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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 27 Nov 2014 14:46:20 +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/2014/Nov/27/t14170996030p1t0v0vp4prul6.htm/, Retrieved Sun, 19 May 2024 20:21:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260310, Retrieved Sun, 19 May 2024 20:21:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact52
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-27 14:46:20] [072d4f39c76834f6beee313555a90f83] [Current]
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Dataseries X:
164,88
164,88
164,57
164,53
165,03
165,92
165,92
165,92
165,92
166,12
166,34
165,48
165,61
165,61
165,94
165,88
166,23
166,32
166,43
166,43
166,2
166,21
168,02
168,68
168,65
168,65
168,75
168,8
168,58
168,98
169
169
168,94
169,96
171,59
172,41
172,65
172,65
172,65
172,38
171,95
171,95
171,87
171,87
171,91
171,99
172,15
172,73
173,2
164,97
164,97
164,43
163,16
162,98
161,69
162,19
162
162,22
164,08
164,58
164,68




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260310&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]2 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=260310&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260310&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999919364920202
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999919364920202 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260310&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]0.999919364920202[/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=260310&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260310&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
alpha0.999919364920202
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2164.88164.880
3164.57164.88-0.310000000000002
4164.53164.570024996875-0.0400249968747346
5165.03164.5300032274190.49999677258117
6165.92165.029959682720.890040317279642
7165.92165.9199282315287.17684719973022e-05
8165.92165.9199999942135.78705794396228e-09
9165.92165.924.54747350886464e-13
10166.12165.920.200000000000017
11166.34166.1199838729840.220016127015953
12165.48166.339982258982-0.859982258982029
13165.61165.4800693447380.129930655261944
14165.61165.6099895230311.04769687538919e-05
15165.94165.6099999991550.330000000844791
16165.88165.939973390424-0.0599733904236075
17166.23165.8800048359590.349995164040877
18166.32166.2299717781120.0900282218879909
19166.43166.3199927405670.110007259432876
20166.43166.4299911295568.87044413389049e-06
21166.2166.429999999285-0.229999999284757
22166.21166.2000185460680.00998145393171512
23168.02166.2099991951451.81000080485535
24168.68168.0198540504410.660145949559336
25168.65168.679946769079-0.0299467690786912
26168.65168.65000241476-2.41476013229658e-06
27168.75168.6500000001950.0999999998052772
28168.8168.7499919364920.0500080635079883
29168.58168.799995967596-0.219995967595821
30168.98168.5800177393920.399982260607572
31169168.9799677473980.02003225260151
32169168.9999983846981.61530226705509e-06
33168.94168.99999999987-0.059999999869774
34169.96168.9400048381051.01999516189522
35171.59169.9599177526091.63008224739127
36172.41171.5898685581880.820131441812066
37172.65172.4099338686360.240066131364244
38172.65172.6499806422481.93577516824917e-05
39172.65172.6499999984391.56092028191779e-09
40172.38172.65-0.269999999999868
41171.95172.380021771472-0.430021771471559
42171.95171.95003467484-3.46748398385444e-05
43171.87171.950000002796-0.0800000027959982
44171.87171.870006450807-6.45080660888198e-06
45171.91171.870000000520.0399999994798463
46171.99171.9099967745970.0800032254031748
47172.15171.9899935489340.160006451066465
48172.73172.1499870978670.580012902132921
49173.2172.7299532306130.47004676938667
50164.97173.199962097741-8.22996209774121
51164.97164.97066362365-0.000663623650467571
52164.43164.970000053511-0.540000053511335
53163.16164.430043542947-1.27004354294741
54162.98163.160102410062-0.18010241006246
55161.69162.980014522572-1.29001452257219
56162.19161.6901040204240.499895979576024
57162162.189959690848-0.189959690847786
58162.22162.0000153174150.219984682585164
59164.08162.2199822615181.86001773848244
60164.58164.0798500173210.500149982678749
61164.68164.5799596703660.100040329633771

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 164.88 & 164.88 & 0 \tabularnewline
3 & 164.57 & 164.88 & -0.310000000000002 \tabularnewline
4 & 164.53 & 164.570024996875 & -0.0400249968747346 \tabularnewline
5 & 165.03 & 164.530003227419 & 0.49999677258117 \tabularnewline
6 & 165.92 & 165.02995968272 & 0.890040317279642 \tabularnewline
7 & 165.92 & 165.919928231528 & 7.17684719973022e-05 \tabularnewline
8 & 165.92 & 165.919999994213 & 5.78705794396228e-09 \tabularnewline
9 & 165.92 & 165.92 & 4.54747350886464e-13 \tabularnewline
10 & 166.12 & 165.92 & 0.200000000000017 \tabularnewline
11 & 166.34 & 166.119983872984 & 0.220016127015953 \tabularnewline
12 & 165.48 & 166.339982258982 & -0.859982258982029 \tabularnewline
13 & 165.61 & 165.480069344738 & 0.129930655261944 \tabularnewline
14 & 165.61 & 165.609989523031 & 1.04769687538919e-05 \tabularnewline
15 & 165.94 & 165.609999999155 & 0.330000000844791 \tabularnewline
16 & 165.88 & 165.939973390424 & -0.0599733904236075 \tabularnewline
17 & 166.23 & 165.880004835959 & 0.349995164040877 \tabularnewline
18 & 166.32 & 166.229971778112 & 0.0900282218879909 \tabularnewline
19 & 166.43 & 166.319992740567 & 0.110007259432876 \tabularnewline
20 & 166.43 & 166.429991129556 & 8.87044413389049e-06 \tabularnewline
21 & 166.2 & 166.429999999285 & -0.229999999284757 \tabularnewline
22 & 166.21 & 166.200018546068 & 0.00998145393171512 \tabularnewline
23 & 168.02 & 166.209999195145 & 1.81000080485535 \tabularnewline
24 & 168.68 & 168.019854050441 & 0.660145949559336 \tabularnewline
25 & 168.65 & 168.679946769079 & -0.0299467690786912 \tabularnewline
26 & 168.65 & 168.65000241476 & -2.41476013229658e-06 \tabularnewline
27 & 168.75 & 168.650000000195 & 0.0999999998052772 \tabularnewline
28 & 168.8 & 168.749991936492 & 0.0500080635079883 \tabularnewline
29 & 168.58 & 168.799995967596 & -0.219995967595821 \tabularnewline
30 & 168.98 & 168.580017739392 & 0.399982260607572 \tabularnewline
31 & 169 & 168.979967747398 & 0.02003225260151 \tabularnewline
32 & 169 & 168.999998384698 & 1.61530226705509e-06 \tabularnewline
33 & 168.94 & 168.99999999987 & -0.059999999869774 \tabularnewline
34 & 169.96 & 168.940004838105 & 1.01999516189522 \tabularnewline
35 & 171.59 & 169.959917752609 & 1.63008224739127 \tabularnewline
36 & 172.41 & 171.589868558188 & 0.820131441812066 \tabularnewline
37 & 172.65 & 172.409933868636 & 0.240066131364244 \tabularnewline
38 & 172.65 & 172.649980642248 & 1.93577516824917e-05 \tabularnewline
39 & 172.65 & 172.649999998439 & 1.56092028191779e-09 \tabularnewline
40 & 172.38 & 172.65 & -0.269999999999868 \tabularnewline
41 & 171.95 & 172.380021771472 & -0.430021771471559 \tabularnewline
42 & 171.95 & 171.95003467484 & -3.46748398385444e-05 \tabularnewline
43 & 171.87 & 171.950000002796 & -0.0800000027959982 \tabularnewline
44 & 171.87 & 171.870006450807 & -6.45080660888198e-06 \tabularnewline
45 & 171.91 & 171.87000000052 & 0.0399999994798463 \tabularnewline
46 & 171.99 & 171.909996774597 & 0.0800032254031748 \tabularnewline
47 & 172.15 & 171.989993548934 & 0.160006451066465 \tabularnewline
48 & 172.73 & 172.149987097867 & 0.580012902132921 \tabularnewline
49 & 173.2 & 172.729953230613 & 0.47004676938667 \tabularnewline
50 & 164.97 & 173.199962097741 & -8.22996209774121 \tabularnewline
51 & 164.97 & 164.97066362365 & -0.000663623650467571 \tabularnewline
52 & 164.43 & 164.970000053511 & -0.540000053511335 \tabularnewline
53 & 163.16 & 164.430043542947 & -1.27004354294741 \tabularnewline
54 & 162.98 & 163.160102410062 & -0.18010241006246 \tabularnewline
55 & 161.69 & 162.980014522572 & -1.29001452257219 \tabularnewline
56 & 162.19 & 161.690104020424 & 0.499895979576024 \tabularnewline
57 & 162 & 162.189959690848 & -0.189959690847786 \tabularnewline
58 & 162.22 & 162.000015317415 & 0.219984682585164 \tabularnewline
59 & 164.08 & 162.219982261518 & 1.86001773848244 \tabularnewline
60 & 164.58 & 164.079850017321 & 0.500149982678749 \tabularnewline
61 & 164.68 & 164.579959670366 & 0.100040329633771 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260310&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]164.88[/C][C]164.88[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]164.57[/C][C]164.88[/C][C]-0.310000000000002[/C][/ROW]
[ROW][C]4[/C][C]164.53[/C][C]164.570024996875[/C][C]-0.0400249968747346[/C][/ROW]
[ROW][C]5[/C][C]165.03[/C][C]164.530003227419[/C][C]0.49999677258117[/C][/ROW]
[ROW][C]6[/C][C]165.92[/C][C]165.02995968272[/C][C]0.890040317279642[/C][/ROW]
[ROW][C]7[/C][C]165.92[/C][C]165.919928231528[/C][C]7.17684719973022e-05[/C][/ROW]
[ROW][C]8[/C][C]165.92[/C][C]165.919999994213[/C][C]5.78705794396228e-09[/C][/ROW]
[ROW][C]9[/C][C]165.92[/C][C]165.92[/C][C]4.54747350886464e-13[/C][/ROW]
[ROW][C]10[/C][C]166.12[/C][C]165.92[/C][C]0.200000000000017[/C][/ROW]
[ROW][C]11[/C][C]166.34[/C][C]166.119983872984[/C][C]0.220016127015953[/C][/ROW]
[ROW][C]12[/C][C]165.48[/C][C]166.339982258982[/C][C]-0.859982258982029[/C][/ROW]
[ROW][C]13[/C][C]165.61[/C][C]165.480069344738[/C][C]0.129930655261944[/C][/ROW]
[ROW][C]14[/C][C]165.61[/C][C]165.609989523031[/C][C]1.04769687538919e-05[/C][/ROW]
[ROW][C]15[/C][C]165.94[/C][C]165.609999999155[/C][C]0.330000000844791[/C][/ROW]
[ROW][C]16[/C][C]165.88[/C][C]165.939973390424[/C][C]-0.0599733904236075[/C][/ROW]
[ROW][C]17[/C][C]166.23[/C][C]165.880004835959[/C][C]0.349995164040877[/C][/ROW]
[ROW][C]18[/C][C]166.32[/C][C]166.229971778112[/C][C]0.0900282218879909[/C][/ROW]
[ROW][C]19[/C][C]166.43[/C][C]166.319992740567[/C][C]0.110007259432876[/C][/ROW]
[ROW][C]20[/C][C]166.43[/C][C]166.429991129556[/C][C]8.87044413389049e-06[/C][/ROW]
[ROW][C]21[/C][C]166.2[/C][C]166.429999999285[/C][C]-0.229999999284757[/C][/ROW]
[ROW][C]22[/C][C]166.21[/C][C]166.200018546068[/C][C]0.00998145393171512[/C][/ROW]
[ROW][C]23[/C][C]168.02[/C][C]166.209999195145[/C][C]1.81000080485535[/C][/ROW]
[ROW][C]24[/C][C]168.68[/C][C]168.019854050441[/C][C]0.660145949559336[/C][/ROW]
[ROW][C]25[/C][C]168.65[/C][C]168.679946769079[/C][C]-0.0299467690786912[/C][/ROW]
[ROW][C]26[/C][C]168.65[/C][C]168.65000241476[/C][C]-2.41476013229658e-06[/C][/ROW]
[ROW][C]27[/C][C]168.75[/C][C]168.650000000195[/C][C]0.0999999998052772[/C][/ROW]
[ROW][C]28[/C][C]168.8[/C][C]168.749991936492[/C][C]0.0500080635079883[/C][/ROW]
[ROW][C]29[/C][C]168.58[/C][C]168.799995967596[/C][C]-0.219995967595821[/C][/ROW]
[ROW][C]30[/C][C]168.98[/C][C]168.580017739392[/C][C]0.399982260607572[/C][/ROW]
[ROW][C]31[/C][C]169[/C][C]168.979967747398[/C][C]0.02003225260151[/C][/ROW]
[ROW][C]32[/C][C]169[/C][C]168.999998384698[/C][C]1.61530226705509e-06[/C][/ROW]
[ROW][C]33[/C][C]168.94[/C][C]168.99999999987[/C][C]-0.059999999869774[/C][/ROW]
[ROW][C]34[/C][C]169.96[/C][C]168.940004838105[/C][C]1.01999516189522[/C][/ROW]
[ROW][C]35[/C][C]171.59[/C][C]169.959917752609[/C][C]1.63008224739127[/C][/ROW]
[ROW][C]36[/C][C]172.41[/C][C]171.589868558188[/C][C]0.820131441812066[/C][/ROW]
[ROW][C]37[/C][C]172.65[/C][C]172.409933868636[/C][C]0.240066131364244[/C][/ROW]
[ROW][C]38[/C][C]172.65[/C][C]172.649980642248[/C][C]1.93577516824917e-05[/C][/ROW]
[ROW][C]39[/C][C]172.65[/C][C]172.649999998439[/C][C]1.56092028191779e-09[/C][/ROW]
[ROW][C]40[/C][C]172.38[/C][C]172.65[/C][C]-0.269999999999868[/C][/ROW]
[ROW][C]41[/C][C]171.95[/C][C]172.380021771472[/C][C]-0.430021771471559[/C][/ROW]
[ROW][C]42[/C][C]171.95[/C][C]171.95003467484[/C][C]-3.46748398385444e-05[/C][/ROW]
[ROW][C]43[/C][C]171.87[/C][C]171.950000002796[/C][C]-0.0800000027959982[/C][/ROW]
[ROW][C]44[/C][C]171.87[/C][C]171.870006450807[/C][C]-6.45080660888198e-06[/C][/ROW]
[ROW][C]45[/C][C]171.91[/C][C]171.87000000052[/C][C]0.0399999994798463[/C][/ROW]
[ROW][C]46[/C][C]171.99[/C][C]171.909996774597[/C][C]0.0800032254031748[/C][/ROW]
[ROW][C]47[/C][C]172.15[/C][C]171.989993548934[/C][C]0.160006451066465[/C][/ROW]
[ROW][C]48[/C][C]172.73[/C][C]172.149987097867[/C][C]0.580012902132921[/C][/ROW]
[ROW][C]49[/C][C]173.2[/C][C]172.729953230613[/C][C]0.47004676938667[/C][/ROW]
[ROW][C]50[/C][C]164.97[/C][C]173.199962097741[/C][C]-8.22996209774121[/C][/ROW]
[ROW][C]51[/C][C]164.97[/C][C]164.97066362365[/C][C]-0.000663623650467571[/C][/ROW]
[ROW][C]52[/C][C]164.43[/C][C]164.970000053511[/C][C]-0.540000053511335[/C][/ROW]
[ROW][C]53[/C][C]163.16[/C][C]164.430043542947[/C][C]-1.27004354294741[/C][/ROW]
[ROW][C]54[/C][C]162.98[/C][C]163.160102410062[/C][C]-0.18010241006246[/C][/ROW]
[ROW][C]55[/C][C]161.69[/C][C]162.980014522572[/C][C]-1.29001452257219[/C][/ROW]
[ROW][C]56[/C][C]162.19[/C][C]161.690104020424[/C][C]0.499895979576024[/C][/ROW]
[ROW][C]57[/C][C]162[/C][C]162.189959690848[/C][C]-0.189959690847786[/C][/ROW]
[ROW][C]58[/C][C]162.22[/C][C]162.000015317415[/C][C]0.219984682585164[/C][/ROW]
[ROW][C]59[/C][C]164.08[/C][C]162.219982261518[/C][C]1.86001773848244[/C][/ROW]
[ROW][C]60[/C][C]164.58[/C][C]164.079850017321[/C][C]0.500149982678749[/C][/ROW]
[ROW][C]61[/C][C]164.68[/C][C]164.579959670366[/C][C]0.100040329633771[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260310&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260310&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
2164.88164.880
3164.57164.88-0.310000000000002
4164.53164.570024996875-0.0400249968747346
5165.03164.5300032274190.49999677258117
6165.92165.029959682720.890040317279642
7165.92165.9199282315287.17684719973022e-05
8165.92165.9199999942135.78705794396228e-09
9165.92165.924.54747350886464e-13
10166.12165.920.200000000000017
11166.34166.1199838729840.220016127015953
12165.48166.339982258982-0.859982258982029
13165.61165.4800693447380.129930655261944
14165.61165.6099895230311.04769687538919e-05
15165.94165.6099999991550.330000000844791
16165.88165.939973390424-0.0599733904236075
17166.23165.8800048359590.349995164040877
18166.32166.2299717781120.0900282218879909
19166.43166.3199927405670.110007259432876
20166.43166.4299911295568.87044413389049e-06
21166.2166.429999999285-0.229999999284757
22166.21166.2000185460680.00998145393171512
23168.02166.2099991951451.81000080485535
24168.68168.0198540504410.660145949559336
25168.65168.679946769079-0.0299467690786912
26168.65168.65000241476-2.41476013229658e-06
27168.75168.6500000001950.0999999998052772
28168.8168.7499919364920.0500080635079883
29168.58168.799995967596-0.219995967595821
30168.98168.5800177393920.399982260607572
31169168.9799677473980.02003225260151
32169168.9999983846981.61530226705509e-06
33168.94168.99999999987-0.059999999869774
34169.96168.9400048381051.01999516189522
35171.59169.9599177526091.63008224739127
36172.41171.5898685581880.820131441812066
37172.65172.4099338686360.240066131364244
38172.65172.6499806422481.93577516824917e-05
39172.65172.6499999984391.56092028191779e-09
40172.38172.65-0.269999999999868
41171.95172.380021771472-0.430021771471559
42171.95171.95003467484-3.46748398385444e-05
43171.87171.950000002796-0.0800000027959982
44171.87171.870006450807-6.45080660888198e-06
45171.91171.870000000520.0399999994798463
46171.99171.9099967745970.0800032254031748
47172.15171.9899935489340.160006451066465
48172.73172.1499870978670.580012902132921
49173.2172.7299532306130.47004676938667
50164.97173.199962097741-8.22996209774121
51164.97164.97066362365-0.000663623650467571
52164.43164.970000053511-0.540000053511335
53163.16164.430043542947-1.27004354294741
54162.98163.160102410062-0.18010241006246
55161.69162.980014522572-1.29001452257219
56162.19161.6901040204240.499895979576024
57162162.189959690848-0.189959690847786
58162.22162.0000153174150.219984682585164
59164.08162.2199822615181.86001773848244
60164.58164.0798500173210.500149982678749
61164.68164.5799596703660.100040329633771







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
62164.67999193324162.301326083117167.058657783363
63164.67999193324161.316186050754168.043797815727
64164.67999193324160.5602432997168.799740566781
65164.67999193324159.922947935959169.437035930521
66164.67999193324159.361476503106169.998507363374
67164.67999193324158.853865847316170.506118019164
68164.67999193324158.38706860957170.97291525691
69164.67999193324157.952583610112171.407400256368
70164.67999193324157.544505857673171.815478008807
71164.67999193324157.158535935688172.201447930792
72164.67999193324156.791428115179172.568555751301
73164.67999193324156.440660777125172.919323089355

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 164.67999193324 & 162.301326083117 & 167.058657783363 \tabularnewline
63 & 164.67999193324 & 161.316186050754 & 168.043797815727 \tabularnewline
64 & 164.67999193324 & 160.5602432997 & 168.799740566781 \tabularnewline
65 & 164.67999193324 & 159.922947935959 & 169.437035930521 \tabularnewline
66 & 164.67999193324 & 159.361476503106 & 169.998507363374 \tabularnewline
67 & 164.67999193324 & 158.853865847316 & 170.506118019164 \tabularnewline
68 & 164.67999193324 & 158.38706860957 & 170.97291525691 \tabularnewline
69 & 164.67999193324 & 157.952583610112 & 171.407400256368 \tabularnewline
70 & 164.67999193324 & 157.544505857673 & 171.815478008807 \tabularnewline
71 & 164.67999193324 & 157.158535935688 & 172.201447930792 \tabularnewline
72 & 164.67999193324 & 156.791428115179 & 172.568555751301 \tabularnewline
73 & 164.67999193324 & 156.440660777125 & 172.919323089355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260310&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]62[/C][C]164.67999193324[/C][C]162.301326083117[/C][C]167.058657783363[/C][/ROW]
[ROW][C]63[/C][C]164.67999193324[/C][C]161.316186050754[/C][C]168.043797815727[/C][/ROW]
[ROW][C]64[/C][C]164.67999193324[/C][C]160.5602432997[/C][C]168.799740566781[/C][/ROW]
[ROW][C]65[/C][C]164.67999193324[/C][C]159.922947935959[/C][C]169.437035930521[/C][/ROW]
[ROW][C]66[/C][C]164.67999193324[/C][C]159.361476503106[/C][C]169.998507363374[/C][/ROW]
[ROW][C]67[/C][C]164.67999193324[/C][C]158.853865847316[/C][C]170.506118019164[/C][/ROW]
[ROW][C]68[/C][C]164.67999193324[/C][C]158.38706860957[/C][C]170.97291525691[/C][/ROW]
[ROW][C]69[/C][C]164.67999193324[/C][C]157.952583610112[/C][C]171.407400256368[/C][/ROW]
[ROW][C]70[/C][C]164.67999193324[/C][C]157.544505857673[/C][C]171.815478008807[/C][/ROW]
[ROW][C]71[/C][C]164.67999193324[/C][C]157.158535935688[/C][C]172.201447930792[/C][/ROW]
[ROW][C]72[/C][C]164.67999193324[/C][C]156.791428115179[/C][C]172.568555751301[/C][/ROW]
[ROW][C]73[/C][C]164.67999193324[/C][C]156.440660777125[/C][C]172.919323089355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260310&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260310&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
62164.67999193324162.301326083117167.058657783363
63164.67999193324161.316186050754168.043797815727
64164.67999193324160.5602432997168.799740566781
65164.67999193324159.922947935959169.437035930521
66164.67999193324159.361476503106169.998507363374
67164.67999193324158.853865847316170.506118019164
68164.67999193324158.38706860957170.97291525691
69164.67999193324157.952583610112171.407400256368
70164.67999193324157.544505857673171.815478008807
71164.67999193324157.158535935688172.201447930792
72164.67999193324156.791428115179172.568555751301
73164.67999193324156.440660777125172.919323089355



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')