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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 18 Dec 2010 12:59:24 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/18/t12926770215x6b6a0z7txnly9.htm/, Retrieved Tue, 30 Apr 2024 01:28:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111929, Retrieved Tue, 30 Apr 2024 01:28:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2010-12-18 12:59:24] [aedc5b8e4f26bdca34b1a0cf88d6dfa2] [Current]
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Dataseries X:
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111929&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111929&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111929&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.458869668369215
beta0.0711214003368765
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.458869668369215 \tabularnewline
beta & 0.0711214003368765 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111929&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]0.458869668369215[/C][/ROW]
[ROW][C]beta[/C][C]0.0711214003368765[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111929&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111929&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
alpha0.458869668369215
beta0.0711214003368765
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3472324
43527.79612292213807.20387707786197
53025.12011628368294.87988371631707
64321.536956799679021.4630432003210
78226.263762354511155.7362376454889
84048.5364746639713-8.53647466397128
94741.03779706981815.96220293018186
101940.3867020508952-21.3867020508952
115226.488059355170625.5119406448294
1213634.9423750299138101.057624970086
138081.3603752267783-1.36037522677834
144280.7374651759678-38.7374651759678
155461.6991275165035-7.69912751650345
166656.65207704838749.34792295161262
178159.732474678997321.2675253210027
186368.9764916272027-5.9764916272027
1913765.524010039425271.4759899605748
207299.9447743308188-27.9447743308188
2110787.83237510273619.1676248972640
225897.963971013387-39.9639710133869
233679.6576288052268-43.6576288052268
245258.231592561216-6.23159256121597
257953.775858308313225.2241416916868
267764.577407700744512.4225922992555
275469.910131300781-15.910131300781
288461.722593070031822.2774069299682
294871.7851911184991-23.7851911184991
309659.934819580204136.0651804197959
318376.72497169592816.27502830407185
326680.0501149833582-14.0501149833582
336173.5901346383135-12.5901346383135
345367.3892102379062-14.3892102379062
353059.8931462137544-29.8931462137544
367444.307219850111629.6927801498884
376957.032505098924511.9674949010755
385962.0147592058625-3.01475920586248
394260.023723305792-18.023723305792
406550.557316644823414.4426833551766
417056.460102760927913.5398972390721
4210062.390508396531437.6094916034686
436380.5931236260234-17.5931236260234
4410572.890773546024432.1092264539756
458289.0432235276216-7.04322352762159
468186.9999429771944-5.99994297719438
477585.2395813676036-10.2395813676036
4810281.199604915380320.8003950846197
4912192.081762488182628.9182375118174
5098107.632711515764-9.63271151576438
5176105.179431440083-29.1794314400825
527792.8044705004144-15.8044705004144
536386.0510873912678-23.0510873912678
543775.2201689045499-38.2201689045499
553556.1812864736566-21.1812864736566
562344.2697694858315-21.2697694858315
574031.62350175695628.37649824304384
582932.8543778871680-3.85437788716804
593728.34708657377398.6529134262261
605129.861403630333421.1385963696666
612037.7948895549917-17.7948895549917
622827.28223541635400.717764583645952
631325.2879013155591-12.2879013155591
642216.92464038607285.07535961392715
652516.69448990320838.30551009679168
661318.2176115888137-5.21761158881375
671613.36510379143312.63489620856690
681312.20186467529620.798135324703777
691610.22183920969305.77816079030695
701710.71556927509346.28443072490658
71911.6467065034724-2.64670650347244
72178.393239286983318.60676071301669
732510.584532378187114.4154676218129
741415.911720203901-1.91172020390099
75813.6844669110252-5.68446691102515
7679.54049943290813-2.54049943290813
77106.756292918017073.24370708198293
7876.732143179666750.267856820333247
79105.351207647411064.64879235258894
8036.13226599611504-3.13226599611504

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 47 & 23 & 24 \tabularnewline
4 & 35 & 27.7961229221380 & 7.20387707786197 \tabularnewline
5 & 30 & 25.1201162836829 & 4.87988371631707 \tabularnewline
6 & 43 & 21.5369567996790 & 21.4630432003210 \tabularnewline
7 & 82 & 26.2637623545111 & 55.7362376454889 \tabularnewline
8 & 40 & 48.5364746639713 & -8.53647466397128 \tabularnewline
9 & 47 & 41.0377970698181 & 5.96220293018186 \tabularnewline
10 & 19 & 40.3867020508952 & -21.3867020508952 \tabularnewline
11 & 52 & 26.4880593551706 & 25.5119406448294 \tabularnewline
12 & 136 & 34.9423750299138 & 101.057624970086 \tabularnewline
13 & 80 & 81.3603752267783 & -1.36037522677834 \tabularnewline
14 & 42 & 80.7374651759678 & -38.7374651759678 \tabularnewline
15 & 54 & 61.6991275165035 & -7.69912751650345 \tabularnewline
16 & 66 & 56.6520770483874 & 9.34792295161262 \tabularnewline
17 & 81 & 59.7324746789973 & 21.2675253210027 \tabularnewline
18 & 63 & 68.9764916272027 & -5.9764916272027 \tabularnewline
19 & 137 & 65.5240100394252 & 71.4759899605748 \tabularnewline
20 & 72 & 99.9447743308188 & -27.9447743308188 \tabularnewline
21 & 107 & 87.832375102736 & 19.1676248972640 \tabularnewline
22 & 58 & 97.963971013387 & -39.9639710133869 \tabularnewline
23 & 36 & 79.6576288052268 & -43.6576288052268 \tabularnewline
24 & 52 & 58.231592561216 & -6.23159256121597 \tabularnewline
25 & 79 & 53.7758583083132 & 25.2241416916868 \tabularnewline
26 & 77 & 64.5774077007445 & 12.4225922992555 \tabularnewline
27 & 54 & 69.910131300781 & -15.910131300781 \tabularnewline
28 & 84 & 61.7225930700318 & 22.2774069299682 \tabularnewline
29 & 48 & 71.7851911184991 & -23.7851911184991 \tabularnewline
30 & 96 & 59.9348195802041 & 36.0651804197959 \tabularnewline
31 & 83 & 76.7249716959281 & 6.27502830407185 \tabularnewline
32 & 66 & 80.0501149833582 & -14.0501149833582 \tabularnewline
33 & 61 & 73.5901346383135 & -12.5901346383135 \tabularnewline
34 & 53 & 67.3892102379062 & -14.3892102379062 \tabularnewline
35 & 30 & 59.8931462137544 & -29.8931462137544 \tabularnewline
36 & 74 & 44.3072198501116 & 29.6927801498884 \tabularnewline
37 & 69 & 57.0325050989245 & 11.9674949010755 \tabularnewline
38 & 59 & 62.0147592058625 & -3.01475920586248 \tabularnewline
39 & 42 & 60.023723305792 & -18.023723305792 \tabularnewline
40 & 65 & 50.5573166448234 & 14.4426833551766 \tabularnewline
41 & 70 & 56.4601027609279 & 13.5398972390721 \tabularnewline
42 & 100 & 62.3905083965314 & 37.6094916034686 \tabularnewline
43 & 63 & 80.5931236260234 & -17.5931236260234 \tabularnewline
44 & 105 & 72.8907735460244 & 32.1092264539756 \tabularnewline
45 & 82 & 89.0432235276216 & -7.04322352762159 \tabularnewline
46 & 81 & 86.9999429771944 & -5.99994297719438 \tabularnewline
47 & 75 & 85.2395813676036 & -10.2395813676036 \tabularnewline
48 & 102 & 81.1996049153803 & 20.8003950846197 \tabularnewline
49 & 121 & 92.0817624881826 & 28.9182375118174 \tabularnewline
50 & 98 & 107.632711515764 & -9.63271151576438 \tabularnewline
51 & 76 & 105.179431440083 & -29.1794314400825 \tabularnewline
52 & 77 & 92.8044705004144 & -15.8044705004144 \tabularnewline
53 & 63 & 86.0510873912678 & -23.0510873912678 \tabularnewline
54 & 37 & 75.2201689045499 & -38.2201689045499 \tabularnewline
55 & 35 & 56.1812864736566 & -21.1812864736566 \tabularnewline
56 & 23 & 44.2697694858315 & -21.2697694858315 \tabularnewline
57 & 40 & 31.6235017569562 & 8.37649824304384 \tabularnewline
58 & 29 & 32.8543778871680 & -3.85437788716804 \tabularnewline
59 & 37 & 28.3470865737739 & 8.6529134262261 \tabularnewline
60 & 51 & 29.8614036303334 & 21.1385963696666 \tabularnewline
61 & 20 & 37.7948895549917 & -17.7948895549917 \tabularnewline
62 & 28 & 27.2822354163540 & 0.717764583645952 \tabularnewline
63 & 13 & 25.2879013155591 & -12.2879013155591 \tabularnewline
64 & 22 & 16.9246403860728 & 5.07535961392715 \tabularnewline
65 & 25 & 16.6944899032083 & 8.30551009679168 \tabularnewline
66 & 13 & 18.2176115888137 & -5.21761158881375 \tabularnewline
67 & 16 & 13.3651037914331 & 2.63489620856690 \tabularnewline
68 & 13 & 12.2018646752962 & 0.798135324703777 \tabularnewline
69 & 16 & 10.2218392096930 & 5.77816079030695 \tabularnewline
70 & 17 & 10.7155692750934 & 6.28443072490658 \tabularnewline
71 & 9 & 11.6467065034724 & -2.64670650347244 \tabularnewline
72 & 17 & 8.39323928698331 & 8.60676071301669 \tabularnewline
73 & 25 & 10.5845323781871 & 14.4154676218129 \tabularnewline
74 & 14 & 15.911720203901 & -1.91172020390099 \tabularnewline
75 & 8 & 13.6844669110252 & -5.68446691102515 \tabularnewline
76 & 7 & 9.54049943290813 & -2.54049943290813 \tabularnewline
77 & 10 & 6.75629291801707 & 3.24370708198293 \tabularnewline
78 & 7 & 6.73214317966675 & 0.267856820333247 \tabularnewline
79 & 10 & 5.35120764741106 & 4.64879235258894 \tabularnewline
80 & 3 & 6.13226599611504 & -3.13226599611504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111929&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]3[/C][C]47[/C][C]23[/C][C]24[/C][/ROW]
[ROW][C]4[/C][C]35[/C][C]27.7961229221380[/C][C]7.20387707786197[/C][/ROW]
[ROW][C]5[/C][C]30[/C][C]25.1201162836829[/C][C]4.87988371631707[/C][/ROW]
[ROW][C]6[/C][C]43[/C][C]21.5369567996790[/C][C]21.4630432003210[/C][/ROW]
[ROW][C]7[/C][C]82[/C][C]26.2637623545111[/C][C]55.7362376454889[/C][/ROW]
[ROW][C]8[/C][C]40[/C][C]48.5364746639713[/C][C]-8.53647466397128[/C][/ROW]
[ROW][C]9[/C][C]47[/C][C]41.0377970698181[/C][C]5.96220293018186[/C][/ROW]
[ROW][C]10[/C][C]19[/C][C]40.3867020508952[/C][C]-21.3867020508952[/C][/ROW]
[ROW][C]11[/C][C]52[/C][C]26.4880593551706[/C][C]25.5119406448294[/C][/ROW]
[ROW][C]12[/C][C]136[/C][C]34.9423750299138[/C][C]101.057624970086[/C][/ROW]
[ROW][C]13[/C][C]80[/C][C]81.3603752267783[/C][C]-1.36037522677834[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]80.7374651759678[/C][C]-38.7374651759678[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]61.6991275165035[/C][C]-7.69912751650345[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]56.6520770483874[/C][C]9.34792295161262[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]59.7324746789973[/C][C]21.2675253210027[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]68.9764916272027[/C][C]-5.9764916272027[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]65.5240100394252[/C][C]71.4759899605748[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]99.9447743308188[/C][C]-27.9447743308188[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]87.832375102736[/C][C]19.1676248972640[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]97.963971013387[/C][C]-39.9639710133869[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]79.6576288052268[/C][C]-43.6576288052268[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]58.231592561216[/C][C]-6.23159256121597[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]53.7758583083132[/C][C]25.2241416916868[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]64.5774077007445[/C][C]12.4225922992555[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]69.910131300781[/C][C]-15.910131300781[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]61.7225930700318[/C][C]22.2774069299682[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]71.7851911184991[/C][C]-23.7851911184991[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]59.9348195802041[/C][C]36.0651804197959[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]76.7249716959281[/C][C]6.27502830407185[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]80.0501149833582[/C][C]-14.0501149833582[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]73.5901346383135[/C][C]-12.5901346383135[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]67.3892102379062[/C][C]-14.3892102379062[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]59.8931462137544[/C][C]-29.8931462137544[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]44.3072198501116[/C][C]29.6927801498884[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]57.0325050989245[/C][C]11.9674949010755[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]62.0147592058625[/C][C]-3.01475920586248[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]60.023723305792[/C][C]-18.023723305792[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]50.5573166448234[/C][C]14.4426833551766[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]56.4601027609279[/C][C]13.5398972390721[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]62.3905083965314[/C][C]37.6094916034686[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]80.5931236260234[/C][C]-17.5931236260234[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]72.8907735460244[/C][C]32.1092264539756[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]89.0432235276216[/C][C]-7.04322352762159[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]86.9999429771944[/C][C]-5.99994297719438[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]85.2395813676036[/C][C]-10.2395813676036[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]81.1996049153803[/C][C]20.8003950846197[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]92.0817624881826[/C][C]28.9182375118174[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]107.632711515764[/C][C]-9.63271151576438[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]105.179431440083[/C][C]-29.1794314400825[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]92.8044705004144[/C][C]-15.8044705004144[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]86.0510873912678[/C][C]-23.0510873912678[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]75.2201689045499[/C][C]-38.2201689045499[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]56.1812864736566[/C][C]-21.1812864736566[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]44.2697694858315[/C][C]-21.2697694858315[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]31.6235017569562[/C][C]8.37649824304384[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]32.8543778871680[/C][C]-3.85437788716804[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]28.3470865737739[/C][C]8.6529134262261[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]29.8614036303334[/C][C]21.1385963696666[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]37.7948895549917[/C][C]-17.7948895549917[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]27.2822354163540[/C][C]0.717764583645952[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]25.2879013155591[/C][C]-12.2879013155591[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]16.9246403860728[/C][C]5.07535961392715[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]16.6944899032083[/C][C]8.30551009679168[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]18.2176115888137[/C][C]-5.21761158881375[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]13.3651037914331[/C][C]2.63489620856690[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]12.2018646752962[/C][C]0.798135324703777[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]10.2218392096930[/C][C]5.77816079030695[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]10.7155692750934[/C][C]6.28443072490658[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]11.6467065034724[/C][C]-2.64670650347244[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]8.39323928698331[/C][C]8.60676071301669[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]10.5845323781871[/C][C]14.4154676218129[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]15.911720203901[/C][C]-1.91172020390099[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]13.6844669110252[/C][C]-5.68446691102515[/C][/ROW]
[ROW][C]76[/C][C]7[/C][C]9.54049943290813[/C][C]-2.54049943290813[/C][/ROW]
[ROW][C]77[/C][C]10[/C][C]6.75629291801707[/C][C]3.24370708198293[/C][/ROW]
[ROW][C]78[/C][C]7[/C][C]6.73214317966675[/C][C]0.267856820333247[/C][/ROW]
[ROW][C]79[/C][C]10[/C][C]5.35120764741106[/C][C]4.64879235258894[/C][/ROW]
[ROW][C]80[/C][C]3[/C][C]6.13226599611504[/C][C]-3.13226599611504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111929&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111929&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
3472324
43527.79612292213807.20387707786197
53025.12011628368294.87988371631707
64321.536956799679021.4630432003210
78226.263762354511155.7362376454889
84048.5364746639713-8.53647466397128
94741.03779706981815.96220293018186
101940.3867020508952-21.3867020508952
115226.488059355170625.5119406448294
1213634.9423750299138101.057624970086
138081.3603752267783-1.36037522677834
144280.7374651759678-38.7374651759678
155461.6991275165035-7.69912751650345
166656.65207704838749.34792295161262
178159.732474678997321.2675253210027
186368.9764916272027-5.9764916272027
1913765.524010039425271.4759899605748
207299.9447743308188-27.9447743308188
2110787.83237510273619.1676248972640
225897.963971013387-39.9639710133869
233679.6576288052268-43.6576288052268
245258.231592561216-6.23159256121597
257953.775858308313225.2241416916868
267764.577407700744512.4225922992555
275469.910131300781-15.910131300781
288461.722593070031822.2774069299682
294871.7851911184991-23.7851911184991
309659.934819580204136.0651804197959
318376.72497169592816.27502830407185
326680.0501149833582-14.0501149833582
336173.5901346383135-12.5901346383135
345367.3892102379062-14.3892102379062
353059.8931462137544-29.8931462137544
367444.307219850111629.6927801498884
376957.032505098924511.9674949010755
385962.0147592058625-3.01475920586248
394260.023723305792-18.023723305792
406550.557316644823414.4426833551766
417056.460102760927913.5398972390721
4210062.390508396531437.6094916034686
436380.5931236260234-17.5931236260234
4410572.890773546024432.1092264539756
458289.0432235276216-7.04322352762159
468186.9999429771944-5.99994297719438
477585.2395813676036-10.2395813676036
4810281.199604915380320.8003950846197
4912192.081762488182628.9182375118174
5098107.632711515764-9.63271151576438
5176105.179431440083-29.1794314400825
527792.8044705004144-15.8044705004144
536386.0510873912678-23.0510873912678
543775.2201689045499-38.2201689045499
553556.1812864736566-21.1812864736566
562344.2697694858315-21.2697694858315
574031.62350175695628.37649824304384
582932.8543778871680-3.85437788716804
593728.34708657377398.6529134262261
605129.861403630333421.1385963696666
612037.7948895549917-17.7948895549917
622827.28223541635400.717764583645952
631325.2879013155591-12.2879013155591
642216.92464038607285.07535961392715
652516.69448990320838.30551009679168
661318.2176115888137-5.21761158881375
671613.36510379143312.63489620856690
681312.20186467529620.798135324703777
691610.22183920969305.77816079030695
701710.71556927509346.28443072490658
71911.6467065034724-2.64670650347244
72178.393239286983318.60676071301669
732510.584532378187114.4154676218129
741415.911720203901-1.91172020390099
75813.6844669110252-5.68446691102515
7679.54049943290813-2.54049943290813
77106.756292918017073.24370708198293
7876.732143179666750.267856820333247
79105.351207647411064.64879235258894
8036.13226599611504-3.13226599611504







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
813.24060975987728-43.515313575413849.9965330951684
821.78625538252099-50.312040395025253.8845511600672
830.331901005164704-57.24248234686257.9062843571914
84-1.12245337219158-64.308723237547962.0638164931648
85-2.57680774954787-71.511373915999766.357758416904
86-4.03116212690416-78.8501136283970.7877893745816
87-5.48551650426044-86.32402663037375.3529936218522
88-6.93987088161673-93.931817667962580.052075904729
89-8.39422525897302-101.67195308735584.8835025694094
90-9.8485796363293-109.54275486783189.8455955951728
91-11.3029340136856-117.54246408939394.9365960620216
92-12.7572883910419-125.669284130717100.154707348633

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 3.24060975987728 & -43.5153135754138 & 49.9965330951684 \tabularnewline
82 & 1.78625538252099 & -50.3120403950252 & 53.8845511600672 \tabularnewline
83 & 0.331901005164704 & -57.242482346862 & 57.9062843571914 \tabularnewline
84 & -1.12245337219158 & -64.3087232375479 & 62.0638164931648 \tabularnewline
85 & -2.57680774954787 & -71.5113739159997 & 66.357758416904 \tabularnewline
86 & -4.03116212690416 & -78.85011362839 & 70.7877893745816 \tabularnewline
87 & -5.48551650426044 & -86.324026630373 & 75.3529936218522 \tabularnewline
88 & -6.93987088161673 & -93.9318176679625 & 80.052075904729 \tabularnewline
89 & -8.39422525897302 & -101.671953087355 & 84.8835025694094 \tabularnewline
90 & -9.8485796363293 & -109.542754867831 & 89.8455955951728 \tabularnewline
91 & -11.3029340136856 & -117.542464089393 & 94.9365960620216 \tabularnewline
92 & -12.7572883910419 & -125.669284130717 & 100.154707348633 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111929&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]81[/C][C]3.24060975987728[/C][C]-43.5153135754138[/C][C]49.9965330951684[/C][/ROW]
[ROW][C]82[/C][C]1.78625538252099[/C][C]-50.3120403950252[/C][C]53.8845511600672[/C][/ROW]
[ROW][C]83[/C][C]0.331901005164704[/C][C]-57.242482346862[/C][C]57.9062843571914[/C][/ROW]
[ROW][C]84[/C][C]-1.12245337219158[/C][C]-64.3087232375479[/C][C]62.0638164931648[/C][/ROW]
[ROW][C]85[/C][C]-2.57680774954787[/C][C]-71.5113739159997[/C][C]66.357758416904[/C][/ROW]
[ROW][C]86[/C][C]-4.03116212690416[/C][C]-78.85011362839[/C][C]70.7877893745816[/C][/ROW]
[ROW][C]87[/C][C]-5.48551650426044[/C][C]-86.324026630373[/C][C]75.3529936218522[/C][/ROW]
[ROW][C]88[/C][C]-6.93987088161673[/C][C]-93.9318176679625[/C][C]80.052075904729[/C][/ROW]
[ROW][C]89[/C][C]-8.39422525897302[/C][C]-101.671953087355[/C][C]84.8835025694094[/C][/ROW]
[ROW][C]90[/C][C]-9.8485796363293[/C][C]-109.542754867831[/C][C]89.8455955951728[/C][/ROW]
[ROW][C]91[/C][C]-11.3029340136856[/C][C]-117.542464089393[/C][C]94.9365960620216[/C][/ROW]
[ROW][C]92[/C][C]-12.7572883910419[/C][C]-125.669284130717[/C][C]100.154707348633[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111929&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111929&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
813.24060975987728-43.515313575413849.9965330951684
821.78625538252099-50.312040395025253.8845511600672
830.331901005164704-57.24248234686257.9062843571914
84-1.12245337219158-64.308723237547962.0638164931648
85-2.57680774954787-71.511373915999766.357758416904
86-4.03116212690416-78.8501136283970.7877893745816
87-5.48551650426044-86.32402663037375.3529936218522
88-6.93987088161673-93.931817667962580.052075904729
89-8.39422525897302-101.67195308735584.8835025694094
90-9.8485796363293-109.54275486783189.8455955951728
91-11.3029340136856-117.54246408939394.9365960620216
92-12.7572883910419-125.669284130717100.154707348633



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')