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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 17 Jan 2010 05:31:49 -0700
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/Jan/17/t1263731998ujzkqj7amo6i1d0.htm/, Retrieved Sun, 28 Apr 2024 13:37:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72260, Retrieved Sun, 28 Apr 2024 13:37:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact179
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-01-17 12:31:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
3,81
3,95
3,99
4
4,06
4,16
4,19
4,2
4,2
4,2
4,2
4,2
4,23
4,38
4,43
4,44
4,44
4,44
4,44
4,44
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,46
4,46
4,46
4,48
4,58
4,67
4,68
4,68
4,69
4,69
4,69
4,69
4,69
4,69
4,69
4,73
4,78
4,79
4,79
4,8
4,8
4,81
5,16
5,26
5,29
5,29
5,29
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,35
5,44
5,47
5,47
5,48
5,48
5,48
5,48
5,48




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72260&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72260&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72260&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.344199179309432
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.344199179309432 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72260&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.344199179309432[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72260&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72260&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
alpha1
beta0.344199179309432
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33.994.09-0.0999999999999996
444.09558008206906-0.0955800820690573
54.064.07268149626256-0.0126814962625597
64.164.128316535656570.0316834643434296
74.194.23922195808126-0.049221958081259
84.24.25227980050569-0.0522798005056861
94.24.24428513607717-0.0442851360771686
104.24.2290422285838-0.0290422285838003
114.24.21904591733994-0.0190459173399393
124.24.21249032822234-0.0124903282223370
134.234.20819116749890.0218088325010974
144.384.245697749747480.134302250252522
154.434.44192447406381-0.0119244740638056
164.444.48782007987735-0.0478200798773463
174.444.48136044762905-0.041360447629053
184.444.46712421549926-0.0271242154992626
194.444.457788082785-0.0177880827850041
204.444.45166543928892-0.0116654392889171
214.454.447650204659390.00234979534061175
224.454.45845900228717-0.00845900228717156
234.454.45554742064215-0.00554742064215041
244.454.45363800300984-0.00363800300983819
254.454.45238580535953-0.00238580535952693
264.454.45156461311279-0.00156461311278555
274.454.45102607456343-0.00102607456342785
284.454.45067290054079-0.000672900540785726
294.464.450441288726890.00955871127310903
304.464.46373138930235-0.00373138930235051
314.464.4624470481668-0.00244704816679775
324.484.461604776196060.0183952238039451
334.584.487936397132590.0920636028674133
344.674.619624613683820.0503753863161807
354.684.72696378031124-0.0469637803112448
364.684.72079888567085-0.0407988856708457
374.694.7067559427062-0.0167559427062001
384.694.71098856097817-0.0209885609781715
394.694.7037643155146-0.0137643155145986
404.694.69902664941072-0.00902664941071762
414.694.69591968409163-0.00591968409163446
424.694.69388213368552-0.00388213368552304
434.694.692545906457-0.00254590645699615
444.734.69166960754390.0383303924561007
454.784.74486289716990.0351371028301015
464.794.80695705912733-0.0169570591273303
474.794.8111204532922-0.0211204532922018
484.84.80385081060238-0.00385081060238246
494.84.81252536475337-0.0125253647533663
504.814.808214144484710.0017858555152932
515.164.818828834487440.341171165512565
525.265.2862596696609-0.0262596696609032
535.295.37722111291468-0.0872211129146834
545.295.37719967743099-0.087199677430994
555.295.3471856200232-0.0571856200231986
565.35.32750237654291-0.0275023765429125
575.35.32803608110778-0.0280360811077829
585.35.31838608499943-0.0183860849994311
595.35.31205760963191-0.0120576096319134
605.35.30790739029218-0.0079073902921758
615.35.30518567304313-0.00518567304312967
625.35.30340076863752-0.00340076863751726
635.35.30223022686346-0.00223022686346219
645.355.301462584607380.048537415392615
655.445.368169123151320.0718308768486766
665.475.48289325201172-0.0128932520117164
675.475.50845540525065-0.0384554052506534
685.485.49521908632337-0.0152190863233663
695.485.49998068930103-0.0199806893010246
705.485.49310335244158-0.0131033524415756
715.485.48859318928498-0.00859318928498265
725.485.48563542058544-0.00563542058544098

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3.99 & 4.09 & -0.0999999999999996 \tabularnewline
4 & 4 & 4.09558008206906 & -0.0955800820690573 \tabularnewline
5 & 4.06 & 4.07268149626256 & -0.0126814962625597 \tabularnewline
6 & 4.16 & 4.12831653565657 & 0.0316834643434296 \tabularnewline
7 & 4.19 & 4.23922195808126 & -0.049221958081259 \tabularnewline
8 & 4.2 & 4.25227980050569 & -0.0522798005056861 \tabularnewline
9 & 4.2 & 4.24428513607717 & -0.0442851360771686 \tabularnewline
10 & 4.2 & 4.2290422285838 & -0.0290422285838003 \tabularnewline
11 & 4.2 & 4.21904591733994 & -0.0190459173399393 \tabularnewline
12 & 4.2 & 4.21249032822234 & -0.0124903282223370 \tabularnewline
13 & 4.23 & 4.2081911674989 & 0.0218088325010974 \tabularnewline
14 & 4.38 & 4.24569774974748 & 0.134302250252522 \tabularnewline
15 & 4.43 & 4.44192447406381 & -0.0119244740638056 \tabularnewline
16 & 4.44 & 4.48782007987735 & -0.0478200798773463 \tabularnewline
17 & 4.44 & 4.48136044762905 & -0.041360447629053 \tabularnewline
18 & 4.44 & 4.46712421549926 & -0.0271242154992626 \tabularnewline
19 & 4.44 & 4.457788082785 & -0.0177880827850041 \tabularnewline
20 & 4.44 & 4.45166543928892 & -0.0116654392889171 \tabularnewline
21 & 4.45 & 4.44765020465939 & 0.00234979534061175 \tabularnewline
22 & 4.45 & 4.45845900228717 & -0.00845900228717156 \tabularnewline
23 & 4.45 & 4.45554742064215 & -0.00554742064215041 \tabularnewline
24 & 4.45 & 4.45363800300984 & -0.00363800300983819 \tabularnewline
25 & 4.45 & 4.45238580535953 & -0.00238580535952693 \tabularnewline
26 & 4.45 & 4.45156461311279 & -0.00156461311278555 \tabularnewline
27 & 4.45 & 4.45102607456343 & -0.00102607456342785 \tabularnewline
28 & 4.45 & 4.45067290054079 & -0.000672900540785726 \tabularnewline
29 & 4.46 & 4.45044128872689 & 0.00955871127310903 \tabularnewline
30 & 4.46 & 4.46373138930235 & -0.00373138930235051 \tabularnewline
31 & 4.46 & 4.4624470481668 & -0.00244704816679775 \tabularnewline
32 & 4.48 & 4.46160477619606 & 0.0183952238039451 \tabularnewline
33 & 4.58 & 4.48793639713259 & 0.0920636028674133 \tabularnewline
34 & 4.67 & 4.61962461368382 & 0.0503753863161807 \tabularnewline
35 & 4.68 & 4.72696378031124 & -0.0469637803112448 \tabularnewline
36 & 4.68 & 4.72079888567085 & -0.0407988856708457 \tabularnewline
37 & 4.69 & 4.7067559427062 & -0.0167559427062001 \tabularnewline
38 & 4.69 & 4.71098856097817 & -0.0209885609781715 \tabularnewline
39 & 4.69 & 4.7037643155146 & -0.0137643155145986 \tabularnewline
40 & 4.69 & 4.69902664941072 & -0.00902664941071762 \tabularnewline
41 & 4.69 & 4.69591968409163 & -0.00591968409163446 \tabularnewline
42 & 4.69 & 4.69388213368552 & -0.00388213368552304 \tabularnewline
43 & 4.69 & 4.692545906457 & -0.00254590645699615 \tabularnewline
44 & 4.73 & 4.6916696075439 & 0.0383303924561007 \tabularnewline
45 & 4.78 & 4.7448628971699 & 0.0351371028301015 \tabularnewline
46 & 4.79 & 4.80695705912733 & -0.0169570591273303 \tabularnewline
47 & 4.79 & 4.8111204532922 & -0.0211204532922018 \tabularnewline
48 & 4.8 & 4.80385081060238 & -0.00385081060238246 \tabularnewline
49 & 4.8 & 4.81252536475337 & -0.0125253647533663 \tabularnewline
50 & 4.81 & 4.80821414448471 & 0.0017858555152932 \tabularnewline
51 & 5.16 & 4.81882883448744 & 0.341171165512565 \tabularnewline
52 & 5.26 & 5.2862596696609 & -0.0262596696609032 \tabularnewline
53 & 5.29 & 5.37722111291468 & -0.0872211129146834 \tabularnewline
54 & 5.29 & 5.37719967743099 & -0.087199677430994 \tabularnewline
55 & 5.29 & 5.3471856200232 & -0.0571856200231986 \tabularnewline
56 & 5.3 & 5.32750237654291 & -0.0275023765429125 \tabularnewline
57 & 5.3 & 5.32803608110778 & -0.0280360811077829 \tabularnewline
58 & 5.3 & 5.31838608499943 & -0.0183860849994311 \tabularnewline
59 & 5.3 & 5.31205760963191 & -0.0120576096319134 \tabularnewline
60 & 5.3 & 5.30790739029218 & -0.0079073902921758 \tabularnewline
61 & 5.3 & 5.30518567304313 & -0.00518567304312967 \tabularnewline
62 & 5.3 & 5.30340076863752 & -0.00340076863751726 \tabularnewline
63 & 5.3 & 5.30223022686346 & -0.00223022686346219 \tabularnewline
64 & 5.35 & 5.30146258460738 & 0.048537415392615 \tabularnewline
65 & 5.44 & 5.36816912315132 & 0.0718308768486766 \tabularnewline
66 & 5.47 & 5.48289325201172 & -0.0128932520117164 \tabularnewline
67 & 5.47 & 5.50845540525065 & -0.0384554052506534 \tabularnewline
68 & 5.48 & 5.49521908632337 & -0.0152190863233663 \tabularnewline
69 & 5.48 & 5.49998068930103 & -0.0199806893010246 \tabularnewline
70 & 5.48 & 5.49310335244158 & -0.0131033524415756 \tabularnewline
71 & 5.48 & 5.48859318928498 & -0.00859318928498265 \tabularnewline
72 & 5.48 & 5.48563542058544 & -0.00563542058544098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72260&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]3.99[/C][C]4.09[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]4[/C][C]4[/C][C]4.09558008206906[/C][C]-0.0955800820690573[/C][/ROW]
[ROW][C]5[/C][C]4.06[/C][C]4.07268149626256[/C][C]-0.0126814962625597[/C][/ROW]
[ROW][C]6[/C][C]4.16[/C][C]4.12831653565657[/C][C]0.0316834643434296[/C][/ROW]
[ROW][C]7[/C][C]4.19[/C][C]4.23922195808126[/C][C]-0.049221958081259[/C][/ROW]
[ROW][C]8[/C][C]4.2[/C][C]4.25227980050569[/C][C]-0.0522798005056861[/C][/ROW]
[ROW][C]9[/C][C]4.2[/C][C]4.24428513607717[/C][C]-0.0442851360771686[/C][/ROW]
[ROW][C]10[/C][C]4.2[/C][C]4.2290422285838[/C][C]-0.0290422285838003[/C][/ROW]
[ROW][C]11[/C][C]4.2[/C][C]4.21904591733994[/C][C]-0.0190459173399393[/C][/ROW]
[ROW][C]12[/C][C]4.2[/C][C]4.21249032822234[/C][C]-0.0124903282223370[/C][/ROW]
[ROW][C]13[/C][C]4.23[/C][C]4.2081911674989[/C][C]0.0218088325010974[/C][/ROW]
[ROW][C]14[/C][C]4.38[/C][C]4.24569774974748[/C][C]0.134302250252522[/C][/ROW]
[ROW][C]15[/C][C]4.43[/C][C]4.44192447406381[/C][C]-0.0119244740638056[/C][/ROW]
[ROW][C]16[/C][C]4.44[/C][C]4.48782007987735[/C][C]-0.0478200798773463[/C][/ROW]
[ROW][C]17[/C][C]4.44[/C][C]4.48136044762905[/C][C]-0.041360447629053[/C][/ROW]
[ROW][C]18[/C][C]4.44[/C][C]4.46712421549926[/C][C]-0.0271242154992626[/C][/ROW]
[ROW][C]19[/C][C]4.44[/C][C]4.457788082785[/C][C]-0.0177880827850041[/C][/ROW]
[ROW][C]20[/C][C]4.44[/C][C]4.45166543928892[/C][C]-0.0116654392889171[/C][/ROW]
[ROW][C]21[/C][C]4.45[/C][C]4.44765020465939[/C][C]0.00234979534061175[/C][/ROW]
[ROW][C]22[/C][C]4.45[/C][C]4.45845900228717[/C][C]-0.00845900228717156[/C][/ROW]
[ROW][C]23[/C][C]4.45[/C][C]4.45554742064215[/C][C]-0.00554742064215041[/C][/ROW]
[ROW][C]24[/C][C]4.45[/C][C]4.45363800300984[/C][C]-0.00363800300983819[/C][/ROW]
[ROW][C]25[/C][C]4.45[/C][C]4.45238580535953[/C][C]-0.00238580535952693[/C][/ROW]
[ROW][C]26[/C][C]4.45[/C][C]4.45156461311279[/C][C]-0.00156461311278555[/C][/ROW]
[ROW][C]27[/C][C]4.45[/C][C]4.45102607456343[/C][C]-0.00102607456342785[/C][/ROW]
[ROW][C]28[/C][C]4.45[/C][C]4.45067290054079[/C][C]-0.000672900540785726[/C][/ROW]
[ROW][C]29[/C][C]4.46[/C][C]4.45044128872689[/C][C]0.00955871127310903[/C][/ROW]
[ROW][C]30[/C][C]4.46[/C][C]4.46373138930235[/C][C]-0.00373138930235051[/C][/ROW]
[ROW][C]31[/C][C]4.46[/C][C]4.4624470481668[/C][C]-0.00244704816679775[/C][/ROW]
[ROW][C]32[/C][C]4.48[/C][C]4.46160477619606[/C][C]0.0183952238039451[/C][/ROW]
[ROW][C]33[/C][C]4.58[/C][C]4.48793639713259[/C][C]0.0920636028674133[/C][/ROW]
[ROW][C]34[/C][C]4.67[/C][C]4.61962461368382[/C][C]0.0503753863161807[/C][/ROW]
[ROW][C]35[/C][C]4.68[/C][C]4.72696378031124[/C][C]-0.0469637803112448[/C][/ROW]
[ROW][C]36[/C][C]4.68[/C][C]4.72079888567085[/C][C]-0.0407988856708457[/C][/ROW]
[ROW][C]37[/C][C]4.69[/C][C]4.7067559427062[/C][C]-0.0167559427062001[/C][/ROW]
[ROW][C]38[/C][C]4.69[/C][C]4.71098856097817[/C][C]-0.0209885609781715[/C][/ROW]
[ROW][C]39[/C][C]4.69[/C][C]4.7037643155146[/C][C]-0.0137643155145986[/C][/ROW]
[ROW][C]40[/C][C]4.69[/C][C]4.69902664941072[/C][C]-0.00902664941071762[/C][/ROW]
[ROW][C]41[/C][C]4.69[/C][C]4.69591968409163[/C][C]-0.00591968409163446[/C][/ROW]
[ROW][C]42[/C][C]4.69[/C][C]4.69388213368552[/C][C]-0.00388213368552304[/C][/ROW]
[ROW][C]43[/C][C]4.69[/C][C]4.692545906457[/C][C]-0.00254590645699615[/C][/ROW]
[ROW][C]44[/C][C]4.73[/C][C]4.6916696075439[/C][C]0.0383303924561007[/C][/ROW]
[ROW][C]45[/C][C]4.78[/C][C]4.7448628971699[/C][C]0.0351371028301015[/C][/ROW]
[ROW][C]46[/C][C]4.79[/C][C]4.80695705912733[/C][C]-0.0169570591273303[/C][/ROW]
[ROW][C]47[/C][C]4.79[/C][C]4.8111204532922[/C][C]-0.0211204532922018[/C][/ROW]
[ROW][C]48[/C][C]4.8[/C][C]4.80385081060238[/C][C]-0.00385081060238246[/C][/ROW]
[ROW][C]49[/C][C]4.8[/C][C]4.81252536475337[/C][C]-0.0125253647533663[/C][/ROW]
[ROW][C]50[/C][C]4.81[/C][C]4.80821414448471[/C][C]0.0017858555152932[/C][/ROW]
[ROW][C]51[/C][C]5.16[/C][C]4.81882883448744[/C][C]0.341171165512565[/C][/ROW]
[ROW][C]52[/C][C]5.26[/C][C]5.2862596696609[/C][C]-0.0262596696609032[/C][/ROW]
[ROW][C]53[/C][C]5.29[/C][C]5.37722111291468[/C][C]-0.0872211129146834[/C][/ROW]
[ROW][C]54[/C][C]5.29[/C][C]5.37719967743099[/C][C]-0.087199677430994[/C][/ROW]
[ROW][C]55[/C][C]5.29[/C][C]5.3471856200232[/C][C]-0.0571856200231986[/C][/ROW]
[ROW][C]56[/C][C]5.3[/C][C]5.32750237654291[/C][C]-0.0275023765429125[/C][/ROW]
[ROW][C]57[/C][C]5.3[/C][C]5.32803608110778[/C][C]-0.0280360811077829[/C][/ROW]
[ROW][C]58[/C][C]5.3[/C][C]5.31838608499943[/C][C]-0.0183860849994311[/C][/ROW]
[ROW][C]59[/C][C]5.3[/C][C]5.31205760963191[/C][C]-0.0120576096319134[/C][/ROW]
[ROW][C]60[/C][C]5.3[/C][C]5.30790739029218[/C][C]-0.0079073902921758[/C][/ROW]
[ROW][C]61[/C][C]5.3[/C][C]5.30518567304313[/C][C]-0.00518567304312967[/C][/ROW]
[ROW][C]62[/C][C]5.3[/C][C]5.30340076863752[/C][C]-0.00340076863751726[/C][/ROW]
[ROW][C]63[/C][C]5.3[/C][C]5.30223022686346[/C][C]-0.00223022686346219[/C][/ROW]
[ROW][C]64[/C][C]5.35[/C][C]5.30146258460738[/C][C]0.048537415392615[/C][/ROW]
[ROW][C]65[/C][C]5.44[/C][C]5.36816912315132[/C][C]0.0718308768486766[/C][/ROW]
[ROW][C]66[/C][C]5.47[/C][C]5.48289325201172[/C][C]-0.0128932520117164[/C][/ROW]
[ROW][C]67[/C][C]5.47[/C][C]5.50845540525065[/C][C]-0.0384554052506534[/C][/ROW]
[ROW][C]68[/C][C]5.48[/C][C]5.49521908632337[/C][C]-0.0152190863233663[/C][/ROW]
[ROW][C]69[/C][C]5.48[/C][C]5.49998068930103[/C][C]-0.0199806893010246[/C][/ROW]
[ROW][C]70[/C][C]5.48[/C][C]5.49310335244158[/C][C]-0.0131033524415756[/C][/ROW]
[ROW][C]71[/C][C]5.48[/C][C]5.48859318928498[/C][C]-0.00859318928498265[/C][/ROW]
[ROW][C]72[/C][C]5.48[/C][C]5.48563542058544[/C][C]-0.00563542058544098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72260&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72260&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
33.994.09-0.0999999999999996
444.09558008206906-0.0955800820690573
54.064.07268149626256-0.0126814962625597
64.164.128316535656570.0316834643434296
74.194.23922195808126-0.049221958081259
84.24.25227980050569-0.0522798005056861
94.24.24428513607717-0.0442851360771686
104.24.2290422285838-0.0290422285838003
114.24.21904591733994-0.0190459173399393
124.24.21249032822234-0.0124903282223370
134.234.20819116749890.0218088325010974
144.384.245697749747480.134302250252522
154.434.44192447406381-0.0119244740638056
164.444.48782007987735-0.0478200798773463
174.444.48136044762905-0.041360447629053
184.444.46712421549926-0.0271242154992626
194.444.457788082785-0.0177880827850041
204.444.45166543928892-0.0116654392889171
214.454.447650204659390.00234979534061175
224.454.45845900228717-0.00845900228717156
234.454.45554742064215-0.00554742064215041
244.454.45363800300984-0.00363800300983819
254.454.45238580535953-0.00238580535952693
264.454.45156461311279-0.00156461311278555
274.454.45102607456343-0.00102607456342785
284.454.45067290054079-0.000672900540785726
294.464.450441288726890.00955871127310903
304.464.46373138930235-0.00373138930235051
314.464.4624470481668-0.00244704816679775
324.484.461604776196060.0183952238039451
334.584.487936397132590.0920636028674133
344.674.619624613683820.0503753863161807
354.684.72696378031124-0.0469637803112448
364.684.72079888567085-0.0407988856708457
374.694.7067559427062-0.0167559427062001
384.694.71098856097817-0.0209885609781715
394.694.7037643155146-0.0137643155145986
404.694.69902664941072-0.00902664941071762
414.694.69591968409163-0.00591968409163446
424.694.69388213368552-0.00388213368552304
434.694.692545906457-0.00254590645699615
444.734.69166960754390.0383303924561007
454.784.74486289716990.0351371028301015
464.794.80695705912733-0.0169570591273303
474.794.8111204532922-0.0211204532922018
484.84.80385081060238-0.00385081060238246
494.84.81252536475337-0.0125253647533663
504.814.808214144484710.0017858555152932
515.164.818828834487440.341171165512565
525.265.2862596696609-0.0262596696609032
535.295.37722111291468-0.0872211129146834
545.295.37719967743099-0.087199677430994
555.295.3471856200232-0.0571856200231986
565.35.32750237654291-0.0275023765429125
575.35.32803608110778-0.0280360811077829
585.35.31838608499943-0.0183860849994311
595.35.31205760963191-0.0120576096319134
605.35.30790739029218-0.0079073902921758
615.35.30518567304313-0.00518567304312967
625.35.30340076863752-0.00340076863751726
635.35.30223022686346-0.00223022686346219
645.355.301462584607380.048537415392615
655.445.368169123151320.0718308768486766
665.475.48289325201172-0.0128932520117164
675.475.50845540525065-0.0384554052506534
685.485.49521908632337-0.0152190863233663
695.485.49998068930103-0.0199806893010246
705.485.49310335244158-0.0131033524415756
715.485.48859318928498-0.00859318928498265
725.485.48563542058544-0.00563542058544098







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
735.483695713444875.373459342726255.59393208416349
745.487391426889745.302704494871775.6720783589077
755.491087140334615.228883022307595.75329125836162
765.494782853779485.149881925092855.8396837824661
775.498478567224345.065343946837965.93161318761073
785.502174280669214.975318295566316.02903026577212
795.505869994114084.87996990399056.13177008423767
805.509565707558954.779493064642866.23963835047504
815.513261421003824.674082038740776.35244080326687
825.516957134448694.563920817678556.46999345121882
835.520652847893564.44918002809836.59212566768881
845.524348561338434.330016628302076.71868049437478

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 5.48369571344487 & 5.37345934272625 & 5.59393208416349 \tabularnewline
74 & 5.48739142688974 & 5.30270449487177 & 5.6720783589077 \tabularnewline
75 & 5.49108714033461 & 5.22888302230759 & 5.75329125836162 \tabularnewline
76 & 5.49478285377948 & 5.14988192509285 & 5.8396837824661 \tabularnewline
77 & 5.49847856722434 & 5.06534394683796 & 5.93161318761073 \tabularnewline
78 & 5.50217428066921 & 4.97531829556631 & 6.02903026577212 \tabularnewline
79 & 5.50586999411408 & 4.8799699039905 & 6.13177008423767 \tabularnewline
80 & 5.50956570755895 & 4.77949306464286 & 6.23963835047504 \tabularnewline
81 & 5.51326142100382 & 4.67408203874077 & 6.35244080326687 \tabularnewline
82 & 5.51695713444869 & 4.56392081767855 & 6.46999345121882 \tabularnewline
83 & 5.52065284789356 & 4.4491800280983 & 6.59212566768881 \tabularnewline
84 & 5.52434856133843 & 4.33001662830207 & 6.71868049437478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72260&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]73[/C][C]5.48369571344487[/C][C]5.37345934272625[/C][C]5.59393208416349[/C][/ROW]
[ROW][C]74[/C][C]5.48739142688974[/C][C]5.30270449487177[/C][C]5.6720783589077[/C][/ROW]
[ROW][C]75[/C][C]5.49108714033461[/C][C]5.22888302230759[/C][C]5.75329125836162[/C][/ROW]
[ROW][C]76[/C][C]5.49478285377948[/C][C]5.14988192509285[/C][C]5.8396837824661[/C][/ROW]
[ROW][C]77[/C][C]5.49847856722434[/C][C]5.06534394683796[/C][C]5.93161318761073[/C][/ROW]
[ROW][C]78[/C][C]5.50217428066921[/C][C]4.97531829556631[/C][C]6.02903026577212[/C][/ROW]
[ROW][C]79[/C][C]5.50586999411408[/C][C]4.8799699039905[/C][C]6.13177008423767[/C][/ROW]
[ROW][C]80[/C][C]5.50956570755895[/C][C]4.77949306464286[/C][C]6.23963835047504[/C][/ROW]
[ROW][C]81[/C][C]5.51326142100382[/C][C]4.67408203874077[/C][C]6.35244080326687[/C][/ROW]
[ROW][C]82[/C][C]5.51695713444869[/C][C]4.56392081767855[/C][C]6.46999345121882[/C][/ROW]
[ROW][C]83[/C][C]5.52065284789356[/C][C]4.4491800280983[/C][C]6.59212566768881[/C][/ROW]
[ROW][C]84[/C][C]5.52434856133843[/C][C]4.33001662830207[/C][C]6.71868049437478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72260&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72260&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
735.483695713444875.373459342726255.59393208416349
745.487391426889745.302704494871775.6720783589077
755.491087140334615.228883022307595.75329125836162
765.494782853779485.149881925092855.8396837824661
775.498478567224345.065343946837965.93161318761073
785.502174280669214.975318295566316.02903026577212
795.505869994114084.87996990399056.13177008423767
805.509565707558954.779493064642866.23963835047504
815.513261421003824.674082038740776.35244080326687
825.516957134448694.563920817678556.46999345121882
835.520652847893564.44918002809836.59212566768881
845.524348561338434.330016628302076.71868049437478



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')