Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 11 Dec 2009 05:15:32 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/11/t12605338092cs0pfvmhr1avql.htm/, Retrieved Mon, 29 Apr 2024 01:38:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66066, Retrieved Mon, 29 Apr 2024 01:38:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D    [Exponential Smoothing] [workshop 9 - ad h...] [2009-12-04 10:36:21] [f1a50df816abcbb519e7637ff6b72fa0]
-    D        [Exponential Smoothing] [workshop 9 - revi...] [2009-12-11 12:15:32] [a18540c86166a2b66550d1fef0503cc2] [Current]
Feedback Forum

Post a new message
Dataseries X:
5.4
5.4
5.6
5.7
5.8
5.8
5.8
5.9
6.1
6.4
6.4
6.3
6.2
6.2
6.3
6.4
6.5
6.6
6.6
6.6
6.8
7
7.2
7.3
7.5
7.6
7.6
7.7
7.7
7.7
7.7
7.6
7.7
7.9
7.9
7.9
7.8
7.6
7.4
7
7
7.2
7.5
7.8
7.8
7.7
7.6
7.6
7.5
7.5
7.6
7.6
7.9
7.6
7.5
7.5
7.6
7.7
7.8
7.9
7.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66066&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66066&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66066&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66066&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[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66066&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66066&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
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136.25.832225097658950.367774902341054
146.26.198772533445050.00122746655494854
156.36.30285764898377-0.0028576489837695
166.46.40700240339455-0.00700240339454616
176.56.50289753406811-0.00289753406810789
186.66.586242011763240.0137579882367573
196.66.529893577728470.070106422271528
206.66.69937666821261-0.0993766682126065
216.86.81497786457103-0.0149778645710335
2277.13045746695204-0.130457466952037
237.26.997341264414020.202658735585979
247.37.078320228772430.221679771227565
257.57.168353528337360.331646471662637
267.67.485985648199150.114014351800849
277.67.71249733960818-0.11249733960818
287.77.71657530472002-0.0165753047200248
297.77.81140647404256-0.111406474042564
307.77.79085739637863-0.0908573963786266
317.77.60820343688340.0917965631165982
327.67.80587460308918-0.20587460308918
337.77.83818804107117-0.138188041071166
347.98.06569609505028-0.165696095050285
357.97.888821994637140.0111780053628561
367.97.760464430579660.139535569420337
377.87.752573017457510.0474269825424853
387.67.78303482852702-0.183034828527020
397.47.71249733960818-0.312497339608179
4077.51510255066995-0.515102550669953
4177.10682473713324-0.106824737133241
427.27.088165088686320.111834911313681
437.57.118062591812980.381937408187021
447.87.604693160384350.195306839615652
457.88.0428300763712-0.242830076371194
467.78.16961149817231-0.469611498172314
477.67.69071516569867-0.0907151656986738
487.67.468116915519420.131883084480577
497.57.460463272897440.0395367271025613
507.57.485985648199150.0140143518008493
517.67.61180879027787-0.0118087902778656
527.67.71657530472002-0.116575304720025
537.97.710751940198370.189248059801626
547.67.99162662714786-0.391626627147859
557.57.51017526786932-0.0101752678693172
567.57.60469316038435-0.104693160384348
577.67.73586702342115-0.135867023421153
587.77.96178069192826-0.261780691928258
597.87.690715165698670.109284834301326
607.97.663015258892920.236984741107084
617.97.752573017457510.147426982542486

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6.2 & 5.83222509765895 & 0.367774902341054 \tabularnewline
14 & 6.2 & 6.19877253344505 & 0.00122746655494854 \tabularnewline
15 & 6.3 & 6.30285764898377 & -0.0028576489837695 \tabularnewline
16 & 6.4 & 6.40700240339455 & -0.00700240339454616 \tabularnewline
17 & 6.5 & 6.50289753406811 & -0.00289753406810789 \tabularnewline
18 & 6.6 & 6.58624201176324 & 0.0137579882367573 \tabularnewline
19 & 6.6 & 6.52989357772847 & 0.070106422271528 \tabularnewline
20 & 6.6 & 6.69937666821261 & -0.0993766682126065 \tabularnewline
21 & 6.8 & 6.81497786457103 & -0.0149778645710335 \tabularnewline
22 & 7 & 7.13045746695204 & -0.130457466952037 \tabularnewline
23 & 7.2 & 6.99734126441402 & 0.202658735585979 \tabularnewline
24 & 7.3 & 7.07832022877243 & 0.221679771227565 \tabularnewline
25 & 7.5 & 7.16835352833736 & 0.331646471662637 \tabularnewline
26 & 7.6 & 7.48598564819915 & 0.114014351800849 \tabularnewline
27 & 7.6 & 7.71249733960818 & -0.11249733960818 \tabularnewline
28 & 7.7 & 7.71657530472002 & -0.0165753047200248 \tabularnewline
29 & 7.7 & 7.81140647404256 & -0.111406474042564 \tabularnewline
30 & 7.7 & 7.79085739637863 & -0.0908573963786266 \tabularnewline
31 & 7.7 & 7.6082034368834 & 0.0917965631165982 \tabularnewline
32 & 7.6 & 7.80587460308918 & -0.20587460308918 \tabularnewline
33 & 7.7 & 7.83818804107117 & -0.138188041071166 \tabularnewline
34 & 7.9 & 8.06569609505028 & -0.165696095050285 \tabularnewline
35 & 7.9 & 7.88882199463714 & 0.0111780053628561 \tabularnewline
36 & 7.9 & 7.76046443057966 & 0.139535569420337 \tabularnewline
37 & 7.8 & 7.75257301745751 & 0.0474269825424853 \tabularnewline
38 & 7.6 & 7.78303482852702 & -0.183034828527020 \tabularnewline
39 & 7.4 & 7.71249733960818 & -0.312497339608179 \tabularnewline
40 & 7 & 7.51510255066995 & -0.515102550669953 \tabularnewline
41 & 7 & 7.10682473713324 & -0.106824737133241 \tabularnewline
42 & 7.2 & 7.08816508868632 & 0.111834911313681 \tabularnewline
43 & 7.5 & 7.11806259181298 & 0.381937408187021 \tabularnewline
44 & 7.8 & 7.60469316038435 & 0.195306839615652 \tabularnewline
45 & 7.8 & 8.0428300763712 & -0.242830076371194 \tabularnewline
46 & 7.7 & 8.16961149817231 & -0.469611498172314 \tabularnewline
47 & 7.6 & 7.69071516569867 & -0.0907151656986738 \tabularnewline
48 & 7.6 & 7.46811691551942 & 0.131883084480577 \tabularnewline
49 & 7.5 & 7.46046327289744 & 0.0395367271025613 \tabularnewline
50 & 7.5 & 7.48598564819915 & 0.0140143518008493 \tabularnewline
51 & 7.6 & 7.61180879027787 & -0.0118087902778656 \tabularnewline
52 & 7.6 & 7.71657530472002 & -0.116575304720025 \tabularnewline
53 & 7.9 & 7.71075194019837 & 0.189248059801626 \tabularnewline
54 & 7.6 & 7.99162662714786 & -0.391626627147859 \tabularnewline
55 & 7.5 & 7.51017526786932 & -0.0101752678693172 \tabularnewline
56 & 7.5 & 7.60469316038435 & -0.104693160384348 \tabularnewline
57 & 7.6 & 7.73586702342115 & -0.135867023421153 \tabularnewline
58 & 7.7 & 7.96178069192826 & -0.261780691928258 \tabularnewline
59 & 7.8 & 7.69071516569867 & 0.109284834301326 \tabularnewline
60 & 7.9 & 7.66301525889292 & 0.236984741107084 \tabularnewline
61 & 7.9 & 7.75257301745751 & 0.147426982542486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66066&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]6.2[/C][C]5.83222509765895[/C][C]0.367774902341054[/C][/ROW]
[ROW][C]14[/C][C]6.2[/C][C]6.19877253344505[/C][C]0.00122746655494854[/C][/ROW]
[ROW][C]15[/C][C]6.3[/C][C]6.30285764898377[/C][C]-0.0028576489837695[/C][/ROW]
[ROW][C]16[/C][C]6.4[/C][C]6.40700240339455[/C][C]-0.00700240339454616[/C][/ROW]
[ROW][C]17[/C][C]6.5[/C][C]6.50289753406811[/C][C]-0.00289753406810789[/C][/ROW]
[ROW][C]18[/C][C]6.6[/C][C]6.58624201176324[/C][C]0.0137579882367573[/C][/ROW]
[ROW][C]19[/C][C]6.6[/C][C]6.52989357772847[/C][C]0.070106422271528[/C][/ROW]
[ROW][C]20[/C][C]6.6[/C][C]6.69937666821261[/C][C]-0.0993766682126065[/C][/ROW]
[ROW][C]21[/C][C]6.8[/C][C]6.81497786457103[/C][C]-0.0149778645710335[/C][/ROW]
[ROW][C]22[/C][C]7[/C][C]7.13045746695204[/C][C]-0.130457466952037[/C][/ROW]
[ROW][C]23[/C][C]7.2[/C][C]6.99734126441402[/C][C]0.202658735585979[/C][/ROW]
[ROW][C]24[/C][C]7.3[/C][C]7.07832022877243[/C][C]0.221679771227565[/C][/ROW]
[ROW][C]25[/C][C]7.5[/C][C]7.16835352833736[/C][C]0.331646471662637[/C][/ROW]
[ROW][C]26[/C][C]7.6[/C][C]7.48598564819915[/C][C]0.114014351800849[/C][/ROW]
[ROW][C]27[/C][C]7.6[/C][C]7.71249733960818[/C][C]-0.11249733960818[/C][/ROW]
[ROW][C]28[/C][C]7.7[/C][C]7.71657530472002[/C][C]-0.0165753047200248[/C][/ROW]
[ROW][C]29[/C][C]7.7[/C][C]7.81140647404256[/C][C]-0.111406474042564[/C][/ROW]
[ROW][C]30[/C][C]7.7[/C][C]7.79085739637863[/C][C]-0.0908573963786266[/C][/ROW]
[ROW][C]31[/C][C]7.7[/C][C]7.6082034368834[/C][C]0.0917965631165982[/C][/ROW]
[ROW][C]32[/C][C]7.6[/C][C]7.80587460308918[/C][C]-0.20587460308918[/C][/ROW]
[ROW][C]33[/C][C]7.7[/C][C]7.83818804107117[/C][C]-0.138188041071166[/C][/ROW]
[ROW][C]34[/C][C]7.9[/C][C]8.06569609505028[/C][C]-0.165696095050285[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.88882199463714[/C][C]0.0111780053628561[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]7.76046443057966[/C][C]0.139535569420337[/C][/ROW]
[ROW][C]37[/C][C]7.8[/C][C]7.75257301745751[/C][C]0.0474269825424853[/C][/ROW]
[ROW][C]38[/C][C]7.6[/C][C]7.78303482852702[/C][C]-0.183034828527020[/C][/ROW]
[ROW][C]39[/C][C]7.4[/C][C]7.71249733960818[/C][C]-0.312497339608179[/C][/ROW]
[ROW][C]40[/C][C]7[/C][C]7.51510255066995[/C][C]-0.515102550669953[/C][/ROW]
[ROW][C]41[/C][C]7[/C][C]7.10682473713324[/C][C]-0.106824737133241[/C][/ROW]
[ROW][C]42[/C][C]7.2[/C][C]7.08816508868632[/C][C]0.111834911313681[/C][/ROW]
[ROW][C]43[/C][C]7.5[/C][C]7.11806259181298[/C][C]0.381937408187021[/C][/ROW]
[ROW][C]44[/C][C]7.8[/C][C]7.60469316038435[/C][C]0.195306839615652[/C][/ROW]
[ROW][C]45[/C][C]7.8[/C][C]8.0428300763712[/C][C]-0.242830076371194[/C][/ROW]
[ROW][C]46[/C][C]7.7[/C][C]8.16961149817231[/C][C]-0.469611498172314[/C][/ROW]
[ROW][C]47[/C][C]7.6[/C][C]7.69071516569867[/C][C]-0.0907151656986738[/C][/ROW]
[ROW][C]48[/C][C]7.6[/C][C]7.46811691551942[/C][C]0.131883084480577[/C][/ROW]
[ROW][C]49[/C][C]7.5[/C][C]7.46046327289744[/C][C]0.0395367271025613[/C][/ROW]
[ROW][C]50[/C][C]7.5[/C][C]7.48598564819915[/C][C]0.0140143518008493[/C][/ROW]
[ROW][C]51[/C][C]7.6[/C][C]7.61180879027787[/C][C]-0.0118087902778656[/C][/ROW]
[ROW][C]52[/C][C]7.6[/C][C]7.71657530472002[/C][C]-0.116575304720025[/C][/ROW]
[ROW][C]53[/C][C]7.9[/C][C]7.71075194019837[/C][C]0.189248059801626[/C][/ROW]
[ROW][C]54[/C][C]7.6[/C][C]7.99162662714786[/C][C]-0.391626627147859[/C][/ROW]
[ROW][C]55[/C][C]7.5[/C][C]7.51017526786932[/C][C]-0.0101752678693172[/C][/ROW]
[ROW][C]56[/C][C]7.5[/C][C]7.60469316038435[/C][C]-0.104693160384348[/C][/ROW]
[ROW][C]57[/C][C]7.6[/C][C]7.73586702342115[/C][C]-0.135867023421153[/C][/ROW]
[ROW][C]58[/C][C]7.7[/C][C]7.96178069192826[/C][C]-0.261780691928258[/C][/ROW]
[ROW][C]59[/C][C]7.8[/C][C]7.69071516569867[/C][C]0.109284834301326[/C][/ROW]
[ROW][C]60[/C][C]7.9[/C][C]7.66301525889292[/C][C]0.236984741107084[/C][/ROW]
[ROW][C]61[/C][C]7.9[/C][C]7.75257301745751[/C][C]0.147426982542486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66066&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66066&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
136.25.832225097658950.367774902341054
146.26.198772533445050.00122746655494854
156.36.30285764898377-0.0028576489837695
166.46.40700240339455-0.00700240339454616
176.56.50289753406811-0.00289753406810789
186.66.586242011763240.0137579882367573
196.66.529893577728470.070106422271528
206.66.69937666821261-0.0993766682126065
216.86.81497786457103-0.0149778645710335
2277.13045746695204-0.130457466952037
237.26.997341264414020.202658735585979
247.37.078320228772430.221679771227565
257.57.168353528337360.331646471662637
267.67.485985648199150.114014351800849
277.67.71249733960818-0.11249733960818
287.77.71657530472002-0.0165753047200248
297.77.81140647404256-0.111406474042564
307.77.79085739637863-0.0908573963786266
317.77.60820343688340.0917965631165982
327.67.80587460308918-0.20587460308918
337.77.83818804107117-0.138188041071166
347.98.06569609505028-0.165696095050285
357.97.888821994637140.0111780053628561
367.97.760464430579660.139535569420337
377.87.752573017457510.0474269825424853
387.67.78303482852702-0.183034828527020
397.47.71249733960818-0.312497339608179
4077.51510255066995-0.515102550669953
4177.10682473713324-0.106824737133241
427.27.088165088686320.111834911313681
437.57.118062591812980.381937408187021
447.87.604693160384350.195306839615652
457.88.0428300763712-0.242830076371194
467.78.16961149817231-0.469611498172314
477.67.69071516569867-0.0907151656986738
487.67.468116915519420.131883084480577
497.57.460463272897440.0395367271025613
507.57.485985648199150.0140143518008493
517.67.61180879027787-0.0118087902778656
527.67.71657530472002-0.116575304720025
537.97.710751940198370.189248059801626
547.67.99162662714786-0.391626627147859
557.57.51017526786932-0.0101752678693172
567.57.60469316038435-0.104693160384348
577.67.73586702342115-0.135867023421153
587.77.96178069192826-0.261780691928258
597.87.690715165698670.109284834301326
607.97.663015258892920.236984741107084
617.97.752573017457510.147426982542486







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
627.882051221969647.500422791050298.263679652889
637.996490623377847.45492526865218.53805597810358
648.115985593954857.450201333400868.78176985450883
658.23011483449687.458927037493799.0013026314998
668.323011134085037.459903651651879.18611861651818
678.218929844380837.290756399259759.14710328950192
688.327869876864837.319229968353649.33650978537602
698.582951906247167.482602534875569.68330127761876
708.983219127800657.777782233116610.1886560224847
718.961787526907567.7082567887773910.2153182650377
728.795167580624287.5153872627932910.0749478984553
738.624196928506252.3622032079412114.8861906490713

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 7.88205122196964 & 7.50042279105029 & 8.263679652889 \tabularnewline
63 & 7.99649062337784 & 7.4549252686521 & 8.53805597810358 \tabularnewline
64 & 8.11598559395485 & 7.45020133340086 & 8.78176985450883 \tabularnewline
65 & 8.2301148344968 & 7.45892703749379 & 9.0013026314998 \tabularnewline
66 & 8.32301113408503 & 7.45990365165187 & 9.18611861651818 \tabularnewline
67 & 8.21892984438083 & 7.29075639925975 & 9.14710328950192 \tabularnewline
68 & 8.32786987686483 & 7.31922996835364 & 9.33650978537602 \tabularnewline
69 & 8.58295190624716 & 7.48260253487556 & 9.68330127761876 \tabularnewline
70 & 8.98321912780065 & 7.7777822331166 & 10.1886560224847 \tabularnewline
71 & 8.96178752690756 & 7.70825678877739 & 10.2153182650377 \tabularnewline
72 & 8.79516758062428 & 7.51538726279329 & 10.0749478984553 \tabularnewline
73 & 8.62419692850625 & 2.36220320794121 & 14.8861906490713 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66066&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]62[/C][C]7.88205122196964[/C][C]7.50042279105029[/C][C]8.263679652889[/C][/ROW]
[ROW][C]63[/C][C]7.99649062337784[/C][C]7.4549252686521[/C][C]8.53805597810358[/C][/ROW]
[ROW][C]64[/C][C]8.11598559395485[/C][C]7.45020133340086[/C][C]8.78176985450883[/C][/ROW]
[ROW][C]65[/C][C]8.2301148344968[/C][C]7.45892703749379[/C][C]9.0013026314998[/C][/ROW]
[ROW][C]66[/C][C]8.32301113408503[/C][C]7.45990365165187[/C][C]9.18611861651818[/C][/ROW]
[ROW][C]67[/C][C]8.21892984438083[/C][C]7.29075639925975[/C][C]9.14710328950192[/C][/ROW]
[ROW][C]68[/C][C]8.32786987686483[/C][C]7.31922996835364[/C][C]9.33650978537602[/C][/ROW]
[ROW][C]69[/C][C]8.58295190624716[/C][C]7.48260253487556[/C][C]9.68330127761876[/C][/ROW]
[ROW][C]70[/C][C]8.98321912780065[/C][C]7.7777822331166[/C][C]10.1886560224847[/C][/ROW]
[ROW][C]71[/C][C]8.96178752690756[/C][C]7.70825678877739[/C][C]10.2153182650377[/C][/ROW]
[ROW][C]72[/C][C]8.79516758062428[/C][C]7.51538726279329[/C][C]10.0749478984553[/C][/ROW]
[ROW][C]73[/C][C]8.62419692850625[/C][C]2.36220320794121[/C][C]14.8861906490713[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66066&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66066&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
627.882051221969647.500422791050298.263679652889
637.996490623377847.45492526865218.53805597810358
648.115985593954857.450201333400868.78176985450883
658.23011483449687.458927037493799.0013026314998
668.323011134085037.459903651651879.18611861651818
678.218929844380837.290756399259759.14710328950192
688.327869876864837.319229968353649.33650978537602
698.582951906247167.482602534875569.68330127761876
708.983219127800657.777782233116610.1886560224847
718.961787526907567.7082567887773910.2153182650377
728.795167580624287.5153872627932910.0749478984553
738.624196928506252.3622032079412114.8861906490713



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')