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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 May 2012 13:47:52 -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/2012/May/28/t1338227296lkf893ooxbslkr7.htm/, Retrieved Thu, 02 May 2024 04:33:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167853, Retrieved Thu, 02 May 2024 04:33:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Notched Boxplots] [] [2012-02-17 19:34:18] [2e3d5d2fadc43e8101372c775eeeade1]
- RMPD    [Exponential Smoothing] [michelle vandeweyer] [2012-05-28 17:47:52] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
2,71
2,69
2,67
2,66
2,67
2,67
2,66
2,72
2,63
2,63
2,65
2,66
2,65
2,62
2,61
2,61
2,62
2,61
2,62
2,65
2,64
2,66
2,67
2,68
2,68
2,71
2,72
2,72
2,71
2,7
2,7
2,7
2,68
2,67
2,66
2,64
2,64
2,63
2,61
2,62
2,61
2,6
2,58
2,55
2,53
2,5
2,48
2,47
2,47
2,46
2,46
2,45
2,44
2,42
2,39
2,37
2,34
2,32
2,3
2,29
2,3
2,29
2,29
2,29
2,29
2,28
2,28
2,28
2,29




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167853&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167853&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167853&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999946007209914
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999946007209914 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167853&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]0.999946007209914[/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=167853&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167853&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
alpha0.999946007209914
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
22.692.71-0.02
32.672.6900010798558-0.0200010798558017
42.662.67000107991411-0.0100010799141059
52.672.660000539986210.00999946001379115
62.672.669999460101255.39898745710587e-07
72.662.66999999997085-0.00999999997084933
82.722.66000053992790.0599994600721008
92.632.71999676046175-0.0899967604617475
102.632.6300048591762-4.85917619608145e-06
112.652.630000000262360.0199999997376397
122.662.649998920144210.0100010798557877
132.652.6599994600138-0.00999946001379515
142.622.65000053989875-0.0300005398987455
152.612.62000161981285-0.0100016198128534
162.612.61000054001536-5.40015359096202e-07
172.622.610000000029160.00999999997084311
182.612.6199994600721-0.00999946007210095
192.622.610000539898750.00999946010125141
202.652.619999460101250.03000053989875
212.642.64999838018715-0.0099983801871466
222.662.640000539840440.0199994601595574
232.672.659998920173350.0100010798266541
242.682.66999946001380.010000539986204
252.682.679999460042945.39957056400198e-07
262.712.679999999970850.0300000000291534
272.722.70999838021630.0100016197837043
282.722.719999459984645.40015357319845e-07
292.712.71999999997084-0.00999999997084311
302.72.7100005399279-0.0100005399278991
312.72.70000053995705-5.39957053291573e-07
322.72.70000000002915-2.91535684482369e-11
332.682.7-0.0200000000000018
342.672.6800010798558-0.0100010798558019
352.662.67000053998621-0.0100005399862049
362.642.66000053995706-0.0200005399570564
372.642.64000107988496-1.07988495567923e-06
382.632.64000000005831-0.010000000058306
392.612.6300005399279-0.0200005399279042
402.622.610001079884950.00999892011504633
412.612.61999946013041-0.00999946013040542
422.62.61000053989875-0.0100005398987517
432.582.60000053995705-0.0200005399570515
442.552.58000107988496-0.0300010798849559
452.532.55000161984201-0.0200016198420085
462.52.53000107994326-0.0300010799432613
472.482.50000161984201-0.0200016198420117
482.472.48000107994326-0.0100010799432613
492.472.47000053998621-5.39986209968646e-07
502.462.47000000002916-0.0100000000291556
512.462.4600005399279-5.3992790238766e-07
522.452.46000000002915-0.010000000029152
532.442.4500005399279-0.0100005399279026
542.422.44000053995705-0.0200005399570533
552.392.42000107988496-0.0300010798849555
562.372.39000161984201-0.0200016198420085
572.342.37000107994326-0.0300010799432617
582.322.34000161984201-0.0200016198420117
592.32.32000107994326-0.0200010799432615
602.292.30000107991411-0.0100010799141108
612.32.290000539986210.00999946001379115
622.292.29999946010125-0.00999946010125408
632.292.29000053989875-5.3989875015148e-07
642.292.29000000002915-2.9150459823768e-11
652.292.29-1.77635683940025e-15
662.282.29-0.0100000000000002
672.282.2800005399279-5.39927901055393e-07
682.282.28000000002915-2.91522361806074e-11
692.292.280.00999999999999845

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2.69 & 2.71 & -0.02 \tabularnewline
3 & 2.67 & 2.6900010798558 & -0.0200010798558017 \tabularnewline
4 & 2.66 & 2.67000107991411 & -0.0100010799141059 \tabularnewline
5 & 2.67 & 2.66000053998621 & 0.00999946001379115 \tabularnewline
6 & 2.67 & 2.66999946010125 & 5.39898745710587e-07 \tabularnewline
7 & 2.66 & 2.66999999997085 & -0.00999999997084933 \tabularnewline
8 & 2.72 & 2.6600005399279 & 0.0599994600721008 \tabularnewline
9 & 2.63 & 2.71999676046175 & -0.0899967604617475 \tabularnewline
10 & 2.63 & 2.6300048591762 & -4.85917619608145e-06 \tabularnewline
11 & 2.65 & 2.63000000026236 & 0.0199999997376397 \tabularnewline
12 & 2.66 & 2.64999892014421 & 0.0100010798557877 \tabularnewline
13 & 2.65 & 2.6599994600138 & -0.00999946001379515 \tabularnewline
14 & 2.62 & 2.65000053989875 & -0.0300005398987455 \tabularnewline
15 & 2.61 & 2.62000161981285 & -0.0100016198128534 \tabularnewline
16 & 2.61 & 2.61000054001536 & -5.40015359096202e-07 \tabularnewline
17 & 2.62 & 2.61000000002916 & 0.00999999997084311 \tabularnewline
18 & 2.61 & 2.6199994600721 & -0.00999946007210095 \tabularnewline
19 & 2.62 & 2.61000053989875 & 0.00999946010125141 \tabularnewline
20 & 2.65 & 2.61999946010125 & 0.03000053989875 \tabularnewline
21 & 2.64 & 2.64999838018715 & -0.0099983801871466 \tabularnewline
22 & 2.66 & 2.64000053984044 & 0.0199994601595574 \tabularnewline
23 & 2.67 & 2.65999892017335 & 0.0100010798266541 \tabularnewline
24 & 2.68 & 2.6699994600138 & 0.010000539986204 \tabularnewline
25 & 2.68 & 2.67999946004294 & 5.39957056400198e-07 \tabularnewline
26 & 2.71 & 2.67999999997085 & 0.0300000000291534 \tabularnewline
27 & 2.72 & 2.7099983802163 & 0.0100016197837043 \tabularnewline
28 & 2.72 & 2.71999945998464 & 5.40015357319845e-07 \tabularnewline
29 & 2.71 & 2.71999999997084 & -0.00999999997084311 \tabularnewline
30 & 2.7 & 2.7100005399279 & -0.0100005399278991 \tabularnewline
31 & 2.7 & 2.70000053995705 & -5.39957053291573e-07 \tabularnewline
32 & 2.7 & 2.70000000002915 & -2.91535684482369e-11 \tabularnewline
33 & 2.68 & 2.7 & -0.0200000000000018 \tabularnewline
34 & 2.67 & 2.6800010798558 & -0.0100010798558019 \tabularnewline
35 & 2.66 & 2.67000053998621 & -0.0100005399862049 \tabularnewline
36 & 2.64 & 2.66000053995706 & -0.0200005399570564 \tabularnewline
37 & 2.64 & 2.64000107988496 & -1.07988495567923e-06 \tabularnewline
38 & 2.63 & 2.64000000005831 & -0.010000000058306 \tabularnewline
39 & 2.61 & 2.6300005399279 & -0.0200005399279042 \tabularnewline
40 & 2.62 & 2.61000107988495 & 0.00999892011504633 \tabularnewline
41 & 2.61 & 2.61999946013041 & -0.00999946013040542 \tabularnewline
42 & 2.6 & 2.61000053989875 & -0.0100005398987517 \tabularnewline
43 & 2.58 & 2.60000053995705 & -0.0200005399570515 \tabularnewline
44 & 2.55 & 2.58000107988496 & -0.0300010798849559 \tabularnewline
45 & 2.53 & 2.55000161984201 & -0.0200016198420085 \tabularnewline
46 & 2.5 & 2.53000107994326 & -0.0300010799432613 \tabularnewline
47 & 2.48 & 2.50000161984201 & -0.0200016198420117 \tabularnewline
48 & 2.47 & 2.48000107994326 & -0.0100010799432613 \tabularnewline
49 & 2.47 & 2.47000053998621 & -5.39986209968646e-07 \tabularnewline
50 & 2.46 & 2.47000000002916 & -0.0100000000291556 \tabularnewline
51 & 2.46 & 2.4600005399279 & -5.3992790238766e-07 \tabularnewline
52 & 2.45 & 2.46000000002915 & -0.010000000029152 \tabularnewline
53 & 2.44 & 2.4500005399279 & -0.0100005399279026 \tabularnewline
54 & 2.42 & 2.44000053995705 & -0.0200005399570533 \tabularnewline
55 & 2.39 & 2.42000107988496 & -0.0300010798849555 \tabularnewline
56 & 2.37 & 2.39000161984201 & -0.0200016198420085 \tabularnewline
57 & 2.34 & 2.37000107994326 & -0.0300010799432617 \tabularnewline
58 & 2.32 & 2.34000161984201 & -0.0200016198420117 \tabularnewline
59 & 2.3 & 2.32000107994326 & -0.0200010799432615 \tabularnewline
60 & 2.29 & 2.30000107991411 & -0.0100010799141108 \tabularnewline
61 & 2.3 & 2.29000053998621 & 0.00999946001379115 \tabularnewline
62 & 2.29 & 2.29999946010125 & -0.00999946010125408 \tabularnewline
63 & 2.29 & 2.29000053989875 & -5.3989875015148e-07 \tabularnewline
64 & 2.29 & 2.29000000002915 & -2.9150459823768e-11 \tabularnewline
65 & 2.29 & 2.29 & -1.77635683940025e-15 \tabularnewline
66 & 2.28 & 2.29 & -0.0100000000000002 \tabularnewline
67 & 2.28 & 2.2800005399279 & -5.39927901055393e-07 \tabularnewline
68 & 2.28 & 2.28000000002915 & -2.91522361806074e-11 \tabularnewline
69 & 2.29 & 2.28 & 0.00999999999999845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167853&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]2.69[/C][C]2.71[/C][C]-0.02[/C][/ROW]
[ROW][C]3[/C][C]2.67[/C][C]2.6900010798558[/C][C]-0.0200010798558017[/C][/ROW]
[ROW][C]4[/C][C]2.66[/C][C]2.67000107991411[/C][C]-0.0100010799141059[/C][/ROW]
[ROW][C]5[/C][C]2.67[/C][C]2.66000053998621[/C][C]0.00999946001379115[/C][/ROW]
[ROW][C]6[/C][C]2.67[/C][C]2.66999946010125[/C][C]5.39898745710587e-07[/C][/ROW]
[ROW][C]7[/C][C]2.66[/C][C]2.66999999997085[/C][C]-0.00999999997084933[/C][/ROW]
[ROW][C]8[/C][C]2.72[/C][C]2.6600005399279[/C][C]0.0599994600721008[/C][/ROW]
[ROW][C]9[/C][C]2.63[/C][C]2.71999676046175[/C][C]-0.0899967604617475[/C][/ROW]
[ROW][C]10[/C][C]2.63[/C][C]2.6300048591762[/C][C]-4.85917619608145e-06[/C][/ROW]
[ROW][C]11[/C][C]2.65[/C][C]2.63000000026236[/C][C]0.0199999997376397[/C][/ROW]
[ROW][C]12[/C][C]2.66[/C][C]2.64999892014421[/C][C]0.0100010798557877[/C][/ROW]
[ROW][C]13[/C][C]2.65[/C][C]2.6599994600138[/C][C]-0.00999946001379515[/C][/ROW]
[ROW][C]14[/C][C]2.62[/C][C]2.65000053989875[/C][C]-0.0300005398987455[/C][/ROW]
[ROW][C]15[/C][C]2.61[/C][C]2.62000161981285[/C][C]-0.0100016198128534[/C][/ROW]
[ROW][C]16[/C][C]2.61[/C][C]2.61000054001536[/C][C]-5.40015359096202e-07[/C][/ROW]
[ROW][C]17[/C][C]2.62[/C][C]2.61000000002916[/C][C]0.00999999997084311[/C][/ROW]
[ROW][C]18[/C][C]2.61[/C][C]2.6199994600721[/C][C]-0.00999946007210095[/C][/ROW]
[ROW][C]19[/C][C]2.62[/C][C]2.61000053989875[/C][C]0.00999946010125141[/C][/ROW]
[ROW][C]20[/C][C]2.65[/C][C]2.61999946010125[/C][C]0.03000053989875[/C][/ROW]
[ROW][C]21[/C][C]2.64[/C][C]2.64999838018715[/C][C]-0.0099983801871466[/C][/ROW]
[ROW][C]22[/C][C]2.66[/C][C]2.64000053984044[/C][C]0.0199994601595574[/C][/ROW]
[ROW][C]23[/C][C]2.67[/C][C]2.65999892017335[/C][C]0.0100010798266541[/C][/ROW]
[ROW][C]24[/C][C]2.68[/C][C]2.6699994600138[/C][C]0.010000539986204[/C][/ROW]
[ROW][C]25[/C][C]2.68[/C][C]2.67999946004294[/C][C]5.39957056400198e-07[/C][/ROW]
[ROW][C]26[/C][C]2.71[/C][C]2.67999999997085[/C][C]0.0300000000291534[/C][/ROW]
[ROW][C]27[/C][C]2.72[/C][C]2.7099983802163[/C][C]0.0100016197837043[/C][/ROW]
[ROW][C]28[/C][C]2.72[/C][C]2.71999945998464[/C][C]5.40015357319845e-07[/C][/ROW]
[ROW][C]29[/C][C]2.71[/C][C]2.71999999997084[/C][C]-0.00999999997084311[/C][/ROW]
[ROW][C]30[/C][C]2.7[/C][C]2.7100005399279[/C][C]-0.0100005399278991[/C][/ROW]
[ROW][C]31[/C][C]2.7[/C][C]2.70000053995705[/C][C]-5.39957053291573e-07[/C][/ROW]
[ROW][C]32[/C][C]2.7[/C][C]2.70000000002915[/C][C]-2.91535684482369e-11[/C][/ROW]
[ROW][C]33[/C][C]2.68[/C][C]2.7[/C][C]-0.0200000000000018[/C][/ROW]
[ROW][C]34[/C][C]2.67[/C][C]2.6800010798558[/C][C]-0.0100010798558019[/C][/ROW]
[ROW][C]35[/C][C]2.66[/C][C]2.67000053998621[/C][C]-0.0100005399862049[/C][/ROW]
[ROW][C]36[/C][C]2.64[/C][C]2.66000053995706[/C][C]-0.0200005399570564[/C][/ROW]
[ROW][C]37[/C][C]2.64[/C][C]2.64000107988496[/C][C]-1.07988495567923e-06[/C][/ROW]
[ROW][C]38[/C][C]2.63[/C][C]2.64000000005831[/C][C]-0.010000000058306[/C][/ROW]
[ROW][C]39[/C][C]2.61[/C][C]2.6300005399279[/C][C]-0.0200005399279042[/C][/ROW]
[ROW][C]40[/C][C]2.62[/C][C]2.61000107988495[/C][C]0.00999892011504633[/C][/ROW]
[ROW][C]41[/C][C]2.61[/C][C]2.61999946013041[/C][C]-0.00999946013040542[/C][/ROW]
[ROW][C]42[/C][C]2.6[/C][C]2.61000053989875[/C][C]-0.0100005398987517[/C][/ROW]
[ROW][C]43[/C][C]2.58[/C][C]2.60000053995705[/C][C]-0.0200005399570515[/C][/ROW]
[ROW][C]44[/C][C]2.55[/C][C]2.58000107988496[/C][C]-0.0300010798849559[/C][/ROW]
[ROW][C]45[/C][C]2.53[/C][C]2.55000161984201[/C][C]-0.0200016198420085[/C][/ROW]
[ROW][C]46[/C][C]2.5[/C][C]2.53000107994326[/C][C]-0.0300010799432613[/C][/ROW]
[ROW][C]47[/C][C]2.48[/C][C]2.50000161984201[/C][C]-0.0200016198420117[/C][/ROW]
[ROW][C]48[/C][C]2.47[/C][C]2.48000107994326[/C][C]-0.0100010799432613[/C][/ROW]
[ROW][C]49[/C][C]2.47[/C][C]2.47000053998621[/C][C]-5.39986209968646e-07[/C][/ROW]
[ROW][C]50[/C][C]2.46[/C][C]2.47000000002916[/C][C]-0.0100000000291556[/C][/ROW]
[ROW][C]51[/C][C]2.46[/C][C]2.4600005399279[/C][C]-5.3992790238766e-07[/C][/ROW]
[ROW][C]52[/C][C]2.45[/C][C]2.46000000002915[/C][C]-0.010000000029152[/C][/ROW]
[ROW][C]53[/C][C]2.44[/C][C]2.4500005399279[/C][C]-0.0100005399279026[/C][/ROW]
[ROW][C]54[/C][C]2.42[/C][C]2.44000053995705[/C][C]-0.0200005399570533[/C][/ROW]
[ROW][C]55[/C][C]2.39[/C][C]2.42000107988496[/C][C]-0.0300010798849555[/C][/ROW]
[ROW][C]56[/C][C]2.37[/C][C]2.39000161984201[/C][C]-0.0200016198420085[/C][/ROW]
[ROW][C]57[/C][C]2.34[/C][C]2.37000107994326[/C][C]-0.0300010799432617[/C][/ROW]
[ROW][C]58[/C][C]2.32[/C][C]2.34000161984201[/C][C]-0.0200016198420117[/C][/ROW]
[ROW][C]59[/C][C]2.3[/C][C]2.32000107994326[/C][C]-0.0200010799432615[/C][/ROW]
[ROW][C]60[/C][C]2.29[/C][C]2.30000107991411[/C][C]-0.0100010799141108[/C][/ROW]
[ROW][C]61[/C][C]2.3[/C][C]2.29000053998621[/C][C]0.00999946001379115[/C][/ROW]
[ROW][C]62[/C][C]2.29[/C][C]2.29999946010125[/C][C]-0.00999946010125408[/C][/ROW]
[ROW][C]63[/C][C]2.29[/C][C]2.29000053989875[/C][C]-5.3989875015148e-07[/C][/ROW]
[ROW][C]64[/C][C]2.29[/C][C]2.29000000002915[/C][C]-2.9150459823768e-11[/C][/ROW]
[ROW][C]65[/C][C]2.29[/C][C]2.29[/C][C]-1.77635683940025e-15[/C][/ROW]
[ROW][C]66[/C][C]2.28[/C][C]2.29[/C][C]-0.0100000000000002[/C][/ROW]
[ROW][C]67[/C][C]2.28[/C][C]2.2800005399279[/C][C]-5.39927901055393e-07[/C][/ROW]
[ROW][C]68[/C][C]2.28[/C][C]2.28000000002915[/C][C]-2.91522361806074e-11[/C][/ROW]
[ROW][C]69[/C][C]2.29[/C][C]2.28[/C][C]0.00999999999999845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167853&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167853&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
22.692.71-0.02
32.672.6900010798558-0.0200010798558017
42.662.67000107991411-0.0100010799141059
52.672.660000539986210.00999946001379115
62.672.669999460101255.39898745710587e-07
72.662.66999999997085-0.00999999997084933
82.722.66000053992790.0599994600721008
92.632.71999676046175-0.0899967604617475
102.632.6300048591762-4.85917619608145e-06
112.652.630000000262360.0199999997376397
122.662.649998920144210.0100010798557877
132.652.6599994600138-0.00999946001379515
142.622.65000053989875-0.0300005398987455
152.612.62000161981285-0.0100016198128534
162.612.61000054001536-5.40015359096202e-07
172.622.610000000029160.00999999997084311
182.612.6199994600721-0.00999946007210095
192.622.610000539898750.00999946010125141
202.652.619999460101250.03000053989875
212.642.64999838018715-0.0099983801871466
222.662.640000539840440.0199994601595574
232.672.659998920173350.0100010798266541
242.682.66999946001380.010000539986204
252.682.679999460042945.39957056400198e-07
262.712.679999999970850.0300000000291534
272.722.70999838021630.0100016197837043
282.722.719999459984645.40015357319845e-07
292.712.71999999997084-0.00999999997084311
302.72.7100005399279-0.0100005399278991
312.72.70000053995705-5.39957053291573e-07
322.72.70000000002915-2.91535684482369e-11
332.682.7-0.0200000000000018
342.672.6800010798558-0.0100010798558019
352.662.67000053998621-0.0100005399862049
362.642.66000053995706-0.0200005399570564
372.642.64000107988496-1.07988495567923e-06
382.632.64000000005831-0.010000000058306
392.612.6300005399279-0.0200005399279042
402.622.610001079884950.00999892011504633
412.612.61999946013041-0.00999946013040542
422.62.61000053989875-0.0100005398987517
432.582.60000053995705-0.0200005399570515
442.552.58000107988496-0.0300010798849559
452.532.55000161984201-0.0200016198420085
462.52.53000107994326-0.0300010799432613
472.482.50000161984201-0.0200016198420117
482.472.48000107994326-0.0100010799432613
492.472.47000053998621-5.39986209968646e-07
502.462.47000000002916-0.0100000000291556
512.462.4600005399279-5.3992790238766e-07
522.452.46000000002915-0.010000000029152
532.442.4500005399279-0.0100005399279026
542.422.44000053995705-0.0200005399570533
552.392.42000107988496-0.0300010798849555
562.372.39000161984201-0.0200016198420085
572.342.37000107994326-0.0300010799432617
582.322.34000161984201-0.0200016198420117
592.32.32000107994326-0.0200010799432615
602.292.30000107991411-0.0100010799141108
612.32.290000539986210.00999946001379115
622.292.29999946010125-0.00999946010125408
632.292.29000053989875-5.3989875015148e-07
642.292.29000000002915-2.9150459823768e-11
652.292.29-1.77635683940025e-15
662.282.29-0.0100000000000002
672.282.2800005399279-5.39927901055393e-07
682.282.28000000002915-2.91522361806074e-11
692.292.280.00999999999999845







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
702.28999946007212.252899897520462.32709902262374
712.28999946007212.237534171946222.34246474819797
722.28999946007212.225743445764182.35425547438002
732.28999946007212.215803339611882.36419558053232
742.28999946007212.20704589952192.3729530206223
752.28999946007212.199128550950622.38087036919357
762.28999946007212.191847786417642.38815113372656
772.28999946007212.185071008459682.39492791168452
782.28999946007212.178706114024872.40129280611933
792.28999946007212.172686043145492.40731287699871
802.28999946007212.166960170787722.41303874935647
812.28999946007212.161489166226772.41850975391743

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
70 & 2.2899994600721 & 2.25289989752046 & 2.32709902262374 \tabularnewline
71 & 2.2899994600721 & 2.23753417194622 & 2.34246474819797 \tabularnewline
72 & 2.2899994600721 & 2.22574344576418 & 2.35425547438002 \tabularnewline
73 & 2.2899994600721 & 2.21580333961188 & 2.36419558053232 \tabularnewline
74 & 2.2899994600721 & 2.2070458995219 & 2.3729530206223 \tabularnewline
75 & 2.2899994600721 & 2.19912855095062 & 2.38087036919357 \tabularnewline
76 & 2.2899994600721 & 2.19184778641764 & 2.38815113372656 \tabularnewline
77 & 2.2899994600721 & 2.18507100845968 & 2.39492791168452 \tabularnewline
78 & 2.2899994600721 & 2.17870611402487 & 2.40129280611933 \tabularnewline
79 & 2.2899994600721 & 2.17268604314549 & 2.40731287699871 \tabularnewline
80 & 2.2899994600721 & 2.16696017078772 & 2.41303874935647 \tabularnewline
81 & 2.2899994600721 & 2.16148916622677 & 2.41850975391743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167853&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]70[/C][C]2.2899994600721[/C][C]2.25289989752046[/C][C]2.32709902262374[/C][/ROW]
[ROW][C]71[/C][C]2.2899994600721[/C][C]2.23753417194622[/C][C]2.34246474819797[/C][/ROW]
[ROW][C]72[/C][C]2.2899994600721[/C][C]2.22574344576418[/C][C]2.35425547438002[/C][/ROW]
[ROW][C]73[/C][C]2.2899994600721[/C][C]2.21580333961188[/C][C]2.36419558053232[/C][/ROW]
[ROW][C]74[/C][C]2.2899994600721[/C][C]2.2070458995219[/C][C]2.3729530206223[/C][/ROW]
[ROW][C]75[/C][C]2.2899994600721[/C][C]2.19912855095062[/C][C]2.38087036919357[/C][/ROW]
[ROW][C]76[/C][C]2.2899994600721[/C][C]2.19184778641764[/C][C]2.38815113372656[/C][/ROW]
[ROW][C]77[/C][C]2.2899994600721[/C][C]2.18507100845968[/C][C]2.39492791168452[/C][/ROW]
[ROW][C]78[/C][C]2.2899994600721[/C][C]2.17870611402487[/C][C]2.40129280611933[/C][/ROW]
[ROW][C]79[/C][C]2.2899994600721[/C][C]2.17268604314549[/C][C]2.40731287699871[/C][/ROW]
[ROW][C]80[/C][C]2.2899994600721[/C][C]2.16696017078772[/C][C]2.41303874935647[/C][/ROW]
[ROW][C]81[/C][C]2.2899994600721[/C][C]2.16148916622677[/C][C]2.41850975391743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167853&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167853&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
702.28999946007212.252899897520462.32709902262374
712.28999946007212.237534171946222.34246474819797
722.28999946007212.225743445764182.35425547438002
732.28999946007212.215803339611882.36419558053232
742.28999946007212.20704589952192.3729530206223
752.28999946007212.199128550950622.38087036919357
762.28999946007212.191847786417642.38815113372656
772.28999946007212.185071008459682.39492791168452
782.28999946007212.178706114024872.40129280611933
792.28999946007212.172686043145492.40731287699871
802.28999946007212.166960170787722.41303874935647
812.28999946007212.161489166226772.41850975391743



Parameters (Session):
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')