Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 11 Aug 2010 12:20:32 +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/2010/Aug/11/t1281529214rggvmoj5e0irjb9.htm/, Retrieved Mon, 06 May 2024 05:01:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78626, Retrieved Mon, 06 May 2024 05:01:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPlatini Olivier
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks B - Sta...] [2010-08-11 12:20:32] [49dea061148f13f4e9d1975b9f021cec] [Current]
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Dataseries X:
335
334
333
331
329
328
329
331
332
332
333
335
335
333
325
322
322
315
321
324
329
332
322
324
324
323
309
306
305
300
301
302
308
311
301
301
308
302
290
286
286
275
284
289
292
293
285
280
281
280
265
260
254
238
247
246
247
237
222
216
212
209
185
186
178
158
166
162
164
147
132
124
117
120
89
81
71
52
63
62
74
67
53
42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78626&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78626&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78626&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.425790716300877
beta0.363870669843029
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.425790716300877 \tabularnewline
beta & 0.363870669843029 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78626&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]0.425790716300877[/C][/ROW]
[ROW][C]beta[/C][C]0.363870669843029[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78626&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78626&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
alpha0.425790716300877
beta0.363870669843029
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13335339.209935897436-4.20993589743597
14333334.806502608272-1.80650260827230
15325324.9382091448710.0617908551285495
16322320.5833244541501.41667554584967
17322320.3581598623731.64184013762673
18315313.9415764095081.05842359049183
19321321.482230754681-0.482230754680756
20324322.3755087775061.62449122249444
21329323.7508296909465.24917030905351
22332326.81610705015.18389294990004
23322331.615078055855-9.61507805585484
24324329.789760748242-5.78976074824214
25324324.320486854873-0.320486854872513
26323322.6777830829070.322216917093328
27309314.84304297509-5.84304297508993
28306307.891442956403-1.89144295640341
29305305.013988640078-0.0139886400780824
30300295.9278081801494.07219181985096
31301302.704413151532-1.70441315153158
32302302.935014611054-0.9350146110541
33308303.5533128361174.44668716388315
34311304.366553285326.6334467146803
35301299.6367434707121.36325652928838
36301304.735054607852-3.73505460785196
37308303.6521274245334.34787257546719
38302305.460460076224-3.46046007622425
39290292.983127039846-2.98312703984573
40286290.469578026084-4.46957802608426
41286288.124271799629-2.12427179962901
42275280.710765506471-5.71076550647092
43284278.7140877448715.28591225512861
44289282.1551208893346.84487911066577
45292290.1738293477841.82617065221626
46293291.7185125834571.28148741654326
47285281.4460790193103.55392098068967
48280284.651445795886-4.65144579588645
49281287.779429210232-6.77942921023185
50280278.6020690943591.39793090564052
51265267.456032914917-2.45603291491665
52260263.383595893844-3.38359589384396
53254262.085855751076-8.08585575107566
54238248.389388125156-10.3893881251562
55247248.304942615335-1.30494261533491
56246246.403636761513-0.403636761513155
57247243.8999855218733.10001447812749
58237241.317437649337-4.31743764933694
59222224.741569532141-2.74156953214072
60216214.3550827490671.64491725093265
61212213.717909759370-1.71790975937031
62209206.9512273706342.04877262936591
63185189.530182090152-4.53018209015232
64186179.3814730301776.61852696982254
65178176.5316158121691.46838418783119
66158163.949963007569-5.94996300756875
67166170.029386631934-4.02938663193359
68162166.120700569582-4.12070056958191
69164162.1054167798851.89458322011507
70147152.622906454696-5.62290645469568
71132134.066268925498-2.06626892549755
72124124.260915470264-0.260915470263527
73117118.360849366878-1.36084936687803
74120111.4439435790428.55605642095763
758991.5590134460137-2.55901344601374
768187.4997715210822-6.49977152108222
777172.9230202749115-1.92302027491149
785250.92823095580741.07176904419259
796358.47872781404714.5212721859529
806256.86164882474865.13835117525135
817460.38059472516613.6194052748341
826753.528131000223813.4718689997762
835350.05687058987082.94312941012920
844249.1099877427967-7.10998774279665

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 335 & 339.209935897436 & -4.20993589743597 \tabularnewline
14 & 333 & 334.806502608272 & -1.80650260827230 \tabularnewline
15 & 325 & 324.938209144871 & 0.0617908551285495 \tabularnewline
16 & 322 & 320.583324454150 & 1.41667554584967 \tabularnewline
17 & 322 & 320.358159862373 & 1.64184013762673 \tabularnewline
18 & 315 & 313.941576409508 & 1.05842359049183 \tabularnewline
19 & 321 & 321.482230754681 & -0.482230754680756 \tabularnewline
20 & 324 & 322.375508777506 & 1.62449122249444 \tabularnewline
21 & 329 & 323.750829690946 & 5.24917030905351 \tabularnewline
22 & 332 & 326.8161070501 & 5.18389294990004 \tabularnewline
23 & 322 & 331.615078055855 & -9.61507805585484 \tabularnewline
24 & 324 & 329.789760748242 & -5.78976074824214 \tabularnewline
25 & 324 & 324.320486854873 & -0.320486854872513 \tabularnewline
26 & 323 & 322.677783082907 & 0.322216917093328 \tabularnewline
27 & 309 & 314.84304297509 & -5.84304297508993 \tabularnewline
28 & 306 & 307.891442956403 & -1.89144295640341 \tabularnewline
29 & 305 & 305.013988640078 & -0.0139886400780824 \tabularnewline
30 & 300 & 295.927808180149 & 4.07219181985096 \tabularnewline
31 & 301 & 302.704413151532 & -1.70441315153158 \tabularnewline
32 & 302 & 302.935014611054 & -0.9350146110541 \tabularnewline
33 & 308 & 303.553312836117 & 4.44668716388315 \tabularnewline
34 & 311 & 304.36655328532 & 6.6334467146803 \tabularnewline
35 & 301 & 299.636743470712 & 1.36325652928838 \tabularnewline
36 & 301 & 304.735054607852 & -3.73505460785196 \tabularnewline
37 & 308 & 303.652127424533 & 4.34787257546719 \tabularnewline
38 & 302 & 305.460460076224 & -3.46046007622425 \tabularnewline
39 & 290 & 292.983127039846 & -2.98312703984573 \tabularnewline
40 & 286 & 290.469578026084 & -4.46957802608426 \tabularnewline
41 & 286 & 288.124271799629 & -2.12427179962901 \tabularnewline
42 & 275 & 280.710765506471 & -5.71076550647092 \tabularnewline
43 & 284 & 278.714087744871 & 5.28591225512861 \tabularnewline
44 & 289 & 282.155120889334 & 6.84487911066577 \tabularnewline
45 & 292 & 290.173829347784 & 1.82617065221626 \tabularnewline
46 & 293 & 291.718512583457 & 1.28148741654326 \tabularnewline
47 & 285 & 281.446079019310 & 3.55392098068967 \tabularnewline
48 & 280 & 284.651445795886 & -4.65144579588645 \tabularnewline
49 & 281 & 287.779429210232 & -6.77942921023185 \tabularnewline
50 & 280 & 278.602069094359 & 1.39793090564052 \tabularnewline
51 & 265 & 267.456032914917 & -2.45603291491665 \tabularnewline
52 & 260 & 263.383595893844 & -3.38359589384396 \tabularnewline
53 & 254 & 262.085855751076 & -8.08585575107566 \tabularnewline
54 & 238 & 248.389388125156 & -10.3893881251562 \tabularnewline
55 & 247 & 248.304942615335 & -1.30494261533491 \tabularnewline
56 & 246 & 246.403636761513 & -0.403636761513155 \tabularnewline
57 & 247 & 243.899985521873 & 3.10001447812749 \tabularnewline
58 & 237 & 241.317437649337 & -4.31743764933694 \tabularnewline
59 & 222 & 224.741569532141 & -2.74156953214072 \tabularnewline
60 & 216 & 214.355082749067 & 1.64491725093265 \tabularnewline
61 & 212 & 213.717909759370 & -1.71790975937031 \tabularnewline
62 & 209 & 206.951227370634 & 2.04877262936591 \tabularnewline
63 & 185 & 189.530182090152 & -4.53018209015232 \tabularnewline
64 & 186 & 179.381473030177 & 6.61852696982254 \tabularnewline
65 & 178 & 176.531615812169 & 1.46838418783119 \tabularnewline
66 & 158 & 163.949963007569 & -5.94996300756875 \tabularnewline
67 & 166 & 170.029386631934 & -4.02938663193359 \tabularnewline
68 & 162 & 166.120700569582 & -4.12070056958191 \tabularnewline
69 & 164 & 162.105416779885 & 1.89458322011507 \tabularnewline
70 & 147 & 152.622906454696 & -5.62290645469568 \tabularnewline
71 & 132 & 134.066268925498 & -2.06626892549755 \tabularnewline
72 & 124 & 124.260915470264 & -0.260915470263527 \tabularnewline
73 & 117 & 118.360849366878 & -1.36084936687803 \tabularnewline
74 & 120 & 111.443943579042 & 8.55605642095763 \tabularnewline
75 & 89 & 91.5590134460137 & -2.55901344601374 \tabularnewline
76 & 81 & 87.4997715210822 & -6.49977152108222 \tabularnewline
77 & 71 & 72.9230202749115 & -1.92302027491149 \tabularnewline
78 & 52 & 50.9282309558074 & 1.07176904419259 \tabularnewline
79 & 63 & 58.4787278140471 & 4.5212721859529 \tabularnewline
80 & 62 & 56.8616488247486 & 5.13835117525135 \tabularnewline
81 & 74 & 60.380594725166 & 13.6194052748341 \tabularnewline
82 & 67 & 53.5281310002238 & 13.4718689997762 \tabularnewline
83 & 53 & 50.0568705898708 & 2.94312941012920 \tabularnewline
84 & 42 & 49.1099877427967 & -7.10998774279665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78626&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]335[/C][C]339.209935897436[/C][C]-4.20993589743597[/C][/ROW]
[ROW][C]14[/C][C]333[/C][C]334.806502608272[/C][C]-1.80650260827230[/C][/ROW]
[ROW][C]15[/C][C]325[/C][C]324.938209144871[/C][C]0.0617908551285495[/C][/ROW]
[ROW][C]16[/C][C]322[/C][C]320.583324454150[/C][C]1.41667554584967[/C][/ROW]
[ROW][C]17[/C][C]322[/C][C]320.358159862373[/C][C]1.64184013762673[/C][/ROW]
[ROW][C]18[/C][C]315[/C][C]313.941576409508[/C][C]1.05842359049183[/C][/ROW]
[ROW][C]19[/C][C]321[/C][C]321.482230754681[/C][C]-0.482230754680756[/C][/ROW]
[ROW][C]20[/C][C]324[/C][C]322.375508777506[/C][C]1.62449122249444[/C][/ROW]
[ROW][C]21[/C][C]329[/C][C]323.750829690946[/C][C]5.24917030905351[/C][/ROW]
[ROW][C]22[/C][C]332[/C][C]326.8161070501[/C][C]5.18389294990004[/C][/ROW]
[ROW][C]23[/C][C]322[/C][C]331.615078055855[/C][C]-9.61507805585484[/C][/ROW]
[ROW][C]24[/C][C]324[/C][C]329.789760748242[/C][C]-5.78976074824214[/C][/ROW]
[ROW][C]25[/C][C]324[/C][C]324.320486854873[/C][C]-0.320486854872513[/C][/ROW]
[ROW][C]26[/C][C]323[/C][C]322.677783082907[/C][C]0.322216917093328[/C][/ROW]
[ROW][C]27[/C][C]309[/C][C]314.84304297509[/C][C]-5.84304297508993[/C][/ROW]
[ROW][C]28[/C][C]306[/C][C]307.891442956403[/C][C]-1.89144295640341[/C][/ROW]
[ROW][C]29[/C][C]305[/C][C]305.013988640078[/C][C]-0.0139886400780824[/C][/ROW]
[ROW][C]30[/C][C]300[/C][C]295.927808180149[/C][C]4.07219181985096[/C][/ROW]
[ROW][C]31[/C][C]301[/C][C]302.704413151532[/C][C]-1.70441315153158[/C][/ROW]
[ROW][C]32[/C][C]302[/C][C]302.935014611054[/C][C]-0.9350146110541[/C][/ROW]
[ROW][C]33[/C][C]308[/C][C]303.553312836117[/C][C]4.44668716388315[/C][/ROW]
[ROW][C]34[/C][C]311[/C][C]304.36655328532[/C][C]6.6334467146803[/C][/ROW]
[ROW][C]35[/C][C]301[/C][C]299.636743470712[/C][C]1.36325652928838[/C][/ROW]
[ROW][C]36[/C][C]301[/C][C]304.735054607852[/C][C]-3.73505460785196[/C][/ROW]
[ROW][C]37[/C][C]308[/C][C]303.652127424533[/C][C]4.34787257546719[/C][/ROW]
[ROW][C]38[/C][C]302[/C][C]305.460460076224[/C][C]-3.46046007622425[/C][/ROW]
[ROW][C]39[/C][C]290[/C][C]292.983127039846[/C][C]-2.98312703984573[/C][/ROW]
[ROW][C]40[/C][C]286[/C][C]290.469578026084[/C][C]-4.46957802608426[/C][/ROW]
[ROW][C]41[/C][C]286[/C][C]288.124271799629[/C][C]-2.12427179962901[/C][/ROW]
[ROW][C]42[/C][C]275[/C][C]280.710765506471[/C][C]-5.71076550647092[/C][/ROW]
[ROW][C]43[/C][C]284[/C][C]278.714087744871[/C][C]5.28591225512861[/C][/ROW]
[ROW][C]44[/C][C]289[/C][C]282.155120889334[/C][C]6.84487911066577[/C][/ROW]
[ROW][C]45[/C][C]292[/C][C]290.173829347784[/C][C]1.82617065221626[/C][/ROW]
[ROW][C]46[/C][C]293[/C][C]291.718512583457[/C][C]1.28148741654326[/C][/ROW]
[ROW][C]47[/C][C]285[/C][C]281.446079019310[/C][C]3.55392098068967[/C][/ROW]
[ROW][C]48[/C][C]280[/C][C]284.651445795886[/C][C]-4.65144579588645[/C][/ROW]
[ROW][C]49[/C][C]281[/C][C]287.779429210232[/C][C]-6.77942921023185[/C][/ROW]
[ROW][C]50[/C][C]280[/C][C]278.602069094359[/C][C]1.39793090564052[/C][/ROW]
[ROW][C]51[/C][C]265[/C][C]267.456032914917[/C][C]-2.45603291491665[/C][/ROW]
[ROW][C]52[/C][C]260[/C][C]263.383595893844[/C][C]-3.38359589384396[/C][/ROW]
[ROW][C]53[/C][C]254[/C][C]262.085855751076[/C][C]-8.08585575107566[/C][/ROW]
[ROW][C]54[/C][C]238[/C][C]248.389388125156[/C][C]-10.3893881251562[/C][/ROW]
[ROW][C]55[/C][C]247[/C][C]248.304942615335[/C][C]-1.30494261533491[/C][/ROW]
[ROW][C]56[/C][C]246[/C][C]246.403636761513[/C][C]-0.403636761513155[/C][/ROW]
[ROW][C]57[/C][C]247[/C][C]243.899985521873[/C][C]3.10001447812749[/C][/ROW]
[ROW][C]58[/C][C]237[/C][C]241.317437649337[/C][C]-4.31743764933694[/C][/ROW]
[ROW][C]59[/C][C]222[/C][C]224.741569532141[/C][C]-2.74156953214072[/C][/ROW]
[ROW][C]60[/C][C]216[/C][C]214.355082749067[/C][C]1.64491725093265[/C][/ROW]
[ROW][C]61[/C][C]212[/C][C]213.717909759370[/C][C]-1.71790975937031[/C][/ROW]
[ROW][C]62[/C][C]209[/C][C]206.951227370634[/C][C]2.04877262936591[/C][/ROW]
[ROW][C]63[/C][C]185[/C][C]189.530182090152[/C][C]-4.53018209015232[/C][/ROW]
[ROW][C]64[/C][C]186[/C][C]179.381473030177[/C][C]6.61852696982254[/C][/ROW]
[ROW][C]65[/C][C]178[/C][C]176.531615812169[/C][C]1.46838418783119[/C][/ROW]
[ROW][C]66[/C][C]158[/C][C]163.949963007569[/C][C]-5.94996300756875[/C][/ROW]
[ROW][C]67[/C][C]166[/C][C]170.029386631934[/C][C]-4.02938663193359[/C][/ROW]
[ROW][C]68[/C][C]162[/C][C]166.120700569582[/C][C]-4.12070056958191[/C][/ROW]
[ROW][C]69[/C][C]164[/C][C]162.105416779885[/C][C]1.89458322011507[/C][/ROW]
[ROW][C]70[/C][C]147[/C][C]152.622906454696[/C][C]-5.62290645469568[/C][/ROW]
[ROW][C]71[/C][C]132[/C][C]134.066268925498[/C][C]-2.06626892549755[/C][/ROW]
[ROW][C]72[/C][C]124[/C][C]124.260915470264[/C][C]-0.260915470263527[/C][/ROW]
[ROW][C]73[/C][C]117[/C][C]118.360849366878[/C][C]-1.36084936687803[/C][/ROW]
[ROW][C]74[/C][C]120[/C][C]111.443943579042[/C][C]8.55605642095763[/C][/ROW]
[ROW][C]75[/C][C]89[/C][C]91.5590134460137[/C][C]-2.55901344601374[/C][/ROW]
[ROW][C]76[/C][C]81[/C][C]87.4997715210822[/C][C]-6.49977152108222[/C][/ROW]
[ROW][C]77[/C][C]71[/C][C]72.9230202749115[/C][C]-1.92302027491149[/C][/ROW]
[ROW][C]78[/C][C]52[/C][C]50.9282309558074[/C][C]1.07176904419259[/C][/ROW]
[ROW][C]79[/C][C]63[/C][C]58.4787278140471[/C][C]4.5212721859529[/C][/ROW]
[ROW][C]80[/C][C]62[/C][C]56.8616488247486[/C][C]5.13835117525135[/C][/ROW]
[ROW][C]81[/C][C]74[/C][C]60.380594725166[/C][C]13.6194052748341[/C][/ROW]
[ROW][C]82[/C][C]67[/C][C]53.5281310002238[/C][C]13.4718689997762[/C][/ROW]
[ROW][C]83[/C][C]53[/C][C]50.0568705898708[/C][C]2.94312941012920[/C][/ROW]
[ROW][C]84[/C][C]42[/C][C]49.1099877427967[/C][C]-7.10998774279665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78626&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78626&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
13335339.209935897436-4.20993589743597
14333334.806502608272-1.80650260827230
15325324.9382091448710.0617908551285495
16322320.5833244541501.41667554584967
17322320.3581598623731.64184013762673
18315313.9415764095081.05842359049183
19321321.482230754681-0.482230754680756
20324322.3755087775061.62449122249444
21329323.7508296909465.24917030905351
22332326.81610705015.18389294990004
23322331.615078055855-9.61507805585484
24324329.789760748242-5.78976074824214
25324324.320486854873-0.320486854872513
26323322.6777830829070.322216917093328
27309314.84304297509-5.84304297508993
28306307.891442956403-1.89144295640341
29305305.013988640078-0.0139886400780824
30300295.9278081801494.07219181985096
31301302.704413151532-1.70441315153158
32302302.935014611054-0.9350146110541
33308303.5533128361174.44668716388315
34311304.366553285326.6334467146803
35301299.6367434707121.36325652928838
36301304.735054607852-3.73505460785196
37308303.6521274245334.34787257546719
38302305.460460076224-3.46046007622425
39290292.983127039846-2.98312703984573
40286290.469578026084-4.46957802608426
41286288.124271799629-2.12427179962901
42275280.710765506471-5.71076550647092
43284278.7140877448715.28591225512861
44289282.1551208893346.84487911066577
45292290.1738293477841.82617065221626
46293291.7185125834571.28148741654326
47285281.4460790193103.55392098068967
48280284.651445795886-4.65144579588645
49281287.779429210232-6.77942921023185
50280278.6020690943591.39793090564052
51265267.456032914917-2.45603291491665
52260263.383595893844-3.38359589384396
53254262.085855751076-8.08585575107566
54238248.389388125156-10.3893881251562
55247248.304942615335-1.30494261533491
56246246.403636761513-0.403636761513155
57247243.8999855218733.10001447812749
58237241.317437649337-4.31743764933694
59222224.741569532141-2.74156953214072
60216214.3550827490671.64491725093265
61212213.717909759370-1.71790975937031
62209206.9512273706342.04877262936591
63185189.530182090152-4.53018209015232
64186179.3814730301776.61852696982254
65178176.5316158121691.46838418783119
66158163.949963007569-5.94996300756875
67166170.029386631934-4.02938663193359
68162166.120700569582-4.12070056958191
69164162.1054167798851.89458322011507
70147152.622906454696-5.62290645469568
71132134.066268925498-2.06626892549755
72124124.260915470264-0.260915470263527
73117118.360849366878-1.36084936687803
74120111.4439435790428.55605642095763
758991.5590134460137-2.55901344601374
768187.4997715210822-6.49977152108222
777172.9230202749115-1.92302027491149
785250.92823095580741.07176904419259
796358.47872781404714.5212721859529
806256.86164882474865.13835117525135
817460.38059472516613.6194052748341
826753.528131000223813.4718689997762
835350.05687058987082.94312941012920
844249.1099877427967-7.10998774279665







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8544.289776960114934.945858221540453.6336956986894
8648.485246671475537.680024741005159.2904686019458
8722.08779656579389.2814119608535234.8941811707341
8820.76475966221145.4921579278367136.0373613965860
8916.5000120638199-1.6298252637230334.6298493913629
902.25804980163866-19.061212598914223.5773122021915
9116.3812689970839-8.41598400346341.1785219976307
9217.5412485401361-10.990505209442946.0730022897152
9327.2939750888902-5.2048578987576459.792808076538
9415.9994292583403-20.680740128745352.6795986454259
950.100689245155060-40.960661967881641.1620404581917
96-8.9735139568271-54.60425914446536.6572312308108

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 44.2897769601149 & 34.9458582215404 & 53.6336956986894 \tabularnewline
86 & 48.4852466714755 & 37.6800247410051 & 59.2904686019458 \tabularnewline
87 & 22.0877965657938 & 9.28141196085352 & 34.8941811707341 \tabularnewline
88 & 20.7647596622114 & 5.49215792783671 & 36.0373613965860 \tabularnewline
89 & 16.5000120638199 & -1.62982526372303 & 34.6298493913629 \tabularnewline
90 & 2.25804980163866 & -19.0612125989142 & 23.5773122021915 \tabularnewline
91 & 16.3812689970839 & -8.415984003463 & 41.1785219976307 \tabularnewline
92 & 17.5412485401361 & -10.9905052094429 & 46.0730022897152 \tabularnewline
93 & 27.2939750888902 & -5.20485789875764 & 59.792808076538 \tabularnewline
94 & 15.9994292583403 & -20.6807401287453 & 52.6795986454259 \tabularnewline
95 & 0.100689245155060 & -40.9606619678816 & 41.1620404581917 \tabularnewline
96 & -8.9735139568271 & -54.604259144465 & 36.6572312308108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78626&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]85[/C][C]44.2897769601149[/C][C]34.9458582215404[/C][C]53.6336956986894[/C][/ROW]
[ROW][C]86[/C][C]48.4852466714755[/C][C]37.6800247410051[/C][C]59.2904686019458[/C][/ROW]
[ROW][C]87[/C][C]22.0877965657938[/C][C]9.28141196085352[/C][C]34.8941811707341[/C][/ROW]
[ROW][C]88[/C][C]20.7647596622114[/C][C]5.49215792783671[/C][C]36.0373613965860[/C][/ROW]
[ROW][C]89[/C][C]16.5000120638199[/C][C]-1.62982526372303[/C][C]34.6298493913629[/C][/ROW]
[ROW][C]90[/C][C]2.25804980163866[/C][C]-19.0612125989142[/C][C]23.5773122021915[/C][/ROW]
[ROW][C]91[/C][C]16.3812689970839[/C][C]-8.415984003463[/C][C]41.1785219976307[/C][/ROW]
[ROW][C]92[/C][C]17.5412485401361[/C][C]-10.9905052094429[/C][C]46.0730022897152[/C][/ROW]
[ROW][C]93[/C][C]27.2939750888902[/C][C]-5.20485789875764[/C][C]59.792808076538[/C][/ROW]
[ROW][C]94[/C][C]15.9994292583403[/C][C]-20.6807401287453[/C][C]52.6795986454259[/C][/ROW]
[ROW][C]95[/C][C]0.100689245155060[/C][C]-40.9606619678816[/C][C]41.1620404581917[/C][/ROW]
[ROW][C]96[/C][C]-8.9735139568271[/C][C]-54.604259144465[/C][C]36.6572312308108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78626&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78626&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
8544.289776960114934.945858221540453.6336956986894
8648.485246671475537.680024741005159.2904686019458
8722.08779656579389.2814119608535234.8941811707341
8820.76475966221145.4921579278367136.0373613965860
8916.5000120638199-1.6298252637230334.6298493913629
902.25804980163866-19.061212598914223.5773122021915
9116.3812689970839-8.41598400346341.1785219976307
9217.5412485401361-10.990505209442946.0730022897152
9327.2939750888902-5.2048578987576459.792808076538
9415.9994292583403-20.680740128745352.6795986454259
950.100689245155060-40.960661967881641.1620404581917
96-8.9735139568271-54.60425914446536.6572312308108



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')