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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 22 May 2014 05:08:58 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/22/t1400749859bej6y3108gxwcc3.htm/, Retrieved Wed, 15 May 2024 15:23:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235080, Retrieved Wed, 15 May 2024 15:23:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [indicator consume...] [2014-05-22 09:08:58] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
0
-2
-4
-6
-2
1
7
2
2
13
7
-1
1
0
0
5
3
6
7
-6
-8
-5
-14
-13
-15
-14
-10
-14
-18
-22
-24
-17
-16
-17
-22
-25
-18
-23
-20
-9
-4
0
3
14
13
12
16
7
2
1
7
10
3
2
12
14
11
13
17
14
7
16
5
5
15
9
4
-9
-14
-4
-19
-10
-22




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235080&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235080&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235080&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.725823838612672
beta0
gamma0.611252415623625

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.725823838612672 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.611252415623625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235080&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]0.725823838612672[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.611252415623625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235080&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235080&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
alpha0.725823838612672
beta0
gamma0.611252415623625







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131-1.623130341880342.62313034188034
140-0.5541357053912810.554135705391281
1500.429799968638928-0.429799968638928
1656.11623834146325-1.11623834146325
1734.76277671288652-1.76277671288652
1867.69004212175297-1.69004212175297
1974.336766697422562.66323330257744
20-60.976535685451189-6.97653568545119
21-8-4.50546945675051-3.49453054324949
22-53.16484773942969-8.16484773942969
23-14-9.59632928592706-4.40367071407294
24-13-21.37755436503768.37755436503758
25-15-13.2339156417935-1.76608435820655
26-14-15.6974622184761.697462218476
27-10-14.04857151298684.04857151298677
28-14-5.22666514480038-8.77333485519962
29-18-12.2461838669811-5.75381613301893
30-22-12.2035203587951-9.79647964120493
31-24-20.7110722916982-3.28892770830185
32-17-30.007060647936613.0070606479366
33-16-20.40094302016354.40094302016348
34-17-7.78260528095373-9.21739471904627
35-22-20.677407174718-1.32259282528202
36-25-28.08029621408583.08029621408583
37-18-25.4815146800547.48151468005404
38-23-20.6524747413644-2.34752525863558
39-20-21.54550798980971.5455079898097
40-9-16.68921886719027.6892188671902
41-4-11.25377997129077.25377997129072
420-2.447406504584092.44740650458409
433-0.9774478946243053.97744789462431
4414-2.2682692251400616.2682692251401
45138.262604840064314.73739515993569
461218.8428388887575-6.84283888875753
47168.994642711278037.00535728872197
4878.37426226816804-1.37426226816804
4928.47742296922141-6.47742296922141
5011.52747613125943-0.527476131259434
5172.60791464288044.3920853571196
521010.5599471496697-0.559947149669725
5339.93496913111068-6.93496913111068
5427.63730608797387-5.63730608797387
55123.495608493174948.50439150682506
56147.550379835251476.44962016474853
57119.022175467924681.97782453207532
581315.658706207912-2.65870620791203
591711.16828411719415.83171588280592
60148.291699275270055.70830072472995
61712.6803100416296-5.68031004162962
62167.306083362788238.69391663721177
63515.9041020179405-10.9041020179405
64511.9238817957786-6.92388179577858
65155.611413008728059.38858699127195
66915.3792525708231-6.37925257082314
67413.0690515242328-9.06905152423279
68-94.02423813067817-13.0242381306782
69-14-9.38798880789044-4.61201119210956
70-4-8.311558014883364.31155801488336
71-19-6.31987919302601-12.680120806974
72-10-22.653479651025512.6534796510255
73-22-15.132519312167-6.86748068783302

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1 & -1.62313034188034 & 2.62313034188034 \tabularnewline
14 & 0 & -0.554135705391281 & 0.554135705391281 \tabularnewline
15 & 0 & 0.429799968638928 & -0.429799968638928 \tabularnewline
16 & 5 & 6.11623834146325 & -1.11623834146325 \tabularnewline
17 & 3 & 4.76277671288652 & -1.76277671288652 \tabularnewline
18 & 6 & 7.69004212175297 & -1.69004212175297 \tabularnewline
19 & 7 & 4.33676669742256 & 2.66323330257744 \tabularnewline
20 & -6 & 0.976535685451189 & -6.97653568545119 \tabularnewline
21 & -8 & -4.50546945675051 & -3.49453054324949 \tabularnewline
22 & -5 & 3.16484773942969 & -8.16484773942969 \tabularnewline
23 & -14 & -9.59632928592706 & -4.40367071407294 \tabularnewline
24 & -13 & -21.3775543650376 & 8.37755436503758 \tabularnewline
25 & -15 & -13.2339156417935 & -1.76608435820655 \tabularnewline
26 & -14 & -15.697462218476 & 1.697462218476 \tabularnewline
27 & -10 & -14.0485715129868 & 4.04857151298677 \tabularnewline
28 & -14 & -5.22666514480038 & -8.77333485519962 \tabularnewline
29 & -18 & -12.2461838669811 & -5.75381613301893 \tabularnewline
30 & -22 & -12.2035203587951 & -9.79647964120493 \tabularnewline
31 & -24 & -20.7110722916982 & -3.28892770830185 \tabularnewline
32 & -17 & -30.0070606479366 & 13.0070606479366 \tabularnewline
33 & -16 & -20.4009430201635 & 4.40094302016348 \tabularnewline
34 & -17 & -7.78260528095373 & -9.21739471904627 \tabularnewline
35 & -22 & -20.677407174718 & -1.32259282528202 \tabularnewline
36 & -25 & -28.0802962140858 & 3.08029621408583 \tabularnewline
37 & -18 & -25.481514680054 & 7.48151468005404 \tabularnewline
38 & -23 & -20.6524747413644 & -2.34752525863558 \tabularnewline
39 & -20 & -21.5455079898097 & 1.5455079898097 \tabularnewline
40 & -9 & -16.6892188671902 & 7.6892188671902 \tabularnewline
41 & -4 & -11.2537799712907 & 7.25377997129072 \tabularnewline
42 & 0 & -2.44740650458409 & 2.44740650458409 \tabularnewline
43 & 3 & -0.977447894624305 & 3.97744789462431 \tabularnewline
44 & 14 & -2.26826922514006 & 16.2682692251401 \tabularnewline
45 & 13 & 8.26260484006431 & 4.73739515993569 \tabularnewline
46 & 12 & 18.8428388887575 & -6.84283888875753 \tabularnewline
47 & 16 & 8.99464271127803 & 7.00535728872197 \tabularnewline
48 & 7 & 8.37426226816804 & -1.37426226816804 \tabularnewline
49 & 2 & 8.47742296922141 & -6.47742296922141 \tabularnewline
50 & 1 & 1.52747613125943 & -0.527476131259434 \tabularnewline
51 & 7 & 2.6079146428804 & 4.3920853571196 \tabularnewline
52 & 10 & 10.5599471496697 & -0.559947149669725 \tabularnewline
53 & 3 & 9.93496913111068 & -6.93496913111068 \tabularnewline
54 & 2 & 7.63730608797387 & -5.63730608797387 \tabularnewline
55 & 12 & 3.49560849317494 & 8.50439150682506 \tabularnewline
56 & 14 & 7.55037983525147 & 6.44962016474853 \tabularnewline
57 & 11 & 9.02217546792468 & 1.97782453207532 \tabularnewline
58 & 13 & 15.658706207912 & -2.65870620791203 \tabularnewline
59 & 17 & 11.1682841171941 & 5.83171588280592 \tabularnewline
60 & 14 & 8.29169927527005 & 5.70830072472995 \tabularnewline
61 & 7 & 12.6803100416296 & -5.68031004162962 \tabularnewline
62 & 16 & 7.30608336278823 & 8.69391663721177 \tabularnewline
63 & 5 & 15.9041020179405 & -10.9041020179405 \tabularnewline
64 & 5 & 11.9238817957786 & -6.92388179577858 \tabularnewline
65 & 15 & 5.61141300872805 & 9.38858699127195 \tabularnewline
66 & 9 & 15.3792525708231 & -6.37925257082314 \tabularnewline
67 & 4 & 13.0690515242328 & -9.06905152423279 \tabularnewline
68 & -9 & 4.02423813067817 & -13.0242381306782 \tabularnewline
69 & -14 & -9.38798880789044 & -4.61201119210956 \tabularnewline
70 & -4 & -8.31155801488336 & 4.31155801488336 \tabularnewline
71 & -19 & -6.31987919302601 & -12.680120806974 \tabularnewline
72 & -10 & -22.6534796510255 & 12.6534796510255 \tabularnewline
73 & -22 & -15.132519312167 & -6.86748068783302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235080&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]-1.62313034188034[/C][C]2.62313034188034[/C][/ROW]
[ROW][C]14[/C][C]0[/C][C]-0.554135705391281[/C][C]0.554135705391281[/C][/ROW]
[ROW][C]15[/C][C]0[/C][C]0.429799968638928[/C][C]-0.429799968638928[/C][/ROW]
[ROW][C]16[/C][C]5[/C][C]6.11623834146325[/C][C]-1.11623834146325[/C][/ROW]
[ROW][C]17[/C][C]3[/C][C]4.76277671288652[/C][C]-1.76277671288652[/C][/ROW]
[ROW][C]18[/C][C]6[/C][C]7.69004212175297[/C][C]-1.69004212175297[/C][/ROW]
[ROW][C]19[/C][C]7[/C][C]4.33676669742256[/C][C]2.66323330257744[/C][/ROW]
[ROW][C]20[/C][C]-6[/C][C]0.976535685451189[/C][C]-6.97653568545119[/C][/ROW]
[ROW][C]21[/C][C]-8[/C][C]-4.50546945675051[/C][C]-3.49453054324949[/C][/ROW]
[ROW][C]22[/C][C]-5[/C][C]3.16484773942969[/C][C]-8.16484773942969[/C][/ROW]
[ROW][C]23[/C][C]-14[/C][C]-9.59632928592706[/C][C]-4.40367071407294[/C][/ROW]
[ROW][C]24[/C][C]-13[/C][C]-21.3775543650376[/C][C]8.37755436503758[/C][/ROW]
[ROW][C]25[/C][C]-15[/C][C]-13.2339156417935[/C][C]-1.76608435820655[/C][/ROW]
[ROW][C]26[/C][C]-14[/C][C]-15.697462218476[/C][C]1.697462218476[/C][/ROW]
[ROW][C]27[/C][C]-10[/C][C]-14.0485715129868[/C][C]4.04857151298677[/C][/ROW]
[ROW][C]28[/C][C]-14[/C][C]-5.22666514480038[/C][C]-8.77333485519962[/C][/ROW]
[ROW][C]29[/C][C]-18[/C][C]-12.2461838669811[/C][C]-5.75381613301893[/C][/ROW]
[ROW][C]30[/C][C]-22[/C][C]-12.2035203587951[/C][C]-9.79647964120493[/C][/ROW]
[ROW][C]31[/C][C]-24[/C][C]-20.7110722916982[/C][C]-3.28892770830185[/C][/ROW]
[ROW][C]32[/C][C]-17[/C][C]-30.0070606479366[/C][C]13.0070606479366[/C][/ROW]
[ROW][C]33[/C][C]-16[/C][C]-20.4009430201635[/C][C]4.40094302016348[/C][/ROW]
[ROW][C]34[/C][C]-17[/C][C]-7.78260528095373[/C][C]-9.21739471904627[/C][/ROW]
[ROW][C]35[/C][C]-22[/C][C]-20.677407174718[/C][C]-1.32259282528202[/C][/ROW]
[ROW][C]36[/C][C]-25[/C][C]-28.0802962140858[/C][C]3.08029621408583[/C][/ROW]
[ROW][C]37[/C][C]-18[/C][C]-25.481514680054[/C][C]7.48151468005404[/C][/ROW]
[ROW][C]38[/C][C]-23[/C][C]-20.6524747413644[/C][C]-2.34752525863558[/C][/ROW]
[ROW][C]39[/C][C]-20[/C][C]-21.5455079898097[/C][C]1.5455079898097[/C][/ROW]
[ROW][C]40[/C][C]-9[/C][C]-16.6892188671902[/C][C]7.6892188671902[/C][/ROW]
[ROW][C]41[/C][C]-4[/C][C]-11.2537799712907[/C][C]7.25377997129072[/C][/ROW]
[ROW][C]42[/C][C]0[/C][C]-2.44740650458409[/C][C]2.44740650458409[/C][/ROW]
[ROW][C]43[/C][C]3[/C][C]-0.977447894624305[/C][C]3.97744789462431[/C][/ROW]
[ROW][C]44[/C][C]14[/C][C]-2.26826922514006[/C][C]16.2682692251401[/C][/ROW]
[ROW][C]45[/C][C]13[/C][C]8.26260484006431[/C][C]4.73739515993569[/C][/ROW]
[ROW][C]46[/C][C]12[/C][C]18.8428388887575[/C][C]-6.84283888875753[/C][/ROW]
[ROW][C]47[/C][C]16[/C][C]8.99464271127803[/C][C]7.00535728872197[/C][/ROW]
[ROW][C]48[/C][C]7[/C][C]8.37426226816804[/C][C]-1.37426226816804[/C][/ROW]
[ROW][C]49[/C][C]2[/C][C]8.47742296922141[/C][C]-6.47742296922141[/C][/ROW]
[ROW][C]50[/C][C]1[/C][C]1.52747613125943[/C][C]-0.527476131259434[/C][/ROW]
[ROW][C]51[/C][C]7[/C][C]2.6079146428804[/C][C]4.3920853571196[/C][/ROW]
[ROW][C]52[/C][C]10[/C][C]10.5599471496697[/C][C]-0.559947149669725[/C][/ROW]
[ROW][C]53[/C][C]3[/C][C]9.93496913111068[/C][C]-6.93496913111068[/C][/ROW]
[ROW][C]54[/C][C]2[/C][C]7.63730608797387[/C][C]-5.63730608797387[/C][/ROW]
[ROW][C]55[/C][C]12[/C][C]3.49560849317494[/C][C]8.50439150682506[/C][/ROW]
[ROW][C]56[/C][C]14[/C][C]7.55037983525147[/C][C]6.44962016474853[/C][/ROW]
[ROW][C]57[/C][C]11[/C][C]9.02217546792468[/C][C]1.97782453207532[/C][/ROW]
[ROW][C]58[/C][C]13[/C][C]15.658706207912[/C][C]-2.65870620791203[/C][/ROW]
[ROW][C]59[/C][C]17[/C][C]11.1682841171941[/C][C]5.83171588280592[/C][/ROW]
[ROW][C]60[/C][C]14[/C][C]8.29169927527005[/C][C]5.70830072472995[/C][/ROW]
[ROW][C]61[/C][C]7[/C][C]12.6803100416296[/C][C]-5.68031004162962[/C][/ROW]
[ROW][C]62[/C][C]16[/C][C]7.30608336278823[/C][C]8.69391663721177[/C][/ROW]
[ROW][C]63[/C][C]5[/C][C]15.9041020179405[/C][C]-10.9041020179405[/C][/ROW]
[ROW][C]64[/C][C]5[/C][C]11.9238817957786[/C][C]-6.92388179577858[/C][/ROW]
[ROW][C]65[/C][C]15[/C][C]5.61141300872805[/C][C]9.38858699127195[/C][/ROW]
[ROW][C]66[/C][C]9[/C][C]15.3792525708231[/C][C]-6.37925257082314[/C][/ROW]
[ROW][C]67[/C][C]4[/C][C]13.0690515242328[/C][C]-9.06905152423279[/C][/ROW]
[ROW][C]68[/C][C]-9[/C][C]4.02423813067817[/C][C]-13.0242381306782[/C][/ROW]
[ROW][C]69[/C][C]-14[/C][C]-9.38798880789044[/C][C]-4.61201119210956[/C][/ROW]
[ROW][C]70[/C][C]-4[/C][C]-8.31155801488336[/C][C]4.31155801488336[/C][/ROW]
[ROW][C]71[/C][C]-19[/C][C]-6.31987919302601[/C][C]-12.680120806974[/C][/ROW]
[ROW][C]72[/C][C]-10[/C][C]-22.6534796510255[/C][C]12.6534796510255[/C][/ROW]
[ROW][C]73[/C][C]-22[/C][C]-15.132519312167[/C][C]-6.86748068783302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235080&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235080&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
131-1.623130341880342.62313034188034
140-0.5541357053912810.554135705391281
1500.429799968638928-0.429799968638928
1656.11623834146325-1.11623834146325
1734.76277671288652-1.76277671288652
1867.69004212175297-1.69004212175297
1974.336766697422562.66323330257744
20-60.976535685451189-6.97653568545119
21-8-4.50546945675051-3.49453054324949
22-53.16484773942969-8.16484773942969
23-14-9.59632928592706-4.40367071407294
24-13-21.37755436503768.37755436503758
25-15-13.2339156417935-1.76608435820655
26-14-15.6974622184761.697462218476
27-10-14.04857151298684.04857151298677
28-14-5.22666514480038-8.77333485519962
29-18-12.2461838669811-5.75381613301893
30-22-12.2035203587951-9.79647964120493
31-24-20.7110722916982-3.28892770830185
32-17-30.007060647936613.0070606479366
33-16-20.40094302016354.40094302016348
34-17-7.78260528095373-9.21739471904627
35-22-20.677407174718-1.32259282528202
36-25-28.08029621408583.08029621408583
37-18-25.4815146800547.48151468005404
38-23-20.6524747413644-2.34752525863558
39-20-21.54550798980971.5455079898097
40-9-16.68921886719027.6892188671902
41-4-11.25377997129077.25377997129072
420-2.447406504584092.44740650458409
433-0.9774478946243053.97744789462431
4414-2.2682692251400616.2682692251401
45138.262604840064314.73739515993569
461218.8428388887575-6.84283888875753
47168.994642711278037.00535728872197
4878.37426226816804-1.37426226816804
4928.47742296922141-6.47742296922141
5011.52747613125943-0.527476131259434
5172.60791464288044.3920853571196
521010.5599471496697-0.559947149669725
5339.93496913111068-6.93496913111068
5427.63730608797387-5.63730608797387
55123.495608493174948.50439150682506
56147.550379835251476.44962016474853
57119.022175467924681.97782453207532
581315.658706207912-2.65870620791203
591711.16828411719415.83171588280592
60148.291699275270055.70830072472995
61712.6803100416296-5.68031004162962
62167.306083362788238.69391663721177
63515.9041020179405-10.9041020179405
64511.9238817957786-6.92388179577858
65155.611413008728059.38858699127195
66915.3792525708231-6.37925257082314
67413.0690515242328-9.06905152423279
68-94.02423813067817-13.0242381306782
69-14-9.38798880789044-4.61201119210956
70-4-8.311558014883364.31155801488336
71-19-6.31987919302601-12.680120806974
72-10-22.653479651025512.6534796510255
73-22-15.132519312167-6.86748068783302







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74-18.9594340093476-32.2037751996427-5.71509281905242
75-19.9561157278522-36.3214286944171-3.59080276128735
76-15.3548303125125-34.33467128714363.62501066211858
77-13.9079602743861-35.18342168773637.36750113896405
78-13.5971264536909-36.94356415368329.74931124630139
79-11.7278995804469-36.976009375207613.5202102143138
80-14.8530322336126-41.869285547811412.1632210805862
81-17.4021444702327-46.077723593689411.273434653224
82-11.4826975423292-41.72670079907918.7613057144206
83-15.4681000522181-47.203106400460216.2669062960239
84-18.352487146868-51.511520951423114.8065466576872
85-23.2872581395513-57.811632395724211.2371161166217

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & -18.9594340093476 & -32.2037751996427 & -5.71509281905242 \tabularnewline
75 & -19.9561157278522 & -36.3214286944171 & -3.59080276128735 \tabularnewline
76 & -15.3548303125125 & -34.3346712871436 & 3.62501066211858 \tabularnewline
77 & -13.9079602743861 & -35.1834216877363 & 7.36750113896405 \tabularnewline
78 & -13.5971264536909 & -36.9435641536832 & 9.74931124630139 \tabularnewline
79 & -11.7278995804469 & -36.9760093752076 & 13.5202102143138 \tabularnewline
80 & -14.8530322336126 & -41.8692855478114 & 12.1632210805862 \tabularnewline
81 & -17.4021444702327 & -46.0777235936894 & 11.273434653224 \tabularnewline
82 & -11.4826975423292 & -41.726700799079 & 18.7613057144206 \tabularnewline
83 & -15.4681000522181 & -47.2031064004602 & 16.2669062960239 \tabularnewline
84 & -18.352487146868 & -51.5115209514231 & 14.8065466576872 \tabularnewline
85 & -23.2872581395513 & -57.8116323957242 & 11.2371161166217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235080&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]74[/C][C]-18.9594340093476[/C][C]-32.2037751996427[/C][C]-5.71509281905242[/C][/ROW]
[ROW][C]75[/C][C]-19.9561157278522[/C][C]-36.3214286944171[/C][C]-3.59080276128735[/C][/ROW]
[ROW][C]76[/C][C]-15.3548303125125[/C][C]-34.3346712871436[/C][C]3.62501066211858[/C][/ROW]
[ROW][C]77[/C][C]-13.9079602743861[/C][C]-35.1834216877363[/C][C]7.36750113896405[/C][/ROW]
[ROW][C]78[/C][C]-13.5971264536909[/C][C]-36.9435641536832[/C][C]9.74931124630139[/C][/ROW]
[ROW][C]79[/C][C]-11.7278995804469[/C][C]-36.9760093752076[/C][C]13.5202102143138[/C][/ROW]
[ROW][C]80[/C][C]-14.8530322336126[/C][C]-41.8692855478114[/C][C]12.1632210805862[/C][/ROW]
[ROW][C]81[/C][C]-17.4021444702327[/C][C]-46.0777235936894[/C][C]11.273434653224[/C][/ROW]
[ROW][C]82[/C][C]-11.4826975423292[/C][C]-41.726700799079[/C][C]18.7613057144206[/C][/ROW]
[ROW][C]83[/C][C]-15.4681000522181[/C][C]-47.2031064004602[/C][C]16.2669062960239[/C][/ROW]
[ROW][C]84[/C][C]-18.352487146868[/C][C]-51.5115209514231[/C][C]14.8065466576872[/C][/ROW]
[ROW][C]85[/C][C]-23.2872581395513[/C][C]-57.8116323957242[/C][C]11.2371161166217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235080&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235080&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
74-18.9594340093476-32.2037751996427-5.71509281905242
75-19.9561157278522-36.3214286944171-3.59080276128735
76-15.3548303125125-34.33467128714363.62501066211858
77-13.9079602743861-35.18342168773637.36750113896405
78-13.5971264536909-36.94356415368329.74931124630139
79-11.7278995804469-36.976009375207613.5202102143138
80-14.8530322336126-41.869285547811412.1632210805862
81-17.4021444702327-46.077723593689411.273434653224
82-11.4826975423292-41.72670079907918.7613057144206
83-15.4681000522181-47.203106400460216.2669062960239
84-18.352487146868-51.511520951423114.8065466576872
85-23.2872581395513-57.811632395724211.2371161166217



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):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')