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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Jan 2010 18:30:26 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/27/t1264556003ueggivinw1v7cir.htm/, Retrieved Mon, 06 May 2024 02:52:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72687, Retrieved Mon, 06 May 2024 02:52:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W61
Estimated Impact205
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [KDGP2W62] [2010-01-20 22:23:55] [8c77cc01643940e7a8195154a75bb218]
-   P   [Exponential Smoothing] [Exponental smooth...] [2010-01-23 15:31:48] [74be16979710d4c4e7c6647856088456]
-   P       [Exponential Smoothing] [] [2010-01-27 01:30:26] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1
4
-3
-3
0
6
-1
0
-1
1
-4
-1
-1
0
3
0
8
8
8
8
11
13
5
12
13
9
11
7
12
11
10
13
14
10
13
12
13
17
15
6
9
6
11
12
13
11
16
16
19
14
15
12
14
16
13
13
15
12
13
12
15
10
8
11
8
13
9
8
8
6
8
6
12
16




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72687&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72687&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72687&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.715895076963664
beta0
gamma0.990005082021168

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.715895076963664 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.990005082021168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72687&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]0.715895076963664[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.990005082021168[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72687&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72687&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
alpha0.715895076963664
beta0
gamma0.990005082021168







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13-1-2.912393162393161.91239316239316
140-0.6892993331959450.689299333195945
1532.533187645014350.466812354985652
160-0.5702693758312980.570269375831298
1787.525337975223780.474662024776218
1887.510833827670330.489166172329673
1985.298379794612612.70162020538739
2089.04481071182932-1.04481071182932
21117.775856845892793.22414315410721
221312.27135936969860.728640630301447
2357.89701058882804-2.89701058882804
24128.968742616062093.03125738393791
251311.78071570351411.21928429648594
26913.1636024334441-4.16360243344406
271112.8493430573329-1.84934305733293
2878.1168606511552-1.11686065115520
291214.9777688897305-2.97776888973049
301112.4957659605931-1.49576596059315
31109.484595371825840.515404628174158
321310.61218423821252.38781576178749
331413.00133943085750.99866056914247
341015.2017316182060-5.20173161820597
35135.562088598291397.43791140170861
361215.6999565737289-3.69995657372891
371313.1834415409131-0.183441540913101
381712.04810440364214.95189559635794
391518.9105060896457-3.91050608964569
40612.9084691124501-6.90846911245007
41915.0997844190741-6.09978441907414
42610.7995819668727-4.79958196687273
43115.988898298480315.01110170151969
441210.86157887943071.13842112056930
451311.96557742274171.03442257725828
461112.4476161776176-1.4476161776176
47169.050619128740116.94938087125989
481615.70605452861480.293945471385197
491917.03782802543821.96217197456183
501418.8829172720305-4.88291727203047
511516.2119386174891-1.21193861748908
521211.29856978660300.701430213397018
531419.1652295139376-5.16522951393758
541615.89977217318160.100227826818426
551317.3562432723403-4.35624327234029
561314.4336369685910-1.43363696859104
571513.66706060488981.33293939511016
581213.6646946612886-1.66469466128865
591312.47407623675390.525923763246066
601212.6590471641812-0.659047164181242
611513.77779218212011.22220781787992
621013.1678585306438-3.16785853064381
63812.7572009630589-4.75720096305892
64115.843960564403375.15603943559663
65815.2495651920529-7.24956519205291
661311.97293273202621.02706726797375
67912.8394728650157-3.83947286501575
68811.1088477421315-3.10884774213148
6989.92113821246912-1.92113821246912
7066.7460636345231-0.7460636345231
7186.829233626585821.17076637341418
7267.14255297975992-1.14255297975992
73128.444290344721163.55570965527884
74168.270125764776077.72987423522393

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & -1 & -2.91239316239316 & 1.91239316239316 \tabularnewline
14 & 0 & -0.689299333195945 & 0.689299333195945 \tabularnewline
15 & 3 & 2.53318764501435 & 0.466812354985652 \tabularnewline
16 & 0 & -0.570269375831298 & 0.570269375831298 \tabularnewline
17 & 8 & 7.52533797522378 & 0.474662024776218 \tabularnewline
18 & 8 & 7.51083382767033 & 0.489166172329673 \tabularnewline
19 & 8 & 5.29837979461261 & 2.70162020538739 \tabularnewline
20 & 8 & 9.04481071182932 & -1.04481071182932 \tabularnewline
21 & 11 & 7.77585684589279 & 3.22414315410721 \tabularnewline
22 & 13 & 12.2713593696986 & 0.728640630301447 \tabularnewline
23 & 5 & 7.89701058882804 & -2.89701058882804 \tabularnewline
24 & 12 & 8.96874261606209 & 3.03125738393791 \tabularnewline
25 & 13 & 11.7807157035141 & 1.21928429648594 \tabularnewline
26 & 9 & 13.1636024334441 & -4.16360243344406 \tabularnewline
27 & 11 & 12.8493430573329 & -1.84934305733293 \tabularnewline
28 & 7 & 8.1168606511552 & -1.11686065115520 \tabularnewline
29 & 12 & 14.9777688897305 & -2.97776888973049 \tabularnewline
30 & 11 & 12.4957659605931 & -1.49576596059315 \tabularnewline
31 & 10 & 9.48459537182584 & 0.515404628174158 \tabularnewline
32 & 13 & 10.6121842382125 & 2.38781576178749 \tabularnewline
33 & 14 & 13.0013394308575 & 0.99866056914247 \tabularnewline
34 & 10 & 15.2017316182060 & -5.20173161820597 \tabularnewline
35 & 13 & 5.56208859829139 & 7.43791140170861 \tabularnewline
36 & 12 & 15.6999565737289 & -3.69995657372891 \tabularnewline
37 & 13 & 13.1834415409131 & -0.183441540913101 \tabularnewline
38 & 17 & 12.0481044036421 & 4.95189559635794 \tabularnewline
39 & 15 & 18.9105060896457 & -3.91050608964569 \tabularnewline
40 & 6 & 12.9084691124501 & -6.90846911245007 \tabularnewline
41 & 9 & 15.0997844190741 & -6.09978441907414 \tabularnewline
42 & 6 & 10.7995819668727 & -4.79958196687273 \tabularnewline
43 & 11 & 5.98889829848031 & 5.01110170151969 \tabularnewline
44 & 12 & 10.8615788794307 & 1.13842112056930 \tabularnewline
45 & 13 & 11.9655774227417 & 1.03442257725828 \tabularnewline
46 & 11 & 12.4476161776176 & -1.4476161776176 \tabularnewline
47 & 16 & 9.05061912874011 & 6.94938087125989 \tabularnewline
48 & 16 & 15.7060545286148 & 0.293945471385197 \tabularnewline
49 & 19 & 17.0378280254382 & 1.96217197456183 \tabularnewline
50 & 14 & 18.8829172720305 & -4.88291727203047 \tabularnewline
51 & 15 & 16.2119386174891 & -1.21193861748908 \tabularnewline
52 & 12 & 11.2985697866030 & 0.701430213397018 \tabularnewline
53 & 14 & 19.1652295139376 & -5.16522951393758 \tabularnewline
54 & 16 & 15.8997721731816 & 0.100227826818426 \tabularnewline
55 & 13 & 17.3562432723403 & -4.35624327234029 \tabularnewline
56 & 13 & 14.4336369685910 & -1.43363696859104 \tabularnewline
57 & 15 & 13.6670606048898 & 1.33293939511016 \tabularnewline
58 & 12 & 13.6646946612886 & -1.66469466128865 \tabularnewline
59 & 13 & 12.4740762367539 & 0.525923763246066 \tabularnewline
60 & 12 & 12.6590471641812 & -0.659047164181242 \tabularnewline
61 & 15 & 13.7777921821201 & 1.22220781787992 \tabularnewline
62 & 10 & 13.1678585306438 & -3.16785853064381 \tabularnewline
63 & 8 & 12.7572009630589 & -4.75720096305892 \tabularnewline
64 & 11 & 5.84396056440337 & 5.15603943559663 \tabularnewline
65 & 8 & 15.2495651920529 & -7.24956519205291 \tabularnewline
66 & 13 & 11.9729327320262 & 1.02706726797375 \tabularnewline
67 & 9 & 12.8394728650157 & -3.83947286501575 \tabularnewline
68 & 8 & 11.1088477421315 & -3.10884774213148 \tabularnewline
69 & 8 & 9.92113821246912 & -1.92113821246912 \tabularnewline
70 & 6 & 6.7460636345231 & -0.7460636345231 \tabularnewline
71 & 8 & 6.82923362658582 & 1.17076637341418 \tabularnewline
72 & 6 & 7.14255297975992 & -1.14255297975992 \tabularnewline
73 & 12 & 8.44429034472116 & 3.55570965527884 \tabularnewline
74 & 16 & 8.27012576477607 & 7.72987423522393 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72687&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]13[/C][C]-1[/C][C]-2.91239316239316[/C][C]1.91239316239316[/C][/ROW]
[ROW][C]14[/C][C]0[/C][C]-0.689299333195945[/C][C]0.689299333195945[/C][/ROW]
[ROW][C]15[/C][C]3[/C][C]2.53318764501435[/C][C]0.466812354985652[/C][/ROW]
[ROW][C]16[/C][C]0[/C][C]-0.570269375831298[/C][C]0.570269375831298[/C][/ROW]
[ROW][C]17[/C][C]8[/C][C]7.52533797522378[/C][C]0.474662024776218[/C][/ROW]
[ROW][C]18[/C][C]8[/C][C]7.51083382767033[/C][C]0.489166172329673[/C][/ROW]
[ROW][C]19[/C][C]8[/C][C]5.29837979461261[/C][C]2.70162020538739[/C][/ROW]
[ROW][C]20[/C][C]8[/C][C]9.04481071182932[/C][C]-1.04481071182932[/C][/ROW]
[ROW][C]21[/C][C]11[/C][C]7.77585684589279[/C][C]3.22414315410721[/C][/ROW]
[ROW][C]22[/C][C]13[/C][C]12.2713593696986[/C][C]0.728640630301447[/C][/ROW]
[ROW][C]23[/C][C]5[/C][C]7.89701058882804[/C][C]-2.89701058882804[/C][/ROW]
[ROW][C]24[/C][C]12[/C][C]8.96874261606209[/C][C]3.03125738393791[/C][/ROW]
[ROW][C]25[/C][C]13[/C][C]11.7807157035141[/C][C]1.21928429648594[/C][/ROW]
[ROW][C]26[/C][C]9[/C][C]13.1636024334441[/C][C]-4.16360243344406[/C][/ROW]
[ROW][C]27[/C][C]11[/C][C]12.8493430573329[/C][C]-1.84934305733293[/C][/ROW]
[ROW][C]28[/C][C]7[/C][C]8.1168606511552[/C][C]-1.11686065115520[/C][/ROW]
[ROW][C]29[/C][C]12[/C][C]14.9777688897305[/C][C]-2.97776888973049[/C][/ROW]
[ROW][C]30[/C][C]11[/C][C]12.4957659605931[/C][C]-1.49576596059315[/C][/ROW]
[ROW][C]31[/C][C]10[/C][C]9.48459537182584[/C][C]0.515404628174158[/C][/ROW]
[ROW][C]32[/C][C]13[/C][C]10.6121842382125[/C][C]2.38781576178749[/C][/ROW]
[ROW][C]33[/C][C]14[/C][C]13.0013394308575[/C][C]0.99866056914247[/C][/ROW]
[ROW][C]34[/C][C]10[/C][C]15.2017316182060[/C][C]-5.20173161820597[/C][/ROW]
[ROW][C]35[/C][C]13[/C][C]5.56208859829139[/C][C]7.43791140170861[/C][/ROW]
[ROW][C]36[/C][C]12[/C][C]15.6999565737289[/C][C]-3.69995657372891[/C][/ROW]
[ROW][C]37[/C][C]13[/C][C]13.1834415409131[/C][C]-0.183441540913101[/C][/ROW]
[ROW][C]38[/C][C]17[/C][C]12.0481044036421[/C][C]4.95189559635794[/C][/ROW]
[ROW][C]39[/C][C]15[/C][C]18.9105060896457[/C][C]-3.91050608964569[/C][/ROW]
[ROW][C]40[/C][C]6[/C][C]12.9084691124501[/C][C]-6.90846911245007[/C][/ROW]
[ROW][C]41[/C][C]9[/C][C]15.0997844190741[/C][C]-6.09978441907414[/C][/ROW]
[ROW][C]42[/C][C]6[/C][C]10.7995819668727[/C][C]-4.79958196687273[/C][/ROW]
[ROW][C]43[/C][C]11[/C][C]5.98889829848031[/C][C]5.01110170151969[/C][/ROW]
[ROW][C]44[/C][C]12[/C][C]10.8615788794307[/C][C]1.13842112056930[/C][/ROW]
[ROW][C]45[/C][C]13[/C][C]11.9655774227417[/C][C]1.03442257725828[/C][/ROW]
[ROW][C]46[/C][C]11[/C][C]12.4476161776176[/C][C]-1.4476161776176[/C][/ROW]
[ROW][C]47[/C][C]16[/C][C]9.05061912874011[/C][C]6.94938087125989[/C][/ROW]
[ROW][C]48[/C][C]16[/C][C]15.7060545286148[/C][C]0.293945471385197[/C][/ROW]
[ROW][C]49[/C][C]19[/C][C]17.0378280254382[/C][C]1.96217197456183[/C][/ROW]
[ROW][C]50[/C][C]14[/C][C]18.8829172720305[/C][C]-4.88291727203047[/C][/ROW]
[ROW][C]51[/C][C]15[/C][C]16.2119386174891[/C][C]-1.21193861748908[/C][/ROW]
[ROW][C]52[/C][C]12[/C][C]11.2985697866030[/C][C]0.701430213397018[/C][/ROW]
[ROW][C]53[/C][C]14[/C][C]19.1652295139376[/C][C]-5.16522951393758[/C][/ROW]
[ROW][C]54[/C][C]16[/C][C]15.8997721731816[/C][C]0.100227826818426[/C][/ROW]
[ROW][C]55[/C][C]13[/C][C]17.3562432723403[/C][C]-4.35624327234029[/C][/ROW]
[ROW][C]56[/C][C]13[/C][C]14.4336369685910[/C][C]-1.43363696859104[/C][/ROW]
[ROW][C]57[/C][C]15[/C][C]13.6670606048898[/C][C]1.33293939511016[/C][/ROW]
[ROW][C]58[/C][C]12[/C][C]13.6646946612886[/C][C]-1.66469466128865[/C][/ROW]
[ROW][C]59[/C][C]13[/C][C]12.4740762367539[/C][C]0.525923763246066[/C][/ROW]
[ROW][C]60[/C][C]12[/C][C]12.6590471641812[/C][C]-0.659047164181242[/C][/ROW]
[ROW][C]61[/C][C]15[/C][C]13.7777921821201[/C][C]1.22220781787992[/C][/ROW]
[ROW][C]62[/C][C]10[/C][C]13.1678585306438[/C][C]-3.16785853064381[/C][/ROW]
[ROW][C]63[/C][C]8[/C][C]12.7572009630589[/C][C]-4.75720096305892[/C][/ROW]
[ROW][C]64[/C][C]11[/C][C]5.84396056440337[/C][C]5.15603943559663[/C][/ROW]
[ROW][C]65[/C][C]8[/C][C]15.2495651920529[/C][C]-7.24956519205291[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]11.9729327320262[/C][C]1.02706726797375[/C][/ROW]
[ROW][C]67[/C][C]9[/C][C]12.8394728650157[/C][C]-3.83947286501575[/C][/ROW]
[ROW][C]68[/C][C]8[/C][C]11.1088477421315[/C][C]-3.10884774213148[/C][/ROW]
[ROW][C]69[/C][C]8[/C][C]9.92113821246912[/C][C]-1.92113821246912[/C][/ROW]
[ROW][C]70[/C][C]6[/C][C]6.7460636345231[/C][C]-0.7460636345231[/C][/ROW]
[ROW][C]71[/C][C]8[/C][C]6.82923362658582[/C][C]1.17076637341418[/C][/ROW]
[ROW][C]72[/C][C]6[/C][C]7.14255297975992[/C][C]-1.14255297975992[/C][/ROW]
[ROW][C]73[/C][C]12[/C][C]8.44429034472116[/C][C]3.55570965527884[/C][/ROW]
[ROW][C]74[/C][C]16[/C][C]8.27012576477607[/C][C]7.72987423522393[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72687&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72687&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
13-1-2.912393162393161.91239316239316
140-0.6892993331959450.689299333195945
1532.533187645014350.466812354985652
160-0.5702693758312980.570269375831298
1787.525337975223780.474662024776218
1887.510833827670330.489166172329673
1985.298379794612612.70162020538739
2089.04481071182932-1.04481071182932
21117.775856845892793.22414315410721
221312.27135936969860.728640630301447
2357.89701058882804-2.89701058882804
24128.968742616062093.03125738393791
251311.78071570351411.21928429648594
26913.1636024334441-4.16360243344406
271112.8493430573329-1.84934305733293
2878.1168606511552-1.11686065115520
291214.9777688897305-2.97776888973049
301112.4957659605931-1.49576596059315
31109.484595371825840.515404628174158
321310.61218423821252.38781576178749
331413.00133943085750.99866056914247
341015.2017316182060-5.20173161820597
35135.562088598291397.43791140170861
361215.6999565737289-3.69995657372891
371313.1834415409131-0.183441540913101
381712.04810440364214.95189559635794
391518.9105060896457-3.91050608964569
40612.9084691124501-6.90846911245007
41915.0997844190741-6.09978441907414
42610.7995819668727-4.79958196687273
43115.988898298480315.01110170151969
441210.86157887943071.13842112056930
451311.96557742274171.03442257725828
461112.4476161776176-1.4476161776176
47169.050619128740116.94938087125989
481615.70605452861480.293945471385197
491917.03782802543821.96217197456183
501418.8829172720305-4.88291727203047
511516.2119386174891-1.21193861748908
521211.29856978660300.701430213397018
531419.1652295139376-5.16522951393758
541615.89977217318160.100227826818426
551317.3562432723403-4.35624327234029
561314.4336369685910-1.43363696859104
571513.66706060488981.33293939511016
581213.6646946612886-1.66469466128865
591312.47407623675390.525923763246066
601212.6590471641812-0.659047164181242
611513.77779218212011.22220781787992
621013.1678585306438-3.16785853064381
63812.7572009630589-4.75720096305892
64115.843960564403375.15603943559663
65815.2495651920529-7.24956519205291
661311.97293273202621.02706726797375
67912.8394728650157-3.83947286501575
68811.1088477421315-3.10884774213148
6989.92113821246912-1.92113821246912
7066.7460636345231-0.7460636345231
7186.829233626585821.17076637341418
7267.14255297975992-1.14255297975992
73128.444290344721163.55570965527884
74168.270125764776077.72987423522393







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7515.21407453026038.5838090620175521.8443399985031
7614.49474159068776.3405776981117222.6489054832636
7716.71989664373537.2848366336131526.1549566538574
7820.961121872629110.399383095220331.5228606500379
7919.72360064848568.1442960661785631.3029052307927
8020.94713475506068.4327325233335633.4615369867876
8122.31909551713628.9347676735323335.7034233607401
8220.84986205207236.6487986963694535.0509254077752
8322.00627312822317.0329578961075536.9795883603386
8420.83079009573785.1231442616887536.5384359297869
8524.27193384644777.8627868163448340.6810808765506
8622.72630195560795.6444380390690739.8081658721467

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
75 & 15.2140745302603 & 8.58380906201755 & 21.8443399985031 \tabularnewline
76 & 14.4947415906877 & 6.34057769811172 & 22.6489054832636 \tabularnewline
77 & 16.7198966437353 & 7.28483663361315 & 26.1549566538574 \tabularnewline
78 & 20.9611218726291 & 10.3993830952203 & 31.5228606500379 \tabularnewline
79 & 19.7236006484856 & 8.14429606617856 & 31.3029052307927 \tabularnewline
80 & 20.9471347550606 & 8.43273252333356 & 33.4615369867876 \tabularnewline
81 & 22.3190955171362 & 8.93476767353233 & 35.7034233607401 \tabularnewline
82 & 20.8498620520723 & 6.64879869636945 & 35.0509254077752 \tabularnewline
83 & 22.0062731282231 & 7.03295789610755 & 36.9795883603386 \tabularnewline
84 & 20.8307900957378 & 5.12314426168875 & 36.5384359297869 \tabularnewline
85 & 24.2719338464477 & 7.86278681634483 & 40.6810808765506 \tabularnewline
86 & 22.7263019556079 & 5.64443803906907 & 39.8081658721467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72687&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]15.2140745302603[/C][C]8.58380906201755[/C][C]21.8443399985031[/C][/ROW]
[ROW][C]76[/C][C]14.4947415906877[/C][C]6.34057769811172[/C][C]22.6489054832636[/C][/ROW]
[ROW][C]77[/C][C]16.7198966437353[/C][C]7.28483663361315[/C][C]26.1549566538574[/C][/ROW]
[ROW][C]78[/C][C]20.9611218726291[/C][C]10.3993830952203[/C][C]31.5228606500379[/C][/ROW]
[ROW][C]79[/C][C]19.7236006484856[/C][C]8.14429606617856[/C][C]31.3029052307927[/C][/ROW]
[ROW][C]80[/C][C]20.9471347550606[/C][C]8.43273252333356[/C][C]33.4615369867876[/C][/ROW]
[ROW][C]81[/C][C]22.3190955171362[/C][C]8.93476767353233[/C][C]35.7034233607401[/C][/ROW]
[ROW][C]82[/C][C]20.8498620520723[/C][C]6.64879869636945[/C][C]35.0509254077752[/C][/ROW]
[ROW][C]83[/C][C]22.0062731282231[/C][C]7.03295789610755[/C][C]36.9795883603386[/C][/ROW]
[ROW][C]84[/C][C]20.8307900957378[/C][C]5.12314426168875[/C][C]36.5384359297869[/C][/ROW]
[ROW][C]85[/C][C]24.2719338464477[/C][C]7.86278681634483[/C][C]40.6810808765506[/C][/ROW]
[ROW][C]86[/C][C]22.7263019556079[/C][C]5.64443803906907[/C][C]39.8081658721467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72687&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72687&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
7515.21407453026038.5838090620175521.8443399985031
7614.49474159068776.3405776981117222.6489054832636
7716.71989664373537.2848366336131526.1549566538574
7820.961121872629110.399383095220331.5228606500379
7919.72360064848568.1442960661785631.3029052307927
8020.94713475506068.4327325233335633.4615369867876
8122.31909551713628.9347676735323335.7034233607401
8220.84986205207236.6487986963694535.0509254077752
8322.00627312822317.0329578961075536.9795883603386
8420.83079009573785.1231442616887536.5384359297869
8524.27193384644777.8627868163448340.6810808765506
8622.72630195560795.6444380390690739.8081658721467



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')