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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 25 May 2013 15:48:16 -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/25/t1369511584nyro9r4v26r73e1.htm/, Retrieved Thu, 02 May 2024 15:47:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210558, Retrieved Thu, 02 May 2024 15:47:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [] [2013-05-25 08:16:57] [b52ab2fdde0d078a054c398d2d11afcd]
- RMP     [Exponential Smoothing] [] [2013-05-25 19:48:16] [e21b4433303b1715f3bab05278c9d12d] [Current]
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Dataseries X:
16,68
16,68
16,69
16,61
16,58
16,6
16,6
16,62
16,62
16,6
16,63
16,66
16,66
16,65
16,5
16,39
16,34
16,35
16,35
16,38
16,36
16,38
16,39
16,41
16,41
16,41
16,45
16,41
16,44
16,47
16,47
16,49
16,54
16,62
16,69
16,72
16,72
16,71
16,89
16,93
16,91
16,93
16,93
16,93
16,95
16,93
16,95
16,95
16,95
16,95
16,92
16,91
16,9
16,96
16,96
16,95
16,92
16,87
16,87
16,88
16,88
16,86
16,88
16,88
16,88
16,88
16,88
16,87
16,92
16,94
17,03
17,02




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210558&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210558&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210558&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.170287662769946
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.170287662769946 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210558&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.170287662769946[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210558&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210558&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.170287662769946
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
316.6916.680.0100000000000016
416.6116.6917028766277-0.0817028766277019
516.5816.5977898847252-0.0177898847251896
616.616.56476048683440.0352395131656138
716.616.59076134116850.00923865883148878
816.6216.59233457078810.0276654292119467
916.6216.61704565206810.00295434793191518
1016.616.6175487410724-0.0175487410724173
1116.6316.59456040697060.0354395930293556
1216.6616.63059533243710.0294046675628721
1316.6616.6656025845509-0.00560258455093887
1416.6516.6646485335223-0.0146485335222906
1516.516.6521540689858-0.152154068985769
1616.3916.4762441081972-0.0862441081972456
1716.3416.3515578005847-0.0115578005846579
1816.3516.29958964973630.0504103502636646
1916.3516.31817391046210.0318260895378515
2016.3816.32359350086470.0564064991353384
2116.3616.3631988317674-0.00319883176744895
2216.3816.34265411018220.0373458898178249
2316.3916.36901365447330.0209863455266834
2416.4116.38258737020310.02741262979686
2516.4116.40725540286160.00274459713837416
2616.4116.40772277389360.0022772261064361
2716.4516.40811055740480.0418894425951706
2816.4116.4552438126791-0.0452438126790931
2916.4416.40753934956320.0324606504368319
3016.4716.44306699785810.0269330021419485
3116.4716.4776533558442-0.00765335584418025
3216.4916.47635008376510.013649916234872
3316.5416.49867449609780.0413255039022289
3416.6216.55571171957010.0642882804299312
3516.6916.6466592205880.0433407794120164
3616.7216.7240396206167-0.0040396206166875
3716.7216.7533517230634-0.0333517230633902
3816.7116.7476723360936-0.0376723360935749
3916.8916.73125720202910.158742797970884
4016.9316.9382891420771-0.00828914207714249
4116.9116.9768776034465-0.0668776034464571
4216.9316.9454891726639-0.015489172663905
4316.9316.9628515576527-0.0328515576527266
4416.9316.9572573426817-0.0272573426816933
4516.9516.9526157535031-0.0026157535031075
4616.9316.9721703229527-0.042170322952682
4716.9516.94498923721880.00501076278118617
4816.9516.9658425083015-0.0158425083015175
4916.9516.9631447245904-0.0131447245904397
5016.9516.9609063401622-0.0109063401621796
5116.9216.9590491249866-0.0390491249865832
5216.9116.9223995407594-0.0123995407594109
5316.916.9102880519441-0.0102880519440696
5416.9616.89853612362410.0614638763759459
5516.9616.9690026634769-0.00900266347689893
5616.9516.9674696209547-0.0174696209547136
5716.9216.9544947600329-0.0344947600328567
5816.8716.9186207279691-0.0486207279690518
5916.8716.8603412178410.0096587821589722
6016.8816.86198598928010.0180140107199129
6116.8816.87505355306270.00494644693731061
6216.8616.8758958719507-0.0158958719506614
6316.8816.85318900106850.0268109989315057
6416.8816.87775458341310.00224541658693411
6516.8816.87813695015560.001863049844399
6616.8816.87845420455920.00154579544077293
6716.8816.8787174344520.00128256554804196
6816.8716.8789358395415-0.00893583954147914
6916.9216.86741417631110.0525858236889256
7016.9416.92636889332190.0136311066781047
7117.0316.94869010261910.0813098973809225
7217.0217.0525361750041-0.0325361750041395

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 16.69 & 16.68 & 0.0100000000000016 \tabularnewline
4 & 16.61 & 16.6917028766277 & -0.0817028766277019 \tabularnewline
5 & 16.58 & 16.5977898847252 & -0.0177898847251896 \tabularnewline
6 & 16.6 & 16.5647604868344 & 0.0352395131656138 \tabularnewline
7 & 16.6 & 16.5907613411685 & 0.00923865883148878 \tabularnewline
8 & 16.62 & 16.5923345707881 & 0.0276654292119467 \tabularnewline
9 & 16.62 & 16.6170456520681 & 0.00295434793191518 \tabularnewline
10 & 16.6 & 16.6175487410724 & -0.0175487410724173 \tabularnewline
11 & 16.63 & 16.5945604069706 & 0.0354395930293556 \tabularnewline
12 & 16.66 & 16.6305953324371 & 0.0294046675628721 \tabularnewline
13 & 16.66 & 16.6656025845509 & -0.00560258455093887 \tabularnewline
14 & 16.65 & 16.6646485335223 & -0.0146485335222906 \tabularnewline
15 & 16.5 & 16.6521540689858 & -0.152154068985769 \tabularnewline
16 & 16.39 & 16.4762441081972 & -0.0862441081972456 \tabularnewline
17 & 16.34 & 16.3515578005847 & -0.0115578005846579 \tabularnewline
18 & 16.35 & 16.2995896497363 & 0.0504103502636646 \tabularnewline
19 & 16.35 & 16.3181739104621 & 0.0318260895378515 \tabularnewline
20 & 16.38 & 16.3235935008647 & 0.0564064991353384 \tabularnewline
21 & 16.36 & 16.3631988317674 & -0.00319883176744895 \tabularnewline
22 & 16.38 & 16.3426541101822 & 0.0373458898178249 \tabularnewline
23 & 16.39 & 16.3690136544733 & 0.0209863455266834 \tabularnewline
24 & 16.41 & 16.3825873702031 & 0.02741262979686 \tabularnewline
25 & 16.41 & 16.4072554028616 & 0.00274459713837416 \tabularnewline
26 & 16.41 & 16.4077227738936 & 0.0022772261064361 \tabularnewline
27 & 16.45 & 16.4081105574048 & 0.0418894425951706 \tabularnewline
28 & 16.41 & 16.4552438126791 & -0.0452438126790931 \tabularnewline
29 & 16.44 & 16.4075393495632 & 0.0324606504368319 \tabularnewline
30 & 16.47 & 16.4430669978581 & 0.0269330021419485 \tabularnewline
31 & 16.47 & 16.4776533558442 & -0.00765335584418025 \tabularnewline
32 & 16.49 & 16.4763500837651 & 0.013649916234872 \tabularnewline
33 & 16.54 & 16.4986744960978 & 0.0413255039022289 \tabularnewline
34 & 16.62 & 16.5557117195701 & 0.0642882804299312 \tabularnewline
35 & 16.69 & 16.646659220588 & 0.0433407794120164 \tabularnewline
36 & 16.72 & 16.7240396206167 & -0.0040396206166875 \tabularnewline
37 & 16.72 & 16.7533517230634 & -0.0333517230633902 \tabularnewline
38 & 16.71 & 16.7476723360936 & -0.0376723360935749 \tabularnewline
39 & 16.89 & 16.7312572020291 & 0.158742797970884 \tabularnewline
40 & 16.93 & 16.9382891420771 & -0.00828914207714249 \tabularnewline
41 & 16.91 & 16.9768776034465 & -0.0668776034464571 \tabularnewline
42 & 16.93 & 16.9454891726639 & -0.015489172663905 \tabularnewline
43 & 16.93 & 16.9628515576527 & -0.0328515576527266 \tabularnewline
44 & 16.93 & 16.9572573426817 & -0.0272573426816933 \tabularnewline
45 & 16.95 & 16.9526157535031 & -0.0026157535031075 \tabularnewline
46 & 16.93 & 16.9721703229527 & -0.042170322952682 \tabularnewline
47 & 16.95 & 16.9449892372188 & 0.00501076278118617 \tabularnewline
48 & 16.95 & 16.9658425083015 & -0.0158425083015175 \tabularnewline
49 & 16.95 & 16.9631447245904 & -0.0131447245904397 \tabularnewline
50 & 16.95 & 16.9609063401622 & -0.0109063401621796 \tabularnewline
51 & 16.92 & 16.9590491249866 & -0.0390491249865832 \tabularnewline
52 & 16.91 & 16.9223995407594 & -0.0123995407594109 \tabularnewline
53 & 16.9 & 16.9102880519441 & -0.0102880519440696 \tabularnewline
54 & 16.96 & 16.8985361236241 & 0.0614638763759459 \tabularnewline
55 & 16.96 & 16.9690026634769 & -0.00900266347689893 \tabularnewline
56 & 16.95 & 16.9674696209547 & -0.0174696209547136 \tabularnewline
57 & 16.92 & 16.9544947600329 & -0.0344947600328567 \tabularnewline
58 & 16.87 & 16.9186207279691 & -0.0486207279690518 \tabularnewline
59 & 16.87 & 16.860341217841 & 0.0096587821589722 \tabularnewline
60 & 16.88 & 16.8619859892801 & 0.0180140107199129 \tabularnewline
61 & 16.88 & 16.8750535530627 & 0.00494644693731061 \tabularnewline
62 & 16.86 & 16.8758958719507 & -0.0158958719506614 \tabularnewline
63 & 16.88 & 16.8531890010685 & 0.0268109989315057 \tabularnewline
64 & 16.88 & 16.8777545834131 & 0.00224541658693411 \tabularnewline
65 & 16.88 & 16.8781369501556 & 0.001863049844399 \tabularnewline
66 & 16.88 & 16.8784542045592 & 0.00154579544077293 \tabularnewline
67 & 16.88 & 16.878717434452 & 0.00128256554804196 \tabularnewline
68 & 16.87 & 16.8789358395415 & -0.00893583954147914 \tabularnewline
69 & 16.92 & 16.8674141763111 & 0.0525858236889256 \tabularnewline
70 & 16.94 & 16.9263688933219 & 0.0136311066781047 \tabularnewline
71 & 17.03 & 16.9486901026191 & 0.0813098973809225 \tabularnewline
72 & 17.02 & 17.0525361750041 & -0.0325361750041395 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210558&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]16.69[/C][C]16.68[/C][C]0.0100000000000016[/C][/ROW]
[ROW][C]4[/C][C]16.61[/C][C]16.6917028766277[/C][C]-0.0817028766277019[/C][/ROW]
[ROW][C]5[/C][C]16.58[/C][C]16.5977898847252[/C][C]-0.0177898847251896[/C][/ROW]
[ROW][C]6[/C][C]16.6[/C][C]16.5647604868344[/C][C]0.0352395131656138[/C][/ROW]
[ROW][C]7[/C][C]16.6[/C][C]16.5907613411685[/C][C]0.00923865883148878[/C][/ROW]
[ROW][C]8[/C][C]16.62[/C][C]16.5923345707881[/C][C]0.0276654292119467[/C][/ROW]
[ROW][C]9[/C][C]16.62[/C][C]16.6170456520681[/C][C]0.00295434793191518[/C][/ROW]
[ROW][C]10[/C][C]16.6[/C][C]16.6175487410724[/C][C]-0.0175487410724173[/C][/ROW]
[ROW][C]11[/C][C]16.63[/C][C]16.5945604069706[/C][C]0.0354395930293556[/C][/ROW]
[ROW][C]12[/C][C]16.66[/C][C]16.6305953324371[/C][C]0.0294046675628721[/C][/ROW]
[ROW][C]13[/C][C]16.66[/C][C]16.6656025845509[/C][C]-0.00560258455093887[/C][/ROW]
[ROW][C]14[/C][C]16.65[/C][C]16.6646485335223[/C][C]-0.0146485335222906[/C][/ROW]
[ROW][C]15[/C][C]16.5[/C][C]16.6521540689858[/C][C]-0.152154068985769[/C][/ROW]
[ROW][C]16[/C][C]16.39[/C][C]16.4762441081972[/C][C]-0.0862441081972456[/C][/ROW]
[ROW][C]17[/C][C]16.34[/C][C]16.3515578005847[/C][C]-0.0115578005846579[/C][/ROW]
[ROW][C]18[/C][C]16.35[/C][C]16.2995896497363[/C][C]0.0504103502636646[/C][/ROW]
[ROW][C]19[/C][C]16.35[/C][C]16.3181739104621[/C][C]0.0318260895378515[/C][/ROW]
[ROW][C]20[/C][C]16.38[/C][C]16.3235935008647[/C][C]0.0564064991353384[/C][/ROW]
[ROW][C]21[/C][C]16.36[/C][C]16.3631988317674[/C][C]-0.00319883176744895[/C][/ROW]
[ROW][C]22[/C][C]16.38[/C][C]16.3426541101822[/C][C]0.0373458898178249[/C][/ROW]
[ROW][C]23[/C][C]16.39[/C][C]16.3690136544733[/C][C]0.0209863455266834[/C][/ROW]
[ROW][C]24[/C][C]16.41[/C][C]16.3825873702031[/C][C]0.02741262979686[/C][/ROW]
[ROW][C]25[/C][C]16.41[/C][C]16.4072554028616[/C][C]0.00274459713837416[/C][/ROW]
[ROW][C]26[/C][C]16.41[/C][C]16.4077227738936[/C][C]0.0022772261064361[/C][/ROW]
[ROW][C]27[/C][C]16.45[/C][C]16.4081105574048[/C][C]0.0418894425951706[/C][/ROW]
[ROW][C]28[/C][C]16.41[/C][C]16.4552438126791[/C][C]-0.0452438126790931[/C][/ROW]
[ROW][C]29[/C][C]16.44[/C][C]16.4075393495632[/C][C]0.0324606504368319[/C][/ROW]
[ROW][C]30[/C][C]16.47[/C][C]16.4430669978581[/C][C]0.0269330021419485[/C][/ROW]
[ROW][C]31[/C][C]16.47[/C][C]16.4776533558442[/C][C]-0.00765335584418025[/C][/ROW]
[ROW][C]32[/C][C]16.49[/C][C]16.4763500837651[/C][C]0.013649916234872[/C][/ROW]
[ROW][C]33[/C][C]16.54[/C][C]16.4986744960978[/C][C]0.0413255039022289[/C][/ROW]
[ROW][C]34[/C][C]16.62[/C][C]16.5557117195701[/C][C]0.0642882804299312[/C][/ROW]
[ROW][C]35[/C][C]16.69[/C][C]16.646659220588[/C][C]0.0433407794120164[/C][/ROW]
[ROW][C]36[/C][C]16.72[/C][C]16.7240396206167[/C][C]-0.0040396206166875[/C][/ROW]
[ROW][C]37[/C][C]16.72[/C][C]16.7533517230634[/C][C]-0.0333517230633902[/C][/ROW]
[ROW][C]38[/C][C]16.71[/C][C]16.7476723360936[/C][C]-0.0376723360935749[/C][/ROW]
[ROW][C]39[/C][C]16.89[/C][C]16.7312572020291[/C][C]0.158742797970884[/C][/ROW]
[ROW][C]40[/C][C]16.93[/C][C]16.9382891420771[/C][C]-0.00828914207714249[/C][/ROW]
[ROW][C]41[/C][C]16.91[/C][C]16.9768776034465[/C][C]-0.0668776034464571[/C][/ROW]
[ROW][C]42[/C][C]16.93[/C][C]16.9454891726639[/C][C]-0.015489172663905[/C][/ROW]
[ROW][C]43[/C][C]16.93[/C][C]16.9628515576527[/C][C]-0.0328515576527266[/C][/ROW]
[ROW][C]44[/C][C]16.93[/C][C]16.9572573426817[/C][C]-0.0272573426816933[/C][/ROW]
[ROW][C]45[/C][C]16.95[/C][C]16.9526157535031[/C][C]-0.0026157535031075[/C][/ROW]
[ROW][C]46[/C][C]16.93[/C][C]16.9721703229527[/C][C]-0.042170322952682[/C][/ROW]
[ROW][C]47[/C][C]16.95[/C][C]16.9449892372188[/C][C]0.00501076278118617[/C][/ROW]
[ROW][C]48[/C][C]16.95[/C][C]16.9658425083015[/C][C]-0.0158425083015175[/C][/ROW]
[ROW][C]49[/C][C]16.95[/C][C]16.9631447245904[/C][C]-0.0131447245904397[/C][/ROW]
[ROW][C]50[/C][C]16.95[/C][C]16.9609063401622[/C][C]-0.0109063401621796[/C][/ROW]
[ROW][C]51[/C][C]16.92[/C][C]16.9590491249866[/C][C]-0.0390491249865832[/C][/ROW]
[ROW][C]52[/C][C]16.91[/C][C]16.9223995407594[/C][C]-0.0123995407594109[/C][/ROW]
[ROW][C]53[/C][C]16.9[/C][C]16.9102880519441[/C][C]-0.0102880519440696[/C][/ROW]
[ROW][C]54[/C][C]16.96[/C][C]16.8985361236241[/C][C]0.0614638763759459[/C][/ROW]
[ROW][C]55[/C][C]16.96[/C][C]16.9690026634769[/C][C]-0.00900266347689893[/C][/ROW]
[ROW][C]56[/C][C]16.95[/C][C]16.9674696209547[/C][C]-0.0174696209547136[/C][/ROW]
[ROW][C]57[/C][C]16.92[/C][C]16.9544947600329[/C][C]-0.0344947600328567[/C][/ROW]
[ROW][C]58[/C][C]16.87[/C][C]16.9186207279691[/C][C]-0.0486207279690518[/C][/ROW]
[ROW][C]59[/C][C]16.87[/C][C]16.860341217841[/C][C]0.0096587821589722[/C][/ROW]
[ROW][C]60[/C][C]16.88[/C][C]16.8619859892801[/C][C]0.0180140107199129[/C][/ROW]
[ROW][C]61[/C][C]16.88[/C][C]16.8750535530627[/C][C]0.00494644693731061[/C][/ROW]
[ROW][C]62[/C][C]16.86[/C][C]16.8758958719507[/C][C]-0.0158958719506614[/C][/ROW]
[ROW][C]63[/C][C]16.88[/C][C]16.8531890010685[/C][C]0.0268109989315057[/C][/ROW]
[ROW][C]64[/C][C]16.88[/C][C]16.8777545834131[/C][C]0.00224541658693411[/C][/ROW]
[ROW][C]65[/C][C]16.88[/C][C]16.8781369501556[/C][C]0.001863049844399[/C][/ROW]
[ROW][C]66[/C][C]16.88[/C][C]16.8784542045592[/C][C]0.00154579544077293[/C][/ROW]
[ROW][C]67[/C][C]16.88[/C][C]16.878717434452[/C][C]0.00128256554804196[/C][/ROW]
[ROW][C]68[/C][C]16.87[/C][C]16.8789358395415[/C][C]-0.00893583954147914[/C][/ROW]
[ROW][C]69[/C][C]16.92[/C][C]16.8674141763111[/C][C]0.0525858236889256[/C][/ROW]
[ROW][C]70[/C][C]16.94[/C][C]16.9263688933219[/C][C]0.0136311066781047[/C][/ROW]
[ROW][C]71[/C][C]17.03[/C][C]16.9486901026191[/C][C]0.0813098973809225[/C][/ROW]
[ROW][C]72[/C][C]17.02[/C][C]17.0525361750041[/C][C]-0.0325361750041395[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210558&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210558&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
316.6916.680.0100000000000016
416.6116.6917028766277-0.0817028766277019
516.5816.5977898847252-0.0177898847251896
616.616.56476048683440.0352395131656138
716.616.59076134116850.00923865883148878
816.6216.59233457078810.0276654292119467
916.6216.61704565206810.00295434793191518
1016.616.6175487410724-0.0175487410724173
1116.6316.59456040697060.0354395930293556
1216.6616.63059533243710.0294046675628721
1316.6616.6656025845509-0.00560258455093887
1416.6516.6646485335223-0.0146485335222906
1516.516.6521540689858-0.152154068985769
1616.3916.4762441081972-0.0862441081972456
1716.3416.3515578005847-0.0115578005846579
1816.3516.29958964973630.0504103502636646
1916.3516.31817391046210.0318260895378515
2016.3816.32359350086470.0564064991353384
2116.3616.3631988317674-0.00319883176744895
2216.3816.34265411018220.0373458898178249
2316.3916.36901365447330.0209863455266834
2416.4116.38258737020310.02741262979686
2516.4116.40725540286160.00274459713837416
2616.4116.40772277389360.0022772261064361
2716.4516.40811055740480.0418894425951706
2816.4116.4552438126791-0.0452438126790931
2916.4416.40753934956320.0324606504368319
3016.4716.44306699785810.0269330021419485
3116.4716.4776533558442-0.00765335584418025
3216.4916.47635008376510.013649916234872
3316.5416.49867449609780.0413255039022289
3416.6216.55571171957010.0642882804299312
3516.6916.6466592205880.0433407794120164
3616.7216.7240396206167-0.0040396206166875
3716.7216.7533517230634-0.0333517230633902
3816.7116.7476723360936-0.0376723360935749
3916.8916.73125720202910.158742797970884
4016.9316.9382891420771-0.00828914207714249
4116.9116.9768776034465-0.0668776034464571
4216.9316.9454891726639-0.015489172663905
4316.9316.9628515576527-0.0328515576527266
4416.9316.9572573426817-0.0272573426816933
4516.9516.9526157535031-0.0026157535031075
4616.9316.9721703229527-0.042170322952682
4716.9516.94498923721880.00501076278118617
4816.9516.9658425083015-0.0158425083015175
4916.9516.9631447245904-0.0131447245904397
5016.9516.9609063401622-0.0109063401621796
5116.9216.9590491249866-0.0390491249865832
5216.9116.9223995407594-0.0123995407594109
5316.916.9102880519441-0.0102880519440696
5416.9616.89853612362410.0614638763759459
5516.9616.9690026634769-0.00900266347689893
5616.9516.9674696209547-0.0174696209547136
5716.9216.9544947600329-0.0344947600328567
5816.8716.9186207279691-0.0486207279690518
5916.8716.8603412178410.0096587821589722
6016.8816.86198598928010.0180140107199129
6116.8816.87505355306270.00494644693731061
6216.8616.8758958719507-0.0158958719506614
6316.8816.85318900106850.0268109989315057
6416.8816.87775458341310.00224541658693411
6516.8816.87813695015560.001863049844399
6616.8816.87845420455920.00154579544077293
6716.8816.8787174344520.00128256554804196
6816.8716.8789358395415-0.00893583954147914
6916.9216.86741417631110.0525858236889256
7016.9416.92636889332190.0136311066781047
7117.0316.94869010261910.0813098973809225
7217.0217.0525361750041-0.0325361750041395







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7317.036995665807216.954018669920817.1199726616936
7417.053991331614416.926261372426917.1817212908019
7517.070986997421616.901609922973917.2403640718694
7617.087982663228816.877256665936217.2987086605215
7717.104978329036116.852263446809317.3576932112628
7817.121973994843316.826227478201917.4177205114847
7917.138969660650516.798957412900117.4789819084009
8017.155965326457716.770360473391217.5415701795242
8117.172960992264916.740394655346117.6055273291837
8217.189956658072116.709045814498817.6708675016454
8317.206952323879316.676315701446517.7375889463121
8417.223947989686516.64221531559817.8056806637751

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 17.0369956658072 & 16.9540186699208 & 17.1199726616936 \tabularnewline
74 & 17.0539913316144 & 16.9262613724269 & 17.1817212908019 \tabularnewline
75 & 17.0709869974216 & 16.9016099229739 & 17.2403640718694 \tabularnewline
76 & 17.0879826632288 & 16.8772566659362 & 17.2987086605215 \tabularnewline
77 & 17.1049783290361 & 16.8522634468093 & 17.3576932112628 \tabularnewline
78 & 17.1219739948433 & 16.8262274782019 & 17.4177205114847 \tabularnewline
79 & 17.1389696606505 & 16.7989574129001 & 17.4789819084009 \tabularnewline
80 & 17.1559653264577 & 16.7703604733912 & 17.5415701795242 \tabularnewline
81 & 17.1729609922649 & 16.7403946553461 & 17.6055273291837 \tabularnewline
82 & 17.1899566580721 & 16.7090458144988 & 17.6708675016454 \tabularnewline
83 & 17.2069523238793 & 16.6763157014465 & 17.7375889463121 \tabularnewline
84 & 17.2239479896865 & 16.642215315598 & 17.8056806637751 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210558&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]17.0369956658072[/C][C]16.9540186699208[/C][C]17.1199726616936[/C][/ROW]
[ROW][C]74[/C][C]17.0539913316144[/C][C]16.9262613724269[/C][C]17.1817212908019[/C][/ROW]
[ROW][C]75[/C][C]17.0709869974216[/C][C]16.9016099229739[/C][C]17.2403640718694[/C][/ROW]
[ROW][C]76[/C][C]17.0879826632288[/C][C]16.8772566659362[/C][C]17.2987086605215[/C][/ROW]
[ROW][C]77[/C][C]17.1049783290361[/C][C]16.8522634468093[/C][C]17.3576932112628[/C][/ROW]
[ROW][C]78[/C][C]17.1219739948433[/C][C]16.8262274782019[/C][C]17.4177205114847[/C][/ROW]
[ROW][C]79[/C][C]17.1389696606505[/C][C]16.7989574129001[/C][C]17.4789819084009[/C][/ROW]
[ROW][C]80[/C][C]17.1559653264577[/C][C]16.7703604733912[/C][C]17.5415701795242[/C][/ROW]
[ROW][C]81[/C][C]17.1729609922649[/C][C]16.7403946553461[/C][C]17.6055273291837[/C][/ROW]
[ROW][C]82[/C][C]17.1899566580721[/C][C]16.7090458144988[/C][C]17.6708675016454[/C][/ROW]
[ROW][C]83[/C][C]17.2069523238793[/C][C]16.6763157014465[/C][C]17.7375889463121[/C][/ROW]
[ROW][C]84[/C][C]17.2239479896865[/C][C]16.642215315598[/C][C]17.8056806637751[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210558&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210558&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
7317.036995665807216.954018669920817.1199726616936
7417.053991331614416.926261372426917.1817212908019
7517.070986997421616.901609922973917.2403640718694
7617.087982663228816.877256665936217.2987086605215
7717.104978329036116.852263446809317.3576932112628
7817.121973994843316.826227478201917.4177205114847
7917.138969660650516.798957412900117.4789819084009
8017.155965326457716.770360473391217.5415701795242
8117.172960992264916.740394655346117.6055273291837
8217.189956658072116.709045814498817.6708675016454
8317.206952323879316.676315701446517.7375889463121
8417.223947989686516.64221531559817.8056806637751



Parameters (Session):
par1 = 0 ; par2 = no ; par3 = 512 ;
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')