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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 03:43:22 -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/t1260528739v1ocfbomc3f8yqu.htm/, Retrieved Sun, 28 Apr 2024 22:06:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65977, Retrieved Sun, 28 Apr 2024 22:06:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
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] [SHW WS9] [2009-12-03 18:54:20] [253127ae8da904b75450fbd69fe4eb21]
-    D      [Exponential Smoothing] [SHW WS9] [2009-12-06 10:49:38] [253127ae8da904b75450fbd69fe4eb21]
-    D          [Exponential Smoothing] [ws9 techniek 4 fo...] [2009-12-11 10:43:22] [95523ebdb89b97dbf680ec91e0b4bca2] [Current]
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Dataseries X:
100
96.21064363
96.31280765
107.1793443
114.9066592
92.56060184
114.9995356
107.1236185
117.7765394
107.3650971
106.2970187
114.5072908
98.0031578
103.0649206
100.2879168
104.6066685
111.1544534
104.9874617
109.9284852
111.5352466
132.4974459
100.3436426
123.0983561
114.2379493
104.569518
109.0833101
106.9843039
133.6769759
124.8537197
122.5132349
116.8013374
116.0118882
129.7575926
125.1973623
143.7912139
127.9465032
130.2962757
108.4424631
129.3675118
143.6797622
131.8844618
117.6186496
118.9560695
104.8202842
134.624315
140.401226
143.8005015
153.4317823
153.2924677
127.3149438
153.5525216
136.9276493
131.7730101
144.3391845
107.4208229
113.6249652
124.2221603
102.0618557
96.36853348
111.6838488




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65977&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]5 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=65977&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65977&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.55295284543749
beta0
gamma0.87258335845831

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.55295284543749 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.87258335845831 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65977&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]0.55295284543749[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.87258335845831[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65977&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65977&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
alpha0.55295284543749
beta0
gamma0.87258335845831







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1398.003157896.68499419024121.31816360975880
14103.0649206102.7299197711010.335000828898856
15100.287916899.65315970242750.634757097572475
16104.6066685104.2615942937720.345074206227878
17111.1544534110.8496947862150.304758613785467
18104.9874617104.4570565660900.530405133909838
19109.9284852118.600549445868-8.67206424586843
20111.5352466106.0803993698385.45484723016195
21132.4974459119.73580731001512.7616385899850
22100.3436426115.790977365521-15.4473347655211
23123.0983561106.71300495756116.3853511424389
24114.2379493124.582167311732-10.3442180117317
25104.569518102.2223650401112.34715295988909
26109.0833101108.7193981244160.363911975583534
27106.9843039105.5810633435981.40324055640188
28133.6769759110.73773117647122.9392447235295
29124.8537197130.903104883016-6.04938518301611
30122.5132349120.0896558046702.42357909532954
31116.8013374133.091280991619-16.2899435916185
32116.0118882121.495298450408-5.4834102504085
33129.7575926132.515410863898-2.75781826389837
34125.1973623108.63983758828716.5575247117133
35143.7912139130.99322038029912.7979935197014
36127.9465032135.985594812993-8.03909161299299
37130.2962757118.10034798487412.1959277151264
38108.4424631130.083515431763-21.6410523317633
39129.3675118114.91409661806414.4534151819358
40143.6797622136.5019625696537.17779963034687
41131.8844618136.327549068236-4.44308726823581
42117.6186496129.389904257857-11.7712546578571
43118.9560695126.796296925452-7.8402274254519
44104.8202842124.085632563013-19.2653483630133
45134.624315128.1678663385306.45644866147046
46140.401226116.20122593777024.2000000622302
47143.8005015141.5376516882092.26284981179072
48153.4317823132.49059271904820.9411895809517
49153.2924677137.52686890665315.7655987933468
50127.3149438136.266407416698-8.95146361669761
51153.5525216143.8490875981089.70343400189162
52136.9276493161.564637853673-24.6369885536727
53131.7730101138.940612081119-7.16760198111947
54144.3391845127.22625325705417.1129312429455
55107.4208229142.819436773032-35.3986138730316
56113.6249652119.585715351972-5.96075015197157
57124.2221603143.378525102862-19.1563648028615
58102.0618557123.304085676272-21.2422299762719
5996.36853348114.336595284823-17.9680618048235
60111.6838488101.813601221279.87024757872994

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 98.0031578 & 96.6849941902412 & 1.31816360975880 \tabularnewline
14 & 103.0649206 & 102.729919771101 & 0.335000828898856 \tabularnewline
15 & 100.2879168 & 99.6531597024275 & 0.634757097572475 \tabularnewline
16 & 104.6066685 & 104.261594293772 & 0.345074206227878 \tabularnewline
17 & 111.1544534 & 110.849694786215 & 0.304758613785467 \tabularnewline
18 & 104.9874617 & 104.457056566090 & 0.530405133909838 \tabularnewline
19 & 109.9284852 & 118.600549445868 & -8.67206424586843 \tabularnewline
20 & 111.5352466 & 106.080399369838 & 5.45484723016195 \tabularnewline
21 & 132.4974459 & 119.735807310015 & 12.7616385899850 \tabularnewline
22 & 100.3436426 & 115.790977365521 & -15.4473347655211 \tabularnewline
23 & 123.0983561 & 106.713004957561 & 16.3853511424389 \tabularnewline
24 & 114.2379493 & 124.582167311732 & -10.3442180117317 \tabularnewline
25 & 104.569518 & 102.222365040111 & 2.34715295988909 \tabularnewline
26 & 109.0833101 & 108.719398124416 & 0.363911975583534 \tabularnewline
27 & 106.9843039 & 105.581063343598 & 1.40324055640188 \tabularnewline
28 & 133.6769759 & 110.737731176471 & 22.9392447235295 \tabularnewline
29 & 124.8537197 & 130.903104883016 & -6.04938518301611 \tabularnewline
30 & 122.5132349 & 120.089655804670 & 2.42357909532954 \tabularnewline
31 & 116.8013374 & 133.091280991619 & -16.2899435916185 \tabularnewline
32 & 116.0118882 & 121.495298450408 & -5.4834102504085 \tabularnewline
33 & 129.7575926 & 132.515410863898 & -2.75781826389837 \tabularnewline
34 & 125.1973623 & 108.639837588287 & 16.5575247117133 \tabularnewline
35 & 143.7912139 & 130.993220380299 & 12.7979935197014 \tabularnewline
36 & 127.9465032 & 135.985594812993 & -8.03909161299299 \tabularnewline
37 & 130.2962757 & 118.100347984874 & 12.1959277151264 \tabularnewline
38 & 108.4424631 & 130.083515431763 & -21.6410523317633 \tabularnewline
39 & 129.3675118 & 114.914096618064 & 14.4534151819358 \tabularnewline
40 & 143.6797622 & 136.501962569653 & 7.17779963034687 \tabularnewline
41 & 131.8844618 & 136.327549068236 & -4.44308726823581 \tabularnewline
42 & 117.6186496 & 129.389904257857 & -11.7712546578571 \tabularnewline
43 & 118.9560695 & 126.796296925452 & -7.8402274254519 \tabularnewline
44 & 104.8202842 & 124.085632563013 & -19.2653483630133 \tabularnewline
45 & 134.624315 & 128.167866338530 & 6.45644866147046 \tabularnewline
46 & 140.401226 & 116.201225937770 & 24.2000000622302 \tabularnewline
47 & 143.8005015 & 141.537651688209 & 2.26284981179072 \tabularnewline
48 & 153.4317823 & 132.490592719048 & 20.9411895809517 \tabularnewline
49 & 153.2924677 & 137.526868906653 & 15.7655987933468 \tabularnewline
50 & 127.3149438 & 136.266407416698 & -8.95146361669761 \tabularnewline
51 & 153.5525216 & 143.849087598108 & 9.70343400189162 \tabularnewline
52 & 136.9276493 & 161.564637853673 & -24.6369885536727 \tabularnewline
53 & 131.7730101 & 138.940612081119 & -7.16760198111947 \tabularnewline
54 & 144.3391845 & 127.226253257054 & 17.1129312429455 \tabularnewline
55 & 107.4208229 & 142.819436773032 & -35.3986138730316 \tabularnewline
56 & 113.6249652 & 119.585715351972 & -5.96075015197157 \tabularnewline
57 & 124.2221603 & 143.378525102862 & -19.1563648028615 \tabularnewline
58 & 102.0618557 & 123.304085676272 & -21.2422299762719 \tabularnewline
59 & 96.36853348 & 114.336595284823 & -17.9680618048235 \tabularnewline
60 & 111.6838488 & 101.81360122127 & 9.87024757872994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65977&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]98.0031578[/C][C]96.6849941902412[/C][C]1.31816360975880[/C][/ROW]
[ROW][C]14[/C][C]103.0649206[/C][C]102.729919771101[/C][C]0.335000828898856[/C][/ROW]
[ROW][C]15[/C][C]100.2879168[/C][C]99.6531597024275[/C][C]0.634757097572475[/C][/ROW]
[ROW][C]16[/C][C]104.6066685[/C][C]104.261594293772[/C][C]0.345074206227878[/C][/ROW]
[ROW][C]17[/C][C]111.1544534[/C][C]110.849694786215[/C][C]0.304758613785467[/C][/ROW]
[ROW][C]18[/C][C]104.9874617[/C][C]104.457056566090[/C][C]0.530405133909838[/C][/ROW]
[ROW][C]19[/C][C]109.9284852[/C][C]118.600549445868[/C][C]-8.67206424586843[/C][/ROW]
[ROW][C]20[/C][C]111.5352466[/C][C]106.080399369838[/C][C]5.45484723016195[/C][/ROW]
[ROW][C]21[/C][C]132.4974459[/C][C]119.735807310015[/C][C]12.7616385899850[/C][/ROW]
[ROW][C]22[/C][C]100.3436426[/C][C]115.790977365521[/C][C]-15.4473347655211[/C][/ROW]
[ROW][C]23[/C][C]123.0983561[/C][C]106.713004957561[/C][C]16.3853511424389[/C][/ROW]
[ROW][C]24[/C][C]114.2379493[/C][C]124.582167311732[/C][C]-10.3442180117317[/C][/ROW]
[ROW][C]25[/C][C]104.569518[/C][C]102.222365040111[/C][C]2.34715295988909[/C][/ROW]
[ROW][C]26[/C][C]109.0833101[/C][C]108.719398124416[/C][C]0.363911975583534[/C][/ROW]
[ROW][C]27[/C][C]106.9843039[/C][C]105.581063343598[/C][C]1.40324055640188[/C][/ROW]
[ROW][C]28[/C][C]133.6769759[/C][C]110.737731176471[/C][C]22.9392447235295[/C][/ROW]
[ROW][C]29[/C][C]124.8537197[/C][C]130.903104883016[/C][C]-6.04938518301611[/C][/ROW]
[ROW][C]30[/C][C]122.5132349[/C][C]120.089655804670[/C][C]2.42357909532954[/C][/ROW]
[ROW][C]31[/C][C]116.8013374[/C][C]133.091280991619[/C][C]-16.2899435916185[/C][/ROW]
[ROW][C]32[/C][C]116.0118882[/C][C]121.495298450408[/C][C]-5.4834102504085[/C][/ROW]
[ROW][C]33[/C][C]129.7575926[/C][C]132.515410863898[/C][C]-2.75781826389837[/C][/ROW]
[ROW][C]34[/C][C]125.1973623[/C][C]108.639837588287[/C][C]16.5575247117133[/C][/ROW]
[ROW][C]35[/C][C]143.7912139[/C][C]130.993220380299[/C][C]12.7979935197014[/C][/ROW]
[ROW][C]36[/C][C]127.9465032[/C][C]135.985594812993[/C][C]-8.03909161299299[/C][/ROW]
[ROW][C]37[/C][C]130.2962757[/C][C]118.100347984874[/C][C]12.1959277151264[/C][/ROW]
[ROW][C]38[/C][C]108.4424631[/C][C]130.083515431763[/C][C]-21.6410523317633[/C][/ROW]
[ROW][C]39[/C][C]129.3675118[/C][C]114.914096618064[/C][C]14.4534151819358[/C][/ROW]
[ROW][C]40[/C][C]143.6797622[/C][C]136.501962569653[/C][C]7.17779963034687[/C][/ROW]
[ROW][C]41[/C][C]131.8844618[/C][C]136.327549068236[/C][C]-4.44308726823581[/C][/ROW]
[ROW][C]42[/C][C]117.6186496[/C][C]129.389904257857[/C][C]-11.7712546578571[/C][/ROW]
[ROW][C]43[/C][C]118.9560695[/C][C]126.796296925452[/C][C]-7.8402274254519[/C][/ROW]
[ROW][C]44[/C][C]104.8202842[/C][C]124.085632563013[/C][C]-19.2653483630133[/C][/ROW]
[ROW][C]45[/C][C]134.624315[/C][C]128.167866338530[/C][C]6.45644866147046[/C][/ROW]
[ROW][C]46[/C][C]140.401226[/C][C]116.201225937770[/C][C]24.2000000622302[/C][/ROW]
[ROW][C]47[/C][C]143.8005015[/C][C]141.537651688209[/C][C]2.26284981179072[/C][/ROW]
[ROW][C]48[/C][C]153.4317823[/C][C]132.490592719048[/C][C]20.9411895809517[/C][/ROW]
[ROW][C]49[/C][C]153.2924677[/C][C]137.526868906653[/C][C]15.7655987933468[/C][/ROW]
[ROW][C]50[/C][C]127.3149438[/C][C]136.266407416698[/C][C]-8.95146361669761[/C][/ROW]
[ROW][C]51[/C][C]153.5525216[/C][C]143.849087598108[/C][C]9.70343400189162[/C][/ROW]
[ROW][C]52[/C][C]136.9276493[/C][C]161.564637853673[/C][C]-24.6369885536727[/C][/ROW]
[ROW][C]53[/C][C]131.7730101[/C][C]138.940612081119[/C][C]-7.16760198111947[/C][/ROW]
[ROW][C]54[/C][C]144.3391845[/C][C]127.226253257054[/C][C]17.1129312429455[/C][/ROW]
[ROW][C]55[/C][C]107.4208229[/C][C]142.819436773032[/C][C]-35.3986138730316[/C][/ROW]
[ROW][C]56[/C][C]113.6249652[/C][C]119.585715351972[/C][C]-5.96075015197157[/C][/ROW]
[ROW][C]57[/C][C]124.2221603[/C][C]143.378525102862[/C][C]-19.1563648028615[/C][/ROW]
[ROW][C]58[/C][C]102.0618557[/C][C]123.304085676272[/C][C]-21.2422299762719[/C][/ROW]
[ROW][C]59[/C][C]96.36853348[/C][C]114.336595284823[/C][C]-17.9680618048235[/C][/ROW]
[ROW][C]60[/C][C]111.6838488[/C][C]101.81360122127[/C][C]9.87024757872994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65977&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65977&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
1398.003157896.68499419024121.31816360975880
14103.0649206102.7299197711010.335000828898856
15100.287916899.65315970242750.634757097572475
16104.6066685104.2615942937720.345074206227878
17111.1544534110.8496947862150.304758613785467
18104.9874617104.4570565660900.530405133909838
19109.9284852118.600549445868-8.67206424586843
20111.5352466106.0803993698385.45484723016195
21132.4974459119.73580731001512.7616385899850
22100.3436426115.790977365521-15.4473347655211
23123.0983561106.71300495756116.3853511424389
24114.2379493124.582167311732-10.3442180117317
25104.569518102.2223650401112.34715295988909
26109.0833101108.7193981244160.363911975583534
27106.9843039105.5810633435981.40324055640188
28133.6769759110.73773117647122.9392447235295
29124.8537197130.903104883016-6.04938518301611
30122.5132349120.0896558046702.42357909532954
31116.8013374133.091280991619-16.2899435916185
32116.0118882121.495298450408-5.4834102504085
33129.7575926132.515410863898-2.75781826389837
34125.1973623108.63983758828716.5575247117133
35143.7912139130.99322038029912.7979935197014
36127.9465032135.985594812993-8.03909161299299
37130.2962757118.10034798487412.1959277151264
38108.4424631130.083515431763-21.6410523317633
39129.3675118114.91409661806414.4534151819358
40143.6797622136.5019625696537.17779963034687
41131.8844618136.327549068236-4.44308726823581
42117.6186496129.389904257857-11.7712546578571
43118.9560695126.796296925452-7.8402274254519
44104.8202842124.085632563013-19.2653483630133
45134.624315128.1678663385306.45644866147046
46140.401226116.20122593777024.2000000622302
47143.8005015141.5376516882092.26284981179072
48153.4317823132.49059271904820.9411895809517
49153.2924677137.52686890665315.7655987933468
50127.3149438136.266407416698-8.95146361669761
51153.5525216143.8490875981089.70343400189162
52136.9276493161.564637853673-24.6369885536727
53131.7730101138.940612081119-7.16760198111947
54144.3391845127.22625325705417.1129312429455
55107.4208229142.819436773032-35.3986138730316
56113.6249652119.585715351972-5.96075015197157
57124.2221603143.378525102862-19.1563648028615
58102.0618557123.304085676272-21.2422299762719
5996.36853348114.336595284823-17.9680618048235
60111.6838488101.813601221279.87024757872994







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61101.05959689179675.9540972253128126.165096558279
6288.040396032235859.8646351150197116.216156949452
63101.67452271769567.9879186353936135.361126799996
64100.4807046237563.9988507218644136.962558525636
6598.90436308709259.9893066988752137.819419475309
6699.912134593518558.1063903635552141.717878823482
6788.451074715966347.5804235382225129.32172589371
6894.76850236589449.3206767130205140.216328018767
69112.56795233753658.2646839814761166.871220693595
70102.56299897074450.3714650725433154.754532868944
71105.93026647003550.4139746882573161.446558251813
72114.688153885615-2.35476202226654231.731069793497

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 101.059596891796 & 75.9540972253128 & 126.165096558279 \tabularnewline
62 & 88.0403960322358 & 59.8646351150197 & 116.216156949452 \tabularnewline
63 & 101.674522717695 & 67.9879186353936 & 135.361126799996 \tabularnewline
64 & 100.48070462375 & 63.9988507218644 & 136.962558525636 \tabularnewline
65 & 98.904363087092 & 59.9893066988752 & 137.819419475309 \tabularnewline
66 & 99.9121345935185 & 58.1063903635552 & 141.717878823482 \tabularnewline
67 & 88.4510747159663 & 47.5804235382225 & 129.32172589371 \tabularnewline
68 & 94.768502365894 & 49.3206767130205 & 140.216328018767 \tabularnewline
69 & 112.567952337536 & 58.2646839814761 & 166.871220693595 \tabularnewline
70 & 102.562998970744 & 50.3714650725433 & 154.754532868944 \tabularnewline
71 & 105.930266470035 & 50.4139746882573 & 161.446558251813 \tabularnewline
72 & 114.688153885615 & -2.35476202226654 & 231.731069793497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65977&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]101.059596891796[/C][C]75.9540972253128[/C][C]126.165096558279[/C][/ROW]
[ROW][C]62[/C][C]88.0403960322358[/C][C]59.8646351150197[/C][C]116.216156949452[/C][/ROW]
[ROW][C]63[/C][C]101.674522717695[/C][C]67.9879186353936[/C][C]135.361126799996[/C][/ROW]
[ROW][C]64[/C][C]100.48070462375[/C][C]63.9988507218644[/C][C]136.962558525636[/C][/ROW]
[ROW][C]65[/C][C]98.904363087092[/C][C]59.9893066988752[/C][C]137.819419475309[/C][/ROW]
[ROW][C]66[/C][C]99.9121345935185[/C][C]58.1063903635552[/C][C]141.717878823482[/C][/ROW]
[ROW][C]67[/C][C]88.4510747159663[/C][C]47.5804235382225[/C][C]129.32172589371[/C][/ROW]
[ROW][C]68[/C][C]94.768502365894[/C][C]49.3206767130205[/C][C]140.216328018767[/C][/ROW]
[ROW][C]69[/C][C]112.567952337536[/C][C]58.2646839814761[/C][C]166.871220693595[/C][/ROW]
[ROW][C]70[/C][C]102.562998970744[/C][C]50.3714650725433[/C][C]154.754532868944[/C][/ROW]
[ROW][C]71[/C][C]105.930266470035[/C][C]50.4139746882573[/C][C]161.446558251813[/C][/ROW]
[ROW][C]72[/C][C]114.688153885615[/C][C]-2.35476202226654[/C][C]231.731069793497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65977&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65977&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
61101.05959689179675.9540972253128126.165096558279
6288.040396032235859.8646351150197116.216156949452
63101.67452271769567.9879186353936135.361126799996
64100.4807046237563.9988507218644136.962558525636
6598.90436308709259.9893066988752137.819419475309
6699.912134593518558.1063903635552141.717878823482
6788.451074715966347.5804235382225129.32172589371
6894.76850236589449.3206767130205140.216328018767
69112.56795233753658.2646839814761166.871220693595
70102.56299897074450.3714650725433154.754532868944
71105.93026647003550.4139746882573161.446558251813
72114.688153885615-2.35476202226654231.731069793497



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')