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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 14:26:37 -0400
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/May/26/t136959515717el0oa2rmh00dg.htm/, Retrieved Mon, 29 Apr 2024 08:32:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210655, Retrieved Mon, 29 Apr 2024 08:32:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [10] [2013-05-26 18:26:37] [2e0e1d085c58e19aaf0ceb191a09c63d] [Current]
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Dataseries X:
98,01
99,2
100,7
106,41
107,51
107,1
99,75
98,96
107,26
107,11
107,2
107,65
104,78
105,56
107,95
107,11
107,47
107,06
99,71
99,6
107,19
107,26
113,24
113,52
110,48
111,41
115,5
118,32
118,42
117,5
110,23
109,19
118,41
118,3
116,1
114,11
113,41
114,33
116,61
123,64
123,77
123,39
116,03
114,95
123,4
123,53
114,45
114,26
114,35
112,77
115,31
114,93
116,38
115,07
105
103,43
114,52
115,04
117,16
115
116,22
112,92
116,56
114,32
113,22
111,56
103,87
102,85
112,27
112,76
118,55
122,73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210655&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210655&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210655&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.936933289425276
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.936933289425276 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210655&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]0.936933289425276[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210655&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210655&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
alpha0.936933289425276
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13104.78103.7717387820511.00826121794871
14105.56105.608785533332-0.0487855333321647
15107.95108.066699994859-0.116699994859161
16107.11107.251399803215-0.141399803214767
17107.47107.3583742055460.111625794453758
18107.06106.6940833800770.365916619923212
1999.71102.136796094185-2.42679609418511
2099.698.66333996531070.936660034689254
21107.19107.4112178511-0.221217851100278
22107.26106.8600747339380.399925266062453
23113.24107.4346512807425.80534871925802
24113.52113.4645823376190.0554176623812168
25110.48110.850799293824-0.370799293823538
26111.41111.3290938819660.0809061180338375
27115.5113.904237627331.59576237267046
28118.32114.6918426990473.62815730095316
29118.42118.3465981307990.0734018692010636
30117.5117.662531323199-0.162531323199417
31110.23112.433996363209-2.20399636320879
32109.19109.381410833372-0.191410833371648
33118.41116.999338020541.41066197945993
34118.3118.0163308941660.283669105833553
35116.1118.822885450808-2.72288545080816
36114.11116.499800775947-2.38980077594717
37113.41111.5681310759471.84186892405343
38114.33114.1480357503460.18196424965393
39116.61116.913401224365-0.303401224364919
40123.64116.0497931626717.59020683732933
41123.77123.1925379674270.577462032572669
42123.39122.9658623764040.42413762359628
43116.03118.158248597711-2.12824859771138
44114.95115.303560820085-0.353560820085434
45123.4122.8706017492280.529398250771663
46123.53122.9908335653030.539166434697123
47114.45123.847158568665-9.39715856866528
48114.26115.291731781754-1.03173178175406
49114.35111.8993596199672.45064038003295
50112.77114.944957809444-2.17495780944368
51115.31115.47143414184-0.161434141840289
52114.93115.238663660783-0.308663660783125
53116.38114.5384230000631.84157699993696
54115.07115.486469137499-0.416469137498808
55105109.730292297926-4.73029229792638
56103.43104.549586877462-1.11958687746173
57114.52111.4545978170533.06540218294734
58115.04113.9515121865241.08848781347555
59117.16114.6958633430942.46413665690611
60115117.781258858726-2.78125885872576
61116.22112.9693182950143.25068170498604
62112.92116.472780572504-3.55278057250436
63116.56115.8353152056420.724684794358367
64114.32116.42349377284-2.1034937728399
65113.22114.177225636687-0.957225636686559
66111.56112.360572871124-0.800572871124473
67103.87105.972457820196-2.10245782019639
68102.85103.481573314739-0.631573314739484
69112.27111.1077539007671.16224609923289
70112.76111.6968604940641.06313950593591
71118.55112.504219624936.04578037506985
72122.73118.6145665301364.11543346986377

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 104.78 & 103.771738782051 & 1.00826121794871 \tabularnewline
14 & 105.56 & 105.608785533332 & -0.0487855333321647 \tabularnewline
15 & 107.95 & 108.066699994859 & -0.116699994859161 \tabularnewline
16 & 107.11 & 107.251399803215 & -0.141399803214767 \tabularnewline
17 & 107.47 & 107.358374205546 & 0.111625794453758 \tabularnewline
18 & 107.06 & 106.694083380077 & 0.365916619923212 \tabularnewline
19 & 99.71 & 102.136796094185 & -2.42679609418511 \tabularnewline
20 & 99.6 & 98.6633399653107 & 0.936660034689254 \tabularnewline
21 & 107.19 & 107.4112178511 & -0.221217851100278 \tabularnewline
22 & 107.26 & 106.860074733938 & 0.399925266062453 \tabularnewline
23 & 113.24 & 107.434651280742 & 5.80534871925802 \tabularnewline
24 & 113.52 & 113.464582337619 & 0.0554176623812168 \tabularnewline
25 & 110.48 & 110.850799293824 & -0.370799293823538 \tabularnewline
26 & 111.41 & 111.329093881966 & 0.0809061180338375 \tabularnewline
27 & 115.5 & 113.90423762733 & 1.59576237267046 \tabularnewline
28 & 118.32 & 114.691842699047 & 3.62815730095316 \tabularnewline
29 & 118.42 & 118.346598130799 & 0.0734018692010636 \tabularnewline
30 & 117.5 & 117.662531323199 & -0.162531323199417 \tabularnewline
31 & 110.23 & 112.433996363209 & -2.20399636320879 \tabularnewline
32 & 109.19 & 109.381410833372 & -0.191410833371648 \tabularnewline
33 & 118.41 & 116.99933802054 & 1.41066197945993 \tabularnewline
34 & 118.3 & 118.016330894166 & 0.283669105833553 \tabularnewline
35 & 116.1 & 118.822885450808 & -2.72288545080816 \tabularnewline
36 & 114.11 & 116.499800775947 & -2.38980077594717 \tabularnewline
37 & 113.41 & 111.568131075947 & 1.84186892405343 \tabularnewline
38 & 114.33 & 114.148035750346 & 0.18196424965393 \tabularnewline
39 & 116.61 & 116.913401224365 & -0.303401224364919 \tabularnewline
40 & 123.64 & 116.049793162671 & 7.59020683732933 \tabularnewline
41 & 123.77 & 123.192537967427 & 0.577462032572669 \tabularnewline
42 & 123.39 & 122.965862376404 & 0.42413762359628 \tabularnewline
43 & 116.03 & 118.158248597711 & -2.12824859771138 \tabularnewline
44 & 114.95 & 115.303560820085 & -0.353560820085434 \tabularnewline
45 & 123.4 & 122.870601749228 & 0.529398250771663 \tabularnewline
46 & 123.53 & 122.990833565303 & 0.539166434697123 \tabularnewline
47 & 114.45 & 123.847158568665 & -9.39715856866528 \tabularnewline
48 & 114.26 & 115.291731781754 & -1.03173178175406 \tabularnewline
49 & 114.35 & 111.899359619967 & 2.45064038003295 \tabularnewline
50 & 112.77 & 114.944957809444 & -2.17495780944368 \tabularnewline
51 & 115.31 & 115.47143414184 & -0.161434141840289 \tabularnewline
52 & 114.93 & 115.238663660783 & -0.308663660783125 \tabularnewline
53 & 116.38 & 114.538423000063 & 1.84157699993696 \tabularnewline
54 & 115.07 & 115.486469137499 & -0.416469137498808 \tabularnewline
55 & 105 & 109.730292297926 & -4.73029229792638 \tabularnewline
56 & 103.43 & 104.549586877462 & -1.11958687746173 \tabularnewline
57 & 114.52 & 111.454597817053 & 3.06540218294734 \tabularnewline
58 & 115.04 & 113.951512186524 & 1.08848781347555 \tabularnewline
59 & 117.16 & 114.695863343094 & 2.46413665690611 \tabularnewline
60 & 115 & 117.781258858726 & -2.78125885872576 \tabularnewline
61 & 116.22 & 112.969318295014 & 3.25068170498604 \tabularnewline
62 & 112.92 & 116.472780572504 & -3.55278057250436 \tabularnewline
63 & 116.56 & 115.835315205642 & 0.724684794358367 \tabularnewline
64 & 114.32 & 116.42349377284 & -2.1034937728399 \tabularnewline
65 & 113.22 & 114.177225636687 & -0.957225636686559 \tabularnewline
66 & 111.56 & 112.360572871124 & -0.800572871124473 \tabularnewline
67 & 103.87 & 105.972457820196 & -2.10245782019639 \tabularnewline
68 & 102.85 & 103.481573314739 & -0.631573314739484 \tabularnewline
69 & 112.27 & 111.107753900767 & 1.16224609923289 \tabularnewline
70 & 112.76 & 111.696860494064 & 1.06313950593591 \tabularnewline
71 & 118.55 & 112.50421962493 & 6.04578037506985 \tabularnewline
72 & 122.73 & 118.614566530136 & 4.11543346986377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210655&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]104.78[/C][C]103.771738782051[/C][C]1.00826121794871[/C][/ROW]
[ROW][C]14[/C][C]105.56[/C][C]105.608785533332[/C][C]-0.0487855333321647[/C][/ROW]
[ROW][C]15[/C][C]107.95[/C][C]108.066699994859[/C][C]-0.116699994859161[/C][/ROW]
[ROW][C]16[/C][C]107.11[/C][C]107.251399803215[/C][C]-0.141399803214767[/C][/ROW]
[ROW][C]17[/C][C]107.47[/C][C]107.358374205546[/C][C]0.111625794453758[/C][/ROW]
[ROW][C]18[/C][C]107.06[/C][C]106.694083380077[/C][C]0.365916619923212[/C][/ROW]
[ROW][C]19[/C][C]99.71[/C][C]102.136796094185[/C][C]-2.42679609418511[/C][/ROW]
[ROW][C]20[/C][C]99.6[/C][C]98.6633399653107[/C][C]0.936660034689254[/C][/ROW]
[ROW][C]21[/C][C]107.19[/C][C]107.4112178511[/C][C]-0.221217851100278[/C][/ROW]
[ROW][C]22[/C][C]107.26[/C][C]106.860074733938[/C][C]0.399925266062453[/C][/ROW]
[ROW][C]23[/C][C]113.24[/C][C]107.434651280742[/C][C]5.80534871925802[/C][/ROW]
[ROW][C]24[/C][C]113.52[/C][C]113.464582337619[/C][C]0.0554176623812168[/C][/ROW]
[ROW][C]25[/C][C]110.48[/C][C]110.850799293824[/C][C]-0.370799293823538[/C][/ROW]
[ROW][C]26[/C][C]111.41[/C][C]111.329093881966[/C][C]0.0809061180338375[/C][/ROW]
[ROW][C]27[/C][C]115.5[/C][C]113.90423762733[/C][C]1.59576237267046[/C][/ROW]
[ROW][C]28[/C][C]118.32[/C][C]114.691842699047[/C][C]3.62815730095316[/C][/ROW]
[ROW][C]29[/C][C]118.42[/C][C]118.346598130799[/C][C]0.0734018692010636[/C][/ROW]
[ROW][C]30[/C][C]117.5[/C][C]117.662531323199[/C][C]-0.162531323199417[/C][/ROW]
[ROW][C]31[/C][C]110.23[/C][C]112.433996363209[/C][C]-2.20399636320879[/C][/ROW]
[ROW][C]32[/C][C]109.19[/C][C]109.381410833372[/C][C]-0.191410833371648[/C][/ROW]
[ROW][C]33[/C][C]118.41[/C][C]116.99933802054[/C][C]1.41066197945993[/C][/ROW]
[ROW][C]34[/C][C]118.3[/C][C]118.016330894166[/C][C]0.283669105833553[/C][/ROW]
[ROW][C]35[/C][C]116.1[/C][C]118.822885450808[/C][C]-2.72288545080816[/C][/ROW]
[ROW][C]36[/C][C]114.11[/C][C]116.499800775947[/C][C]-2.38980077594717[/C][/ROW]
[ROW][C]37[/C][C]113.41[/C][C]111.568131075947[/C][C]1.84186892405343[/C][/ROW]
[ROW][C]38[/C][C]114.33[/C][C]114.148035750346[/C][C]0.18196424965393[/C][/ROW]
[ROW][C]39[/C][C]116.61[/C][C]116.913401224365[/C][C]-0.303401224364919[/C][/ROW]
[ROW][C]40[/C][C]123.64[/C][C]116.049793162671[/C][C]7.59020683732933[/C][/ROW]
[ROW][C]41[/C][C]123.77[/C][C]123.192537967427[/C][C]0.577462032572669[/C][/ROW]
[ROW][C]42[/C][C]123.39[/C][C]122.965862376404[/C][C]0.42413762359628[/C][/ROW]
[ROW][C]43[/C][C]116.03[/C][C]118.158248597711[/C][C]-2.12824859771138[/C][/ROW]
[ROW][C]44[/C][C]114.95[/C][C]115.303560820085[/C][C]-0.353560820085434[/C][/ROW]
[ROW][C]45[/C][C]123.4[/C][C]122.870601749228[/C][C]0.529398250771663[/C][/ROW]
[ROW][C]46[/C][C]123.53[/C][C]122.990833565303[/C][C]0.539166434697123[/C][/ROW]
[ROW][C]47[/C][C]114.45[/C][C]123.847158568665[/C][C]-9.39715856866528[/C][/ROW]
[ROW][C]48[/C][C]114.26[/C][C]115.291731781754[/C][C]-1.03173178175406[/C][/ROW]
[ROW][C]49[/C][C]114.35[/C][C]111.899359619967[/C][C]2.45064038003295[/C][/ROW]
[ROW][C]50[/C][C]112.77[/C][C]114.944957809444[/C][C]-2.17495780944368[/C][/ROW]
[ROW][C]51[/C][C]115.31[/C][C]115.47143414184[/C][C]-0.161434141840289[/C][/ROW]
[ROW][C]52[/C][C]114.93[/C][C]115.238663660783[/C][C]-0.308663660783125[/C][/ROW]
[ROW][C]53[/C][C]116.38[/C][C]114.538423000063[/C][C]1.84157699993696[/C][/ROW]
[ROW][C]54[/C][C]115.07[/C][C]115.486469137499[/C][C]-0.416469137498808[/C][/ROW]
[ROW][C]55[/C][C]105[/C][C]109.730292297926[/C][C]-4.73029229792638[/C][/ROW]
[ROW][C]56[/C][C]103.43[/C][C]104.549586877462[/C][C]-1.11958687746173[/C][/ROW]
[ROW][C]57[/C][C]114.52[/C][C]111.454597817053[/C][C]3.06540218294734[/C][/ROW]
[ROW][C]58[/C][C]115.04[/C][C]113.951512186524[/C][C]1.08848781347555[/C][/ROW]
[ROW][C]59[/C][C]117.16[/C][C]114.695863343094[/C][C]2.46413665690611[/C][/ROW]
[ROW][C]60[/C][C]115[/C][C]117.781258858726[/C][C]-2.78125885872576[/C][/ROW]
[ROW][C]61[/C][C]116.22[/C][C]112.969318295014[/C][C]3.25068170498604[/C][/ROW]
[ROW][C]62[/C][C]112.92[/C][C]116.472780572504[/C][C]-3.55278057250436[/C][/ROW]
[ROW][C]63[/C][C]116.56[/C][C]115.835315205642[/C][C]0.724684794358367[/C][/ROW]
[ROW][C]64[/C][C]114.32[/C][C]116.42349377284[/C][C]-2.1034937728399[/C][/ROW]
[ROW][C]65[/C][C]113.22[/C][C]114.177225636687[/C][C]-0.957225636686559[/C][/ROW]
[ROW][C]66[/C][C]111.56[/C][C]112.360572871124[/C][C]-0.800572871124473[/C][/ROW]
[ROW][C]67[/C][C]103.87[/C][C]105.972457820196[/C][C]-2.10245782019639[/C][/ROW]
[ROW][C]68[/C][C]102.85[/C][C]103.481573314739[/C][C]-0.631573314739484[/C][/ROW]
[ROW][C]69[/C][C]112.27[/C][C]111.107753900767[/C][C]1.16224609923289[/C][/ROW]
[ROW][C]70[/C][C]112.76[/C][C]111.696860494064[/C][C]1.06313950593591[/C][/ROW]
[ROW][C]71[/C][C]118.55[/C][C]112.50421962493[/C][C]6.04578037506985[/C][/ROW]
[ROW][C]72[/C][C]122.73[/C][C]118.614566530136[/C][C]4.11543346986377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210655&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210655&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
13104.78103.7717387820511.00826121794871
14105.56105.608785533332-0.0487855333321647
15107.95108.066699994859-0.116699994859161
16107.11107.251399803215-0.141399803214767
17107.47107.3583742055460.111625794453758
18107.06106.6940833800770.365916619923212
1999.71102.136796094185-2.42679609418511
2099.698.66333996531070.936660034689254
21107.19107.4112178511-0.221217851100278
22107.26106.8600747339380.399925266062453
23113.24107.4346512807425.80534871925802
24113.52113.4645823376190.0554176623812168
25110.48110.850799293824-0.370799293823538
26111.41111.3290938819660.0809061180338375
27115.5113.904237627331.59576237267046
28118.32114.6918426990473.62815730095316
29118.42118.3465981307990.0734018692010636
30117.5117.662531323199-0.162531323199417
31110.23112.433996363209-2.20399636320879
32109.19109.381410833372-0.191410833371648
33118.41116.999338020541.41066197945993
34118.3118.0163308941660.283669105833553
35116.1118.822885450808-2.72288545080816
36114.11116.499800775947-2.38980077594717
37113.41111.5681310759471.84186892405343
38114.33114.1480357503460.18196424965393
39116.61116.913401224365-0.303401224364919
40123.64116.0497931626717.59020683732933
41123.77123.1925379674270.577462032572669
42123.39122.9658623764040.42413762359628
43116.03118.158248597711-2.12824859771138
44114.95115.303560820085-0.353560820085434
45123.4122.8706017492280.529398250771663
46123.53122.9908335653030.539166434697123
47114.45123.847158568665-9.39715856866528
48114.26115.291731781754-1.03173178175406
49114.35111.8993596199672.45064038003295
50112.77114.944957809444-2.17495780944368
51115.31115.47143414184-0.161434141840289
52114.93115.238663660783-0.308663660783125
53116.38114.5384230000631.84157699993696
54115.07115.486469137499-0.416469137498808
55105109.730292297926-4.73029229792638
56103.43104.549586877462-1.11958687746173
57114.52111.4545978170533.06540218294734
58115.04113.9515121865241.08848781347555
59117.16114.6958633430942.46413665690611
60115117.781258858726-2.78125885872576
61116.22112.9693182950143.25068170498604
62112.92116.472780572504-3.55278057250436
63116.56115.8353152056420.724684794358367
64114.32116.42349377284-2.1034937728399
65113.22114.177225636687-0.957225636686559
66111.56112.360572871124-0.800572871124473
67103.87105.972457820196-2.10245782019639
68102.85103.481573314739-0.631573314739484
69112.27111.1077539007671.16224609923289
70112.76111.6968604940641.06313950593591
71118.55112.504219624936.04578037506985
72122.73118.6145665301364.11543346986377







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73120.644781245739115.633073701104125.656488790375
74120.673499634142113.80573387418127.541265394104
75123.634518325967115.314950996205131.95408565573
76123.36535166584113.812122129437132.918581202243
77123.162208230343112.517341458234133.807075002452
78122.25229160391110.617766146604133.886817061216
79116.532154325265103.985793233799129.078515416731
80116.103896388557102.707621881882129.500170895232
81124.434949327681110.239556952725138.630341702636
82123.928858533266108.976997154171138.880719912362
83124.054365639309108.382507015635139.726224262984
84124.378479020979108.018278938425140.738679103533

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 120.644781245739 & 115.633073701104 & 125.656488790375 \tabularnewline
74 & 120.673499634142 & 113.80573387418 & 127.541265394104 \tabularnewline
75 & 123.634518325967 & 115.314950996205 & 131.95408565573 \tabularnewline
76 & 123.36535166584 & 113.812122129437 & 132.918581202243 \tabularnewline
77 & 123.162208230343 & 112.517341458234 & 133.807075002452 \tabularnewline
78 & 122.25229160391 & 110.617766146604 & 133.886817061216 \tabularnewline
79 & 116.532154325265 & 103.985793233799 & 129.078515416731 \tabularnewline
80 & 116.103896388557 & 102.707621881882 & 129.500170895232 \tabularnewline
81 & 124.434949327681 & 110.239556952725 & 138.630341702636 \tabularnewline
82 & 123.928858533266 & 108.976997154171 & 138.880719912362 \tabularnewline
83 & 124.054365639309 & 108.382507015635 & 139.726224262984 \tabularnewline
84 & 124.378479020979 & 108.018278938425 & 140.738679103533 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210655&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]120.644781245739[/C][C]115.633073701104[/C][C]125.656488790375[/C][/ROW]
[ROW][C]74[/C][C]120.673499634142[/C][C]113.80573387418[/C][C]127.541265394104[/C][/ROW]
[ROW][C]75[/C][C]123.634518325967[/C][C]115.314950996205[/C][C]131.95408565573[/C][/ROW]
[ROW][C]76[/C][C]123.36535166584[/C][C]113.812122129437[/C][C]132.918581202243[/C][/ROW]
[ROW][C]77[/C][C]123.162208230343[/C][C]112.517341458234[/C][C]133.807075002452[/C][/ROW]
[ROW][C]78[/C][C]122.25229160391[/C][C]110.617766146604[/C][C]133.886817061216[/C][/ROW]
[ROW][C]79[/C][C]116.532154325265[/C][C]103.985793233799[/C][C]129.078515416731[/C][/ROW]
[ROW][C]80[/C][C]116.103896388557[/C][C]102.707621881882[/C][C]129.500170895232[/C][/ROW]
[ROW][C]81[/C][C]124.434949327681[/C][C]110.239556952725[/C][C]138.630341702636[/C][/ROW]
[ROW][C]82[/C][C]123.928858533266[/C][C]108.976997154171[/C][C]138.880719912362[/C][/ROW]
[ROW][C]83[/C][C]124.054365639309[/C][C]108.382507015635[/C][C]139.726224262984[/C][/ROW]
[ROW][C]84[/C][C]124.378479020979[/C][C]108.018278938425[/C][C]140.738679103533[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210655&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210655&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
73120.644781245739115.633073701104125.656488790375
74120.673499634142113.80573387418127.541265394104
75123.634518325967115.314950996205131.95408565573
76123.36535166584113.812122129437132.918581202243
77123.162208230343112.517341458234133.807075002452
78122.25229160391110.617766146604133.886817061216
79116.532154325265103.985793233799129.078515416731
80116.103896388557102.707621881882129.500170895232
81124.434949327681110.239556952725138.630341702636
82123.928858533266108.976997154171138.880719912362
83124.054365639309108.382507015635139.726224262984
84124.378479020979108.018278938425140.738679103533



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')