Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 27 Nov 2016 18:38:05 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/27/t148027190050ys11xve929b4g.htm/, Retrieved Mon, 29 Apr 2024 20:47:09 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 20:47:09 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
102.59
102.91
101.94
101.8
102.25
102.6
102.49
102.13
100.76
100.86
101.12
100.74
99.99
99.39
99.52
99.21
99.38
99.37
99.38
99.26
99.36
99.2
98.53
98.65
99.15
100.17
99.98
100.07
99.94
100.05
99.13
98.74
98.64
98.44
98.81
98.88
99.63
100.08
100.07
100.55
99.98
99.89
99.86
99.61
100.12
100.24
100.1
99.86
97.99
97.57
98.28
97.97
97.99
97.84
97.33
96.7
96.79
96.76
96.23
96.29
96.46
97.23
97.59
97.13
97.37
96.12
96.96
96.7
97
97.15
96.51
96.68




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999931067825166
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999931067825166 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \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]0.999931067825166[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/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
alpha0.999931067825166
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2102.91102.590.319999999999993
3101.94102.909977941704-0.969977941704059
4101.8101.940066862689-0.140066862689068
5102.25101.8000096551130.44999034488653
6102.6102.2499689811870.350031018813127
7102.49102.599975871601-0.109975871600611
8102.13102.490007580876-0.360007580876015
9100.76102.130024816106-1.3700248161055
10100.86100.760094438790.0999055612098516
11101.12100.8599931132920.260006886707629
12100.74101.11998207716-0.379982077159838
1399.99100.740026192991-0.750026192990987
1499.3999.9900517009367-0.60005170093666
1599.5299.39004136286880.129958637131239
1699.2199.5199910416685-0.309991041668511
1799.3899.21002136835670.169978631643318
1899.3799.3799882830032-0.00998828300323851
1999.3899.37000068851410.00999931148592736
2099.2699.3799993107257-0.119999310725703
2199.3699.26000827181350.0999917281865237
2299.299.3599931073527-0.159993107352705
2398.5399.2000110286728-0.670011028672846
2498.6598.53004618531740.119953814682631
2599.1598.64999173132270.50000826867732
26100.1799.14996553334261.02003446665739
2799.98100.169929686806-0.189929686805797
28100.0799.98001309226640.0899869077336035
2999.94100.069993797007-0.129993797006748
30100.0599.94000896075510.109991039244861
3199.13100.049992418078-0.919992418078451
3298.7499.1300634170782-0.39006341707821
3398.6498.7400268879197-0.100026887919668
3498.4498.6400068950709-0.200006895070928
3598.8198.44001378691030.369986213089746
3698.8898.80997449604570.0700255039543265
3799.6398.87999517298970.750004827010287
38100.0899.62994830053610.450051699463856
39100.07100.079968976958-0.00996897695756616
40100.55100.0700006871830.479999312816744
4199.98100.549966912603-0.569966912603434
4299.8999.9800392890589-0.090039289058879
4399.8699.890006206604-0.0300062066040283
4499.6199.8600020683931-0.250002068393087
45100.1299.61001723318630.509982766813721
46100.24100.1199648457790.120035154221242
47100.1100.239991725716-0.13999172571576
4899.86100.100009649934-0.240009649934109
4997.9999.8600165443872-1.87001654438716
5097.5797.9901289043074-0.420128904307376
5198.2897.57002896039910.70997103960093
5297.9798.2799510601522-0.309951060152173
5397.9997.97002136560070.0199786343993225
5497.8497.9899986228293-0.149998622829273
5597.3397.8400103397313-0.510010339731295
5696.797.3300351561219-0.630035156121892
5796.7996.70004342969350.0899565703064695
5896.7696.789993799098-0.0299937990979657
5996.2396.7600020675378-0.530002067537808
6096.2996.23003653419520.0599634658048132
6196.4696.28999586658790.170004133412093
6297.2396.45998828124530.77001171875466
6397.5997.22994692141760.360053078582425
6497.1397.5899751807582-0.459975180758249
6597.3797.13003170708960.239968292910433
6696.1297.3699834584637-1.24998345846367
6796.9696.12008616407830.839913835921692
6896.796.9599421029126-0.259942102912603
699796.70001791837450.299982081625515
7097.1596.99997932158270.150020678417306
7196.5197.1499896587484-0.639989658748362
7296.6896.51004411587910.169955884120952

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 102.91 & 102.59 & 0.319999999999993 \tabularnewline
3 & 101.94 & 102.909977941704 & -0.969977941704059 \tabularnewline
4 & 101.8 & 101.940066862689 & -0.140066862689068 \tabularnewline
5 & 102.25 & 101.800009655113 & 0.44999034488653 \tabularnewline
6 & 102.6 & 102.249968981187 & 0.350031018813127 \tabularnewline
7 & 102.49 & 102.599975871601 & -0.109975871600611 \tabularnewline
8 & 102.13 & 102.490007580876 & -0.360007580876015 \tabularnewline
9 & 100.76 & 102.130024816106 & -1.3700248161055 \tabularnewline
10 & 100.86 & 100.76009443879 & 0.0999055612098516 \tabularnewline
11 & 101.12 & 100.859993113292 & 0.260006886707629 \tabularnewline
12 & 100.74 & 101.11998207716 & -0.379982077159838 \tabularnewline
13 & 99.99 & 100.740026192991 & -0.750026192990987 \tabularnewline
14 & 99.39 & 99.9900517009367 & -0.60005170093666 \tabularnewline
15 & 99.52 & 99.3900413628688 & 0.129958637131239 \tabularnewline
16 & 99.21 & 99.5199910416685 & -0.309991041668511 \tabularnewline
17 & 99.38 & 99.2100213683567 & 0.169978631643318 \tabularnewline
18 & 99.37 & 99.3799882830032 & -0.00998828300323851 \tabularnewline
19 & 99.38 & 99.3700006885141 & 0.00999931148592736 \tabularnewline
20 & 99.26 & 99.3799993107257 & -0.119999310725703 \tabularnewline
21 & 99.36 & 99.2600082718135 & 0.0999917281865237 \tabularnewline
22 & 99.2 & 99.3599931073527 & -0.159993107352705 \tabularnewline
23 & 98.53 & 99.2000110286728 & -0.670011028672846 \tabularnewline
24 & 98.65 & 98.5300461853174 & 0.119953814682631 \tabularnewline
25 & 99.15 & 98.6499917313227 & 0.50000826867732 \tabularnewline
26 & 100.17 & 99.1499655333426 & 1.02003446665739 \tabularnewline
27 & 99.98 & 100.169929686806 & -0.189929686805797 \tabularnewline
28 & 100.07 & 99.9800130922664 & 0.0899869077336035 \tabularnewline
29 & 99.94 & 100.069993797007 & -0.129993797006748 \tabularnewline
30 & 100.05 & 99.9400089607551 & 0.109991039244861 \tabularnewline
31 & 99.13 & 100.049992418078 & -0.919992418078451 \tabularnewline
32 & 98.74 & 99.1300634170782 & -0.39006341707821 \tabularnewline
33 & 98.64 & 98.7400268879197 & -0.100026887919668 \tabularnewline
34 & 98.44 & 98.6400068950709 & -0.200006895070928 \tabularnewline
35 & 98.81 & 98.4400137869103 & 0.369986213089746 \tabularnewline
36 & 98.88 & 98.8099744960457 & 0.0700255039543265 \tabularnewline
37 & 99.63 & 98.8799951729897 & 0.750004827010287 \tabularnewline
38 & 100.08 & 99.6299483005361 & 0.450051699463856 \tabularnewline
39 & 100.07 & 100.079968976958 & -0.00996897695756616 \tabularnewline
40 & 100.55 & 100.070000687183 & 0.479999312816744 \tabularnewline
41 & 99.98 & 100.549966912603 & -0.569966912603434 \tabularnewline
42 & 99.89 & 99.9800392890589 & -0.090039289058879 \tabularnewline
43 & 99.86 & 99.890006206604 & -0.0300062066040283 \tabularnewline
44 & 99.61 & 99.8600020683931 & -0.250002068393087 \tabularnewline
45 & 100.12 & 99.6100172331863 & 0.509982766813721 \tabularnewline
46 & 100.24 & 100.119964845779 & 0.120035154221242 \tabularnewline
47 & 100.1 & 100.239991725716 & -0.13999172571576 \tabularnewline
48 & 99.86 & 100.100009649934 & -0.240009649934109 \tabularnewline
49 & 97.99 & 99.8600165443872 & -1.87001654438716 \tabularnewline
50 & 97.57 & 97.9901289043074 & -0.420128904307376 \tabularnewline
51 & 98.28 & 97.5700289603991 & 0.70997103960093 \tabularnewline
52 & 97.97 & 98.2799510601522 & -0.309951060152173 \tabularnewline
53 & 97.99 & 97.9700213656007 & 0.0199786343993225 \tabularnewline
54 & 97.84 & 97.9899986228293 & -0.149998622829273 \tabularnewline
55 & 97.33 & 97.8400103397313 & -0.510010339731295 \tabularnewline
56 & 96.7 & 97.3300351561219 & -0.630035156121892 \tabularnewline
57 & 96.79 & 96.7000434296935 & 0.0899565703064695 \tabularnewline
58 & 96.76 & 96.789993799098 & -0.0299937990979657 \tabularnewline
59 & 96.23 & 96.7600020675378 & -0.530002067537808 \tabularnewline
60 & 96.29 & 96.2300365341952 & 0.0599634658048132 \tabularnewline
61 & 96.46 & 96.2899958665879 & 0.170004133412093 \tabularnewline
62 & 97.23 & 96.4599882812453 & 0.77001171875466 \tabularnewline
63 & 97.59 & 97.2299469214176 & 0.360053078582425 \tabularnewline
64 & 97.13 & 97.5899751807582 & -0.459975180758249 \tabularnewline
65 & 97.37 & 97.1300317070896 & 0.239968292910433 \tabularnewline
66 & 96.12 & 97.3699834584637 & -1.24998345846367 \tabularnewline
67 & 96.96 & 96.1200861640783 & 0.839913835921692 \tabularnewline
68 & 96.7 & 96.9599421029126 & -0.259942102912603 \tabularnewline
69 & 97 & 96.7000179183745 & 0.299982081625515 \tabularnewline
70 & 97.15 & 96.9999793215827 & 0.150020678417306 \tabularnewline
71 & 96.51 & 97.1499896587484 & -0.639989658748362 \tabularnewline
72 & 96.68 & 96.5100441158791 & 0.169955884120952 \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]2[/C][C]102.91[/C][C]102.59[/C][C]0.319999999999993[/C][/ROW]
[ROW][C]3[/C][C]101.94[/C][C]102.909977941704[/C][C]-0.969977941704059[/C][/ROW]
[ROW][C]4[/C][C]101.8[/C][C]101.940066862689[/C][C]-0.140066862689068[/C][/ROW]
[ROW][C]5[/C][C]102.25[/C][C]101.800009655113[/C][C]0.44999034488653[/C][/ROW]
[ROW][C]6[/C][C]102.6[/C][C]102.249968981187[/C][C]0.350031018813127[/C][/ROW]
[ROW][C]7[/C][C]102.49[/C][C]102.599975871601[/C][C]-0.109975871600611[/C][/ROW]
[ROW][C]8[/C][C]102.13[/C][C]102.490007580876[/C][C]-0.360007580876015[/C][/ROW]
[ROW][C]9[/C][C]100.76[/C][C]102.130024816106[/C][C]-1.3700248161055[/C][/ROW]
[ROW][C]10[/C][C]100.86[/C][C]100.76009443879[/C][C]0.0999055612098516[/C][/ROW]
[ROW][C]11[/C][C]101.12[/C][C]100.859993113292[/C][C]0.260006886707629[/C][/ROW]
[ROW][C]12[/C][C]100.74[/C][C]101.11998207716[/C][C]-0.379982077159838[/C][/ROW]
[ROW][C]13[/C][C]99.99[/C][C]100.740026192991[/C][C]-0.750026192990987[/C][/ROW]
[ROW][C]14[/C][C]99.39[/C][C]99.9900517009367[/C][C]-0.60005170093666[/C][/ROW]
[ROW][C]15[/C][C]99.52[/C][C]99.3900413628688[/C][C]0.129958637131239[/C][/ROW]
[ROW][C]16[/C][C]99.21[/C][C]99.5199910416685[/C][C]-0.309991041668511[/C][/ROW]
[ROW][C]17[/C][C]99.38[/C][C]99.2100213683567[/C][C]0.169978631643318[/C][/ROW]
[ROW][C]18[/C][C]99.37[/C][C]99.3799882830032[/C][C]-0.00998828300323851[/C][/ROW]
[ROW][C]19[/C][C]99.38[/C][C]99.3700006885141[/C][C]0.00999931148592736[/C][/ROW]
[ROW][C]20[/C][C]99.26[/C][C]99.3799993107257[/C][C]-0.119999310725703[/C][/ROW]
[ROW][C]21[/C][C]99.36[/C][C]99.2600082718135[/C][C]0.0999917281865237[/C][/ROW]
[ROW][C]22[/C][C]99.2[/C][C]99.3599931073527[/C][C]-0.159993107352705[/C][/ROW]
[ROW][C]23[/C][C]98.53[/C][C]99.2000110286728[/C][C]-0.670011028672846[/C][/ROW]
[ROW][C]24[/C][C]98.65[/C][C]98.5300461853174[/C][C]0.119953814682631[/C][/ROW]
[ROW][C]25[/C][C]99.15[/C][C]98.6499917313227[/C][C]0.50000826867732[/C][/ROW]
[ROW][C]26[/C][C]100.17[/C][C]99.1499655333426[/C][C]1.02003446665739[/C][/ROW]
[ROW][C]27[/C][C]99.98[/C][C]100.169929686806[/C][C]-0.189929686805797[/C][/ROW]
[ROW][C]28[/C][C]100.07[/C][C]99.9800130922664[/C][C]0.0899869077336035[/C][/ROW]
[ROW][C]29[/C][C]99.94[/C][C]100.069993797007[/C][C]-0.129993797006748[/C][/ROW]
[ROW][C]30[/C][C]100.05[/C][C]99.9400089607551[/C][C]0.109991039244861[/C][/ROW]
[ROW][C]31[/C][C]99.13[/C][C]100.049992418078[/C][C]-0.919992418078451[/C][/ROW]
[ROW][C]32[/C][C]98.74[/C][C]99.1300634170782[/C][C]-0.39006341707821[/C][/ROW]
[ROW][C]33[/C][C]98.64[/C][C]98.7400268879197[/C][C]-0.100026887919668[/C][/ROW]
[ROW][C]34[/C][C]98.44[/C][C]98.6400068950709[/C][C]-0.200006895070928[/C][/ROW]
[ROW][C]35[/C][C]98.81[/C][C]98.4400137869103[/C][C]0.369986213089746[/C][/ROW]
[ROW][C]36[/C][C]98.88[/C][C]98.8099744960457[/C][C]0.0700255039543265[/C][/ROW]
[ROW][C]37[/C][C]99.63[/C][C]98.8799951729897[/C][C]0.750004827010287[/C][/ROW]
[ROW][C]38[/C][C]100.08[/C][C]99.6299483005361[/C][C]0.450051699463856[/C][/ROW]
[ROW][C]39[/C][C]100.07[/C][C]100.079968976958[/C][C]-0.00996897695756616[/C][/ROW]
[ROW][C]40[/C][C]100.55[/C][C]100.070000687183[/C][C]0.479999312816744[/C][/ROW]
[ROW][C]41[/C][C]99.98[/C][C]100.549966912603[/C][C]-0.569966912603434[/C][/ROW]
[ROW][C]42[/C][C]99.89[/C][C]99.9800392890589[/C][C]-0.090039289058879[/C][/ROW]
[ROW][C]43[/C][C]99.86[/C][C]99.890006206604[/C][C]-0.0300062066040283[/C][/ROW]
[ROW][C]44[/C][C]99.61[/C][C]99.8600020683931[/C][C]-0.250002068393087[/C][/ROW]
[ROW][C]45[/C][C]100.12[/C][C]99.6100172331863[/C][C]0.509982766813721[/C][/ROW]
[ROW][C]46[/C][C]100.24[/C][C]100.119964845779[/C][C]0.120035154221242[/C][/ROW]
[ROW][C]47[/C][C]100.1[/C][C]100.239991725716[/C][C]-0.13999172571576[/C][/ROW]
[ROW][C]48[/C][C]99.86[/C][C]100.100009649934[/C][C]-0.240009649934109[/C][/ROW]
[ROW][C]49[/C][C]97.99[/C][C]99.8600165443872[/C][C]-1.87001654438716[/C][/ROW]
[ROW][C]50[/C][C]97.57[/C][C]97.9901289043074[/C][C]-0.420128904307376[/C][/ROW]
[ROW][C]51[/C][C]98.28[/C][C]97.5700289603991[/C][C]0.70997103960093[/C][/ROW]
[ROW][C]52[/C][C]97.97[/C][C]98.2799510601522[/C][C]-0.309951060152173[/C][/ROW]
[ROW][C]53[/C][C]97.99[/C][C]97.9700213656007[/C][C]0.0199786343993225[/C][/ROW]
[ROW][C]54[/C][C]97.84[/C][C]97.9899986228293[/C][C]-0.149998622829273[/C][/ROW]
[ROW][C]55[/C][C]97.33[/C][C]97.8400103397313[/C][C]-0.510010339731295[/C][/ROW]
[ROW][C]56[/C][C]96.7[/C][C]97.3300351561219[/C][C]-0.630035156121892[/C][/ROW]
[ROW][C]57[/C][C]96.79[/C][C]96.7000434296935[/C][C]0.0899565703064695[/C][/ROW]
[ROW][C]58[/C][C]96.76[/C][C]96.789993799098[/C][C]-0.0299937990979657[/C][/ROW]
[ROW][C]59[/C][C]96.23[/C][C]96.7600020675378[/C][C]-0.530002067537808[/C][/ROW]
[ROW][C]60[/C][C]96.29[/C][C]96.2300365341952[/C][C]0.0599634658048132[/C][/ROW]
[ROW][C]61[/C][C]96.46[/C][C]96.2899958665879[/C][C]0.170004133412093[/C][/ROW]
[ROW][C]62[/C][C]97.23[/C][C]96.4599882812453[/C][C]0.77001171875466[/C][/ROW]
[ROW][C]63[/C][C]97.59[/C][C]97.2299469214176[/C][C]0.360053078582425[/C][/ROW]
[ROW][C]64[/C][C]97.13[/C][C]97.5899751807582[/C][C]-0.459975180758249[/C][/ROW]
[ROW][C]65[/C][C]97.37[/C][C]97.1300317070896[/C][C]0.239968292910433[/C][/ROW]
[ROW][C]66[/C][C]96.12[/C][C]97.3699834584637[/C][C]-1.24998345846367[/C][/ROW]
[ROW][C]67[/C][C]96.96[/C][C]96.1200861640783[/C][C]0.839913835921692[/C][/ROW]
[ROW][C]68[/C][C]96.7[/C][C]96.9599421029126[/C][C]-0.259942102912603[/C][/ROW]
[ROW][C]69[/C][C]97[/C][C]96.7000179183745[/C][C]0.299982081625515[/C][/ROW]
[ROW][C]70[/C][C]97.15[/C][C]96.9999793215827[/C][C]0.150020678417306[/C][/ROW]
[ROW][C]71[/C][C]96.51[/C][C]97.1499896587484[/C][C]-0.639989658748362[/C][/ROW]
[ROW][C]72[/C][C]96.68[/C][C]96.5100441158791[/C][C]0.169955884120952[/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
2102.91102.590.319999999999993
3101.94102.909977941704-0.969977941704059
4101.8101.940066862689-0.140066862689068
5102.25101.8000096551130.44999034488653
6102.6102.2499689811870.350031018813127
7102.49102.599975871601-0.109975871600611
8102.13102.490007580876-0.360007580876015
9100.76102.130024816106-1.3700248161055
10100.86100.760094438790.0999055612098516
11101.12100.8599931132920.260006886707629
12100.74101.11998207716-0.379982077159838
1399.99100.740026192991-0.750026192990987
1499.3999.9900517009367-0.60005170093666
1599.5299.39004136286880.129958637131239
1699.2199.5199910416685-0.309991041668511
1799.3899.21002136835670.169978631643318
1899.3799.3799882830032-0.00998828300323851
1999.3899.37000068851410.00999931148592736
2099.2699.3799993107257-0.119999310725703
2199.3699.26000827181350.0999917281865237
2299.299.3599931073527-0.159993107352705
2398.5399.2000110286728-0.670011028672846
2498.6598.53004618531740.119953814682631
2599.1598.64999173132270.50000826867732
26100.1799.14996553334261.02003446665739
2799.98100.169929686806-0.189929686805797
28100.0799.98001309226640.0899869077336035
2999.94100.069993797007-0.129993797006748
30100.0599.94000896075510.109991039244861
3199.13100.049992418078-0.919992418078451
3298.7499.1300634170782-0.39006341707821
3398.6498.7400268879197-0.100026887919668
3498.4498.6400068950709-0.200006895070928
3598.8198.44001378691030.369986213089746
3698.8898.80997449604570.0700255039543265
3799.6398.87999517298970.750004827010287
38100.0899.62994830053610.450051699463856
39100.07100.079968976958-0.00996897695756616
40100.55100.0700006871830.479999312816744
4199.98100.549966912603-0.569966912603434
4299.8999.9800392890589-0.090039289058879
4399.8699.890006206604-0.0300062066040283
4499.6199.8600020683931-0.250002068393087
45100.1299.61001723318630.509982766813721
46100.24100.1199648457790.120035154221242
47100.1100.239991725716-0.13999172571576
4899.86100.100009649934-0.240009649934109
4997.9999.8600165443872-1.87001654438716
5097.5797.9901289043074-0.420128904307376
5198.2897.57002896039910.70997103960093
5297.9798.2799510601522-0.309951060152173
5397.9997.97002136560070.0199786343993225
5497.8497.9899986228293-0.149998622829273
5597.3397.8400103397313-0.510010339731295
5696.797.3300351561219-0.630035156121892
5796.7996.70004342969350.0899565703064695
5896.7696.789993799098-0.0299937990979657
5996.2396.7600020675378-0.530002067537808
6096.2996.23003653419520.0599634658048132
6196.4696.28999586658790.170004133412093
6297.2396.45998828124530.77001171875466
6397.5997.22994692141760.360053078582425
6497.1397.5899751807582-0.459975180758249
6597.3797.13003170708960.239968292910433
6696.1297.3699834584637-1.24998345846367
6796.9696.12008616407830.839913835921692
6896.796.9599421029126-0.259942102912603
699796.70001791837450.299982081625515
7097.1596.99997932158270.150020678417306
7196.5197.1499896587484-0.639989658748362
7296.6896.51004411587910.169955884120952







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7396.679988284571395.681527192761597.6784493763811
7496.679988284571395.267999733591598.0919768355511
7596.679988284571394.950682416791498.4092941523512
7696.679988284571394.683169339203998.6768072299386
7796.679988284571394.44748452940898.9124920397345
7896.679988284571394.234408571485399.1255679976573
7996.679988284571394.038464624011499.3215119451312
8096.679988284571393.856084184652599.50389238449
8196.679988284571393.684788544691299.6751880244514
8296.679988284571393.522772961217899.8372036079247
8396.679988284571393.368674993102599.9913015760401
8496.679988284571393.2214361553562100.138540413786

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 96.6799882845713 & 95.6815271927615 & 97.6784493763811 \tabularnewline
74 & 96.6799882845713 & 95.2679997335915 & 98.0919768355511 \tabularnewline
75 & 96.6799882845713 & 94.9506824167914 & 98.4092941523512 \tabularnewline
76 & 96.6799882845713 & 94.6831693392039 & 98.6768072299386 \tabularnewline
77 & 96.6799882845713 & 94.447484529408 & 98.9124920397345 \tabularnewline
78 & 96.6799882845713 & 94.2344085714853 & 99.1255679976573 \tabularnewline
79 & 96.6799882845713 & 94.0384646240114 & 99.3215119451312 \tabularnewline
80 & 96.6799882845713 & 93.8560841846525 & 99.50389238449 \tabularnewline
81 & 96.6799882845713 & 93.6847885446912 & 99.6751880244514 \tabularnewline
82 & 96.6799882845713 & 93.5227729612178 & 99.8372036079247 \tabularnewline
83 & 96.6799882845713 & 93.3686749931025 & 99.9913015760401 \tabularnewline
84 & 96.6799882845713 & 93.2214361553562 & 100.138540413786 \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]96.6799882845713[/C][C]95.6815271927615[/C][C]97.6784493763811[/C][/ROW]
[ROW][C]74[/C][C]96.6799882845713[/C][C]95.2679997335915[/C][C]98.0919768355511[/C][/ROW]
[ROW][C]75[/C][C]96.6799882845713[/C][C]94.9506824167914[/C][C]98.4092941523512[/C][/ROW]
[ROW][C]76[/C][C]96.6799882845713[/C][C]94.6831693392039[/C][C]98.6768072299386[/C][/ROW]
[ROW][C]77[/C][C]96.6799882845713[/C][C]94.447484529408[/C][C]98.9124920397345[/C][/ROW]
[ROW][C]78[/C][C]96.6799882845713[/C][C]94.2344085714853[/C][C]99.1255679976573[/C][/ROW]
[ROW][C]79[/C][C]96.6799882845713[/C][C]94.0384646240114[/C][C]99.3215119451312[/C][/ROW]
[ROW][C]80[/C][C]96.6799882845713[/C][C]93.8560841846525[/C][C]99.50389238449[/C][/ROW]
[ROW][C]81[/C][C]96.6799882845713[/C][C]93.6847885446912[/C][C]99.6751880244514[/C][/ROW]
[ROW][C]82[/C][C]96.6799882845713[/C][C]93.5227729612178[/C][C]99.8372036079247[/C][/ROW]
[ROW][C]83[/C][C]96.6799882845713[/C][C]93.3686749931025[/C][C]99.9913015760401[/C][/ROW]
[ROW][C]84[/C][C]96.6799882845713[/C][C]93.2214361553562[/C][C]100.138540413786[/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
7396.679988284571395.681527192761597.6784493763811
7496.679988284571395.267999733591598.0919768355511
7596.679988284571394.950682416791498.4092941523512
7696.679988284571394.683169339203998.6768072299386
7796.679988284571394.44748452940898.9124920397345
7896.679988284571394.234408571485399.1255679976573
7996.679988284571394.038464624011499.3215119451312
8096.679988284571393.856084184652599.50389238449
8196.679988284571393.684788544691299.6751880244514
8296.679988284571393.522772961217899.8372036079247
8396.679988284571393.368674993102599.9913015760401
8496.679988284571393.2214361553562100.138540413786



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')