Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 26 Nov 2014 20:49:16 +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/2014/Nov/26/t1417035003zyrsqlt9u703xks.htm/, Retrieved Sun, 19 May 2024 23:08:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=259437, Retrieved Sun, 19 May 2024 23:08:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Invoergegevens EU] [2014-11-26 20:49:16] [c53767938e2c856c14b03e8e32322294] [Current]
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Dataseries X:
13396
13637
15467
13722
14727
14961
14026
13895
14474
15759
15995
14119
15342
15796
15435
16195
15572
16223
15921
14143
16290
16579
14314
13318
11938
12574
13298
12124
11757
12803
12800
11293
12992
13426
13174
13648
12801
13183
15703
14859
14350
16444
14207
13329
14795
15248
16081
15670
14805
15779
17945
15280
16773
16362
15774
15505
16397
16060
16748
16137
15523
16267
18066
16105
16883
17034
16452
16234
16658
18133
17488
15853
17198
16719
17635
16726
17503
17074
17054
15451
16374
17242
16684
16489




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259437&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259437&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259437&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.462876868952292
beta0.057463071958549
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.462876868952292 \tabularnewline
beta & 0.057463071958549 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259437&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]0.462876868952292[/C][/ROW]
[ROW][C]beta[/C][C]0.057463071958549[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259437&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259437&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
alpha0.462876868952292
beta0.057463071958549
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
315467138781589
41372214896.7760860958-1174.77608609576
51472714605.017072686121.982927314042
61496114916.742352957144.2576470428539
71402615193.6675782187-1167.66757821868
81389514878.5626459343-983.562645934282
91447414622.5145075514-148.514507551447
101575914749.04059947711009.95940052294
111599515438.6606969538556.339303046245
121411915933.1082386266-1814.1082386266
131534215282.078200360959.9217996391089
141579615500.0871381411295.912861858884
151543515835.2016669149-400.201666914854
161619515837.4561874437357.543812556331
171557216199.9636301548-627.963630154762
181622316089.5996915833133.400308416742
191592116335.2017340332-414.201734033215
201414316316.3143845473-2173.31438454729
211629015425.3679529557864.632047044344
221657915963.6144194377615.385580562326
231431416402.8586887144-2088.85868871445
241331815534.8106916451-2216.81069164512
251193814548.5732167897-2610.57321678966
261257413310.6352975545-736.635297554503
271329812920.5066285881377.493371411909
281212413056.1230415913-932.12304159126
291175712560.7553965103-803.755396510322
301280312103.4276163326699.572383667368
311280012360.5629469536439.437053046393
321129312508.9759405904-1215.97594059038
331299211858.79362542611133.20637457386
341342612326.13485841831099.86514158166
351317412807.2977783792366.702221620777
361364812958.8502070561689.149792943883
371280113277.9863893749-476.986389374872
381318313044.6580669726138.341933027423
391570313099.83065577032603.16934422972
401485914365.154788181493.845211819016
411435014667.2570269226-317.257026922585
421644414585.48029490451858.51970509546
431420715560.2537986757-1353.25379867569
441332915012.3773524182-1683.37735241816
451479514266.9193282415528.080671758487
461524814559.1401324144688.859867585554
471608114944.10442724161136.89557275841
481567015566.6936064721103.306393527851
491480515713.606039856-908.606039856026
501577915367.9602140148411.039785985209
511794515644.08088673212300.91911326792
521528016856.1835837404-1576.18358374043
531677316231.7412776489541.258722351069
541636216601.8106127841-239.810612784084
551577416603.9624585814-829.962458581442
561550516310.8710530609-805.871053060924
571639716007.4961802454389.50381975458
581606016267.7928356818-207.792835681801
591674816246.087743658501.912256341981
601613716566.2387487431-429.238748743148
611552316443.9644595461-920.96445954614
621626716069.5855992568197.41440074319
631806616218.12933687231847.87066312773
641610517179.7813693978-1074.78136939776
651688316760.0179939383122.982006061688
661703416897.9426950485136.057304951479
671645217045.538546234-593.538546233965
681623416839.634221984-605.634221984034
691665816612.022232240245.9777677598395
701813316687.24929177441445.75070822557
711748817448.853417085639.146582914389
721585317560.414262624-1707.41426262396
731719816818.1181299558379.881870044166
741671917052.087317889-333.08731788904
751763516947.1799951086687.82000489139
761672617333.1219186766-607.121918676567
771750317103.5167519706399.483248029406
781707417350.4714190943-276.471419094298
791705417277.1886291823-223.188629182267
801545117222.6327661304-1771.63276613035
811637416404.2154618867-30.2154618866698
821724216391.0562662401850.943733759894
831668416808.3989596662-124.3989596662
841648916770.9692768174-281.969276817395

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 15467 & 13878 & 1589 \tabularnewline
4 & 13722 & 14896.7760860958 & -1174.77608609576 \tabularnewline
5 & 14727 & 14605.017072686 & 121.982927314042 \tabularnewline
6 & 14961 & 14916.7423529571 & 44.2576470428539 \tabularnewline
7 & 14026 & 15193.6675782187 & -1167.66757821868 \tabularnewline
8 & 13895 & 14878.5626459343 & -983.562645934282 \tabularnewline
9 & 14474 & 14622.5145075514 & -148.514507551447 \tabularnewline
10 & 15759 & 14749.0405994771 & 1009.95940052294 \tabularnewline
11 & 15995 & 15438.6606969538 & 556.339303046245 \tabularnewline
12 & 14119 & 15933.1082386266 & -1814.1082386266 \tabularnewline
13 & 15342 & 15282.0782003609 & 59.9217996391089 \tabularnewline
14 & 15796 & 15500.0871381411 & 295.912861858884 \tabularnewline
15 & 15435 & 15835.2016669149 & -400.201666914854 \tabularnewline
16 & 16195 & 15837.4561874437 & 357.543812556331 \tabularnewline
17 & 15572 & 16199.9636301548 & -627.963630154762 \tabularnewline
18 & 16223 & 16089.5996915833 & 133.400308416742 \tabularnewline
19 & 15921 & 16335.2017340332 & -414.201734033215 \tabularnewline
20 & 14143 & 16316.3143845473 & -2173.31438454729 \tabularnewline
21 & 16290 & 15425.3679529557 & 864.632047044344 \tabularnewline
22 & 16579 & 15963.6144194377 & 615.385580562326 \tabularnewline
23 & 14314 & 16402.8586887144 & -2088.85868871445 \tabularnewline
24 & 13318 & 15534.8106916451 & -2216.81069164512 \tabularnewline
25 & 11938 & 14548.5732167897 & -2610.57321678966 \tabularnewline
26 & 12574 & 13310.6352975545 & -736.635297554503 \tabularnewline
27 & 13298 & 12920.5066285881 & 377.493371411909 \tabularnewline
28 & 12124 & 13056.1230415913 & -932.12304159126 \tabularnewline
29 & 11757 & 12560.7553965103 & -803.755396510322 \tabularnewline
30 & 12803 & 12103.4276163326 & 699.572383667368 \tabularnewline
31 & 12800 & 12360.5629469536 & 439.437053046393 \tabularnewline
32 & 11293 & 12508.9759405904 & -1215.97594059038 \tabularnewline
33 & 12992 & 11858.7936254261 & 1133.20637457386 \tabularnewline
34 & 13426 & 12326.1348584183 & 1099.86514158166 \tabularnewline
35 & 13174 & 12807.2977783792 & 366.702221620777 \tabularnewline
36 & 13648 & 12958.8502070561 & 689.149792943883 \tabularnewline
37 & 12801 & 13277.9863893749 & -476.986389374872 \tabularnewline
38 & 13183 & 13044.6580669726 & 138.341933027423 \tabularnewline
39 & 15703 & 13099.8306557703 & 2603.16934422972 \tabularnewline
40 & 14859 & 14365.154788181 & 493.845211819016 \tabularnewline
41 & 14350 & 14667.2570269226 & -317.257026922585 \tabularnewline
42 & 16444 & 14585.4802949045 & 1858.51970509546 \tabularnewline
43 & 14207 & 15560.2537986757 & -1353.25379867569 \tabularnewline
44 & 13329 & 15012.3773524182 & -1683.37735241816 \tabularnewline
45 & 14795 & 14266.9193282415 & 528.080671758487 \tabularnewline
46 & 15248 & 14559.1401324144 & 688.859867585554 \tabularnewline
47 & 16081 & 14944.1044272416 & 1136.89557275841 \tabularnewline
48 & 15670 & 15566.6936064721 & 103.306393527851 \tabularnewline
49 & 14805 & 15713.606039856 & -908.606039856026 \tabularnewline
50 & 15779 & 15367.9602140148 & 411.039785985209 \tabularnewline
51 & 17945 & 15644.0808867321 & 2300.91911326792 \tabularnewline
52 & 15280 & 16856.1835837404 & -1576.18358374043 \tabularnewline
53 & 16773 & 16231.7412776489 & 541.258722351069 \tabularnewline
54 & 16362 & 16601.8106127841 & -239.810612784084 \tabularnewline
55 & 15774 & 16603.9624585814 & -829.962458581442 \tabularnewline
56 & 15505 & 16310.8710530609 & -805.871053060924 \tabularnewline
57 & 16397 & 16007.4961802454 & 389.50381975458 \tabularnewline
58 & 16060 & 16267.7928356818 & -207.792835681801 \tabularnewline
59 & 16748 & 16246.087743658 & 501.912256341981 \tabularnewline
60 & 16137 & 16566.2387487431 & -429.238748743148 \tabularnewline
61 & 15523 & 16443.9644595461 & -920.96445954614 \tabularnewline
62 & 16267 & 16069.5855992568 & 197.41440074319 \tabularnewline
63 & 18066 & 16218.1293368723 & 1847.87066312773 \tabularnewline
64 & 16105 & 17179.7813693978 & -1074.78136939776 \tabularnewline
65 & 16883 & 16760.0179939383 & 122.982006061688 \tabularnewline
66 & 17034 & 16897.9426950485 & 136.057304951479 \tabularnewline
67 & 16452 & 17045.538546234 & -593.538546233965 \tabularnewline
68 & 16234 & 16839.634221984 & -605.634221984034 \tabularnewline
69 & 16658 & 16612.0222322402 & 45.9777677598395 \tabularnewline
70 & 18133 & 16687.2492917744 & 1445.75070822557 \tabularnewline
71 & 17488 & 17448.8534170856 & 39.146582914389 \tabularnewline
72 & 15853 & 17560.414262624 & -1707.41426262396 \tabularnewline
73 & 17198 & 16818.1181299558 & 379.881870044166 \tabularnewline
74 & 16719 & 17052.087317889 & -333.08731788904 \tabularnewline
75 & 17635 & 16947.1799951086 & 687.82000489139 \tabularnewline
76 & 16726 & 17333.1219186766 & -607.121918676567 \tabularnewline
77 & 17503 & 17103.5167519706 & 399.483248029406 \tabularnewline
78 & 17074 & 17350.4714190943 & -276.471419094298 \tabularnewline
79 & 17054 & 17277.1886291823 & -223.188629182267 \tabularnewline
80 & 15451 & 17222.6327661304 & -1771.63276613035 \tabularnewline
81 & 16374 & 16404.2154618867 & -30.2154618866698 \tabularnewline
82 & 17242 & 16391.0562662401 & 850.943733759894 \tabularnewline
83 & 16684 & 16808.3989596662 & -124.3989596662 \tabularnewline
84 & 16489 & 16770.9692768174 & -281.969276817395 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259437&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]15467[/C][C]13878[/C][C]1589[/C][/ROW]
[ROW][C]4[/C][C]13722[/C][C]14896.7760860958[/C][C]-1174.77608609576[/C][/ROW]
[ROW][C]5[/C][C]14727[/C][C]14605.017072686[/C][C]121.982927314042[/C][/ROW]
[ROW][C]6[/C][C]14961[/C][C]14916.7423529571[/C][C]44.2576470428539[/C][/ROW]
[ROW][C]7[/C][C]14026[/C][C]15193.6675782187[/C][C]-1167.66757821868[/C][/ROW]
[ROW][C]8[/C][C]13895[/C][C]14878.5626459343[/C][C]-983.562645934282[/C][/ROW]
[ROW][C]9[/C][C]14474[/C][C]14622.5145075514[/C][C]-148.514507551447[/C][/ROW]
[ROW][C]10[/C][C]15759[/C][C]14749.0405994771[/C][C]1009.95940052294[/C][/ROW]
[ROW][C]11[/C][C]15995[/C][C]15438.6606969538[/C][C]556.339303046245[/C][/ROW]
[ROW][C]12[/C][C]14119[/C][C]15933.1082386266[/C][C]-1814.1082386266[/C][/ROW]
[ROW][C]13[/C][C]15342[/C][C]15282.0782003609[/C][C]59.9217996391089[/C][/ROW]
[ROW][C]14[/C][C]15796[/C][C]15500.0871381411[/C][C]295.912861858884[/C][/ROW]
[ROW][C]15[/C][C]15435[/C][C]15835.2016669149[/C][C]-400.201666914854[/C][/ROW]
[ROW][C]16[/C][C]16195[/C][C]15837.4561874437[/C][C]357.543812556331[/C][/ROW]
[ROW][C]17[/C][C]15572[/C][C]16199.9636301548[/C][C]-627.963630154762[/C][/ROW]
[ROW][C]18[/C][C]16223[/C][C]16089.5996915833[/C][C]133.400308416742[/C][/ROW]
[ROW][C]19[/C][C]15921[/C][C]16335.2017340332[/C][C]-414.201734033215[/C][/ROW]
[ROW][C]20[/C][C]14143[/C][C]16316.3143845473[/C][C]-2173.31438454729[/C][/ROW]
[ROW][C]21[/C][C]16290[/C][C]15425.3679529557[/C][C]864.632047044344[/C][/ROW]
[ROW][C]22[/C][C]16579[/C][C]15963.6144194377[/C][C]615.385580562326[/C][/ROW]
[ROW][C]23[/C][C]14314[/C][C]16402.8586887144[/C][C]-2088.85868871445[/C][/ROW]
[ROW][C]24[/C][C]13318[/C][C]15534.8106916451[/C][C]-2216.81069164512[/C][/ROW]
[ROW][C]25[/C][C]11938[/C][C]14548.5732167897[/C][C]-2610.57321678966[/C][/ROW]
[ROW][C]26[/C][C]12574[/C][C]13310.6352975545[/C][C]-736.635297554503[/C][/ROW]
[ROW][C]27[/C][C]13298[/C][C]12920.5066285881[/C][C]377.493371411909[/C][/ROW]
[ROW][C]28[/C][C]12124[/C][C]13056.1230415913[/C][C]-932.12304159126[/C][/ROW]
[ROW][C]29[/C][C]11757[/C][C]12560.7553965103[/C][C]-803.755396510322[/C][/ROW]
[ROW][C]30[/C][C]12803[/C][C]12103.4276163326[/C][C]699.572383667368[/C][/ROW]
[ROW][C]31[/C][C]12800[/C][C]12360.5629469536[/C][C]439.437053046393[/C][/ROW]
[ROW][C]32[/C][C]11293[/C][C]12508.9759405904[/C][C]-1215.97594059038[/C][/ROW]
[ROW][C]33[/C][C]12992[/C][C]11858.7936254261[/C][C]1133.20637457386[/C][/ROW]
[ROW][C]34[/C][C]13426[/C][C]12326.1348584183[/C][C]1099.86514158166[/C][/ROW]
[ROW][C]35[/C][C]13174[/C][C]12807.2977783792[/C][C]366.702221620777[/C][/ROW]
[ROW][C]36[/C][C]13648[/C][C]12958.8502070561[/C][C]689.149792943883[/C][/ROW]
[ROW][C]37[/C][C]12801[/C][C]13277.9863893749[/C][C]-476.986389374872[/C][/ROW]
[ROW][C]38[/C][C]13183[/C][C]13044.6580669726[/C][C]138.341933027423[/C][/ROW]
[ROW][C]39[/C][C]15703[/C][C]13099.8306557703[/C][C]2603.16934422972[/C][/ROW]
[ROW][C]40[/C][C]14859[/C][C]14365.154788181[/C][C]493.845211819016[/C][/ROW]
[ROW][C]41[/C][C]14350[/C][C]14667.2570269226[/C][C]-317.257026922585[/C][/ROW]
[ROW][C]42[/C][C]16444[/C][C]14585.4802949045[/C][C]1858.51970509546[/C][/ROW]
[ROW][C]43[/C][C]14207[/C][C]15560.2537986757[/C][C]-1353.25379867569[/C][/ROW]
[ROW][C]44[/C][C]13329[/C][C]15012.3773524182[/C][C]-1683.37735241816[/C][/ROW]
[ROW][C]45[/C][C]14795[/C][C]14266.9193282415[/C][C]528.080671758487[/C][/ROW]
[ROW][C]46[/C][C]15248[/C][C]14559.1401324144[/C][C]688.859867585554[/C][/ROW]
[ROW][C]47[/C][C]16081[/C][C]14944.1044272416[/C][C]1136.89557275841[/C][/ROW]
[ROW][C]48[/C][C]15670[/C][C]15566.6936064721[/C][C]103.306393527851[/C][/ROW]
[ROW][C]49[/C][C]14805[/C][C]15713.606039856[/C][C]-908.606039856026[/C][/ROW]
[ROW][C]50[/C][C]15779[/C][C]15367.9602140148[/C][C]411.039785985209[/C][/ROW]
[ROW][C]51[/C][C]17945[/C][C]15644.0808867321[/C][C]2300.91911326792[/C][/ROW]
[ROW][C]52[/C][C]15280[/C][C]16856.1835837404[/C][C]-1576.18358374043[/C][/ROW]
[ROW][C]53[/C][C]16773[/C][C]16231.7412776489[/C][C]541.258722351069[/C][/ROW]
[ROW][C]54[/C][C]16362[/C][C]16601.8106127841[/C][C]-239.810612784084[/C][/ROW]
[ROW][C]55[/C][C]15774[/C][C]16603.9624585814[/C][C]-829.962458581442[/C][/ROW]
[ROW][C]56[/C][C]15505[/C][C]16310.8710530609[/C][C]-805.871053060924[/C][/ROW]
[ROW][C]57[/C][C]16397[/C][C]16007.4961802454[/C][C]389.50381975458[/C][/ROW]
[ROW][C]58[/C][C]16060[/C][C]16267.7928356818[/C][C]-207.792835681801[/C][/ROW]
[ROW][C]59[/C][C]16748[/C][C]16246.087743658[/C][C]501.912256341981[/C][/ROW]
[ROW][C]60[/C][C]16137[/C][C]16566.2387487431[/C][C]-429.238748743148[/C][/ROW]
[ROW][C]61[/C][C]15523[/C][C]16443.9644595461[/C][C]-920.96445954614[/C][/ROW]
[ROW][C]62[/C][C]16267[/C][C]16069.5855992568[/C][C]197.41440074319[/C][/ROW]
[ROW][C]63[/C][C]18066[/C][C]16218.1293368723[/C][C]1847.87066312773[/C][/ROW]
[ROW][C]64[/C][C]16105[/C][C]17179.7813693978[/C][C]-1074.78136939776[/C][/ROW]
[ROW][C]65[/C][C]16883[/C][C]16760.0179939383[/C][C]122.982006061688[/C][/ROW]
[ROW][C]66[/C][C]17034[/C][C]16897.9426950485[/C][C]136.057304951479[/C][/ROW]
[ROW][C]67[/C][C]16452[/C][C]17045.538546234[/C][C]-593.538546233965[/C][/ROW]
[ROW][C]68[/C][C]16234[/C][C]16839.634221984[/C][C]-605.634221984034[/C][/ROW]
[ROW][C]69[/C][C]16658[/C][C]16612.0222322402[/C][C]45.9777677598395[/C][/ROW]
[ROW][C]70[/C][C]18133[/C][C]16687.2492917744[/C][C]1445.75070822557[/C][/ROW]
[ROW][C]71[/C][C]17488[/C][C]17448.8534170856[/C][C]39.146582914389[/C][/ROW]
[ROW][C]72[/C][C]15853[/C][C]17560.414262624[/C][C]-1707.41426262396[/C][/ROW]
[ROW][C]73[/C][C]17198[/C][C]16818.1181299558[/C][C]379.881870044166[/C][/ROW]
[ROW][C]74[/C][C]16719[/C][C]17052.087317889[/C][C]-333.08731788904[/C][/ROW]
[ROW][C]75[/C][C]17635[/C][C]16947.1799951086[/C][C]687.82000489139[/C][/ROW]
[ROW][C]76[/C][C]16726[/C][C]17333.1219186766[/C][C]-607.121918676567[/C][/ROW]
[ROW][C]77[/C][C]17503[/C][C]17103.5167519706[/C][C]399.483248029406[/C][/ROW]
[ROW][C]78[/C][C]17074[/C][C]17350.4714190943[/C][C]-276.471419094298[/C][/ROW]
[ROW][C]79[/C][C]17054[/C][C]17277.1886291823[/C][C]-223.188629182267[/C][/ROW]
[ROW][C]80[/C][C]15451[/C][C]17222.6327661304[/C][C]-1771.63276613035[/C][/ROW]
[ROW][C]81[/C][C]16374[/C][C]16404.2154618867[/C][C]-30.2154618866698[/C][/ROW]
[ROW][C]82[/C][C]17242[/C][C]16391.0562662401[/C][C]850.943733759894[/C][/ROW]
[ROW][C]83[/C][C]16684[/C][C]16808.3989596662[/C][C]-124.3989596662[/C][/ROW]
[ROW][C]84[/C][C]16489[/C][C]16770.9692768174[/C][C]-281.969276817395[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259437&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259437&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
315467138781589
41372214896.7760860958-1174.77608609576
51472714605.017072686121.982927314042
61496114916.742352957144.2576470428539
71402615193.6675782187-1167.66757821868
81389514878.5626459343-983.562645934282
91447414622.5145075514-148.514507551447
101575914749.04059947711009.95940052294
111599515438.6606969538556.339303046245
121411915933.1082386266-1814.1082386266
131534215282.078200360959.9217996391089
141579615500.0871381411295.912861858884
151543515835.2016669149-400.201666914854
161619515837.4561874437357.543812556331
171557216199.9636301548-627.963630154762
181622316089.5996915833133.400308416742
191592116335.2017340332-414.201734033215
201414316316.3143845473-2173.31438454729
211629015425.3679529557864.632047044344
221657915963.6144194377615.385580562326
231431416402.8586887144-2088.85868871445
241331815534.8106916451-2216.81069164512
251193814548.5732167897-2610.57321678966
261257413310.6352975545-736.635297554503
271329812920.5066285881377.493371411909
281212413056.1230415913-932.12304159126
291175712560.7553965103-803.755396510322
301280312103.4276163326699.572383667368
311280012360.5629469536439.437053046393
321129312508.9759405904-1215.97594059038
331299211858.79362542611133.20637457386
341342612326.13485841831099.86514158166
351317412807.2977783792366.702221620777
361364812958.8502070561689.149792943883
371280113277.9863893749-476.986389374872
381318313044.6580669726138.341933027423
391570313099.83065577032603.16934422972
401485914365.154788181493.845211819016
411435014667.2570269226-317.257026922585
421644414585.48029490451858.51970509546
431420715560.2537986757-1353.25379867569
441332915012.3773524182-1683.37735241816
451479514266.9193282415528.080671758487
461524814559.1401324144688.859867585554
471608114944.10442724161136.89557275841
481567015566.6936064721103.306393527851
491480515713.606039856-908.606039856026
501577915367.9602140148411.039785985209
511794515644.08088673212300.91911326792
521528016856.1835837404-1576.18358374043
531677316231.7412776489541.258722351069
541636216601.8106127841-239.810612784084
551577416603.9624585814-829.962458581442
561550516310.8710530609-805.871053060924
571639716007.4961802454389.50381975458
581606016267.7928356818-207.792835681801
591674816246.087743658501.912256341981
601613716566.2387487431-429.238748743148
611552316443.9644595461-920.96445954614
621626716069.5855992568197.41440074319
631806616218.12933687231847.87066312773
641610517179.7813693978-1074.78136939776
651688316760.0179939383122.982006061688
661703416897.9426950485136.057304951479
671645217045.538546234-593.538546233965
681623416839.634221984-605.634221984034
691665816612.022232240245.9777677598395
701813316687.24929177441445.75070822557
711748817448.853417085639.146582914389
721585317560.414262624-1707.41426262396
731719816818.1181299558379.881870044166
741671917052.087317889-333.08731788904
751763516947.1799951086687.82000489139
761672617333.1219186766-607.121918676567
771750317103.5167519706399.483248029406
781707417350.4714190943-276.471419094298
791705417277.1886291823-223.188629182267
801545117222.6327661304-1771.63276613035
811637416404.2154618867-30.2154618866698
821724216391.0562662401850.943733759894
831668416808.3989596662-124.3989596662
841648916770.9692768174-281.969276817395







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8516653.104027945414638.696836269118667.5112196217
8616665.755835067414422.981442264618908.5302278703
8716678.407642189414206.410846167519150.4044382114
8816691.059449311413988.140381998119393.9785166248
8916703.711256433413767.593316925619639.8291959413
9016716.363063555513544.366693242119888.3594338688
9116729.014870677513318.174747897220139.8549934577
9216741.666677799513088.813235990420394.5201196085
9316754.318484921512856.136043223120652.5009266198
9416766.970292043512620.039355744820913.9012283422
9516779.622099165512380.450654982821178.7935433482
9616792.273906287512137.320891875321447.2269206997

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 16653.1040279454 & 14638.6968362691 & 18667.5112196217 \tabularnewline
86 & 16665.7558350674 & 14422.9814422646 & 18908.5302278703 \tabularnewline
87 & 16678.4076421894 & 14206.4108461675 & 19150.4044382114 \tabularnewline
88 & 16691.0594493114 & 13988.1403819981 & 19393.9785166248 \tabularnewline
89 & 16703.7112564334 & 13767.5933169256 & 19639.8291959413 \tabularnewline
90 & 16716.3630635555 & 13544.3666932421 & 19888.3594338688 \tabularnewline
91 & 16729.0148706775 & 13318.1747478972 & 20139.8549934577 \tabularnewline
92 & 16741.6666777995 & 13088.8132359904 & 20394.5201196085 \tabularnewline
93 & 16754.3184849215 & 12856.1360432231 & 20652.5009266198 \tabularnewline
94 & 16766.9702920435 & 12620.0393557448 & 20913.9012283422 \tabularnewline
95 & 16779.6220991655 & 12380.4506549828 & 21178.7935433482 \tabularnewline
96 & 16792.2739062875 & 12137.3208918753 & 21447.2269206997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259437&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]85[/C][C]16653.1040279454[/C][C]14638.6968362691[/C][C]18667.5112196217[/C][/ROW]
[ROW][C]86[/C][C]16665.7558350674[/C][C]14422.9814422646[/C][C]18908.5302278703[/C][/ROW]
[ROW][C]87[/C][C]16678.4076421894[/C][C]14206.4108461675[/C][C]19150.4044382114[/C][/ROW]
[ROW][C]88[/C][C]16691.0594493114[/C][C]13988.1403819981[/C][C]19393.9785166248[/C][/ROW]
[ROW][C]89[/C][C]16703.7112564334[/C][C]13767.5933169256[/C][C]19639.8291959413[/C][/ROW]
[ROW][C]90[/C][C]16716.3630635555[/C][C]13544.3666932421[/C][C]19888.3594338688[/C][/ROW]
[ROW][C]91[/C][C]16729.0148706775[/C][C]13318.1747478972[/C][C]20139.8549934577[/C][/ROW]
[ROW][C]92[/C][C]16741.6666777995[/C][C]13088.8132359904[/C][C]20394.5201196085[/C][/ROW]
[ROW][C]93[/C][C]16754.3184849215[/C][C]12856.1360432231[/C][C]20652.5009266198[/C][/ROW]
[ROW][C]94[/C][C]16766.9702920435[/C][C]12620.0393557448[/C][C]20913.9012283422[/C][/ROW]
[ROW][C]95[/C][C]16779.6220991655[/C][C]12380.4506549828[/C][C]21178.7935433482[/C][/ROW]
[ROW][C]96[/C][C]16792.2739062875[/C][C]12137.3208918753[/C][C]21447.2269206997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259437&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259437&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
8516653.104027945414638.696836269118667.5112196217
8616665.755835067414422.981442264618908.5302278703
8716678.407642189414206.410846167519150.4044382114
8816691.059449311413988.140381998119393.9785166248
8916703.711256433413767.593316925619639.8291959413
9016716.363063555513544.366693242119888.3594338688
9116729.014870677513318.174747897220139.8549934577
9216741.666677799513088.813235990420394.5201196085
9316754.318484921512856.136043223120652.5009266198
9416766.970292043512620.039355744820913.9012283422
9516779.622099165512380.450654982821178.7935433482
9616792.273906287512137.320891875321447.2269206997



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')