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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 31 May 2008 14:19:36 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/31/t1212265545d3ku7xfnhilngm9.htm/, Retrieved Thu, 16 May 2024 01:18:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13632, Retrieved Thu, 16 May 2024 01:18:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponentional Smo...] [2008-05-31 20:19:36] [f907c40368cff310b72a5f11c2582b2e] [Current]
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Dataseries X:
101,22
101,25
101,25
101,26
101,26
101,26
101,29
101,31
101,31
101,31
101,32
101,34
101,34
101,34
101,34
101,34
101,34
101,34
101,34
101,39
102,16
102,19
102,31
102,32
102,32
102,32
102,36
102,36
102,37
102,37
102,37
102,37
103,45
103,8
103,81
103,81
103,81
103,84
103,9
103,91
103,92
103,92
103,93
104
104,51
105
105,01
105,01
105,01
105,01
105,13
105,14
105,15
105,22
105,23
105,23
105,57
106,05
106,09
106,09
106,19
106,2
106,2
106,22
106,22
106,23
106,23
106,61
106,95
107,74
107,8
107,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13632&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13632&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13632&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.564996882250498
beta0.0602692712103975
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.564996882250498 \tabularnewline
beta & 0.0602692712103975 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13632&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]0.564996882250498[/C][/ROW]
[ROW][C]beta[/C][C]0.0602692712103975[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13632&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13632&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
alpha0.564996882250498
beta0.0602692712103975
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13101.34101.0553222222220.284677777777773
14101.34101.2854028590380.0545971409617465
15101.34101.354014459186-0.0140144591858444
16101.34101.350050166162-0.0100501661623724
17101.34101.342150125245-0.00215012524522251
18101.34101.3344737001910.00552629980882102
19101.34101.3317392793130.00826072068720407
20101.39101.3808310913560.00916890864405673
21102.16102.1490815793180.0109184206817048
22102.19102.1770256629790.0129743370205802
23102.31102.2961564677750.0138435322246977
24102.32102.3058330977570.014166902243403
25102.32102.3150105623290.00498943767085791
26102.32102.2906678395460.0293321604544445
27102.36102.3179836975480.0420163024515574
28102.36102.3521341997470.00786580025264527
29102.37102.3631363497870.006863650212793
30102.37102.3695420685910.000457931409172829
31102.37102.370611049142-0.000611049141767239
32102.37102.420260834585-0.0502608345845914
33103.45103.1588464785370.291153521463443
34103.8103.3587111346220.441288865378027
35103.81103.7474956443990.0625043556006943
36103.81103.813742379996-0.00374237999585603
37103.81103.837135309402-0.027135309402297
38103.84103.8324638338580.00753616614248642
39103.9103.8794729371000.020527062899518
40103.91103.912385033261-0.00238503326063721
41103.92103.942569017299-0.0225690172989061
42103.92103.953966084705-0.0339660847046162
43103.93103.958355610351-0.0283556103509142
44104103.9930222540740.00697774592559597
45104.51104.936703172511-0.426703172511296
46105104.7960853024260.203914697574348
47105.01104.8776935765270.132306423472713
48105.01104.9486494946380.0613505053624408
49105.01104.9949490121190.0150509878813381
50105.01105.026936696687-0.0169366966870825
51105.13105.0626782743290.0673217256708938
52105.14105.1105643103350.0294356896646093
53105.15105.1495322998470.000467700153194528
54105.22105.1693572183090.0506427816913231
55105.23105.2272420978040.00275790219559724
56105.23105.299168409326-0.0691684093262381
57105.57106.012892020798-0.442892020798439
58106.05106.138614564618-0.0886145646178278
59106.09106.0150000263360.07499997366439
60106.09106.0119656682010.0780343317992163
61106.19106.0373729128070.152627087192570
62106.2106.1276825082020.0723174917983727
63106.2106.248050965841-0.0480509658406874
64106.22106.2078884472560.0121115527439457
65106.22106.2174944672090.00250553279082055
66106.23106.253393743378-0.0233937433779658
67106.23106.239193728807-0.0091937288066788
68106.61106.2632478436120.346752156387566
69106.95107.053725855553-0.103725855552668
70107.74107.5410688064430.19893119355703
71107.8107.6767618363260.123238163674145
72107.8107.7296167418810.0703832581187811

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 101.34 & 101.055322222222 & 0.284677777777773 \tabularnewline
14 & 101.34 & 101.285402859038 & 0.0545971409617465 \tabularnewline
15 & 101.34 & 101.354014459186 & -0.0140144591858444 \tabularnewline
16 & 101.34 & 101.350050166162 & -0.0100501661623724 \tabularnewline
17 & 101.34 & 101.342150125245 & -0.00215012524522251 \tabularnewline
18 & 101.34 & 101.334473700191 & 0.00552629980882102 \tabularnewline
19 & 101.34 & 101.331739279313 & 0.00826072068720407 \tabularnewline
20 & 101.39 & 101.380831091356 & 0.00916890864405673 \tabularnewline
21 & 102.16 & 102.149081579318 & 0.0109184206817048 \tabularnewline
22 & 102.19 & 102.177025662979 & 0.0129743370205802 \tabularnewline
23 & 102.31 & 102.296156467775 & 0.0138435322246977 \tabularnewline
24 & 102.32 & 102.305833097757 & 0.014166902243403 \tabularnewline
25 & 102.32 & 102.315010562329 & 0.00498943767085791 \tabularnewline
26 & 102.32 & 102.290667839546 & 0.0293321604544445 \tabularnewline
27 & 102.36 & 102.317983697548 & 0.0420163024515574 \tabularnewline
28 & 102.36 & 102.352134199747 & 0.00786580025264527 \tabularnewline
29 & 102.37 & 102.363136349787 & 0.006863650212793 \tabularnewline
30 & 102.37 & 102.369542068591 & 0.000457931409172829 \tabularnewline
31 & 102.37 & 102.370611049142 & -0.000611049141767239 \tabularnewline
32 & 102.37 & 102.420260834585 & -0.0502608345845914 \tabularnewline
33 & 103.45 & 103.158846478537 & 0.291153521463443 \tabularnewline
34 & 103.8 & 103.358711134622 & 0.441288865378027 \tabularnewline
35 & 103.81 & 103.747495644399 & 0.0625043556006943 \tabularnewline
36 & 103.81 & 103.813742379996 & -0.00374237999585603 \tabularnewline
37 & 103.81 & 103.837135309402 & -0.027135309402297 \tabularnewline
38 & 103.84 & 103.832463833858 & 0.00753616614248642 \tabularnewline
39 & 103.9 & 103.879472937100 & 0.020527062899518 \tabularnewline
40 & 103.91 & 103.912385033261 & -0.00238503326063721 \tabularnewline
41 & 103.92 & 103.942569017299 & -0.0225690172989061 \tabularnewline
42 & 103.92 & 103.953966084705 & -0.0339660847046162 \tabularnewline
43 & 103.93 & 103.958355610351 & -0.0283556103509142 \tabularnewline
44 & 104 & 103.993022254074 & 0.00697774592559597 \tabularnewline
45 & 104.51 & 104.936703172511 & -0.426703172511296 \tabularnewline
46 & 105 & 104.796085302426 & 0.203914697574348 \tabularnewline
47 & 105.01 & 104.877693576527 & 0.132306423472713 \tabularnewline
48 & 105.01 & 104.948649494638 & 0.0613505053624408 \tabularnewline
49 & 105.01 & 104.994949012119 & 0.0150509878813381 \tabularnewline
50 & 105.01 & 105.026936696687 & -0.0169366966870825 \tabularnewline
51 & 105.13 & 105.062678274329 & 0.0673217256708938 \tabularnewline
52 & 105.14 & 105.110564310335 & 0.0294356896646093 \tabularnewline
53 & 105.15 & 105.149532299847 & 0.000467700153194528 \tabularnewline
54 & 105.22 & 105.169357218309 & 0.0506427816913231 \tabularnewline
55 & 105.23 & 105.227242097804 & 0.00275790219559724 \tabularnewline
56 & 105.23 & 105.299168409326 & -0.0691684093262381 \tabularnewline
57 & 105.57 & 106.012892020798 & -0.442892020798439 \tabularnewline
58 & 106.05 & 106.138614564618 & -0.0886145646178278 \tabularnewline
59 & 106.09 & 106.015000026336 & 0.07499997366439 \tabularnewline
60 & 106.09 & 106.011965668201 & 0.0780343317992163 \tabularnewline
61 & 106.19 & 106.037372912807 & 0.152627087192570 \tabularnewline
62 & 106.2 & 106.127682508202 & 0.0723174917983727 \tabularnewline
63 & 106.2 & 106.248050965841 & -0.0480509658406874 \tabularnewline
64 & 106.22 & 106.207888447256 & 0.0121115527439457 \tabularnewline
65 & 106.22 & 106.217494467209 & 0.00250553279082055 \tabularnewline
66 & 106.23 & 106.253393743378 & -0.0233937433779658 \tabularnewline
67 & 106.23 & 106.239193728807 & -0.0091937288066788 \tabularnewline
68 & 106.61 & 106.263247843612 & 0.346752156387566 \tabularnewline
69 & 106.95 & 107.053725855553 & -0.103725855552668 \tabularnewline
70 & 107.74 & 107.541068806443 & 0.19893119355703 \tabularnewline
71 & 107.8 & 107.676761836326 & 0.123238163674145 \tabularnewline
72 & 107.8 & 107.729616741881 & 0.0703832581187811 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13632&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]101.34[/C][C]101.055322222222[/C][C]0.284677777777773[/C][/ROW]
[ROW][C]14[/C][C]101.34[/C][C]101.285402859038[/C][C]0.0545971409617465[/C][/ROW]
[ROW][C]15[/C][C]101.34[/C][C]101.354014459186[/C][C]-0.0140144591858444[/C][/ROW]
[ROW][C]16[/C][C]101.34[/C][C]101.350050166162[/C][C]-0.0100501661623724[/C][/ROW]
[ROW][C]17[/C][C]101.34[/C][C]101.342150125245[/C][C]-0.00215012524522251[/C][/ROW]
[ROW][C]18[/C][C]101.34[/C][C]101.334473700191[/C][C]0.00552629980882102[/C][/ROW]
[ROW][C]19[/C][C]101.34[/C][C]101.331739279313[/C][C]0.00826072068720407[/C][/ROW]
[ROW][C]20[/C][C]101.39[/C][C]101.380831091356[/C][C]0.00916890864405673[/C][/ROW]
[ROW][C]21[/C][C]102.16[/C][C]102.149081579318[/C][C]0.0109184206817048[/C][/ROW]
[ROW][C]22[/C][C]102.19[/C][C]102.177025662979[/C][C]0.0129743370205802[/C][/ROW]
[ROW][C]23[/C][C]102.31[/C][C]102.296156467775[/C][C]0.0138435322246977[/C][/ROW]
[ROW][C]24[/C][C]102.32[/C][C]102.305833097757[/C][C]0.014166902243403[/C][/ROW]
[ROW][C]25[/C][C]102.32[/C][C]102.315010562329[/C][C]0.00498943767085791[/C][/ROW]
[ROW][C]26[/C][C]102.32[/C][C]102.290667839546[/C][C]0.0293321604544445[/C][/ROW]
[ROW][C]27[/C][C]102.36[/C][C]102.317983697548[/C][C]0.0420163024515574[/C][/ROW]
[ROW][C]28[/C][C]102.36[/C][C]102.352134199747[/C][C]0.00786580025264527[/C][/ROW]
[ROW][C]29[/C][C]102.37[/C][C]102.363136349787[/C][C]0.006863650212793[/C][/ROW]
[ROW][C]30[/C][C]102.37[/C][C]102.369542068591[/C][C]0.000457931409172829[/C][/ROW]
[ROW][C]31[/C][C]102.37[/C][C]102.370611049142[/C][C]-0.000611049141767239[/C][/ROW]
[ROW][C]32[/C][C]102.37[/C][C]102.420260834585[/C][C]-0.0502608345845914[/C][/ROW]
[ROW][C]33[/C][C]103.45[/C][C]103.158846478537[/C][C]0.291153521463443[/C][/ROW]
[ROW][C]34[/C][C]103.8[/C][C]103.358711134622[/C][C]0.441288865378027[/C][/ROW]
[ROW][C]35[/C][C]103.81[/C][C]103.747495644399[/C][C]0.0625043556006943[/C][/ROW]
[ROW][C]36[/C][C]103.81[/C][C]103.813742379996[/C][C]-0.00374237999585603[/C][/ROW]
[ROW][C]37[/C][C]103.81[/C][C]103.837135309402[/C][C]-0.027135309402297[/C][/ROW]
[ROW][C]38[/C][C]103.84[/C][C]103.832463833858[/C][C]0.00753616614248642[/C][/ROW]
[ROW][C]39[/C][C]103.9[/C][C]103.879472937100[/C][C]0.020527062899518[/C][/ROW]
[ROW][C]40[/C][C]103.91[/C][C]103.912385033261[/C][C]-0.00238503326063721[/C][/ROW]
[ROW][C]41[/C][C]103.92[/C][C]103.942569017299[/C][C]-0.0225690172989061[/C][/ROW]
[ROW][C]42[/C][C]103.92[/C][C]103.953966084705[/C][C]-0.0339660847046162[/C][/ROW]
[ROW][C]43[/C][C]103.93[/C][C]103.958355610351[/C][C]-0.0283556103509142[/C][/ROW]
[ROW][C]44[/C][C]104[/C][C]103.993022254074[/C][C]0.00697774592559597[/C][/ROW]
[ROW][C]45[/C][C]104.51[/C][C]104.936703172511[/C][C]-0.426703172511296[/C][/ROW]
[ROW][C]46[/C][C]105[/C][C]104.796085302426[/C][C]0.203914697574348[/C][/ROW]
[ROW][C]47[/C][C]105.01[/C][C]104.877693576527[/C][C]0.132306423472713[/C][/ROW]
[ROW][C]48[/C][C]105.01[/C][C]104.948649494638[/C][C]0.0613505053624408[/C][/ROW]
[ROW][C]49[/C][C]105.01[/C][C]104.994949012119[/C][C]0.0150509878813381[/C][/ROW]
[ROW][C]50[/C][C]105.01[/C][C]105.026936696687[/C][C]-0.0169366966870825[/C][/ROW]
[ROW][C]51[/C][C]105.13[/C][C]105.062678274329[/C][C]0.0673217256708938[/C][/ROW]
[ROW][C]52[/C][C]105.14[/C][C]105.110564310335[/C][C]0.0294356896646093[/C][/ROW]
[ROW][C]53[/C][C]105.15[/C][C]105.149532299847[/C][C]0.000467700153194528[/C][/ROW]
[ROW][C]54[/C][C]105.22[/C][C]105.169357218309[/C][C]0.0506427816913231[/C][/ROW]
[ROW][C]55[/C][C]105.23[/C][C]105.227242097804[/C][C]0.00275790219559724[/C][/ROW]
[ROW][C]56[/C][C]105.23[/C][C]105.299168409326[/C][C]-0.0691684093262381[/C][/ROW]
[ROW][C]57[/C][C]105.57[/C][C]106.012892020798[/C][C]-0.442892020798439[/C][/ROW]
[ROW][C]58[/C][C]106.05[/C][C]106.138614564618[/C][C]-0.0886145646178278[/C][/ROW]
[ROW][C]59[/C][C]106.09[/C][C]106.015000026336[/C][C]0.07499997366439[/C][/ROW]
[ROW][C]60[/C][C]106.09[/C][C]106.011965668201[/C][C]0.0780343317992163[/C][/ROW]
[ROW][C]61[/C][C]106.19[/C][C]106.037372912807[/C][C]0.152627087192570[/C][/ROW]
[ROW][C]62[/C][C]106.2[/C][C]106.127682508202[/C][C]0.0723174917983727[/C][/ROW]
[ROW][C]63[/C][C]106.2[/C][C]106.248050965841[/C][C]-0.0480509658406874[/C][/ROW]
[ROW][C]64[/C][C]106.22[/C][C]106.207888447256[/C][C]0.0121115527439457[/C][/ROW]
[ROW][C]65[/C][C]106.22[/C][C]106.217494467209[/C][C]0.00250553279082055[/C][/ROW]
[ROW][C]66[/C][C]106.23[/C][C]106.253393743378[/C][C]-0.0233937433779658[/C][/ROW]
[ROW][C]67[/C][C]106.23[/C][C]106.239193728807[/C][C]-0.0091937288066788[/C][/ROW]
[ROW][C]68[/C][C]106.61[/C][C]106.263247843612[/C][C]0.346752156387566[/C][/ROW]
[ROW][C]69[/C][C]106.95[/C][C]107.053725855553[/C][C]-0.103725855552668[/C][/ROW]
[ROW][C]70[/C][C]107.74[/C][C]107.541068806443[/C][C]0.19893119355703[/C][/ROW]
[ROW][C]71[/C][C]107.8[/C][C]107.676761836326[/C][C]0.123238163674145[/C][/ROW]
[ROW][C]72[/C][C]107.8[/C][C]107.729616741881[/C][C]0.0703832581187811[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13632&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13632&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
13101.34101.0553222222220.284677777777773
14101.34101.2854028590380.0545971409617465
15101.34101.354014459186-0.0140144591858444
16101.34101.350050166162-0.0100501661623724
17101.34101.342150125245-0.00215012524522251
18101.34101.3344737001910.00552629980882102
19101.34101.3317392793130.00826072068720407
20101.39101.3808310913560.00916890864405673
21102.16102.1490815793180.0109184206817048
22102.19102.1770256629790.0129743370205802
23102.31102.2961564677750.0138435322246977
24102.32102.3058330977570.014166902243403
25102.32102.3150105623290.00498943767085791
26102.32102.2906678395460.0293321604544445
27102.36102.3179836975480.0420163024515574
28102.36102.3521341997470.00786580025264527
29102.37102.3631363497870.006863650212793
30102.37102.3695420685910.000457931409172829
31102.37102.370611049142-0.000611049141767239
32102.37102.420260834585-0.0502608345845914
33103.45103.1588464785370.291153521463443
34103.8103.3587111346220.441288865378027
35103.81103.7474956443990.0625043556006943
36103.81103.813742379996-0.00374237999585603
37103.81103.837135309402-0.027135309402297
38103.84103.8324638338580.00753616614248642
39103.9103.8794729371000.020527062899518
40103.91103.912385033261-0.00238503326063721
41103.92103.942569017299-0.0225690172989061
42103.92103.953966084705-0.0339660847046162
43103.93103.958355610351-0.0283556103509142
44104103.9930222540740.00697774592559597
45104.51104.936703172511-0.426703172511296
46105104.7960853024260.203914697574348
47105.01104.8776935765270.132306423472713
48105.01104.9486494946380.0613505053624408
49105.01104.9949490121190.0150509878813381
50105.01105.026936696687-0.0169366966870825
51105.13105.0626782743290.0673217256708938
52105.14105.1105643103350.0294356896646093
53105.15105.1495322998470.000467700153194528
54105.22105.1693572183090.0506427816913231
55105.23105.2272420978040.00275790219559724
56105.23105.299168409326-0.0691684093262381
57105.57106.012892020798-0.442892020798439
58106.05106.138614564618-0.0886145646178278
59106.09106.0150000263360.07499997366439
60106.09106.0119656682010.0780343317992163
61106.19106.0373729128070.152627087192570
62106.2106.1276825082020.0723174917983727
63106.2106.248050965841-0.0480509658406874
64106.22106.2078884472560.0121115527439457
65106.22106.2174944672090.00250553279082055
66106.23106.253393743378-0.0233937433779658
67106.23106.239193728807-0.0091937288066788
68106.61106.2632478436120.346752156387566
69106.95107.053725855553-0.103725855552668
70107.74107.5410688064430.19893119355703
71107.8107.6767618363260.123238163674145
72107.8107.7296167418810.0703832581187811







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73107.810203582369107.551132399128108.069274765611
74107.801201522479107.499201909271108.103201135686
75107.847744714236107.504079577628108.191409850844
76107.881932499667107.497251582135108.266613417200
77107.901135234431107.475717246965108.326553221896
78107.944885661203107.478769211744108.411002110663
79107.971409726603107.464470577782108.478348875424
80108.177138541015107.629138191005108.725138891025
81108.585578440489107.996196183743109.174960697236
82109.276550118507108.645405020626109.907695216387
83109.273514127294108.600180551164109.946847703424
84109.236144493104108.520163343796109.952125642412

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 107.810203582369 & 107.551132399128 & 108.069274765611 \tabularnewline
74 & 107.801201522479 & 107.499201909271 & 108.103201135686 \tabularnewline
75 & 107.847744714236 & 107.504079577628 & 108.191409850844 \tabularnewline
76 & 107.881932499667 & 107.497251582135 & 108.266613417200 \tabularnewline
77 & 107.901135234431 & 107.475717246965 & 108.326553221896 \tabularnewline
78 & 107.944885661203 & 107.478769211744 & 108.411002110663 \tabularnewline
79 & 107.971409726603 & 107.464470577782 & 108.478348875424 \tabularnewline
80 & 108.177138541015 & 107.629138191005 & 108.725138891025 \tabularnewline
81 & 108.585578440489 & 107.996196183743 & 109.174960697236 \tabularnewline
82 & 109.276550118507 & 108.645405020626 & 109.907695216387 \tabularnewline
83 & 109.273514127294 & 108.600180551164 & 109.946847703424 \tabularnewline
84 & 109.236144493104 & 108.520163343796 & 109.952125642412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13632&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]107.810203582369[/C][C]107.551132399128[/C][C]108.069274765611[/C][/ROW]
[ROW][C]74[/C][C]107.801201522479[/C][C]107.499201909271[/C][C]108.103201135686[/C][/ROW]
[ROW][C]75[/C][C]107.847744714236[/C][C]107.504079577628[/C][C]108.191409850844[/C][/ROW]
[ROW][C]76[/C][C]107.881932499667[/C][C]107.497251582135[/C][C]108.266613417200[/C][/ROW]
[ROW][C]77[/C][C]107.901135234431[/C][C]107.475717246965[/C][C]108.326553221896[/C][/ROW]
[ROW][C]78[/C][C]107.944885661203[/C][C]107.478769211744[/C][C]108.411002110663[/C][/ROW]
[ROW][C]79[/C][C]107.971409726603[/C][C]107.464470577782[/C][C]108.478348875424[/C][/ROW]
[ROW][C]80[/C][C]108.177138541015[/C][C]107.629138191005[/C][C]108.725138891025[/C][/ROW]
[ROW][C]81[/C][C]108.585578440489[/C][C]107.996196183743[/C][C]109.174960697236[/C][/ROW]
[ROW][C]82[/C][C]109.276550118507[/C][C]108.645405020626[/C][C]109.907695216387[/C][/ROW]
[ROW][C]83[/C][C]109.273514127294[/C][C]108.600180551164[/C][C]109.946847703424[/C][/ROW]
[ROW][C]84[/C][C]109.236144493104[/C][C]108.520163343796[/C][C]109.952125642412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13632&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13632&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
73107.810203582369107.551132399128108.069274765611
74107.801201522479107.499201909271108.103201135686
75107.847744714236107.504079577628108.191409850844
76107.881932499667107.497251582135108.266613417200
77107.901135234431107.475717246965108.326553221896
78107.944885661203107.478769211744108.411002110663
79107.971409726603107.464470577782108.478348875424
80108.177138541015107.629138191005108.725138891025
81108.585578440489107.996196183743109.174960697236
82109.276550118507108.645405020626109.907695216387
83109.273514127294108.600180551164109.946847703424
84109.236144493104108.520163343796109.952125642412



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')