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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 computationMon, 15 Aug 2011 13:12:10 -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/15/t1313428383ewitcxraimi9i85.htm/, Retrieved Tue, 14 May 2024 21:56:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123801, Retrieved Tue, 14 May 2024 21:56:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBerns Sophie
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2011-08-15 17:12:10] [adf65953347764930908a56f01d4e8ba] [Current]
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Dataseries X:
860
950
780
840
840
900
860
810
870
930
790
930
820
930
730
860
800
890
850
890
850
1040
740
940
790
920
770
780
770
890
890
860
830
1020
740
940
780
860
820
760
780
900
820
980
830
930
770
960
750
850
850
820
730
960
760
940
880
890
830
850
850
860
800
840
760
910
650
990
780
910
820
780
890
810
830
890
760
860
670
940
740
920
800
800
920
810
790
850
780
900
710
960
760
920
740
800
870
740
710
900
740
880
700
1040
880
900
820
740




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=123801&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=123801&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123801&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
beta0
gamma0.97909557178997

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.97909557178997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123801&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.97909557178997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123801&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123801&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
beta0
gamma0.97909557178997







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13820829.983974358974-9.98397435897425
14930937.297494172494-7.29749417249411
15730735.02768065268-5.02768065268049
16860861.507867132867-1.50786713286698
17800799.2380536130530.761946386946533
18890891.134906759907-1.1349067599067
19850860.948426573427-10.9484265734266
20890813.67861305361376.321386946387
21850876.825466200466-26.8254662004663
221040938.305652680653101.694347319347
23740799.369172494173-59.3691724941726
24940941.682692307692-1.68269230769238
25790822.970947037476-32.9709470374759
26920932.91478770528-12.9147877052799
27770732.86733855150537.1326614484952
28780862.793758862467-82.7937588624671
29770802.746309708692-32.746309708692
30890892.785962339125-2.78596233912538
31890852.99110835955537.0088916404452
32860891.166782807927-31.1667828079272
33830853.323008794626-23.3230087946262
3410201040.63637557933-20.6363755793348
35740744.003316366531-4.00331636653118
36940942.797413482784-2.79741348278355
37780793.451476557599-13.4514765575994
38860923.032214014671-63.0322140146707
39820771.9860007067448.0139992932595
40760784.492993950617-24.4929939506169
41780773.4467806426876.55321935731331
42900892.8204767119527.17952328804802
43820891.988588043807-71.9885880438075
44980863.413761535984116.586238464016
45830833.249791925227-3.24979192522699
469301023.19362939405-93.1936293940513
47770742.84592480182427.154075198176
48960942.82071609156317.1792839084375
49750783.043433188255-33.0434331882551
50850864.079890155027-14.0798901550268
51850821.75853256093528.2414674390645
52820763.27424979592756.7257502040727
53730782.625246458638-52.6252464586383
54960902.61215393308157.3878460669193
55760824.267118032941-64.2671180329411
56940980.325069109989-40.3250691099894
57880832.83017280423647.1698271957637
58890934.710397297538-44.710397297538
59830772.19459734664857.8054026533522
60850962.403114655074-112.403114655074
61850753.45299183913596.5470081608653
62860853.0565698151896.94343018481129
63800852.171866033612-52.171866033612
64840821.57641838943718.4235816105632
65760733.86233844886826.1376615511324
66910961.562577654004-51.5625776540037
67650764.105705117423-114.105705117423
68990943.60521027451246.3947897254878
69780881.776179495944-101.776179495944
70910893.69688305278616.3031169472138
71820831.553848872319-11.553848872319
72780855.111960603129-75.1119606031286
73890850.74397776124639.2560222387541
74810862.617089324408-52.6170893244081
75830803.85286079032126.1471392096792
76890842.37710332308847.6228966769118
77760762.215844892764-2.21584489276415
78860913.84012396513-53.8401239651301
79670655.1475522832214.85244771678
80940991.792381211102-51.792381211102
81740784.889810600002-44.889810600002
82920912.4214304244157.57856957558488
83800823.003764366539-23.0037643665388
84800784.33241035038115.6675896496195
85920891.94161306353628.0583869364635
86810813.862167928641-3.8621679286407
87790832.215646767731-42.2156467677314
88850891.766708337502-41.7667083375017
89780762.80855873272317.1914412672768
90900863.88773476848636.1122652315139
91710672.45175583519937.5482441648007
92960943.84492787709216.1550721229081
93760743.70063358528816.2993664147125
94920922.60381209861-2.60381209861032
95740803.243118302999-63.2431183029986
96800802.434715759183-2.43471575918318
97870922.175693226835-52.1756932268353
98740812.842974174437-72.8429741744372
99710793.644731719434-83.6447317194339
100900853.63534691824846.3646530817516
101740782.402860512439-42.4028605124391
102880902.007331506204-22.0073315062041
103700711.977313187682-11.9773131876821
1041040962.42452521681777.5754747831834
105880762.421508827153117.578491172847
106900922.816668965326-22.8166689653257
107820744.08429898858175.9157010114186
108740802.813134103038-62.8131341030376

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 820 & 829.983974358974 & -9.98397435897425 \tabularnewline
14 & 930 & 937.297494172494 & -7.29749417249411 \tabularnewline
15 & 730 & 735.02768065268 & -5.02768065268049 \tabularnewline
16 & 860 & 861.507867132867 & -1.50786713286698 \tabularnewline
17 & 800 & 799.238053613053 & 0.761946386946533 \tabularnewline
18 & 890 & 891.134906759907 & -1.1349067599067 \tabularnewline
19 & 850 & 860.948426573427 & -10.9484265734266 \tabularnewline
20 & 890 & 813.678613053613 & 76.321386946387 \tabularnewline
21 & 850 & 876.825466200466 & -26.8254662004663 \tabularnewline
22 & 1040 & 938.305652680653 & 101.694347319347 \tabularnewline
23 & 740 & 799.369172494173 & -59.3691724941726 \tabularnewline
24 & 940 & 941.682692307692 & -1.68269230769238 \tabularnewline
25 & 790 & 822.970947037476 & -32.9709470374759 \tabularnewline
26 & 920 & 932.91478770528 & -12.9147877052799 \tabularnewline
27 & 770 & 732.867338551505 & 37.1326614484952 \tabularnewline
28 & 780 & 862.793758862467 & -82.7937588624671 \tabularnewline
29 & 770 & 802.746309708692 & -32.746309708692 \tabularnewline
30 & 890 & 892.785962339125 & -2.78596233912538 \tabularnewline
31 & 890 & 852.991108359555 & 37.0088916404452 \tabularnewline
32 & 860 & 891.166782807927 & -31.1667828079272 \tabularnewline
33 & 830 & 853.323008794626 & -23.3230087946262 \tabularnewline
34 & 1020 & 1040.63637557933 & -20.6363755793348 \tabularnewline
35 & 740 & 744.003316366531 & -4.00331636653118 \tabularnewline
36 & 940 & 942.797413482784 & -2.79741348278355 \tabularnewline
37 & 780 & 793.451476557599 & -13.4514765575994 \tabularnewline
38 & 860 & 923.032214014671 & -63.0322140146707 \tabularnewline
39 & 820 & 771.98600070674 & 48.0139992932595 \tabularnewline
40 & 760 & 784.492993950617 & -24.4929939506169 \tabularnewline
41 & 780 & 773.446780642687 & 6.55321935731331 \tabularnewline
42 & 900 & 892.820476711952 & 7.17952328804802 \tabularnewline
43 & 820 & 891.988588043807 & -71.9885880438075 \tabularnewline
44 & 980 & 863.413761535984 & 116.586238464016 \tabularnewline
45 & 830 & 833.249791925227 & -3.24979192522699 \tabularnewline
46 & 930 & 1023.19362939405 & -93.1936293940513 \tabularnewline
47 & 770 & 742.845924801824 & 27.154075198176 \tabularnewline
48 & 960 & 942.820716091563 & 17.1792839084375 \tabularnewline
49 & 750 & 783.043433188255 & -33.0434331882551 \tabularnewline
50 & 850 & 864.079890155027 & -14.0798901550268 \tabularnewline
51 & 850 & 821.758532560935 & 28.2414674390645 \tabularnewline
52 & 820 & 763.274249795927 & 56.7257502040727 \tabularnewline
53 & 730 & 782.625246458638 & -52.6252464586383 \tabularnewline
54 & 960 & 902.612153933081 & 57.3878460669193 \tabularnewline
55 & 760 & 824.267118032941 & -64.2671180329411 \tabularnewline
56 & 940 & 980.325069109989 & -40.3250691099894 \tabularnewline
57 & 880 & 832.830172804236 & 47.1698271957637 \tabularnewline
58 & 890 & 934.710397297538 & -44.710397297538 \tabularnewline
59 & 830 & 772.194597346648 & 57.8054026533522 \tabularnewline
60 & 850 & 962.403114655074 & -112.403114655074 \tabularnewline
61 & 850 & 753.452991839135 & 96.5470081608653 \tabularnewline
62 & 860 & 853.056569815189 & 6.94343018481129 \tabularnewline
63 & 800 & 852.171866033612 & -52.171866033612 \tabularnewline
64 & 840 & 821.576418389437 & 18.4235816105632 \tabularnewline
65 & 760 & 733.862338448868 & 26.1376615511324 \tabularnewline
66 & 910 & 961.562577654004 & -51.5625776540037 \tabularnewline
67 & 650 & 764.105705117423 & -114.105705117423 \tabularnewline
68 & 990 & 943.605210274512 & 46.3947897254878 \tabularnewline
69 & 780 & 881.776179495944 & -101.776179495944 \tabularnewline
70 & 910 & 893.696883052786 & 16.3031169472138 \tabularnewline
71 & 820 & 831.553848872319 & -11.553848872319 \tabularnewline
72 & 780 & 855.111960603129 & -75.1119606031286 \tabularnewline
73 & 890 & 850.743977761246 & 39.2560222387541 \tabularnewline
74 & 810 & 862.617089324408 & -52.6170893244081 \tabularnewline
75 & 830 & 803.852860790321 & 26.1471392096792 \tabularnewline
76 & 890 & 842.377103323088 & 47.6228966769118 \tabularnewline
77 & 760 & 762.215844892764 & -2.21584489276415 \tabularnewline
78 & 860 & 913.84012396513 & -53.8401239651301 \tabularnewline
79 & 670 & 655.14755228322 & 14.85244771678 \tabularnewline
80 & 940 & 991.792381211102 & -51.792381211102 \tabularnewline
81 & 740 & 784.889810600002 & -44.889810600002 \tabularnewline
82 & 920 & 912.421430424415 & 7.57856957558488 \tabularnewline
83 & 800 & 823.003764366539 & -23.0037643665388 \tabularnewline
84 & 800 & 784.332410350381 & 15.6675896496195 \tabularnewline
85 & 920 & 891.941613063536 & 28.0583869364635 \tabularnewline
86 & 810 & 813.862167928641 & -3.8621679286407 \tabularnewline
87 & 790 & 832.215646767731 & -42.2156467677314 \tabularnewline
88 & 850 & 891.766708337502 & -41.7667083375017 \tabularnewline
89 & 780 & 762.808558732723 & 17.1914412672768 \tabularnewline
90 & 900 & 863.887734768486 & 36.1122652315139 \tabularnewline
91 & 710 & 672.451755835199 & 37.5482441648007 \tabularnewline
92 & 960 & 943.844927877092 & 16.1550721229081 \tabularnewline
93 & 760 & 743.700633585288 & 16.2993664147125 \tabularnewline
94 & 920 & 922.60381209861 & -2.60381209861032 \tabularnewline
95 & 740 & 803.243118302999 & -63.2431183029986 \tabularnewline
96 & 800 & 802.434715759183 & -2.43471575918318 \tabularnewline
97 & 870 & 922.175693226835 & -52.1756932268353 \tabularnewline
98 & 740 & 812.842974174437 & -72.8429741744372 \tabularnewline
99 & 710 & 793.644731719434 & -83.6447317194339 \tabularnewline
100 & 900 & 853.635346918248 & 46.3646530817516 \tabularnewline
101 & 740 & 782.402860512439 & -42.4028605124391 \tabularnewline
102 & 880 & 902.007331506204 & -22.0073315062041 \tabularnewline
103 & 700 & 711.977313187682 & -11.9773131876821 \tabularnewline
104 & 1040 & 962.424525216817 & 77.5754747831834 \tabularnewline
105 & 880 & 762.421508827153 & 117.578491172847 \tabularnewline
106 & 900 & 922.816668965326 & -22.8166689653257 \tabularnewline
107 & 820 & 744.084298988581 & 75.9157010114186 \tabularnewline
108 & 740 & 802.813134103038 & -62.8131341030376 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123801&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]820[/C][C]829.983974358974[/C][C]-9.98397435897425[/C][/ROW]
[ROW][C]14[/C][C]930[/C][C]937.297494172494[/C][C]-7.29749417249411[/C][/ROW]
[ROW][C]15[/C][C]730[/C][C]735.02768065268[/C][C]-5.02768065268049[/C][/ROW]
[ROW][C]16[/C][C]860[/C][C]861.507867132867[/C][C]-1.50786713286698[/C][/ROW]
[ROW][C]17[/C][C]800[/C][C]799.238053613053[/C][C]0.761946386946533[/C][/ROW]
[ROW][C]18[/C][C]890[/C][C]891.134906759907[/C][C]-1.1349067599067[/C][/ROW]
[ROW][C]19[/C][C]850[/C][C]860.948426573427[/C][C]-10.9484265734266[/C][/ROW]
[ROW][C]20[/C][C]890[/C][C]813.678613053613[/C][C]76.321386946387[/C][/ROW]
[ROW][C]21[/C][C]850[/C][C]876.825466200466[/C][C]-26.8254662004663[/C][/ROW]
[ROW][C]22[/C][C]1040[/C][C]938.305652680653[/C][C]101.694347319347[/C][/ROW]
[ROW][C]23[/C][C]740[/C][C]799.369172494173[/C][C]-59.3691724941726[/C][/ROW]
[ROW][C]24[/C][C]940[/C][C]941.682692307692[/C][C]-1.68269230769238[/C][/ROW]
[ROW][C]25[/C][C]790[/C][C]822.970947037476[/C][C]-32.9709470374759[/C][/ROW]
[ROW][C]26[/C][C]920[/C][C]932.91478770528[/C][C]-12.9147877052799[/C][/ROW]
[ROW][C]27[/C][C]770[/C][C]732.867338551505[/C][C]37.1326614484952[/C][/ROW]
[ROW][C]28[/C][C]780[/C][C]862.793758862467[/C][C]-82.7937588624671[/C][/ROW]
[ROW][C]29[/C][C]770[/C][C]802.746309708692[/C][C]-32.746309708692[/C][/ROW]
[ROW][C]30[/C][C]890[/C][C]892.785962339125[/C][C]-2.78596233912538[/C][/ROW]
[ROW][C]31[/C][C]890[/C][C]852.991108359555[/C][C]37.0088916404452[/C][/ROW]
[ROW][C]32[/C][C]860[/C][C]891.166782807927[/C][C]-31.1667828079272[/C][/ROW]
[ROW][C]33[/C][C]830[/C][C]853.323008794626[/C][C]-23.3230087946262[/C][/ROW]
[ROW][C]34[/C][C]1020[/C][C]1040.63637557933[/C][C]-20.6363755793348[/C][/ROW]
[ROW][C]35[/C][C]740[/C][C]744.003316366531[/C][C]-4.00331636653118[/C][/ROW]
[ROW][C]36[/C][C]940[/C][C]942.797413482784[/C][C]-2.79741348278355[/C][/ROW]
[ROW][C]37[/C][C]780[/C][C]793.451476557599[/C][C]-13.4514765575994[/C][/ROW]
[ROW][C]38[/C][C]860[/C][C]923.032214014671[/C][C]-63.0322140146707[/C][/ROW]
[ROW][C]39[/C][C]820[/C][C]771.98600070674[/C][C]48.0139992932595[/C][/ROW]
[ROW][C]40[/C][C]760[/C][C]784.492993950617[/C][C]-24.4929939506169[/C][/ROW]
[ROW][C]41[/C][C]780[/C][C]773.446780642687[/C][C]6.55321935731331[/C][/ROW]
[ROW][C]42[/C][C]900[/C][C]892.820476711952[/C][C]7.17952328804802[/C][/ROW]
[ROW][C]43[/C][C]820[/C][C]891.988588043807[/C][C]-71.9885880438075[/C][/ROW]
[ROW][C]44[/C][C]980[/C][C]863.413761535984[/C][C]116.586238464016[/C][/ROW]
[ROW][C]45[/C][C]830[/C][C]833.249791925227[/C][C]-3.24979192522699[/C][/ROW]
[ROW][C]46[/C][C]930[/C][C]1023.19362939405[/C][C]-93.1936293940513[/C][/ROW]
[ROW][C]47[/C][C]770[/C][C]742.845924801824[/C][C]27.154075198176[/C][/ROW]
[ROW][C]48[/C][C]960[/C][C]942.820716091563[/C][C]17.1792839084375[/C][/ROW]
[ROW][C]49[/C][C]750[/C][C]783.043433188255[/C][C]-33.0434331882551[/C][/ROW]
[ROW][C]50[/C][C]850[/C][C]864.079890155027[/C][C]-14.0798901550268[/C][/ROW]
[ROW][C]51[/C][C]850[/C][C]821.758532560935[/C][C]28.2414674390645[/C][/ROW]
[ROW][C]52[/C][C]820[/C][C]763.274249795927[/C][C]56.7257502040727[/C][/ROW]
[ROW][C]53[/C][C]730[/C][C]782.625246458638[/C][C]-52.6252464586383[/C][/ROW]
[ROW][C]54[/C][C]960[/C][C]902.612153933081[/C][C]57.3878460669193[/C][/ROW]
[ROW][C]55[/C][C]760[/C][C]824.267118032941[/C][C]-64.2671180329411[/C][/ROW]
[ROW][C]56[/C][C]940[/C][C]980.325069109989[/C][C]-40.3250691099894[/C][/ROW]
[ROW][C]57[/C][C]880[/C][C]832.830172804236[/C][C]47.1698271957637[/C][/ROW]
[ROW][C]58[/C][C]890[/C][C]934.710397297538[/C][C]-44.710397297538[/C][/ROW]
[ROW][C]59[/C][C]830[/C][C]772.194597346648[/C][C]57.8054026533522[/C][/ROW]
[ROW][C]60[/C][C]850[/C][C]962.403114655074[/C][C]-112.403114655074[/C][/ROW]
[ROW][C]61[/C][C]850[/C][C]753.452991839135[/C][C]96.5470081608653[/C][/ROW]
[ROW][C]62[/C][C]860[/C][C]853.056569815189[/C][C]6.94343018481129[/C][/ROW]
[ROW][C]63[/C][C]800[/C][C]852.171866033612[/C][C]-52.171866033612[/C][/ROW]
[ROW][C]64[/C][C]840[/C][C]821.576418389437[/C][C]18.4235816105632[/C][/ROW]
[ROW][C]65[/C][C]760[/C][C]733.862338448868[/C][C]26.1376615511324[/C][/ROW]
[ROW][C]66[/C][C]910[/C][C]961.562577654004[/C][C]-51.5625776540037[/C][/ROW]
[ROW][C]67[/C][C]650[/C][C]764.105705117423[/C][C]-114.105705117423[/C][/ROW]
[ROW][C]68[/C][C]990[/C][C]943.605210274512[/C][C]46.3947897254878[/C][/ROW]
[ROW][C]69[/C][C]780[/C][C]881.776179495944[/C][C]-101.776179495944[/C][/ROW]
[ROW][C]70[/C][C]910[/C][C]893.696883052786[/C][C]16.3031169472138[/C][/ROW]
[ROW][C]71[/C][C]820[/C][C]831.553848872319[/C][C]-11.553848872319[/C][/ROW]
[ROW][C]72[/C][C]780[/C][C]855.111960603129[/C][C]-75.1119606031286[/C][/ROW]
[ROW][C]73[/C][C]890[/C][C]850.743977761246[/C][C]39.2560222387541[/C][/ROW]
[ROW][C]74[/C][C]810[/C][C]862.617089324408[/C][C]-52.6170893244081[/C][/ROW]
[ROW][C]75[/C][C]830[/C][C]803.852860790321[/C][C]26.1471392096792[/C][/ROW]
[ROW][C]76[/C][C]890[/C][C]842.377103323088[/C][C]47.6228966769118[/C][/ROW]
[ROW][C]77[/C][C]760[/C][C]762.215844892764[/C][C]-2.21584489276415[/C][/ROW]
[ROW][C]78[/C][C]860[/C][C]913.84012396513[/C][C]-53.8401239651301[/C][/ROW]
[ROW][C]79[/C][C]670[/C][C]655.14755228322[/C][C]14.85244771678[/C][/ROW]
[ROW][C]80[/C][C]940[/C][C]991.792381211102[/C][C]-51.792381211102[/C][/ROW]
[ROW][C]81[/C][C]740[/C][C]784.889810600002[/C][C]-44.889810600002[/C][/ROW]
[ROW][C]82[/C][C]920[/C][C]912.421430424415[/C][C]7.57856957558488[/C][/ROW]
[ROW][C]83[/C][C]800[/C][C]823.003764366539[/C][C]-23.0037643665388[/C][/ROW]
[ROW][C]84[/C][C]800[/C][C]784.332410350381[/C][C]15.6675896496195[/C][/ROW]
[ROW][C]85[/C][C]920[/C][C]891.941613063536[/C][C]28.0583869364635[/C][/ROW]
[ROW][C]86[/C][C]810[/C][C]813.862167928641[/C][C]-3.8621679286407[/C][/ROW]
[ROW][C]87[/C][C]790[/C][C]832.215646767731[/C][C]-42.2156467677314[/C][/ROW]
[ROW][C]88[/C][C]850[/C][C]891.766708337502[/C][C]-41.7667083375017[/C][/ROW]
[ROW][C]89[/C][C]780[/C][C]762.808558732723[/C][C]17.1914412672768[/C][/ROW]
[ROW][C]90[/C][C]900[/C][C]863.887734768486[/C][C]36.1122652315139[/C][/ROW]
[ROW][C]91[/C][C]710[/C][C]672.451755835199[/C][C]37.5482441648007[/C][/ROW]
[ROW][C]92[/C][C]960[/C][C]943.844927877092[/C][C]16.1550721229081[/C][/ROW]
[ROW][C]93[/C][C]760[/C][C]743.700633585288[/C][C]16.2993664147125[/C][/ROW]
[ROW][C]94[/C][C]920[/C][C]922.60381209861[/C][C]-2.60381209861032[/C][/ROW]
[ROW][C]95[/C][C]740[/C][C]803.243118302999[/C][C]-63.2431183029986[/C][/ROW]
[ROW][C]96[/C][C]800[/C][C]802.434715759183[/C][C]-2.43471575918318[/C][/ROW]
[ROW][C]97[/C][C]870[/C][C]922.175693226835[/C][C]-52.1756932268353[/C][/ROW]
[ROW][C]98[/C][C]740[/C][C]812.842974174437[/C][C]-72.8429741744372[/C][/ROW]
[ROW][C]99[/C][C]710[/C][C]793.644731719434[/C][C]-83.6447317194339[/C][/ROW]
[ROW][C]100[/C][C]900[/C][C]853.635346918248[/C][C]46.3646530817516[/C][/ROW]
[ROW][C]101[/C][C]740[/C][C]782.402860512439[/C][C]-42.4028605124391[/C][/ROW]
[ROW][C]102[/C][C]880[/C][C]902.007331506204[/C][C]-22.0073315062041[/C][/ROW]
[ROW][C]103[/C][C]700[/C][C]711.977313187682[/C][C]-11.9773131876821[/C][/ROW]
[ROW][C]104[/C][C]1040[/C][C]962.424525216817[/C][C]77.5754747831834[/C][/ROW]
[ROW][C]105[/C][C]880[/C][C]762.421508827153[/C][C]117.578491172847[/C][/ROW]
[ROW][C]106[/C][C]900[/C][C]922.816668965326[/C][C]-22.8166689653257[/C][/ROW]
[ROW][C]107[/C][C]820[/C][C]744.084298988581[/C][C]75.9157010114186[/C][/ROW]
[ROW][C]108[/C][C]740[/C][C]802.813134103038[/C][C]-62.8131341030376[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123801&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123801&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
13820829.983974358974-9.98397435897425
14930937.297494172494-7.29749417249411
15730735.02768065268-5.02768065268049
16860861.507867132867-1.50786713286698
17800799.2380536130530.761946386946533
18890891.134906759907-1.1349067599067
19850860.948426573427-10.9484265734266
20890813.67861305361376.321386946387
21850876.825466200466-26.8254662004663
221040938.305652680653101.694347319347
23740799.369172494173-59.3691724941726
24940941.682692307692-1.68269230769238
25790822.970947037476-32.9709470374759
26920932.91478770528-12.9147877052799
27770732.86733855150537.1326614484952
28780862.793758862467-82.7937588624671
29770802.746309708692-32.746309708692
30890892.785962339125-2.78596233912538
31890852.99110835955537.0088916404452
32860891.166782807927-31.1667828079272
33830853.323008794626-23.3230087946262
3410201040.63637557933-20.6363755793348
35740744.003316366531-4.00331636653118
36940942.797413482784-2.79741348278355
37780793.451476557599-13.4514765575994
38860923.032214014671-63.0322140146707
39820771.9860007067448.0139992932595
40760784.492993950617-24.4929939506169
41780773.4467806426876.55321935731331
42900892.8204767119527.17952328804802
43820891.988588043807-71.9885880438075
44980863.413761535984116.586238464016
45830833.249791925227-3.24979192522699
469301023.19362939405-93.1936293940513
47770742.84592480182427.154075198176
48960942.82071609156317.1792839084375
49750783.043433188255-33.0434331882551
50850864.079890155027-14.0798901550268
51850821.75853256093528.2414674390645
52820763.27424979592756.7257502040727
53730782.625246458638-52.6252464586383
54960902.61215393308157.3878460669193
55760824.267118032941-64.2671180329411
56940980.325069109989-40.3250691099894
57880832.83017280423647.1698271957637
58890934.710397297538-44.710397297538
59830772.19459734664857.8054026533522
60850962.403114655074-112.403114655074
61850753.45299183913596.5470081608653
62860853.0565698151896.94343018481129
63800852.171866033612-52.171866033612
64840821.57641838943718.4235816105632
65760733.86233844886826.1376615511324
66910961.562577654004-51.5625776540037
67650764.105705117423-114.105705117423
68990943.60521027451246.3947897254878
69780881.776179495944-101.776179495944
70910893.69688305278616.3031169472138
71820831.553848872319-11.553848872319
72780855.111960603129-75.1119606031286
73890850.74397776124639.2560222387541
74810862.617089324408-52.6170893244081
75830803.85286079032126.1471392096792
76890842.37710332308847.6228966769118
77760762.215844892764-2.21584489276415
78860913.84012396513-53.8401239651301
79670655.1475522832214.85244771678
80940991.792381211102-51.792381211102
81740784.889810600002-44.889810600002
82920912.4214304244157.57856957558488
83800823.003764366539-23.0037643665388
84800784.33241035038115.6675896496195
85920891.94161306353628.0583869364635
86810813.862167928641-3.8621679286407
87790832.215646767731-42.2156467677314
88850891.766708337502-41.7667083375017
89780762.80855873272317.1914412672768
90900863.88773476848636.1122652315139
91710672.45175583519937.5482441648007
92960943.84492787709216.1550721229081
93760743.70063358528816.2993664147125
94920922.60381209861-2.60381209861032
95740803.243118302999-63.2431183029986
96800802.434715759183-2.43471575918318
97870922.175693226835-52.1756932268353
98740812.842974174437-72.8429741744372
99710793.644731719434-83.6447317194339
100900853.63534691824846.3646530817516
101740782.402860512439-42.4028605124391
102880902.007331506204-22.0073315062041
103700711.977313187682-11.9773131876821
1041040962.42452521681777.5754747831834
105880762.421508827153117.578491172847
106900922.816668965326-22.8166689653257
107820744.08429898858175.9157010114186
108740802.813134103038-62.8131341030376







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109873.852940795607777.718910749652969.986970841562
110744.284978486472648.150948440517840.419008532427
111714.510783051614618.376753005659810.644813097569
112901.793011200407805.658981154452997.927041246362
113743.64864531572647.514615269765839.782675361675
114883.222288443804787.088258397849979.356318489759
115703.012616645919606.878586599964799.146646691874
1161041.14056681877945.0065367728191137.27459686473
117880.304326634472784.170296588517976.438356680427
118903.239207180616807.105177134661999.373237226571
119821.175263440431725.041233394476917.309293486386
120744.075310414742647.941280368787840.209340460697

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 873.852940795607 & 777.718910749652 & 969.986970841562 \tabularnewline
110 & 744.284978486472 & 648.150948440517 & 840.419008532427 \tabularnewline
111 & 714.510783051614 & 618.376753005659 & 810.644813097569 \tabularnewline
112 & 901.793011200407 & 805.658981154452 & 997.927041246362 \tabularnewline
113 & 743.64864531572 & 647.514615269765 & 839.782675361675 \tabularnewline
114 & 883.222288443804 & 787.088258397849 & 979.356318489759 \tabularnewline
115 & 703.012616645919 & 606.878586599964 & 799.146646691874 \tabularnewline
116 & 1041.14056681877 & 945.006536772819 & 1137.27459686473 \tabularnewline
117 & 880.304326634472 & 784.170296588517 & 976.438356680427 \tabularnewline
118 & 903.239207180616 & 807.105177134661 & 999.373237226571 \tabularnewline
119 & 821.175263440431 & 725.041233394476 & 917.309293486386 \tabularnewline
120 & 744.075310414742 & 647.941280368787 & 840.209340460697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123801&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]873.852940795607[/C][C]777.718910749652[/C][C]969.986970841562[/C][/ROW]
[ROW][C]110[/C][C]744.284978486472[/C][C]648.150948440517[/C][C]840.419008532427[/C][/ROW]
[ROW][C]111[/C][C]714.510783051614[/C][C]618.376753005659[/C][C]810.644813097569[/C][/ROW]
[ROW][C]112[/C][C]901.793011200407[/C][C]805.658981154452[/C][C]997.927041246362[/C][/ROW]
[ROW][C]113[/C][C]743.64864531572[/C][C]647.514615269765[/C][C]839.782675361675[/C][/ROW]
[ROW][C]114[/C][C]883.222288443804[/C][C]787.088258397849[/C][C]979.356318489759[/C][/ROW]
[ROW][C]115[/C][C]703.012616645919[/C][C]606.878586599964[/C][C]799.146646691874[/C][/ROW]
[ROW][C]116[/C][C]1041.14056681877[/C][C]945.006536772819[/C][C]1137.27459686473[/C][/ROW]
[ROW][C]117[/C][C]880.304326634472[/C][C]784.170296588517[/C][C]976.438356680427[/C][/ROW]
[ROW][C]118[/C][C]903.239207180616[/C][C]807.105177134661[/C][C]999.373237226571[/C][/ROW]
[ROW][C]119[/C][C]821.175263440431[/C][C]725.041233394476[/C][C]917.309293486386[/C][/ROW]
[ROW][C]120[/C][C]744.075310414742[/C][C]647.941280368787[/C][C]840.209340460697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123801&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123801&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
109873.852940795607777.718910749652969.986970841562
110744.284978486472648.150948440517840.419008532427
111714.510783051614618.376753005659810.644813097569
112901.793011200407805.658981154452997.927041246362
113743.64864531572647.514615269765839.782675361675
114883.222288443804787.088258397849979.356318489759
115703.012616645919606.878586599964799.146646691874
1161041.14056681877945.0065367728191137.27459686473
117880.304326634472784.170296588517976.438356680427
118903.239207180616807.105177134661999.373237226571
119821.175263440431725.041233394476917.309293486386
120744.075310414742647.941280368787840.209340460697



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')