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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 18 Aug 2014 00:05:53 +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/18/t14083167606d2mr5n4quajifz.htm/, Retrieved Thu, 16 May 2024 19:38:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235658, Retrieved Thu, 16 May 2024 19:38:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-08-17 23:05:53] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
740
730
740
820
820
850
870
930
890
790
840
880
730
730
770
880
820
900
940
1080
920
710
880
910
680
740
740
810
800
900
920
1030
910
720
930
900
680
770
770
810
810
910
820
980
830
760
930
910
640
780
690
820
800
910
850
980
830
820
1010
930
630
760
670
850
780
900
840
1050
810
860
1020
820
670
780
690
800
810
910
870
1010
810
960
990
780
700
810
760
810
840
900
920
1050
860
870
880
860
650
830
730
810
840
940
870
940
770
870
860
760




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=235658&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=235658&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235658&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
alpha0.154810139601681
beta0.0450854079408801
gamma0.814530331866268

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.154810139601681 \tabularnewline
beta & 0.0450854079408801 \tabularnewline
gamma & 0.814530331866268 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235658&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]0.154810139601681[/C][/ROW]
[ROW][C]beta[/C][C]0.0450854079408801[/C][/ROW]
[ROW][C]gamma[/C][C]0.814530331866268[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235658&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235658&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
alpha0.154810139601681
beta0.0450854079408801
gamma0.814530331866268







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13730715.3979700854714.6020299145298
14730711.9431221539918.0568778460098
15770750.81581757817119.1841824218291
16880869.58026393614310.4197360638572
17820816.6439448689083.35605513109215
18900898.05418722221.94581277780048
19940902.17635757378837.8236424262118
201080972.533443264688107.466556735312
21920952.755373569114-32.7553735691142
22710848.540905297874-138.540905297874
23880878.2327931418671.76720685813302
24910920.074800618001-10.0748006180011
25680777.14907574061-97.14907574061
26740758.224548759885-18.2245487598852
27740791.455446861209-51.4554468612085
28810891.956250286481-81.9562502864809
29800817.91738781292-17.9173878129197
30900892.9760120662087.02398793379189
31920920.531836998528-0.531836998527524
3210301030.57588924859-0.575889248593057
33910894.46459770256915.5354022974315
34720722.163075078066-2.16307507806607
35930867.77548191197362.2245180880273
36900909.461585365359-9.46158536535904
37680705.327404685836-25.3274046858359
38770750.99852143565819.0014785643421
39770766.517661728293.48233827170952
40810854.31160177104-44.3116017710397
41810830.235675334095-20.2356753340954
42910922.138395636318-12.1383956363183
43820941.424794360245-121.424794360245
449801031.77805265213-51.7780526521267
45830897.529302261544-67.5293022615438
46760698.30215830785261.6978416921484
47930896.6909899518233.3090100481803
48910882.91137308900227.0886269109982
49640672.129851363294-32.1298513632942
50780745.83472327305834.1652767269425
51690751.692713514506-61.6927135145058
52820794.71430400098525.2856959990149
53800796.6934928035723.30650719642824
54910896.68562223118213.3143777688182
55850843.7240893239576.27591067604317
569801001.73318124488-21.7331812448797
57830861.44107842925-31.4410784292497
58820757.16591663104162.8340833689585
591010936.59573593906373.4042640609366
60930925.4296954309844.57030456901612
61630670.925737081431-40.9257370814312
62760789.378832885204-29.3788328852045
63670719.434427763739-49.4344277637393
64850824.34473169439925.6552683056012
65780811.36473801266-31.3647380126602
66900912.7519570958-12.7519570958001
67840850.600448999351-10.6004489993512
681050986.28761001572863.7123899842724
69810852.709573626-42.7095736260004
70860811.68285576375548.317144236245
711020996.13165075162323.8683492483767
72820929.553135889898-109.553135889898
73670624.90794202448445.0920579755164
74780764.07430510488315.9256948951171
75690687.1003554852732.89964451472724
76800851.935771582786-51.9357715827859
77810787.27695547162522.7230445283753
78910909.8161741150250.183825884974794
79870851.20372661713918.7962733828613
8010101042.86167367334-32.8616736733416
81810820.655050317626-10.6550503176255
82960847.066629450968112.933370549032
839901024.9484756523-34.9484756522966
84780857.263429848199-77.2634298481987
85700664.15583550073235.8441644992677
86810781.8229085164228.1770914835799
87760697.87500803670162.1249919632992
88810834.638953271313-24.6389532713127
89840826.30440320170413.6955967982957
90900932.56720147713-32.5672014771296
91920882.10724712127437.8927528787257
9210501041.701051480188.29894851982249
93860841.98411770581118.0158822941889
94870958.946522165345-88.946522165345
958801003.38950157207-123.389501572071
96860791.88549454214768.1145054578529
97650699.16915299448-49.1691529944802
98830797.8219714918632.1780285081395
99730737.317162703882-7.31716270388176
100810802.5677892329237.43221076707744
101840824.78096248647515.2190375135247
102940898.63343241035141.3665675896485
103870907.844805456141-37.8448054561411
1049401034.53038732573-94.5303873257296
105770824.056234157717-54.0562341577174
106870854.19402756973215.8059724302677
107860889.842526573714-29.8425265737138
108760824.011550314936-64.0115503149364

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 730 & 715.39797008547 & 14.6020299145298 \tabularnewline
14 & 730 & 711.94312215399 & 18.0568778460098 \tabularnewline
15 & 770 & 750.815817578171 & 19.1841824218291 \tabularnewline
16 & 880 & 869.580263936143 & 10.4197360638572 \tabularnewline
17 & 820 & 816.643944868908 & 3.35605513109215 \tabularnewline
18 & 900 & 898.0541872222 & 1.94581277780048 \tabularnewline
19 & 940 & 902.176357573788 & 37.8236424262118 \tabularnewline
20 & 1080 & 972.533443264688 & 107.466556735312 \tabularnewline
21 & 920 & 952.755373569114 & -32.7553735691142 \tabularnewline
22 & 710 & 848.540905297874 & -138.540905297874 \tabularnewline
23 & 880 & 878.232793141867 & 1.76720685813302 \tabularnewline
24 & 910 & 920.074800618001 & -10.0748006180011 \tabularnewline
25 & 680 & 777.14907574061 & -97.14907574061 \tabularnewline
26 & 740 & 758.224548759885 & -18.2245487598852 \tabularnewline
27 & 740 & 791.455446861209 & -51.4554468612085 \tabularnewline
28 & 810 & 891.956250286481 & -81.9562502864809 \tabularnewline
29 & 800 & 817.91738781292 & -17.9173878129197 \tabularnewline
30 & 900 & 892.976012066208 & 7.02398793379189 \tabularnewline
31 & 920 & 920.531836998528 & -0.531836998527524 \tabularnewline
32 & 1030 & 1030.57588924859 & -0.575889248593057 \tabularnewline
33 & 910 & 894.464597702569 & 15.5354022974315 \tabularnewline
34 & 720 & 722.163075078066 & -2.16307507806607 \tabularnewline
35 & 930 & 867.775481911973 & 62.2245180880273 \tabularnewline
36 & 900 & 909.461585365359 & -9.46158536535904 \tabularnewline
37 & 680 & 705.327404685836 & -25.3274046858359 \tabularnewline
38 & 770 & 750.998521435658 & 19.0014785643421 \tabularnewline
39 & 770 & 766.51766172829 & 3.48233827170952 \tabularnewline
40 & 810 & 854.31160177104 & -44.3116017710397 \tabularnewline
41 & 810 & 830.235675334095 & -20.2356753340954 \tabularnewline
42 & 910 & 922.138395636318 & -12.1383956363183 \tabularnewline
43 & 820 & 941.424794360245 & -121.424794360245 \tabularnewline
44 & 980 & 1031.77805265213 & -51.7780526521267 \tabularnewline
45 & 830 & 897.529302261544 & -67.5293022615438 \tabularnewline
46 & 760 & 698.302158307852 & 61.6978416921484 \tabularnewline
47 & 930 & 896.69098995182 & 33.3090100481803 \tabularnewline
48 & 910 & 882.911373089002 & 27.0886269109982 \tabularnewline
49 & 640 & 672.129851363294 & -32.1298513632942 \tabularnewline
50 & 780 & 745.834723273058 & 34.1652767269425 \tabularnewline
51 & 690 & 751.692713514506 & -61.6927135145058 \tabularnewline
52 & 820 & 794.714304000985 & 25.2856959990149 \tabularnewline
53 & 800 & 796.693492803572 & 3.30650719642824 \tabularnewline
54 & 910 & 896.685622231182 & 13.3143777688182 \tabularnewline
55 & 850 & 843.724089323957 & 6.27591067604317 \tabularnewline
56 & 980 & 1001.73318124488 & -21.7331812448797 \tabularnewline
57 & 830 & 861.44107842925 & -31.4410784292497 \tabularnewline
58 & 820 & 757.165916631041 & 62.8340833689585 \tabularnewline
59 & 1010 & 936.595735939063 & 73.4042640609366 \tabularnewline
60 & 930 & 925.429695430984 & 4.57030456901612 \tabularnewline
61 & 630 & 670.925737081431 & -40.9257370814312 \tabularnewline
62 & 760 & 789.378832885204 & -29.3788328852045 \tabularnewline
63 & 670 & 719.434427763739 & -49.4344277637393 \tabularnewline
64 & 850 & 824.344731694399 & 25.6552683056012 \tabularnewline
65 & 780 & 811.36473801266 & -31.3647380126602 \tabularnewline
66 & 900 & 912.7519570958 & -12.7519570958001 \tabularnewline
67 & 840 & 850.600448999351 & -10.6004489993512 \tabularnewline
68 & 1050 & 986.287610015728 & 63.7123899842724 \tabularnewline
69 & 810 & 852.709573626 & -42.7095736260004 \tabularnewline
70 & 860 & 811.682855763755 & 48.317144236245 \tabularnewline
71 & 1020 & 996.131650751623 & 23.8683492483767 \tabularnewline
72 & 820 & 929.553135889898 & -109.553135889898 \tabularnewline
73 & 670 & 624.907942024484 & 45.0920579755164 \tabularnewline
74 & 780 & 764.074305104883 & 15.9256948951171 \tabularnewline
75 & 690 & 687.100355485273 & 2.89964451472724 \tabularnewline
76 & 800 & 851.935771582786 & -51.9357715827859 \tabularnewline
77 & 810 & 787.276955471625 & 22.7230445283753 \tabularnewline
78 & 910 & 909.816174115025 & 0.183825884974794 \tabularnewline
79 & 870 & 851.203726617139 & 18.7962733828613 \tabularnewline
80 & 1010 & 1042.86167367334 & -32.8616736733416 \tabularnewline
81 & 810 & 820.655050317626 & -10.6550503176255 \tabularnewline
82 & 960 & 847.066629450968 & 112.933370549032 \tabularnewline
83 & 990 & 1024.9484756523 & -34.9484756522966 \tabularnewline
84 & 780 & 857.263429848199 & -77.2634298481987 \tabularnewline
85 & 700 & 664.155835500732 & 35.8441644992677 \tabularnewline
86 & 810 & 781.82290851642 & 28.1770914835799 \tabularnewline
87 & 760 & 697.875008036701 & 62.1249919632992 \tabularnewline
88 & 810 & 834.638953271313 & -24.6389532713127 \tabularnewline
89 & 840 & 826.304403201704 & 13.6955967982957 \tabularnewline
90 & 900 & 932.56720147713 & -32.5672014771296 \tabularnewline
91 & 920 & 882.107247121274 & 37.8927528787257 \tabularnewline
92 & 1050 & 1041.70105148018 & 8.29894851982249 \tabularnewline
93 & 860 & 841.984117705811 & 18.0158822941889 \tabularnewline
94 & 870 & 958.946522165345 & -88.946522165345 \tabularnewline
95 & 880 & 1003.38950157207 & -123.389501572071 \tabularnewline
96 & 860 & 791.885494542147 & 68.1145054578529 \tabularnewline
97 & 650 & 699.16915299448 & -49.1691529944802 \tabularnewline
98 & 830 & 797.82197149186 & 32.1780285081395 \tabularnewline
99 & 730 & 737.317162703882 & -7.31716270388176 \tabularnewline
100 & 810 & 802.567789232923 & 7.43221076707744 \tabularnewline
101 & 840 & 824.780962486475 & 15.2190375135247 \tabularnewline
102 & 940 & 898.633432410351 & 41.3665675896485 \tabularnewline
103 & 870 & 907.844805456141 & -37.8448054561411 \tabularnewline
104 & 940 & 1034.53038732573 & -94.5303873257296 \tabularnewline
105 & 770 & 824.056234157717 & -54.0562341577174 \tabularnewline
106 & 870 & 854.194027569732 & 15.8059724302677 \tabularnewline
107 & 860 & 889.842526573714 & -29.8425265737138 \tabularnewline
108 & 760 & 824.011550314936 & -64.0115503149364 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235658&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]730[/C][C]715.39797008547[/C][C]14.6020299145298[/C][/ROW]
[ROW][C]14[/C][C]730[/C][C]711.94312215399[/C][C]18.0568778460098[/C][/ROW]
[ROW][C]15[/C][C]770[/C][C]750.815817578171[/C][C]19.1841824218291[/C][/ROW]
[ROW][C]16[/C][C]880[/C][C]869.580263936143[/C][C]10.4197360638572[/C][/ROW]
[ROW][C]17[/C][C]820[/C][C]816.643944868908[/C][C]3.35605513109215[/C][/ROW]
[ROW][C]18[/C][C]900[/C][C]898.0541872222[/C][C]1.94581277780048[/C][/ROW]
[ROW][C]19[/C][C]940[/C][C]902.176357573788[/C][C]37.8236424262118[/C][/ROW]
[ROW][C]20[/C][C]1080[/C][C]972.533443264688[/C][C]107.466556735312[/C][/ROW]
[ROW][C]21[/C][C]920[/C][C]952.755373569114[/C][C]-32.7553735691142[/C][/ROW]
[ROW][C]22[/C][C]710[/C][C]848.540905297874[/C][C]-138.540905297874[/C][/ROW]
[ROW][C]23[/C][C]880[/C][C]878.232793141867[/C][C]1.76720685813302[/C][/ROW]
[ROW][C]24[/C][C]910[/C][C]920.074800618001[/C][C]-10.0748006180011[/C][/ROW]
[ROW][C]25[/C][C]680[/C][C]777.14907574061[/C][C]-97.14907574061[/C][/ROW]
[ROW][C]26[/C][C]740[/C][C]758.224548759885[/C][C]-18.2245487598852[/C][/ROW]
[ROW][C]27[/C][C]740[/C][C]791.455446861209[/C][C]-51.4554468612085[/C][/ROW]
[ROW][C]28[/C][C]810[/C][C]891.956250286481[/C][C]-81.9562502864809[/C][/ROW]
[ROW][C]29[/C][C]800[/C][C]817.91738781292[/C][C]-17.9173878129197[/C][/ROW]
[ROW][C]30[/C][C]900[/C][C]892.976012066208[/C][C]7.02398793379189[/C][/ROW]
[ROW][C]31[/C][C]920[/C][C]920.531836998528[/C][C]-0.531836998527524[/C][/ROW]
[ROW][C]32[/C][C]1030[/C][C]1030.57588924859[/C][C]-0.575889248593057[/C][/ROW]
[ROW][C]33[/C][C]910[/C][C]894.464597702569[/C][C]15.5354022974315[/C][/ROW]
[ROW][C]34[/C][C]720[/C][C]722.163075078066[/C][C]-2.16307507806607[/C][/ROW]
[ROW][C]35[/C][C]930[/C][C]867.775481911973[/C][C]62.2245180880273[/C][/ROW]
[ROW][C]36[/C][C]900[/C][C]909.461585365359[/C][C]-9.46158536535904[/C][/ROW]
[ROW][C]37[/C][C]680[/C][C]705.327404685836[/C][C]-25.3274046858359[/C][/ROW]
[ROW][C]38[/C][C]770[/C][C]750.998521435658[/C][C]19.0014785643421[/C][/ROW]
[ROW][C]39[/C][C]770[/C][C]766.51766172829[/C][C]3.48233827170952[/C][/ROW]
[ROW][C]40[/C][C]810[/C][C]854.31160177104[/C][C]-44.3116017710397[/C][/ROW]
[ROW][C]41[/C][C]810[/C][C]830.235675334095[/C][C]-20.2356753340954[/C][/ROW]
[ROW][C]42[/C][C]910[/C][C]922.138395636318[/C][C]-12.1383956363183[/C][/ROW]
[ROW][C]43[/C][C]820[/C][C]941.424794360245[/C][C]-121.424794360245[/C][/ROW]
[ROW][C]44[/C][C]980[/C][C]1031.77805265213[/C][C]-51.7780526521267[/C][/ROW]
[ROW][C]45[/C][C]830[/C][C]897.529302261544[/C][C]-67.5293022615438[/C][/ROW]
[ROW][C]46[/C][C]760[/C][C]698.302158307852[/C][C]61.6978416921484[/C][/ROW]
[ROW][C]47[/C][C]930[/C][C]896.69098995182[/C][C]33.3090100481803[/C][/ROW]
[ROW][C]48[/C][C]910[/C][C]882.911373089002[/C][C]27.0886269109982[/C][/ROW]
[ROW][C]49[/C][C]640[/C][C]672.129851363294[/C][C]-32.1298513632942[/C][/ROW]
[ROW][C]50[/C][C]780[/C][C]745.834723273058[/C][C]34.1652767269425[/C][/ROW]
[ROW][C]51[/C][C]690[/C][C]751.692713514506[/C][C]-61.6927135145058[/C][/ROW]
[ROW][C]52[/C][C]820[/C][C]794.714304000985[/C][C]25.2856959990149[/C][/ROW]
[ROW][C]53[/C][C]800[/C][C]796.693492803572[/C][C]3.30650719642824[/C][/ROW]
[ROW][C]54[/C][C]910[/C][C]896.685622231182[/C][C]13.3143777688182[/C][/ROW]
[ROW][C]55[/C][C]850[/C][C]843.724089323957[/C][C]6.27591067604317[/C][/ROW]
[ROW][C]56[/C][C]980[/C][C]1001.73318124488[/C][C]-21.7331812448797[/C][/ROW]
[ROW][C]57[/C][C]830[/C][C]861.44107842925[/C][C]-31.4410784292497[/C][/ROW]
[ROW][C]58[/C][C]820[/C][C]757.165916631041[/C][C]62.8340833689585[/C][/ROW]
[ROW][C]59[/C][C]1010[/C][C]936.595735939063[/C][C]73.4042640609366[/C][/ROW]
[ROW][C]60[/C][C]930[/C][C]925.429695430984[/C][C]4.57030456901612[/C][/ROW]
[ROW][C]61[/C][C]630[/C][C]670.925737081431[/C][C]-40.9257370814312[/C][/ROW]
[ROW][C]62[/C][C]760[/C][C]789.378832885204[/C][C]-29.3788328852045[/C][/ROW]
[ROW][C]63[/C][C]670[/C][C]719.434427763739[/C][C]-49.4344277637393[/C][/ROW]
[ROW][C]64[/C][C]850[/C][C]824.344731694399[/C][C]25.6552683056012[/C][/ROW]
[ROW][C]65[/C][C]780[/C][C]811.36473801266[/C][C]-31.3647380126602[/C][/ROW]
[ROW][C]66[/C][C]900[/C][C]912.7519570958[/C][C]-12.7519570958001[/C][/ROW]
[ROW][C]67[/C][C]840[/C][C]850.600448999351[/C][C]-10.6004489993512[/C][/ROW]
[ROW][C]68[/C][C]1050[/C][C]986.287610015728[/C][C]63.7123899842724[/C][/ROW]
[ROW][C]69[/C][C]810[/C][C]852.709573626[/C][C]-42.7095736260004[/C][/ROW]
[ROW][C]70[/C][C]860[/C][C]811.682855763755[/C][C]48.317144236245[/C][/ROW]
[ROW][C]71[/C][C]1020[/C][C]996.131650751623[/C][C]23.8683492483767[/C][/ROW]
[ROW][C]72[/C][C]820[/C][C]929.553135889898[/C][C]-109.553135889898[/C][/ROW]
[ROW][C]73[/C][C]670[/C][C]624.907942024484[/C][C]45.0920579755164[/C][/ROW]
[ROW][C]74[/C][C]780[/C][C]764.074305104883[/C][C]15.9256948951171[/C][/ROW]
[ROW][C]75[/C][C]690[/C][C]687.100355485273[/C][C]2.89964451472724[/C][/ROW]
[ROW][C]76[/C][C]800[/C][C]851.935771582786[/C][C]-51.9357715827859[/C][/ROW]
[ROW][C]77[/C][C]810[/C][C]787.276955471625[/C][C]22.7230445283753[/C][/ROW]
[ROW][C]78[/C][C]910[/C][C]909.816174115025[/C][C]0.183825884974794[/C][/ROW]
[ROW][C]79[/C][C]870[/C][C]851.203726617139[/C][C]18.7962733828613[/C][/ROW]
[ROW][C]80[/C][C]1010[/C][C]1042.86167367334[/C][C]-32.8616736733416[/C][/ROW]
[ROW][C]81[/C][C]810[/C][C]820.655050317626[/C][C]-10.6550503176255[/C][/ROW]
[ROW][C]82[/C][C]960[/C][C]847.066629450968[/C][C]112.933370549032[/C][/ROW]
[ROW][C]83[/C][C]990[/C][C]1024.9484756523[/C][C]-34.9484756522966[/C][/ROW]
[ROW][C]84[/C][C]780[/C][C]857.263429848199[/C][C]-77.2634298481987[/C][/ROW]
[ROW][C]85[/C][C]700[/C][C]664.155835500732[/C][C]35.8441644992677[/C][/ROW]
[ROW][C]86[/C][C]810[/C][C]781.82290851642[/C][C]28.1770914835799[/C][/ROW]
[ROW][C]87[/C][C]760[/C][C]697.875008036701[/C][C]62.1249919632992[/C][/ROW]
[ROW][C]88[/C][C]810[/C][C]834.638953271313[/C][C]-24.6389532713127[/C][/ROW]
[ROW][C]89[/C][C]840[/C][C]826.304403201704[/C][C]13.6955967982957[/C][/ROW]
[ROW][C]90[/C][C]900[/C][C]932.56720147713[/C][C]-32.5672014771296[/C][/ROW]
[ROW][C]91[/C][C]920[/C][C]882.107247121274[/C][C]37.8927528787257[/C][/ROW]
[ROW][C]92[/C][C]1050[/C][C]1041.70105148018[/C][C]8.29894851982249[/C][/ROW]
[ROW][C]93[/C][C]860[/C][C]841.984117705811[/C][C]18.0158822941889[/C][/ROW]
[ROW][C]94[/C][C]870[/C][C]958.946522165345[/C][C]-88.946522165345[/C][/ROW]
[ROW][C]95[/C][C]880[/C][C]1003.38950157207[/C][C]-123.389501572071[/C][/ROW]
[ROW][C]96[/C][C]860[/C][C]791.885494542147[/C][C]68.1145054578529[/C][/ROW]
[ROW][C]97[/C][C]650[/C][C]699.16915299448[/C][C]-49.1691529944802[/C][/ROW]
[ROW][C]98[/C][C]830[/C][C]797.82197149186[/C][C]32.1780285081395[/C][/ROW]
[ROW][C]99[/C][C]730[/C][C]737.317162703882[/C][C]-7.31716270388176[/C][/ROW]
[ROW][C]100[/C][C]810[/C][C]802.567789232923[/C][C]7.43221076707744[/C][/ROW]
[ROW][C]101[/C][C]840[/C][C]824.780962486475[/C][C]15.2190375135247[/C][/ROW]
[ROW][C]102[/C][C]940[/C][C]898.633432410351[/C][C]41.3665675896485[/C][/ROW]
[ROW][C]103[/C][C]870[/C][C]907.844805456141[/C][C]-37.8448054561411[/C][/ROW]
[ROW][C]104[/C][C]940[/C][C]1034.53038732573[/C][C]-94.5303873257296[/C][/ROW]
[ROW][C]105[/C][C]770[/C][C]824.056234157717[/C][C]-54.0562341577174[/C][/ROW]
[ROW][C]106[/C][C]870[/C][C]854.194027569732[/C][C]15.8059724302677[/C][/ROW]
[ROW][C]107[/C][C]860[/C][C]889.842526573714[/C][C]-29.8425265737138[/C][/ROW]
[ROW][C]108[/C][C]760[/C][C]824.011550314936[/C][C]-64.0115503149364[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235658&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235658&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
13730715.3979700854714.6020299145298
14730711.9431221539918.0568778460098
15770750.81581757817119.1841824218291
16880869.58026393614310.4197360638572
17820816.6439448689083.35605513109215
18900898.05418722221.94581277780048
19940902.17635757378837.8236424262118
201080972.533443264688107.466556735312
21920952.755373569114-32.7553735691142
22710848.540905297874-138.540905297874
23880878.2327931418671.76720685813302
24910920.074800618001-10.0748006180011
25680777.14907574061-97.14907574061
26740758.224548759885-18.2245487598852
27740791.455446861209-51.4554468612085
28810891.956250286481-81.9562502864809
29800817.91738781292-17.9173878129197
30900892.9760120662087.02398793379189
31920920.531836998528-0.531836998527524
3210301030.57588924859-0.575889248593057
33910894.46459770256915.5354022974315
34720722.163075078066-2.16307507806607
35930867.77548191197362.2245180880273
36900909.461585365359-9.46158536535904
37680705.327404685836-25.3274046858359
38770750.99852143565819.0014785643421
39770766.517661728293.48233827170952
40810854.31160177104-44.3116017710397
41810830.235675334095-20.2356753340954
42910922.138395636318-12.1383956363183
43820941.424794360245-121.424794360245
449801031.77805265213-51.7780526521267
45830897.529302261544-67.5293022615438
46760698.30215830785261.6978416921484
47930896.6909899518233.3090100481803
48910882.91137308900227.0886269109982
49640672.129851363294-32.1298513632942
50780745.83472327305834.1652767269425
51690751.692713514506-61.6927135145058
52820794.71430400098525.2856959990149
53800796.6934928035723.30650719642824
54910896.68562223118213.3143777688182
55850843.7240893239576.27591067604317
569801001.73318124488-21.7331812448797
57830861.44107842925-31.4410784292497
58820757.16591663104162.8340833689585
591010936.59573593906373.4042640609366
60930925.4296954309844.57030456901612
61630670.925737081431-40.9257370814312
62760789.378832885204-29.3788328852045
63670719.434427763739-49.4344277637393
64850824.34473169439925.6552683056012
65780811.36473801266-31.3647380126602
66900912.7519570958-12.7519570958001
67840850.600448999351-10.6004489993512
681050986.28761001572863.7123899842724
69810852.709573626-42.7095736260004
70860811.68285576375548.317144236245
711020996.13165075162323.8683492483767
72820929.553135889898-109.553135889898
73670624.90794202448445.0920579755164
74780764.07430510488315.9256948951171
75690687.1003554852732.89964451472724
76800851.935771582786-51.9357715827859
77810787.27695547162522.7230445283753
78910909.8161741150250.183825884974794
79870851.20372661713918.7962733828613
8010101042.86167367334-32.8616736733416
81810820.655050317626-10.6550503176255
82960847.066629450968112.933370549032
839901024.9484756523-34.9484756522966
84780857.263429848199-77.2634298481987
85700664.15583550073235.8441644992677
86810781.8229085164228.1770914835799
87760697.87500803670162.1249919632992
88810834.638953271313-24.6389532713127
89840826.30440320170413.6955967982957
90900932.56720147713-32.5672014771296
91920882.10724712127437.8927528787257
9210501041.701051480188.29894851982249
93860841.98411770581118.0158822941889
94870958.946522165345-88.946522165345
958801003.38950157207-123.389501572071
96860791.88549454214768.1145054578529
97650699.16915299448-49.1691529944802
98830797.8219714918632.1780285081395
99730737.317162703882-7.31716270388176
100810802.5677892329237.43221076707744
101840824.78096248647515.2190375135247
102940898.63343241035141.3665675896485
103870907.844805456141-37.8448054561411
1049401034.53038732573-94.5303873257296
105770824.056234157717-54.0562341577174
106870854.19402756973215.8059724302677
107860889.842526573714-29.8425265737138
108760824.011550314936-64.0115503149364







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109628.53001857682534.524659589339722.5353775643
110789.571149175603694.343398269242884.798900081964
111695.444841391931598.904537424294791.985145359569
112770.583032760041672.639243949746868.526821570335
113795.555298466501696.116613954639894.993982978364
114883.495267111515782.470072587195984.520461635834
115829.924988454586727.221723531279932.628253377893
116921.863279892397817.3906754697471026.33588431505
117752.965077079276646.632371474554859.297782683997
118839.022005909018730.739139070702947.304872747334
119840.142585893839729.820371498576950.464800289102
120754.961679393535642.511955063147867.411403723924

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 628.53001857682 & 534.524659589339 & 722.5353775643 \tabularnewline
110 & 789.571149175603 & 694.343398269242 & 884.798900081964 \tabularnewline
111 & 695.444841391931 & 598.904537424294 & 791.985145359569 \tabularnewline
112 & 770.583032760041 & 672.639243949746 & 868.526821570335 \tabularnewline
113 & 795.555298466501 & 696.116613954639 & 894.993982978364 \tabularnewline
114 & 883.495267111515 & 782.470072587195 & 984.520461635834 \tabularnewline
115 & 829.924988454586 & 727.221723531279 & 932.628253377893 \tabularnewline
116 & 921.863279892397 & 817.390675469747 & 1026.33588431505 \tabularnewline
117 & 752.965077079276 & 646.632371474554 & 859.297782683997 \tabularnewline
118 & 839.022005909018 & 730.739139070702 & 947.304872747334 \tabularnewline
119 & 840.142585893839 & 729.820371498576 & 950.464800289102 \tabularnewline
120 & 754.961679393535 & 642.511955063147 & 867.411403723924 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235658&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]628.53001857682[/C][C]534.524659589339[/C][C]722.5353775643[/C][/ROW]
[ROW][C]110[/C][C]789.571149175603[/C][C]694.343398269242[/C][C]884.798900081964[/C][/ROW]
[ROW][C]111[/C][C]695.444841391931[/C][C]598.904537424294[/C][C]791.985145359569[/C][/ROW]
[ROW][C]112[/C][C]770.583032760041[/C][C]672.639243949746[/C][C]868.526821570335[/C][/ROW]
[ROW][C]113[/C][C]795.555298466501[/C][C]696.116613954639[/C][C]894.993982978364[/C][/ROW]
[ROW][C]114[/C][C]883.495267111515[/C][C]782.470072587195[/C][C]984.520461635834[/C][/ROW]
[ROW][C]115[/C][C]829.924988454586[/C][C]727.221723531279[/C][C]932.628253377893[/C][/ROW]
[ROW][C]116[/C][C]921.863279892397[/C][C]817.390675469747[/C][C]1026.33588431505[/C][/ROW]
[ROW][C]117[/C][C]752.965077079276[/C][C]646.632371474554[/C][C]859.297782683997[/C][/ROW]
[ROW][C]118[/C][C]839.022005909018[/C][C]730.739139070702[/C][C]947.304872747334[/C][/ROW]
[ROW][C]119[/C][C]840.142585893839[/C][C]729.820371498576[/C][C]950.464800289102[/C][/ROW]
[ROW][C]120[/C][C]754.961679393535[/C][C]642.511955063147[/C][C]867.411403723924[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235658&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235658&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
109628.53001857682534.524659589339722.5353775643
110789.571149175603694.343398269242884.798900081964
111695.444841391931598.904537424294791.985145359569
112770.583032760041672.639243949746868.526821570335
113795.555298466501696.116613954639894.993982978364
114883.495267111515782.470072587195984.520461635834
115829.924988454586727.221723531279932.628253377893
116921.863279892397817.3906754697471026.33588431505
117752.965077079276646.632371474554859.297782683997
118839.022005909018730.739139070702947.304872747334
119840.142585893839729.820371498576950.464800289102
120754.961679393535642.511955063147867.411403723924



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')