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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 May 2008 14:07:08 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/27/t12119189363uou3qhbzmya0i4.htm/, Retrieved Sun, 19 May 2024 22:25:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13396, Retrieved Sun, 19 May 2024 22:25:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Voorspelling Prij...] [2008-05-27 20:07:08] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
47,87
47,87
47,89
47,88
47,91
47,92
47,92
47,91
47,93
48,05
48,03
48,04
48,04
48,06
48,04
48,09
48,12
48,16
48,16
48,16
48,08
48,13
48,16
48,15
48,15
48,15
48,27
48,47
48,51
48,53
48,53
48,53
48,68
48,64
48,67
48,66
48,66
48,67
48,71
48,96
49,01
49,04
49,04
49,04
49,06
49,13
49,19
49,26
49,26
49,26
49,29
49,43
49,43
49,45
49,45
49,46
49,57
49,68
49,71
49,7
49,7
49,8
49,84
50,09
50,2
50,16
50,16
50,29
50,36
51,02
51,03
51,04




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13396&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13396&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13396&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.686758989105527
beta0.135239935983842
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.686758989105527 \tabularnewline
beta & 0.135239935983842 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13396&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]0.686758989105527[/C][/ROW]
[ROW][C]beta[/C][C]0.135239935983842[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13396&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13396&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
alpha0.686758989105527
beta0.135239935983842
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1348.0447.91668707712080.123312922879236
1448.0648.03271970806090.0272802919391211
1548.0448.0490772950521-0.00907729505211563
1648.0948.1167163506858-0.0267163506857599
1748.1248.1506047560502-0.0306047560502307
1848.1648.1877432868974-0.0277432868973762
1948.1648.1850937169537-0.0250937169537195
2048.1648.1827649173209-0.0227649173209485
2148.0848.0948899595994-0.0148899595994081
2248.1348.12898497311690.0010150268830742
2348.1648.14743336564560.0125666343543784
2448.1548.13541103981480.0145889601852076
2548.1548.2820007051115-0.132000705111466
2648.1548.1708476595438-0.0208476595438043
2748.2748.11655713875270.153442861247321
2848.4748.27938816333680.190611836663173
2948.5148.47060421789690.0393957821030995
3048.5348.5726268733716-0.0426268733716171
3148.5348.5748065685705-0.0448065685704577
3248.5348.5720630313411-0.0420630313411294
3348.6848.48332172842190.196678271578065
3448.6448.6983388676371-0.0583388676370689
3548.6748.7044607912358-0.0344607912358228
3648.6648.6807465854872-0.0207465854872382
3748.6648.7749629822466-0.114962982246652
3848.6748.7291053898704-0.0591053898703606
3948.7148.7182815292995-0.00828152929945958
4048.9648.78209944640750.177900553592465
4149.0148.91591124907480.0940887509252235
4249.0449.03386911005970.00613088994034428
4349.0449.0772949799023-0.0372949799022777
4449.0449.089731790502-0.0497317905020296
4549.0649.0786790947428-0.0186790947427511
4649.1349.05401864869220.0759813513077674
4749.1949.16093469637940.0290653036205981
4849.2649.19163335380960.0683666461904338
4949.2649.3331170381074-0.0731170381074406
5049.2649.3528147517729-0.0928147517728704
5149.2949.3509763751709-0.0609763751709096
5249.4349.4491397677637-0.0191397677636616
5349.4349.41356722349010.0164327765099159
5449.4549.4359939306660.0140060693340018
5549.4549.4573072614544-0.00730726145442873
5649.4649.4754044338477-0.0154044338476922
5749.5749.48983823746460.0801617625354396
5849.6849.56390917857940.116090821420649
5949.7149.68876451018250.0212354898174922
6049.749.7305345292593-0.0305345292593273
6149.749.7549483236664-0.0549483236664159
6249.849.77797995296320.0220200470368468
6349.8449.8728975063549-0.0328975063549137
6450.0950.01501847330960.0749815266903937
6550.250.07360816539940.126391834600604
6650.1650.1995860519914-0.0395860519914208
6750.1650.2011296136076-0.0411296136076373
6850.2950.21426330612150.0757366938784685
6950.3650.35103664760310.00896335239689705
7051.0250.41010678284710.609893217152887
7151.0350.91221439250530.117785607494660
7251.0451.0805565342605-0.040556534260503

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 48.04 & 47.9166870771208 & 0.123312922879236 \tabularnewline
14 & 48.06 & 48.0327197080609 & 0.0272802919391211 \tabularnewline
15 & 48.04 & 48.0490772950521 & -0.00907729505211563 \tabularnewline
16 & 48.09 & 48.1167163506858 & -0.0267163506857599 \tabularnewline
17 & 48.12 & 48.1506047560502 & -0.0306047560502307 \tabularnewline
18 & 48.16 & 48.1877432868974 & -0.0277432868973762 \tabularnewline
19 & 48.16 & 48.1850937169537 & -0.0250937169537195 \tabularnewline
20 & 48.16 & 48.1827649173209 & -0.0227649173209485 \tabularnewline
21 & 48.08 & 48.0948899595994 & -0.0148899595994081 \tabularnewline
22 & 48.13 & 48.1289849731169 & 0.0010150268830742 \tabularnewline
23 & 48.16 & 48.1474333656456 & 0.0125666343543784 \tabularnewline
24 & 48.15 & 48.1354110398148 & 0.0145889601852076 \tabularnewline
25 & 48.15 & 48.2820007051115 & -0.132000705111466 \tabularnewline
26 & 48.15 & 48.1708476595438 & -0.0208476595438043 \tabularnewline
27 & 48.27 & 48.1165571387527 & 0.153442861247321 \tabularnewline
28 & 48.47 & 48.2793881633368 & 0.190611836663173 \tabularnewline
29 & 48.51 & 48.4706042178969 & 0.0393957821030995 \tabularnewline
30 & 48.53 & 48.5726268733716 & -0.0426268733716171 \tabularnewline
31 & 48.53 & 48.5748065685705 & -0.0448065685704577 \tabularnewline
32 & 48.53 & 48.5720630313411 & -0.0420630313411294 \tabularnewline
33 & 48.68 & 48.4833217284219 & 0.196678271578065 \tabularnewline
34 & 48.64 & 48.6983388676371 & -0.0583388676370689 \tabularnewline
35 & 48.67 & 48.7044607912358 & -0.0344607912358228 \tabularnewline
36 & 48.66 & 48.6807465854872 & -0.0207465854872382 \tabularnewline
37 & 48.66 & 48.7749629822466 & -0.114962982246652 \tabularnewline
38 & 48.67 & 48.7291053898704 & -0.0591053898703606 \tabularnewline
39 & 48.71 & 48.7182815292995 & -0.00828152929945958 \tabularnewline
40 & 48.96 & 48.7820994464075 & 0.177900553592465 \tabularnewline
41 & 49.01 & 48.9159112490748 & 0.0940887509252235 \tabularnewline
42 & 49.04 & 49.0338691100597 & 0.00613088994034428 \tabularnewline
43 & 49.04 & 49.0772949799023 & -0.0372949799022777 \tabularnewline
44 & 49.04 & 49.089731790502 & -0.0497317905020296 \tabularnewline
45 & 49.06 & 49.0786790947428 & -0.0186790947427511 \tabularnewline
46 & 49.13 & 49.0540186486922 & 0.0759813513077674 \tabularnewline
47 & 49.19 & 49.1609346963794 & 0.0290653036205981 \tabularnewline
48 & 49.26 & 49.1916333538096 & 0.0683666461904338 \tabularnewline
49 & 49.26 & 49.3331170381074 & -0.0731170381074406 \tabularnewline
50 & 49.26 & 49.3528147517729 & -0.0928147517728704 \tabularnewline
51 & 49.29 & 49.3509763751709 & -0.0609763751709096 \tabularnewline
52 & 49.43 & 49.4491397677637 & -0.0191397677636616 \tabularnewline
53 & 49.43 & 49.4135672234901 & 0.0164327765099159 \tabularnewline
54 & 49.45 & 49.435993930666 & 0.0140060693340018 \tabularnewline
55 & 49.45 & 49.4573072614544 & -0.00730726145442873 \tabularnewline
56 & 49.46 & 49.4754044338477 & -0.0154044338476922 \tabularnewline
57 & 49.57 & 49.4898382374646 & 0.0801617625354396 \tabularnewline
58 & 49.68 & 49.5639091785794 & 0.116090821420649 \tabularnewline
59 & 49.71 & 49.6887645101825 & 0.0212354898174922 \tabularnewline
60 & 49.7 & 49.7305345292593 & -0.0305345292593273 \tabularnewline
61 & 49.7 & 49.7549483236664 & -0.0549483236664159 \tabularnewline
62 & 49.8 & 49.7779799529632 & 0.0220200470368468 \tabularnewline
63 & 49.84 & 49.8728975063549 & -0.0328975063549137 \tabularnewline
64 & 50.09 & 50.0150184733096 & 0.0749815266903937 \tabularnewline
65 & 50.2 & 50.0736081653994 & 0.126391834600604 \tabularnewline
66 & 50.16 & 50.1995860519914 & -0.0395860519914208 \tabularnewline
67 & 50.16 & 50.2011296136076 & -0.0411296136076373 \tabularnewline
68 & 50.29 & 50.2142633061215 & 0.0757366938784685 \tabularnewline
69 & 50.36 & 50.3510366476031 & 0.00896335239689705 \tabularnewline
70 & 51.02 & 50.4101067828471 & 0.609893217152887 \tabularnewline
71 & 51.03 & 50.9122143925053 & 0.117785607494660 \tabularnewline
72 & 51.04 & 51.0805565342605 & -0.040556534260503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13396&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]48.04[/C][C]47.9166870771208[/C][C]0.123312922879236[/C][/ROW]
[ROW][C]14[/C][C]48.06[/C][C]48.0327197080609[/C][C]0.0272802919391211[/C][/ROW]
[ROW][C]15[/C][C]48.04[/C][C]48.0490772950521[/C][C]-0.00907729505211563[/C][/ROW]
[ROW][C]16[/C][C]48.09[/C][C]48.1167163506858[/C][C]-0.0267163506857599[/C][/ROW]
[ROW][C]17[/C][C]48.12[/C][C]48.1506047560502[/C][C]-0.0306047560502307[/C][/ROW]
[ROW][C]18[/C][C]48.16[/C][C]48.1877432868974[/C][C]-0.0277432868973762[/C][/ROW]
[ROW][C]19[/C][C]48.16[/C][C]48.1850937169537[/C][C]-0.0250937169537195[/C][/ROW]
[ROW][C]20[/C][C]48.16[/C][C]48.1827649173209[/C][C]-0.0227649173209485[/C][/ROW]
[ROW][C]21[/C][C]48.08[/C][C]48.0948899595994[/C][C]-0.0148899595994081[/C][/ROW]
[ROW][C]22[/C][C]48.13[/C][C]48.1289849731169[/C][C]0.0010150268830742[/C][/ROW]
[ROW][C]23[/C][C]48.16[/C][C]48.1474333656456[/C][C]0.0125666343543784[/C][/ROW]
[ROW][C]24[/C][C]48.15[/C][C]48.1354110398148[/C][C]0.0145889601852076[/C][/ROW]
[ROW][C]25[/C][C]48.15[/C][C]48.2820007051115[/C][C]-0.132000705111466[/C][/ROW]
[ROW][C]26[/C][C]48.15[/C][C]48.1708476595438[/C][C]-0.0208476595438043[/C][/ROW]
[ROW][C]27[/C][C]48.27[/C][C]48.1165571387527[/C][C]0.153442861247321[/C][/ROW]
[ROW][C]28[/C][C]48.47[/C][C]48.2793881633368[/C][C]0.190611836663173[/C][/ROW]
[ROW][C]29[/C][C]48.51[/C][C]48.4706042178969[/C][C]0.0393957821030995[/C][/ROW]
[ROW][C]30[/C][C]48.53[/C][C]48.5726268733716[/C][C]-0.0426268733716171[/C][/ROW]
[ROW][C]31[/C][C]48.53[/C][C]48.5748065685705[/C][C]-0.0448065685704577[/C][/ROW]
[ROW][C]32[/C][C]48.53[/C][C]48.5720630313411[/C][C]-0.0420630313411294[/C][/ROW]
[ROW][C]33[/C][C]48.68[/C][C]48.4833217284219[/C][C]0.196678271578065[/C][/ROW]
[ROW][C]34[/C][C]48.64[/C][C]48.6983388676371[/C][C]-0.0583388676370689[/C][/ROW]
[ROW][C]35[/C][C]48.67[/C][C]48.7044607912358[/C][C]-0.0344607912358228[/C][/ROW]
[ROW][C]36[/C][C]48.66[/C][C]48.6807465854872[/C][C]-0.0207465854872382[/C][/ROW]
[ROW][C]37[/C][C]48.66[/C][C]48.7749629822466[/C][C]-0.114962982246652[/C][/ROW]
[ROW][C]38[/C][C]48.67[/C][C]48.7291053898704[/C][C]-0.0591053898703606[/C][/ROW]
[ROW][C]39[/C][C]48.71[/C][C]48.7182815292995[/C][C]-0.00828152929945958[/C][/ROW]
[ROW][C]40[/C][C]48.96[/C][C]48.7820994464075[/C][C]0.177900553592465[/C][/ROW]
[ROW][C]41[/C][C]49.01[/C][C]48.9159112490748[/C][C]0.0940887509252235[/C][/ROW]
[ROW][C]42[/C][C]49.04[/C][C]49.0338691100597[/C][C]0.00613088994034428[/C][/ROW]
[ROW][C]43[/C][C]49.04[/C][C]49.0772949799023[/C][C]-0.0372949799022777[/C][/ROW]
[ROW][C]44[/C][C]49.04[/C][C]49.089731790502[/C][C]-0.0497317905020296[/C][/ROW]
[ROW][C]45[/C][C]49.06[/C][C]49.0786790947428[/C][C]-0.0186790947427511[/C][/ROW]
[ROW][C]46[/C][C]49.13[/C][C]49.0540186486922[/C][C]0.0759813513077674[/C][/ROW]
[ROW][C]47[/C][C]49.19[/C][C]49.1609346963794[/C][C]0.0290653036205981[/C][/ROW]
[ROW][C]48[/C][C]49.26[/C][C]49.1916333538096[/C][C]0.0683666461904338[/C][/ROW]
[ROW][C]49[/C][C]49.26[/C][C]49.3331170381074[/C][C]-0.0731170381074406[/C][/ROW]
[ROW][C]50[/C][C]49.26[/C][C]49.3528147517729[/C][C]-0.0928147517728704[/C][/ROW]
[ROW][C]51[/C][C]49.29[/C][C]49.3509763751709[/C][C]-0.0609763751709096[/C][/ROW]
[ROW][C]52[/C][C]49.43[/C][C]49.4491397677637[/C][C]-0.0191397677636616[/C][/ROW]
[ROW][C]53[/C][C]49.43[/C][C]49.4135672234901[/C][C]0.0164327765099159[/C][/ROW]
[ROW][C]54[/C][C]49.45[/C][C]49.435993930666[/C][C]0.0140060693340018[/C][/ROW]
[ROW][C]55[/C][C]49.45[/C][C]49.4573072614544[/C][C]-0.00730726145442873[/C][/ROW]
[ROW][C]56[/C][C]49.46[/C][C]49.4754044338477[/C][C]-0.0154044338476922[/C][/ROW]
[ROW][C]57[/C][C]49.57[/C][C]49.4898382374646[/C][C]0.0801617625354396[/C][/ROW]
[ROW][C]58[/C][C]49.68[/C][C]49.5639091785794[/C][C]0.116090821420649[/C][/ROW]
[ROW][C]59[/C][C]49.71[/C][C]49.6887645101825[/C][C]0.0212354898174922[/C][/ROW]
[ROW][C]60[/C][C]49.7[/C][C]49.7305345292593[/C][C]-0.0305345292593273[/C][/ROW]
[ROW][C]61[/C][C]49.7[/C][C]49.7549483236664[/C][C]-0.0549483236664159[/C][/ROW]
[ROW][C]62[/C][C]49.8[/C][C]49.7779799529632[/C][C]0.0220200470368468[/C][/ROW]
[ROW][C]63[/C][C]49.84[/C][C]49.8728975063549[/C][C]-0.0328975063549137[/C][/ROW]
[ROW][C]64[/C][C]50.09[/C][C]50.0150184733096[/C][C]0.0749815266903937[/C][/ROW]
[ROW][C]65[/C][C]50.2[/C][C]50.0736081653994[/C][C]0.126391834600604[/C][/ROW]
[ROW][C]66[/C][C]50.16[/C][C]50.1995860519914[/C][C]-0.0395860519914208[/C][/ROW]
[ROW][C]67[/C][C]50.16[/C][C]50.2011296136076[/C][C]-0.0411296136076373[/C][/ROW]
[ROW][C]68[/C][C]50.29[/C][C]50.2142633061215[/C][C]0.0757366938784685[/C][/ROW]
[ROW][C]69[/C][C]50.36[/C][C]50.3510366476031[/C][C]0.00896335239689705[/C][/ROW]
[ROW][C]70[/C][C]51.02[/C][C]50.4101067828471[/C][C]0.609893217152887[/C][/ROW]
[ROW][C]71[/C][C]51.03[/C][C]50.9122143925053[/C][C]0.117785607494660[/C][/ROW]
[ROW][C]72[/C][C]51.04[/C][C]51.0805565342605[/C][C]-0.040556534260503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13396&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13396&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
1348.0447.91668707712080.123312922879236
1448.0648.03271970806090.0272802919391211
1548.0448.0490772950521-0.00907729505211563
1648.0948.1167163506858-0.0267163506857599
1748.1248.1506047560502-0.0306047560502307
1848.1648.1877432868974-0.0277432868973762
1948.1648.1850937169537-0.0250937169537195
2048.1648.1827649173209-0.0227649173209485
2148.0848.0948899595994-0.0148899595994081
2248.1348.12898497311690.0010150268830742
2348.1648.14743336564560.0125666343543784
2448.1548.13541103981480.0145889601852076
2548.1548.2820007051115-0.132000705111466
2648.1548.1708476595438-0.0208476595438043
2748.2748.11655713875270.153442861247321
2848.4748.27938816333680.190611836663173
2948.5148.47060421789690.0393957821030995
3048.5348.5726268733716-0.0426268733716171
3148.5348.5748065685705-0.0448065685704577
3248.5348.5720630313411-0.0420630313411294
3348.6848.48332172842190.196678271578065
3448.6448.6983388676371-0.0583388676370689
3548.6748.7044607912358-0.0344607912358228
3648.6648.6807465854872-0.0207465854872382
3748.6648.7749629822466-0.114962982246652
3848.6748.7291053898704-0.0591053898703606
3948.7148.7182815292995-0.00828152929945958
4048.9648.78209944640750.177900553592465
4149.0148.91591124907480.0940887509252235
4249.0449.03386911005970.00613088994034428
4349.0449.0772949799023-0.0372949799022777
4449.0449.089731790502-0.0497317905020296
4549.0649.0786790947428-0.0186790947427511
4649.1349.05401864869220.0759813513077674
4749.1949.16093469637940.0290653036205981
4849.2649.19163335380960.0683666461904338
4949.2649.3331170381074-0.0731170381074406
5049.2649.3528147517729-0.0928147517728704
5149.2949.3509763751709-0.0609763751709096
5249.4349.4491397677637-0.0191397677636616
5349.4349.41356722349010.0164327765099159
5449.4549.4359939306660.0140060693340018
5549.4549.4573072614544-0.00730726145442873
5649.4649.4754044338477-0.0154044338476922
5749.5749.48983823746460.0801617625354396
5849.6849.56390917857940.116090821420649
5949.7149.68876451018250.0212354898174922
6049.749.7305345292593-0.0305345292593273
6149.749.7549483236664-0.0549483236664159
6249.849.77797995296320.0220200470368468
6349.8449.8728975063549-0.0328975063549137
6450.0950.01501847330960.0749815266903937
6550.250.07360816539940.126391834600604
6650.1650.1995860519914-0.0395860519914208
6750.1650.2011296136076-0.0411296136076373
6850.2950.21426330612150.0757366938784685
6950.3650.35103664760310.00896335239689705
7051.0250.41010678284710.609893217152887
7151.0350.91221439250530.117785607494660
7251.0451.0805565342605-0.040556534260503







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7351.166710237895750.959006067781451.37441440801
7451.334549598332751.071099641639851.5979995550257
7551.477383285980451.157545252844451.7972213191163
7651.764014724457951.385674883523552.1423545653922
7751.862281389700451.424729125813452.2998336535875
7851.911184090823651.413042628140252.409325553507
7952.006208236867351.445306194583752.5671102791509
8052.15671983489551.530614172658252.7828254971317
8152.285299414531151.592294341775552.9783044872868
8252.595682367903951.831431149785453.3599335860224
8352.526026479562951.693896947685353.3581560114404
8452.557398294517150.698799697586854.4159968914474

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 51.1667102378957 & 50.9590060677814 & 51.37441440801 \tabularnewline
74 & 51.3345495983327 & 51.0710996416398 & 51.5979995550257 \tabularnewline
75 & 51.4773832859804 & 51.1575452528444 & 51.7972213191163 \tabularnewline
76 & 51.7640147244579 & 51.3856748835235 & 52.1423545653922 \tabularnewline
77 & 51.8622813897004 & 51.4247291258134 & 52.2998336535875 \tabularnewline
78 & 51.9111840908236 & 51.4130426281402 & 52.409325553507 \tabularnewline
79 & 52.0062082368673 & 51.4453061945837 & 52.5671102791509 \tabularnewline
80 & 52.156719834895 & 51.5306141726582 & 52.7828254971317 \tabularnewline
81 & 52.2852994145311 & 51.5922943417755 & 52.9783044872868 \tabularnewline
82 & 52.5956823679039 & 51.8314311497854 & 53.3599335860224 \tabularnewline
83 & 52.5260264795629 & 51.6938969476853 & 53.3581560114404 \tabularnewline
84 & 52.5573982945171 & 50.6987996975868 & 54.4159968914474 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13396&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]51.1667102378957[/C][C]50.9590060677814[/C][C]51.37441440801[/C][/ROW]
[ROW][C]74[/C][C]51.3345495983327[/C][C]51.0710996416398[/C][C]51.5979995550257[/C][/ROW]
[ROW][C]75[/C][C]51.4773832859804[/C][C]51.1575452528444[/C][C]51.7972213191163[/C][/ROW]
[ROW][C]76[/C][C]51.7640147244579[/C][C]51.3856748835235[/C][C]52.1423545653922[/C][/ROW]
[ROW][C]77[/C][C]51.8622813897004[/C][C]51.4247291258134[/C][C]52.2998336535875[/C][/ROW]
[ROW][C]78[/C][C]51.9111840908236[/C][C]51.4130426281402[/C][C]52.409325553507[/C][/ROW]
[ROW][C]79[/C][C]52.0062082368673[/C][C]51.4453061945837[/C][C]52.5671102791509[/C][/ROW]
[ROW][C]80[/C][C]52.156719834895[/C][C]51.5306141726582[/C][C]52.7828254971317[/C][/ROW]
[ROW][C]81[/C][C]52.2852994145311[/C][C]51.5922943417755[/C][C]52.9783044872868[/C][/ROW]
[ROW][C]82[/C][C]52.5956823679039[/C][C]51.8314311497854[/C][C]53.3599335860224[/C][/ROW]
[ROW][C]83[/C][C]52.5260264795629[/C][C]51.6938969476853[/C][C]53.3581560114404[/C][/ROW]
[ROW][C]84[/C][C]52.5573982945171[/C][C]50.6987996975868[/C][C]54.4159968914474[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13396&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13396&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
7351.166710237895750.959006067781451.37441440801
7451.334549598332751.071099641639851.5979995550257
7551.477383285980451.157545252844451.7972213191163
7651.764014724457951.385674883523552.1423545653922
7751.862281389700451.424729125813452.2998336535875
7851.911184090823651.413042628140252.409325553507
7952.006208236867351.445306194583752.5671102791509
8052.15671983489551.530614172658252.7828254971317
8152.285299414531151.592294341775552.9783044872868
8252.595682367903951.831431149785453.3599335860224
8352.526026479562951.693896947685353.3581560114404
8452.557398294517150.698799697586854.4159968914474



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')