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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 20:47:04 -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/t1369615630w2rbnbbfbxxpcbs.htm/, Retrieved Mon, 29 Apr 2024 16:24:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210719, Retrieved Mon, 29 Apr 2024 16:24:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact47
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-05-27 00:47:04] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
106,1
106,17
105,75
106,49
106,61
106,61
106,61
106,61
106,92
106,94
107,28
107,36
107,36
107,39
107,46
107,51
108,21
108,33
108,33
108,36
108,89
109,3
109,55
109,45
109,45
109,4
109,45
109,5
109,91
109,9
109,9
109,92
109,74
110,28
110,97
111,02
111,02
111
111,43
111,52
112,29
112,27
112,27
112,39
112,31
112,91
112,9
113,08
113,08
113,54
114
115,28
116,4
116,56
116,56
116,59
116,96
117,17
117,83
117,84
117,84
117,84
117,69
117,9
118,05
118,08
118,08
118,08
118,16
118,53
118,5
118,62




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=210719&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=210719&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210719&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
alpha0.953856088022835
beta0.0154438423748729
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.953856088022835 \tabularnewline
beta & 0.0154438423748729 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210719&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]0.953856088022835[/C][/ROW]
[ROW][C]beta[/C][C]0.0154438423748729[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210719&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210719&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
alpha0.953856088022835
beta0.0154438423748729
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13107.36106.6076949786330.752305021367448
14107.39107.364766954130.025233045870408
15107.46107.4582719458240.00172805417585664
16107.51107.4839653477420.0260346522577635
17108.21108.1707272679690.0392727320307955
18108.33108.3019449457720.028055054227849
19108.33108.34912585801-0.0191258580102698
20108.36108.383104556307-0.023104556306663
21108.89108.70419779110.185802208900213
22109.3108.9456284391180.354371560881518
23109.55109.677653642538-0.127653642538149
24109.45109.658849012698-0.208849012697769
25109.45109.50923338418-0.0592333841799189
26109.4109.461942712852-0.0619427128518737
27109.45109.473203907498-0.0232039074977166
28109.5109.4778640731230.0221359268765582
29109.91110.163087259896-0.253087259896446
30109.9110.012180370256-0.112180370255658
31109.9109.918616339004-0.0186163390039837
32109.92109.948101540002-0.0281015400020692
33109.74110.269198622879-0.529198622878695
34110.28109.8209974774720.459002522527868
35110.97110.6167220256090.353277974391332
36111.02111.04613396931-0.0261339693103366
37111.02111.073621354927-0.0536213549268894
38111111.02755671202-0.0275567120200151
39111.43111.0699092892630.360090710736714
40111.52111.4444204345190.0755795654809077
41112.29112.1708594931240.119140506876064
42112.27112.389927889172-0.11992788917162
43112.27112.301598689092-0.0315986890915241
44112.39112.3263791053410.0636208946593371
45112.31112.721310986253-0.411310986253142
46112.91112.4423611491390.467638850861263
47112.9113.252776192623-0.352776192622542
48113.08112.9921367172280.087863282771707
49113.08113.129702214846-0.0497022148462491
50113.54113.0912458403890.448754159611042
51114113.6155018912940.384498108706026
52115.28114.0102091551991.26979084480055
53116.4115.9053995848280.494600415172471
54116.56116.5047377249560.0552622750438303
55116.56116.623337922061-0.0633379220611374
56116.59116.657517262371-0.0675172623708278
57116.96116.9387949566650.0212050433349447
58117.17117.1526807906660.0173192093344738
59117.83117.5287842320940.301215767906356
60117.84117.955011576434-0.115011576434114
61117.84117.93244703103-0.0924470310295078
62117.84117.915320484675-0.0753204846752453
63117.69117.968100974166-0.278100974166094
64117.9117.7932553115730.106744688427241
65118.05118.54778406876-0.497784068759742
66118.08118.170125732823-0.0901257328232958
67118.08118.132300562234-0.0523005622342936
68118.08118.164704243679-0.0847042436794254
69118.16118.421317979951-0.261317979951016
70118.53118.3490122510410.180987748958572
71118.5118.880217108151-0.380217108150759
72118.62118.6130959560020.00690404399783517

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 107.36 & 106.607694978633 & 0.752305021367448 \tabularnewline
14 & 107.39 & 107.36476695413 & 0.025233045870408 \tabularnewline
15 & 107.46 & 107.458271945824 & 0.00172805417585664 \tabularnewline
16 & 107.51 & 107.483965347742 & 0.0260346522577635 \tabularnewline
17 & 108.21 & 108.170727267969 & 0.0392727320307955 \tabularnewline
18 & 108.33 & 108.301944945772 & 0.028055054227849 \tabularnewline
19 & 108.33 & 108.34912585801 & -0.0191258580102698 \tabularnewline
20 & 108.36 & 108.383104556307 & -0.023104556306663 \tabularnewline
21 & 108.89 & 108.7041977911 & 0.185802208900213 \tabularnewline
22 & 109.3 & 108.945628439118 & 0.354371560881518 \tabularnewline
23 & 109.55 & 109.677653642538 & -0.127653642538149 \tabularnewline
24 & 109.45 & 109.658849012698 & -0.208849012697769 \tabularnewline
25 & 109.45 & 109.50923338418 & -0.0592333841799189 \tabularnewline
26 & 109.4 & 109.461942712852 & -0.0619427128518737 \tabularnewline
27 & 109.45 & 109.473203907498 & -0.0232039074977166 \tabularnewline
28 & 109.5 & 109.477864073123 & 0.0221359268765582 \tabularnewline
29 & 109.91 & 110.163087259896 & -0.253087259896446 \tabularnewline
30 & 109.9 & 110.012180370256 & -0.112180370255658 \tabularnewline
31 & 109.9 & 109.918616339004 & -0.0186163390039837 \tabularnewline
32 & 109.92 & 109.948101540002 & -0.0281015400020692 \tabularnewline
33 & 109.74 & 110.269198622879 & -0.529198622878695 \tabularnewline
34 & 110.28 & 109.820997477472 & 0.459002522527868 \tabularnewline
35 & 110.97 & 110.616722025609 & 0.353277974391332 \tabularnewline
36 & 111.02 & 111.04613396931 & -0.0261339693103366 \tabularnewline
37 & 111.02 & 111.073621354927 & -0.0536213549268894 \tabularnewline
38 & 111 & 111.02755671202 & -0.0275567120200151 \tabularnewline
39 & 111.43 & 111.069909289263 & 0.360090710736714 \tabularnewline
40 & 111.52 & 111.444420434519 & 0.0755795654809077 \tabularnewline
41 & 112.29 & 112.170859493124 & 0.119140506876064 \tabularnewline
42 & 112.27 & 112.389927889172 & -0.11992788917162 \tabularnewline
43 & 112.27 & 112.301598689092 & -0.0315986890915241 \tabularnewline
44 & 112.39 & 112.326379105341 & 0.0636208946593371 \tabularnewline
45 & 112.31 & 112.721310986253 & -0.411310986253142 \tabularnewline
46 & 112.91 & 112.442361149139 & 0.467638850861263 \tabularnewline
47 & 112.9 & 113.252776192623 & -0.352776192622542 \tabularnewline
48 & 113.08 & 112.992136717228 & 0.087863282771707 \tabularnewline
49 & 113.08 & 113.129702214846 & -0.0497022148462491 \tabularnewline
50 & 113.54 & 113.091245840389 & 0.448754159611042 \tabularnewline
51 & 114 & 113.615501891294 & 0.384498108706026 \tabularnewline
52 & 115.28 & 114.010209155199 & 1.26979084480055 \tabularnewline
53 & 116.4 & 115.905399584828 & 0.494600415172471 \tabularnewline
54 & 116.56 & 116.504737724956 & 0.0552622750438303 \tabularnewline
55 & 116.56 & 116.623337922061 & -0.0633379220611374 \tabularnewline
56 & 116.59 & 116.657517262371 & -0.0675172623708278 \tabularnewline
57 & 116.96 & 116.938794956665 & 0.0212050433349447 \tabularnewline
58 & 117.17 & 117.152680790666 & 0.0173192093344738 \tabularnewline
59 & 117.83 & 117.528784232094 & 0.301215767906356 \tabularnewline
60 & 117.84 & 117.955011576434 & -0.115011576434114 \tabularnewline
61 & 117.84 & 117.93244703103 & -0.0924470310295078 \tabularnewline
62 & 117.84 & 117.915320484675 & -0.0753204846752453 \tabularnewline
63 & 117.69 & 117.968100974166 & -0.278100974166094 \tabularnewline
64 & 117.9 & 117.793255311573 & 0.106744688427241 \tabularnewline
65 & 118.05 & 118.54778406876 & -0.497784068759742 \tabularnewline
66 & 118.08 & 118.170125732823 & -0.0901257328232958 \tabularnewline
67 & 118.08 & 118.132300562234 & -0.0523005622342936 \tabularnewline
68 & 118.08 & 118.164704243679 & -0.0847042436794254 \tabularnewline
69 & 118.16 & 118.421317979951 & -0.261317979951016 \tabularnewline
70 & 118.53 & 118.349012251041 & 0.180987748958572 \tabularnewline
71 & 118.5 & 118.880217108151 & -0.380217108150759 \tabularnewline
72 & 118.62 & 118.613095956002 & 0.00690404399783517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210719&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]107.36[/C][C]106.607694978633[/C][C]0.752305021367448[/C][/ROW]
[ROW][C]14[/C][C]107.39[/C][C]107.36476695413[/C][C]0.025233045870408[/C][/ROW]
[ROW][C]15[/C][C]107.46[/C][C]107.458271945824[/C][C]0.00172805417585664[/C][/ROW]
[ROW][C]16[/C][C]107.51[/C][C]107.483965347742[/C][C]0.0260346522577635[/C][/ROW]
[ROW][C]17[/C][C]108.21[/C][C]108.170727267969[/C][C]0.0392727320307955[/C][/ROW]
[ROW][C]18[/C][C]108.33[/C][C]108.301944945772[/C][C]0.028055054227849[/C][/ROW]
[ROW][C]19[/C][C]108.33[/C][C]108.34912585801[/C][C]-0.0191258580102698[/C][/ROW]
[ROW][C]20[/C][C]108.36[/C][C]108.383104556307[/C][C]-0.023104556306663[/C][/ROW]
[ROW][C]21[/C][C]108.89[/C][C]108.7041977911[/C][C]0.185802208900213[/C][/ROW]
[ROW][C]22[/C][C]109.3[/C][C]108.945628439118[/C][C]0.354371560881518[/C][/ROW]
[ROW][C]23[/C][C]109.55[/C][C]109.677653642538[/C][C]-0.127653642538149[/C][/ROW]
[ROW][C]24[/C][C]109.45[/C][C]109.658849012698[/C][C]-0.208849012697769[/C][/ROW]
[ROW][C]25[/C][C]109.45[/C][C]109.50923338418[/C][C]-0.0592333841799189[/C][/ROW]
[ROW][C]26[/C][C]109.4[/C][C]109.461942712852[/C][C]-0.0619427128518737[/C][/ROW]
[ROW][C]27[/C][C]109.45[/C][C]109.473203907498[/C][C]-0.0232039074977166[/C][/ROW]
[ROW][C]28[/C][C]109.5[/C][C]109.477864073123[/C][C]0.0221359268765582[/C][/ROW]
[ROW][C]29[/C][C]109.91[/C][C]110.163087259896[/C][C]-0.253087259896446[/C][/ROW]
[ROW][C]30[/C][C]109.9[/C][C]110.012180370256[/C][C]-0.112180370255658[/C][/ROW]
[ROW][C]31[/C][C]109.9[/C][C]109.918616339004[/C][C]-0.0186163390039837[/C][/ROW]
[ROW][C]32[/C][C]109.92[/C][C]109.948101540002[/C][C]-0.0281015400020692[/C][/ROW]
[ROW][C]33[/C][C]109.74[/C][C]110.269198622879[/C][C]-0.529198622878695[/C][/ROW]
[ROW][C]34[/C][C]110.28[/C][C]109.820997477472[/C][C]0.459002522527868[/C][/ROW]
[ROW][C]35[/C][C]110.97[/C][C]110.616722025609[/C][C]0.353277974391332[/C][/ROW]
[ROW][C]36[/C][C]111.02[/C][C]111.04613396931[/C][C]-0.0261339693103366[/C][/ROW]
[ROW][C]37[/C][C]111.02[/C][C]111.073621354927[/C][C]-0.0536213549268894[/C][/ROW]
[ROW][C]38[/C][C]111[/C][C]111.02755671202[/C][C]-0.0275567120200151[/C][/ROW]
[ROW][C]39[/C][C]111.43[/C][C]111.069909289263[/C][C]0.360090710736714[/C][/ROW]
[ROW][C]40[/C][C]111.52[/C][C]111.444420434519[/C][C]0.0755795654809077[/C][/ROW]
[ROW][C]41[/C][C]112.29[/C][C]112.170859493124[/C][C]0.119140506876064[/C][/ROW]
[ROW][C]42[/C][C]112.27[/C][C]112.389927889172[/C][C]-0.11992788917162[/C][/ROW]
[ROW][C]43[/C][C]112.27[/C][C]112.301598689092[/C][C]-0.0315986890915241[/C][/ROW]
[ROW][C]44[/C][C]112.39[/C][C]112.326379105341[/C][C]0.0636208946593371[/C][/ROW]
[ROW][C]45[/C][C]112.31[/C][C]112.721310986253[/C][C]-0.411310986253142[/C][/ROW]
[ROW][C]46[/C][C]112.91[/C][C]112.442361149139[/C][C]0.467638850861263[/C][/ROW]
[ROW][C]47[/C][C]112.9[/C][C]113.252776192623[/C][C]-0.352776192622542[/C][/ROW]
[ROW][C]48[/C][C]113.08[/C][C]112.992136717228[/C][C]0.087863282771707[/C][/ROW]
[ROW][C]49[/C][C]113.08[/C][C]113.129702214846[/C][C]-0.0497022148462491[/C][/ROW]
[ROW][C]50[/C][C]113.54[/C][C]113.091245840389[/C][C]0.448754159611042[/C][/ROW]
[ROW][C]51[/C][C]114[/C][C]113.615501891294[/C][C]0.384498108706026[/C][/ROW]
[ROW][C]52[/C][C]115.28[/C][C]114.010209155199[/C][C]1.26979084480055[/C][/ROW]
[ROW][C]53[/C][C]116.4[/C][C]115.905399584828[/C][C]0.494600415172471[/C][/ROW]
[ROW][C]54[/C][C]116.56[/C][C]116.504737724956[/C][C]0.0552622750438303[/C][/ROW]
[ROW][C]55[/C][C]116.56[/C][C]116.623337922061[/C][C]-0.0633379220611374[/C][/ROW]
[ROW][C]56[/C][C]116.59[/C][C]116.657517262371[/C][C]-0.0675172623708278[/C][/ROW]
[ROW][C]57[/C][C]116.96[/C][C]116.938794956665[/C][C]0.0212050433349447[/C][/ROW]
[ROW][C]58[/C][C]117.17[/C][C]117.152680790666[/C][C]0.0173192093344738[/C][/ROW]
[ROW][C]59[/C][C]117.83[/C][C]117.528784232094[/C][C]0.301215767906356[/C][/ROW]
[ROW][C]60[/C][C]117.84[/C][C]117.955011576434[/C][C]-0.115011576434114[/C][/ROW]
[ROW][C]61[/C][C]117.84[/C][C]117.93244703103[/C][C]-0.0924470310295078[/C][/ROW]
[ROW][C]62[/C][C]117.84[/C][C]117.915320484675[/C][C]-0.0753204846752453[/C][/ROW]
[ROW][C]63[/C][C]117.69[/C][C]117.968100974166[/C][C]-0.278100974166094[/C][/ROW]
[ROW][C]64[/C][C]117.9[/C][C]117.793255311573[/C][C]0.106744688427241[/C][/ROW]
[ROW][C]65[/C][C]118.05[/C][C]118.54778406876[/C][C]-0.497784068759742[/C][/ROW]
[ROW][C]66[/C][C]118.08[/C][C]118.170125732823[/C][C]-0.0901257328232958[/C][/ROW]
[ROW][C]67[/C][C]118.08[/C][C]118.132300562234[/C][C]-0.0523005622342936[/C][/ROW]
[ROW][C]68[/C][C]118.08[/C][C]118.164704243679[/C][C]-0.0847042436794254[/C][/ROW]
[ROW][C]69[/C][C]118.16[/C][C]118.421317979951[/C][C]-0.261317979951016[/C][/ROW]
[ROW][C]70[/C][C]118.53[/C][C]118.349012251041[/C][C]0.180987748958572[/C][/ROW]
[ROW][C]71[/C][C]118.5[/C][C]118.880217108151[/C][C]-0.380217108150759[/C][/ROW]
[ROW][C]72[/C][C]118.62[/C][C]118.613095956002[/C][C]0.00690404399783517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210719&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210719&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
13107.36106.6076949786330.752305021367448
14107.39107.364766954130.025233045870408
15107.46107.4582719458240.00172805417585664
16107.51107.4839653477420.0260346522577635
17108.21108.1707272679690.0392727320307955
18108.33108.3019449457720.028055054227849
19108.33108.34912585801-0.0191258580102698
20108.36108.383104556307-0.023104556306663
21108.89108.70419779110.185802208900213
22109.3108.9456284391180.354371560881518
23109.55109.677653642538-0.127653642538149
24109.45109.658849012698-0.208849012697769
25109.45109.50923338418-0.0592333841799189
26109.4109.461942712852-0.0619427128518737
27109.45109.473203907498-0.0232039074977166
28109.5109.4778640731230.0221359268765582
29109.91110.163087259896-0.253087259896446
30109.9110.012180370256-0.112180370255658
31109.9109.918616339004-0.0186163390039837
32109.92109.948101540002-0.0281015400020692
33109.74110.269198622879-0.529198622878695
34110.28109.8209974774720.459002522527868
35110.97110.6167220256090.353277974391332
36111.02111.04613396931-0.0261339693103366
37111.02111.073621354927-0.0536213549268894
38111111.02755671202-0.0275567120200151
39111.43111.0699092892630.360090710736714
40111.52111.4444204345190.0755795654809077
41112.29112.1708594931240.119140506876064
42112.27112.389927889172-0.11992788917162
43112.27112.301598689092-0.0315986890915241
44112.39112.3263791053410.0636208946593371
45112.31112.721310986253-0.411310986253142
46112.91112.4423611491390.467638850861263
47112.9113.252776192623-0.352776192622542
48113.08112.9921367172280.087863282771707
49113.08113.129702214846-0.0497022148462491
50113.54113.0912458403890.448754159611042
51114113.6155018912940.384498108706026
52115.28114.0102091551991.26979084480055
53116.4115.9053995848280.494600415172471
54116.56116.5047377249560.0552622750438303
55116.56116.623337922061-0.0633379220611374
56116.59116.657517262371-0.0675172623708278
57116.96116.9387949566650.0212050433349447
58117.17117.1526807906660.0173192093344738
59117.83117.5287842320940.301215767906356
60117.84117.955011576434-0.115011576434114
61117.84117.93244703103-0.0924470310295078
62117.84117.915320484675-0.0753204846752453
63117.69117.968100974166-0.278100974166094
64117.9117.7932553115730.106744688427241
65118.05118.54778406876-0.497784068759742
66118.08118.170125732823-0.0901257328232958
67118.08118.132300562234-0.0523005622342936
68118.08118.164704243679-0.0847042436794254
69118.16118.421317979951-0.261317979951016
70118.53118.3490122510410.180987748958572
71118.5118.880217108151-0.380217108150759
72118.62118.6130959560020.00690404399783517







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73118.685505306387118.11205899827119.258951614505
74118.736354787854117.938015091697119.534694484011
75118.831737235109117.854338989223119.809135480995
76118.924129066075117.791492066665120.056766065485
77119.531581854787118.258724157748120.804439551826
78119.637520216135118.234897498923121.040142933346
79119.678706468708118.154055490764121.203357446653
80119.751571620306118.110858424047121.392284816565
81120.074148654889118.322112475848121.82618483393
82120.268679205413118.409169520642122.128188890184
83120.595852258236118.632050078794122.559654437678
84120.709368498711118.643938351823122.774798645599

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 118.685505306387 & 118.11205899827 & 119.258951614505 \tabularnewline
74 & 118.736354787854 & 117.938015091697 & 119.534694484011 \tabularnewline
75 & 118.831737235109 & 117.854338989223 & 119.809135480995 \tabularnewline
76 & 118.924129066075 & 117.791492066665 & 120.056766065485 \tabularnewline
77 & 119.531581854787 & 118.258724157748 & 120.804439551826 \tabularnewline
78 & 119.637520216135 & 118.234897498923 & 121.040142933346 \tabularnewline
79 & 119.678706468708 & 118.154055490764 & 121.203357446653 \tabularnewline
80 & 119.751571620306 & 118.110858424047 & 121.392284816565 \tabularnewline
81 & 120.074148654889 & 118.322112475848 & 121.82618483393 \tabularnewline
82 & 120.268679205413 & 118.409169520642 & 122.128188890184 \tabularnewline
83 & 120.595852258236 & 118.632050078794 & 122.559654437678 \tabularnewline
84 & 120.709368498711 & 118.643938351823 & 122.774798645599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210719&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]118.685505306387[/C][C]118.11205899827[/C][C]119.258951614505[/C][/ROW]
[ROW][C]74[/C][C]118.736354787854[/C][C]117.938015091697[/C][C]119.534694484011[/C][/ROW]
[ROW][C]75[/C][C]118.831737235109[/C][C]117.854338989223[/C][C]119.809135480995[/C][/ROW]
[ROW][C]76[/C][C]118.924129066075[/C][C]117.791492066665[/C][C]120.056766065485[/C][/ROW]
[ROW][C]77[/C][C]119.531581854787[/C][C]118.258724157748[/C][C]120.804439551826[/C][/ROW]
[ROW][C]78[/C][C]119.637520216135[/C][C]118.234897498923[/C][C]121.040142933346[/C][/ROW]
[ROW][C]79[/C][C]119.678706468708[/C][C]118.154055490764[/C][C]121.203357446653[/C][/ROW]
[ROW][C]80[/C][C]119.751571620306[/C][C]118.110858424047[/C][C]121.392284816565[/C][/ROW]
[ROW][C]81[/C][C]120.074148654889[/C][C]118.322112475848[/C][C]121.82618483393[/C][/ROW]
[ROW][C]82[/C][C]120.268679205413[/C][C]118.409169520642[/C][C]122.128188890184[/C][/ROW]
[ROW][C]83[/C][C]120.595852258236[/C][C]118.632050078794[/C][C]122.559654437678[/C][/ROW]
[ROW][C]84[/C][C]120.709368498711[/C][C]118.643938351823[/C][C]122.774798645599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210719&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210719&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
73118.685505306387118.11205899827119.258951614505
74118.736354787854117.938015091697119.534694484011
75118.831737235109117.854338989223119.809135480995
76118.924129066075117.791492066665120.056766065485
77119.531581854787118.258724157748120.804439551826
78119.637520216135118.234897498923121.040142933346
79119.678706468708118.154055490764121.203357446653
80119.751571620306118.110858424047121.392284816565
81120.074148654889118.322112475848121.82618483393
82120.268679205413118.409169520642122.128188890184
83120.595852258236118.632050078794122.559654437678
84120.709368498711118.643938351823122.774798645599



Parameters (Session):
par1 = 12 ; par2 = Double ; 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')