597490716[/C][/ROW]
[ROW][C]77[/C][C]1090[/C][C]1096.08437107121[/C][C]-6.08437107121472[/C][/ROW]
[ROW][C]78[/C][C]850[/C][C]794.069930451466[/C][C]55.9300695485343[/C][/ROW]
[ROW][C]79[/C][C]1200[/C][C]1173.71637881869[/C][C]26.2836211813101[/C][/ROW]
[ROW][C]80[/C][C]790[/C][C]847.631225957088[/C][C]-57.6312259570883[/C][/ROW]
[ROW][C]81[/C][C]800[/C][C]814.493160655963[/C][C]-14.4931606559635[/C][/ROW]
[ROW][C]82[/C][C]850[/C][C]843.441552391687[/C][C]6.55844760831292[/C][/ROW]
[ROW][C]83[/C][C]1230[/C][C]1151.19046905163[/C][C]78.809530948371[/C][/ROW]
[ROW][C]84[/C][C]800[/C][C]824.30766113015[/C][C]-24.3076611301503[/C][/ROW]
[ROW][C]85[/C][C]930[/C][C]910.668106231706[/C][C]19.331893768294[/C][/ROW]
[ROW][C]86[/C][C]700[/C][C]833.269193335944[/C][C]-133.269193335944[/C][/ROW]
[ROW][C]87[/C][C]1030[/C][C]963.11860491999[/C][C]66.8813950800104[/C][/ROW]
[ROW][C]88[/C][C]1040[/C][C]1103.39398258851[/C][C]-63.3939825885066[/C][/ROW]
[ROW][C]89[/C][C]1000[/C][C]1099.90949867226[/C][C]-99.9094986722614[/C][/ROW]
[ROW][C]90[/C][C]830[/C][C]850.392081174073[/C][C]-20.3920811740734[/C][/ROW]
[ROW][C]91[/C][C]1190[/C][C]1197.07702002316[/C][C]-7.07702002315614[/C][/ROW]
[ROW][C]92[/C][C]720[/C][C]789.378762258636[/C][C]-69.3787622586356[/C][/ROW]
[ROW][C]93[/C][C]810[/C][C]795.461374977066[/C][C]14.5386250229344[/C][/ROW]
[ROW][C]94[/C][C]870[/C][C]845.310841225469[/C][C]24.6891587745309[/C][/ROW]
[ROW][C]95[/C][C]1190[/C][C]1221.56437833357[/C][C]-31.5643783335724[/C][/ROW]
[ROW][C]96[/C][C]800[/C][C]790.273195426782[/C][C]9.72680457321792[/C][/ROW]
[ROW][C]97[/C][C]970[/C][C]918.935137323918[/C][C]51.0648626760816[/C][/ROW]
[ROW][C]98[/C][C]690[/C][C]699.063197352056[/C][C]-9.06319735205602[/C][/ROW]
[ROW][C]99[/C][C]1010[/C][C]1024.24866666885[/C][C]-14.248666668846[/C][/ROW]
[ROW][C]100[/C][C]1030[/C][C]1036.55826633795[/C][C]-6.55826633794823[/C][/ROW]
[ROW][C]101[/C][C]950[/C][C]1001.6139558763[/C][C]-51.6139558762993[/C][/ROW]
[ROW][C]102[/C][C]830[/C][C]829.488110664636[/C][C]0.511889335363549[/C][/ROW]
[ROW][C]103[/C][C]1150[/C][C]1189.69573309587[/C][C]-39.6957330958653[/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]28.1074844878008[/C][/ROW]
[ROW][C]106[/C][C]880[/C][C]872.067050257252[/C][C]7.93294974274772[/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]25.2807704747147[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169162&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169162&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
13870855.68376068376114.3162393162395
14860840.93279186965819.0672081303418
15930917.34491427631612.6550857236841
16980975.4978883212734.50211167872737
1710101007.76776752142.23223247860187
18860858.6604032082621.33959679173836
191140996.170900556282143.829099443718
20880886.594375530448-6.59437553044779
21800929.422621292094-129.422621292094
22900951.363538318142-51.3635383181417
23900884.83144797837715.1685520216233
2410001015.57765999756-15.5776599975624
25890894.20399603183-4.20399603182966
26890882.8159643653227.18403563467814
27870952.44078413781-82.4407841378101
281000997.0303310451192.96966895488106
2910501026.7613080381623.2386919618398
30790877.790286708096-87.790286708096
3111601143.7033679599916.2966320400076
32830884.211641365666-54.2116413656661
33730807.663082999912-77.6630829999118
34950905.29567439719244.7043256028077
35980906.46165489117373.5383451088269
369101011.28006672331-101.280066723308
37840894.94279276767-54.9427927676703
38860890.52094422664-30.5209442266404
39880872.6911835330537.30881646694695
4010301002.3089559052827.6910440947174
4110601051.999426513848.0005734861561
42770797.009386258671-27.0093862586708
4311401164.01884351561-24.0188435156138
44890835.23386069666654.7661393033344
45740742.739813168593-2.73981316859283
46860959.890081224932-99.8900812249317
471050979.26060282327870.7393971767222
48840918.896272599194-78.8962725991942
49810847.09106914016-37.0910691401604
50830866.353708044819-36.3537080448189
51920883.42399262496536.5760073750348
5210701033.6562302894736.3437697105251
5310401065.05349517609-25.0534951760876
54740774.813900187964-34.8139001879641
5512501143.80516174557106.194838254428
56850896.795954831742-46.7959548317423
57790743.9118441710246.08815582898
58810872.310377580901-62.3103775809008
5910801054.4345499321425.5654500678552
60760850.376392993717-90.3763929937168
61840817.03016810409922.9698318959006
62820840.452881108679-20.452881108679
63900927.089932535315-27.0899325353146
6410101073.1810035462-63.1810035461986
6510801040.4912424345539.5087575654516
66780744.57313352112935.4268664788709
6711501250.32805503337-100.328055033366
68820846.542641190855-26.5426411908554
69790781.6905356439388.30946435606245
70820805.14415748145814.8558425185421
7111301074.0311424324655.9688575675393
72800762.21613671251537.7838632874846
73890843.02465534348446.9753446565155
74810826.984982682248-16.9849826822477
75950907.59055680544142.4094431945595
7610901023.9854025092866.014597490716
7710901096.08437107121-6.08437107121472
78850794.06993045146655.9300695485343
7912001173.7163788186926.2836211813101
80790847.631225957088-57.6312259570883
81800814.493160655963-14.4931606559635
82850843.4415523916876.55844760831292
8312301151.1904690516378.809530948371
84800824.30766113015-24.3076611301503
85930910.66810623170619.331893768294
86700833.269193335944-133.269193335944
871030963.1186049199966.8813950800104
8810401103.39398258851-63.3939825885066
8910001099.90949867226-99.9094986722614
90830850.392081174073-20.3920811740734
9111901197.07702002316-7.07702002315614
92720789.378762258636-69.3787622586356
93810795.46137497706614.5386250229344
94870845.31084122546924.6891587745309
9511901221.56437833357-31.5643783335724
96800790.2731954267829.72680457321792
97970918.93513732391851.0648626760816
98690699.063197352056-9.06319735205602
9910101024.24866666885-14.248666668846
10010301036.55826633795-6.55826633794823
1019501001.6139558763-51.6139558762993
102830829.4881106646360.511889335363549
10311501189.69573309587-39.6957330958653
104750721.11279378205828.8872062179419
105840811.89251551219928.1074844878008
106880872.0670502572527.93294974274772
10712101194.3141109602415.6858890397571
108830804.71922952528525.2807704747147







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109973.303057922568873.4075897592611073.19852608588
110693.795457394015593.712128429036793.878786358994
1111014.61638300206914.3288753437621114.90389066037
1121035.02406911389934.5154554697071135.53268275807
113958.093374144876857.3461315022141058.84061678754
114838.241582351679737.237606524534939.245558178824
1151160.748009157941059.468630183981262.02738813191
116759.335708586083657.761706952849860.909710219318
117847.891980222701746.003603895947949.780356549456
118887.557093043724785.334075264957989.780110822491
1191216.746027612421114.167605427341319.32444979749
120835.329973826138732.374907300253938.285040352023

\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 & 693.795457394015 & 593.712128429036 & 793.878786358994 \tabularnewline
111 & 1014.61638300206 & 914.328875343762 & 1114.90389066037 \tabularnewline
112 & 1035.02406911389 & 934.515455469707 & 1135.53268275807 \tabularnewline
113 & 958.093374144876 & 857.346131502214 & 1058.84061678754 \tabularnewline
114 & 838.241582351679 & 737.237606524534 & 939.245558178824 \tabularnewline
115 & 1160.74800915794 & 1059.46863018398 & 1262.02738813191 \tabularnewline
116 & 759.335708586083 & 657.761706952849 & 860.909710219318 \tabularnewline
117 & 847.891980222701 & 746.003603895947 & 949.780356549456 \tabularnewline
118 & 887.557093043724 & 785.334075264957 & 989.780110822491 \tabularnewline
119 & 1216.74602761242 & 1114.16760542734 & 1319.32444979749 \tabularnewline
120 & 835.329973826138 & 732.374907300253 & 938.285040352023 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169162&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]693.795457394015[/C][C]593.712128429036[/C][C]793.878786358994[/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]857.346131502214[/C][C]1058.84061678754[/C][/ROW]
[ROW][C]114[/C][C]838.241582351679[/C][C]737.237606524534[/C][C]939.245558178824[/C][/ROW]
[ROW][C]115[/C][C]1160.74800915794[/C][C]1059.46863018398[/C][C]1262.02738813191[/C][/ROW]
[ROW][C]116[/C][C]759.335708586083[/C][C]657.761706952849[/C][C]860.909710219318[/C][/ROW]
[ROW][C]117[/C][C]847.891980222701[/C][C]746.003603895947[/C][C]949.780356549456[/C][/ROW]
[ROW][C]118[/C][C]887.557093043724[/C][C]785.334075264957[/C][C]989.780110822491[/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]732.374907300253[/C][C]938.285040352023[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169162&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169162&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
110693.795457394015593.712128429036793.878786358994
1111014.61638300206914.3288753437621114.90389066037
1121035.02406911389934.5154554697071135.53268275807
113958.093374144876857.3461315022141058.84061678754
114838.241582351679737.237606524534939.245558178824
1151160.748009157941059.468630183981262.02738813191
116759.335708586083657.761706952849860.909710219318
117847.891980222701746.003603895947949.780356549456
118887.557093043724785.334075264957989.780110822491
1191216.746027612421114.167605427341319.32444979749
120835.329973826138732.374907300253938.285040352023



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')