Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 22 May 2013 17:41:02 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/22/t1369258959vcc5cvnvz6gz58y.htm/, Retrieved Sat, 27 Apr 2024 22:32:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210312, Retrieved Sat, 27 Apr 2024 22:32:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Triple exponentia...] [2013-05-22 21:41:02] [2a3542871793008b9eb9a15b7c7c93cc] [Current]
Feedback Forum

Post a new message
Dataseries X:
163,93
164,28
164,58
165,97
166,3
166,27
166,27
166,44
166,26
166,64
166,07
166,19
166,19
166,19
166,35
166,52
167,17
167,16
167,16
167,16
167,39
168,46
168,55
168,58
168,58
169,21
169,29
169,24
169,53
169,57
169,57
169,67
170,04
170,39
170,57
170,48
170,48
170,48
170,49
170,72
171,11
171,07
171,07
171,07
171,05
172,28
172,74
172,86
172,86
173,24
173,2
173,38
172,89
172,98
172,98
172,69
172,77
172,65
172,3
172,17
172,17
173,07
173,27
173,05
173,41
173,37
173,37
173,08
173,97
175,23
174,9
174,83




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210312&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210312&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210312&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0538182498493872
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0538182498493872 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210312&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0538182498493872[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210312&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210312&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
alpha1
beta0.0538182498493872
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3164.58164.63-0.0499999999999829
4165.97164.9273090875081.04269091249245
5166.3166.373424887552-0.0734248875517096
6166.27166.699473288608-0.429473288608307
7166.27166.646359787858-0.376359787858348
8166.44166.626104762762-0.186104762762142
9166.26166.786088930142-0.52608893014164
10166.64166.5777757446560.0622242553437218
11166.07166.961124545177-0.891124545177036
12166.19166.343165781758-0.153165781757792
13166.19166.454922667447-0.264922667446768
14166.19166.440664993139-0.250664993139367
15166.35166.42717464191-0.0771746419100907
16166.52166.58302123775-0.063021237749723
17167.17166.7496295450310.420370454969287
18167.16167.422253147206-0.262253147205541
19167.16167.398139141805-0.238139141805448
20167.16167.385322909973-0.225322909972846
21167.39167.3731964253070.0168035746928581
22168.46167.6041007642880.855899235711718
23168.55168.720163763202-0.170163763201742
24168.58168.801005847278-0.221005847278434
25168.58168.819111699371-0.239111699371449
26169.21168.8062431261930.403756873807254
27169.29169.457972614506-0.167972614505743
28169.24169.52893262237-0.288932622370368
29169.53169.463382774310.0666172256899529
30169.57169.756967996806-0.186967996806487
31169.57169.786905706441-0.216905706440514
32169.67169.775232220938-0.105232220937552
33170.04169.8695688069790.170431193021102
34170.39170.2487411155070.141258884492942
35170.57170.606343421446-0.0363434214461336
36170.48170.78438748211-0.304387482110371
37170.48170.678005880547-0.198005880547129
38170.48170.667349550596-0.187349550596196
39170.49170.657266725673-0.167266725673016
40170.72170.6582647232390.0617352767607144
41171.11170.8915872077890.218412792211495
42171.07171.29334180201-0.223341802010083
43171.07171.241321937108-0.171321937107649
44171.07171.232101690292-0.162101690291706
45171.05171.223377661023-0.173377661022585
46172.28171.1940467787431.0859532212566
47172.74172.482490880530.257509119470285
48172.86172.95634957066-0.0963495706598678
49172.86173.071164205393-0.211164205393203
50173.24173.0597997174280.180200282571889
51173.2173.449497781258-0.249497781258498
52173.38173.39607024733-0.01607024732985
53172.89173.575205374744-0.68520537474393
54172.98173.048328820688-0.0683288206878103
55172.98173.134651483144-0.154651483144107
56172.69173.126328410985-0.436328410984686
57172.77172.812845979546-0.0428459795459162
58172.65172.890540083914-0.240540083913686
59172.3172.757594637579-0.457594637578808
60172.17172.382967695044-0.212967695043886
61172.17172.241506146422-0.0715061464221378
62173.07172.2376578107680.832342189231781
63173.27173.1824530106680.0875469893315142
64173.05173.387164636414-0.337164636413888
65173.41173.1490190257710.260980974229
66173.37173.523064565048-0.15306456504797
67173.37173.474826898043-0.104826898043143
68173.08173.469185297853-0.389185297853317
69173.97173.1582400262560.811759973744245
70175.23174.091927527341.13807247265953
71174.9175.413176596021-0.513176596020742
72174.83175.055558329759-0.225558329759252

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 164.58 & 164.63 & -0.0499999999999829 \tabularnewline
4 & 165.97 & 164.927309087508 & 1.04269091249245 \tabularnewline
5 & 166.3 & 166.373424887552 & -0.0734248875517096 \tabularnewline
6 & 166.27 & 166.699473288608 & -0.429473288608307 \tabularnewline
7 & 166.27 & 166.646359787858 & -0.376359787858348 \tabularnewline
8 & 166.44 & 166.626104762762 & -0.186104762762142 \tabularnewline
9 & 166.26 & 166.786088930142 & -0.52608893014164 \tabularnewline
10 & 166.64 & 166.577775744656 & 0.0622242553437218 \tabularnewline
11 & 166.07 & 166.961124545177 & -0.891124545177036 \tabularnewline
12 & 166.19 & 166.343165781758 & -0.153165781757792 \tabularnewline
13 & 166.19 & 166.454922667447 & -0.264922667446768 \tabularnewline
14 & 166.19 & 166.440664993139 & -0.250664993139367 \tabularnewline
15 & 166.35 & 166.42717464191 & -0.0771746419100907 \tabularnewline
16 & 166.52 & 166.58302123775 & -0.063021237749723 \tabularnewline
17 & 167.17 & 166.749629545031 & 0.420370454969287 \tabularnewline
18 & 167.16 & 167.422253147206 & -0.262253147205541 \tabularnewline
19 & 167.16 & 167.398139141805 & -0.238139141805448 \tabularnewline
20 & 167.16 & 167.385322909973 & -0.225322909972846 \tabularnewline
21 & 167.39 & 167.373196425307 & 0.0168035746928581 \tabularnewline
22 & 168.46 & 167.604100764288 & 0.855899235711718 \tabularnewline
23 & 168.55 & 168.720163763202 & -0.170163763201742 \tabularnewline
24 & 168.58 & 168.801005847278 & -0.221005847278434 \tabularnewline
25 & 168.58 & 168.819111699371 & -0.239111699371449 \tabularnewline
26 & 169.21 & 168.806243126193 & 0.403756873807254 \tabularnewline
27 & 169.29 & 169.457972614506 & -0.167972614505743 \tabularnewline
28 & 169.24 & 169.52893262237 & -0.288932622370368 \tabularnewline
29 & 169.53 & 169.46338277431 & 0.0666172256899529 \tabularnewline
30 & 169.57 & 169.756967996806 & -0.186967996806487 \tabularnewline
31 & 169.57 & 169.786905706441 & -0.216905706440514 \tabularnewline
32 & 169.67 & 169.775232220938 & -0.105232220937552 \tabularnewline
33 & 170.04 & 169.869568806979 & 0.170431193021102 \tabularnewline
34 & 170.39 & 170.248741115507 & 0.141258884492942 \tabularnewline
35 & 170.57 & 170.606343421446 & -0.0363434214461336 \tabularnewline
36 & 170.48 & 170.78438748211 & -0.304387482110371 \tabularnewline
37 & 170.48 & 170.678005880547 & -0.198005880547129 \tabularnewline
38 & 170.48 & 170.667349550596 & -0.187349550596196 \tabularnewline
39 & 170.49 & 170.657266725673 & -0.167266725673016 \tabularnewline
40 & 170.72 & 170.658264723239 & 0.0617352767607144 \tabularnewline
41 & 171.11 & 170.891587207789 & 0.218412792211495 \tabularnewline
42 & 171.07 & 171.29334180201 & -0.223341802010083 \tabularnewline
43 & 171.07 & 171.241321937108 & -0.171321937107649 \tabularnewline
44 & 171.07 & 171.232101690292 & -0.162101690291706 \tabularnewline
45 & 171.05 & 171.223377661023 & -0.173377661022585 \tabularnewline
46 & 172.28 & 171.194046778743 & 1.0859532212566 \tabularnewline
47 & 172.74 & 172.48249088053 & 0.257509119470285 \tabularnewline
48 & 172.86 & 172.95634957066 & -0.0963495706598678 \tabularnewline
49 & 172.86 & 173.071164205393 & -0.211164205393203 \tabularnewline
50 & 173.24 & 173.059799717428 & 0.180200282571889 \tabularnewline
51 & 173.2 & 173.449497781258 & -0.249497781258498 \tabularnewline
52 & 173.38 & 173.39607024733 & -0.01607024732985 \tabularnewline
53 & 172.89 & 173.575205374744 & -0.68520537474393 \tabularnewline
54 & 172.98 & 173.048328820688 & -0.0683288206878103 \tabularnewline
55 & 172.98 & 173.134651483144 & -0.154651483144107 \tabularnewline
56 & 172.69 & 173.126328410985 & -0.436328410984686 \tabularnewline
57 & 172.77 & 172.812845979546 & -0.0428459795459162 \tabularnewline
58 & 172.65 & 172.890540083914 & -0.240540083913686 \tabularnewline
59 & 172.3 & 172.757594637579 & -0.457594637578808 \tabularnewline
60 & 172.17 & 172.382967695044 & -0.212967695043886 \tabularnewline
61 & 172.17 & 172.241506146422 & -0.0715061464221378 \tabularnewline
62 & 173.07 & 172.237657810768 & 0.832342189231781 \tabularnewline
63 & 173.27 & 173.182453010668 & 0.0875469893315142 \tabularnewline
64 & 173.05 & 173.387164636414 & -0.337164636413888 \tabularnewline
65 & 173.41 & 173.149019025771 & 0.260980974229 \tabularnewline
66 & 173.37 & 173.523064565048 & -0.15306456504797 \tabularnewline
67 & 173.37 & 173.474826898043 & -0.104826898043143 \tabularnewline
68 & 173.08 & 173.469185297853 & -0.389185297853317 \tabularnewline
69 & 173.97 & 173.158240026256 & 0.811759973744245 \tabularnewline
70 & 175.23 & 174.09192752734 & 1.13807247265953 \tabularnewline
71 & 174.9 & 175.413176596021 & -0.513176596020742 \tabularnewline
72 & 174.83 & 175.055558329759 & -0.225558329759252 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210312&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]3[/C][C]164.58[/C][C]164.63[/C][C]-0.0499999999999829[/C][/ROW]
[ROW][C]4[/C][C]165.97[/C][C]164.927309087508[/C][C]1.04269091249245[/C][/ROW]
[ROW][C]5[/C][C]166.3[/C][C]166.373424887552[/C][C]-0.0734248875517096[/C][/ROW]
[ROW][C]6[/C][C]166.27[/C][C]166.699473288608[/C][C]-0.429473288608307[/C][/ROW]
[ROW][C]7[/C][C]166.27[/C][C]166.646359787858[/C][C]-0.376359787858348[/C][/ROW]
[ROW][C]8[/C][C]166.44[/C][C]166.626104762762[/C][C]-0.186104762762142[/C][/ROW]
[ROW][C]9[/C][C]166.26[/C][C]166.786088930142[/C][C]-0.52608893014164[/C][/ROW]
[ROW][C]10[/C][C]166.64[/C][C]166.577775744656[/C][C]0.0622242553437218[/C][/ROW]
[ROW][C]11[/C][C]166.07[/C][C]166.961124545177[/C][C]-0.891124545177036[/C][/ROW]
[ROW][C]12[/C][C]166.19[/C][C]166.343165781758[/C][C]-0.153165781757792[/C][/ROW]
[ROW][C]13[/C][C]166.19[/C][C]166.454922667447[/C][C]-0.264922667446768[/C][/ROW]
[ROW][C]14[/C][C]166.19[/C][C]166.440664993139[/C][C]-0.250664993139367[/C][/ROW]
[ROW][C]15[/C][C]166.35[/C][C]166.42717464191[/C][C]-0.0771746419100907[/C][/ROW]
[ROW][C]16[/C][C]166.52[/C][C]166.58302123775[/C][C]-0.063021237749723[/C][/ROW]
[ROW][C]17[/C][C]167.17[/C][C]166.749629545031[/C][C]0.420370454969287[/C][/ROW]
[ROW][C]18[/C][C]167.16[/C][C]167.422253147206[/C][C]-0.262253147205541[/C][/ROW]
[ROW][C]19[/C][C]167.16[/C][C]167.398139141805[/C][C]-0.238139141805448[/C][/ROW]
[ROW][C]20[/C][C]167.16[/C][C]167.385322909973[/C][C]-0.225322909972846[/C][/ROW]
[ROW][C]21[/C][C]167.39[/C][C]167.373196425307[/C][C]0.0168035746928581[/C][/ROW]
[ROW][C]22[/C][C]168.46[/C][C]167.604100764288[/C][C]0.855899235711718[/C][/ROW]
[ROW][C]23[/C][C]168.55[/C][C]168.720163763202[/C][C]-0.170163763201742[/C][/ROW]
[ROW][C]24[/C][C]168.58[/C][C]168.801005847278[/C][C]-0.221005847278434[/C][/ROW]
[ROW][C]25[/C][C]168.58[/C][C]168.819111699371[/C][C]-0.239111699371449[/C][/ROW]
[ROW][C]26[/C][C]169.21[/C][C]168.806243126193[/C][C]0.403756873807254[/C][/ROW]
[ROW][C]27[/C][C]169.29[/C][C]169.457972614506[/C][C]-0.167972614505743[/C][/ROW]
[ROW][C]28[/C][C]169.24[/C][C]169.52893262237[/C][C]-0.288932622370368[/C][/ROW]
[ROW][C]29[/C][C]169.53[/C][C]169.46338277431[/C][C]0.0666172256899529[/C][/ROW]
[ROW][C]30[/C][C]169.57[/C][C]169.756967996806[/C][C]-0.186967996806487[/C][/ROW]
[ROW][C]31[/C][C]169.57[/C][C]169.786905706441[/C][C]-0.216905706440514[/C][/ROW]
[ROW][C]32[/C][C]169.67[/C][C]169.775232220938[/C][C]-0.105232220937552[/C][/ROW]
[ROW][C]33[/C][C]170.04[/C][C]169.869568806979[/C][C]0.170431193021102[/C][/ROW]
[ROW][C]34[/C][C]170.39[/C][C]170.248741115507[/C][C]0.141258884492942[/C][/ROW]
[ROW][C]35[/C][C]170.57[/C][C]170.606343421446[/C][C]-0.0363434214461336[/C][/ROW]
[ROW][C]36[/C][C]170.48[/C][C]170.78438748211[/C][C]-0.304387482110371[/C][/ROW]
[ROW][C]37[/C][C]170.48[/C][C]170.678005880547[/C][C]-0.198005880547129[/C][/ROW]
[ROW][C]38[/C][C]170.48[/C][C]170.667349550596[/C][C]-0.187349550596196[/C][/ROW]
[ROW][C]39[/C][C]170.49[/C][C]170.657266725673[/C][C]-0.167266725673016[/C][/ROW]
[ROW][C]40[/C][C]170.72[/C][C]170.658264723239[/C][C]0.0617352767607144[/C][/ROW]
[ROW][C]41[/C][C]171.11[/C][C]170.891587207789[/C][C]0.218412792211495[/C][/ROW]
[ROW][C]42[/C][C]171.07[/C][C]171.29334180201[/C][C]-0.223341802010083[/C][/ROW]
[ROW][C]43[/C][C]171.07[/C][C]171.241321937108[/C][C]-0.171321937107649[/C][/ROW]
[ROW][C]44[/C][C]171.07[/C][C]171.232101690292[/C][C]-0.162101690291706[/C][/ROW]
[ROW][C]45[/C][C]171.05[/C][C]171.223377661023[/C][C]-0.173377661022585[/C][/ROW]
[ROW][C]46[/C][C]172.28[/C][C]171.194046778743[/C][C]1.0859532212566[/C][/ROW]
[ROW][C]47[/C][C]172.74[/C][C]172.48249088053[/C][C]0.257509119470285[/C][/ROW]
[ROW][C]48[/C][C]172.86[/C][C]172.95634957066[/C][C]-0.0963495706598678[/C][/ROW]
[ROW][C]49[/C][C]172.86[/C][C]173.071164205393[/C][C]-0.211164205393203[/C][/ROW]
[ROW][C]50[/C][C]173.24[/C][C]173.059799717428[/C][C]0.180200282571889[/C][/ROW]
[ROW][C]51[/C][C]173.2[/C][C]173.449497781258[/C][C]-0.249497781258498[/C][/ROW]
[ROW][C]52[/C][C]173.38[/C][C]173.39607024733[/C][C]-0.01607024732985[/C][/ROW]
[ROW][C]53[/C][C]172.89[/C][C]173.575205374744[/C][C]-0.68520537474393[/C][/ROW]
[ROW][C]54[/C][C]172.98[/C][C]173.048328820688[/C][C]-0.0683288206878103[/C][/ROW]
[ROW][C]55[/C][C]172.98[/C][C]173.134651483144[/C][C]-0.154651483144107[/C][/ROW]
[ROW][C]56[/C][C]172.69[/C][C]173.126328410985[/C][C]-0.436328410984686[/C][/ROW]
[ROW][C]57[/C][C]172.77[/C][C]172.812845979546[/C][C]-0.0428459795459162[/C][/ROW]
[ROW][C]58[/C][C]172.65[/C][C]172.890540083914[/C][C]-0.240540083913686[/C][/ROW]
[ROW][C]59[/C][C]172.3[/C][C]172.757594637579[/C][C]-0.457594637578808[/C][/ROW]
[ROW][C]60[/C][C]172.17[/C][C]172.382967695044[/C][C]-0.212967695043886[/C][/ROW]
[ROW][C]61[/C][C]172.17[/C][C]172.241506146422[/C][C]-0.0715061464221378[/C][/ROW]
[ROW][C]62[/C][C]173.07[/C][C]172.237657810768[/C][C]0.832342189231781[/C][/ROW]
[ROW][C]63[/C][C]173.27[/C][C]173.182453010668[/C][C]0.0875469893315142[/C][/ROW]
[ROW][C]64[/C][C]173.05[/C][C]173.387164636414[/C][C]-0.337164636413888[/C][/ROW]
[ROW][C]65[/C][C]173.41[/C][C]173.149019025771[/C][C]0.260980974229[/C][/ROW]
[ROW][C]66[/C][C]173.37[/C][C]173.523064565048[/C][C]-0.15306456504797[/C][/ROW]
[ROW][C]67[/C][C]173.37[/C][C]173.474826898043[/C][C]-0.104826898043143[/C][/ROW]
[ROW][C]68[/C][C]173.08[/C][C]173.469185297853[/C][C]-0.389185297853317[/C][/ROW]
[ROW][C]69[/C][C]173.97[/C][C]173.158240026256[/C][C]0.811759973744245[/C][/ROW]
[ROW][C]70[/C][C]175.23[/C][C]174.09192752734[/C][C]1.13807247265953[/C][/ROW]
[ROW][C]71[/C][C]174.9[/C][C]175.413176596021[/C][C]-0.513176596020742[/C][/ROW]
[ROW][C]72[/C][C]174.83[/C][C]175.055558329759[/C][C]-0.225558329759252[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210312&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210312&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
3164.58164.63-0.0499999999999829
4165.97164.9273090875081.04269091249245
5166.3166.373424887552-0.0734248875517096
6166.27166.699473288608-0.429473288608307
7166.27166.646359787858-0.376359787858348
8166.44166.626104762762-0.186104762762142
9166.26166.786088930142-0.52608893014164
10166.64166.5777757446560.0622242553437218
11166.07166.961124545177-0.891124545177036
12166.19166.343165781758-0.153165781757792
13166.19166.454922667447-0.264922667446768
14166.19166.440664993139-0.250664993139367
15166.35166.42717464191-0.0771746419100907
16166.52166.58302123775-0.063021237749723
17167.17166.7496295450310.420370454969287
18167.16167.422253147206-0.262253147205541
19167.16167.398139141805-0.238139141805448
20167.16167.385322909973-0.225322909972846
21167.39167.3731964253070.0168035746928581
22168.46167.6041007642880.855899235711718
23168.55168.720163763202-0.170163763201742
24168.58168.801005847278-0.221005847278434
25168.58168.819111699371-0.239111699371449
26169.21168.8062431261930.403756873807254
27169.29169.457972614506-0.167972614505743
28169.24169.52893262237-0.288932622370368
29169.53169.463382774310.0666172256899529
30169.57169.756967996806-0.186967996806487
31169.57169.786905706441-0.216905706440514
32169.67169.775232220938-0.105232220937552
33170.04169.8695688069790.170431193021102
34170.39170.2487411155070.141258884492942
35170.57170.606343421446-0.0363434214461336
36170.48170.78438748211-0.304387482110371
37170.48170.678005880547-0.198005880547129
38170.48170.667349550596-0.187349550596196
39170.49170.657266725673-0.167266725673016
40170.72170.6582647232390.0617352767607144
41171.11170.8915872077890.218412792211495
42171.07171.29334180201-0.223341802010083
43171.07171.241321937108-0.171321937107649
44171.07171.232101690292-0.162101690291706
45171.05171.223377661023-0.173377661022585
46172.28171.1940467787431.0859532212566
47172.74172.482490880530.257509119470285
48172.86172.95634957066-0.0963495706598678
49172.86173.071164205393-0.211164205393203
50173.24173.0597997174280.180200282571889
51173.2173.449497781258-0.249497781258498
52173.38173.39607024733-0.01607024732985
53172.89173.575205374744-0.68520537474393
54172.98173.048328820688-0.0683288206878103
55172.98173.134651483144-0.154651483144107
56172.69173.126328410985-0.436328410984686
57172.77172.812845979546-0.0428459795459162
58172.65172.890540083914-0.240540083913686
59172.3172.757594637579-0.457594637578808
60172.17172.382967695044-0.212967695043886
61172.17172.241506146422-0.0715061464221378
62173.07172.2376578107680.832342189231781
63173.27173.1824530106680.0875469893315142
64173.05173.387164636414-0.337164636413888
65173.41173.1490190257710.260980974229
66173.37173.523064565048-0.15306456504797
67173.37173.474826898043-0.104826898043143
68173.08173.469185297853-0.389185297853317
69173.97173.1582400262560.811759973744245
70175.23174.091927527341.13807247265953
71174.9175.413176596021-0.513176596020742
72174.83175.055558329759-0.225558329759252







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73174.973419175213174.217972590104175.728865760321
74175.116838350425174.019350234984176.214326465867
75175.260257525638173.880167740643176.640347310633
76175.403676700851173.768284255843177.039069145858
77175.547095876063173.671631128314177.422560623812
78175.690515051276173.584207267467177.796822835084
79175.833934226489173.502559571412178.165308881565
80175.977353401701173.424511871259178.530194932143
81176.120772576914173.348604702366178.892940451462
82176.264191752127173.273814138745179.254569365508
83176.407610927339173.199397020777179.615824833901
84176.551030102552173.124799626284179.97726057882

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 174.973419175213 & 174.217972590104 & 175.728865760321 \tabularnewline
74 & 175.116838350425 & 174.019350234984 & 176.214326465867 \tabularnewline
75 & 175.260257525638 & 173.880167740643 & 176.640347310633 \tabularnewline
76 & 175.403676700851 & 173.768284255843 & 177.039069145858 \tabularnewline
77 & 175.547095876063 & 173.671631128314 & 177.422560623812 \tabularnewline
78 & 175.690515051276 & 173.584207267467 & 177.796822835084 \tabularnewline
79 & 175.833934226489 & 173.502559571412 & 178.165308881565 \tabularnewline
80 & 175.977353401701 & 173.424511871259 & 178.530194932143 \tabularnewline
81 & 176.120772576914 & 173.348604702366 & 178.892940451462 \tabularnewline
82 & 176.264191752127 & 173.273814138745 & 179.254569365508 \tabularnewline
83 & 176.407610927339 & 173.199397020777 & 179.615824833901 \tabularnewline
84 & 176.551030102552 & 173.124799626284 & 179.97726057882 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210312&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]174.973419175213[/C][C]174.217972590104[/C][C]175.728865760321[/C][/ROW]
[ROW][C]74[/C][C]175.116838350425[/C][C]174.019350234984[/C][C]176.214326465867[/C][/ROW]
[ROW][C]75[/C][C]175.260257525638[/C][C]173.880167740643[/C][C]176.640347310633[/C][/ROW]
[ROW][C]76[/C][C]175.403676700851[/C][C]173.768284255843[/C][C]177.039069145858[/C][/ROW]
[ROW][C]77[/C][C]175.547095876063[/C][C]173.671631128314[/C][C]177.422560623812[/C][/ROW]
[ROW][C]78[/C][C]175.690515051276[/C][C]173.584207267467[/C][C]177.796822835084[/C][/ROW]
[ROW][C]79[/C][C]175.833934226489[/C][C]173.502559571412[/C][C]178.165308881565[/C][/ROW]
[ROW][C]80[/C][C]175.977353401701[/C][C]173.424511871259[/C][C]178.530194932143[/C][/ROW]
[ROW][C]81[/C][C]176.120772576914[/C][C]173.348604702366[/C][C]178.892940451462[/C][/ROW]
[ROW][C]82[/C][C]176.264191752127[/C][C]173.273814138745[/C][C]179.254569365508[/C][/ROW]
[ROW][C]83[/C][C]176.407610927339[/C][C]173.199397020777[/C][C]179.615824833901[/C][/ROW]
[ROW][C]84[/C][C]176.551030102552[/C][C]173.124799626284[/C][C]179.97726057882[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210312&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210312&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
73174.973419175213174.217972590104175.728865760321
74175.116838350425174.019350234984176.214326465867
75175.260257525638173.880167740643176.640347310633
76175.403676700851173.768284255843177.039069145858
77175.547095876063173.671631128314177.422560623812
78175.690515051276173.584207267467177.796822835084
79175.833934226489173.502559571412178.165308881565
80175.977353401701173.424511871259178.530194932143
81176.120772576914173.348604702366178.892940451462
82176.264191752127173.273814138745179.254569365508
83176.407610927339173.199397020777179.615824833901
84176.551030102552173.124799626284179.97726057882



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