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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 Aug 2011 10:23:49 -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/2011/Aug/01/t1312208648p0mg0dxnlgis2pr.htm/, Retrieved Tue, 14 May 2024 02:04:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123271, Retrieved Tue, 14 May 2024 02:04:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKatrien Monnens
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B stap 27] [2011-08-01 14:23:49] [3f9379635061ebc5737ab9ab2503b0b0] [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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123271&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123271&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123271&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.154810139603247
beta0.045085407938114
gamma0.814530331887456

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.154810139603247 \tabularnewline
beta & 0.045085407938114 \tabularnewline
gamma & 0.814530331887456 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123271&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]0.154810139603247[/C][/ROW]
[ROW][C]beta[/C][C]0.045085407938114[/C][/ROW]
[ROW][C]gamma[/C][C]0.814530331887456[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123271&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123271&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
alpha0.154810139603247
beta0.045085407938114
gamma0.814530331887456







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13730715.3979700854714.6020299145298
14730711.94312215400818.0568778459922
15770750.81581757820219.1841824217977
16880869.58026393618110.4197360638193
17820816.6439448689333.3560551310668
18900898.0541872222021.94581277779798
19940902.17635757376937.8236424262315
201080972.533443264692107.466556735308
21920952.755373569209-32.7553735692095
22710848.540905297838-138.540905297838
23880878.2327931416031.76720685839655
24910920.074800617766-10.0748006177663
25680777.149075740629-97.1490757406291
26740758.22454875982-18.2245487598196
27740791.455446861166-51.4554468611659
28810891.956250286265-81.9562502862651
29800817.917387812582-17.9173878125816
30900892.9760120659777.0239879340229
31920920.531836999045-0.531836999044799
3210301030.57588925026-0.575889250257205
33910894.46459770165415.5354022983458
34720722.163075075724-2.16307507572446
35930867.77548191257362.2245180874269
36900909.461585365813-9.46158536581333
37680705.327404684891-25.3274046848912
38770750.99852143631819.0014785636819
39770766.517661728393.48233827161039
40810854.31160177066-44.3116017706596
41810830.235675334832-20.2356753348322
42910922.138395637332-12.1383956373321
43820941.42479436114-121.42479436114
449801031.77805265317-51.7780526531687
45830897.529302262127-67.5293022621269
46760698.30215830741361.6978416925866
47930896.69098995321833.3090100467822
48910882.91137308904227.0886269109582
49640672.129851362794-32.1298513627939
50780745.83472327375334.1652767262475
51690751.692713514818-61.692713514818
52820794.71430400027225.2856959997284
53800796.6934928037983.30650719620166
54910896.68562223177113.3143777682287
55850843.7240893228176.27591067718254
569801001.73318124545-21.7331812454478
57830861.441078429514-31.4410784295142
58820757.16591663321362.834083366787
591010936.59573594088473.4042640591157
60930925.429695432214.57030456779012
61630670.925737081219-40.9257370812195
62760789.378832886345-29.3788328863451
63670719.434427762953-49.4344277629527
64850824.34473169488725.6552683051132
65780811.36473801284-31.3647380128399
66900912.751957096175-12.7519570961747
67840850.600448999036-10.6004489990358
681050986.28761001529863.712389984702
69810852.709573625553-42.709573625553
70860811.68285576552148.3171442344786
711020996.13165075346323.8683492465367
72820929.553135890311-109.553135890311
73670624.90794202367145.0920579763293
74780764.07430510491615.9256948950843
75690687.100355484612.89964451539026
76800851.935771583808-51.9357715838083
77810787.27695547139922.7230445286011
78910909.8161741153010.183825884698649
79870851.20372661725118.7962733827486
8010101042.8616736746-32.8616736746008
81810820.655050316686-10.655050316686
82960847.06662945234112.93337054766
839901024.94847565341-34.948475653408
84780857.263429846654-77.2634298466544
85700664.15583550172135.8441644982793
86810781.82290851687328.1770914831269
87760697.87500803664762.1249919633528
88810834.638953270818-24.6389532708178
89840826.30440320228813.6955967977124
90900932.567201477301-32.5672014773006
91920882.10724712162737.8927528783731
9210501041.701051479978.29894852002963
93860841.98411770552518.0158822944753
94870958.946522167708-88.9465221677082
958801003.38950157142-123.389501571419
96860791.88549454013868.114505459862
97650699.169152995432-49.1691529954319
98830797.82197149241232.1780285075882
99730737.31716270485-7.31716270485003
100810802.567789232087.43221076791986
101840824.78096248673815.2190375132617
102940898.63343240979841.3665675902021
103870907.844805457052-37.8448054570522
1049401034.5303873258-94.5303873258003
105770824.056234157787-54.0562341577872
106870854.1940275687715.8059724312297
107860889.842526571994-29.8425265719936
108760824.011550316339-64.0115503163394

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 730 & 715.39797008547 & 14.6020299145298 \tabularnewline
14 & 730 & 711.943122154008 & 18.0568778459922 \tabularnewline
15 & 770 & 750.815817578202 & 19.1841824217977 \tabularnewline
16 & 880 & 869.580263936181 & 10.4197360638193 \tabularnewline
17 & 820 & 816.643944868933 & 3.3560551310668 \tabularnewline
18 & 900 & 898.054187222202 & 1.94581277779798 \tabularnewline
19 & 940 & 902.176357573769 & 37.8236424262315 \tabularnewline
20 & 1080 & 972.533443264692 & 107.466556735308 \tabularnewline
21 & 920 & 952.755373569209 & -32.7553735692095 \tabularnewline
22 & 710 & 848.540905297838 & -138.540905297838 \tabularnewline
23 & 880 & 878.232793141603 & 1.76720685839655 \tabularnewline
24 & 910 & 920.074800617766 & -10.0748006177663 \tabularnewline
25 & 680 & 777.149075740629 & -97.1490757406291 \tabularnewline
26 & 740 & 758.22454875982 & -18.2245487598196 \tabularnewline
27 & 740 & 791.455446861166 & -51.4554468611659 \tabularnewline
28 & 810 & 891.956250286265 & -81.9562502862651 \tabularnewline
29 & 800 & 817.917387812582 & -17.9173878125816 \tabularnewline
30 & 900 & 892.976012065977 & 7.0239879340229 \tabularnewline
31 & 920 & 920.531836999045 & -0.531836999044799 \tabularnewline
32 & 1030 & 1030.57588925026 & -0.575889250257205 \tabularnewline
33 & 910 & 894.464597701654 & 15.5354022983458 \tabularnewline
34 & 720 & 722.163075075724 & -2.16307507572446 \tabularnewline
35 & 930 & 867.775481912573 & 62.2245180874269 \tabularnewline
36 & 900 & 909.461585365813 & -9.46158536581333 \tabularnewline
37 & 680 & 705.327404684891 & -25.3274046848912 \tabularnewline
38 & 770 & 750.998521436318 & 19.0014785636819 \tabularnewline
39 & 770 & 766.51766172839 & 3.48233827161039 \tabularnewline
40 & 810 & 854.31160177066 & -44.3116017706596 \tabularnewline
41 & 810 & 830.235675334832 & -20.2356753348322 \tabularnewline
42 & 910 & 922.138395637332 & -12.1383956373321 \tabularnewline
43 & 820 & 941.42479436114 & -121.42479436114 \tabularnewline
44 & 980 & 1031.77805265317 & -51.7780526531687 \tabularnewline
45 & 830 & 897.529302262127 & -67.5293022621269 \tabularnewline
46 & 760 & 698.302158307413 & 61.6978416925866 \tabularnewline
47 & 930 & 896.690989953218 & 33.3090100467822 \tabularnewline
48 & 910 & 882.911373089042 & 27.0886269109582 \tabularnewline
49 & 640 & 672.129851362794 & -32.1298513627939 \tabularnewline
50 & 780 & 745.834723273753 & 34.1652767262475 \tabularnewline
51 & 690 & 751.692713514818 & -61.692713514818 \tabularnewline
52 & 820 & 794.714304000272 & 25.2856959997284 \tabularnewline
53 & 800 & 796.693492803798 & 3.30650719620166 \tabularnewline
54 & 910 & 896.685622231771 & 13.3143777682287 \tabularnewline
55 & 850 & 843.724089322817 & 6.27591067718254 \tabularnewline
56 & 980 & 1001.73318124545 & -21.7331812454478 \tabularnewline
57 & 830 & 861.441078429514 & -31.4410784295142 \tabularnewline
58 & 820 & 757.165916633213 & 62.834083366787 \tabularnewline
59 & 1010 & 936.595735940884 & 73.4042640591157 \tabularnewline
60 & 930 & 925.42969543221 & 4.57030456779012 \tabularnewline
61 & 630 & 670.925737081219 & -40.9257370812195 \tabularnewline
62 & 760 & 789.378832886345 & -29.3788328863451 \tabularnewline
63 & 670 & 719.434427762953 & -49.4344277629527 \tabularnewline
64 & 850 & 824.344731694887 & 25.6552683051132 \tabularnewline
65 & 780 & 811.36473801284 & -31.3647380128399 \tabularnewline
66 & 900 & 912.751957096175 & -12.7519570961747 \tabularnewline
67 & 840 & 850.600448999036 & -10.6004489990358 \tabularnewline
68 & 1050 & 986.287610015298 & 63.712389984702 \tabularnewline
69 & 810 & 852.709573625553 & -42.709573625553 \tabularnewline
70 & 860 & 811.682855765521 & 48.3171442344786 \tabularnewline
71 & 1020 & 996.131650753463 & 23.8683492465367 \tabularnewline
72 & 820 & 929.553135890311 & -109.553135890311 \tabularnewline
73 & 670 & 624.907942023671 & 45.0920579763293 \tabularnewline
74 & 780 & 764.074305104916 & 15.9256948950843 \tabularnewline
75 & 690 & 687.10035548461 & 2.89964451539026 \tabularnewline
76 & 800 & 851.935771583808 & -51.9357715838083 \tabularnewline
77 & 810 & 787.276955471399 & 22.7230445286011 \tabularnewline
78 & 910 & 909.816174115301 & 0.183825884698649 \tabularnewline
79 & 870 & 851.203726617251 & 18.7962733827486 \tabularnewline
80 & 1010 & 1042.8616736746 & -32.8616736746008 \tabularnewline
81 & 810 & 820.655050316686 & -10.655050316686 \tabularnewline
82 & 960 & 847.06662945234 & 112.93337054766 \tabularnewline
83 & 990 & 1024.94847565341 & -34.948475653408 \tabularnewline
84 & 780 & 857.263429846654 & -77.2634298466544 \tabularnewline
85 & 700 & 664.155835501721 & 35.8441644982793 \tabularnewline
86 & 810 & 781.822908516873 & 28.1770914831269 \tabularnewline
87 & 760 & 697.875008036647 & 62.1249919633528 \tabularnewline
88 & 810 & 834.638953270818 & -24.6389532708178 \tabularnewline
89 & 840 & 826.304403202288 & 13.6955967977124 \tabularnewline
90 & 900 & 932.567201477301 & -32.5672014773006 \tabularnewline
91 & 920 & 882.107247121627 & 37.8927528783731 \tabularnewline
92 & 1050 & 1041.70105147997 & 8.29894852002963 \tabularnewline
93 & 860 & 841.984117705525 & 18.0158822944753 \tabularnewline
94 & 870 & 958.946522167708 & -88.9465221677082 \tabularnewline
95 & 880 & 1003.38950157142 & -123.389501571419 \tabularnewline
96 & 860 & 791.885494540138 & 68.114505459862 \tabularnewline
97 & 650 & 699.169152995432 & -49.1691529954319 \tabularnewline
98 & 830 & 797.821971492412 & 32.1780285075882 \tabularnewline
99 & 730 & 737.31716270485 & -7.31716270485003 \tabularnewline
100 & 810 & 802.56778923208 & 7.43221076791986 \tabularnewline
101 & 840 & 824.780962486738 & 15.2190375132617 \tabularnewline
102 & 940 & 898.633432409798 & 41.3665675902021 \tabularnewline
103 & 870 & 907.844805457052 & -37.8448054570522 \tabularnewline
104 & 940 & 1034.5303873258 & -94.5303873258003 \tabularnewline
105 & 770 & 824.056234157787 & -54.0562341577872 \tabularnewline
106 & 870 & 854.19402756877 & 15.8059724312297 \tabularnewline
107 & 860 & 889.842526571994 & -29.8425265719936 \tabularnewline
108 & 760 & 824.011550316339 & -64.0115503163394 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123271&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]711.943122154008[/C][C]18.0568778459922[/C][/ROW]
[ROW][C]15[/C][C]770[/C][C]750.815817578202[/C][C]19.1841824217977[/C][/ROW]
[ROW][C]16[/C][C]880[/C][C]869.580263936181[/C][C]10.4197360638193[/C][/ROW]
[ROW][C]17[/C][C]820[/C][C]816.643944868933[/C][C]3.3560551310668[/C][/ROW]
[ROW][C]18[/C][C]900[/C][C]898.054187222202[/C][C]1.94581277779798[/C][/ROW]
[ROW][C]19[/C][C]940[/C][C]902.176357573769[/C][C]37.8236424262315[/C][/ROW]
[ROW][C]20[/C][C]1080[/C][C]972.533443264692[/C][C]107.466556735308[/C][/ROW]
[ROW][C]21[/C][C]920[/C][C]952.755373569209[/C][C]-32.7553735692095[/C][/ROW]
[ROW][C]22[/C][C]710[/C][C]848.540905297838[/C][C]-138.540905297838[/C][/ROW]
[ROW][C]23[/C][C]880[/C][C]878.232793141603[/C][C]1.76720685839655[/C][/ROW]
[ROW][C]24[/C][C]910[/C][C]920.074800617766[/C][C]-10.0748006177663[/C][/ROW]
[ROW][C]25[/C][C]680[/C][C]777.149075740629[/C][C]-97.1490757406291[/C][/ROW]
[ROW][C]26[/C][C]740[/C][C]758.22454875982[/C][C]-18.2245487598196[/C][/ROW]
[ROW][C]27[/C][C]740[/C][C]791.455446861166[/C][C]-51.4554468611659[/C][/ROW]
[ROW][C]28[/C][C]810[/C][C]891.956250286265[/C][C]-81.9562502862651[/C][/ROW]
[ROW][C]29[/C][C]800[/C][C]817.917387812582[/C][C]-17.9173878125816[/C][/ROW]
[ROW][C]30[/C][C]900[/C][C]892.976012065977[/C][C]7.0239879340229[/C][/ROW]
[ROW][C]31[/C][C]920[/C][C]920.531836999045[/C][C]-0.531836999044799[/C][/ROW]
[ROW][C]32[/C][C]1030[/C][C]1030.57588925026[/C][C]-0.575889250257205[/C][/ROW]
[ROW][C]33[/C][C]910[/C][C]894.464597701654[/C][C]15.5354022983458[/C][/ROW]
[ROW][C]34[/C][C]720[/C][C]722.163075075724[/C][C]-2.16307507572446[/C][/ROW]
[ROW][C]35[/C][C]930[/C][C]867.775481912573[/C][C]62.2245180874269[/C][/ROW]
[ROW][C]36[/C][C]900[/C][C]909.461585365813[/C][C]-9.46158536581333[/C][/ROW]
[ROW][C]37[/C][C]680[/C][C]705.327404684891[/C][C]-25.3274046848912[/C][/ROW]
[ROW][C]38[/C][C]770[/C][C]750.998521436318[/C][C]19.0014785636819[/C][/ROW]
[ROW][C]39[/C][C]770[/C][C]766.51766172839[/C][C]3.48233827161039[/C][/ROW]
[ROW][C]40[/C][C]810[/C][C]854.31160177066[/C][C]-44.3116017706596[/C][/ROW]
[ROW][C]41[/C][C]810[/C][C]830.235675334832[/C][C]-20.2356753348322[/C][/ROW]
[ROW][C]42[/C][C]910[/C][C]922.138395637332[/C][C]-12.1383956373321[/C][/ROW]
[ROW][C]43[/C][C]820[/C][C]941.42479436114[/C][C]-121.42479436114[/C][/ROW]
[ROW][C]44[/C][C]980[/C][C]1031.77805265317[/C][C]-51.7780526531687[/C][/ROW]
[ROW][C]45[/C][C]830[/C][C]897.529302262127[/C][C]-67.5293022621269[/C][/ROW]
[ROW][C]46[/C][C]760[/C][C]698.302158307413[/C][C]61.6978416925866[/C][/ROW]
[ROW][C]47[/C][C]930[/C][C]896.690989953218[/C][C]33.3090100467822[/C][/ROW]
[ROW][C]48[/C][C]910[/C][C]882.911373089042[/C][C]27.0886269109582[/C][/ROW]
[ROW][C]49[/C][C]640[/C][C]672.129851362794[/C][C]-32.1298513627939[/C][/ROW]
[ROW][C]50[/C][C]780[/C][C]745.834723273753[/C][C]34.1652767262475[/C][/ROW]
[ROW][C]51[/C][C]690[/C][C]751.692713514818[/C][C]-61.692713514818[/C][/ROW]
[ROW][C]52[/C][C]820[/C][C]794.714304000272[/C][C]25.2856959997284[/C][/ROW]
[ROW][C]53[/C][C]800[/C][C]796.693492803798[/C][C]3.30650719620166[/C][/ROW]
[ROW][C]54[/C][C]910[/C][C]896.685622231771[/C][C]13.3143777682287[/C][/ROW]
[ROW][C]55[/C][C]850[/C][C]843.724089322817[/C][C]6.27591067718254[/C][/ROW]
[ROW][C]56[/C][C]980[/C][C]1001.73318124545[/C][C]-21.7331812454478[/C][/ROW]
[ROW][C]57[/C][C]830[/C][C]861.441078429514[/C][C]-31.4410784295142[/C][/ROW]
[ROW][C]58[/C][C]820[/C][C]757.165916633213[/C][C]62.834083366787[/C][/ROW]
[ROW][C]59[/C][C]1010[/C][C]936.595735940884[/C][C]73.4042640591157[/C][/ROW]
[ROW][C]60[/C][C]930[/C][C]925.42969543221[/C][C]4.57030456779012[/C][/ROW]
[ROW][C]61[/C][C]630[/C][C]670.925737081219[/C][C]-40.9257370812195[/C][/ROW]
[ROW][C]62[/C][C]760[/C][C]789.378832886345[/C][C]-29.3788328863451[/C][/ROW]
[ROW][C]63[/C][C]670[/C][C]719.434427762953[/C][C]-49.4344277629527[/C][/ROW]
[ROW][C]64[/C][C]850[/C][C]824.344731694887[/C][C]25.6552683051132[/C][/ROW]
[ROW][C]65[/C][C]780[/C][C]811.36473801284[/C][C]-31.3647380128399[/C][/ROW]
[ROW][C]66[/C][C]900[/C][C]912.751957096175[/C][C]-12.7519570961747[/C][/ROW]
[ROW][C]67[/C][C]840[/C][C]850.600448999036[/C][C]-10.6004489990358[/C][/ROW]
[ROW][C]68[/C][C]1050[/C][C]986.287610015298[/C][C]63.712389984702[/C][/ROW]
[ROW][C]69[/C][C]810[/C][C]852.709573625553[/C][C]-42.709573625553[/C][/ROW]
[ROW][C]70[/C][C]860[/C][C]811.682855765521[/C][C]48.3171442344786[/C][/ROW]
[ROW][C]71[/C][C]1020[/C][C]996.131650753463[/C][C]23.8683492465367[/C][/ROW]
[ROW][C]72[/C][C]820[/C][C]929.553135890311[/C][C]-109.553135890311[/C][/ROW]
[ROW][C]73[/C][C]670[/C][C]624.907942023671[/C][C]45.0920579763293[/C][/ROW]
[ROW][C]74[/C][C]780[/C][C]764.074305104916[/C][C]15.9256948950843[/C][/ROW]
[ROW][C]75[/C][C]690[/C][C]687.10035548461[/C][C]2.89964451539026[/C][/ROW]
[ROW][C]76[/C][C]800[/C][C]851.935771583808[/C][C]-51.9357715838083[/C][/ROW]
[ROW][C]77[/C][C]810[/C][C]787.276955471399[/C][C]22.7230445286011[/C][/ROW]
[ROW][C]78[/C][C]910[/C][C]909.816174115301[/C][C]0.183825884698649[/C][/ROW]
[ROW][C]79[/C][C]870[/C][C]851.203726617251[/C][C]18.7962733827486[/C][/ROW]
[ROW][C]80[/C][C]1010[/C][C]1042.8616736746[/C][C]-32.8616736746008[/C][/ROW]
[ROW][C]81[/C][C]810[/C][C]820.655050316686[/C][C]-10.655050316686[/C][/ROW]
[ROW][C]82[/C][C]960[/C][C]847.06662945234[/C][C]112.93337054766[/C][/ROW]
[ROW][C]83[/C][C]990[/C][C]1024.94847565341[/C][C]-34.948475653408[/C][/ROW]
[ROW][C]84[/C][C]780[/C][C]857.263429846654[/C][C]-77.2634298466544[/C][/ROW]
[ROW][C]85[/C][C]700[/C][C]664.155835501721[/C][C]35.8441644982793[/C][/ROW]
[ROW][C]86[/C][C]810[/C][C]781.822908516873[/C][C]28.1770914831269[/C][/ROW]
[ROW][C]87[/C][C]760[/C][C]697.875008036647[/C][C]62.1249919633528[/C][/ROW]
[ROW][C]88[/C][C]810[/C][C]834.638953270818[/C][C]-24.6389532708178[/C][/ROW]
[ROW][C]89[/C][C]840[/C][C]826.304403202288[/C][C]13.6955967977124[/C][/ROW]
[ROW][C]90[/C][C]900[/C][C]932.567201477301[/C][C]-32.5672014773006[/C][/ROW]
[ROW][C]91[/C][C]920[/C][C]882.107247121627[/C][C]37.8927528783731[/C][/ROW]
[ROW][C]92[/C][C]1050[/C][C]1041.70105147997[/C][C]8.29894852002963[/C][/ROW]
[ROW][C]93[/C][C]860[/C][C]841.984117705525[/C][C]18.0158822944753[/C][/ROW]
[ROW][C]94[/C][C]870[/C][C]958.946522167708[/C][C]-88.9465221677082[/C][/ROW]
[ROW][C]95[/C][C]880[/C][C]1003.38950157142[/C][C]-123.389501571419[/C][/ROW]
[ROW][C]96[/C][C]860[/C][C]791.885494540138[/C][C]68.114505459862[/C][/ROW]
[ROW][C]97[/C][C]650[/C][C]699.169152995432[/C][C]-49.1691529954319[/C][/ROW]
[ROW][C]98[/C][C]830[/C][C]797.821971492412[/C][C]32.1780285075882[/C][/ROW]
[ROW][C]99[/C][C]730[/C][C]737.31716270485[/C][C]-7.31716270485003[/C][/ROW]
[ROW][C]100[/C][C]810[/C][C]802.56778923208[/C][C]7.43221076791986[/C][/ROW]
[ROW][C]101[/C][C]840[/C][C]824.780962486738[/C][C]15.2190375132617[/C][/ROW]
[ROW][C]102[/C][C]940[/C][C]898.633432409798[/C][C]41.3665675902021[/C][/ROW]
[ROW][C]103[/C][C]870[/C][C]907.844805457052[/C][C]-37.8448054570522[/C][/ROW]
[ROW][C]104[/C][C]940[/C][C]1034.5303873258[/C][C]-94.5303873258003[/C][/ROW]
[ROW][C]105[/C][C]770[/C][C]824.056234157787[/C][C]-54.0562341577872[/C][/ROW]
[ROW][C]106[/C][C]870[/C][C]854.19402756877[/C][C]15.8059724312297[/C][/ROW]
[ROW][C]107[/C][C]860[/C][C]889.842526571994[/C][C]-29.8425265719936[/C][/ROW]
[ROW][C]108[/C][C]760[/C][C]824.011550316339[/C][C]-64.0115503163394[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123271&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123271&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
14730711.94312215400818.0568778459922
15770750.81581757820219.1841824217977
16880869.58026393618110.4197360638193
17820816.6439448689333.3560551310668
18900898.0541872222021.94581277779798
19940902.17635757376937.8236424262315
201080972.533443264692107.466556735308
21920952.755373569209-32.7553735692095
22710848.540905297838-138.540905297838
23880878.2327931416031.76720685839655
24910920.074800617766-10.0748006177663
25680777.149075740629-97.1490757406291
26740758.22454875982-18.2245487598196
27740791.455446861166-51.4554468611659
28810891.956250286265-81.9562502862651
29800817.917387812582-17.9173878125816
30900892.9760120659777.0239879340229
31920920.531836999045-0.531836999044799
3210301030.57588925026-0.575889250257205
33910894.46459770165415.5354022983458
34720722.163075075724-2.16307507572446
35930867.77548191257362.2245180874269
36900909.461585365813-9.46158536581333
37680705.327404684891-25.3274046848912
38770750.99852143631819.0014785636819
39770766.517661728393.48233827161039
40810854.31160177066-44.3116017706596
41810830.235675334832-20.2356753348322
42910922.138395637332-12.1383956373321
43820941.42479436114-121.42479436114
449801031.77805265317-51.7780526531687
45830897.529302262127-67.5293022621269
46760698.30215830741361.6978416925866
47930896.69098995321833.3090100467822
48910882.91137308904227.0886269109582
49640672.129851362794-32.1298513627939
50780745.83472327375334.1652767262475
51690751.692713514818-61.692713514818
52820794.71430400027225.2856959997284
53800796.6934928037983.30650719620166
54910896.68562223177113.3143777682287
55850843.7240893228176.27591067718254
569801001.73318124545-21.7331812454478
57830861.441078429514-31.4410784295142
58820757.16591663321362.834083366787
591010936.59573594088473.4042640591157
60930925.429695432214.57030456779012
61630670.925737081219-40.9257370812195
62760789.378832886345-29.3788328863451
63670719.434427762953-49.4344277629527
64850824.34473169488725.6552683051132
65780811.36473801284-31.3647380128399
66900912.751957096175-12.7519570961747
67840850.600448999036-10.6004489990358
681050986.28761001529863.712389984702
69810852.709573625553-42.709573625553
70860811.68285576552148.3171442344786
711020996.13165075346323.8683492465367
72820929.553135890311-109.553135890311
73670624.90794202367145.0920579763293
74780764.07430510491615.9256948950843
75690687.100355484612.89964451539026
76800851.935771583808-51.9357715838083
77810787.27695547139922.7230445286011
78910909.8161741153010.183825884698649
79870851.20372661725118.7962733827486
8010101042.8616736746-32.8616736746008
81810820.655050316686-10.655050316686
82960847.06662945234112.93337054766
839901024.94847565341-34.948475653408
84780857.263429846654-77.2634298466544
85700664.15583550172135.8441644982793
86810781.82290851687328.1770914831269
87760697.87500803664762.1249919633528
88810834.638953270818-24.6389532708178
89840826.30440320228813.6955967977124
90900932.567201477301-32.5672014773006
91920882.10724712162737.8927528783731
9210501041.701051479978.29894852002963
93860841.98411770552518.0158822944753
94870958.946522167708-88.9465221677082
958801003.38950157142-123.389501571419
96860791.88549454013868.114505459862
97650699.169152995432-49.1691529954319
98830797.82197149241232.1780285075882
99730737.31716270485-7.31716270485003
100810802.567789232087.43221076791986
101840824.78096248673815.2190375132617
102940898.63343240979841.3665675902021
103870907.844805457052-37.8448054570522
1049401034.5303873258-94.5303873258003
105770824.056234157787-54.0562341577872
106870854.1940275687715.8059724312297
107860889.842526571994-29.8425265719936
108760824.011550316339-64.0115503163394







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109628.530018576532534.5246595891722.535377563964
110789.57114917683694.3433982705884.79890008316
111695.444841392743598.904537425124791.985145360362
112770.583032760776672.639243950493868.526821571059
113795.555298467646696.116613955795894.993982979498
114883.495267112942782.470072588639984.520461637246
115829.924988455098727.221723531818932.628253378378
116921.863279891994817.3906754693891026.3358843146
117752.96507707976646.632371475107859.297782684413
118839.022005910475730.739139072258947.304872748693
119840.142585894163729.820371499035950.46480028929
120754.961679394057642.511955063846867.411403724268

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 628.530018576532 & 534.5246595891 & 722.535377563964 \tabularnewline
110 & 789.57114917683 & 694.3433982705 & 884.79890008316 \tabularnewline
111 & 695.444841392743 & 598.904537425124 & 791.985145360362 \tabularnewline
112 & 770.583032760776 & 672.639243950493 & 868.526821571059 \tabularnewline
113 & 795.555298467646 & 696.116613955795 & 894.993982979498 \tabularnewline
114 & 883.495267112942 & 782.470072588639 & 984.520461637246 \tabularnewline
115 & 829.924988455098 & 727.221723531818 & 932.628253378378 \tabularnewline
116 & 921.863279891994 & 817.390675469389 & 1026.3358843146 \tabularnewline
117 & 752.96507707976 & 646.632371475107 & 859.297782684413 \tabularnewline
118 & 839.022005910475 & 730.739139072258 & 947.304872748693 \tabularnewline
119 & 840.142585894163 & 729.820371499035 & 950.46480028929 \tabularnewline
120 & 754.961679394057 & 642.511955063846 & 867.411403724268 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123271&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]628.530018576532[/C][C]534.5246595891[/C][C]722.535377563964[/C][/ROW]
[ROW][C]110[/C][C]789.57114917683[/C][C]694.3433982705[/C][C]884.79890008316[/C][/ROW]
[ROW][C]111[/C][C]695.444841392743[/C][C]598.904537425124[/C][C]791.985145360362[/C][/ROW]
[ROW][C]112[/C][C]770.583032760776[/C][C]672.639243950493[/C][C]868.526821571059[/C][/ROW]
[ROW][C]113[/C][C]795.555298467646[/C][C]696.116613955795[/C][C]894.993982979498[/C][/ROW]
[ROW][C]114[/C][C]883.495267112942[/C][C]782.470072588639[/C][C]984.520461637246[/C][/ROW]
[ROW][C]115[/C][C]829.924988455098[/C][C]727.221723531818[/C][C]932.628253378378[/C][/ROW]
[ROW][C]116[/C][C]921.863279891994[/C][C]817.390675469389[/C][C]1026.3358843146[/C][/ROW]
[ROW][C]117[/C][C]752.96507707976[/C][C]646.632371475107[/C][C]859.297782684413[/C][/ROW]
[ROW][C]118[/C][C]839.022005910475[/C][C]730.739139072258[/C][C]947.304872748693[/C][/ROW]
[ROW][C]119[/C][C]840.142585894163[/C][C]729.820371499035[/C][C]950.46480028929[/C][/ROW]
[ROW][C]120[/C][C]754.961679394057[/C][C]642.511955063846[/C][C]867.411403724268[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123271&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123271&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
109628.530018576532534.5246595891722.535377563964
110789.57114917683694.3433982705884.79890008316
111695.444841392743598.904537425124791.985145360362
112770.583032760776672.639243950493868.526821571059
113795.555298467646696.116613955795894.993982979498
114883.495267112942782.470072588639984.520461637246
115829.924988455098727.221723531818932.628253378378
116921.863279891994817.3906754693891026.3358843146
117752.96507707976646.632371475107859.297782684413
118839.022005910475730.739139072258947.304872748693
119840.142585894163729.820371499035950.46480028929
120754.961679394057642.511955063846867.411403724268



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')