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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 03 Jan 2013 19:27:01 -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/2013/Jan/03/t1357259287aosqzpas5ec5h13.htm/, Retrieved Sat, 27 Apr 2024 09:10:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204996, Retrieved Sat, 27 Apr 2024 09:10:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-04 00:27:01] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
227,81
227,81
227,01
227,26
227,1
227,59
227,59
227,7
227,75
226,33
225,95
226,33
226,33
226,22
224,84
221,88
222,37
221,8
221,8
221,8
221,9
220,2
219,95
220,05
220,05
220,05
220,62
221,53
221,61
221,5
221,5
221,87
222,27
220,86
221,49
221,67
221,67
221,72
221,67
220,29
220,75
219,59
219,59
219,59
219,82
221,59
220,9
221,01
221,01
219,69
221
219,82
218,04
217,97
217,97
217,53
217
217,18
217,68
217,71
217,71
218,5
218,8
218,94
220
219,89
219,89
220,08
220,16
221
222,16
221,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204996&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204996&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204996&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.310566161589671
beta0.923250739700174
gamma0.896712472112486

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.310566161589671 \tabularnewline
beta & 0.923250739700174 \tabularnewline
gamma & 0.896712472112486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204996&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]0.310566161589671[/C][/ROW]
[ROW][C]beta[/C][C]0.923250739700174[/C][/ROW]
[ROW][C]gamma[/C][C]0.896712472112486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204996&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204996&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
alpha0.310566161589671
beta0.923250739700174
gamma0.896712472112486







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13226.33228.542465277778-2.21246527777777
14226.22227.174433198827-0.954433198826905
15224.84224.6559382642560.184061735743569
16221.88220.9733807670230.906619232976936
17222.37221.2314305083791.1385694916211
18221.8220.8342286807380.965771319261677
19221.8222.074444288424-0.274444288424178
20221.8221.7328826974810.0671173025192218
21221.9221.485393152360.414606847640414
22220.2220.1526191713190.0473808286808719
23219.95219.8660494075810.0839505924187733
24220.05220.3919914985-0.341991498500306
25220.05218.9839587231221.06604127687808
26220.05220.35900758398-0.30900758398019
27220.62219.877010195920.742989804079883
28221.53218.1072062506163.42279374938417
29221.61221.3040227517720.305977248227947
30221.5222.316619344038-0.816619344037747
31221.5223.500689472913-2.00068947291305
32221.87223.603344753279-1.73334475327857
33222.27223.264440359092-0.994440359091755
34220.86221.115940754064-0.255940754063744
35221.49220.5197110110550.970288988944816
36221.67221.0736655605090.596334439490846
37221.67221.11264455640.557355443599846
38221.72221.6188889416750.101111058325131
39221.67222.171488205283-0.501488205282612
40220.29221.571938408762-1.28193840876204
41220.75219.9317718708350.818228129165249
42219.59219.1073561938170.482643806182693
43219.59219.0333673148050.556632685195382
44219.59219.899235627487-0.309235627486885
45219.82220.671471549163-0.851471549163392
46221.59219.2769766888522.31302331114773
47220.9221.2263103563-0.326310356299587
48221.01221.764268418167-0.754268418166902
49221.01221.590310213773-0.580310213773373
50219.69221.365581669637-1.67558166963667
51221220.3888358477260.611164152274341
52219.82219.366353371180.453646628819513
53218.04219.775227201818-1.73522720181825
54217.97217.4298282734060.540171726594394
55217.97216.9154421463181.05455785368153
56217.53217.03941379690.490586203100065
57217217.592922494082-0.592922494081904
58217.18218.177322925281-0.997322925281338
59217.68216.4599311120491.22006888795107
60217.71216.6500175813331.05998241866664
61217.71217.1036996091040.606300390896308
62218.5216.8672567202981.63274327970214
63218.8219.577170681251-0.777170681250595
64218.94218.8735444602390.0664555397613071
65220218.5453433832211.45465661677861
66219.89220.248344968925-0.35834496892474
67219.89221.166308175194-1.27630817519389
68220.08220.942793112076-0.862793112076076
69220.16220.743144117492-0.58314411749177
70221221.420382242491-0.420382242490831
71222.16221.7582506813780.40174931862154
72221.5221.865825705653-0.365825705653293

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 226.33 & 228.542465277778 & -2.21246527777777 \tabularnewline
14 & 226.22 & 227.174433198827 & -0.954433198826905 \tabularnewline
15 & 224.84 & 224.655938264256 & 0.184061735743569 \tabularnewline
16 & 221.88 & 220.973380767023 & 0.906619232976936 \tabularnewline
17 & 222.37 & 221.231430508379 & 1.1385694916211 \tabularnewline
18 & 221.8 & 220.834228680738 & 0.965771319261677 \tabularnewline
19 & 221.8 & 222.074444288424 & -0.274444288424178 \tabularnewline
20 & 221.8 & 221.732882697481 & 0.0671173025192218 \tabularnewline
21 & 221.9 & 221.48539315236 & 0.414606847640414 \tabularnewline
22 & 220.2 & 220.152619171319 & 0.0473808286808719 \tabularnewline
23 & 219.95 & 219.866049407581 & 0.0839505924187733 \tabularnewline
24 & 220.05 & 220.3919914985 & -0.341991498500306 \tabularnewline
25 & 220.05 & 218.983958723122 & 1.06604127687808 \tabularnewline
26 & 220.05 & 220.35900758398 & -0.30900758398019 \tabularnewline
27 & 220.62 & 219.87701019592 & 0.742989804079883 \tabularnewline
28 & 221.53 & 218.107206250616 & 3.42279374938417 \tabularnewline
29 & 221.61 & 221.304022751772 & 0.305977248227947 \tabularnewline
30 & 221.5 & 222.316619344038 & -0.816619344037747 \tabularnewline
31 & 221.5 & 223.500689472913 & -2.00068947291305 \tabularnewline
32 & 221.87 & 223.603344753279 & -1.73334475327857 \tabularnewline
33 & 222.27 & 223.264440359092 & -0.994440359091755 \tabularnewline
34 & 220.86 & 221.115940754064 & -0.255940754063744 \tabularnewline
35 & 221.49 & 220.519711011055 & 0.970288988944816 \tabularnewline
36 & 221.67 & 221.073665560509 & 0.596334439490846 \tabularnewline
37 & 221.67 & 221.1126445564 & 0.557355443599846 \tabularnewline
38 & 221.72 & 221.618888941675 & 0.101111058325131 \tabularnewline
39 & 221.67 & 222.171488205283 & -0.501488205282612 \tabularnewline
40 & 220.29 & 221.571938408762 & -1.28193840876204 \tabularnewline
41 & 220.75 & 219.931771870835 & 0.818228129165249 \tabularnewline
42 & 219.59 & 219.107356193817 & 0.482643806182693 \tabularnewline
43 & 219.59 & 219.033367314805 & 0.556632685195382 \tabularnewline
44 & 219.59 & 219.899235627487 & -0.309235627486885 \tabularnewline
45 & 219.82 & 220.671471549163 & -0.851471549163392 \tabularnewline
46 & 221.59 & 219.276976688852 & 2.31302331114773 \tabularnewline
47 & 220.9 & 221.2263103563 & -0.326310356299587 \tabularnewline
48 & 221.01 & 221.764268418167 & -0.754268418166902 \tabularnewline
49 & 221.01 & 221.590310213773 & -0.580310213773373 \tabularnewline
50 & 219.69 & 221.365581669637 & -1.67558166963667 \tabularnewline
51 & 221 & 220.388835847726 & 0.611164152274341 \tabularnewline
52 & 219.82 & 219.36635337118 & 0.453646628819513 \tabularnewline
53 & 218.04 & 219.775227201818 & -1.73522720181825 \tabularnewline
54 & 217.97 & 217.429828273406 & 0.540171726594394 \tabularnewline
55 & 217.97 & 216.915442146318 & 1.05455785368153 \tabularnewline
56 & 217.53 & 217.0394137969 & 0.490586203100065 \tabularnewline
57 & 217 & 217.592922494082 & -0.592922494081904 \tabularnewline
58 & 217.18 & 218.177322925281 & -0.997322925281338 \tabularnewline
59 & 217.68 & 216.459931112049 & 1.22006888795107 \tabularnewline
60 & 217.71 & 216.650017581333 & 1.05998241866664 \tabularnewline
61 & 217.71 & 217.103699609104 & 0.606300390896308 \tabularnewline
62 & 218.5 & 216.867256720298 & 1.63274327970214 \tabularnewline
63 & 218.8 & 219.577170681251 & -0.777170681250595 \tabularnewline
64 & 218.94 & 218.873544460239 & 0.0664555397613071 \tabularnewline
65 & 220 & 218.545343383221 & 1.45465661677861 \tabularnewline
66 & 219.89 & 220.248344968925 & -0.35834496892474 \tabularnewline
67 & 219.89 & 221.166308175194 & -1.27630817519389 \tabularnewline
68 & 220.08 & 220.942793112076 & -0.862793112076076 \tabularnewline
69 & 220.16 & 220.743144117492 & -0.58314411749177 \tabularnewline
70 & 221 & 221.420382242491 & -0.420382242490831 \tabularnewline
71 & 222.16 & 221.758250681378 & 0.40174931862154 \tabularnewline
72 & 221.5 & 221.865825705653 & -0.365825705653293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204996&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]226.33[/C][C]228.542465277778[/C][C]-2.21246527777777[/C][/ROW]
[ROW][C]14[/C][C]226.22[/C][C]227.174433198827[/C][C]-0.954433198826905[/C][/ROW]
[ROW][C]15[/C][C]224.84[/C][C]224.655938264256[/C][C]0.184061735743569[/C][/ROW]
[ROW][C]16[/C][C]221.88[/C][C]220.973380767023[/C][C]0.906619232976936[/C][/ROW]
[ROW][C]17[/C][C]222.37[/C][C]221.231430508379[/C][C]1.1385694916211[/C][/ROW]
[ROW][C]18[/C][C]221.8[/C][C]220.834228680738[/C][C]0.965771319261677[/C][/ROW]
[ROW][C]19[/C][C]221.8[/C][C]222.074444288424[/C][C]-0.274444288424178[/C][/ROW]
[ROW][C]20[/C][C]221.8[/C][C]221.732882697481[/C][C]0.0671173025192218[/C][/ROW]
[ROW][C]21[/C][C]221.9[/C][C]221.48539315236[/C][C]0.414606847640414[/C][/ROW]
[ROW][C]22[/C][C]220.2[/C][C]220.152619171319[/C][C]0.0473808286808719[/C][/ROW]
[ROW][C]23[/C][C]219.95[/C][C]219.866049407581[/C][C]0.0839505924187733[/C][/ROW]
[ROW][C]24[/C][C]220.05[/C][C]220.3919914985[/C][C]-0.341991498500306[/C][/ROW]
[ROW][C]25[/C][C]220.05[/C][C]218.983958723122[/C][C]1.06604127687808[/C][/ROW]
[ROW][C]26[/C][C]220.05[/C][C]220.35900758398[/C][C]-0.30900758398019[/C][/ROW]
[ROW][C]27[/C][C]220.62[/C][C]219.87701019592[/C][C]0.742989804079883[/C][/ROW]
[ROW][C]28[/C][C]221.53[/C][C]218.107206250616[/C][C]3.42279374938417[/C][/ROW]
[ROW][C]29[/C][C]221.61[/C][C]221.304022751772[/C][C]0.305977248227947[/C][/ROW]
[ROW][C]30[/C][C]221.5[/C][C]222.316619344038[/C][C]-0.816619344037747[/C][/ROW]
[ROW][C]31[/C][C]221.5[/C][C]223.500689472913[/C][C]-2.00068947291305[/C][/ROW]
[ROW][C]32[/C][C]221.87[/C][C]223.603344753279[/C][C]-1.73334475327857[/C][/ROW]
[ROW][C]33[/C][C]222.27[/C][C]223.264440359092[/C][C]-0.994440359091755[/C][/ROW]
[ROW][C]34[/C][C]220.86[/C][C]221.115940754064[/C][C]-0.255940754063744[/C][/ROW]
[ROW][C]35[/C][C]221.49[/C][C]220.519711011055[/C][C]0.970288988944816[/C][/ROW]
[ROW][C]36[/C][C]221.67[/C][C]221.073665560509[/C][C]0.596334439490846[/C][/ROW]
[ROW][C]37[/C][C]221.67[/C][C]221.1126445564[/C][C]0.557355443599846[/C][/ROW]
[ROW][C]38[/C][C]221.72[/C][C]221.618888941675[/C][C]0.101111058325131[/C][/ROW]
[ROW][C]39[/C][C]221.67[/C][C]222.171488205283[/C][C]-0.501488205282612[/C][/ROW]
[ROW][C]40[/C][C]220.29[/C][C]221.571938408762[/C][C]-1.28193840876204[/C][/ROW]
[ROW][C]41[/C][C]220.75[/C][C]219.931771870835[/C][C]0.818228129165249[/C][/ROW]
[ROW][C]42[/C][C]219.59[/C][C]219.107356193817[/C][C]0.482643806182693[/C][/ROW]
[ROW][C]43[/C][C]219.59[/C][C]219.033367314805[/C][C]0.556632685195382[/C][/ROW]
[ROW][C]44[/C][C]219.59[/C][C]219.899235627487[/C][C]-0.309235627486885[/C][/ROW]
[ROW][C]45[/C][C]219.82[/C][C]220.671471549163[/C][C]-0.851471549163392[/C][/ROW]
[ROW][C]46[/C][C]221.59[/C][C]219.276976688852[/C][C]2.31302331114773[/C][/ROW]
[ROW][C]47[/C][C]220.9[/C][C]221.2263103563[/C][C]-0.326310356299587[/C][/ROW]
[ROW][C]48[/C][C]221.01[/C][C]221.764268418167[/C][C]-0.754268418166902[/C][/ROW]
[ROW][C]49[/C][C]221.01[/C][C]221.590310213773[/C][C]-0.580310213773373[/C][/ROW]
[ROW][C]50[/C][C]219.69[/C][C]221.365581669637[/C][C]-1.67558166963667[/C][/ROW]
[ROW][C]51[/C][C]221[/C][C]220.388835847726[/C][C]0.611164152274341[/C][/ROW]
[ROW][C]52[/C][C]219.82[/C][C]219.36635337118[/C][C]0.453646628819513[/C][/ROW]
[ROW][C]53[/C][C]218.04[/C][C]219.775227201818[/C][C]-1.73522720181825[/C][/ROW]
[ROW][C]54[/C][C]217.97[/C][C]217.429828273406[/C][C]0.540171726594394[/C][/ROW]
[ROW][C]55[/C][C]217.97[/C][C]216.915442146318[/C][C]1.05455785368153[/C][/ROW]
[ROW][C]56[/C][C]217.53[/C][C]217.0394137969[/C][C]0.490586203100065[/C][/ROW]
[ROW][C]57[/C][C]217[/C][C]217.592922494082[/C][C]-0.592922494081904[/C][/ROW]
[ROW][C]58[/C][C]217.18[/C][C]218.177322925281[/C][C]-0.997322925281338[/C][/ROW]
[ROW][C]59[/C][C]217.68[/C][C]216.459931112049[/C][C]1.22006888795107[/C][/ROW]
[ROW][C]60[/C][C]217.71[/C][C]216.650017581333[/C][C]1.05998241866664[/C][/ROW]
[ROW][C]61[/C][C]217.71[/C][C]217.103699609104[/C][C]0.606300390896308[/C][/ROW]
[ROW][C]62[/C][C]218.5[/C][C]216.867256720298[/C][C]1.63274327970214[/C][/ROW]
[ROW][C]63[/C][C]218.8[/C][C]219.577170681251[/C][C]-0.777170681250595[/C][/ROW]
[ROW][C]64[/C][C]218.94[/C][C]218.873544460239[/C][C]0.0664555397613071[/C][/ROW]
[ROW][C]65[/C][C]220[/C][C]218.545343383221[/C][C]1.45465661677861[/C][/ROW]
[ROW][C]66[/C][C]219.89[/C][C]220.248344968925[/C][C]-0.35834496892474[/C][/ROW]
[ROW][C]67[/C][C]219.89[/C][C]221.166308175194[/C][C]-1.27630817519389[/C][/ROW]
[ROW][C]68[/C][C]220.08[/C][C]220.942793112076[/C][C]-0.862793112076076[/C][/ROW]
[ROW][C]69[/C][C]220.16[/C][C]220.743144117492[/C][C]-0.58314411749177[/C][/ROW]
[ROW][C]70[/C][C]221[/C][C]221.420382242491[/C][C]-0.420382242490831[/C][/ROW]
[ROW][C]71[/C][C]222.16[/C][C]221.758250681378[/C][C]0.40174931862154[/C][/ROW]
[ROW][C]72[/C][C]221.5[/C][C]221.865825705653[/C][C]-0.365825705653293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204996&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204996&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
13226.33228.542465277778-2.21246527777777
14226.22227.174433198827-0.954433198826905
15224.84224.6559382642560.184061735743569
16221.88220.9733807670230.906619232976936
17222.37221.2314305083791.1385694916211
18221.8220.8342286807380.965771319261677
19221.8222.074444288424-0.274444288424178
20221.8221.7328826974810.0671173025192218
21221.9221.485393152360.414606847640414
22220.2220.1526191713190.0473808286808719
23219.95219.8660494075810.0839505924187733
24220.05220.3919914985-0.341991498500306
25220.05218.9839587231221.06604127687808
26220.05220.35900758398-0.30900758398019
27220.62219.877010195920.742989804079883
28221.53218.1072062506163.42279374938417
29221.61221.3040227517720.305977248227947
30221.5222.316619344038-0.816619344037747
31221.5223.500689472913-2.00068947291305
32221.87223.603344753279-1.73334475327857
33222.27223.264440359092-0.994440359091755
34220.86221.115940754064-0.255940754063744
35221.49220.5197110110550.970288988944816
36221.67221.0736655605090.596334439490846
37221.67221.11264455640.557355443599846
38221.72221.6188889416750.101111058325131
39221.67222.171488205283-0.501488205282612
40220.29221.571938408762-1.28193840876204
41220.75219.9317718708350.818228129165249
42219.59219.1073561938170.482643806182693
43219.59219.0333673148050.556632685195382
44219.59219.899235627487-0.309235627486885
45219.82220.671471549163-0.851471549163392
46221.59219.2769766888522.31302331114773
47220.9221.2263103563-0.326310356299587
48221.01221.764268418167-0.754268418166902
49221.01221.590310213773-0.580310213773373
50219.69221.365581669637-1.67558166963667
51221220.3888358477260.611164152274341
52219.82219.366353371180.453646628819513
53218.04219.775227201818-1.73522720181825
54217.97217.4298282734060.540171726594394
55217.97216.9154421463181.05455785368153
56217.53217.03941379690.490586203100065
57217217.592922494082-0.592922494081904
58217.18218.177322925281-0.997322925281338
59217.68216.4599311120491.22006888795107
60217.71216.6500175813331.05998241866664
61217.71217.1036996091040.606300390896308
62218.5216.8672567202981.63274327970214
63218.8219.577170681251-0.777170681250595
64218.94218.8735444602390.0664555397613071
65220218.5453433832211.45465661677861
66219.89220.248344968925-0.35834496892474
67219.89221.166308175194-1.27630817519389
68220.08220.942793112076-0.862793112076076
69220.16220.743144117492-0.58314411749177
70221221.420382242491-0.420382242490831
71222.16221.7582506813780.40174931862154
72221.5221.865825705653-0.365825705653293







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73221.45800051357219.407966824507223.508034202633
74221.355765629563218.9678827028223.743648556326
75221.28851396317218.290787731975224.286240194366
76220.790414703959216.95025774649224.630571661427
77220.723353208498215.857723973736225.588982443261
78219.860211702305213.821998058384225.898425346226
79219.431171307063212.0966728094226.765669804727
80219.334849071735210.595860873216228.073837270253
81219.298598960455209.057690902556229.539507018355
82220.147329208932208.314968842648231.979689575217
83221.134315938348207.627036013376234.641595863319
84220.537694612224205.276868634316235.798520590131

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 221.45800051357 & 219.407966824507 & 223.508034202633 \tabularnewline
74 & 221.355765629563 & 218.9678827028 & 223.743648556326 \tabularnewline
75 & 221.28851396317 & 218.290787731975 & 224.286240194366 \tabularnewline
76 & 220.790414703959 & 216.95025774649 & 224.630571661427 \tabularnewline
77 & 220.723353208498 & 215.857723973736 & 225.588982443261 \tabularnewline
78 & 219.860211702305 & 213.821998058384 & 225.898425346226 \tabularnewline
79 & 219.431171307063 & 212.0966728094 & 226.765669804727 \tabularnewline
80 & 219.334849071735 & 210.595860873216 & 228.073837270253 \tabularnewline
81 & 219.298598960455 & 209.057690902556 & 229.539507018355 \tabularnewline
82 & 220.147329208932 & 208.314968842648 & 231.979689575217 \tabularnewline
83 & 221.134315938348 & 207.627036013376 & 234.641595863319 \tabularnewline
84 & 220.537694612224 & 205.276868634316 & 235.798520590131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204996&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]221.45800051357[/C][C]219.407966824507[/C][C]223.508034202633[/C][/ROW]
[ROW][C]74[/C][C]221.355765629563[/C][C]218.9678827028[/C][C]223.743648556326[/C][/ROW]
[ROW][C]75[/C][C]221.28851396317[/C][C]218.290787731975[/C][C]224.286240194366[/C][/ROW]
[ROW][C]76[/C][C]220.790414703959[/C][C]216.95025774649[/C][C]224.630571661427[/C][/ROW]
[ROW][C]77[/C][C]220.723353208498[/C][C]215.857723973736[/C][C]225.588982443261[/C][/ROW]
[ROW][C]78[/C][C]219.860211702305[/C][C]213.821998058384[/C][C]225.898425346226[/C][/ROW]
[ROW][C]79[/C][C]219.431171307063[/C][C]212.0966728094[/C][C]226.765669804727[/C][/ROW]
[ROW][C]80[/C][C]219.334849071735[/C][C]210.595860873216[/C][C]228.073837270253[/C][/ROW]
[ROW][C]81[/C][C]219.298598960455[/C][C]209.057690902556[/C][C]229.539507018355[/C][/ROW]
[ROW][C]82[/C][C]220.147329208932[/C][C]208.314968842648[/C][C]231.979689575217[/C][/ROW]
[ROW][C]83[/C][C]221.134315938348[/C][C]207.627036013376[/C][C]234.641595863319[/C][/ROW]
[ROW][C]84[/C][C]220.537694612224[/C][C]205.276868634316[/C][C]235.798520590131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204996&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204996&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
73221.45800051357219.407966824507223.508034202633
74221.355765629563218.9678827028223.743648556326
75221.28851396317218.290787731975224.286240194366
76220.790414703959216.95025774649224.630571661427
77220.723353208498215.857723973736225.588982443261
78219.860211702305213.821998058384225.898425346226
79219.431171307063212.0966728094226.765669804727
80219.334849071735210.595860873216228.073837270253
81219.298598960455209.057690902556229.539507018355
82220.147329208932208.314968842648231.979689575217
83221.134315938348207.627036013376234.641595863319
84220.537694612224205.276868634316235.798520590131



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')