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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 11 Aug 2016 22:48:04 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Aug/11/t1470952101megsepsem9amfvq.htm/, Retrieved Sun, 05 May 2024 20:07:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296380, Retrieved Sun, 05 May 2024 20:07:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-08-11 21:48:04] [50e1ac7d003038f762f5217b1e15faa4] [Current]
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Dataseries X:
940
950
920
930
930
900
940
840
890
850
830
940
960
900
940
920
930
970
930
780
810
870
720
880
920
920
950
950
890
960
780
780
760
860
740
1020
890
1040
920
900
950
990
840
740
840
960
790
1010
900
970
920
980
890
1000
880
740
860
940
760
1010
870
980
920
950
880
980
910
730
880
820
690
990
800
960
910
950
940
1010
890
660
860
840
740
980
820
1080
930
970
930
1010
880
740
860
810
750
890
790
1000
890
970
900
990
910
730
850
840
830
950




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296380&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296380&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296380&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.15308162521635
beta0.00940485503399172
gamma0.766853296738313

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.15308162521635 \tabularnewline
beta & 0.00940485503399172 \tabularnewline
gamma & 0.766853296738313 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296380&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]0.15308162521635[/C][/ROW]
[ROW][C]beta[/C][C]0.00940485503399172[/C][/ROW]
[ROW][C]gamma[/C][C]0.766853296738313[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296380&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296380&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
alpha0.15308162521635
beta0.00940485503399172
gamma0.766853296738313







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13960952.2302350427357.76976495726467
14900895.0960392922934.90396070770657
15940940.446868520135-0.446868520134558
16920921.644607418892-1.64460741889161
17930933.906626741883-3.90662674188343
18970979.15008139246-9.15008139245981
19930927.327686015182.67231398481965
20780827.735596161357-47.7355961613573
21810870.35825605989-60.3582560598898
22870819.29505358531450.7049464146855
23720806.13992042404-86.1399204240399
24880898.579002763899-18.579002763899
25920916.796506698533.20349330146962
26920856.86238968187563.1376103181254
27950907.49672159115342.5032784088472
28950894.39745048412155.6025495158794
29890913.942278811153-23.9422788111528
30960952.6727895323247.32721046767574
31780911.034257166413-131.034257166413
32780758.02691385765321.9730861423473
33760803.013907995232-43.0139079952318
34860826.65327903668833.3467209633116
35740721.85649507308818.1435049269116
361020874.17898596869145.82101403131
37890931.987980398623-41.9879803986229
381040904.273718925798135.726281074202
39920952.93623109945-32.9362310994503
40900937.004833057667-37.0048330576674
41950890.78728492237759.212715077623
42990962.75083325534827.2491667446521
43840834.5253185806295.47468141937088
44740802.207864793759-62.2078647937589
45840792.40091469814647.5990853018542
46960879.9344699232580.0655300767497
47790772.9124872220517.0875127779505
4810101008.490437460471.50956253952916
49900922.520803806661-22.5208038066606
509701013.52095875016-43.5209587501639
51920925.261694038639-5.26169403863946
52980911.02179876988768.9782012301127
53890943.767988749406-53.767988749406
541000977.76452058232722.2354794176733
55880834.70994824963945.2900517503608
56740764.66771659024-24.6677165902404
57860832.11445034588127.8855496541194
58940937.8790899692342.12091003076625
59760778.074299609854-18.0742996098542
601010998.1526304449911.8473695550098
61870898.173892202909-28.173892202909
62980974.6768990949545.32310090504643
63920918.8200695953991.17993040460146
64950953.868907517398-3.86890751739827
65880895.726297796234-15.7262977962339
66980984.94421647526-4.94421647525985
67910852.69940058731257.3005994126884
68730739.075528717327-9.0755287173273
69880843.07763345046436.9223665495357
70820933.542632254516-113.542632254516
71690742.79947937029-52.7994793702903
72990976.82864530113713.171354698863
73800850.895826922796-50.8958269227962
74960945.47837588374214.5216241162581
75910888.15490574165621.8450942583444
76950922.93399015093627.066009849064
77940861.71637776361778.2836222363831
781010972.35374461313137.6462553868694
79890887.1414202733092.858579726691
80660722.083333149189-62.0833331491888
81860847.7771333269412.2228666730601
82840836.6365355742853.36346442571494
83740703.30501175036436.6949882496358
84980994.073617189507-14.0736171895071
85820822.515581358317-2.51558135831681
861080967.214765239832112.785234760168
87930930.055786161393-0.0557861613931436
88970965.2073255269084.79267447309212
89930934.146198423032-4.14619842303159
9010101005.956190845094.0438091549106
91880893.141841119389-13.1418411193891
92740683.56920362225956.4307963777413
93860875.947163795256-15.947163795256
94810854.982609203017-44.9826092030168
95750736.07035217525213.9296478247484
96890990.521538545106-100.521538545106
97790813.251784981052-23.2517849810519
9810001029.64566244719-29.6456624471878
99890897.177608741447-7.17760874144665
100970934.15801662888235.8419833711179
101900901.85940765895-1.85940765894952
102990979.15675701195310.8432429880472
103910856.04982691864853.9501730813516
104730701.85711223492628.1428877650735
105850842.7818151849447.21818481505579
106840806.42322573280633.5767742671944
107830737.82854921284392.1714507871574
108950930.06835160097419.9316483990256

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 960 & 952.230235042735 & 7.76976495726467 \tabularnewline
14 & 900 & 895.096039292293 & 4.90396070770657 \tabularnewline
15 & 940 & 940.446868520135 & -0.446868520134558 \tabularnewline
16 & 920 & 921.644607418892 & -1.64460741889161 \tabularnewline
17 & 930 & 933.906626741883 & -3.90662674188343 \tabularnewline
18 & 970 & 979.15008139246 & -9.15008139245981 \tabularnewline
19 & 930 & 927.32768601518 & 2.67231398481965 \tabularnewline
20 & 780 & 827.735596161357 & -47.7355961613573 \tabularnewline
21 & 810 & 870.35825605989 & -60.3582560598898 \tabularnewline
22 & 870 & 819.295053585314 & 50.7049464146855 \tabularnewline
23 & 720 & 806.13992042404 & -86.1399204240399 \tabularnewline
24 & 880 & 898.579002763899 & -18.579002763899 \tabularnewline
25 & 920 & 916.79650669853 & 3.20349330146962 \tabularnewline
26 & 920 & 856.862389681875 & 63.1376103181254 \tabularnewline
27 & 950 & 907.496721591153 & 42.5032784088472 \tabularnewline
28 & 950 & 894.397450484121 & 55.6025495158794 \tabularnewline
29 & 890 & 913.942278811153 & -23.9422788111528 \tabularnewline
30 & 960 & 952.672789532324 & 7.32721046767574 \tabularnewline
31 & 780 & 911.034257166413 & -131.034257166413 \tabularnewline
32 & 780 & 758.026913857653 & 21.9730861423473 \tabularnewline
33 & 760 & 803.013907995232 & -43.0139079952318 \tabularnewline
34 & 860 & 826.653279036688 & 33.3467209633116 \tabularnewline
35 & 740 & 721.856495073088 & 18.1435049269116 \tabularnewline
36 & 1020 & 874.17898596869 & 145.82101403131 \tabularnewline
37 & 890 & 931.987980398623 & -41.9879803986229 \tabularnewline
38 & 1040 & 904.273718925798 & 135.726281074202 \tabularnewline
39 & 920 & 952.93623109945 & -32.9362310994503 \tabularnewline
40 & 900 & 937.004833057667 & -37.0048330576674 \tabularnewline
41 & 950 & 890.787284922377 & 59.212715077623 \tabularnewline
42 & 990 & 962.750833255348 & 27.2491667446521 \tabularnewline
43 & 840 & 834.525318580629 & 5.47468141937088 \tabularnewline
44 & 740 & 802.207864793759 & -62.2078647937589 \tabularnewline
45 & 840 & 792.400914698146 & 47.5990853018542 \tabularnewline
46 & 960 & 879.93446992325 & 80.0655300767497 \tabularnewline
47 & 790 & 772.91248722205 & 17.0875127779505 \tabularnewline
48 & 1010 & 1008.49043746047 & 1.50956253952916 \tabularnewline
49 & 900 & 922.520803806661 & -22.5208038066606 \tabularnewline
50 & 970 & 1013.52095875016 & -43.5209587501639 \tabularnewline
51 & 920 & 925.261694038639 & -5.26169403863946 \tabularnewline
52 & 980 & 911.021798769887 & 68.9782012301127 \tabularnewline
53 & 890 & 943.767988749406 & -53.767988749406 \tabularnewline
54 & 1000 & 977.764520582327 & 22.2354794176733 \tabularnewline
55 & 880 & 834.709948249639 & 45.2900517503608 \tabularnewline
56 & 740 & 764.66771659024 & -24.6677165902404 \tabularnewline
57 & 860 & 832.114450345881 & 27.8855496541194 \tabularnewline
58 & 940 & 937.879089969234 & 2.12091003076625 \tabularnewline
59 & 760 & 778.074299609854 & -18.0742996098542 \tabularnewline
60 & 1010 & 998.15263044499 & 11.8473695550098 \tabularnewline
61 & 870 & 898.173892202909 & -28.173892202909 \tabularnewline
62 & 980 & 974.676899094954 & 5.32310090504643 \tabularnewline
63 & 920 & 918.820069595399 & 1.17993040460146 \tabularnewline
64 & 950 & 953.868907517398 & -3.86890751739827 \tabularnewline
65 & 880 & 895.726297796234 & -15.7262977962339 \tabularnewline
66 & 980 & 984.94421647526 & -4.94421647525985 \tabularnewline
67 & 910 & 852.699400587312 & 57.3005994126884 \tabularnewline
68 & 730 & 739.075528717327 & -9.0755287173273 \tabularnewline
69 & 880 & 843.077633450464 & 36.9223665495357 \tabularnewline
70 & 820 & 933.542632254516 & -113.542632254516 \tabularnewline
71 & 690 & 742.79947937029 & -52.7994793702903 \tabularnewline
72 & 990 & 976.828645301137 & 13.171354698863 \tabularnewline
73 & 800 & 850.895826922796 & -50.8958269227962 \tabularnewline
74 & 960 & 945.478375883742 & 14.5216241162581 \tabularnewline
75 & 910 & 888.154905741656 & 21.8450942583444 \tabularnewline
76 & 950 & 922.933990150936 & 27.066009849064 \tabularnewline
77 & 940 & 861.716377763617 & 78.2836222363831 \tabularnewline
78 & 1010 & 972.353744613131 & 37.6462553868694 \tabularnewline
79 & 890 & 887.141420273309 & 2.858579726691 \tabularnewline
80 & 660 & 722.083333149189 & -62.0833331491888 \tabularnewline
81 & 860 & 847.77713332694 & 12.2228666730601 \tabularnewline
82 & 840 & 836.636535574285 & 3.36346442571494 \tabularnewline
83 & 740 & 703.305011750364 & 36.6949882496358 \tabularnewline
84 & 980 & 994.073617189507 & -14.0736171895071 \tabularnewline
85 & 820 & 822.515581358317 & -2.51558135831681 \tabularnewline
86 & 1080 & 967.214765239832 & 112.785234760168 \tabularnewline
87 & 930 & 930.055786161393 & -0.0557861613931436 \tabularnewline
88 & 970 & 965.207325526908 & 4.79267447309212 \tabularnewline
89 & 930 & 934.146198423032 & -4.14619842303159 \tabularnewline
90 & 1010 & 1005.95619084509 & 4.0438091549106 \tabularnewline
91 & 880 & 893.141841119389 & -13.1418411193891 \tabularnewline
92 & 740 & 683.569203622259 & 56.4307963777413 \tabularnewline
93 & 860 & 875.947163795256 & -15.947163795256 \tabularnewline
94 & 810 & 854.982609203017 & -44.9826092030168 \tabularnewline
95 & 750 & 736.070352175252 & 13.9296478247484 \tabularnewline
96 & 890 & 990.521538545106 & -100.521538545106 \tabularnewline
97 & 790 & 813.251784981052 & -23.2517849810519 \tabularnewline
98 & 1000 & 1029.64566244719 & -29.6456624471878 \tabularnewline
99 & 890 & 897.177608741447 & -7.17760874144665 \tabularnewline
100 & 970 & 934.158016628882 & 35.8419833711179 \tabularnewline
101 & 900 & 901.85940765895 & -1.85940765894952 \tabularnewline
102 & 990 & 979.156757011953 & 10.8432429880472 \tabularnewline
103 & 910 & 856.049826918648 & 53.9501730813516 \tabularnewline
104 & 730 & 701.857112234926 & 28.1428877650735 \tabularnewline
105 & 850 & 842.781815184944 & 7.21818481505579 \tabularnewline
106 & 840 & 806.423225732806 & 33.5767742671944 \tabularnewline
107 & 830 & 737.828549212843 & 92.1714507871574 \tabularnewline
108 & 950 & 930.068351600974 & 19.9316483990256 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296380&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]960[/C][C]952.230235042735[/C][C]7.76976495726467[/C][/ROW]
[ROW][C]14[/C][C]900[/C][C]895.096039292293[/C][C]4.90396070770657[/C][/ROW]
[ROW][C]15[/C][C]940[/C][C]940.446868520135[/C][C]-0.446868520134558[/C][/ROW]
[ROW][C]16[/C][C]920[/C][C]921.644607418892[/C][C]-1.64460741889161[/C][/ROW]
[ROW][C]17[/C][C]930[/C][C]933.906626741883[/C][C]-3.90662674188343[/C][/ROW]
[ROW][C]18[/C][C]970[/C][C]979.15008139246[/C][C]-9.15008139245981[/C][/ROW]
[ROW][C]19[/C][C]930[/C][C]927.32768601518[/C][C]2.67231398481965[/C][/ROW]
[ROW][C]20[/C][C]780[/C][C]827.735596161357[/C][C]-47.7355961613573[/C][/ROW]
[ROW][C]21[/C][C]810[/C][C]870.35825605989[/C][C]-60.3582560598898[/C][/ROW]
[ROW][C]22[/C][C]870[/C][C]819.295053585314[/C][C]50.7049464146855[/C][/ROW]
[ROW][C]23[/C][C]720[/C][C]806.13992042404[/C][C]-86.1399204240399[/C][/ROW]
[ROW][C]24[/C][C]880[/C][C]898.579002763899[/C][C]-18.579002763899[/C][/ROW]
[ROW][C]25[/C][C]920[/C][C]916.79650669853[/C][C]3.20349330146962[/C][/ROW]
[ROW][C]26[/C][C]920[/C][C]856.862389681875[/C][C]63.1376103181254[/C][/ROW]
[ROW][C]27[/C][C]950[/C][C]907.496721591153[/C][C]42.5032784088472[/C][/ROW]
[ROW][C]28[/C][C]950[/C][C]894.397450484121[/C][C]55.6025495158794[/C][/ROW]
[ROW][C]29[/C][C]890[/C][C]913.942278811153[/C][C]-23.9422788111528[/C][/ROW]
[ROW][C]30[/C][C]960[/C][C]952.672789532324[/C][C]7.32721046767574[/C][/ROW]
[ROW][C]31[/C][C]780[/C][C]911.034257166413[/C][C]-131.034257166413[/C][/ROW]
[ROW][C]32[/C][C]780[/C][C]758.026913857653[/C][C]21.9730861423473[/C][/ROW]
[ROW][C]33[/C][C]760[/C][C]803.013907995232[/C][C]-43.0139079952318[/C][/ROW]
[ROW][C]34[/C][C]860[/C][C]826.653279036688[/C][C]33.3467209633116[/C][/ROW]
[ROW][C]35[/C][C]740[/C][C]721.856495073088[/C][C]18.1435049269116[/C][/ROW]
[ROW][C]36[/C][C]1020[/C][C]874.17898596869[/C][C]145.82101403131[/C][/ROW]
[ROW][C]37[/C][C]890[/C][C]931.987980398623[/C][C]-41.9879803986229[/C][/ROW]
[ROW][C]38[/C][C]1040[/C][C]904.273718925798[/C][C]135.726281074202[/C][/ROW]
[ROW][C]39[/C][C]920[/C][C]952.93623109945[/C][C]-32.9362310994503[/C][/ROW]
[ROW][C]40[/C][C]900[/C][C]937.004833057667[/C][C]-37.0048330576674[/C][/ROW]
[ROW][C]41[/C][C]950[/C][C]890.787284922377[/C][C]59.212715077623[/C][/ROW]
[ROW][C]42[/C][C]990[/C][C]962.750833255348[/C][C]27.2491667446521[/C][/ROW]
[ROW][C]43[/C][C]840[/C][C]834.525318580629[/C][C]5.47468141937088[/C][/ROW]
[ROW][C]44[/C][C]740[/C][C]802.207864793759[/C][C]-62.2078647937589[/C][/ROW]
[ROW][C]45[/C][C]840[/C][C]792.400914698146[/C][C]47.5990853018542[/C][/ROW]
[ROW][C]46[/C][C]960[/C][C]879.93446992325[/C][C]80.0655300767497[/C][/ROW]
[ROW][C]47[/C][C]790[/C][C]772.91248722205[/C][C]17.0875127779505[/C][/ROW]
[ROW][C]48[/C][C]1010[/C][C]1008.49043746047[/C][C]1.50956253952916[/C][/ROW]
[ROW][C]49[/C][C]900[/C][C]922.520803806661[/C][C]-22.5208038066606[/C][/ROW]
[ROW][C]50[/C][C]970[/C][C]1013.52095875016[/C][C]-43.5209587501639[/C][/ROW]
[ROW][C]51[/C][C]920[/C][C]925.261694038639[/C][C]-5.26169403863946[/C][/ROW]
[ROW][C]52[/C][C]980[/C][C]911.021798769887[/C][C]68.9782012301127[/C][/ROW]
[ROW][C]53[/C][C]890[/C][C]943.767988749406[/C][C]-53.767988749406[/C][/ROW]
[ROW][C]54[/C][C]1000[/C][C]977.764520582327[/C][C]22.2354794176733[/C][/ROW]
[ROW][C]55[/C][C]880[/C][C]834.709948249639[/C][C]45.2900517503608[/C][/ROW]
[ROW][C]56[/C][C]740[/C][C]764.66771659024[/C][C]-24.6677165902404[/C][/ROW]
[ROW][C]57[/C][C]860[/C][C]832.114450345881[/C][C]27.8855496541194[/C][/ROW]
[ROW][C]58[/C][C]940[/C][C]937.879089969234[/C][C]2.12091003076625[/C][/ROW]
[ROW][C]59[/C][C]760[/C][C]778.074299609854[/C][C]-18.0742996098542[/C][/ROW]
[ROW][C]60[/C][C]1010[/C][C]998.15263044499[/C][C]11.8473695550098[/C][/ROW]
[ROW][C]61[/C][C]870[/C][C]898.173892202909[/C][C]-28.173892202909[/C][/ROW]
[ROW][C]62[/C][C]980[/C][C]974.676899094954[/C][C]5.32310090504643[/C][/ROW]
[ROW][C]63[/C][C]920[/C][C]918.820069595399[/C][C]1.17993040460146[/C][/ROW]
[ROW][C]64[/C][C]950[/C][C]953.868907517398[/C][C]-3.86890751739827[/C][/ROW]
[ROW][C]65[/C][C]880[/C][C]895.726297796234[/C][C]-15.7262977962339[/C][/ROW]
[ROW][C]66[/C][C]980[/C][C]984.94421647526[/C][C]-4.94421647525985[/C][/ROW]
[ROW][C]67[/C][C]910[/C][C]852.699400587312[/C][C]57.3005994126884[/C][/ROW]
[ROW][C]68[/C][C]730[/C][C]739.075528717327[/C][C]-9.0755287173273[/C][/ROW]
[ROW][C]69[/C][C]880[/C][C]843.077633450464[/C][C]36.9223665495357[/C][/ROW]
[ROW][C]70[/C][C]820[/C][C]933.542632254516[/C][C]-113.542632254516[/C][/ROW]
[ROW][C]71[/C][C]690[/C][C]742.79947937029[/C][C]-52.7994793702903[/C][/ROW]
[ROW][C]72[/C][C]990[/C][C]976.828645301137[/C][C]13.171354698863[/C][/ROW]
[ROW][C]73[/C][C]800[/C][C]850.895826922796[/C][C]-50.8958269227962[/C][/ROW]
[ROW][C]74[/C][C]960[/C][C]945.478375883742[/C][C]14.5216241162581[/C][/ROW]
[ROW][C]75[/C][C]910[/C][C]888.154905741656[/C][C]21.8450942583444[/C][/ROW]
[ROW][C]76[/C][C]950[/C][C]922.933990150936[/C][C]27.066009849064[/C][/ROW]
[ROW][C]77[/C][C]940[/C][C]861.716377763617[/C][C]78.2836222363831[/C][/ROW]
[ROW][C]78[/C][C]1010[/C][C]972.353744613131[/C][C]37.6462553868694[/C][/ROW]
[ROW][C]79[/C][C]890[/C][C]887.141420273309[/C][C]2.858579726691[/C][/ROW]
[ROW][C]80[/C][C]660[/C][C]722.083333149189[/C][C]-62.0833331491888[/C][/ROW]
[ROW][C]81[/C][C]860[/C][C]847.77713332694[/C][C]12.2228666730601[/C][/ROW]
[ROW][C]82[/C][C]840[/C][C]836.636535574285[/C][C]3.36346442571494[/C][/ROW]
[ROW][C]83[/C][C]740[/C][C]703.305011750364[/C][C]36.6949882496358[/C][/ROW]
[ROW][C]84[/C][C]980[/C][C]994.073617189507[/C][C]-14.0736171895071[/C][/ROW]
[ROW][C]85[/C][C]820[/C][C]822.515581358317[/C][C]-2.51558135831681[/C][/ROW]
[ROW][C]86[/C][C]1080[/C][C]967.214765239832[/C][C]112.785234760168[/C][/ROW]
[ROW][C]87[/C][C]930[/C][C]930.055786161393[/C][C]-0.0557861613931436[/C][/ROW]
[ROW][C]88[/C][C]970[/C][C]965.207325526908[/C][C]4.79267447309212[/C][/ROW]
[ROW][C]89[/C][C]930[/C][C]934.146198423032[/C][C]-4.14619842303159[/C][/ROW]
[ROW][C]90[/C][C]1010[/C][C]1005.95619084509[/C][C]4.0438091549106[/C][/ROW]
[ROW][C]91[/C][C]880[/C][C]893.141841119389[/C][C]-13.1418411193891[/C][/ROW]
[ROW][C]92[/C][C]740[/C][C]683.569203622259[/C][C]56.4307963777413[/C][/ROW]
[ROW][C]93[/C][C]860[/C][C]875.947163795256[/C][C]-15.947163795256[/C][/ROW]
[ROW][C]94[/C][C]810[/C][C]854.982609203017[/C][C]-44.9826092030168[/C][/ROW]
[ROW][C]95[/C][C]750[/C][C]736.070352175252[/C][C]13.9296478247484[/C][/ROW]
[ROW][C]96[/C][C]890[/C][C]990.521538545106[/C][C]-100.521538545106[/C][/ROW]
[ROW][C]97[/C][C]790[/C][C]813.251784981052[/C][C]-23.2517849810519[/C][/ROW]
[ROW][C]98[/C][C]1000[/C][C]1029.64566244719[/C][C]-29.6456624471878[/C][/ROW]
[ROW][C]99[/C][C]890[/C][C]897.177608741447[/C][C]-7.17760874144665[/C][/ROW]
[ROW][C]100[/C][C]970[/C][C]934.158016628882[/C][C]35.8419833711179[/C][/ROW]
[ROW][C]101[/C][C]900[/C][C]901.85940765895[/C][C]-1.85940765894952[/C][/ROW]
[ROW][C]102[/C][C]990[/C][C]979.156757011953[/C][C]10.8432429880472[/C][/ROW]
[ROW][C]103[/C][C]910[/C][C]856.049826918648[/C][C]53.9501730813516[/C][/ROW]
[ROW][C]104[/C][C]730[/C][C]701.857112234926[/C][C]28.1428877650735[/C][/ROW]
[ROW][C]105[/C][C]850[/C][C]842.781815184944[/C][C]7.21818481505579[/C][/ROW]
[ROW][C]106[/C][C]840[/C][C]806.423225732806[/C][C]33.5767742671944[/C][/ROW]
[ROW][C]107[/C][C]830[/C][C]737.828549212843[/C][C]92.1714507871574[/C][/ROW]
[ROW][C]108[/C][C]950[/C][C]930.068351600974[/C][C]19.9316483990256[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296380&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296380&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
13960952.2302350427357.76976495726467
14900895.0960392922934.90396070770657
15940940.446868520135-0.446868520134558
16920921.644607418892-1.64460741889161
17930933.906626741883-3.90662674188343
18970979.15008139246-9.15008139245981
19930927.327686015182.67231398481965
20780827.735596161357-47.7355961613573
21810870.35825605989-60.3582560598898
22870819.29505358531450.7049464146855
23720806.13992042404-86.1399204240399
24880898.579002763899-18.579002763899
25920916.796506698533.20349330146962
26920856.86238968187563.1376103181254
27950907.49672159115342.5032784088472
28950894.39745048412155.6025495158794
29890913.942278811153-23.9422788111528
30960952.6727895323247.32721046767574
31780911.034257166413-131.034257166413
32780758.02691385765321.9730861423473
33760803.013907995232-43.0139079952318
34860826.65327903668833.3467209633116
35740721.85649507308818.1435049269116
361020874.17898596869145.82101403131
37890931.987980398623-41.9879803986229
381040904.273718925798135.726281074202
39920952.93623109945-32.9362310994503
40900937.004833057667-37.0048330576674
41950890.78728492237759.212715077623
42990962.75083325534827.2491667446521
43840834.5253185806295.47468141937088
44740802.207864793759-62.2078647937589
45840792.40091469814647.5990853018542
46960879.9344699232580.0655300767497
47790772.9124872220517.0875127779505
4810101008.490437460471.50956253952916
49900922.520803806661-22.5208038066606
509701013.52095875016-43.5209587501639
51920925.261694038639-5.26169403863946
52980911.02179876988768.9782012301127
53890943.767988749406-53.767988749406
541000977.76452058232722.2354794176733
55880834.70994824963945.2900517503608
56740764.66771659024-24.6677165902404
57860832.11445034588127.8855496541194
58940937.8790899692342.12091003076625
59760778.074299609854-18.0742996098542
601010998.1526304449911.8473695550098
61870898.173892202909-28.173892202909
62980974.6768990949545.32310090504643
63920918.8200695953991.17993040460146
64950953.868907517398-3.86890751739827
65880895.726297796234-15.7262977962339
66980984.94421647526-4.94421647525985
67910852.69940058731257.3005994126884
68730739.075528717327-9.0755287173273
69880843.07763345046436.9223665495357
70820933.542632254516-113.542632254516
71690742.79947937029-52.7994793702903
72990976.82864530113713.171354698863
73800850.895826922796-50.8958269227962
74960945.47837588374214.5216241162581
75910888.15490574165621.8450942583444
76950922.93399015093627.066009849064
77940861.71637776361778.2836222363831
781010972.35374461313137.6462553868694
79890887.1414202733092.858579726691
80660722.083333149189-62.0833331491888
81860847.7771333269412.2228666730601
82840836.6365355742853.36346442571494
83740703.30501175036436.6949882496358
84980994.073617189507-14.0736171895071
85820822.515581358317-2.51558135831681
861080967.214765239832112.785234760168
87930930.055786161393-0.0557861613931436
88970965.2073255269084.79267447309212
89930934.146198423032-4.14619842303159
9010101005.956190845094.0438091549106
91880893.141841119389-13.1418411193891
92740683.56920362225956.4307963777413
93860875.947163795256-15.947163795256
94810854.982609203017-44.9826092030168
95750736.07035217525213.9296478247484
96890990.521538545106-100.521538545106
97790813.251784981052-23.2517849810519
9810001029.64566244719-29.6456624471878
99890897.177608741447-7.17760874144665
100970934.15801662888235.8419833711179
101900901.85940765895-1.85940765894952
102990979.15675701195310.8432429880472
103910856.04982691864853.9501730813516
104730701.85711223492628.1428877650735
105850842.7818151849447.21818481505579
106840806.42322573280633.5767742671944
107830737.82854921284392.1714507871574
108950930.06835160097419.9316483990256







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109821.737912457143730.835457212315912.640367701971
1101037.88847009732945.9071847936861129.86975540096
111924.943294698593831.8758404652711018.01074893192
112991.364914668638897.2040247024451085.52580463483
113929.445183543002834.1836614736541024.70670561235
1141015.63099512475919.261713419941112.00027682956
115919.198802354512821.7147007644551016.68290394457
116740.247099094905641.641183135841838.853015053968
117863.493969467102763.759308943209963.228629990994
118843.359051512671742.488779075795944.229323949548
119807.840808287227705.828118033781909.853498540673
120939.08253378011835.9206798844841042.24438767573

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 821.737912457143 & 730.835457212315 & 912.640367701971 \tabularnewline
110 & 1037.88847009732 & 945.907184793686 & 1129.86975540096 \tabularnewline
111 & 924.943294698593 & 831.875840465271 & 1018.01074893192 \tabularnewline
112 & 991.364914668638 & 897.204024702445 & 1085.52580463483 \tabularnewline
113 & 929.445183543002 & 834.183661473654 & 1024.70670561235 \tabularnewline
114 & 1015.63099512475 & 919.26171341994 & 1112.00027682956 \tabularnewline
115 & 919.198802354512 & 821.714700764455 & 1016.68290394457 \tabularnewline
116 & 740.247099094905 & 641.641183135841 & 838.853015053968 \tabularnewline
117 & 863.493969467102 & 763.759308943209 & 963.228629990994 \tabularnewline
118 & 843.359051512671 & 742.488779075795 & 944.229323949548 \tabularnewline
119 & 807.840808287227 & 705.828118033781 & 909.853498540673 \tabularnewline
120 & 939.08253378011 & 835.920679884484 & 1042.24438767573 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296380&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]821.737912457143[/C][C]730.835457212315[/C][C]912.640367701971[/C][/ROW]
[ROW][C]110[/C][C]1037.88847009732[/C][C]945.907184793686[/C][C]1129.86975540096[/C][/ROW]
[ROW][C]111[/C][C]924.943294698593[/C][C]831.875840465271[/C][C]1018.01074893192[/C][/ROW]
[ROW][C]112[/C][C]991.364914668638[/C][C]897.204024702445[/C][C]1085.52580463483[/C][/ROW]
[ROW][C]113[/C][C]929.445183543002[/C][C]834.183661473654[/C][C]1024.70670561235[/C][/ROW]
[ROW][C]114[/C][C]1015.63099512475[/C][C]919.26171341994[/C][C]1112.00027682956[/C][/ROW]
[ROW][C]115[/C][C]919.198802354512[/C][C]821.714700764455[/C][C]1016.68290394457[/C][/ROW]
[ROW][C]116[/C][C]740.247099094905[/C][C]641.641183135841[/C][C]838.853015053968[/C][/ROW]
[ROW][C]117[/C][C]863.493969467102[/C][C]763.759308943209[/C][C]963.228629990994[/C][/ROW]
[ROW][C]118[/C][C]843.359051512671[/C][C]742.488779075795[/C][C]944.229323949548[/C][/ROW]
[ROW][C]119[/C][C]807.840808287227[/C][C]705.828118033781[/C][C]909.853498540673[/C][/ROW]
[ROW][C]120[/C][C]939.08253378011[/C][C]835.920679884484[/C][C]1042.24438767573[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296380&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296380&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
109821.737912457143730.835457212315912.640367701971
1101037.88847009732945.9071847936861129.86975540096
111924.943294698593831.8758404652711018.01074893192
112991.364914668638897.2040247024451085.52580463483
113929.445183543002834.1836614736541024.70670561235
1141015.63099512475919.261713419941112.00027682956
115919.198802354512821.7147007644551016.68290394457
116740.247099094905641.641183135841838.853015053968
117863.493969467102763.759308943209963.228629990994
118843.359051512671742.488779075795944.229323949548
119807.840808287227705.828118033781909.853498540673
120939.08253378011835.9206798844841042.24438767573



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')