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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 05:35:06 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356086142x6i8p4xdsrhfqyc.htm/, Retrieved Fri, 19 Apr 2024 19:32:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203431, Retrieved Fri, 19 Apr 2024 19:32:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact49
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-21 10:35:06] [b5e28e8a989acbea90caf9c77474d9fd] [Current]
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Dataseries X:
369,82
373,1
374,55
375,01
374,81
375,31
375,31
375,39
375,59
376,26
377,18
377,26
377,26
381,87
387,09
387,14
388,78
389,16
389,16
389,42
389,49
388,97
388,97
389,09
389,09
391,76
390,96
391,76
392,8
393,06
393,06
393,26
393,87
394,47
394,57
394,57
394,57
399,57
406,13
407,03
409,46
409,9
409,9
410,14
410,54
410,69
410,79
410,97
410,97
413,8
423,31
423,85
426,6
426,26
426,26
426,32
427,14
427,55
428,29
428,8
428,8
434,87
435,66
440,75
440,99
441,04
441,04
441,88
441,92
442,48
442,81
442,81




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203431&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203431&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203431&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999921341552912
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999921341552912 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203431&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]0.999921341552912[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203431&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203431&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
alpha0.999921341552912
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2373.1369.823.28000000000003
3374.55373.0997420002941.45025799970642
4375.01374.5498859249580.4601140750421
5374.81375.009963808141-0.199963808141376
6375.31374.8100157288430.499984271157359
7375.31375.3099606720143.93279863146745e-05
8375.39375.3099999969070.0800000030934598
9375.59375.3899937073240.200006292675994
10376.26375.5899842678160.670015732184424
11377.18376.2599472976030.920052702397015
12377.26377.1799276300830.0800723699168202
13377.26377.2599937016326.29836824828089e-06
14381.87377.2599999995054.61000000049546
15387.09381.8696373845595.2203626154411
16387.14387.0895893743830.0504106256165642
17388.78387.1399960347781.64000396522152
18389.16388.7798709998350.380129000165198
19389.16389.1599700996432.99003568215994e-05
20389.42389.1599999976480.260000002351887
21389.49389.4199795488040.0700204511963989
22388.97389.4899944923-0.519994492300043
23388.97388.970040901959-4.09019592666482e-05
24389.09388.9700000032170.119999996782667
25389.09389.0899905609879.43901341088349e-06
26391.76389.0899999992582.67000000074245
27390.96391.759789981946-0.799789981946219
28391.76390.9600629102380.799937089762011
29392.8391.7599370781911.04006292180929
30393.06392.7999181902660.260081809734288
31393.06393.0599795423692.04576312512472e-05
32393.26393.0599999983910.200000001609169
33393.87393.259984268310.610015731689543
34394.47393.869952017110.600047982890203
35394.57394.4699528011570.100047198842503
36394.57394.5699921304437.86955729381589e-06
37394.57394.5699999993816.19024831394199e-10
38399.57394.575.00000000000006
39406.13399.5696067077656.56039329223546
40407.03406.1294839696510.900516030348626
41409.46407.0299291668072.43007083319253
42409.9409.4598088544020.440191145598078
43409.9409.8999653752483.46247519473764e-05
44410.14409.8999999972760.240000002723548
45410.54410.1399811219720.400018878027538
46410.69410.5399685351360.15003146486373
47410.79410.6899881987580.10001180124209
48410.97410.7899921332270.180007866772996
49410.97410.9699858408611.41591392548435e-05
50413.8410.9699999988862.83000000111372
51423.31413.7997773965959.51022260340534
52423.85423.3092519406590.540748059341468
53426.6423.8499574655972.75004253440261
54426.26426.599783685925-0.339783685924829
55426.26426.260026726857-2.672685707239e-05
56426.32426.2600000021020.0599999978977053
57427.14426.3199952804930.820004719506642
58427.55427.1399354997020.410064500297892
59428.29427.5499677449630.740032255036795
60428.8428.2899417902120.510058209787985
61428.8428.7999598796134.01203866999822e-05
62434.87428.7999999968446.07000000315583
63435.66434.8695225432260.790477456774113
64440.75435.6599378222715.09006217772918
65440.99440.7495996236140.240400376386503
66441.04440.989981090480.0500189095203041
67441.04441.039996065593.93440973311954e-06
68441.88441.0399999996910.840000000309431
69441.92441.8799339269040.040066073095602
70442.48441.9199968484650.560003151535113
71442.81442.4799559510220.330044048978266
72442.81442.8099740392482.59607523389604e-05

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 373.1 & 369.82 & 3.28000000000003 \tabularnewline
3 & 374.55 & 373.099742000294 & 1.45025799970642 \tabularnewline
4 & 375.01 & 374.549885924958 & 0.4601140750421 \tabularnewline
5 & 374.81 & 375.009963808141 & -0.199963808141376 \tabularnewline
6 & 375.31 & 374.810015728843 & 0.499984271157359 \tabularnewline
7 & 375.31 & 375.309960672014 & 3.93279863146745e-05 \tabularnewline
8 & 375.39 & 375.309999996907 & 0.0800000030934598 \tabularnewline
9 & 375.59 & 375.389993707324 & 0.200006292675994 \tabularnewline
10 & 376.26 & 375.589984267816 & 0.670015732184424 \tabularnewline
11 & 377.18 & 376.259947297603 & 0.920052702397015 \tabularnewline
12 & 377.26 & 377.179927630083 & 0.0800723699168202 \tabularnewline
13 & 377.26 & 377.259993701632 & 6.29836824828089e-06 \tabularnewline
14 & 381.87 & 377.259999999505 & 4.61000000049546 \tabularnewline
15 & 387.09 & 381.869637384559 & 5.2203626154411 \tabularnewline
16 & 387.14 & 387.089589374383 & 0.0504106256165642 \tabularnewline
17 & 388.78 & 387.139996034778 & 1.64000396522152 \tabularnewline
18 & 389.16 & 388.779870999835 & 0.380129000165198 \tabularnewline
19 & 389.16 & 389.159970099643 & 2.99003568215994e-05 \tabularnewline
20 & 389.42 & 389.159999997648 & 0.260000002351887 \tabularnewline
21 & 389.49 & 389.419979548804 & 0.0700204511963989 \tabularnewline
22 & 388.97 & 389.4899944923 & -0.519994492300043 \tabularnewline
23 & 388.97 & 388.970040901959 & -4.09019592666482e-05 \tabularnewline
24 & 389.09 & 388.970000003217 & 0.119999996782667 \tabularnewline
25 & 389.09 & 389.089990560987 & 9.43901341088349e-06 \tabularnewline
26 & 391.76 & 389.089999999258 & 2.67000000074245 \tabularnewline
27 & 390.96 & 391.759789981946 & -0.799789981946219 \tabularnewline
28 & 391.76 & 390.960062910238 & 0.799937089762011 \tabularnewline
29 & 392.8 & 391.759937078191 & 1.04006292180929 \tabularnewline
30 & 393.06 & 392.799918190266 & 0.260081809734288 \tabularnewline
31 & 393.06 & 393.059979542369 & 2.04576312512472e-05 \tabularnewline
32 & 393.26 & 393.059999998391 & 0.200000001609169 \tabularnewline
33 & 393.87 & 393.25998426831 & 0.610015731689543 \tabularnewline
34 & 394.47 & 393.86995201711 & 0.600047982890203 \tabularnewline
35 & 394.57 & 394.469952801157 & 0.100047198842503 \tabularnewline
36 & 394.57 & 394.569992130443 & 7.86955729381589e-06 \tabularnewline
37 & 394.57 & 394.569999999381 & 6.19024831394199e-10 \tabularnewline
38 & 399.57 & 394.57 & 5.00000000000006 \tabularnewline
39 & 406.13 & 399.569606707765 & 6.56039329223546 \tabularnewline
40 & 407.03 & 406.129483969651 & 0.900516030348626 \tabularnewline
41 & 409.46 & 407.029929166807 & 2.43007083319253 \tabularnewline
42 & 409.9 & 409.459808854402 & 0.440191145598078 \tabularnewline
43 & 409.9 & 409.899965375248 & 3.46247519473764e-05 \tabularnewline
44 & 410.14 & 409.899999997276 & 0.240000002723548 \tabularnewline
45 & 410.54 & 410.139981121972 & 0.400018878027538 \tabularnewline
46 & 410.69 & 410.539968535136 & 0.15003146486373 \tabularnewline
47 & 410.79 & 410.689988198758 & 0.10001180124209 \tabularnewline
48 & 410.97 & 410.789992133227 & 0.180007866772996 \tabularnewline
49 & 410.97 & 410.969985840861 & 1.41591392548435e-05 \tabularnewline
50 & 413.8 & 410.969999998886 & 2.83000000111372 \tabularnewline
51 & 423.31 & 413.799777396595 & 9.51022260340534 \tabularnewline
52 & 423.85 & 423.309251940659 & 0.540748059341468 \tabularnewline
53 & 426.6 & 423.849957465597 & 2.75004253440261 \tabularnewline
54 & 426.26 & 426.599783685925 & -0.339783685924829 \tabularnewline
55 & 426.26 & 426.260026726857 & -2.672685707239e-05 \tabularnewline
56 & 426.32 & 426.260000002102 & 0.0599999978977053 \tabularnewline
57 & 427.14 & 426.319995280493 & 0.820004719506642 \tabularnewline
58 & 427.55 & 427.139935499702 & 0.410064500297892 \tabularnewline
59 & 428.29 & 427.549967744963 & 0.740032255036795 \tabularnewline
60 & 428.8 & 428.289941790212 & 0.510058209787985 \tabularnewline
61 & 428.8 & 428.799959879613 & 4.01203866999822e-05 \tabularnewline
62 & 434.87 & 428.799999996844 & 6.07000000315583 \tabularnewline
63 & 435.66 & 434.869522543226 & 0.790477456774113 \tabularnewline
64 & 440.75 & 435.659937822271 & 5.09006217772918 \tabularnewline
65 & 440.99 & 440.749599623614 & 0.240400376386503 \tabularnewline
66 & 441.04 & 440.98998109048 & 0.0500189095203041 \tabularnewline
67 & 441.04 & 441.03999606559 & 3.93440973311954e-06 \tabularnewline
68 & 441.88 & 441.039999999691 & 0.840000000309431 \tabularnewline
69 & 441.92 & 441.879933926904 & 0.040066073095602 \tabularnewline
70 & 442.48 & 441.919996848465 & 0.560003151535113 \tabularnewline
71 & 442.81 & 442.479955951022 & 0.330044048978266 \tabularnewline
72 & 442.81 & 442.809974039248 & 2.59607523389604e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203431&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]2[/C][C]373.1[/C][C]369.82[/C][C]3.28000000000003[/C][/ROW]
[ROW][C]3[/C][C]374.55[/C][C]373.099742000294[/C][C]1.45025799970642[/C][/ROW]
[ROW][C]4[/C][C]375.01[/C][C]374.549885924958[/C][C]0.4601140750421[/C][/ROW]
[ROW][C]5[/C][C]374.81[/C][C]375.009963808141[/C][C]-0.199963808141376[/C][/ROW]
[ROW][C]6[/C][C]375.31[/C][C]374.810015728843[/C][C]0.499984271157359[/C][/ROW]
[ROW][C]7[/C][C]375.31[/C][C]375.309960672014[/C][C]3.93279863146745e-05[/C][/ROW]
[ROW][C]8[/C][C]375.39[/C][C]375.309999996907[/C][C]0.0800000030934598[/C][/ROW]
[ROW][C]9[/C][C]375.59[/C][C]375.389993707324[/C][C]0.200006292675994[/C][/ROW]
[ROW][C]10[/C][C]376.26[/C][C]375.589984267816[/C][C]0.670015732184424[/C][/ROW]
[ROW][C]11[/C][C]377.18[/C][C]376.259947297603[/C][C]0.920052702397015[/C][/ROW]
[ROW][C]12[/C][C]377.26[/C][C]377.179927630083[/C][C]0.0800723699168202[/C][/ROW]
[ROW][C]13[/C][C]377.26[/C][C]377.259993701632[/C][C]6.29836824828089e-06[/C][/ROW]
[ROW][C]14[/C][C]381.87[/C][C]377.259999999505[/C][C]4.61000000049546[/C][/ROW]
[ROW][C]15[/C][C]387.09[/C][C]381.869637384559[/C][C]5.2203626154411[/C][/ROW]
[ROW][C]16[/C][C]387.14[/C][C]387.089589374383[/C][C]0.0504106256165642[/C][/ROW]
[ROW][C]17[/C][C]388.78[/C][C]387.139996034778[/C][C]1.64000396522152[/C][/ROW]
[ROW][C]18[/C][C]389.16[/C][C]388.779870999835[/C][C]0.380129000165198[/C][/ROW]
[ROW][C]19[/C][C]389.16[/C][C]389.159970099643[/C][C]2.99003568215994e-05[/C][/ROW]
[ROW][C]20[/C][C]389.42[/C][C]389.159999997648[/C][C]0.260000002351887[/C][/ROW]
[ROW][C]21[/C][C]389.49[/C][C]389.419979548804[/C][C]0.0700204511963989[/C][/ROW]
[ROW][C]22[/C][C]388.97[/C][C]389.4899944923[/C][C]-0.519994492300043[/C][/ROW]
[ROW][C]23[/C][C]388.97[/C][C]388.970040901959[/C][C]-4.09019592666482e-05[/C][/ROW]
[ROW][C]24[/C][C]389.09[/C][C]388.970000003217[/C][C]0.119999996782667[/C][/ROW]
[ROW][C]25[/C][C]389.09[/C][C]389.089990560987[/C][C]9.43901341088349e-06[/C][/ROW]
[ROW][C]26[/C][C]391.76[/C][C]389.089999999258[/C][C]2.67000000074245[/C][/ROW]
[ROW][C]27[/C][C]390.96[/C][C]391.759789981946[/C][C]-0.799789981946219[/C][/ROW]
[ROW][C]28[/C][C]391.76[/C][C]390.960062910238[/C][C]0.799937089762011[/C][/ROW]
[ROW][C]29[/C][C]392.8[/C][C]391.759937078191[/C][C]1.04006292180929[/C][/ROW]
[ROW][C]30[/C][C]393.06[/C][C]392.799918190266[/C][C]0.260081809734288[/C][/ROW]
[ROW][C]31[/C][C]393.06[/C][C]393.059979542369[/C][C]2.04576312512472e-05[/C][/ROW]
[ROW][C]32[/C][C]393.26[/C][C]393.059999998391[/C][C]0.200000001609169[/C][/ROW]
[ROW][C]33[/C][C]393.87[/C][C]393.25998426831[/C][C]0.610015731689543[/C][/ROW]
[ROW][C]34[/C][C]394.47[/C][C]393.86995201711[/C][C]0.600047982890203[/C][/ROW]
[ROW][C]35[/C][C]394.57[/C][C]394.469952801157[/C][C]0.100047198842503[/C][/ROW]
[ROW][C]36[/C][C]394.57[/C][C]394.569992130443[/C][C]7.86955729381589e-06[/C][/ROW]
[ROW][C]37[/C][C]394.57[/C][C]394.569999999381[/C][C]6.19024831394199e-10[/C][/ROW]
[ROW][C]38[/C][C]399.57[/C][C]394.57[/C][C]5.00000000000006[/C][/ROW]
[ROW][C]39[/C][C]406.13[/C][C]399.569606707765[/C][C]6.56039329223546[/C][/ROW]
[ROW][C]40[/C][C]407.03[/C][C]406.129483969651[/C][C]0.900516030348626[/C][/ROW]
[ROW][C]41[/C][C]409.46[/C][C]407.029929166807[/C][C]2.43007083319253[/C][/ROW]
[ROW][C]42[/C][C]409.9[/C][C]409.459808854402[/C][C]0.440191145598078[/C][/ROW]
[ROW][C]43[/C][C]409.9[/C][C]409.899965375248[/C][C]3.46247519473764e-05[/C][/ROW]
[ROW][C]44[/C][C]410.14[/C][C]409.899999997276[/C][C]0.240000002723548[/C][/ROW]
[ROW][C]45[/C][C]410.54[/C][C]410.139981121972[/C][C]0.400018878027538[/C][/ROW]
[ROW][C]46[/C][C]410.69[/C][C]410.539968535136[/C][C]0.15003146486373[/C][/ROW]
[ROW][C]47[/C][C]410.79[/C][C]410.689988198758[/C][C]0.10001180124209[/C][/ROW]
[ROW][C]48[/C][C]410.97[/C][C]410.789992133227[/C][C]0.180007866772996[/C][/ROW]
[ROW][C]49[/C][C]410.97[/C][C]410.969985840861[/C][C]1.41591392548435e-05[/C][/ROW]
[ROW][C]50[/C][C]413.8[/C][C]410.969999998886[/C][C]2.83000000111372[/C][/ROW]
[ROW][C]51[/C][C]423.31[/C][C]413.799777396595[/C][C]9.51022260340534[/C][/ROW]
[ROW][C]52[/C][C]423.85[/C][C]423.309251940659[/C][C]0.540748059341468[/C][/ROW]
[ROW][C]53[/C][C]426.6[/C][C]423.849957465597[/C][C]2.75004253440261[/C][/ROW]
[ROW][C]54[/C][C]426.26[/C][C]426.599783685925[/C][C]-0.339783685924829[/C][/ROW]
[ROW][C]55[/C][C]426.26[/C][C]426.260026726857[/C][C]-2.672685707239e-05[/C][/ROW]
[ROW][C]56[/C][C]426.32[/C][C]426.260000002102[/C][C]0.0599999978977053[/C][/ROW]
[ROW][C]57[/C][C]427.14[/C][C]426.319995280493[/C][C]0.820004719506642[/C][/ROW]
[ROW][C]58[/C][C]427.55[/C][C]427.139935499702[/C][C]0.410064500297892[/C][/ROW]
[ROW][C]59[/C][C]428.29[/C][C]427.549967744963[/C][C]0.740032255036795[/C][/ROW]
[ROW][C]60[/C][C]428.8[/C][C]428.289941790212[/C][C]0.510058209787985[/C][/ROW]
[ROW][C]61[/C][C]428.8[/C][C]428.799959879613[/C][C]4.01203866999822e-05[/C][/ROW]
[ROW][C]62[/C][C]434.87[/C][C]428.799999996844[/C][C]6.07000000315583[/C][/ROW]
[ROW][C]63[/C][C]435.66[/C][C]434.869522543226[/C][C]0.790477456774113[/C][/ROW]
[ROW][C]64[/C][C]440.75[/C][C]435.659937822271[/C][C]5.09006217772918[/C][/ROW]
[ROW][C]65[/C][C]440.99[/C][C]440.749599623614[/C][C]0.240400376386503[/C][/ROW]
[ROW][C]66[/C][C]441.04[/C][C]440.98998109048[/C][C]0.0500189095203041[/C][/ROW]
[ROW][C]67[/C][C]441.04[/C][C]441.03999606559[/C][C]3.93440973311954e-06[/C][/ROW]
[ROW][C]68[/C][C]441.88[/C][C]441.039999999691[/C][C]0.840000000309431[/C][/ROW]
[ROW][C]69[/C][C]441.92[/C][C]441.879933926904[/C][C]0.040066073095602[/C][/ROW]
[ROW][C]70[/C][C]442.48[/C][C]441.919996848465[/C][C]0.560003151535113[/C][/ROW]
[ROW][C]71[/C][C]442.81[/C][C]442.479955951022[/C][C]0.330044048978266[/C][/ROW]
[ROW][C]72[/C][C]442.81[/C][C]442.809974039248[/C][C]2.59607523389604e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203431&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203431&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
2373.1369.823.28000000000003
3374.55373.0997420002941.45025799970642
4375.01374.5498859249580.4601140750421
5374.81375.009963808141-0.199963808141376
6375.31374.8100157288430.499984271157359
7375.31375.3099606720143.93279863146745e-05
8375.39375.3099999969070.0800000030934598
9375.59375.3899937073240.200006292675994
10376.26375.5899842678160.670015732184424
11377.18376.2599472976030.920052702397015
12377.26377.1799276300830.0800723699168202
13377.26377.2599937016326.29836824828089e-06
14381.87377.2599999995054.61000000049546
15387.09381.8696373845595.2203626154411
16387.14387.0895893743830.0504106256165642
17388.78387.1399960347781.64000396522152
18389.16388.7798709998350.380129000165198
19389.16389.1599700996432.99003568215994e-05
20389.42389.1599999976480.260000002351887
21389.49389.4199795488040.0700204511963989
22388.97389.4899944923-0.519994492300043
23388.97388.970040901959-4.09019592666482e-05
24389.09388.9700000032170.119999996782667
25389.09389.0899905609879.43901341088349e-06
26391.76389.0899999992582.67000000074245
27390.96391.759789981946-0.799789981946219
28391.76390.9600629102380.799937089762011
29392.8391.7599370781911.04006292180929
30393.06392.7999181902660.260081809734288
31393.06393.0599795423692.04576312512472e-05
32393.26393.0599999983910.200000001609169
33393.87393.259984268310.610015731689543
34394.47393.869952017110.600047982890203
35394.57394.4699528011570.100047198842503
36394.57394.5699921304437.86955729381589e-06
37394.57394.5699999993816.19024831394199e-10
38399.57394.575.00000000000006
39406.13399.5696067077656.56039329223546
40407.03406.1294839696510.900516030348626
41409.46407.0299291668072.43007083319253
42409.9409.4598088544020.440191145598078
43409.9409.8999653752483.46247519473764e-05
44410.14409.8999999972760.240000002723548
45410.54410.1399811219720.400018878027538
46410.69410.5399685351360.15003146486373
47410.79410.6899881987580.10001180124209
48410.97410.7899921332270.180007866772996
49410.97410.9699858408611.41591392548435e-05
50413.8410.9699999988862.83000000111372
51423.31413.7997773965959.51022260340534
52423.85423.3092519406590.540748059341468
53426.6423.8499574655972.75004253440261
54426.26426.599783685925-0.339783685924829
55426.26426.260026726857-2.672685707239e-05
56426.32426.2600000021020.0599999978977053
57427.14426.3199952804930.820004719506642
58427.55427.1399354997020.410064500297892
59428.29427.5499677449630.740032255036795
60428.8428.2899417902120.510058209787985
61428.8428.7999598796134.01203866999822e-05
62434.87428.7999999968446.07000000315583
63435.66434.8695225432260.790477456774113
64440.75435.6599378222715.09006217772918
65440.99440.7495996236140.240400376386503
66441.04440.989981090480.0500189095203041
67441.04441.039996065593.93440973311954e-06
68441.88441.0399999996910.840000000309431
69441.92441.8799339269040.040066073095602
70442.48441.9199968484650.560003151535113
71442.81442.4799559510220.330044048978266
72442.81442.8099740392482.59607523389604e-05







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73442.809999997958439.109145339301446.510854656614
74442.809999997958437.576406984511448.043593011405
75442.809999997958436.400267830675449.21973216524
76442.809999997958435.408727331572450.211272664344
77442.809999997958434.535158143995451.084841851921
78442.809999997958433.745388680643451.874611315273
79442.809999997958433.01911908969452.600880906226
80442.809999997958432.343122737486453.27687725843
81442.809999997958431.708212294544453.911787701372
82442.809999997958431.107698479129454.512301516787
83442.809999997958430.536531398435455.083468597481
84442.809999997958429.990787772186455.62921222373

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 442.809999997958 & 439.109145339301 & 446.510854656614 \tabularnewline
74 & 442.809999997958 & 437.576406984511 & 448.043593011405 \tabularnewline
75 & 442.809999997958 & 436.400267830675 & 449.21973216524 \tabularnewline
76 & 442.809999997958 & 435.408727331572 & 450.211272664344 \tabularnewline
77 & 442.809999997958 & 434.535158143995 & 451.084841851921 \tabularnewline
78 & 442.809999997958 & 433.745388680643 & 451.874611315273 \tabularnewline
79 & 442.809999997958 & 433.01911908969 & 452.600880906226 \tabularnewline
80 & 442.809999997958 & 432.343122737486 & 453.27687725843 \tabularnewline
81 & 442.809999997958 & 431.708212294544 & 453.911787701372 \tabularnewline
82 & 442.809999997958 & 431.107698479129 & 454.512301516787 \tabularnewline
83 & 442.809999997958 & 430.536531398435 & 455.083468597481 \tabularnewline
84 & 442.809999997958 & 429.990787772186 & 455.62921222373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203431&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]442.809999997958[/C][C]439.109145339301[/C][C]446.510854656614[/C][/ROW]
[ROW][C]74[/C][C]442.809999997958[/C][C]437.576406984511[/C][C]448.043593011405[/C][/ROW]
[ROW][C]75[/C][C]442.809999997958[/C][C]436.400267830675[/C][C]449.21973216524[/C][/ROW]
[ROW][C]76[/C][C]442.809999997958[/C][C]435.408727331572[/C][C]450.211272664344[/C][/ROW]
[ROW][C]77[/C][C]442.809999997958[/C][C]434.535158143995[/C][C]451.084841851921[/C][/ROW]
[ROW][C]78[/C][C]442.809999997958[/C][C]433.745388680643[/C][C]451.874611315273[/C][/ROW]
[ROW][C]79[/C][C]442.809999997958[/C][C]433.01911908969[/C][C]452.600880906226[/C][/ROW]
[ROW][C]80[/C][C]442.809999997958[/C][C]432.343122737486[/C][C]453.27687725843[/C][/ROW]
[ROW][C]81[/C][C]442.809999997958[/C][C]431.708212294544[/C][C]453.911787701372[/C][/ROW]
[ROW][C]82[/C][C]442.809999997958[/C][C]431.107698479129[/C][C]454.512301516787[/C][/ROW]
[ROW][C]83[/C][C]442.809999997958[/C][C]430.536531398435[/C][C]455.083468597481[/C][/ROW]
[ROW][C]84[/C][C]442.809999997958[/C][C]429.990787772186[/C][C]455.62921222373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203431&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203431&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
73442.809999997958439.109145339301446.510854656614
74442.809999997958437.576406984511448.043593011405
75442.809999997958436.400267830675449.21973216524
76442.809999997958435.408727331572450.211272664344
77442.809999997958434.535158143995451.084841851921
78442.809999997958433.745388680643451.874611315273
79442.809999997958433.01911908969452.600880906226
80442.809999997958432.343122737486453.27687725843
81442.809999997958431.708212294544453.911787701372
82442.809999997958431.107698479129454.512301516787
83442.809999997958430.536531398435455.083468597481
84442.809999997958429.990787772186455.62921222373



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