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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 18 Aug 2008 09:49:08 -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/Aug/18/t1219074650pcx5g92a14dsp7u.htm/, Retrieved Tue, 14 May 2024 23:48:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14643, Retrieved Tue, 14 May 2024 23:48:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsAfzetprijsindexen van de verwerking en conservering van groenten en fruit
Estimated Impact254
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Sanne Seghers - 2...] [2008-08-18 15:49:08] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
115.6
118.5
118.1
117.7
117.9
118.5
117
115.6
113.7
112.1
113.5
113.5
112.2
112.7
111.9
111.5
110.8
111.2
110.9
114.1
121.3
121.5
122.5
122.4
122.5
122.8
122.9
123.6
123.4
122.9
121
119
119
114.3
113.4
113.7
113.5
114.4
114.6
111.6
111.8
110.8
112.6
115.3
115.4
115.3
115.5
115
116.3
117
116.9
117.2
117.1
116.7
117.4
126.7
128.6
129.2
131.1
131.1
131.5
133.2
133.7
135.7
134.9
135.7
131.2
127.4
127.5
124.1
124.1
124.1
124.5
123.7
125.9
126
125.5
125.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14643&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14643&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14643&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.320159117207958
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.320159117207958 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14643&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]0.320159117207958[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14643&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14643&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
beta0.320159117207958
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3118.1121.4-3.30000000000001
4117.7119.943474913214-2.24347491321373
5117.9118.825205965521-0.92520596552103
6118.5118.728992840364-0.228992840364285
7117119.255678694746-2.25567869474631
8115.6117.033502595132-1.43350259513154
9113.7115.174553669759-1.47455366975889
10112.1112.802461868573-0.702461868573153
11113.5110.9775622968592.52243770314149
12113.5113.1851437251080.314856274891639
13112.2113.285947832125-1.08594783212504
14112.7111.6382717328581.06172826714200
15111.9112.478193717581-0.578193717580916
16111.5111.4930797273850.00692027261496264
17110.8111.095295315756-0.295295315756277
18111.2110.3007538281480.899246171851914
19110.9110.988655688681-0.0886556886808307
20114.1110.6602717616573.43972823834267
21121.3114.9615321178806.33846788211962
22121.5124.190850399471-2.69085039947079
23122.5123.529350111038-1.02935011103754
24122.4124.199794288190-1.79979428818984
25122.5123.523573737727-1.02357373772708
26122.8123.295867273459-0.495867273459126
27122.9123.437110844936-0.537110844936123
28123.6123.3651499109790.234850089021421
29123.4124.140339308156-0.740339308155853
30122.9123.703312928822-0.803312928822336
31121122.946124970689-1.94612497068884
32119120.423055318097-1.42305531809674
33119117.9674511837171.03254881628320
34114.3118.298031101212-3.99803110121215
35113.4112.3180249932781.08197500672190
36113.7111.7644291562711.93557084372873
37113.5112.6841198088930.815880191107084
38114.4112.7453312906251.65466870937479
39114.6114.1750885638900.42491143610971
40111.6114.511127834167-2.91112783416673
41111.8110.5791037167001.22089628329961
42110.8111.169984792964-0.369984792964075
43112.6110.0515307882682.54846921173167
44115.3112.6674464413282.632553558672
45115.4116.210282464675-0.810282464675083
46115.3116.050863146096-0.75086314609564
47115.5115.710467464098-0.210467464097661
48115115.843084386591-0.843084386591158
49116.3115.0731632336481.22683676635168
50117116.7659462097220.234053790278267
51116.9117.540880664596-0.640880664596395
52117.2117.235696876784-0.0356968767835752
53117.1117.524268196225-0.424268196225469
54116.7117.288434865062-0.588434865062496
55117.4116.7000420781300.699957921870293
56126.7117.6241399884789.07586001152158
57128.6129.829859317670-1.22985931767019
58129.2131.336108644235-2.13610864423492
59131.1131.252213986436-0.152213986436351
60131.1133.103481290912-2.00348129091219
61131.5132.462048489471-0.962048489471073
62133.2132.5540398943710.6459601056292
63133.7134.460849911541-0.76084991154059
64135.7134.7172568755340.982743124465998
65134.9137.031891046705-2.13189104670519
66135.7135.5493466912090.150653308791448
67131.2136.397579721556-5.19757972155566
68127.4130.233527186284-2.83352718628441
69127.5125.5263476237391.97365237626114
70124.1126.258230426198-2.15823042619802
71124.1122.1672532782151.93274672178489
72124.1122.7860397624481.31396023755167
73124.5123.2067161121491.29328388785078
74123.7124.020772739983-0.3207727399828
75125.9123.1180744227262.78192557727446
76126126.208733259684-0.208733259683967
77125.5126.241905403532-0.741905403531604
78125.3125.504377624485-0.204377624485119

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 118.1 & 121.4 & -3.30000000000001 \tabularnewline
4 & 117.7 & 119.943474913214 & -2.24347491321373 \tabularnewline
5 & 117.9 & 118.825205965521 & -0.92520596552103 \tabularnewline
6 & 118.5 & 118.728992840364 & -0.228992840364285 \tabularnewline
7 & 117 & 119.255678694746 & -2.25567869474631 \tabularnewline
8 & 115.6 & 117.033502595132 & -1.43350259513154 \tabularnewline
9 & 113.7 & 115.174553669759 & -1.47455366975889 \tabularnewline
10 & 112.1 & 112.802461868573 & -0.702461868573153 \tabularnewline
11 & 113.5 & 110.977562296859 & 2.52243770314149 \tabularnewline
12 & 113.5 & 113.185143725108 & 0.314856274891639 \tabularnewline
13 & 112.2 & 113.285947832125 & -1.08594783212504 \tabularnewline
14 & 112.7 & 111.638271732858 & 1.06172826714200 \tabularnewline
15 & 111.9 & 112.478193717581 & -0.578193717580916 \tabularnewline
16 & 111.5 & 111.493079727385 & 0.00692027261496264 \tabularnewline
17 & 110.8 & 111.095295315756 & -0.295295315756277 \tabularnewline
18 & 111.2 & 110.300753828148 & 0.899246171851914 \tabularnewline
19 & 110.9 & 110.988655688681 & -0.0886556886808307 \tabularnewline
20 & 114.1 & 110.660271761657 & 3.43972823834267 \tabularnewline
21 & 121.3 & 114.961532117880 & 6.33846788211962 \tabularnewline
22 & 121.5 & 124.190850399471 & -2.69085039947079 \tabularnewline
23 & 122.5 & 123.529350111038 & -1.02935011103754 \tabularnewline
24 & 122.4 & 124.199794288190 & -1.79979428818984 \tabularnewline
25 & 122.5 & 123.523573737727 & -1.02357373772708 \tabularnewline
26 & 122.8 & 123.295867273459 & -0.495867273459126 \tabularnewline
27 & 122.9 & 123.437110844936 & -0.537110844936123 \tabularnewline
28 & 123.6 & 123.365149910979 & 0.234850089021421 \tabularnewline
29 & 123.4 & 124.140339308156 & -0.740339308155853 \tabularnewline
30 & 122.9 & 123.703312928822 & -0.803312928822336 \tabularnewline
31 & 121 & 122.946124970689 & -1.94612497068884 \tabularnewline
32 & 119 & 120.423055318097 & -1.42305531809674 \tabularnewline
33 & 119 & 117.967451183717 & 1.03254881628320 \tabularnewline
34 & 114.3 & 118.298031101212 & -3.99803110121215 \tabularnewline
35 & 113.4 & 112.318024993278 & 1.08197500672190 \tabularnewline
36 & 113.7 & 111.764429156271 & 1.93557084372873 \tabularnewline
37 & 113.5 & 112.684119808893 & 0.815880191107084 \tabularnewline
38 & 114.4 & 112.745331290625 & 1.65466870937479 \tabularnewline
39 & 114.6 & 114.175088563890 & 0.42491143610971 \tabularnewline
40 & 111.6 & 114.511127834167 & -2.91112783416673 \tabularnewline
41 & 111.8 & 110.579103716700 & 1.22089628329961 \tabularnewline
42 & 110.8 & 111.169984792964 & -0.369984792964075 \tabularnewline
43 & 112.6 & 110.051530788268 & 2.54846921173167 \tabularnewline
44 & 115.3 & 112.667446441328 & 2.632553558672 \tabularnewline
45 & 115.4 & 116.210282464675 & -0.810282464675083 \tabularnewline
46 & 115.3 & 116.050863146096 & -0.75086314609564 \tabularnewline
47 & 115.5 & 115.710467464098 & -0.210467464097661 \tabularnewline
48 & 115 & 115.843084386591 & -0.843084386591158 \tabularnewline
49 & 116.3 & 115.073163233648 & 1.22683676635168 \tabularnewline
50 & 117 & 116.765946209722 & 0.234053790278267 \tabularnewline
51 & 116.9 & 117.540880664596 & -0.640880664596395 \tabularnewline
52 & 117.2 & 117.235696876784 & -0.0356968767835752 \tabularnewline
53 & 117.1 & 117.524268196225 & -0.424268196225469 \tabularnewline
54 & 116.7 & 117.288434865062 & -0.588434865062496 \tabularnewline
55 & 117.4 & 116.700042078130 & 0.699957921870293 \tabularnewline
56 & 126.7 & 117.624139988478 & 9.07586001152158 \tabularnewline
57 & 128.6 & 129.829859317670 & -1.22985931767019 \tabularnewline
58 & 129.2 & 131.336108644235 & -2.13610864423492 \tabularnewline
59 & 131.1 & 131.252213986436 & -0.152213986436351 \tabularnewline
60 & 131.1 & 133.103481290912 & -2.00348129091219 \tabularnewline
61 & 131.5 & 132.462048489471 & -0.962048489471073 \tabularnewline
62 & 133.2 & 132.554039894371 & 0.6459601056292 \tabularnewline
63 & 133.7 & 134.460849911541 & -0.76084991154059 \tabularnewline
64 & 135.7 & 134.717256875534 & 0.982743124465998 \tabularnewline
65 & 134.9 & 137.031891046705 & -2.13189104670519 \tabularnewline
66 & 135.7 & 135.549346691209 & 0.150653308791448 \tabularnewline
67 & 131.2 & 136.397579721556 & -5.19757972155566 \tabularnewline
68 & 127.4 & 130.233527186284 & -2.83352718628441 \tabularnewline
69 & 127.5 & 125.526347623739 & 1.97365237626114 \tabularnewline
70 & 124.1 & 126.258230426198 & -2.15823042619802 \tabularnewline
71 & 124.1 & 122.167253278215 & 1.93274672178489 \tabularnewline
72 & 124.1 & 122.786039762448 & 1.31396023755167 \tabularnewline
73 & 124.5 & 123.206716112149 & 1.29328388785078 \tabularnewline
74 & 123.7 & 124.020772739983 & -0.3207727399828 \tabularnewline
75 & 125.9 & 123.118074422726 & 2.78192557727446 \tabularnewline
76 & 126 & 126.208733259684 & -0.208733259683967 \tabularnewline
77 & 125.5 & 126.241905403532 & -0.741905403531604 \tabularnewline
78 & 125.3 & 125.504377624485 & -0.204377624485119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14643&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]118.1[/C][C]121.4[/C][C]-3.30000000000001[/C][/ROW]
[ROW][C]4[/C][C]117.7[/C][C]119.943474913214[/C][C]-2.24347491321373[/C][/ROW]
[ROW][C]5[/C][C]117.9[/C][C]118.825205965521[/C][C]-0.92520596552103[/C][/ROW]
[ROW][C]6[/C][C]118.5[/C][C]118.728992840364[/C][C]-0.228992840364285[/C][/ROW]
[ROW][C]7[/C][C]117[/C][C]119.255678694746[/C][C]-2.25567869474631[/C][/ROW]
[ROW][C]8[/C][C]115.6[/C][C]117.033502595132[/C][C]-1.43350259513154[/C][/ROW]
[ROW][C]9[/C][C]113.7[/C][C]115.174553669759[/C][C]-1.47455366975889[/C][/ROW]
[ROW][C]10[/C][C]112.1[/C][C]112.802461868573[/C][C]-0.702461868573153[/C][/ROW]
[ROW][C]11[/C][C]113.5[/C][C]110.977562296859[/C][C]2.52243770314149[/C][/ROW]
[ROW][C]12[/C][C]113.5[/C][C]113.185143725108[/C][C]0.314856274891639[/C][/ROW]
[ROW][C]13[/C][C]112.2[/C][C]113.285947832125[/C][C]-1.08594783212504[/C][/ROW]
[ROW][C]14[/C][C]112.7[/C][C]111.638271732858[/C][C]1.06172826714200[/C][/ROW]
[ROW][C]15[/C][C]111.9[/C][C]112.478193717581[/C][C]-0.578193717580916[/C][/ROW]
[ROW][C]16[/C][C]111.5[/C][C]111.493079727385[/C][C]0.00692027261496264[/C][/ROW]
[ROW][C]17[/C][C]110.8[/C][C]111.095295315756[/C][C]-0.295295315756277[/C][/ROW]
[ROW][C]18[/C][C]111.2[/C][C]110.300753828148[/C][C]0.899246171851914[/C][/ROW]
[ROW][C]19[/C][C]110.9[/C][C]110.988655688681[/C][C]-0.0886556886808307[/C][/ROW]
[ROW][C]20[/C][C]114.1[/C][C]110.660271761657[/C][C]3.43972823834267[/C][/ROW]
[ROW][C]21[/C][C]121.3[/C][C]114.961532117880[/C][C]6.33846788211962[/C][/ROW]
[ROW][C]22[/C][C]121.5[/C][C]124.190850399471[/C][C]-2.69085039947079[/C][/ROW]
[ROW][C]23[/C][C]122.5[/C][C]123.529350111038[/C][C]-1.02935011103754[/C][/ROW]
[ROW][C]24[/C][C]122.4[/C][C]124.199794288190[/C][C]-1.79979428818984[/C][/ROW]
[ROW][C]25[/C][C]122.5[/C][C]123.523573737727[/C][C]-1.02357373772708[/C][/ROW]
[ROW][C]26[/C][C]122.8[/C][C]123.295867273459[/C][C]-0.495867273459126[/C][/ROW]
[ROW][C]27[/C][C]122.9[/C][C]123.437110844936[/C][C]-0.537110844936123[/C][/ROW]
[ROW][C]28[/C][C]123.6[/C][C]123.365149910979[/C][C]0.234850089021421[/C][/ROW]
[ROW][C]29[/C][C]123.4[/C][C]124.140339308156[/C][C]-0.740339308155853[/C][/ROW]
[ROW][C]30[/C][C]122.9[/C][C]123.703312928822[/C][C]-0.803312928822336[/C][/ROW]
[ROW][C]31[/C][C]121[/C][C]122.946124970689[/C][C]-1.94612497068884[/C][/ROW]
[ROW][C]32[/C][C]119[/C][C]120.423055318097[/C][C]-1.42305531809674[/C][/ROW]
[ROW][C]33[/C][C]119[/C][C]117.967451183717[/C][C]1.03254881628320[/C][/ROW]
[ROW][C]34[/C][C]114.3[/C][C]118.298031101212[/C][C]-3.99803110121215[/C][/ROW]
[ROW][C]35[/C][C]113.4[/C][C]112.318024993278[/C][C]1.08197500672190[/C][/ROW]
[ROW][C]36[/C][C]113.7[/C][C]111.764429156271[/C][C]1.93557084372873[/C][/ROW]
[ROW][C]37[/C][C]113.5[/C][C]112.684119808893[/C][C]0.815880191107084[/C][/ROW]
[ROW][C]38[/C][C]114.4[/C][C]112.745331290625[/C][C]1.65466870937479[/C][/ROW]
[ROW][C]39[/C][C]114.6[/C][C]114.175088563890[/C][C]0.42491143610971[/C][/ROW]
[ROW][C]40[/C][C]111.6[/C][C]114.511127834167[/C][C]-2.91112783416673[/C][/ROW]
[ROW][C]41[/C][C]111.8[/C][C]110.579103716700[/C][C]1.22089628329961[/C][/ROW]
[ROW][C]42[/C][C]110.8[/C][C]111.169984792964[/C][C]-0.369984792964075[/C][/ROW]
[ROW][C]43[/C][C]112.6[/C][C]110.051530788268[/C][C]2.54846921173167[/C][/ROW]
[ROW][C]44[/C][C]115.3[/C][C]112.667446441328[/C][C]2.632553558672[/C][/ROW]
[ROW][C]45[/C][C]115.4[/C][C]116.210282464675[/C][C]-0.810282464675083[/C][/ROW]
[ROW][C]46[/C][C]115.3[/C][C]116.050863146096[/C][C]-0.75086314609564[/C][/ROW]
[ROW][C]47[/C][C]115.5[/C][C]115.710467464098[/C][C]-0.210467464097661[/C][/ROW]
[ROW][C]48[/C][C]115[/C][C]115.843084386591[/C][C]-0.843084386591158[/C][/ROW]
[ROW][C]49[/C][C]116.3[/C][C]115.073163233648[/C][C]1.22683676635168[/C][/ROW]
[ROW][C]50[/C][C]117[/C][C]116.765946209722[/C][C]0.234053790278267[/C][/ROW]
[ROW][C]51[/C][C]116.9[/C][C]117.540880664596[/C][C]-0.640880664596395[/C][/ROW]
[ROW][C]52[/C][C]117.2[/C][C]117.235696876784[/C][C]-0.0356968767835752[/C][/ROW]
[ROW][C]53[/C][C]117.1[/C][C]117.524268196225[/C][C]-0.424268196225469[/C][/ROW]
[ROW][C]54[/C][C]116.7[/C][C]117.288434865062[/C][C]-0.588434865062496[/C][/ROW]
[ROW][C]55[/C][C]117.4[/C][C]116.700042078130[/C][C]0.699957921870293[/C][/ROW]
[ROW][C]56[/C][C]126.7[/C][C]117.624139988478[/C][C]9.07586001152158[/C][/ROW]
[ROW][C]57[/C][C]128.6[/C][C]129.829859317670[/C][C]-1.22985931767019[/C][/ROW]
[ROW][C]58[/C][C]129.2[/C][C]131.336108644235[/C][C]-2.13610864423492[/C][/ROW]
[ROW][C]59[/C][C]131.1[/C][C]131.252213986436[/C][C]-0.152213986436351[/C][/ROW]
[ROW][C]60[/C][C]131.1[/C][C]133.103481290912[/C][C]-2.00348129091219[/C][/ROW]
[ROW][C]61[/C][C]131.5[/C][C]132.462048489471[/C][C]-0.962048489471073[/C][/ROW]
[ROW][C]62[/C][C]133.2[/C][C]132.554039894371[/C][C]0.6459601056292[/C][/ROW]
[ROW][C]63[/C][C]133.7[/C][C]134.460849911541[/C][C]-0.76084991154059[/C][/ROW]
[ROW][C]64[/C][C]135.7[/C][C]134.717256875534[/C][C]0.982743124465998[/C][/ROW]
[ROW][C]65[/C][C]134.9[/C][C]137.031891046705[/C][C]-2.13189104670519[/C][/ROW]
[ROW][C]66[/C][C]135.7[/C][C]135.549346691209[/C][C]0.150653308791448[/C][/ROW]
[ROW][C]67[/C][C]131.2[/C][C]136.397579721556[/C][C]-5.19757972155566[/C][/ROW]
[ROW][C]68[/C][C]127.4[/C][C]130.233527186284[/C][C]-2.83352718628441[/C][/ROW]
[ROW][C]69[/C][C]127.5[/C][C]125.526347623739[/C][C]1.97365237626114[/C][/ROW]
[ROW][C]70[/C][C]124.1[/C][C]126.258230426198[/C][C]-2.15823042619802[/C][/ROW]
[ROW][C]71[/C][C]124.1[/C][C]122.167253278215[/C][C]1.93274672178489[/C][/ROW]
[ROW][C]72[/C][C]124.1[/C][C]122.786039762448[/C][C]1.31396023755167[/C][/ROW]
[ROW][C]73[/C][C]124.5[/C][C]123.206716112149[/C][C]1.29328388785078[/C][/ROW]
[ROW][C]74[/C][C]123.7[/C][C]124.020772739983[/C][C]-0.3207727399828[/C][/ROW]
[ROW][C]75[/C][C]125.9[/C][C]123.118074422726[/C][C]2.78192557727446[/C][/ROW]
[ROW][C]76[/C][C]126[/C][C]126.208733259684[/C][C]-0.208733259683967[/C][/ROW]
[ROW][C]77[/C][C]125.5[/C][C]126.241905403532[/C][C]-0.741905403531604[/C][/ROW]
[ROW][C]78[/C][C]125.3[/C][C]125.504377624485[/C][C]-0.204377624485119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14643&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14643&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
3118.1121.4-3.30000000000001
4117.7119.943474913214-2.24347491321373
5117.9118.825205965521-0.92520596552103
6118.5118.728992840364-0.228992840364285
7117119.255678694746-2.25567869474631
8115.6117.033502595132-1.43350259513154
9113.7115.174553669759-1.47455366975889
10112.1112.802461868573-0.702461868573153
11113.5110.9775622968592.52243770314149
12113.5113.1851437251080.314856274891639
13112.2113.285947832125-1.08594783212504
14112.7111.6382717328581.06172826714200
15111.9112.478193717581-0.578193717580916
16111.5111.4930797273850.00692027261496264
17110.8111.095295315756-0.295295315756277
18111.2110.3007538281480.899246171851914
19110.9110.988655688681-0.0886556886808307
20114.1110.6602717616573.43972823834267
21121.3114.9615321178806.33846788211962
22121.5124.190850399471-2.69085039947079
23122.5123.529350111038-1.02935011103754
24122.4124.199794288190-1.79979428818984
25122.5123.523573737727-1.02357373772708
26122.8123.295867273459-0.495867273459126
27122.9123.437110844936-0.537110844936123
28123.6123.3651499109790.234850089021421
29123.4124.140339308156-0.740339308155853
30122.9123.703312928822-0.803312928822336
31121122.946124970689-1.94612497068884
32119120.423055318097-1.42305531809674
33119117.9674511837171.03254881628320
34114.3118.298031101212-3.99803110121215
35113.4112.3180249932781.08197500672190
36113.7111.7644291562711.93557084372873
37113.5112.6841198088930.815880191107084
38114.4112.7453312906251.65466870937479
39114.6114.1750885638900.42491143610971
40111.6114.511127834167-2.91112783416673
41111.8110.5791037167001.22089628329961
42110.8111.169984792964-0.369984792964075
43112.6110.0515307882682.54846921173167
44115.3112.6674464413282.632553558672
45115.4116.210282464675-0.810282464675083
46115.3116.050863146096-0.75086314609564
47115.5115.710467464098-0.210467464097661
48115115.843084386591-0.843084386591158
49116.3115.0731632336481.22683676635168
50117116.7659462097220.234053790278267
51116.9117.540880664596-0.640880664596395
52117.2117.235696876784-0.0356968767835752
53117.1117.524268196225-0.424268196225469
54116.7117.288434865062-0.588434865062496
55117.4116.7000420781300.699957921870293
56126.7117.6241399884789.07586001152158
57128.6129.829859317670-1.22985931767019
58129.2131.336108644235-2.13610864423492
59131.1131.252213986436-0.152213986436351
60131.1133.103481290912-2.00348129091219
61131.5132.462048489471-0.962048489471073
62133.2132.5540398943710.6459601056292
63133.7134.460849911541-0.76084991154059
64135.7134.7172568755340.982743124465998
65134.9137.031891046705-2.13189104670519
66135.7135.5493466912090.150653308791448
67131.2136.397579721556-5.19757972155566
68127.4130.233527186284-2.83352718628441
69127.5125.5263476237391.97365237626114
70124.1126.258230426198-2.15823042619802
71124.1122.1672532782151.93274672178489
72124.1122.7860397624481.31396023755167
73124.5123.2067161121491.29328388785078
74123.7124.020772739983-0.3207727399828
75125.9123.1180744227262.78192557727446
76126126.208733259684-0.208733259683967
77125.5126.241905403532-0.741905403531604
78125.3125.504377624485-0.204377624485119







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
79125.238944264653121.184742062575129.293146466731
80125.177888529306118.463537130918131.892239927694
81125.116832793959115.666571810868134.567093777049
82125.055777058612112.707462826733137.40409129049
83124.994721323264109.568368387637140.421074258892
84124.933665587917106.248069818557143.619261357278
85124.872609852570102.750498911595146.994720793545
86124.81155411722399.081205701149150.541902533297
87124.75049838187695.2460892932217154.254907470531
88124.68944264652991.2509120913367158.127973201721
89124.62838691118287.1011182295478162.155655592816
90124.56733117583582.8017781717002166.332884179969

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
79 & 125.238944264653 & 121.184742062575 & 129.293146466731 \tabularnewline
80 & 125.177888529306 & 118.463537130918 & 131.892239927694 \tabularnewline
81 & 125.116832793959 & 115.666571810868 & 134.567093777049 \tabularnewline
82 & 125.055777058612 & 112.707462826733 & 137.40409129049 \tabularnewline
83 & 124.994721323264 & 109.568368387637 & 140.421074258892 \tabularnewline
84 & 124.933665587917 & 106.248069818557 & 143.619261357278 \tabularnewline
85 & 124.872609852570 & 102.750498911595 & 146.994720793545 \tabularnewline
86 & 124.811554117223 & 99.081205701149 & 150.541902533297 \tabularnewline
87 & 124.750498381876 & 95.2460892932217 & 154.254907470531 \tabularnewline
88 & 124.689442646529 & 91.2509120913367 & 158.127973201721 \tabularnewline
89 & 124.628386911182 & 87.1011182295478 & 162.155655592816 \tabularnewline
90 & 124.567331175835 & 82.8017781717002 & 166.332884179969 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14643&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]79[/C][C]125.238944264653[/C][C]121.184742062575[/C][C]129.293146466731[/C][/ROW]
[ROW][C]80[/C][C]125.177888529306[/C][C]118.463537130918[/C][C]131.892239927694[/C][/ROW]
[ROW][C]81[/C][C]125.116832793959[/C][C]115.666571810868[/C][C]134.567093777049[/C][/ROW]
[ROW][C]82[/C][C]125.055777058612[/C][C]112.707462826733[/C][C]137.40409129049[/C][/ROW]
[ROW][C]83[/C][C]124.994721323264[/C][C]109.568368387637[/C][C]140.421074258892[/C][/ROW]
[ROW][C]84[/C][C]124.933665587917[/C][C]106.248069818557[/C][C]143.619261357278[/C][/ROW]
[ROW][C]85[/C][C]124.872609852570[/C][C]102.750498911595[/C][C]146.994720793545[/C][/ROW]
[ROW][C]86[/C][C]124.811554117223[/C][C]99.081205701149[/C][C]150.541902533297[/C][/ROW]
[ROW][C]87[/C][C]124.750498381876[/C][C]95.2460892932217[/C][C]154.254907470531[/C][/ROW]
[ROW][C]88[/C][C]124.689442646529[/C][C]91.2509120913367[/C][C]158.127973201721[/C][/ROW]
[ROW][C]89[/C][C]124.628386911182[/C][C]87.1011182295478[/C][C]162.155655592816[/C][/ROW]
[ROW][C]90[/C][C]124.567331175835[/C][C]82.8017781717002[/C][C]166.332884179969[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14643&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14643&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
79125.238944264653121.184742062575129.293146466731
80125.177888529306118.463537130918131.892239927694
81125.116832793959115.666571810868134.567093777049
82125.055777058612112.707462826733137.40409129049
83124.994721323264109.568368387637140.421074258892
84124.933665587917106.248069818557143.619261357278
85124.872609852570102.750498911595146.994720793545
86124.81155411722399.081205701149150.541902533297
87124.75049838187695.2460892932217154.254907470531
88124.68944264652991.2509120913367158.127973201721
89124.62838691118287.1011182295478162.155655592816
90124.56733117583582.8017781717002166.332884179969



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')