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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 computationThu, 23 May 2013 05:12:58 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/23/t136930040689t2ezsfa4ffl9d.htm/, Retrieved Mon, 29 Apr 2024 17:08:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210320, Retrieved Mon, 29 Apr 2024 17:08:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opdracht10] [2013-05-23 09:12:58] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
19
14
15
7
12
12
14
9
8
4
7
3
5
0
-2
6
11
9
17
21
21
41
57
65
68
73
71
71
70
69
65
57
57
57
55
65
65
64
60
43
47
40
31
27
24
23
17
16
15
8
5
6
5
12
8
17
22
24
36
31
34
47
33
35
31
35
39
46
40
50
62
57
62
57




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210320&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210320&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210320&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999954412762013
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999954412762013 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210320&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]0.999954412762013[/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=210320&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210320&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
alpha0.999954412762013
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21419-5
31514.00022793618990.999772063810065
4714.999954423153-7.99995442315299
5127.000364695826174.99963530417383
61211.99977208043550.000227919564459
71411.99999998960982.00000001039022
8913.9999088255236-4.99990882552355
989.00022793203354-1.00022793203354
1048.00004559762878-4.00004559762878
1174.000182351030622.99981764896938
1236.99986324659892-3.99986324659892
1353.000182342717741.99981765728226
1404.99990883383653-4.99990883383653
15-20.000227932033921295-2.00022793203392
166-1.999908815133237.99990881513323
17115.999635306252975.00036469374703
18910.9997720471847-1.99977204718468
19179.000091164084247.99990883591576
202116.9996353062524.00036469374798
212120.99981763442270.000182365577327204
224120.999999991686520.0000000083135
235740.999088255239916.0009117447601
246556.99927056262838.00072943737172
256864.99963526884313.00036473115694
267367.9998632216595.00013677834104
277172.9997720575747-1.99977205757472
287171.0000911640847-9.11640847078843e-05
297071.0000000041559-1.00000000415592
306970.0000455872382-1.00004558723818
316569.0000455893162-4.00004558931619
325765.0001823510302-8.00018235103023
335757.0003647062168-0.000364706216778643
345757.0000000166259-1.66259468414864e-08
355557.0000000000008-2.00000000000076
366555.0000911744769.99990882552402
376564.99954413177650.00045586822348298
386464.9999999792182-0.999999979218231
396064.000045587237-4.00004558723704
404360.0001823510301-17.0001823510301
414743.00077499135873.99922500864134
424046.9998176863778-6.99981768637777
433140.0003191023547-9.00031910235474
442731.0004102996889-4.00041029968888
452427.0001823676564-3.00018236765638
462324.0001367700276-1.0001367700276
471723.000045593473-6.00004559347295
481617.0002735255064-1.0002735255064
491516.0000455997073-1.00004559970726
50815.0000455893168-7.00004558931675
5158.0003191127442-3.0003191127442
5265.000136776261430.99986322373857
5355.99995441899727-0.999954418997265
54125.000045585160086.99995441483992
55811.9996808914122-3.99968089141219
56178.000182334404678.99981766559533
572216.99958972317025.00041027682976
582421.99977204510672.00022795489332
593623.999908815132212.0000911848678
603135.9994529489873-4.99945294898729
613431.00022791125142.99977208874861
624733.999863248675913.0001367513241
633346.9994073596721-13.9994073596721
643533.0006381943151.99936180568502
653134.9999088546175-3.99990885461754
663531.00018234479693.99981765520312
673934.99981765936064.00018234063936
684638.99981764273567.00018235726436
694045.9996808810209-5.99968088102093
705040.00027350888029.99972649111983
716249.999544140088612.0004558599114
725761.9994529323628-4.99945293236276
736257.00022791125064.99977208874937
745761.9997720741999-4.99977207419991

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 14 & 19 & -5 \tabularnewline
3 & 15 & 14.0002279361899 & 0.999772063810065 \tabularnewline
4 & 7 & 14.999954423153 & -7.99995442315299 \tabularnewline
5 & 12 & 7.00036469582617 & 4.99963530417383 \tabularnewline
6 & 12 & 11.9997720804355 & 0.000227919564459 \tabularnewline
7 & 14 & 11.9999999896098 & 2.00000001039022 \tabularnewline
8 & 9 & 13.9999088255236 & -4.99990882552355 \tabularnewline
9 & 8 & 9.00022793203354 & -1.00022793203354 \tabularnewline
10 & 4 & 8.00004559762878 & -4.00004559762878 \tabularnewline
11 & 7 & 4.00018235103062 & 2.99981764896938 \tabularnewline
12 & 3 & 6.99986324659892 & -3.99986324659892 \tabularnewline
13 & 5 & 3.00018234271774 & 1.99981765728226 \tabularnewline
14 & 0 & 4.99990883383653 & -4.99990883383653 \tabularnewline
15 & -2 & 0.000227932033921295 & -2.00022793203392 \tabularnewline
16 & 6 & -1.99990881513323 & 7.99990881513323 \tabularnewline
17 & 11 & 5.99963530625297 & 5.00036469374703 \tabularnewline
18 & 9 & 10.9997720471847 & -1.99977204718468 \tabularnewline
19 & 17 & 9.00009116408424 & 7.99990883591576 \tabularnewline
20 & 21 & 16.999635306252 & 4.00036469374798 \tabularnewline
21 & 21 & 20.9998176344227 & 0.000182365577327204 \tabularnewline
22 & 41 & 20.9999999916865 & 20.0000000083135 \tabularnewline
23 & 57 & 40.9990882552399 & 16.0009117447601 \tabularnewline
24 & 65 & 56.9992705626283 & 8.00072943737172 \tabularnewline
25 & 68 & 64.9996352688431 & 3.00036473115694 \tabularnewline
26 & 73 & 67.999863221659 & 5.00013677834104 \tabularnewline
27 & 71 & 72.9997720575747 & -1.99977205757472 \tabularnewline
28 & 71 & 71.0000911640847 & -9.11640847078843e-05 \tabularnewline
29 & 70 & 71.0000000041559 & -1.00000000415592 \tabularnewline
30 & 69 & 70.0000455872382 & -1.00004558723818 \tabularnewline
31 & 65 & 69.0000455893162 & -4.00004558931619 \tabularnewline
32 & 57 & 65.0001823510302 & -8.00018235103023 \tabularnewline
33 & 57 & 57.0003647062168 & -0.000364706216778643 \tabularnewline
34 & 57 & 57.0000000166259 & -1.66259468414864e-08 \tabularnewline
35 & 55 & 57.0000000000008 & -2.00000000000076 \tabularnewline
36 & 65 & 55.000091174476 & 9.99990882552402 \tabularnewline
37 & 65 & 64.9995441317765 & 0.00045586822348298 \tabularnewline
38 & 64 & 64.9999999792182 & -0.999999979218231 \tabularnewline
39 & 60 & 64.000045587237 & -4.00004558723704 \tabularnewline
40 & 43 & 60.0001823510301 & -17.0001823510301 \tabularnewline
41 & 47 & 43.0007749913587 & 3.99922500864134 \tabularnewline
42 & 40 & 46.9998176863778 & -6.99981768637777 \tabularnewline
43 & 31 & 40.0003191023547 & -9.00031910235474 \tabularnewline
44 & 27 & 31.0004102996889 & -4.00041029968888 \tabularnewline
45 & 24 & 27.0001823676564 & -3.00018236765638 \tabularnewline
46 & 23 & 24.0001367700276 & -1.0001367700276 \tabularnewline
47 & 17 & 23.000045593473 & -6.00004559347295 \tabularnewline
48 & 16 & 17.0002735255064 & -1.0002735255064 \tabularnewline
49 & 15 & 16.0000455997073 & -1.00004559970726 \tabularnewline
50 & 8 & 15.0000455893168 & -7.00004558931675 \tabularnewline
51 & 5 & 8.0003191127442 & -3.0003191127442 \tabularnewline
52 & 6 & 5.00013677626143 & 0.99986322373857 \tabularnewline
53 & 5 & 5.99995441899727 & -0.999954418997265 \tabularnewline
54 & 12 & 5.00004558516008 & 6.99995441483992 \tabularnewline
55 & 8 & 11.9996808914122 & -3.99968089141219 \tabularnewline
56 & 17 & 8.00018233440467 & 8.99981766559533 \tabularnewline
57 & 22 & 16.9995897231702 & 5.00041027682976 \tabularnewline
58 & 24 & 21.9997720451067 & 2.00022795489332 \tabularnewline
59 & 36 & 23.9999088151322 & 12.0000911848678 \tabularnewline
60 & 31 & 35.9994529489873 & -4.99945294898729 \tabularnewline
61 & 34 & 31.0002279112514 & 2.99977208874861 \tabularnewline
62 & 47 & 33.9998632486759 & 13.0001367513241 \tabularnewline
63 & 33 & 46.9994073596721 & -13.9994073596721 \tabularnewline
64 & 35 & 33.000638194315 & 1.99936180568502 \tabularnewline
65 & 31 & 34.9999088546175 & -3.99990885461754 \tabularnewline
66 & 35 & 31.0001823447969 & 3.99981765520312 \tabularnewline
67 & 39 & 34.9998176593606 & 4.00018234063936 \tabularnewline
68 & 46 & 38.9998176427356 & 7.00018235726436 \tabularnewline
69 & 40 & 45.9996808810209 & -5.99968088102093 \tabularnewline
70 & 50 & 40.0002735088802 & 9.99972649111983 \tabularnewline
71 & 62 & 49.9995441400886 & 12.0004558599114 \tabularnewline
72 & 57 & 61.9994529323628 & -4.99945293236276 \tabularnewline
73 & 62 & 57.0002279112506 & 4.99977208874937 \tabularnewline
74 & 57 & 61.9997720741999 & -4.99977207419991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210320&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]14[/C][C]19[/C][C]-5[/C][/ROW]
[ROW][C]3[/C][C]15[/C][C]14.0002279361899[/C][C]0.999772063810065[/C][/ROW]
[ROW][C]4[/C][C]7[/C][C]14.999954423153[/C][C]-7.99995442315299[/C][/ROW]
[ROW][C]5[/C][C]12[/C][C]7.00036469582617[/C][C]4.99963530417383[/C][/ROW]
[ROW][C]6[/C][C]12[/C][C]11.9997720804355[/C][C]0.000227919564459[/C][/ROW]
[ROW][C]7[/C][C]14[/C][C]11.9999999896098[/C][C]2.00000001039022[/C][/ROW]
[ROW][C]8[/C][C]9[/C][C]13.9999088255236[/C][C]-4.99990882552355[/C][/ROW]
[ROW][C]9[/C][C]8[/C][C]9.00022793203354[/C][C]-1.00022793203354[/C][/ROW]
[ROW][C]10[/C][C]4[/C][C]8.00004559762878[/C][C]-4.00004559762878[/C][/ROW]
[ROW][C]11[/C][C]7[/C][C]4.00018235103062[/C][C]2.99981764896938[/C][/ROW]
[ROW][C]12[/C][C]3[/C][C]6.99986324659892[/C][C]-3.99986324659892[/C][/ROW]
[ROW][C]13[/C][C]5[/C][C]3.00018234271774[/C][C]1.99981765728226[/C][/ROW]
[ROW][C]14[/C][C]0[/C][C]4.99990883383653[/C][C]-4.99990883383653[/C][/ROW]
[ROW][C]15[/C][C]-2[/C][C]0.000227932033921295[/C][C]-2.00022793203392[/C][/ROW]
[ROW][C]16[/C][C]6[/C][C]-1.99990881513323[/C][C]7.99990881513323[/C][/ROW]
[ROW][C]17[/C][C]11[/C][C]5.99963530625297[/C][C]5.00036469374703[/C][/ROW]
[ROW][C]18[/C][C]9[/C][C]10.9997720471847[/C][C]-1.99977204718468[/C][/ROW]
[ROW][C]19[/C][C]17[/C][C]9.00009116408424[/C][C]7.99990883591576[/C][/ROW]
[ROW][C]20[/C][C]21[/C][C]16.999635306252[/C][C]4.00036469374798[/C][/ROW]
[ROW][C]21[/C][C]21[/C][C]20.9998176344227[/C][C]0.000182365577327204[/C][/ROW]
[ROW][C]22[/C][C]41[/C][C]20.9999999916865[/C][C]20.0000000083135[/C][/ROW]
[ROW][C]23[/C][C]57[/C][C]40.9990882552399[/C][C]16.0009117447601[/C][/ROW]
[ROW][C]24[/C][C]65[/C][C]56.9992705626283[/C][C]8.00072943737172[/C][/ROW]
[ROW][C]25[/C][C]68[/C][C]64.9996352688431[/C][C]3.00036473115694[/C][/ROW]
[ROW][C]26[/C][C]73[/C][C]67.999863221659[/C][C]5.00013677834104[/C][/ROW]
[ROW][C]27[/C][C]71[/C][C]72.9997720575747[/C][C]-1.99977205757472[/C][/ROW]
[ROW][C]28[/C][C]71[/C][C]71.0000911640847[/C][C]-9.11640847078843e-05[/C][/ROW]
[ROW][C]29[/C][C]70[/C][C]71.0000000041559[/C][C]-1.00000000415592[/C][/ROW]
[ROW][C]30[/C][C]69[/C][C]70.0000455872382[/C][C]-1.00004558723818[/C][/ROW]
[ROW][C]31[/C][C]65[/C][C]69.0000455893162[/C][C]-4.00004558931619[/C][/ROW]
[ROW][C]32[/C][C]57[/C][C]65.0001823510302[/C][C]-8.00018235103023[/C][/ROW]
[ROW][C]33[/C][C]57[/C][C]57.0003647062168[/C][C]-0.000364706216778643[/C][/ROW]
[ROW][C]34[/C][C]57[/C][C]57.0000000166259[/C][C]-1.66259468414864e-08[/C][/ROW]
[ROW][C]35[/C][C]55[/C][C]57.0000000000008[/C][C]-2.00000000000076[/C][/ROW]
[ROW][C]36[/C][C]65[/C][C]55.000091174476[/C][C]9.99990882552402[/C][/ROW]
[ROW][C]37[/C][C]65[/C][C]64.9995441317765[/C][C]0.00045586822348298[/C][/ROW]
[ROW][C]38[/C][C]64[/C][C]64.9999999792182[/C][C]-0.999999979218231[/C][/ROW]
[ROW][C]39[/C][C]60[/C][C]64.000045587237[/C][C]-4.00004558723704[/C][/ROW]
[ROW][C]40[/C][C]43[/C][C]60.0001823510301[/C][C]-17.0001823510301[/C][/ROW]
[ROW][C]41[/C][C]47[/C][C]43.0007749913587[/C][C]3.99922500864134[/C][/ROW]
[ROW][C]42[/C][C]40[/C][C]46.9998176863778[/C][C]-6.99981768637777[/C][/ROW]
[ROW][C]43[/C][C]31[/C][C]40.0003191023547[/C][C]-9.00031910235474[/C][/ROW]
[ROW][C]44[/C][C]27[/C][C]31.0004102996889[/C][C]-4.00041029968888[/C][/ROW]
[ROW][C]45[/C][C]24[/C][C]27.0001823676564[/C][C]-3.00018236765638[/C][/ROW]
[ROW][C]46[/C][C]23[/C][C]24.0001367700276[/C][C]-1.0001367700276[/C][/ROW]
[ROW][C]47[/C][C]17[/C][C]23.000045593473[/C][C]-6.00004559347295[/C][/ROW]
[ROW][C]48[/C][C]16[/C][C]17.0002735255064[/C][C]-1.0002735255064[/C][/ROW]
[ROW][C]49[/C][C]15[/C][C]16.0000455997073[/C][C]-1.00004559970726[/C][/ROW]
[ROW][C]50[/C][C]8[/C][C]15.0000455893168[/C][C]-7.00004558931675[/C][/ROW]
[ROW][C]51[/C][C]5[/C][C]8.0003191127442[/C][C]-3.0003191127442[/C][/ROW]
[ROW][C]52[/C][C]6[/C][C]5.00013677626143[/C][C]0.99986322373857[/C][/ROW]
[ROW][C]53[/C][C]5[/C][C]5.99995441899727[/C][C]-0.999954418997265[/C][/ROW]
[ROW][C]54[/C][C]12[/C][C]5.00004558516008[/C][C]6.99995441483992[/C][/ROW]
[ROW][C]55[/C][C]8[/C][C]11.9996808914122[/C][C]-3.99968089141219[/C][/ROW]
[ROW][C]56[/C][C]17[/C][C]8.00018233440467[/C][C]8.99981766559533[/C][/ROW]
[ROW][C]57[/C][C]22[/C][C]16.9995897231702[/C][C]5.00041027682976[/C][/ROW]
[ROW][C]58[/C][C]24[/C][C]21.9997720451067[/C][C]2.00022795489332[/C][/ROW]
[ROW][C]59[/C][C]36[/C][C]23.9999088151322[/C][C]12.0000911848678[/C][/ROW]
[ROW][C]60[/C][C]31[/C][C]35.9994529489873[/C][C]-4.99945294898729[/C][/ROW]
[ROW][C]61[/C][C]34[/C][C]31.0002279112514[/C][C]2.99977208874861[/C][/ROW]
[ROW][C]62[/C][C]47[/C][C]33.9998632486759[/C][C]13.0001367513241[/C][/ROW]
[ROW][C]63[/C][C]33[/C][C]46.9994073596721[/C][C]-13.9994073596721[/C][/ROW]
[ROW][C]64[/C][C]35[/C][C]33.000638194315[/C][C]1.99936180568502[/C][/ROW]
[ROW][C]65[/C][C]31[/C][C]34.9999088546175[/C][C]-3.99990885461754[/C][/ROW]
[ROW][C]66[/C][C]35[/C][C]31.0001823447969[/C][C]3.99981765520312[/C][/ROW]
[ROW][C]67[/C][C]39[/C][C]34.9998176593606[/C][C]4.00018234063936[/C][/ROW]
[ROW][C]68[/C][C]46[/C][C]38.9998176427356[/C][C]7.00018235726436[/C][/ROW]
[ROW][C]69[/C][C]40[/C][C]45.9996808810209[/C][C]-5.99968088102093[/C][/ROW]
[ROW][C]70[/C][C]50[/C][C]40.0002735088802[/C][C]9.99972649111983[/C][/ROW]
[ROW][C]71[/C][C]62[/C][C]49.9995441400886[/C][C]12.0004558599114[/C][/ROW]
[ROW][C]72[/C][C]57[/C][C]61.9994529323628[/C][C]-4.99945293236276[/C][/ROW]
[ROW][C]73[/C][C]62[/C][C]57.0002279112506[/C][C]4.99977208874937[/C][/ROW]
[ROW][C]74[/C][C]57[/C][C]61.9997720741999[/C][C]-4.99977207419991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210320&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210320&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
21419-5
31514.00022793618990.999772063810065
4714.999954423153-7.99995442315299
5127.000364695826174.99963530417383
61211.99977208043550.000227919564459
71411.99999998960982.00000001039022
8913.9999088255236-4.99990882552355
989.00022793203354-1.00022793203354
1048.00004559762878-4.00004559762878
1174.000182351030622.99981764896938
1236.99986324659892-3.99986324659892
1353.000182342717741.99981765728226
1404.99990883383653-4.99990883383653
15-20.000227932033921295-2.00022793203392
166-1.999908815133237.99990881513323
17115.999635306252975.00036469374703
18910.9997720471847-1.99977204718468
19179.000091164084247.99990883591576
202116.9996353062524.00036469374798
212120.99981763442270.000182365577327204
224120.999999991686520.0000000083135
235740.999088255239916.0009117447601
246556.99927056262838.00072943737172
256864.99963526884313.00036473115694
267367.9998632216595.00013677834104
277172.9997720575747-1.99977205757472
287171.0000911640847-9.11640847078843e-05
297071.0000000041559-1.00000000415592
306970.0000455872382-1.00004558723818
316569.0000455893162-4.00004558931619
325765.0001823510302-8.00018235103023
335757.0003647062168-0.000364706216778643
345757.0000000166259-1.66259468414864e-08
355557.0000000000008-2.00000000000076
366555.0000911744769.99990882552402
376564.99954413177650.00045586822348298
386464.9999999792182-0.999999979218231
396064.000045587237-4.00004558723704
404360.0001823510301-17.0001823510301
414743.00077499135873.99922500864134
424046.9998176863778-6.99981768637777
433140.0003191023547-9.00031910235474
442731.0004102996889-4.00041029968888
452427.0001823676564-3.00018236765638
462324.0001367700276-1.0001367700276
471723.000045593473-6.00004559347295
481617.0002735255064-1.0002735255064
491516.0000455997073-1.00004559970726
50815.0000455893168-7.00004558931675
5158.0003191127442-3.0003191127442
5265.000136776261430.99986322373857
5355.99995441899727-0.999954418997265
54125.000045585160086.99995441483992
55811.9996808914122-3.99968089141219
56178.000182334404678.99981766559533
572216.99958972317025.00041027682976
582421.99977204510672.00022795489332
593623.999908815132212.0000911848678
603135.9994529489873-4.99945294898729
613431.00022791125142.99977208874861
624733.999863248675913.0001367513241
633346.9994073596721-13.9994073596721
643533.0006381943151.99936180568502
653134.9999088546175-3.99990885461754
663531.00018234479693.99981765520312
673934.99981765936064.00018234063936
684638.99981764273567.00018235726436
694045.9996808810209-5.99968088102093
705040.00027350888029.99972649111983
716249.999544140088612.0004558599114
725761.9994529323628-4.99945293236276
736257.00022791125064.99977208874937
745761.9997720741999-4.99977207419991







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7557.000227925799444.209803873356469.7906519782424
7657.000227925799438.912249057528975.08820679407
7757.000227925799434.847236894412979.1532189571859
7857.000227925799431.420254436087282.5802014155117
7957.000227925799428.401013324134885.5994425274641
8057.000227925799425.671405606252288.3290502453466
8157.000227925799423.161269017058690.8391868345402
8257.000227925799420.824888644389393.1755672072096
8357.000227925799418.63051064481395.3699452067858
8457.000227925799416.555015151967897.4454406996311
8557.000227925799414.580948483331299.4195073682676
8657.000227925799412.6947508319243101.305705019675

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
75 & 57.0002279257994 & 44.2098038733564 & 69.7906519782424 \tabularnewline
76 & 57.0002279257994 & 38.9122490575289 & 75.08820679407 \tabularnewline
77 & 57.0002279257994 & 34.8472368944129 & 79.1532189571859 \tabularnewline
78 & 57.0002279257994 & 31.4202544360872 & 82.5802014155117 \tabularnewline
79 & 57.0002279257994 & 28.4010133241348 & 85.5994425274641 \tabularnewline
80 & 57.0002279257994 & 25.6714056062522 & 88.3290502453466 \tabularnewline
81 & 57.0002279257994 & 23.1612690170586 & 90.8391868345402 \tabularnewline
82 & 57.0002279257994 & 20.8248886443893 & 93.1755672072096 \tabularnewline
83 & 57.0002279257994 & 18.630510644813 & 95.3699452067858 \tabularnewline
84 & 57.0002279257994 & 16.5550151519678 & 97.4454406996311 \tabularnewline
85 & 57.0002279257994 & 14.5809484833312 & 99.4195073682676 \tabularnewline
86 & 57.0002279257994 & 12.6947508319243 & 101.305705019675 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210320&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]75[/C][C]57.0002279257994[/C][C]44.2098038733564[/C][C]69.7906519782424[/C][/ROW]
[ROW][C]76[/C][C]57.0002279257994[/C][C]38.9122490575289[/C][C]75.08820679407[/C][/ROW]
[ROW][C]77[/C][C]57.0002279257994[/C][C]34.8472368944129[/C][C]79.1532189571859[/C][/ROW]
[ROW][C]78[/C][C]57.0002279257994[/C][C]31.4202544360872[/C][C]82.5802014155117[/C][/ROW]
[ROW][C]79[/C][C]57.0002279257994[/C][C]28.4010133241348[/C][C]85.5994425274641[/C][/ROW]
[ROW][C]80[/C][C]57.0002279257994[/C][C]25.6714056062522[/C][C]88.3290502453466[/C][/ROW]
[ROW][C]81[/C][C]57.0002279257994[/C][C]23.1612690170586[/C][C]90.8391868345402[/C][/ROW]
[ROW][C]82[/C][C]57.0002279257994[/C][C]20.8248886443893[/C][C]93.1755672072096[/C][/ROW]
[ROW][C]83[/C][C]57.0002279257994[/C][C]18.630510644813[/C][C]95.3699452067858[/C][/ROW]
[ROW][C]84[/C][C]57.0002279257994[/C][C]16.5550151519678[/C][C]97.4454406996311[/C][/ROW]
[ROW][C]85[/C][C]57.0002279257994[/C][C]14.5809484833312[/C][C]99.4195073682676[/C][/ROW]
[ROW][C]86[/C][C]57.0002279257994[/C][C]12.6947508319243[/C][C]101.305705019675[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210320&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210320&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
7557.000227925799444.209803873356469.7906519782424
7657.000227925799438.912249057528975.08820679407
7757.000227925799434.847236894412979.1532189571859
7857.000227925799431.420254436087282.5802014155117
7957.000227925799428.401013324134885.5994425274641
8057.000227925799425.671405606252288.3290502453466
8157.000227925799423.161269017058690.8391868345402
8257.000227925799420.824888644389393.1755672072096
8357.000227925799418.63051064481395.3699452067858
8457.000227925799416.555015151967897.4454406996311
8557.000227925799414.580948483331299.4195073682676
8657.000227925799412.6947508319243101.305705019675



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