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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 05:12:12 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/17/t1355739174vvkn1io5xv1hszs.htm/, Retrieved Fri, 29 Mar 2024 14:08:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200746, Retrieved Fri, 29 Mar 2024 14:08:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oef 2] [2012-12-17 10:12:12] [76c30f62b7052b57088120e90a652e05] [Current]
- R PD    [Exponential Smoothing] [opgave 10 oef 2] [2013-01-14 23:21:16] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
0,47
0,47
0,47
0,47
0,47
0,48
0,48
0,48
0,48
0,48
0,49
0,49
0,49
0,49
0,49
0,49
0,49
0,5
0,5
0,5
0,5
0,5
0,5
0,5
0,5
0,51
0,51
0,5
0,51
0,5
0,51
0,51
0,52
0,53
0,53
0,53
0,53
0,53
0,54
0,55
0,54
0,55
0,55
0,55
0,54
0,55
0,55
0,55
0,55
0,56
0,56
0,56
0,56
0,55
0,55
0,56
0,56
0,56
0,56
0,56
0,55
0,55
0,55
0,54
0,54
0,54
0,54
0,55
0,54
0,54
0,54
0,54




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=200746&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=200746&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200746&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
alpha0.6717741154244
beta0.0865680638632208
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.6717741154244 \tabularnewline
beta & 0.0865680638632208 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200746&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]0.6717741154244[/C][/ROW]
[ROW][C]beta[/C][C]0.0865680638632208[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200746&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200746&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
alpha0.6717741154244
beta0.0865680638632208
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
30.470.470
40.470.470
50.470.470
60.480.470.01
70.480.4772992829995010.00270071700049884
80.480.4798521546135790.000147845386421153
90.480.480698670985201-0.0006986709852006
100.480.480935888928688-0.000935888928687789
110.490.4809593241405720.00904067585942842
120.490.4882105104701330.00178948952986724
130.490.490694603821702-0.000694603821702222
140.490.49146955344057-0.00146955344056998
150.490.491638451282771-0.00163845128277101
160.490.491598605128196-0.00159860512819571
170.490.491492561011254-0.00149256101125445
180.50.4913709559187030.00862904408129705
190.50.498550598155660.00144940184434034
200.50.500991431362129-0.000991431362128758
210.50.501734920118046-0.00173492011804577
220.50.501878059507947-0.00187805950794651
230.50.501815824541639-0.00181582454163876
240.50.50168979961931-0.00168979961931026
250.50.501550166058828-0.00155016605882752
260.510.5014141860668910.00858581393310898
270.510.5085865960757670.00141340392423339
280.50.511022962048088-0.0110229620480878
290.510.5044638679012940.00553613209870552
300.50.509350693824819-0.00935069382481946
310.510.5036931534579590.00630684654204072
320.510.508920712938350.00107928706165028
330.520.5106992983319120.00930070166808816
340.530.5185416919712760.0114583080287243
350.530.5284998582744450.00150014172555513
360.530.531855625736776-0.00185562573677622
370.530.532849163079023-0.00284916307902272
380.530.533009576996599-0.00300957699659921
390.540.5328872095005890.00711279049941071
400.550.5399784250064080.0100215749935924
410.540.549606483164181-0.00960648316418078
420.550.5454902627209440.00450973727905568
430.550.551119213872988-0.00111921387298752
440.550.552901694374006-0.00290169437400623
450.540.553318004943129-0.0133180049431287
460.550.5459624099767160.00403759002328408
470.550.550500657221783-0.000500657221782608
480.550.551961112125758-0.00196111212575767
490.550.552326424352061-0.00232642435206076
500.560.5523110379696310.00768896203036951
510.560.5594708742316160.00052912576838382
520.560.561851688699695-0.00185168869969488
530.560.562525450188164-0.00252545018816408
540.550.562599730652457-0.0125997306524569
550.550.555173643207975-0.00517364320797475
560.560.5524353400857870.00756465991421296
570.560.558694215904040.00130578409595961
580.560.560824477765203-0.000824477765202447
590.560.561475738016865-0.00147573801686529
600.560.561603678148112-0.0016036781481118
610.550.561552410815918-0.0115524108159177
620.550.554146021365909-0.00414602136590869
630.550.551473944145608-0.00147394414560753
640.540.550511183216496-0.0105111832164955
650.540.542866169716303-0.00286616971630327
660.540.540190198635046-0.000190198635046324
670.540.5393008148132830.000699185186716966
680.550.5390495565660230.0109504434339766
690.540.546321642367902-0.00632164236790167
700.540.54162315805192-0.00162315805192026
710.540.5399866004482771.33995517230812e-05
720.540.5394502191211660.000549780878834283

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.47 & 0.47 & 0 \tabularnewline
4 & 0.47 & 0.47 & 0 \tabularnewline
5 & 0.47 & 0.47 & 0 \tabularnewline
6 & 0.48 & 0.47 & 0.01 \tabularnewline
7 & 0.48 & 0.477299282999501 & 0.00270071700049884 \tabularnewline
8 & 0.48 & 0.479852154613579 & 0.000147845386421153 \tabularnewline
9 & 0.48 & 0.480698670985201 & -0.0006986709852006 \tabularnewline
10 & 0.48 & 0.480935888928688 & -0.000935888928687789 \tabularnewline
11 & 0.49 & 0.480959324140572 & 0.00904067585942842 \tabularnewline
12 & 0.49 & 0.488210510470133 & 0.00178948952986724 \tabularnewline
13 & 0.49 & 0.490694603821702 & -0.000694603821702222 \tabularnewline
14 & 0.49 & 0.49146955344057 & -0.00146955344056998 \tabularnewline
15 & 0.49 & 0.491638451282771 & -0.00163845128277101 \tabularnewline
16 & 0.49 & 0.491598605128196 & -0.00159860512819571 \tabularnewline
17 & 0.49 & 0.491492561011254 & -0.00149256101125445 \tabularnewline
18 & 0.5 & 0.491370955918703 & 0.00862904408129705 \tabularnewline
19 & 0.5 & 0.49855059815566 & 0.00144940184434034 \tabularnewline
20 & 0.5 & 0.500991431362129 & -0.000991431362128758 \tabularnewline
21 & 0.5 & 0.501734920118046 & -0.00173492011804577 \tabularnewline
22 & 0.5 & 0.501878059507947 & -0.00187805950794651 \tabularnewline
23 & 0.5 & 0.501815824541639 & -0.00181582454163876 \tabularnewline
24 & 0.5 & 0.50168979961931 & -0.00168979961931026 \tabularnewline
25 & 0.5 & 0.501550166058828 & -0.00155016605882752 \tabularnewline
26 & 0.51 & 0.501414186066891 & 0.00858581393310898 \tabularnewline
27 & 0.51 & 0.508586596075767 & 0.00141340392423339 \tabularnewline
28 & 0.5 & 0.511022962048088 & -0.0110229620480878 \tabularnewline
29 & 0.51 & 0.504463867901294 & 0.00553613209870552 \tabularnewline
30 & 0.5 & 0.509350693824819 & -0.00935069382481946 \tabularnewline
31 & 0.51 & 0.503693153457959 & 0.00630684654204072 \tabularnewline
32 & 0.51 & 0.50892071293835 & 0.00107928706165028 \tabularnewline
33 & 0.52 & 0.510699298331912 & 0.00930070166808816 \tabularnewline
34 & 0.53 & 0.518541691971276 & 0.0114583080287243 \tabularnewline
35 & 0.53 & 0.528499858274445 & 0.00150014172555513 \tabularnewline
36 & 0.53 & 0.531855625736776 & -0.00185562573677622 \tabularnewline
37 & 0.53 & 0.532849163079023 & -0.00284916307902272 \tabularnewline
38 & 0.53 & 0.533009576996599 & -0.00300957699659921 \tabularnewline
39 & 0.54 & 0.532887209500589 & 0.00711279049941071 \tabularnewline
40 & 0.55 & 0.539978425006408 & 0.0100215749935924 \tabularnewline
41 & 0.54 & 0.549606483164181 & -0.00960648316418078 \tabularnewline
42 & 0.55 & 0.545490262720944 & 0.00450973727905568 \tabularnewline
43 & 0.55 & 0.551119213872988 & -0.00111921387298752 \tabularnewline
44 & 0.55 & 0.552901694374006 & -0.00290169437400623 \tabularnewline
45 & 0.54 & 0.553318004943129 & -0.0133180049431287 \tabularnewline
46 & 0.55 & 0.545962409976716 & 0.00403759002328408 \tabularnewline
47 & 0.55 & 0.550500657221783 & -0.000500657221782608 \tabularnewline
48 & 0.55 & 0.551961112125758 & -0.00196111212575767 \tabularnewline
49 & 0.55 & 0.552326424352061 & -0.00232642435206076 \tabularnewline
50 & 0.56 & 0.552311037969631 & 0.00768896203036951 \tabularnewline
51 & 0.56 & 0.559470874231616 & 0.00052912576838382 \tabularnewline
52 & 0.56 & 0.561851688699695 & -0.00185168869969488 \tabularnewline
53 & 0.56 & 0.562525450188164 & -0.00252545018816408 \tabularnewline
54 & 0.55 & 0.562599730652457 & -0.0125997306524569 \tabularnewline
55 & 0.55 & 0.555173643207975 & -0.00517364320797475 \tabularnewline
56 & 0.56 & 0.552435340085787 & 0.00756465991421296 \tabularnewline
57 & 0.56 & 0.55869421590404 & 0.00130578409595961 \tabularnewline
58 & 0.56 & 0.560824477765203 & -0.000824477765202447 \tabularnewline
59 & 0.56 & 0.561475738016865 & -0.00147573801686529 \tabularnewline
60 & 0.56 & 0.561603678148112 & -0.0016036781481118 \tabularnewline
61 & 0.55 & 0.561552410815918 & -0.0115524108159177 \tabularnewline
62 & 0.55 & 0.554146021365909 & -0.00414602136590869 \tabularnewline
63 & 0.55 & 0.551473944145608 & -0.00147394414560753 \tabularnewline
64 & 0.54 & 0.550511183216496 & -0.0105111832164955 \tabularnewline
65 & 0.54 & 0.542866169716303 & -0.00286616971630327 \tabularnewline
66 & 0.54 & 0.540190198635046 & -0.000190198635046324 \tabularnewline
67 & 0.54 & 0.539300814813283 & 0.000699185186716966 \tabularnewline
68 & 0.55 & 0.539049556566023 & 0.0109504434339766 \tabularnewline
69 & 0.54 & 0.546321642367902 & -0.00632164236790167 \tabularnewline
70 & 0.54 & 0.54162315805192 & -0.00162315805192026 \tabularnewline
71 & 0.54 & 0.539986600448277 & 1.33995517230812e-05 \tabularnewline
72 & 0.54 & 0.539450219121166 & 0.000549780878834283 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200746&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]0.47[/C][C]0.47[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.47[/C][C]0.47[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.47[/C][C]0.47[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.48[/C][C]0.47[/C][C]0.01[/C][/ROW]
[ROW][C]7[/C][C]0.48[/C][C]0.477299282999501[/C][C]0.00270071700049884[/C][/ROW]
[ROW][C]8[/C][C]0.48[/C][C]0.479852154613579[/C][C]0.000147845386421153[/C][/ROW]
[ROW][C]9[/C][C]0.48[/C][C]0.480698670985201[/C][C]-0.0006986709852006[/C][/ROW]
[ROW][C]10[/C][C]0.48[/C][C]0.480935888928688[/C][C]-0.000935888928687789[/C][/ROW]
[ROW][C]11[/C][C]0.49[/C][C]0.480959324140572[/C][C]0.00904067585942842[/C][/ROW]
[ROW][C]12[/C][C]0.49[/C][C]0.488210510470133[/C][C]0.00178948952986724[/C][/ROW]
[ROW][C]13[/C][C]0.49[/C][C]0.490694603821702[/C][C]-0.000694603821702222[/C][/ROW]
[ROW][C]14[/C][C]0.49[/C][C]0.49146955344057[/C][C]-0.00146955344056998[/C][/ROW]
[ROW][C]15[/C][C]0.49[/C][C]0.491638451282771[/C][C]-0.00163845128277101[/C][/ROW]
[ROW][C]16[/C][C]0.49[/C][C]0.491598605128196[/C][C]-0.00159860512819571[/C][/ROW]
[ROW][C]17[/C][C]0.49[/C][C]0.491492561011254[/C][C]-0.00149256101125445[/C][/ROW]
[ROW][C]18[/C][C]0.5[/C][C]0.491370955918703[/C][C]0.00862904408129705[/C][/ROW]
[ROW][C]19[/C][C]0.5[/C][C]0.49855059815566[/C][C]0.00144940184434034[/C][/ROW]
[ROW][C]20[/C][C]0.5[/C][C]0.500991431362129[/C][C]-0.000991431362128758[/C][/ROW]
[ROW][C]21[/C][C]0.5[/C][C]0.501734920118046[/C][C]-0.00173492011804577[/C][/ROW]
[ROW][C]22[/C][C]0.5[/C][C]0.501878059507947[/C][C]-0.00187805950794651[/C][/ROW]
[ROW][C]23[/C][C]0.5[/C][C]0.501815824541639[/C][C]-0.00181582454163876[/C][/ROW]
[ROW][C]24[/C][C]0.5[/C][C]0.50168979961931[/C][C]-0.00168979961931026[/C][/ROW]
[ROW][C]25[/C][C]0.5[/C][C]0.501550166058828[/C][C]-0.00155016605882752[/C][/ROW]
[ROW][C]26[/C][C]0.51[/C][C]0.501414186066891[/C][C]0.00858581393310898[/C][/ROW]
[ROW][C]27[/C][C]0.51[/C][C]0.508586596075767[/C][C]0.00141340392423339[/C][/ROW]
[ROW][C]28[/C][C]0.5[/C][C]0.511022962048088[/C][C]-0.0110229620480878[/C][/ROW]
[ROW][C]29[/C][C]0.51[/C][C]0.504463867901294[/C][C]0.00553613209870552[/C][/ROW]
[ROW][C]30[/C][C]0.5[/C][C]0.509350693824819[/C][C]-0.00935069382481946[/C][/ROW]
[ROW][C]31[/C][C]0.51[/C][C]0.503693153457959[/C][C]0.00630684654204072[/C][/ROW]
[ROW][C]32[/C][C]0.51[/C][C]0.50892071293835[/C][C]0.00107928706165028[/C][/ROW]
[ROW][C]33[/C][C]0.52[/C][C]0.510699298331912[/C][C]0.00930070166808816[/C][/ROW]
[ROW][C]34[/C][C]0.53[/C][C]0.518541691971276[/C][C]0.0114583080287243[/C][/ROW]
[ROW][C]35[/C][C]0.53[/C][C]0.528499858274445[/C][C]0.00150014172555513[/C][/ROW]
[ROW][C]36[/C][C]0.53[/C][C]0.531855625736776[/C][C]-0.00185562573677622[/C][/ROW]
[ROW][C]37[/C][C]0.53[/C][C]0.532849163079023[/C][C]-0.00284916307902272[/C][/ROW]
[ROW][C]38[/C][C]0.53[/C][C]0.533009576996599[/C][C]-0.00300957699659921[/C][/ROW]
[ROW][C]39[/C][C]0.54[/C][C]0.532887209500589[/C][C]0.00711279049941071[/C][/ROW]
[ROW][C]40[/C][C]0.55[/C][C]0.539978425006408[/C][C]0.0100215749935924[/C][/ROW]
[ROW][C]41[/C][C]0.54[/C][C]0.549606483164181[/C][C]-0.00960648316418078[/C][/ROW]
[ROW][C]42[/C][C]0.55[/C][C]0.545490262720944[/C][C]0.00450973727905568[/C][/ROW]
[ROW][C]43[/C][C]0.55[/C][C]0.551119213872988[/C][C]-0.00111921387298752[/C][/ROW]
[ROW][C]44[/C][C]0.55[/C][C]0.552901694374006[/C][C]-0.00290169437400623[/C][/ROW]
[ROW][C]45[/C][C]0.54[/C][C]0.553318004943129[/C][C]-0.0133180049431287[/C][/ROW]
[ROW][C]46[/C][C]0.55[/C][C]0.545962409976716[/C][C]0.00403759002328408[/C][/ROW]
[ROW][C]47[/C][C]0.55[/C][C]0.550500657221783[/C][C]-0.000500657221782608[/C][/ROW]
[ROW][C]48[/C][C]0.55[/C][C]0.551961112125758[/C][C]-0.00196111212575767[/C][/ROW]
[ROW][C]49[/C][C]0.55[/C][C]0.552326424352061[/C][C]-0.00232642435206076[/C][/ROW]
[ROW][C]50[/C][C]0.56[/C][C]0.552311037969631[/C][C]0.00768896203036951[/C][/ROW]
[ROW][C]51[/C][C]0.56[/C][C]0.559470874231616[/C][C]0.00052912576838382[/C][/ROW]
[ROW][C]52[/C][C]0.56[/C][C]0.561851688699695[/C][C]-0.00185168869969488[/C][/ROW]
[ROW][C]53[/C][C]0.56[/C][C]0.562525450188164[/C][C]-0.00252545018816408[/C][/ROW]
[ROW][C]54[/C][C]0.55[/C][C]0.562599730652457[/C][C]-0.0125997306524569[/C][/ROW]
[ROW][C]55[/C][C]0.55[/C][C]0.555173643207975[/C][C]-0.00517364320797475[/C][/ROW]
[ROW][C]56[/C][C]0.56[/C][C]0.552435340085787[/C][C]0.00756465991421296[/C][/ROW]
[ROW][C]57[/C][C]0.56[/C][C]0.55869421590404[/C][C]0.00130578409595961[/C][/ROW]
[ROW][C]58[/C][C]0.56[/C][C]0.560824477765203[/C][C]-0.000824477765202447[/C][/ROW]
[ROW][C]59[/C][C]0.56[/C][C]0.561475738016865[/C][C]-0.00147573801686529[/C][/ROW]
[ROW][C]60[/C][C]0.56[/C][C]0.561603678148112[/C][C]-0.0016036781481118[/C][/ROW]
[ROW][C]61[/C][C]0.55[/C][C]0.561552410815918[/C][C]-0.0115524108159177[/C][/ROW]
[ROW][C]62[/C][C]0.55[/C][C]0.554146021365909[/C][C]-0.00414602136590869[/C][/ROW]
[ROW][C]63[/C][C]0.55[/C][C]0.551473944145608[/C][C]-0.00147394414560753[/C][/ROW]
[ROW][C]64[/C][C]0.54[/C][C]0.550511183216496[/C][C]-0.0105111832164955[/C][/ROW]
[ROW][C]65[/C][C]0.54[/C][C]0.542866169716303[/C][C]-0.00286616971630327[/C][/ROW]
[ROW][C]66[/C][C]0.54[/C][C]0.540190198635046[/C][C]-0.000190198635046324[/C][/ROW]
[ROW][C]67[/C][C]0.54[/C][C]0.539300814813283[/C][C]0.000699185186716966[/C][/ROW]
[ROW][C]68[/C][C]0.55[/C][C]0.539049556566023[/C][C]0.0109504434339766[/C][/ROW]
[ROW][C]69[/C][C]0.54[/C][C]0.546321642367902[/C][C]-0.00632164236790167[/C][/ROW]
[ROW][C]70[/C][C]0.54[/C][C]0.54162315805192[/C][C]-0.00162315805192026[/C][/ROW]
[ROW][C]71[/C][C]0.54[/C][C]0.539986600448277[/C][C]1.33995517230812e-05[/C][/ROW]
[ROW][C]72[/C][C]0.54[/C][C]0.539450219121166[/C][C]0.000549780878834283[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200746&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200746&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
30.470.470
40.470.470
50.470.470
60.480.470.01
70.480.4772992829995010.00270071700049884
80.480.4798521546135790.000147845386421153
90.480.480698670985201-0.0006986709852006
100.480.480935888928688-0.000935888928687789
110.490.4809593241405720.00904067585942842
120.490.4882105104701330.00178948952986724
130.490.490694603821702-0.000694603821702222
140.490.49146955344057-0.00146955344056998
150.490.491638451282771-0.00163845128277101
160.490.491598605128196-0.00159860512819571
170.490.491492561011254-0.00149256101125445
180.50.4913709559187030.00862904408129705
190.50.498550598155660.00144940184434034
200.50.500991431362129-0.000991431362128758
210.50.501734920118046-0.00173492011804577
220.50.501878059507947-0.00187805950794651
230.50.501815824541639-0.00181582454163876
240.50.50168979961931-0.00168979961931026
250.50.501550166058828-0.00155016605882752
260.510.5014141860668910.00858581393310898
270.510.5085865960757670.00141340392423339
280.50.511022962048088-0.0110229620480878
290.510.5044638679012940.00553613209870552
300.50.509350693824819-0.00935069382481946
310.510.5036931534579590.00630684654204072
320.510.508920712938350.00107928706165028
330.520.5106992983319120.00930070166808816
340.530.5185416919712760.0114583080287243
350.530.5284998582744450.00150014172555513
360.530.531855625736776-0.00185562573677622
370.530.532849163079023-0.00284916307902272
380.530.533009576996599-0.00300957699659921
390.540.5328872095005890.00711279049941071
400.550.5399784250064080.0100215749935924
410.540.549606483164181-0.00960648316418078
420.550.5454902627209440.00450973727905568
430.550.551119213872988-0.00111921387298752
440.550.552901694374006-0.00290169437400623
450.540.553318004943129-0.0133180049431287
460.550.5459624099767160.00403759002328408
470.550.550500657221783-0.000500657221782608
480.550.551961112125758-0.00196111212575767
490.550.552326424352061-0.00232642435206076
500.560.5523110379696310.00768896203036951
510.560.5594708742316160.00052912576838382
520.560.561851688699695-0.00185168869969488
530.560.562525450188164-0.00252545018816408
540.550.562599730652457-0.0125997306524569
550.550.555173643207975-0.00517364320797475
560.560.5524353400857870.00756465991421296
570.560.558694215904040.00130578409595961
580.560.560824477765203-0.000824477765202447
590.560.561475738016865-0.00147573801686529
600.560.561603678148112-0.0016036781481118
610.550.561552410815918-0.0115524108159177
620.550.554146021365909-0.00414602136590869
630.550.551473944145608-0.00147394414560753
640.540.550511183216496-0.0105111832164955
650.540.542866169716303-0.00286616971630327
660.540.540190198635046-0.000190198635046324
670.540.5393008148132830.000699185186716966
680.550.5390495565660230.0109504434339766
690.540.546321642367902-0.00632164236790167
700.540.54162315805192-0.00162315805192026
710.540.5399866004482771.33995517230812e-05
720.540.5394502191211660.000549780878834283







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
730.5393061369442810.528435433032610.550176840855953
740.538792726203840.5253341304042990.552251322003382
750.53827931546340.5223253979410440.554233232985755
760.5377659047229590.5193498098845120.556181999561406
770.5372524939825180.516376472077460.558128515887577
780.5367390832420780.5133875521557660.560090614328389
790.5362256725016370.5103720656952060.562079279308068
800.5357122617611960.5073229586986050.564101564823787
810.5351988510207560.5042355835925820.566162118448929
820.5346854402803150.5011068386928780.568264041867752
830.5341720295398740.4979346525940080.57040940648574
840.5336586187994340.494717660475390.572599577123477

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.539306136944281 & 0.52843543303261 & 0.550176840855953 \tabularnewline
74 & 0.53879272620384 & 0.525334130404299 & 0.552251322003382 \tabularnewline
75 & 0.5382793154634 & 0.522325397941044 & 0.554233232985755 \tabularnewline
76 & 0.537765904722959 & 0.519349809884512 & 0.556181999561406 \tabularnewline
77 & 0.537252493982518 & 0.51637647207746 & 0.558128515887577 \tabularnewline
78 & 0.536739083242078 & 0.513387552155766 & 0.560090614328389 \tabularnewline
79 & 0.536225672501637 & 0.510372065695206 & 0.562079279308068 \tabularnewline
80 & 0.535712261761196 & 0.507322958698605 & 0.564101564823787 \tabularnewline
81 & 0.535198851020756 & 0.504235583592582 & 0.566162118448929 \tabularnewline
82 & 0.534685440280315 & 0.501106838692878 & 0.568264041867752 \tabularnewline
83 & 0.534172029539874 & 0.497934652594008 & 0.57040940648574 \tabularnewline
84 & 0.533658618799434 & 0.49471766047539 & 0.572599577123477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200746&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]0.539306136944281[/C][C]0.52843543303261[/C][C]0.550176840855953[/C][/ROW]
[ROW][C]74[/C][C]0.53879272620384[/C][C]0.525334130404299[/C][C]0.552251322003382[/C][/ROW]
[ROW][C]75[/C][C]0.5382793154634[/C][C]0.522325397941044[/C][C]0.554233232985755[/C][/ROW]
[ROW][C]76[/C][C]0.537765904722959[/C][C]0.519349809884512[/C][C]0.556181999561406[/C][/ROW]
[ROW][C]77[/C][C]0.537252493982518[/C][C]0.51637647207746[/C][C]0.558128515887577[/C][/ROW]
[ROW][C]78[/C][C]0.536739083242078[/C][C]0.513387552155766[/C][C]0.560090614328389[/C][/ROW]
[ROW][C]79[/C][C]0.536225672501637[/C][C]0.510372065695206[/C][C]0.562079279308068[/C][/ROW]
[ROW][C]80[/C][C]0.535712261761196[/C][C]0.507322958698605[/C][C]0.564101564823787[/C][/ROW]
[ROW][C]81[/C][C]0.535198851020756[/C][C]0.504235583592582[/C][C]0.566162118448929[/C][/ROW]
[ROW][C]82[/C][C]0.534685440280315[/C][C]0.501106838692878[/C][C]0.568264041867752[/C][/ROW]
[ROW][C]83[/C][C]0.534172029539874[/C][C]0.497934652594008[/C][C]0.57040940648574[/C][/ROW]
[ROW][C]84[/C][C]0.533658618799434[/C][C]0.49471766047539[/C][C]0.572599577123477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200746&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200746&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
730.5393061369442810.528435433032610.550176840855953
740.538792726203840.5253341304042990.552251322003382
750.53827931546340.5223253979410440.554233232985755
760.5377659047229590.5193498098845120.556181999561406
770.5372524939825180.516376472077460.558128515887577
780.5367390832420780.5133875521557660.560090614328389
790.5362256725016370.5103720656952060.562079279308068
800.5357122617611960.5073229586986050.564101564823787
810.5351988510207560.5042355835925820.566162118448929
820.5346854402803150.5011068386928780.568264041867752
830.5341720295398740.4979346525940080.57040940648574
840.5336586187994340.494717660475390.572599577123477



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