Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 May 2017 15:19:20 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/May/02/t1493734840oo59eyks6uhamy2.htm/, Retrieved Fri, 17 May 2024 07:33:52 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 07:33:52 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
94.72
95.76
96.14
97.11
97.19
97.43
97.43
97.56
97.66
97.75
97.82
97.82
97.82
98.35
98.19
98.19
98.21
98.22
98.26
98.23
98.26
98.5
98.51
98.51
98.51
98.89
99.55
99.9
100.12
100.09
100.09
100.09
100.46
100.71
100.79
100.79
100.93
101.15
101.53
101.91
102.18
102.24
102.2
102.32
102.43
102.45
102.84
102.96
102.96
103.1
103.4
103.74
103.97
104.29
104.33
104.46
104.9
105.31
105.63
105.68
105.87
106.34
106.6
107.1
107.06
107.4
107.4
107.43
107.75
107.84
107.97
108.04




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.832649856257751
beta0.0459987442571242
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.832649856257751 \tabularnewline
beta & 0.0459987442571242 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.832649856257751[/C][/ROW]
[ROW][C]beta[/C][C]0.0459987442571242[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.832649856257751
beta0.0459987442571242
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397.8297.15916132478640.660838675213611
1498.3598.28997273073160.0600272692683745
1598.1998.2424010345156-0.052401034515583
1698.1998.255875589934-0.0658755899339667
1798.2198.2718574677767-0.0618574677767469
1898.2298.2813158409979-0.0613158409979349
1998.2698.6267934176519-0.366793417651934
2098.2398.3063666351538-0.0763666351537609
2198.2698.23858876448650.0214112355134688
2298.598.30596235891470.194037641085274
2398.5198.5474217779527-0.0374217779526873
2498.5198.536806592511-0.0268065925109937
2598.5198.6525115384359-0.14251153843594
2698.8998.9902791425914-0.100279142591361
2799.5598.76068508458020.789314915419808
2899.999.4752694122160.424730587783984
29100.1299.92172759555490.198272404445134
30100.09100.179137614271-0.0891376142712801
31100.09100.480525985004-0.39052598500389
32100.09100.218230576018-0.128230576017799
33100.46100.150934238760.30906576124022
34100.71100.5250326942830.184967305716938
35100.79100.758177839110.0318221608898455
36100.79100.84762007004-0.0576200700404712
37100.93100.957749764523-0.0277497645231506
38101.15101.441981639507-0.291981639506972
39101.53101.238138149080.291861850919986
40101.91101.4949500709260.41504992907403
41102.18101.9125241247090.267475875290785
42102.24102.1991831261970.0408168738025978
43102.2102.583042893313-0.383042893313004
44102.32102.395862260433-0.0758622604329275
45102.43102.47234655589-0.0423465558900631
46102.45102.546608869399-0.0966088693992475
47102.84102.5224213519660.317578648033802
48102.96102.8485257878350.111474212164808
49102.96103.124622343574-0.164622343573939
50103.1103.46559743877-0.36559743877018
51103.4103.3102739039360.0897260960639557
52103.74103.4237609385840.316239061415686
53103.97103.7349469359410.235053064059329
54104.29103.9560191881190.33398081188129
55104.33104.523618816834-0.193618816833848
56104.46104.563393883447-0.103393883446614
57104.9104.6393333968030.260666603197421
58105.31104.9851949904610.324805009538835
59105.63105.4257287509220.204271249078474
60105.68105.6631731525190.0168268474805728
61105.87105.8508086832110.0191913167891613
62106.34106.354795092087-0.0147950920867004
63106.6106.624793673953-0.0247936739529564
64107.1106.7334747457440.366525254255961
65107.06107.127512979706-0.0675129797062368
66107.4107.1561886295560.24381137044422
67107.4107.599940643767-0.199940643766794
68107.43107.688834697984-0.258834697984042
69107.75107.7296021995710.0203978004289382
70107.84107.910265267159-0.0702652671589306
71107.97108.010668636338-0.040668636337756
72108.04108.0124097846920.0275902153075691

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 97.82 & 97.1591613247864 & 0.660838675213611 \tabularnewline
14 & 98.35 & 98.2899727307316 & 0.0600272692683745 \tabularnewline
15 & 98.19 & 98.2424010345156 & -0.052401034515583 \tabularnewline
16 & 98.19 & 98.255875589934 & -0.0658755899339667 \tabularnewline
17 & 98.21 & 98.2718574677767 & -0.0618574677767469 \tabularnewline
18 & 98.22 & 98.2813158409979 & -0.0613158409979349 \tabularnewline
19 & 98.26 & 98.6267934176519 & -0.366793417651934 \tabularnewline
20 & 98.23 & 98.3063666351538 & -0.0763666351537609 \tabularnewline
21 & 98.26 & 98.2385887644865 & 0.0214112355134688 \tabularnewline
22 & 98.5 & 98.3059623589147 & 0.194037641085274 \tabularnewline
23 & 98.51 & 98.5474217779527 & -0.0374217779526873 \tabularnewline
24 & 98.51 & 98.536806592511 & -0.0268065925109937 \tabularnewline
25 & 98.51 & 98.6525115384359 & -0.14251153843594 \tabularnewline
26 & 98.89 & 98.9902791425914 & -0.100279142591361 \tabularnewline
27 & 99.55 & 98.7606850845802 & 0.789314915419808 \tabularnewline
28 & 99.9 & 99.475269412216 & 0.424730587783984 \tabularnewline
29 & 100.12 & 99.9217275955549 & 0.198272404445134 \tabularnewline
30 & 100.09 & 100.179137614271 & -0.0891376142712801 \tabularnewline
31 & 100.09 & 100.480525985004 & -0.39052598500389 \tabularnewline
32 & 100.09 & 100.218230576018 & -0.128230576017799 \tabularnewline
33 & 100.46 & 100.15093423876 & 0.30906576124022 \tabularnewline
34 & 100.71 & 100.525032694283 & 0.184967305716938 \tabularnewline
35 & 100.79 & 100.75817783911 & 0.0318221608898455 \tabularnewline
36 & 100.79 & 100.84762007004 & -0.0576200700404712 \tabularnewline
37 & 100.93 & 100.957749764523 & -0.0277497645231506 \tabularnewline
38 & 101.15 & 101.441981639507 & -0.291981639506972 \tabularnewline
39 & 101.53 & 101.23813814908 & 0.291861850919986 \tabularnewline
40 & 101.91 & 101.494950070926 & 0.41504992907403 \tabularnewline
41 & 102.18 & 101.912524124709 & 0.267475875290785 \tabularnewline
42 & 102.24 & 102.199183126197 & 0.0408168738025978 \tabularnewline
43 & 102.2 & 102.583042893313 & -0.383042893313004 \tabularnewline
44 & 102.32 & 102.395862260433 & -0.0758622604329275 \tabularnewline
45 & 102.43 & 102.47234655589 & -0.0423465558900631 \tabularnewline
46 & 102.45 & 102.546608869399 & -0.0966088693992475 \tabularnewline
47 & 102.84 & 102.522421351966 & 0.317578648033802 \tabularnewline
48 & 102.96 & 102.848525787835 & 0.111474212164808 \tabularnewline
49 & 102.96 & 103.124622343574 & -0.164622343573939 \tabularnewline
50 & 103.1 & 103.46559743877 & -0.36559743877018 \tabularnewline
51 & 103.4 & 103.310273903936 & 0.0897260960639557 \tabularnewline
52 & 103.74 & 103.423760938584 & 0.316239061415686 \tabularnewline
53 & 103.97 & 103.734946935941 & 0.235053064059329 \tabularnewline
54 & 104.29 & 103.956019188119 & 0.33398081188129 \tabularnewline
55 & 104.33 & 104.523618816834 & -0.193618816833848 \tabularnewline
56 & 104.46 & 104.563393883447 & -0.103393883446614 \tabularnewline
57 & 104.9 & 104.639333396803 & 0.260666603197421 \tabularnewline
58 & 105.31 & 104.985194990461 & 0.324805009538835 \tabularnewline
59 & 105.63 & 105.425728750922 & 0.204271249078474 \tabularnewline
60 & 105.68 & 105.663173152519 & 0.0168268474805728 \tabularnewline
61 & 105.87 & 105.850808683211 & 0.0191913167891613 \tabularnewline
62 & 106.34 & 106.354795092087 & -0.0147950920867004 \tabularnewline
63 & 106.6 & 106.624793673953 & -0.0247936739529564 \tabularnewline
64 & 107.1 & 106.733474745744 & 0.366525254255961 \tabularnewline
65 & 107.06 & 107.127512979706 & -0.0675129797062368 \tabularnewline
66 & 107.4 & 107.156188629556 & 0.24381137044422 \tabularnewline
67 & 107.4 & 107.599940643767 & -0.199940643766794 \tabularnewline
68 & 107.43 & 107.688834697984 & -0.258834697984042 \tabularnewline
69 & 107.75 & 107.729602199571 & 0.0203978004289382 \tabularnewline
70 & 107.84 & 107.910265267159 & -0.0702652671589306 \tabularnewline
71 & 107.97 & 108.010668636338 & -0.040668636337756 \tabularnewline
72 & 108.04 & 108.012409784692 & 0.0275902153075691 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]97.82[/C][C]97.1591613247864[/C][C]0.660838675213611[/C][/ROW]
[ROW][C]14[/C][C]98.35[/C][C]98.2899727307316[/C][C]0.0600272692683745[/C][/ROW]
[ROW][C]15[/C][C]98.19[/C][C]98.2424010345156[/C][C]-0.052401034515583[/C][/ROW]
[ROW][C]16[/C][C]98.19[/C][C]98.255875589934[/C][C]-0.0658755899339667[/C][/ROW]
[ROW][C]17[/C][C]98.21[/C][C]98.2718574677767[/C][C]-0.0618574677767469[/C][/ROW]
[ROW][C]18[/C][C]98.22[/C][C]98.2813158409979[/C][C]-0.0613158409979349[/C][/ROW]
[ROW][C]19[/C][C]98.26[/C][C]98.6267934176519[/C][C]-0.366793417651934[/C][/ROW]
[ROW][C]20[/C][C]98.23[/C][C]98.3063666351538[/C][C]-0.0763666351537609[/C][/ROW]
[ROW][C]21[/C][C]98.26[/C][C]98.2385887644865[/C][C]0.0214112355134688[/C][/ROW]
[ROW][C]22[/C][C]98.5[/C][C]98.3059623589147[/C][C]0.194037641085274[/C][/ROW]
[ROW][C]23[/C][C]98.51[/C][C]98.5474217779527[/C][C]-0.0374217779526873[/C][/ROW]
[ROW][C]24[/C][C]98.51[/C][C]98.536806592511[/C][C]-0.0268065925109937[/C][/ROW]
[ROW][C]25[/C][C]98.51[/C][C]98.6525115384359[/C][C]-0.14251153843594[/C][/ROW]
[ROW][C]26[/C][C]98.89[/C][C]98.9902791425914[/C][C]-0.100279142591361[/C][/ROW]
[ROW][C]27[/C][C]99.55[/C][C]98.7606850845802[/C][C]0.789314915419808[/C][/ROW]
[ROW][C]28[/C][C]99.9[/C][C]99.475269412216[/C][C]0.424730587783984[/C][/ROW]
[ROW][C]29[/C][C]100.12[/C][C]99.9217275955549[/C][C]0.198272404445134[/C][/ROW]
[ROW][C]30[/C][C]100.09[/C][C]100.179137614271[/C][C]-0.0891376142712801[/C][/ROW]
[ROW][C]31[/C][C]100.09[/C][C]100.480525985004[/C][C]-0.39052598500389[/C][/ROW]
[ROW][C]32[/C][C]100.09[/C][C]100.218230576018[/C][C]-0.128230576017799[/C][/ROW]
[ROW][C]33[/C][C]100.46[/C][C]100.15093423876[/C][C]0.30906576124022[/C][/ROW]
[ROW][C]34[/C][C]100.71[/C][C]100.525032694283[/C][C]0.184967305716938[/C][/ROW]
[ROW][C]35[/C][C]100.79[/C][C]100.75817783911[/C][C]0.0318221608898455[/C][/ROW]
[ROW][C]36[/C][C]100.79[/C][C]100.84762007004[/C][C]-0.0576200700404712[/C][/ROW]
[ROW][C]37[/C][C]100.93[/C][C]100.957749764523[/C][C]-0.0277497645231506[/C][/ROW]
[ROW][C]38[/C][C]101.15[/C][C]101.441981639507[/C][C]-0.291981639506972[/C][/ROW]
[ROW][C]39[/C][C]101.53[/C][C]101.23813814908[/C][C]0.291861850919986[/C][/ROW]
[ROW][C]40[/C][C]101.91[/C][C]101.494950070926[/C][C]0.41504992907403[/C][/ROW]
[ROW][C]41[/C][C]102.18[/C][C]101.912524124709[/C][C]0.267475875290785[/C][/ROW]
[ROW][C]42[/C][C]102.24[/C][C]102.199183126197[/C][C]0.0408168738025978[/C][/ROW]
[ROW][C]43[/C][C]102.2[/C][C]102.583042893313[/C][C]-0.383042893313004[/C][/ROW]
[ROW][C]44[/C][C]102.32[/C][C]102.395862260433[/C][C]-0.0758622604329275[/C][/ROW]
[ROW][C]45[/C][C]102.43[/C][C]102.47234655589[/C][C]-0.0423465558900631[/C][/ROW]
[ROW][C]46[/C][C]102.45[/C][C]102.546608869399[/C][C]-0.0966088693992475[/C][/ROW]
[ROW][C]47[/C][C]102.84[/C][C]102.522421351966[/C][C]0.317578648033802[/C][/ROW]
[ROW][C]48[/C][C]102.96[/C][C]102.848525787835[/C][C]0.111474212164808[/C][/ROW]
[ROW][C]49[/C][C]102.96[/C][C]103.124622343574[/C][C]-0.164622343573939[/C][/ROW]
[ROW][C]50[/C][C]103.1[/C][C]103.46559743877[/C][C]-0.36559743877018[/C][/ROW]
[ROW][C]51[/C][C]103.4[/C][C]103.310273903936[/C][C]0.0897260960639557[/C][/ROW]
[ROW][C]52[/C][C]103.74[/C][C]103.423760938584[/C][C]0.316239061415686[/C][/ROW]
[ROW][C]53[/C][C]103.97[/C][C]103.734946935941[/C][C]0.235053064059329[/C][/ROW]
[ROW][C]54[/C][C]104.29[/C][C]103.956019188119[/C][C]0.33398081188129[/C][/ROW]
[ROW][C]55[/C][C]104.33[/C][C]104.523618816834[/C][C]-0.193618816833848[/C][/ROW]
[ROW][C]56[/C][C]104.46[/C][C]104.563393883447[/C][C]-0.103393883446614[/C][/ROW]
[ROW][C]57[/C][C]104.9[/C][C]104.639333396803[/C][C]0.260666603197421[/C][/ROW]
[ROW][C]58[/C][C]105.31[/C][C]104.985194990461[/C][C]0.324805009538835[/C][/ROW]
[ROW][C]59[/C][C]105.63[/C][C]105.425728750922[/C][C]0.204271249078474[/C][/ROW]
[ROW][C]60[/C][C]105.68[/C][C]105.663173152519[/C][C]0.0168268474805728[/C][/ROW]
[ROW][C]61[/C][C]105.87[/C][C]105.850808683211[/C][C]0.0191913167891613[/C][/ROW]
[ROW][C]62[/C][C]106.34[/C][C]106.354795092087[/C][C]-0.0147950920867004[/C][/ROW]
[ROW][C]63[/C][C]106.6[/C][C]106.624793673953[/C][C]-0.0247936739529564[/C][/ROW]
[ROW][C]64[/C][C]107.1[/C][C]106.733474745744[/C][C]0.366525254255961[/C][/ROW]
[ROW][C]65[/C][C]107.06[/C][C]107.127512979706[/C][C]-0.0675129797062368[/C][/ROW]
[ROW][C]66[/C][C]107.4[/C][C]107.156188629556[/C][C]0.24381137044422[/C][/ROW]
[ROW][C]67[/C][C]107.4[/C][C]107.599940643767[/C][C]-0.199940643766794[/C][/ROW]
[ROW][C]68[/C][C]107.43[/C][C]107.688834697984[/C][C]-0.258834697984042[/C][/ROW]
[ROW][C]69[/C][C]107.75[/C][C]107.729602199571[/C][C]0.0203978004289382[/C][/ROW]
[ROW][C]70[/C][C]107.84[/C][C]107.910265267159[/C][C]-0.0702652671589306[/C][/ROW]
[ROW][C]71[/C][C]107.97[/C][C]108.010668636338[/C][C]-0.040668636337756[/C][/ROW]
[ROW][C]72[/C][C]108.04[/C][C]108.012409784692[/C][C]0.0275902153075691[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1397.8297.15916132478640.660838675213611
1498.3598.28997273073160.0600272692683745
1598.1998.2424010345156-0.052401034515583
1698.1998.255875589934-0.0658755899339667
1798.2198.2718574677767-0.0618574677767469
1898.2298.2813158409979-0.0613158409979349
1998.2698.6267934176519-0.366793417651934
2098.2398.3063666351538-0.0763666351537609
2198.2698.23858876448650.0214112355134688
2298.598.30596235891470.194037641085274
2398.5198.5474217779527-0.0374217779526873
2498.5198.536806592511-0.0268065925109937
2598.5198.6525115384359-0.14251153843594
2698.8998.9902791425914-0.100279142591361
2799.5598.76068508458020.789314915419808
2899.999.4752694122160.424730587783984
29100.1299.92172759555490.198272404445134
30100.09100.179137614271-0.0891376142712801
31100.09100.480525985004-0.39052598500389
32100.09100.218230576018-0.128230576017799
33100.46100.150934238760.30906576124022
34100.71100.5250326942830.184967305716938
35100.79100.758177839110.0318221608898455
36100.79100.84762007004-0.0576200700404712
37100.93100.957749764523-0.0277497645231506
38101.15101.441981639507-0.291981639506972
39101.53101.238138149080.291861850919986
40101.91101.4949500709260.41504992907403
41102.18101.9125241247090.267475875290785
42102.24102.1991831261970.0408168738025978
43102.2102.583042893313-0.383042893313004
44102.32102.395862260433-0.0758622604329275
45102.43102.47234655589-0.0423465558900631
46102.45102.546608869399-0.0966088693992475
47102.84102.5224213519660.317578648033802
48102.96102.8485257878350.111474212164808
49102.96103.124622343574-0.164622343573939
50103.1103.46559743877-0.36559743877018
51103.4103.3102739039360.0897260960639557
52103.74103.4237609385840.316239061415686
53103.97103.7349469359410.235053064059329
54104.29103.9560191881190.33398081188129
55104.33104.523618816834-0.193618816833848
56104.46104.563393883447-0.103393883446614
57104.9104.6393333968030.260666603197421
58105.31104.9851949904610.324805009538835
59105.63105.4257287509220.204271249078474
60105.68105.6631731525190.0168268474805728
61105.87105.8508086832110.0191913167891613
62106.34106.354795092087-0.0147950920867004
63106.6106.624793673953-0.0247936739529564
64107.1106.7334747457440.366525254255961
65107.06107.127512979706-0.0675129797062368
66107.4107.1561886295560.24381137044422
67107.4107.599940643767-0.199940643766794
68107.43107.688834697984-0.258834697984042
69107.75107.7296021995710.0203978004289382
70107.84107.910265267159-0.0702652671589306
71107.97108.010668636338-0.040668636337756
72108.04108.0124097846920.0275902153075691







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73108.209430127141107.738559869591108.680300384691
74108.691041215541108.066617695857109.315464735226
75108.971544286265108.214439158817109.728649413714
76109.167165326398108.288370908662110.045959744134
77109.170150011673108.176284025327110.16401599802
78109.296496325907108.191811489628110.401181162186
79109.442994508797108.230308606477110.655680411116
80109.67618871363108.357380299821110.994997127439
81109.976793607169108.553092552021111.400494662316
82110.122107837853108.594277746859111.649937928847
83110.28546965744108.653928541542111.917010773338
84110.333553397267108.598456836507112.068649958027

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 108.209430127141 & 107.738559869591 & 108.680300384691 \tabularnewline
74 & 108.691041215541 & 108.066617695857 & 109.315464735226 \tabularnewline
75 & 108.971544286265 & 108.214439158817 & 109.728649413714 \tabularnewline
76 & 109.167165326398 & 108.288370908662 & 110.045959744134 \tabularnewline
77 & 109.170150011673 & 108.176284025327 & 110.16401599802 \tabularnewline
78 & 109.296496325907 & 108.191811489628 & 110.401181162186 \tabularnewline
79 & 109.442994508797 & 108.230308606477 & 110.655680411116 \tabularnewline
80 & 109.67618871363 & 108.357380299821 & 110.994997127439 \tabularnewline
81 & 109.976793607169 & 108.553092552021 & 111.400494662316 \tabularnewline
82 & 110.122107837853 & 108.594277746859 & 111.649937928847 \tabularnewline
83 & 110.28546965744 & 108.653928541542 & 111.917010773338 \tabularnewline
84 & 110.333553397267 & 108.598456836507 & 112.068649958027 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]108.209430127141[/C][C]107.738559869591[/C][C]108.680300384691[/C][/ROW]
[ROW][C]74[/C][C]108.691041215541[/C][C]108.066617695857[/C][C]109.315464735226[/C][/ROW]
[ROW][C]75[/C][C]108.971544286265[/C][C]108.214439158817[/C][C]109.728649413714[/C][/ROW]
[ROW][C]76[/C][C]109.167165326398[/C][C]108.288370908662[/C][C]110.045959744134[/C][/ROW]
[ROW][C]77[/C][C]109.170150011673[/C][C]108.176284025327[/C][C]110.16401599802[/C][/ROW]
[ROW][C]78[/C][C]109.296496325907[/C][C]108.191811489628[/C][C]110.401181162186[/C][/ROW]
[ROW][C]79[/C][C]109.442994508797[/C][C]108.230308606477[/C][C]110.655680411116[/C][/ROW]
[ROW][C]80[/C][C]109.67618871363[/C][C]108.357380299821[/C][C]110.994997127439[/C][/ROW]
[ROW][C]81[/C][C]109.976793607169[/C][C]108.553092552021[/C][C]111.400494662316[/C][/ROW]
[ROW][C]82[/C][C]110.122107837853[/C][C]108.594277746859[/C][C]111.649937928847[/C][/ROW]
[ROW][C]83[/C][C]110.28546965744[/C][C]108.653928541542[/C][C]111.917010773338[/C][/ROW]
[ROW][C]84[/C][C]110.333553397267[/C][C]108.598456836507[/C][C]112.068649958027[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
73108.209430127141107.738559869591108.680300384691
74108.691041215541108.066617695857109.315464735226
75108.971544286265108.214439158817109.728649413714
76109.167165326398108.288370908662110.045959744134
77109.170150011673108.176284025327110.16401599802
78109.296496325907108.191811489628110.401181162186
79109.442994508797108.230308606477110.655680411116
80109.67618871363108.357380299821110.994997127439
81109.976793607169108.553092552021111.400494662316
82110.122107837853108.594277746859111.649937928847
83110.28546965744108.653928541542111.917010773338
84110.333553397267108.598456836507112.068649958027



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')