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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 11 May 2014 13:29:45 -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/11/t139982939897vpodfan34wtbf.htm/, Retrieved Tue, 14 May 2024 18:19:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234797, Retrieved Tue, 14 May 2024 18:19:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [] [2014-05-11 16:46:15] [4512ef39545e98c37276c02512a09398]
- RMPD    [Exponential Smoothing] [] [2014-05-11 17:29:45] [5f7d0cda5d8a9348873c82369b6851b6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
28,33
28,67
28,81
28,99
29,16
29,25
29,25
29,38
29,48
29,65
29,69
29,73
29,81
30,05
30,29
30,37
30,50
30,67
30,72
30,73
30,76
30,82
30,84
30,86
30,92
30,95
30,97
30,99
31,09
31,18
31,19
31,20
31,31
31,34
31,35
31,36
31,37
31,37
31,39
31,39
31,42
31,47
31,48
31,51
31,54
31,55
31,55
31,57
31,66
31,68
31,70
31,70
31,73
31,74
31,75
31,78
31,80
31,82
31,82
31,90

Tables (Output of Computation)





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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234797&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234797&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234797&T=0

As an alternative you can also use a QR Code:  
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' @ jenkins.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.796172702875063
beta0.220125842283903
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.796172702875063 \tabularnewline
beta & 0.220125842283903 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234797&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]0.796172702875063[/C][/ROW]
[ROW][C]beta[/C][C]0.220125842283903[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234797&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234797&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.796172702875063
beta0.220125842283903
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1329.8129.11011485042730.699885149572655
1430.0530.02527442610830.0247255738917289
1530.2930.4151404034624-0.125140403462446
1630.3730.5112553003483-0.141255300348298
1730.530.6252004750724-0.125200475072358
1830.6730.7716523218466-0.101652321846558
1930.7230.65112049714230.0688795028576621
2030.7330.8821831530192-0.152183153019248
2130.7630.8805704131986-0.120570413198614
2230.8230.9529959218845-0.132995921884469
2330.8430.8680532889442-0.0280532889442142
2430.8630.8600798804973-7.9880497349194e-05
2530.9231.0516031682197-0.131603168219733
2630.9530.997991688715-0.0479916887150438
2730.9731.1175242915028-0.147524291502812
2830.9931.006719034283-0.0167190342829961
2931.0931.05910093880440.0308990611955728
3031.1831.1980043959977-0.0180043959976537
3131.1931.05685945551230.13314054448772
3231.231.18331831669280.0166816833071977
3331.3131.24148155611810.0685184438819313
3431.3431.4139480303939-0.0739480303939395
3531.3531.35978275346-0.00978275346004409
3631.3631.33763451520280.0223654847971702
3731.3731.4897308121926-0.119730812192589
3831.3731.4342054663015-0.0642054663014839
3931.3931.4892914292509-0.0992914292509397
4031.3931.4207525350386-0.0307525350385696
4131.4231.4464107238032-0.0264107238031848
4231.4731.4944173328418-0.0244173328417681
4331.4831.34254962987430.137450370125652
4431.5131.41303327199330.0969667280066524
4531.5431.52408454093230.0159154590677346
4631.5531.5948138161619-0.0448138161618736
4731.5531.5512114677819-0.00121146778194259
4831.5731.51823075720410.05176924279586
4931.6631.64571828432280.0142817156771606
5031.6831.7126382935813-0.0326382935812752
5131.731.795668763658-0.0956687636580398
5231.731.7545821991564-0.0545821991564459
5331.7331.7685744604534-0.038574460453372
5431.7431.8115927684405-0.0715927684404889
5531.7531.65118027302770.098819726972259
5631.7831.67190718898470.10809281101535
5731.831.76649782632520.0335021736747585
5831.8231.8331346412426-0.0131346412426225
5931.8231.8234775323688-0.00347753236881587
6031.931.79893020805730.101069791942663

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 29.81 & 29.1101148504273 & 0.699885149572655 \tabularnewline
14 & 30.05 & 30.0252744261083 & 0.0247255738917289 \tabularnewline
15 & 30.29 & 30.4151404034624 & -0.125140403462446 \tabularnewline
16 & 30.37 & 30.5112553003483 & -0.141255300348298 \tabularnewline
17 & 30.5 & 30.6252004750724 & -0.125200475072358 \tabularnewline
18 & 30.67 & 30.7716523218466 & -0.101652321846558 \tabularnewline
19 & 30.72 & 30.6511204971423 & 0.0688795028576621 \tabularnewline
20 & 30.73 & 30.8821831530192 & -0.152183153019248 \tabularnewline
21 & 30.76 & 30.8805704131986 & -0.120570413198614 \tabularnewline
22 & 30.82 & 30.9529959218845 & -0.132995921884469 \tabularnewline
23 & 30.84 & 30.8680532889442 & -0.0280532889442142 \tabularnewline
24 & 30.86 & 30.8600798804973 & -7.9880497349194e-05 \tabularnewline
25 & 30.92 & 31.0516031682197 & -0.131603168219733 \tabularnewline
26 & 30.95 & 30.997991688715 & -0.0479916887150438 \tabularnewline
27 & 30.97 & 31.1175242915028 & -0.147524291502812 \tabularnewline
28 & 30.99 & 31.006719034283 & -0.0167190342829961 \tabularnewline
29 & 31.09 & 31.0591009388044 & 0.0308990611955728 \tabularnewline
30 & 31.18 & 31.1980043959977 & -0.0180043959976537 \tabularnewline
31 & 31.19 & 31.0568594555123 & 0.13314054448772 \tabularnewline
32 & 31.2 & 31.1833183166928 & 0.0166816833071977 \tabularnewline
33 & 31.31 & 31.2414815561181 & 0.0685184438819313 \tabularnewline
34 & 31.34 & 31.4139480303939 & -0.0739480303939395 \tabularnewline
35 & 31.35 & 31.35978275346 & -0.00978275346004409 \tabularnewline
36 & 31.36 & 31.3376345152028 & 0.0223654847971702 \tabularnewline
37 & 31.37 & 31.4897308121926 & -0.119730812192589 \tabularnewline
38 & 31.37 & 31.4342054663015 & -0.0642054663014839 \tabularnewline
39 & 31.39 & 31.4892914292509 & -0.0992914292509397 \tabularnewline
40 & 31.39 & 31.4207525350386 & -0.0307525350385696 \tabularnewline
41 & 31.42 & 31.4464107238032 & -0.0264107238031848 \tabularnewline
42 & 31.47 & 31.4944173328418 & -0.0244173328417681 \tabularnewline
43 & 31.48 & 31.3425496298743 & 0.137450370125652 \tabularnewline
44 & 31.51 & 31.4130332719933 & 0.0969667280066524 \tabularnewline
45 & 31.54 & 31.5240845409323 & 0.0159154590677346 \tabularnewline
46 & 31.55 & 31.5948138161619 & -0.0448138161618736 \tabularnewline
47 & 31.55 & 31.5512114677819 & -0.00121146778194259 \tabularnewline
48 & 31.57 & 31.5182307572041 & 0.05176924279586 \tabularnewline
49 & 31.66 & 31.6457182843228 & 0.0142817156771606 \tabularnewline
50 & 31.68 & 31.7126382935813 & -0.0326382935812752 \tabularnewline
51 & 31.7 & 31.795668763658 & -0.0956687636580398 \tabularnewline
52 & 31.7 & 31.7545821991564 & -0.0545821991564459 \tabularnewline
53 & 31.73 & 31.7685744604534 & -0.038574460453372 \tabularnewline
54 & 31.74 & 31.8115927684405 & -0.0715927684404889 \tabularnewline
55 & 31.75 & 31.6511802730277 & 0.098819726972259 \tabularnewline
56 & 31.78 & 31.6719071889847 & 0.10809281101535 \tabularnewline
57 & 31.8 & 31.7664978263252 & 0.0335021736747585 \tabularnewline
58 & 31.82 & 31.8331346412426 & -0.0131346412426225 \tabularnewline
59 & 31.82 & 31.8234775323688 & -0.00347753236881587 \tabularnewline
60 & 31.9 & 31.7989302080573 & 0.101069791942663 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234797&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]29.81[/C][C]29.1101148504273[/C][C]0.699885149572655[/C][/ROW]
[ROW][C]14[/C][C]30.05[/C][C]30.0252744261083[/C][C]0.0247255738917289[/C][/ROW]
[ROW][C]15[/C][C]30.29[/C][C]30.4151404034624[/C][C]-0.125140403462446[/C][/ROW]
[ROW][C]16[/C][C]30.37[/C][C]30.5112553003483[/C][C]-0.141255300348298[/C][/ROW]
[ROW][C]17[/C][C]30.5[/C][C]30.6252004750724[/C][C]-0.125200475072358[/C][/ROW]
[ROW][C]18[/C][C]30.67[/C][C]30.7716523218466[/C][C]-0.101652321846558[/C][/ROW]
[ROW][C]19[/C][C]30.72[/C][C]30.6511204971423[/C][C]0.0688795028576621[/C][/ROW]
[ROW][C]20[/C][C]30.73[/C][C]30.8821831530192[/C][C]-0.152183153019248[/C][/ROW]
[ROW][C]21[/C][C]30.76[/C][C]30.8805704131986[/C][C]-0.120570413198614[/C][/ROW]
[ROW][C]22[/C][C]30.82[/C][C]30.9529959218845[/C][C]-0.132995921884469[/C][/ROW]
[ROW][C]23[/C][C]30.84[/C][C]30.8680532889442[/C][C]-0.0280532889442142[/C][/ROW]
[ROW][C]24[/C][C]30.86[/C][C]30.8600798804973[/C][C]-7.9880497349194e-05[/C][/ROW]
[ROW][C]25[/C][C]30.92[/C][C]31.0516031682197[/C][C]-0.131603168219733[/C][/ROW]
[ROW][C]26[/C][C]30.95[/C][C]30.997991688715[/C][C]-0.0479916887150438[/C][/ROW]
[ROW][C]27[/C][C]30.97[/C][C]31.1175242915028[/C][C]-0.147524291502812[/C][/ROW]
[ROW][C]28[/C][C]30.99[/C][C]31.006719034283[/C][C]-0.0167190342829961[/C][/ROW]
[ROW][C]29[/C][C]31.09[/C][C]31.0591009388044[/C][C]0.0308990611955728[/C][/ROW]
[ROW][C]30[/C][C]31.18[/C][C]31.1980043959977[/C][C]-0.0180043959976537[/C][/ROW]
[ROW][C]31[/C][C]31.19[/C][C]31.0568594555123[/C][C]0.13314054448772[/C][/ROW]
[ROW][C]32[/C][C]31.2[/C][C]31.1833183166928[/C][C]0.0166816833071977[/C][/ROW]
[ROW][C]33[/C][C]31.31[/C][C]31.2414815561181[/C][C]0.0685184438819313[/C][/ROW]
[ROW][C]34[/C][C]31.34[/C][C]31.4139480303939[/C][C]-0.0739480303939395[/C][/ROW]
[ROW][C]35[/C][C]31.35[/C][C]31.35978275346[/C][C]-0.00978275346004409[/C][/ROW]
[ROW][C]36[/C][C]31.36[/C][C]31.3376345152028[/C][C]0.0223654847971702[/C][/ROW]
[ROW][C]37[/C][C]31.37[/C][C]31.4897308121926[/C][C]-0.119730812192589[/C][/ROW]
[ROW][C]38[/C][C]31.37[/C][C]31.4342054663015[/C][C]-0.0642054663014839[/C][/ROW]
[ROW][C]39[/C][C]31.39[/C][C]31.4892914292509[/C][C]-0.0992914292509397[/C][/ROW]
[ROW][C]40[/C][C]31.39[/C][C]31.4207525350386[/C][C]-0.0307525350385696[/C][/ROW]
[ROW][C]41[/C][C]31.42[/C][C]31.4464107238032[/C][C]-0.0264107238031848[/C][/ROW]
[ROW][C]42[/C][C]31.47[/C][C]31.4944173328418[/C][C]-0.0244173328417681[/C][/ROW]
[ROW][C]43[/C][C]31.48[/C][C]31.3425496298743[/C][C]0.137450370125652[/C][/ROW]
[ROW][C]44[/C][C]31.51[/C][C]31.4130332719933[/C][C]0.0969667280066524[/C][/ROW]
[ROW][C]45[/C][C]31.54[/C][C]31.5240845409323[/C][C]0.0159154590677346[/C][/ROW]
[ROW][C]46[/C][C]31.55[/C][C]31.5948138161619[/C][C]-0.0448138161618736[/C][/ROW]
[ROW][C]47[/C][C]31.55[/C][C]31.5512114677819[/C][C]-0.00121146778194259[/C][/ROW]
[ROW][C]48[/C][C]31.57[/C][C]31.5182307572041[/C][C]0.05176924279586[/C][/ROW]
[ROW][C]49[/C][C]31.66[/C][C]31.6457182843228[/C][C]0.0142817156771606[/C][/ROW]
[ROW][C]50[/C][C]31.68[/C][C]31.7126382935813[/C][C]-0.0326382935812752[/C][/ROW]
[ROW][C]51[/C][C]31.7[/C][C]31.795668763658[/C][C]-0.0956687636580398[/C][/ROW]
[ROW][C]52[/C][C]31.7[/C][C]31.7545821991564[/C][C]-0.0545821991564459[/C][/ROW]
[ROW][C]53[/C][C]31.73[/C][C]31.7685744604534[/C][C]-0.038574460453372[/C][/ROW]
[ROW][C]54[/C][C]31.74[/C][C]31.8115927684405[/C][C]-0.0715927684404889[/C][/ROW]
[ROW][C]55[/C][C]31.75[/C][C]31.6511802730277[/C][C]0.098819726972259[/C][/ROW]
[ROW][C]56[/C][C]31.78[/C][C]31.6719071889847[/C][C]0.10809281101535[/C][/ROW]
[ROW][C]57[/C][C]31.8[/C][C]31.7664978263252[/C][C]0.0335021736747585[/C][/ROW]
[ROW][C]58[/C][C]31.82[/C][C]31.8331346412426[/C][C]-0.0131346412426225[/C][/ROW]
[ROW][C]59[/C][C]31.82[/C][C]31.8234775323688[/C][C]-0.00347753236881587[/C][/ROW]
[ROW][C]60[/C][C]31.9[/C][C]31.7989302080573[/C][C]0.101069791942663[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234797&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234797&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1329.8129.11011485042730.699885149572655
1430.0530.02527442610830.0247255738917289
1530.2930.4151404034624-0.125140403462446
1630.3730.5112553003483-0.141255300348298
1730.530.6252004750724-0.125200475072358
1830.6730.7716523218466-0.101652321846558
1930.7230.65112049714230.0688795028576621
2030.7330.8821831530192-0.152183153019248
2130.7630.8805704131986-0.120570413198614
2230.8230.9529959218845-0.132995921884469
2330.8430.8680532889442-0.0280532889442142
2430.8630.8600798804973-7.9880497349194e-05
2530.9231.0516031682197-0.131603168219733
2630.9530.997991688715-0.0479916887150438
2730.9731.1175242915028-0.147524291502812
2830.9931.006719034283-0.0167190342829961
2931.0931.05910093880440.0308990611955728
3031.1831.1980043959977-0.0180043959976537
3131.1931.05685945551230.13314054448772
3231.231.18331831669280.0166816833071977
3331.3131.24148155611810.0685184438819313
3431.3431.4139480303939-0.0739480303939395
3531.3531.35978275346-0.00978275346004409
3631.3631.33763451520280.0223654847971702
3731.3731.4897308121926-0.119730812192589
3831.3731.4342054663015-0.0642054663014839
3931.3931.4892914292509-0.0992914292509397
4031.3931.4207525350386-0.0307525350385696
4131.4231.4464107238032-0.0264107238031848
4231.4731.4944173328418-0.0244173328417681
4331.4831.34254962987430.137450370125652
4431.5131.41303327199330.0969667280066524
4531.5431.52408454093230.0159154590677346
4631.5531.5948138161619-0.0448138161618736
4731.5531.5512114677819-0.00121146778194259
4831.5731.51823075720410.05176924279586
4931.6631.64571828432280.0142817156771606
5031.6831.7126382935813-0.0326382935812752
5131.731.795668763658-0.0956687636580398
5231.731.7545821991564-0.0545821991564459
5331.7331.7685744604534-0.038574460453372
5431.7431.8115927684405-0.0715927684404889
5531.7531.65118027302770.098819726972259
5631.7831.67190718898470.10809281101535
5731.831.76649782632520.0335021736747585
5831.8231.8331346412426-0.0131346412426225
5931.8231.8234775323688-0.00347753236881587
6031.931.79893020805730.101069791942663






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6131.966107480164431.710620070824432.2215948895043
6232.017669185837331.661479237850632.373859133824
6332.125134159388831.663940546591332.5863277721863
6432.196653865883631.62501722291332.7682905088542
6532.294994625045331.607180830990932.9828084190996
6632.406384149718231.596651189700133.2161171097363
6732.394643116101231.457350615186233.3319356170162
6832.378200139926131.307851159720533.4485491201316
6932.392200043024331.183454240571833.6009458454768
7032.43745937489631.085133420929933.789785328862
7132.457331933702330.9563942338533.9582696335547
7232.474576232750830.820139252660534.1290132128411

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 31.9661074801644 & 31.7106200708244 & 32.2215948895043 \tabularnewline
62 & 32.0176691858373 & 31.6614792378506 & 32.373859133824 \tabularnewline
63 & 32.1251341593888 & 31.6639405465913 & 32.5863277721863 \tabularnewline
64 & 32.1966538658836 & 31.625017222913 & 32.7682905088542 \tabularnewline
65 & 32.2949946250453 & 31.6071808309909 & 32.9828084190996 \tabularnewline
66 & 32.4063841497182 & 31.5966511897001 & 33.2161171097363 \tabularnewline
67 & 32.3946431161012 & 31.4573506151862 & 33.3319356170162 \tabularnewline
68 & 32.3782001399261 & 31.3078511597205 & 33.4485491201316 \tabularnewline
69 & 32.3922000430243 & 31.1834542405718 & 33.6009458454768 \tabularnewline
70 & 32.437459374896 & 31.0851334209299 & 33.789785328862 \tabularnewline
71 & 32.4573319337023 & 30.95639423385 & 33.9582696335547 \tabularnewline
72 & 32.4745762327508 & 30.8201392526605 & 34.1290132128411 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234797&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]61[/C][C]31.9661074801644[/C][C]31.7106200708244[/C][C]32.2215948895043[/C][/ROW]
[ROW][C]62[/C][C]32.0176691858373[/C][C]31.6614792378506[/C][C]32.373859133824[/C][/ROW]
[ROW][C]63[/C][C]32.1251341593888[/C][C]31.6639405465913[/C][C]32.5863277721863[/C][/ROW]
[ROW][C]64[/C][C]32.1966538658836[/C][C]31.625017222913[/C][C]32.7682905088542[/C][/ROW]
[ROW][C]65[/C][C]32.2949946250453[/C][C]31.6071808309909[/C][C]32.9828084190996[/C][/ROW]
[ROW][C]66[/C][C]32.4063841497182[/C][C]31.5966511897001[/C][C]33.2161171097363[/C][/ROW]
[ROW][C]67[/C][C]32.3946431161012[/C][C]31.4573506151862[/C][C]33.3319356170162[/C][/ROW]
[ROW][C]68[/C][C]32.3782001399261[/C][C]31.3078511597205[/C][C]33.4485491201316[/C][/ROW]
[ROW][C]69[/C][C]32.3922000430243[/C][C]31.1834542405718[/C][C]33.6009458454768[/C][/ROW]
[ROW][C]70[/C][C]32.437459374896[/C][C]31.0851334209299[/C][C]33.789785328862[/C][/ROW]
[ROW][C]71[/C][C]32.4573319337023[/C][C]30.95639423385[/C][C]33.9582696335547[/C][/ROW]
[ROW][C]72[/C][C]32.4745762327508[/C][C]30.8201392526605[/C][C]34.1290132128411[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234797&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234797&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6131.966107480164431.710620070824432.2215948895043
6232.017669185837331.661479237850632.373859133824
6332.125134159388831.663940546591332.5863277721863
6432.196653865883631.62501722291332.7682905088542
6532.294994625045331.607180830990932.9828084190996
6632.406384149718231.596651189700133.2161171097363
6732.394643116101231.457350615186233.3319356170162
6832.378200139926131.307851159720533.4485491201316
6932.392200043024331.183454240571833.6009458454768
7032.43745937489631.085133420929933.789785328862
7132.457331933702330.9563942338533.9582696335547
7232.474576232750830.820139252660534.1290132128411


Figures (Output of Computation)

Input Parameters & R Code

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')