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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 29 Dec 2012 10:08:50 -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/29/t1356793861qccniuumiqbg4v1.htm/, Retrieved Thu, 02 May 2024 13:13:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204879, Retrieved Thu, 02 May 2024 13:13:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-29 15:08:50] [606ba890a58836132a627f58687546e9] [Current]
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Dataseries X:
46,83
45,93
45,93
45,93
45,9
45,91
45,85
45,58
45,56
45,5
45,5
45,5
45,51
45,49
45,4
45,38
45,38
45,38
45,49
45,41
44,99
44,98
44,93
44,93
44,91
44,86
44,76
44,89
44,89
45
45,01
45,11
45,05
44,67
44,48
44,48
44,48
44,58
44,79
44,79
44,41
44,41
44,44
44,43
44,36
44,39
44,39
44,41
44,32
44,43
44,82
44,97
44,91
44,79
44,76
44,8
44,65
44,49
44,56
44,4
44,45
44,46
44,39
44,5
44,44
44,41
44,4
44,42
44,49
44,46
44,49
44,5




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=204879&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=204879&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204879&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
alpha1
beta0.682187850039951
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.682187850039951 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204879&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.682187850039951[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204879&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204879&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.682187850039951
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
345.9345.030.899999999999999
445.9345.6439690650360.286030934964046
545.945.8390958936040.0609041063960021
645.9145.85064393500490.0593560649951073
745.8545.9011359213707-0.0511359213707294
845.5845.806251617111-0.226251617111025
945.5645.3819055128660.178094487134011
1045.545.48339940814790.0166005918520895
1145.545.43472413021290.0652758697871221
1245.545.47925453548240.0207454645175602
1345.5145.49340683931980.0165931606802445
1445.4945.5147264919296-0.0247264919295702
1545.445.4778583795611-0.0778583795611141
1645.3845.33474433900070.0452556609992811
1745.3845.345617201080.034382798920042
1845.3845.36907272875360.0109272712464232
1945.4945.3765271804320.113472819568024
2045.4145.5639369592511-0.153936959251062
2144.9945.3789230359779-0.388923035977882
2244.9844.69360446623310.286395533766871
2344.9344.87898001967460.0510199803254139
2444.9344.86378523036190.0662147696381368
2544.9144.90895614170220.0010438582978054
2644.8644.8896682491501-0.029668249150113
2744.7644.8194289300479-0.0594289300479502
2844.8944.67888723602840.211112763971641
2944.8944.9529057985982-0.062905798598166
304544.90999222709740.0900077729025597
3145.0145.0813944361807-0.0713944361807251
3245.1145.04269001925780.0673099807422233
3345.0545.1886080703065-0.138608070306546
3444.6745.0340513288259-0.36405132882593
3544.4844.405699935510.0743000644900107
3644.4844.26638653676230.213613463237742
3744.4844.4121110459880.0678889540119982
3844.5844.45842406556690.121575934433096
3944.7944.64136169089440.148638309105586
4044.7944.9527609394167-0.162760939416728
4144.4144.8417274040855-0.431727404085549
4244.4144.16720821448910.242791785510903
4344.4444.33283782065410.107162179345863
4444.4344.4359425573877-0.00594255738768368
4544.3644.4218886169396-0.0618886169396475
4644.3944.30966895440760.0803310455923594
4744.3944.3944698176918-0.00446981769175636
4844.4144.39142056237050.0185794376294481
4944.3244.4240952289819-0.104095228981926
5044.4344.26308272852330.166917271476663
5144.8244.48695166308650.333048336913464
5244.9745.1041531920049-0.134153192004916
5344.9145.1626355143751-0.252635514375086
5444.7944.9302906359798-0.140290635979802
5544.7644.714586068640.0454139313599953
5644.844.71556690083630.0844330991636539
5744.6544.813166135227-0.163166135227009
5844.4944.5518561802372-0.0618561802371644
5944.5644.34965864562950.210341354370506
6044.444.563150961942-0.163150961942002
6144.4544.29185135798280.158148642017167
6244.4644.44973844006730.0102615599327294
6344.3944.4667387515758-0.0767387515758315
6444.544.34438850762360.155611492376437
6544.4444.5605447770494-0.120544777049354
6644.4144.4183105947605-0.0083105947605091
6744.444.38264120798830.01735879201172
6844.4244.384483164990.0355168350099575
6944.4944.42871231830570.0612876816942887
7044.4644.5405220301147-0.0805220301146718
7144.4944.45559087950990.0344091204901105
7244.544.5090643634388-0.00906436343881012

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 45.93 & 45.03 & 0.899999999999999 \tabularnewline
4 & 45.93 & 45.643969065036 & 0.286030934964046 \tabularnewline
5 & 45.9 & 45.839095893604 & 0.0609041063960021 \tabularnewline
6 & 45.91 & 45.8506439350049 & 0.0593560649951073 \tabularnewline
7 & 45.85 & 45.9011359213707 & -0.0511359213707294 \tabularnewline
8 & 45.58 & 45.806251617111 & -0.226251617111025 \tabularnewline
9 & 45.56 & 45.381905512866 & 0.178094487134011 \tabularnewline
10 & 45.5 & 45.4833994081479 & 0.0166005918520895 \tabularnewline
11 & 45.5 & 45.4347241302129 & 0.0652758697871221 \tabularnewline
12 & 45.5 & 45.4792545354824 & 0.0207454645175602 \tabularnewline
13 & 45.51 & 45.4934068393198 & 0.0165931606802445 \tabularnewline
14 & 45.49 & 45.5147264919296 & -0.0247264919295702 \tabularnewline
15 & 45.4 & 45.4778583795611 & -0.0778583795611141 \tabularnewline
16 & 45.38 & 45.3347443390007 & 0.0452556609992811 \tabularnewline
17 & 45.38 & 45.34561720108 & 0.034382798920042 \tabularnewline
18 & 45.38 & 45.3690727287536 & 0.0109272712464232 \tabularnewline
19 & 45.49 & 45.376527180432 & 0.113472819568024 \tabularnewline
20 & 45.41 & 45.5639369592511 & -0.153936959251062 \tabularnewline
21 & 44.99 & 45.3789230359779 & -0.388923035977882 \tabularnewline
22 & 44.98 & 44.6936044662331 & 0.286395533766871 \tabularnewline
23 & 44.93 & 44.8789800196746 & 0.0510199803254139 \tabularnewline
24 & 44.93 & 44.8637852303619 & 0.0662147696381368 \tabularnewline
25 & 44.91 & 44.9089561417022 & 0.0010438582978054 \tabularnewline
26 & 44.86 & 44.8896682491501 & -0.029668249150113 \tabularnewline
27 & 44.76 & 44.8194289300479 & -0.0594289300479502 \tabularnewline
28 & 44.89 & 44.6788872360284 & 0.211112763971641 \tabularnewline
29 & 44.89 & 44.9529057985982 & -0.062905798598166 \tabularnewline
30 & 45 & 44.9099922270974 & 0.0900077729025597 \tabularnewline
31 & 45.01 & 45.0813944361807 & -0.0713944361807251 \tabularnewline
32 & 45.11 & 45.0426900192578 & 0.0673099807422233 \tabularnewline
33 & 45.05 & 45.1886080703065 & -0.138608070306546 \tabularnewline
34 & 44.67 & 45.0340513288259 & -0.36405132882593 \tabularnewline
35 & 44.48 & 44.40569993551 & 0.0743000644900107 \tabularnewline
36 & 44.48 & 44.2663865367623 & 0.213613463237742 \tabularnewline
37 & 44.48 & 44.412111045988 & 0.0678889540119982 \tabularnewline
38 & 44.58 & 44.4584240655669 & 0.121575934433096 \tabularnewline
39 & 44.79 & 44.6413616908944 & 0.148638309105586 \tabularnewline
40 & 44.79 & 44.9527609394167 & -0.162760939416728 \tabularnewline
41 & 44.41 & 44.8417274040855 & -0.431727404085549 \tabularnewline
42 & 44.41 & 44.1672082144891 & 0.242791785510903 \tabularnewline
43 & 44.44 & 44.3328378206541 & 0.107162179345863 \tabularnewline
44 & 44.43 & 44.4359425573877 & -0.00594255738768368 \tabularnewline
45 & 44.36 & 44.4218886169396 & -0.0618886169396475 \tabularnewline
46 & 44.39 & 44.3096689544076 & 0.0803310455923594 \tabularnewline
47 & 44.39 & 44.3944698176918 & -0.00446981769175636 \tabularnewline
48 & 44.41 & 44.3914205623705 & 0.0185794376294481 \tabularnewline
49 & 44.32 & 44.4240952289819 & -0.104095228981926 \tabularnewline
50 & 44.43 & 44.2630827285233 & 0.166917271476663 \tabularnewline
51 & 44.82 & 44.4869516630865 & 0.333048336913464 \tabularnewline
52 & 44.97 & 45.1041531920049 & -0.134153192004916 \tabularnewline
53 & 44.91 & 45.1626355143751 & -0.252635514375086 \tabularnewline
54 & 44.79 & 44.9302906359798 & -0.140290635979802 \tabularnewline
55 & 44.76 & 44.71458606864 & 0.0454139313599953 \tabularnewline
56 & 44.8 & 44.7155669008363 & 0.0844330991636539 \tabularnewline
57 & 44.65 & 44.813166135227 & -0.163166135227009 \tabularnewline
58 & 44.49 & 44.5518561802372 & -0.0618561802371644 \tabularnewline
59 & 44.56 & 44.3496586456295 & 0.210341354370506 \tabularnewline
60 & 44.4 & 44.563150961942 & -0.163150961942002 \tabularnewline
61 & 44.45 & 44.2918513579828 & 0.158148642017167 \tabularnewline
62 & 44.46 & 44.4497384400673 & 0.0102615599327294 \tabularnewline
63 & 44.39 & 44.4667387515758 & -0.0767387515758315 \tabularnewline
64 & 44.5 & 44.3443885076236 & 0.155611492376437 \tabularnewline
65 & 44.44 & 44.5605447770494 & -0.120544777049354 \tabularnewline
66 & 44.41 & 44.4183105947605 & -0.0083105947605091 \tabularnewline
67 & 44.4 & 44.3826412079883 & 0.01735879201172 \tabularnewline
68 & 44.42 & 44.38448316499 & 0.0355168350099575 \tabularnewline
69 & 44.49 & 44.4287123183057 & 0.0612876816942887 \tabularnewline
70 & 44.46 & 44.5405220301147 & -0.0805220301146718 \tabularnewline
71 & 44.49 & 44.4555908795099 & 0.0344091204901105 \tabularnewline
72 & 44.5 & 44.5090643634388 & -0.00906436343881012 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204879&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]45.93[/C][C]45.03[/C][C]0.899999999999999[/C][/ROW]
[ROW][C]4[/C][C]45.93[/C][C]45.643969065036[/C][C]0.286030934964046[/C][/ROW]
[ROW][C]5[/C][C]45.9[/C][C]45.839095893604[/C][C]0.0609041063960021[/C][/ROW]
[ROW][C]6[/C][C]45.91[/C][C]45.8506439350049[/C][C]0.0593560649951073[/C][/ROW]
[ROW][C]7[/C][C]45.85[/C][C]45.9011359213707[/C][C]-0.0511359213707294[/C][/ROW]
[ROW][C]8[/C][C]45.58[/C][C]45.806251617111[/C][C]-0.226251617111025[/C][/ROW]
[ROW][C]9[/C][C]45.56[/C][C]45.381905512866[/C][C]0.178094487134011[/C][/ROW]
[ROW][C]10[/C][C]45.5[/C][C]45.4833994081479[/C][C]0.0166005918520895[/C][/ROW]
[ROW][C]11[/C][C]45.5[/C][C]45.4347241302129[/C][C]0.0652758697871221[/C][/ROW]
[ROW][C]12[/C][C]45.5[/C][C]45.4792545354824[/C][C]0.0207454645175602[/C][/ROW]
[ROW][C]13[/C][C]45.51[/C][C]45.4934068393198[/C][C]0.0165931606802445[/C][/ROW]
[ROW][C]14[/C][C]45.49[/C][C]45.5147264919296[/C][C]-0.0247264919295702[/C][/ROW]
[ROW][C]15[/C][C]45.4[/C][C]45.4778583795611[/C][C]-0.0778583795611141[/C][/ROW]
[ROW][C]16[/C][C]45.38[/C][C]45.3347443390007[/C][C]0.0452556609992811[/C][/ROW]
[ROW][C]17[/C][C]45.38[/C][C]45.34561720108[/C][C]0.034382798920042[/C][/ROW]
[ROW][C]18[/C][C]45.38[/C][C]45.3690727287536[/C][C]0.0109272712464232[/C][/ROW]
[ROW][C]19[/C][C]45.49[/C][C]45.376527180432[/C][C]0.113472819568024[/C][/ROW]
[ROW][C]20[/C][C]45.41[/C][C]45.5639369592511[/C][C]-0.153936959251062[/C][/ROW]
[ROW][C]21[/C][C]44.99[/C][C]45.3789230359779[/C][C]-0.388923035977882[/C][/ROW]
[ROW][C]22[/C][C]44.98[/C][C]44.6936044662331[/C][C]0.286395533766871[/C][/ROW]
[ROW][C]23[/C][C]44.93[/C][C]44.8789800196746[/C][C]0.0510199803254139[/C][/ROW]
[ROW][C]24[/C][C]44.93[/C][C]44.8637852303619[/C][C]0.0662147696381368[/C][/ROW]
[ROW][C]25[/C][C]44.91[/C][C]44.9089561417022[/C][C]0.0010438582978054[/C][/ROW]
[ROW][C]26[/C][C]44.86[/C][C]44.8896682491501[/C][C]-0.029668249150113[/C][/ROW]
[ROW][C]27[/C][C]44.76[/C][C]44.8194289300479[/C][C]-0.0594289300479502[/C][/ROW]
[ROW][C]28[/C][C]44.89[/C][C]44.6788872360284[/C][C]0.211112763971641[/C][/ROW]
[ROW][C]29[/C][C]44.89[/C][C]44.9529057985982[/C][C]-0.062905798598166[/C][/ROW]
[ROW][C]30[/C][C]45[/C][C]44.9099922270974[/C][C]0.0900077729025597[/C][/ROW]
[ROW][C]31[/C][C]45.01[/C][C]45.0813944361807[/C][C]-0.0713944361807251[/C][/ROW]
[ROW][C]32[/C][C]45.11[/C][C]45.0426900192578[/C][C]0.0673099807422233[/C][/ROW]
[ROW][C]33[/C][C]45.05[/C][C]45.1886080703065[/C][C]-0.138608070306546[/C][/ROW]
[ROW][C]34[/C][C]44.67[/C][C]45.0340513288259[/C][C]-0.36405132882593[/C][/ROW]
[ROW][C]35[/C][C]44.48[/C][C]44.40569993551[/C][C]0.0743000644900107[/C][/ROW]
[ROW][C]36[/C][C]44.48[/C][C]44.2663865367623[/C][C]0.213613463237742[/C][/ROW]
[ROW][C]37[/C][C]44.48[/C][C]44.412111045988[/C][C]0.0678889540119982[/C][/ROW]
[ROW][C]38[/C][C]44.58[/C][C]44.4584240655669[/C][C]0.121575934433096[/C][/ROW]
[ROW][C]39[/C][C]44.79[/C][C]44.6413616908944[/C][C]0.148638309105586[/C][/ROW]
[ROW][C]40[/C][C]44.79[/C][C]44.9527609394167[/C][C]-0.162760939416728[/C][/ROW]
[ROW][C]41[/C][C]44.41[/C][C]44.8417274040855[/C][C]-0.431727404085549[/C][/ROW]
[ROW][C]42[/C][C]44.41[/C][C]44.1672082144891[/C][C]0.242791785510903[/C][/ROW]
[ROW][C]43[/C][C]44.44[/C][C]44.3328378206541[/C][C]0.107162179345863[/C][/ROW]
[ROW][C]44[/C][C]44.43[/C][C]44.4359425573877[/C][C]-0.00594255738768368[/C][/ROW]
[ROW][C]45[/C][C]44.36[/C][C]44.4218886169396[/C][C]-0.0618886169396475[/C][/ROW]
[ROW][C]46[/C][C]44.39[/C][C]44.3096689544076[/C][C]0.0803310455923594[/C][/ROW]
[ROW][C]47[/C][C]44.39[/C][C]44.3944698176918[/C][C]-0.00446981769175636[/C][/ROW]
[ROW][C]48[/C][C]44.41[/C][C]44.3914205623705[/C][C]0.0185794376294481[/C][/ROW]
[ROW][C]49[/C][C]44.32[/C][C]44.4240952289819[/C][C]-0.104095228981926[/C][/ROW]
[ROW][C]50[/C][C]44.43[/C][C]44.2630827285233[/C][C]0.166917271476663[/C][/ROW]
[ROW][C]51[/C][C]44.82[/C][C]44.4869516630865[/C][C]0.333048336913464[/C][/ROW]
[ROW][C]52[/C][C]44.97[/C][C]45.1041531920049[/C][C]-0.134153192004916[/C][/ROW]
[ROW][C]53[/C][C]44.91[/C][C]45.1626355143751[/C][C]-0.252635514375086[/C][/ROW]
[ROW][C]54[/C][C]44.79[/C][C]44.9302906359798[/C][C]-0.140290635979802[/C][/ROW]
[ROW][C]55[/C][C]44.76[/C][C]44.71458606864[/C][C]0.0454139313599953[/C][/ROW]
[ROW][C]56[/C][C]44.8[/C][C]44.7155669008363[/C][C]0.0844330991636539[/C][/ROW]
[ROW][C]57[/C][C]44.65[/C][C]44.813166135227[/C][C]-0.163166135227009[/C][/ROW]
[ROW][C]58[/C][C]44.49[/C][C]44.5518561802372[/C][C]-0.0618561802371644[/C][/ROW]
[ROW][C]59[/C][C]44.56[/C][C]44.3496586456295[/C][C]0.210341354370506[/C][/ROW]
[ROW][C]60[/C][C]44.4[/C][C]44.563150961942[/C][C]-0.163150961942002[/C][/ROW]
[ROW][C]61[/C][C]44.45[/C][C]44.2918513579828[/C][C]0.158148642017167[/C][/ROW]
[ROW][C]62[/C][C]44.46[/C][C]44.4497384400673[/C][C]0.0102615599327294[/C][/ROW]
[ROW][C]63[/C][C]44.39[/C][C]44.4667387515758[/C][C]-0.0767387515758315[/C][/ROW]
[ROW][C]64[/C][C]44.5[/C][C]44.3443885076236[/C][C]0.155611492376437[/C][/ROW]
[ROW][C]65[/C][C]44.44[/C][C]44.5605447770494[/C][C]-0.120544777049354[/C][/ROW]
[ROW][C]66[/C][C]44.41[/C][C]44.4183105947605[/C][C]-0.0083105947605091[/C][/ROW]
[ROW][C]67[/C][C]44.4[/C][C]44.3826412079883[/C][C]0.01735879201172[/C][/ROW]
[ROW][C]68[/C][C]44.42[/C][C]44.38448316499[/C][C]0.0355168350099575[/C][/ROW]
[ROW][C]69[/C][C]44.49[/C][C]44.4287123183057[/C][C]0.0612876816942887[/C][/ROW]
[ROW][C]70[/C][C]44.46[/C][C]44.5405220301147[/C][C]-0.0805220301146718[/C][/ROW]
[ROW][C]71[/C][C]44.49[/C][C]44.4555908795099[/C][C]0.0344091204901105[/C][/ROW]
[ROW][C]72[/C][C]44.5[/C][C]44.5090643634388[/C][C]-0.00906436343881012[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204879&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204879&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
345.9345.030.899999999999999
445.9345.6439690650360.286030934964046
545.945.8390958936040.0609041063960021
645.9145.85064393500490.0593560649951073
745.8545.9011359213707-0.0511359213707294
845.5845.806251617111-0.226251617111025
945.5645.3819055128660.178094487134011
1045.545.48339940814790.0166005918520895
1145.545.43472413021290.0652758697871221
1245.545.47925453548240.0207454645175602
1345.5145.49340683931980.0165931606802445
1445.4945.5147264919296-0.0247264919295702
1545.445.4778583795611-0.0778583795611141
1645.3845.33474433900070.0452556609992811
1745.3845.345617201080.034382798920042
1845.3845.36907272875360.0109272712464232
1945.4945.3765271804320.113472819568024
2045.4145.5639369592511-0.153936959251062
2144.9945.3789230359779-0.388923035977882
2244.9844.69360446623310.286395533766871
2344.9344.87898001967460.0510199803254139
2444.9344.86378523036190.0662147696381368
2544.9144.90895614170220.0010438582978054
2644.8644.8896682491501-0.029668249150113
2744.7644.8194289300479-0.0594289300479502
2844.8944.67888723602840.211112763971641
2944.8944.9529057985982-0.062905798598166
304544.90999222709740.0900077729025597
3145.0145.0813944361807-0.0713944361807251
3245.1145.04269001925780.0673099807422233
3345.0545.1886080703065-0.138608070306546
3444.6745.0340513288259-0.36405132882593
3544.4844.405699935510.0743000644900107
3644.4844.26638653676230.213613463237742
3744.4844.4121110459880.0678889540119982
3844.5844.45842406556690.121575934433096
3944.7944.64136169089440.148638309105586
4044.7944.9527609394167-0.162760939416728
4144.4144.8417274040855-0.431727404085549
4244.4144.16720821448910.242791785510903
4344.4444.33283782065410.107162179345863
4444.4344.4359425573877-0.00594255738768368
4544.3644.4218886169396-0.0618886169396475
4644.3944.30966895440760.0803310455923594
4744.3944.3944698176918-0.00446981769175636
4844.4144.39142056237050.0185794376294481
4944.3244.4240952289819-0.104095228981926
5044.4344.26308272852330.166917271476663
5144.8244.48695166308650.333048336913464
5244.9745.1041531920049-0.134153192004916
5344.9145.1626355143751-0.252635514375086
5444.7944.9302906359798-0.140290635979802
5544.7644.714586068640.0454139313599953
5644.844.71556690083630.0844330991636539
5744.6544.813166135227-0.163166135227009
5844.4944.5518561802372-0.0618561802371644
5944.5644.34965864562950.210341354370506
6044.444.563150961942-0.163150961942002
6144.4544.29185135798280.158148642017167
6244.4644.44973844006730.0102615599327294
6344.3944.4667387515758-0.0767387515758315
6444.544.34438850762360.155611492376437
6544.4444.5605447770494-0.120544777049354
6644.4144.4183105947605-0.0083105947605091
6744.444.38264120798830.01735879201172
6844.4244.384483164990.0355168350099575
6944.4944.42871231830570.0612876816942887
7044.4644.5405220301147-0.0805220301146718
7144.4944.45559087950990.0344091204901105
7244.544.5090643634388-0.00906436343881012







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7344.512880764832544.154680233627744.8710812960373
7444.52576152966543.824771604703545.2267514546265
7544.538642294497543.439250903154945.6380336858401
7644.5515230593343.002473364107446.1005727545526
7744.564403824162542.519045390058146.609762258267
7844.57728458899541.99273557673647.1618336012541
7944.590165353827541.426593631071547.7537370765836
8044.6030461186640.823126524667148.382965712653
8144.615926883492540.184433281873549.0474204851116
8244.62880764832539.512301034846449.7453142618037
8344.641688413157538.808273550564350.4751032757508
8444.654569177990138.073700974661551.2354373813186

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 44.5128807648325 & 44.1546802336277 & 44.8710812960373 \tabularnewline
74 & 44.525761529665 & 43.8247716047035 & 45.2267514546265 \tabularnewline
75 & 44.5386422944975 & 43.4392509031549 & 45.6380336858401 \tabularnewline
76 & 44.55152305933 & 43.0024733641074 & 46.1005727545526 \tabularnewline
77 & 44.5644038241625 & 42.5190453900581 & 46.609762258267 \tabularnewline
78 & 44.577284588995 & 41.992735576736 & 47.1618336012541 \tabularnewline
79 & 44.5901653538275 & 41.4265936310715 & 47.7537370765836 \tabularnewline
80 & 44.60304611866 & 40.8231265246671 & 48.382965712653 \tabularnewline
81 & 44.6159268834925 & 40.1844332818735 & 49.0474204851116 \tabularnewline
82 & 44.628807648325 & 39.5123010348464 & 49.7453142618037 \tabularnewline
83 & 44.6416884131575 & 38.8082735505643 & 50.4751032757508 \tabularnewline
84 & 44.6545691779901 & 38.0737009746615 & 51.2354373813186 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204879&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]44.5128807648325[/C][C]44.1546802336277[/C][C]44.8710812960373[/C][/ROW]
[ROW][C]74[/C][C]44.525761529665[/C][C]43.8247716047035[/C][C]45.2267514546265[/C][/ROW]
[ROW][C]75[/C][C]44.5386422944975[/C][C]43.4392509031549[/C][C]45.6380336858401[/C][/ROW]
[ROW][C]76[/C][C]44.55152305933[/C][C]43.0024733641074[/C][C]46.1005727545526[/C][/ROW]
[ROW][C]77[/C][C]44.5644038241625[/C][C]42.5190453900581[/C][C]46.609762258267[/C][/ROW]
[ROW][C]78[/C][C]44.577284588995[/C][C]41.992735576736[/C][C]47.1618336012541[/C][/ROW]
[ROW][C]79[/C][C]44.5901653538275[/C][C]41.4265936310715[/C][C]47.7537370765836[/C][/ROW]
[ROW][C]80[/C][C]44.60304611866[/C][C]40.8231265246671[/C][C]48.382965712653[/C][/ROW]
[ROW][C]81[/C][C]44.6159268834925[/C][C]40.1844332818735[/C][C]49.0474204851116[/C][/ROW]
[ROW][C]82[/C][C]44.628807648325[/C][C]39.5123010348464[/C][C]49.7453142618037[/C][/ROW]
[ROW][C]83[/C][C]44.6416884131575[/C][C]38.8082735505643[/C][C]50.4751032757508[/C][/ROW]
[ROW][C]84[/C][C]44.6545691779901[/C][C]38.0737009746615[/C][C]51.2354373813186[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204879&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204879&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
7344.512880764832544.154680233627744.8710812960373
7444.52576152966543.824771604703545.2267514546265
7544.538642294497543.439250903154945.6380336858401
7644.5515230593343.002473364107446.1005727545526
7744.564403824162542.519045390058146.609762258267
7844.57728458899541.99273557673647.1618336012541
7944.590165353827541.426593631071547.7537370765836
8044.6030461186640.823126524667148.382965712653
8144.615926883492540.184433281873549.0474204851116
8244.62880764832539.512301034846449.7453142618037
8344.641688413157538.808273550564350.4751032757508
8444.654569177990138.073700974661551.2354373813186



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')