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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Dec 2011 13:41:30 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/19/t1324320125cpdlyelr10m3kum.htm/, Retrieved Wed, 15 May 2024 19:51:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157607, Retrieved Wed, 15 May 2024 19:51:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oefenin...] [2011-12-19 18:41:30] [51ef8b88ac11c4019bf5b5b4dfd04716] [Current]
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Dataseries X:
117,87
117,74
117,61
117,55
117,06
117,08
117,21
117,58
117,27
117,14
116,52
116,16
114,79
114,97
114,66
114,3
114,48
114,96
115,44
116,38
116,5
116,2
116,37
116,46
115,07
115,03
115,15
114,71
114,67
115,49
114,65
114,92
114,17
112,8
112,28
112,05
111,03
110,4
109,08
107,89
107,26
107,76
107,32
107,15
108,04
106,52
106,62
106,47
105,46
106,13
105,15
105,39
104,57
104,29
104,09
104,51
103,39
102,71
102,62
101,94
101,65
101,86
101,27
101,21
102,15
102,07
102,8
103,39
102,71
102,65
101,12
100,29




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157607&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157607&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157607&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0193124823539649
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0193124823539649 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157607&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]0.0193124823539649[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157607&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157607&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
beta0.0193124823539649
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3117.61117.611.4210854715202e-14
4117.55117.480.0700000000000074
5117.06117.421351873765-0.361351873764761
6117.08116.9243732720790.155626727920875
7117.21116.9473788105160.262621189484108
8117.58117.0824506776040.497549322396424
9117.27117.462059590113-0.192059590112592
10117.14117.148350442668-0.00835044266761997
11116.52117.018189174891-0.498189174890967
12116.16116.388567905242-0.228567905241945
13114.79116.024153691605-1.23415369160527
14114.97114.6303191202140.339680879785917
15114.66114.816879201211-0.156879201210913
16114.3114.503849474406-0.203849474405828
17114.48114.1399126350280.340087364971509
18114.96114.3264805662630.63351943373668
19115.44114.8187153991480.621284600851752
20116.38115.3107139470391.069286052961
21116.5116.2713645150680.228635484931871
22116.2116.395780033836-0.195780033836371
23116.37116.0919990353880.278000964612346
24116.46116.2673679241110.192632075888881
25115.07116.361088127678-1.29108812767753
26115.03114.9461540109940.0838459890056669
27115.15114.9077732851770.242226714822536
28114.71115.032451284333-0.322451284333141
29114.67114.5862239495940.0837760504055751
30115.49114.547841873090.942158126910414
31114.65115.38603728529-0.736037285290166
32114.92114.5318225782060.388177421793841
33114.17114.809319247815-0.639319247814754
34112.8114.046972406123-1.24697240612278
35112.28112.652890273534-0.372890273533656
36112.05112.125688836706-0.0756888367060782
37111.03111.894227097383-0.864227097382781
38110.4110.857536726815-0.457536726814766
39109.08110.218700556852-1.13870055685187
40107.89108.876709422441-0.986709422441209
41107.26107.667653614132-0.407653614131817
42107.76107.0297808109020.730219189097625
43107.32107.543883156106-0.223883156106368
44107.15107.0995594166050.0504405833953143
45108.04106.9305335494811.10946645051855
46106.52107.841960100729-1.32196010072941
47106.62106.2964297696110.323570230388597
48106.47106.4026787139760.0673212860239261
49105.46106.253978855124-0.79397885512445
50106.13105.2286451524950.901354847504564
51105.15105.916052552083-0.766052552082513
52105.39104.9212581756880.468741824311763
53104.57105.170310743899-0.600310743898817
54104.29104.33871725325-0.0487172532503592
55104.09104.0577764021570.0322235978433554
56104.51103.8583987198210.651601280178639
57103.39104.290982758047-0.900982758046652
58102.71103.153582544431-0.44358254443064
59102.62102.4650158643690.15498413563121
60101.94102.378008992753-0.438008992753325
61101.65101.68954995181-0.0395499518098887
62101.86101.3987861440630.461213855936535
63101.27101.617693328518-0.34769332851765
64101.21101.0209785072460.189021492753952
65102.15100.9646289814891.18537101851062
66102.07101.9275214383670.142478561632714
67102.8101.8502730530750.949726946925381
68103.39102.5986146379780.791385362021799
69102.71103.203898253817-0.493898253817434
70102.65102.5143598525060.135640147494087
71101.12102.456979400461-1.3369794004609
72100.29100.901159009382-0.611159009381879

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 117.61 & 117.61 & 1.4210854715202e-14 \tabularnewline
4 & 117.55 & 117.48 & 0.0700000000000074 \tabularnewline
5 & 117.06 & 117.421351873765 & -0.361351873764761 \tabularnewline
6 & 117.08 & 116.924373272079 & 0.155626727920875 \tabularnewline
7 & 117.21 & 116.947378810516 & 0.262621189484108 \tabularnewline
8 & 117.58 & 117.082450677604 & 0.497549322396424 \tabularnewline
9 & 117.27 & 117.462059590113 & -0.192059590112592 \tabularnewline
10 & 117.14 & 117.148350442668 & -0.00835044266761997 \tabularnewline
11 & 116.52 & 117.018189174891 & -0.498189174890967 \tabularnewline
12 & 116.16 & 116.388567905242 & -0.228567905241945 \tabularnewline
13 & 114.79 & 116.024153691605 & -1.23415369160527 \tabularnewline
14 & 114.97 & 114.630319120214 & 0.339680879785917 \tabularnewline
15 & 114.66 & 114.816879201211 & -0.156879201210913 \tabularnewline
16 & 114.3 & 114.503849474406 & -0.203849474405828 \tabularnewline
17 & 114.48 & 114.139912635028 & 0.340087364971509 \tabularnewline
18 & 114.96 & 114.326480566263 & 0.63351943373668 \tabularnewline
19 & 115.44 & 114.818715399148 & 0.621284600851752 \tabularnewline
20 & 116.38 & 115.310713947039 & 1.069286052961 \tabularnewline
21 & 116.5 & 116.271364515068 & 0.228635484931871 \tabularnewline
22 & 116.2 & 116.395780033836 & -0.195780033836371 \tabularnewline
23 & 116.37 & 116.091999035388 & 0.278000964612346 \tabularnewline
24 & 116.46 & 116.267367924111 & 0.192632075888881 \tabularnewline
25 & 115.07 & 116.361088127678 & -1.29108812767753 \tabularnewline
26 & 115.03 & 114.946154010994 & 0.0838459890056669 \tabularnewline
27 & 115.15 & 114.907773285177 & 0.242226714822536 \tabularnewline
28 & 114.71 & 115.032451284333 & -0.322451284333141 \tabularnewline
29 & 114.67 & 114.586223949594 & 0.0837760504055751 \tabularnewline
30 & 115.49 & 114.54784187309 & 0.942158126910414 \tabularnewline
31 & 114.65 & 115.38603728529 & -0.736037285290166 \tabularnewline
32 & 114.92 & 114.531822578206 & 0.388177421793841 \tabularnewline
33 & 114.17 & 114.809319247815 & -0.639319247814754 \tabularnewline
34 & 112.8 & 114.046972406123 & -1.24697240612278 \tabularnewline
35 & 112.28 & 112.652890273534 & -0.372890273533656 \tabularnewline
36 & 112.05 & 112.125688836706 & -0.0756888367060782 \tabularnewline
37 & 111.03 & 111.894227097383 & -0.864227097382781 \tabularnewline
38 & 110.4 & 110.857536726815 & -0.457536726814766 \tabularnewline
39 & 109.08 & 110.218700556852 & -1.13870055685187 \tabularnewline
40 & 107.89 & 108.876709422441 & -0.986709422441209 \tabularnewline
41 & 107.26 & 107.667653614132 & -0.407653614131817 \tabularnewline
42 & 107.76 & 107.029780810902 & 0.730219189097625 \tabularnewline
43 & 107.32 & 107.543883156106 & -0.223883156106368 \tabularnewline
44 & 107.15 & 107.099559416605 & 0.0504405833953143 \tabularnewline
45 & 108.04 & 106.930533549481 & 1.10946645051855 \tabularnewline
46 & 106.52 & 107.841960100729 & -1.32196010072941 \tabularnewline
47 & 106.62 & 106.296429769611 & 0.323570230388597 \tabularnewline
48 & 106.47 & 106.402678713976 & 0.0673212860239261 \tabularnewline
49 & 105.46 & 106.253978855124 & -0.79397885512445 \tabularnewline
50 & 106.13 & 105.228645152495 & 0.901354847504564 \tabularnewline
51 & 105.15 & 105.916052552083 & -0.766052552082513 \tabularnewline
52 & 105.39 & 104.921258175688 & 0.468741824311763 \tabularnewline
53 & 104.57 & 105.170310743899 & -0.600310743898817 \tabularnewline
54 & 104.29 & 104.33871725325 & -0.0487172532503592 \tabularnewline
55 & 104.09 & 104.057776402157 & 0.0322235978433554 \tabularnewline
56 & 104.51 & 103.858398719821 & 0.651601280178639 \tabularnewline
57 & 103.39 & 104.290982758047 & -0.900982758046652 \tabularnewline
58 & 102.71 & 103.153582544431 & -0.44358254443064 \tabularnewline
59 & 102.62 & 102.465015864369 & 0.15498413563121 \tabularnewline
60 & 101.94 & 102.378008992753 & -0.438008992753325 \tabularnewline
61 & 101.65 & 101.68954995181 & -0.0395499518098887 \tabularnewline
62 & 101.86 & 101.398786144063 & 0.461213855936535 \tabularnewline
63 & 101.27 & 101.617693328518 & -0.34769332851765 \tabularnewline
64 & 101.21 & 101.020978507246 & 0.189021492753952 \tabularnewline
65 & 102.15 & 100.964628981489 & 1.18537101851062 \tabularnewline
66 & 102.07 & 101.927521438367 & 0.142478561632714 \tabularnewline
67 & 102.8 & 101.850273053075 & 0.949726946925381 \tabularnewline
68 & 103.39 & 102.598614637978 & 0.791385362021799 \tabularnewline
69 & 102.71 & 103.203898253817 & -0.493898253817434 \tabularnewline
70 & 102.65 & 102.514359852506 & 0.135640147494087 \tabularnewline
71 & 101.12 & 102.456979400461 & -1.3369794004609 \tabularnewline
72 & 100.29 & 100.901159009382 & -0.611159009381879 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157607&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]117.61[/C][C]117.61[/C][C]1.4210854715202e-14[/C][/ROW]
[ROW][C]4[/C][C]117.55[/C][C]117.48[/C][C]0.0700000000000074[/C][/ROW]
[ROW][C]5[/C][C]117.06[/C][C]117.421351873765[/C][C]-0.361351873764761[/C][/ROW]
[ROW][C]6[/C][C]117.08[/C][C]116.924373272079[/C][C]0.155626727920875[/C][/ROW]
[ROW][C]7[/C][C]117.21[/C][C]116.947378810516[/C][C]0.262621189484108[/C][/ROW]
[ROW][C]8[/C][C]117.58[/C][C]117.082450677604[/C][C]0.497549322396424[/C][/ROW]
[ROW][C]9[/C][C]117.27[/C][C]117.462059590113[/C][C]-0.192059590112592[/C][/ROW]
[ROW][C]10[/C][C]117.14[/C][C]117.148350442668[/C][C]-0.00835044266761997[/C][/ROW]
[ROW][C]11[/C][C]116.52[/C][C]117.018189174891[/C][C]-0.498189174890967[/C][/ROW]
[ROW][C]12[/C][C]116.16[/C][C]116.388567905242[/C][C]-0.228567905241945[/C][/ROW]
[ROW][C]13[/C][C]114.79[/C][C]116.024153691605[/C][C]-1.23415369160527[/C][/ROW]
[ROW][C]14[/C][C]114.97[/C][C]114.630319120214[/C][C]0.339680879785917[/C][/ROW]
[ROW][C]15[/C][C]114.66[/C][C]114.816879201211[/C][C]-0.156879201210913[/C][/ROW]
[ROW][C]16[/C][C]114.3[/C][C]114.503849474406[/C][C]-0.203849474405828[/C][/ROW]
[ROW][C]17[/C][C]114.48[/C][C]114.139912635028[/C][C]0.340087364971509[/C][/ROW]
[ROW][C]18[/C][C]114.96[/C][C]114.326480566263[/C][C]0.63351943373668[/C][/ROW]
[ROW][C]19[/C][C]115.44[/C][C]114.818715399148[/C][C]0.621284600851752[/C][/ROW]
[ROW][C]20[/C][C]116.38[/C][C]115.310713947039[/C][C]1.069286052961[/C][/ROW]
[ROW][C]21[/C][C]116.5[/C][C]116.271364515068[/C][C]0.228635484931871[/C][/ROW]
[ROW][C]22[/C][C]116.2[/C][C]116.395780033836[/C][C]-0.195780033836371[/C][/ROW]
[ROW][C]23[/C][C]116.37[/C][C]116.091999035388[/C][C]0.278000964612346[/C][/ROW]
[ROW][C]24[/C][C]116.46[/C][C]116.267367924111[/C][C]0.192632075888881[/C][/ROW]
[ROW][C]25[/C][C]115.07[/C][C]116.361088127678[/C][C]-1.29108812767753[/C][/ROW]
[ROW][C]26[/C][C]115.03[/C][C]114.946154010994[/C][C]0.0838459890056669[/C][/ROW]
[ROW][C]27[/C][C]115.15[/C][C]114.907773285177[/C][C]0.242226714822536[/C][/ROW]
[ROW][C]28[/C][C]114.71[/C][C]115.032451284333[/C][C]-0.322451284333141[/C][/ROW]
[ROW][C]29[/C][C]114.67[/C][C]114.586223949594[/C][C]0.0837760504055751[/C][/ROW]
[ROW][C]30[/C][C]115.49[/C][C]114.54784187309[/C][C]0.942158126910414[/C][/ROW]
[ROW][C]31[/C][C]114.65[/C][C]115.38603728529[/C][C]-0.736037285290166[/C][/ROW]
[ROW][C]32[/C][C]114.92[/C][C]114.531822578206[/C][C]0.388177421793841[/C][/ROW]
[ROW][C]33[/C][C]114.17[/C][C]114.809319247815[/C][C]-0.639319247814754[/C][/ROW]
[ROW][C]34[/C][C]112.8[/C][C]114.046972406123[/C][C]-1.24697240612278[/C][/ROW]
[ROW][C]35[/C][C]112.28[/C][C]112.652890273534[/C][C]-0.372890273533656[/C][/ROW]
[ROW][C]36[/C][C]112.05[/C][C]112.125688836706[/C][C]-0.0756888367060782[/C][/ROW]
[ROW][C]37[/C][C]111.03[/C][C]111.894227097383[/C][C]-0.864227097382781[/C][/ROW]
[ROW][C]38[/C][C]110.4[/C][C]110.857536726815[/C][C]-0.457536726814766[/C][/ROW]
[ROW][C]39[/C][C]109.08[/C][C]110.218700556852[/C][C]-1.13870055685187[/C][/ROW]
[ROW][C]40[/C][C]107.89[/C][C]108.876709422441[/C][C]-0.986709422441209[/C][/ROW]
[ROW][C]41[/C][C]107.26[/C][C]107.667653614132[/C][C]-0.407653614131817[/C][/ROW]
[ROW][C]42[/C][C]107.76[/C][C]107.029780810902[/C][C]0.730219189097625[/C][/ROW]
[ROW][C]43[/C][C]107.32[/C][C]107.543883156106[/C][C]-0.223883156106368[/C][/ROW]
[ROW][C]44[/C][C]107.15[/C][C]107.099559416605[/C][C]0.0504405833953143[/C][/ROW]
[ROW][C]45[/C][C]108.04[/C][C]106.930533549481[/C][C]1.10946645051855[/C][/ROW]
[ROW][C]46[/C][C]106.52[/C][C]107.841960100729[/C][C]-1.32196010072941[/C][/ROW]
[ROW][C]47[/C][C]106.62[/C][C]106.296429769611[/C][C]0.323570230388597[/C][/ROW]
[ROW][C]48[/C][C]106.47[/C][C]106.402678713976[/C][C]0.0673212860239261[/C][/ROW]
[ROW][C]49[/C][C]105.46[/C][C]106.253978855124[/C][C]-0.79397885512445[/C][/ROW]
[ROW][C]50[/C][C]106.13[/C][C]105.228645152495[/C][C]0.901354847504564[/C][/ROW]
[ROW][C]51[/C][C]105.15[/C][C]105.916052552083[/C][C]-0.766052552082513[/C][/ROW]
[ROW][C]52[/C][C]105.39[/C][C]104.921258175688[/C][C]0.468741824311763[/C][/ROW]
[ROW][C]53[/C][C]104.57[/C][C]105.170310743899[/C][C]-0.600310743898817[/C][/ROW]
[ROW][C]54[/C][C]104.29[/C][C]104.33871725325[/C][C]-0.0487172532503592[/C][/ROW]
[ROW][C]55[/C][C]104.09[/C][C]104.057776402157[/C][C]0.0322235978433554[/C][/ROW]
[ROW][C]56[/C][C]104.51[/C][C]103.858398719821[/C][C]0.651601280178639[/C][/ROW]
[ROW][C]57[/C][C]103.39[/C][C]104.290982758047[/C][C]-0.900982758046652[/C][/ROW]
[ROW][C]58[/C][C]102.71[/C][C]103.153582544431[/C][C]-0.44358254443064[/C][/ROW]
[ROW][C]59[/C][C]102.62[/C][C]102.465015864369[/C][C]0.15498413563121[/C][/ROW]
[ROW][C]60[/C][C]101.94[/C][C]102.378008992753[/C][C]-0.438008992753325[/C][/ROW]
[ROW][C]61[/C][C]101.65[/C][C]101.68954995181[/C][C]-0.0395499518098887[/C][/ROW]
[ROW][C]62[/C][C]101.86[/C][C]101.398786144063[/C][C]0.461213855936535[/C][/ROW]
[ROW][C]63[/C][C]101.27[/C][C]101.617693328518[/C][C]-0.34769332851765[/C][/ROW]
[ROW][C]64[/C][C]101.21[/C][C]101.020978507246[/C][C]0.189021492753952[/C][/ROW]
[ROW][C]65[/C][C]102.15[/C][C]100.964628981489[/C][C]1.18537101851062[/C][/ROW]
[ROW][C]66[/C][C]102.07[/C][C]101.927521438367[/C][C]0.142478561632714[/C][/ROW]
[ROW][C]67[/C][C]102.8[/C][C]101.850273053075[/C][C]0.949726946925381[/C][/ROW]
[ROW][C]68[/C][C]103.39[/C][C]102.598614637978[/C][C]0.791385362021799[/C][/ROW]
[ROW][C]69[/C][C]102.71[/C][C]103.203898253817[/C][C]-0.493898253817434[/C][/ROW]
[ROW][C]70[/C][C]102.65[/C][C]102.514359852506[/C][C]0.135640147494087[/C][/ROW]
[ROW][C]71[/C][C]101.12[/C][C]102.456979400461[/C][C]-1.3369794004609[/C][/ROW]
[ROW][C]72[/C][C]100.29[/C][C]100.901159009382[/C][C]-0.611159009381879[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157607&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157607&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
3117.61117.611.4210854715202e-14
4117.55117.480.0700000000000074
5117.06117.421351873765-0.361351873764761
6117.08116.9243732720790.155626727920875
7117.21116.9473788105160.262621189484108
8117.58117.0824506776040.497549322396424
9117.27117.462059590113-0.192059590112592
10117.14117.148350442668-0.00835044266761997
11116.52117.018189174891-0.498189174890967
12116.16116.388567905242-0.228567905241945
13114.79116.024153691605-1.23415369160527
14114.97114.6303191202140.339680879785917
15114.66114.816879201211-0.156879201210913
16114.3114.503849474406-0.203849474405828
17114.48114.1399126350280.340087364971509
18114.96114.3264805662630.63351943373668
19115.44114.8187153991480.621284600851752
20116.38115.3107139470391.069286052961
21116.5116.2713645150680.228635484931871
22116.2116.395780033836-0.195780033836371
23116.37116.0919990353880.278000964612346
24116.46116.2673679241110.192632075888881
25115.07116.361088127678-1.29108812767753
26115.03114.9461540109940.0838459890056669
27115.15114.9077732851770.242226714822536
28114.71115.032451284333-0.322451284333141
29114.67114.5862239495940.0837760504055751
30115.49114.547841873090.942158126910414
31114.65115.38603728529-0.736037285290166
32114.92114.5318225782060.388177421793841
33114.17114.809319247815-0.639319247814754
34112.8114.046972406123-1.24697240612278
35112.28112.652890273534-0.372890273533656
36112.05112.125688836706-0.0756888367060782
37111.03111.894227097383-0.864227097382781
38110.4110.857536726815-0.457536726814766
39109.08110.218700556852-1.13870055685187
40107.89108.876709422441-0.986709422441209
41107.26107.667653614132-0.407653614131817
42107.76107.0297808109020.730219189097625
43107.32107.543883156106-0.223883156106368
44107.15107.0995594166050.0504405833953143
45108.04106.9305335494811.10946645051855
46106.52107.841960100729-1.32196010072941
47106.62106.2964297696110.323570230388597
48106.47106.4026787139760.0673212860239261
49105.46106.253978855124-0.79397885512445
50106.13105.2286451524950.901354847504564
51105.15105.916052552083-0.766052552082513
52105.39104.9212581756880.468741824311763
53104.57105.170310743899-0.600310743898817
54104.29104.33871725325-0.0487172532503592
55104.09104.0577764021570.0322235978433554
56104.51103.8583987198210.651601280178639
57103.39104.290982758047-0.900982758046652
58102.71103.153582544431-0.44358254443064
59102.62102.4650158643690.15498413563121
60101.94102.378008992753-0.438008992753325
61101.65101.68954995181-0.0395499518098887
62101.86101.3987861440630.461213855936535
63101.27101.617693328518-0.34769332851765
64101.21101.0209785072460.189021492753952
65102.15100.9646289814891.18537101851062
66102.07101.9275214383670.142478561632714
67102.8101.8502730530750.949726946925381
68103.39102.5986146379780.791385362021799
69102.71103.203898253817-0.493898253817434
70102.65102.5143598525060.135640147494087
71101.12102.456979400461-1.3369794004609
72100.29100.901159009382-0.611159009381879







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73100.05935601179898.8335360554858101.28517596811
7499.828712023595598.0783209877925101.579103059398
7599.598068035393297.4336227207819101.762513350004
7699.367424047190996.8442079106651101.890640183717
7799.136780058988696.2889074996162101.984652618361
7898.906136070786495.7569743204929102.05529782108
7998.675492082584195.2420877373254102.108896427843
8098.444848094381894.7401705104108102.149525678353
8198.214204106179694.248418885056102.179989327303
8297.983560117977393.7648120174245102.20230821853
8397.75291612977593.2878398448895102.217992414661
8497.522272141572892.8163412684053102.22820301474

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 100.059356011798 & 98.8335360554858 & 101.28517596811 \tabularnewline
74 & 99.8287120235955 & 98.0783209877925 & 101.579103059398 \tabularnewline
75 & 99.5980680353932 & 97.4336227207819 & 101.762513350004 \tabularnewline
76 & 99.3674240471909 & 96.8442079106651 & 101.890640183717 \tabularnewline
77 & 99.1367800589886 & 96.2889074996162 & 101.984652618361 \tabularnewline
78 & 98.9061360707864 & 95.7569743204929 & 102.05529782108 \tabularnewline
79 & 98.6754920825841 & 95.2420877373254 & 102.108896427843 \tabularnewline
80 & 98.4448480943818 & 94.7401705104108 & 102.149525678353 \tabularnewline
81 & 98.2142041061796 & 94.248418885056 & 102.179989327303 \tabularnewline
82 & 97.9835601179773 & 93.7648120174245 & 102.20230821853 \tabularnewline
83 & 97.752916129775 & 93.2878398448895 & 102.217992414661 \tabularnewline
84 & 97.5222721415728 & 92.8163412684053 & 102.22820301474 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157607&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]100.059356011798[/C][C]98.8335360554858[/C][C]101.28517596811[/C][/ROW]
[ROW][C]74[/C][C]99.8287120235955[/C][C]98.0783209877925[/C][C]101.579103059398[/C][/ROW]
[ROW][C]75[/C][C]99.5980680353932[/C][C]97.4336227207819[/C][C]101.762513350004[/C][/ROW]
[ROW][C]76[/C][C]99.3674240471909[/C][C]96.8442079106651[/C][C]101.890640183717[/C][/ROW]
[ROW][C]77[/C][C]99.1367800589886[/C][C]96.2889074996162[/C][C]101.984652618361[/C][/ROW]
[ROW][C]78[/C][C]98.9061360707864[/C][C]95.7569743204929[/C][C]102.05529782108[/C][/ROW]
[ROW][C]79[/C][C]98.6754920825841[/C][C]95.2420877373254[/C][C]102.108896427843[/C][/ROW]
[ROW][C]80[/C][C]98.4448480943818[/C][C]94.7401705104108[/C][C]102.149525678353[/C][/ROW]
[ROW][C]81[/C][C]98.2142041061796[/C][C]94.248418885056[/C][C]102.179989327303[/C][/ROW]
[ROW][C]82[/C][C]97.9835601179773[/C][C]93.7648120174245[/C][C]102.20230821853[/C][/ROW]
[ROW][C]83[/C][C]97.752916129775[/C][C]93.2878398448895[/C][C]102.217992414661[/C][/ROW]
[ROW][C]84[/C][C]97.5222721415728[/C][C]92.8163412684053[/C][C]102.22820301474[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157607&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157607&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
73100.05935601179898.8335360554858101.28517596811
7499.828712023595598.0783209877925101.579103059398
7599.598068035393297.4336227207819101.762513350004
7699.367424047190996.8442079106651101.890640183717
7799.136780058988696.2889074996162101.984652618361
7898.906136070786495.7569743204929102.05529782108
7998.675492082584195.2420877373254102.108896427843
8098.444848094381894.7401705104108102.149525678353
8198.214204106179694.248418885056102.179989327303
8297.983560117977393.7648120174245102.20230821853
8397.75291612977593.2878398448895102.217992414661
8497.522272141572892.8163412684053102.22820301474



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=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')