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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 computationSat, 15 Jan 2011 11:38:00 +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/2011/Jan/15/t1295091457b62m4pirh0gvilr.htm/, Retrieved Thu, 31 Oct 2024 23:39:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117327, Retrieved Thu, 31 Oct 2024 23:39:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102 - PAUWELS
Estimated Impact209
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Inschrijvingen ni...] [2010-12-10 14:02:55] [b119b331fded920041428c5246795730]
-   PD  [Classical Decomposition] [Faillissementen d...] [2010-12-10 14:31:58] [b119b331fded920041428c5246795730]
- RMP       [Exponential Smoothing] [Faillissementen d...] [2011-01-15 11:38:00] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
12
13
23
24
21
20
18
13
12
25
21
17
10
15
23
12
10
21
9
13
17
14
20
12
13
14
23
14
21
21
21
7
15
28
28
18
22
30
1
26
29
24
26
19
19
41
36
54
49
33
50
43
51
46
45
23
56
41
48
43




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117327&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117327&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117327&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 time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.292518976579315
beta0.00735790797960356
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.292518976579315 \tabularnewline
beta & 0.00735790797960356 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117327&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]0.292518976579315[/C][/ROW]
[ROW][C]beta[/C][C]0.00735790797960356[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117327&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117327&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
alpha0.292518976579315
beta0.00735790797960356
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
323149
42417.65204173862156.34795826137854
52120.54197382849610.458026171503942
62021.7099748337406-1.70997483374061
71822.2401139774867-4.24011397748669
81322.0210132934853-9.02101329348529
91220.3839926575377-8.38399265753772
102518.91526754634386.08473245365623
112121.6920154353636-0.692015435363558
121722.4849465233526-5.48494652335261
131021.8640489122671-11.8640489122671
141519.3516074776318-4.35160747763176
152319.02733163770233.97266836229768
161221.1466149314395-9.14661493143955
171019.4085723898511-9.4085723898511
182117.57365198953623.42634801046384
19919.500563992972-10.500563992972
201317.3309892953794-4.33098929537942
211716.95681056597560.0431894340244128
221417.8622550796877-3.86225507968769
232017.61697012252282.38302987747725
241219.2036785907176-7.20367859071762
251317.970588231973-4.97058823197304
261417.3800208447811-3.38002084478114
272317.24744968933985.75255031066017
281419.798710275274-5.79871027527405
292118.95852721159072.04147278840928
302120.41614039234620.583859607653775
312121.4486307144321-0.448630714432056
32722.1781324238542-15.1781324238542
331518.5663070526812-3.56630705268125
342818.34348509380279.6565149061973
352822.00937346645935.99062653354065
361824.6158137155926-6.6158137155926
372223.5203915655439-1.52039156554388
383023.91220470716746.08779529283257
39126.542659812741-25.542659812741
402619.86563038754216.13436961245795
412922.46793636458756.53206363541253
422425.200634531798-1.20063453179804
432625.66878758596470.331212414035292
441926.58574781866-7.58574781865996
451925.170519931222-6.17051993122204
464124.155992075998816.8440079240012
473629.90990418047696.09009581952312
485432.5312008039321.46879919607
494939.69726789165969.30273210834043
503343.3245520140049-10.3245520140049
515041.18826125243718.8117387475629
524344.6686644294642-1.66866442946421
535145.07975928231525.92024071768476
544647.7234952003259-1.72349520032594
554548.1275837838765-3.1275837838765
562348.1142182266906-25.1142182266906
575641.615290836015814.3847091639842
584146.7015098698039-5.70150986980394
594845.89985715078762.10014284921237
604347.3848560964186-4.38485609641863

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 23 & 14 & 9 \tabularnewline
4 & 24 & 17.6520417386215 & 6.34795826137854 \tabularnewline
5 & 21 & 20.5419738284961 & 0.458026171503942 \tabularnewline
6 & 20 & 21.7099748337406 & -1.70997483374061 \tabularnewline
7 & 18 & 22.2401139774867 & -4.24011397748669 \tabularnewline
8 & 13 & 22.0210132934853 & -9.02101329348529 \tabularnewline
9 & 12 & 20.3839926575377 & -8.38399265753772 \tabularnewline
10 & 25 & 18.9152675463438 & 6.08473245365623 \tabularnewline
11 & 21 & 21.6920154353636 & -0.692015435363558 \tabularnewline
12 & 17 & 22.4849465233526 & -5.48494652335261 \tabularnewline
13 & 10 & 21.8640489122671 & -11.8640489122671 \tabularnewline
14 & 15 & 19.3516074776318 & -4.35160747763176 \tabularnewline
15 & 23 & 19.0273316377023 & 3.97266836229768 \tabularnewline
16 & 12 & 21.1466149314395 & -9.14661493143955 \tabularnewline
17 & 10 & 19.4085723898511 & -9.4085723898511 \tabularnewline
18 & 21 & 17.5736519895362 & 3.42634801046384 \tabularnewline
19 & 9 & 19.500563992972 & -10.500563992972 \tabularnewline
20 & 13 & 17.3309892953794 & -4.33098929537942 \tabularnewline
21 & 17 & 16.9568105659756 & 0.0431894340244128 \tabularnewline
22 & 14 & 17.8622550796877 & -3.86225507968769 \tabularnewline
23 & 20 & 17.6169701225228 & 2.38302987747725 \tabularnewline
24 & 12 & 19.2036785907176 & -7.20367859071762 \tabularnewline
25 & 13 & 17.970588231973 & -4.97058823197304 \tabularnewline
26 & 14 & 17.3800208447811 & -3.38002084478114 \tabularnewline
27 & 23 & 17.2474496893398 & 5.75255031066017 \tabularnewline
28 & 14 & 19.798710275274 & -5.79871027527405 \tabularnewline
29 & 21 & 18.9585272115907 & 2.04147278840928 \tabularnewline
30 & 21 & 20.4161403923462 & 0.583859607653775 \tabularnewline
31 & 21 & 21.4486307144321 & -0.448630714432056 \tabularnewline
32 & 7 & 22.1781324238542 & -15.1781324238542 \tabularnewline
33 & 15 & 18.5663070526812 & -3.56630705268125 \tabularnewline
34 & 28 & 18.3434850938027 & 9.6565149061973 \tabularnewline
35 & 28 & 22.0093734664593 & 5.99062653354065 \tabularnewline
36 & 18 & 24.6158137155926 & -6.6158137155926 \tabularnewline
37 & 22 & 23.5203915655439 & -1.52039156554388 \tabularnewline
38 & 30 & 23.9122047071674 & 6.08779529283257 \tabularnewline
39 & 1 & 26.542659812741 & -25.542659812741 \tabularnewline
40 & 26 & 19.8656303875421 & 6.13436961245795 \tabularnewline
41 & 29 & 22.4679363645875 & 6.53206363541253 \tabularnewline
42 & 24 & 25.200634531798 & -1.20063453179804 \tabularnewline
43 & 26 & 25.6687875859647 & 0.331212414035292 \tabularnewline
44 & 19 & 26.58574781866 & -7.58574781865996 \tabularnewline
45 & 19 & 25.170519931222 & -6.17051993122204 \tabularnewline
46 & 41 & 24.1559920759988 & 16.8440079240012 \tabularnewline
47 & 36 & 29.9099041804769 & 6.09009581952312 \tabularnewline
48 & 54 & 32.53120080393 & 21.46879919607 \tabularnewline
49 & 49 & 39.6972678916596 & 9.30273210834043 \tabularnewline
50 & 33 & 43.3245520140049 & -10.3245520140049 \tabularnewline
51 & 50 & 41.1882612524371 & 8.8117387475629 \tabularnewline
52 & 43 & 44.6686644294642 & -1.66866442946421 \tabularnewline
53 & 51 & 45.0797592823152 & 5.92024071768476 \tabularnewline
54 & 46 & 47.7234952003259 & -1.72349520032594 \tabularnewline
55 & 45 & 48.1275837838765 & -3.1275837838765 \tabularnewline
56 & 23 & 48.1142182266906 & -25.1142182266906 \tabularnewline
57 & 56 & 41.6152908360158 & 14.3847091639842 \tabularnewline
58 & 41 & 46.7015098698039 & -5.70150986980394 \tabularnewline
59 & 48 & 45.8998571507876 & 2.10014284921237 \tabularnewline
60 & 43 & 47.3848560964186 & -4.38485609641863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117327&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]23[/C][C]14[/C][C]9[/C][/ROW]
[ROW][C]4[/C][C]24[/C][C]17.6520417386215[/C][C]6.34795826137854[/C][/ROW]
[ROW][C]5[/C][C]21[/C][C]20.5419738284961[/C][C]0.458026171503942[/C][/ROW]
[ROW][C]6[/C][C]20[/C][C]21.7099748337406[/C][C]-1.70997483374061[/C][/ROW]
[ROW][C]7[/C][C]18[/C][C]22.2401139774867[/C][C]-4.24011397748669[/C][/ROW]
[ROW][C]8[/C][C]13[/C][C]22.0210132934853[/C][C]-9.02101329348529[/C][/ROW]
[ROW][C]9[/C][C]12[/C][C]20.3839926575377[/C][C]-8.38399265753772[/C][/ROW]
[ROW][C]10[/C][C]25[/C][C]18.9152675463438[/C][C]6.08473245365623[/C][/ROW]
[ROW][C]11[/C][C]21[/C][C]21.6920154353636[/C][C]-0.692015435363558[/C][/ROW]
[ROW][C]12[/C][C]17[/C][C]22.4849465233526[/C][C]-5.48494652335261[/C][/ROW]
[ROW][C]13[/C][C]10[/C][C]21.8640489122671[/C][C]-11.8640489122671[/C][/ROW]
[ROW][C]14[/C][C]15[/C][C]19.3516074776318[/C][C]-4.35160747763176[/C][/ROW]
[ROW][C]15[/C][C]23[/C][C]19.0273316377023[/C][C]3.97266836229768[/C][/ROW]
[ROW][C]16[/C][C]12[/C][C]21.1466149314395[/C][C]-9.14661493143955[/C][/ROW]
[ROW][C]17[/C][C]10[/C][C]19.4085723898511[/C][C]-9.4085723898511[/C][/ROW]
[ROW][C]18[/C][C]21[/C][C]17.5736519895362[/C][C]3.42634801046384[/C][/ROW]
[ROW][C]19[/C][C]9[/C][C]19.500563992972[/C][C]-10.500563992972[/C][/ROW]
[ROW][C]20[/C][C]13[/C][C]17.3309892953794[/C][C]-4.33098929537942[/C][/ROW]
[ROW][C]21[/C][C]17[/C][C]16.9568105659756[/C][C]0.0431894340244128[/C][/ROW]
[ROW][C]22[/C][C]14[/C][C]17.8622550796877[/C][C]-3.86225507968769[/C][/ROW]
[ROW][C]23[/C][C]20[/C][C]17.6169701225228[/C][C]2.38302987747725[/C][/ROW]
[ROW][C]24[/C][C]12[/C][C]19.2036785907176[/C][C]-7.20367859071762[/C][/ROW]
[ROW][C]25[/C][C]13[/C][C]17.970588231973[/C][C]-4.97058823197304[/C][/ROW]
[ROW][C]26[/C][C]14[/C][C]17.3800208447811[/C][C]-3.38002084478114[/C][/ROW]
[ROW][C]27[/C][C]23[/C][C]17.2474496893398[/C][C]5.75255031066017[/C][/ROW]
[ROW][C]28[/C][C]14[/C][C]19.798710275274[/C][C]-5.79871027527405[/C][/ROW]
[ROW][C]29[/C][C]21[/C][C]18.9585272115907[/C][C]2.04147278840928[/C][/ROW]
[ROW][C]30[/C][C]21[/C][C]20.4161403923462[/C][C]0.583859607653775[/C][/ROW]
[ROW][C]31[/C][C]21[/C][C]21.4486307144321[/C][C]-0.448630714432056[/C][/ROW]
[ROW][C]32[/C][C]7[/C][C]22.1781324238542[/C][C]-15.1781324238542[/C][/ROW]
[ROW][C]33[/C][C]15[/C][C]18.5663070526812[/C][C]-3.56630705268125[/C][/ROW]
[ROW][C]34[/C][C]28[/C][C]18.3434850938027[/C][C]9.6565149061973[/C][/ROW]
[ROW][C]35[/C][C]28[/C][C]22.0093734664593[/C][C]5.99062653354065[/C][/ROW]
[ROW][C]36[/C][C]18[/C][C]24.6158137155926[/C][C]-6.6158137155926[/C][/ROW]
[ROW][C]37[/C][C]22[/C][C]23.5203915655439[/C][C]-1.52039156554388[/C][/ROW]
[ROW][C]38[/C][C]30[/C][C]23.9122047071674[/C][C]6.08779529283257[/C][/ROW]
[ROW][C]39[/C][C]1[/C][C]26.542659812741[/C][C]-25.542659812741[/C][/ROW]
[ROW][C]40[/C][C]26[/C][C]19.8656303875421[/C][C]6.13436961245795[/C][/ROW]
[ROW][C]41[/C][C]29[/C][C]22.4679363645875[/C][C]6.53206363541253[/C][/ROW]
[ROW][C]42[/C][C]24[/C][C]25.200634531798[/C][C]-1.20063453179804[/C][/ROW]
[ROW][C]43[/C][C]26[/C][C]25.6687875859647[/C][C]0.331212414035292[/C][/ROW]
[ROW][C]44[/C][C]19[/C][C]26.58574781866[/C][C]-7.58574781865996[/C][/ROW]
[ROW][C]45[/C][C]19[/C][C]25.170519931222[/C][C]-6.17051993122204[/C][/ROW]
[ROW][C]46[/C][C]41[/C][C]24.1559920759988[/C][C]16.8440079240012[/C][/ROW]
[ROW][C]47[/C][C]36[/C][C]29.9099041804769[/C][C]6.09009581952312[/C][/ROW]
[ROW][C]48[/C][C]54[/C][C]32.53120080393[/C][C]21.46879919607[/C][/ROW]
[ROW][C]49[/C][C]49[/C][C]39.6972678916596[/C][C]9.30273210834043[/C][/ROW]
[ROW][C]50[/C][C]33[/C][C]43.3245520140049[/C][C]-10.3245520140049[/C][/ROW]
[ROW][C]51[/C][C]50[/C][C]41.1882612524371[/C][C]8.8117387475629[/C][/ROW]
[ROW][C]52[/C][C]43[/C][C]44.6686644294642[/C][C]-1.66866442946421[/C][/ROW]
[ROW][C]53[/C][C]51[/C][C]45.0797592823152[/C][C]5.92024071768476[/C][/ROW]
[ROW][C]54[/C][C]46[/C][C]47.7234952003259[/C][C]-1.72349520032594[/C][/ROW]
[ROW][C]55[/C][C]45[/C][C]48.1275837838765[/C][C]-3.1275837838765[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]48.1142182266906[/C][C]-25.1142182266906[/C][/ROW]
[ROW][C]57[/C][C]56[/C][C]41.6152908360158[/C][C]14.3847091639842[/C][/ROW]
[ROW][C]58[/C][C]41[/C][C]46.7015098698039[/C][C]-5.70150986980394[/C][/ROW]
[ROW][C]59[/C][C]48[/C][C]45.8998571507876[/C][C]2.10014284921237[/C][/ROW]
[ROW][C]60[/C][C]43[/C][C]47.3848560964186[/C][C]-4.38485609641863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117327&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117327&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
323149
42417.65204173862156.34795826137854
52120.54197382849610.458026171503942
62021.7099748337406-1.70997483374061
71822.2401139774867-4.24011397748669
81322.0210132934853-9.02101329348529
91220.3839926575377-8.38399265753772
102518.91526754634386.08473245365623
112121.6920154353636-0.692015435363558
121722.4849465233526-5.48494652335261
131021.8640489122671-11.8640489122671
141519.3516074776318-4.35160747763176
152319.02733163770233.97266836229768
161221.1466149314395-9.14661493143955
171019.4085723898511-9.4085723898511
182117.57365198953623.42634801046384
19919.500563992972-10.500563992972
201317.3309892953794-4.33098929537942
211716.95681056597560.0431894340244128
221417.8622550796877-3.86225507968769
232017.61697012252282.38302987747725
241219.2036785907176-7.20367859071762
251317.970588231973-4.97058823197304
261417.3800208447811-3.38002084478114
272317.24744968933985.75255031066017
281419.798710275274-5.79871027527405
292118.95852721159072.04147278840928
302120.41614039234620.583859607653775
312121.4486307144321-0.448630714432056
32722.1781324238542-15.1781324238542
331518.5663070526812-3.56630705268125
342818.34348509380279.6565149061973
352822.00937346645935.99062653354065
361824.6158137155926-6.6158137155926
372223.5203915655439-1.52039156554388
383023.91220470716746.08779529283257
39126.542659812741-25.542659812741
402619.86563038754216.13436961245795
412922.46793636458756.53206363541253
422425.200634531798-1.20063453179804
432625.66878758596470.331212414035292
441926.58574781866-7.58574781865996
451925.170519931222-6.17051993122204
464124.155992075998816.8440079240012
473629.90990418047696.09009581952312
485432.5312008039321.46879919607
494939.69726789165969.30273210834043
503343.3245520140049-10.3245520140049
515041.18826125243718.8117387475629
524344.6686644294642-1.66866442946421
535145.07975928231525.92024071768476
544647.7234952003259-1.72349520032594
554548.1275837838765-3.1275837838765
562348.1142182266906-25.1142182266906
575641.615290836015814.3847091639842
584146.7015098698039-5.70150986980394
594845.89985715078762.10014284921237
604347.3848560964186-4.38485609641863







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6146.963432140066430.058068277123863.8687960030091
6247.824661801486230.200617860569665.4487057424028
6348.68589146290630.361417100059567.0103658257524
6449.547121124325730.538378853116968.5558633955345
6550.408350785745530.729749746235370.0869518252557
6651.269580447165330.934040696361771.6051201979688
6752.13081010858531.14997492856673.111645288604
6852.992039770004831.376448396622874.6076311433868
6953.853269431424531.612499176525576.0940396863236
7054.714499092844331.857283469618677.57171471607
7155.575728754264132.110056553530179.041400954998
7256.436958415683832.370157490899980.5037593404677

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 46.9634321400664 & 30.0580682771238 & 63.8687960030091 \tabularnewline
62 & 47.8246618014862 & 30.2006178605696 & 65.4487057424028 \tabularnewline
63 & 48.685891462906 & 30.3614171000595 & 67.0103658257524 \tabularnewline
64 & 49.5471211243257 & 30.5383788531169 & 68.5558633955345 \tabularnewline
65 & 50.4083507857455 & 30.7297497462353 & 70.0869518252557 \tabularnewline
66 & 51.2695804471653 & 30.9340406963617 & 71.6051201979688 \tabularnewline
67 & 52.130810108585 & 31.149974928566 & 73.111645288604 \tabularnewline
68 & 52.9920397700048 & 31.3764483966228 & 74.6076311433868 \tabularnewline
69 & 53.8532694314245 & 31.6124991765255 & 76.0940396863236 \tabularnewline
70 & 54.7144990928443 & 31.8572834696186 & 77.57171471607 \tabularnewline
71 & 55.5757287542641 & 32.1100565535301 & 79.041400954998 \tabularnewline
72 & 56.4369584156838 & 32.3701574908999 & 80.5037593404677 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117327&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]61[/C][C]46.9634321400664[/C][C]30.0580682771238[/C][C]63.8687960030091[/C][/ROW]
[ROW][C]62[/C][C]47.8246618014862[/C][C]30.2006178605696[/C][C]65.4487057424028[/C][/ROW]
[ROW][C]63[/C][C]48.685891462906[/C][C]30.3614171000595[/C][C]67.0103658257524[/C][/ROW]
[ROW][C]64[/C][C]49.5471211243257[/C][C]30.5383788531169[/C][C]68.5558633955345[/C][/ROW]
[ROW][C]65[/C][C]50.4083507857455[/C][C]30.7297497462353[/C][C]70.0869518252557[/C][/ROW]
[ROW][C]66[/C][C]51.2695804471653[/C][C]30.9340406963617[/C][C]71.6051201979688[/C][/ROW]
[ROW][C]67[/C][C]52.130810108585[/C][C]31.149974928566[/C][C]73.111645288604[/C][/ROW]
[ROW][C]68[/C][C]52.9920397700048[/C][C]31.3764483966228[/C][C]74.6076311433868[/C][/ROW]
[ROW][C]69[/C][C]53.8532694314245[/C][C]31.6124991765255[/C][C]76.0940396863236[/C][/ROW]
[ROW][C]70[/C][C]54.7144990928443[/C][C]31.8572834696186[/C][C]77.57171471607[/C][/ROW]
[ROW][C]71[/C][C]55.5757287542641[/C][C]32.1100565535301[/C][C]79.041400954998[/C][/ROW]
[ROW][C]72[/C][C]56.4369584156838[/C][C]32.3701574908999[/C][C]80.5037593404677[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117327&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117327&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
6146.963432140066430.058068277123863.8687960030091
6247.824661801486230.200617860569665.4487057424028
6348.68589146290630.361417100059567.0103658257524
6449.547121124325730.538378853116968.5558633955345
6550.408350785745530.729749746235370.0869518252557
6651.269580447165330.934040696361771.6051201979688
6752.13081010858531.14997492856673.111645288604
6852.992039770004831.376448396622874.6076311433868
6953.853269431424531.612499176525576.0940396863236
7054.714499092844331.857283469618677.57171471607
7155.575728754264132.110056553530179.041400954998
7256.436958415683832.370157490899980.5037593404677



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')