Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 15 Aug 2010 14:22:15 +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/15/t1281882122k8xok8o3fzi3kch.htm/, Retrieved Sat, 27 Apr 2024 21:07:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78875, Retrieved Sat, 27 Apr 2024 21:07:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJacobs Jeff
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2010-08-15 14:22:15] [03859715711bd3369851d387eaa83ba4] [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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78875&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78875&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78875&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.425790716300489
beta0.363870669843828
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.425790716300489 \tabularnewline
beta & 0.363870669843828 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78875&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]0.425790716300489[/C][/ROW]
[ROW][C]beta[/C][C]0.363870669843828[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78875&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78875&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
alpha0.425790716300489
beta0.363870669843828
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13335339.209935897436-4.20993589743614
14333334.806502608273-1.80650260827315
15325324.9382091448710.0617908551287769
16322320.5833244541491.41667554585115
17322320.3581598623711.64184013762895
18315313.9415764095061.05842359049399
19321321.482230754680-0.482230754679506
20324322.3755087775051.62449122249456
21329323.7508296909475.2491703090534
22332326.81610705015.18389294990021
23322331.615078055856-9.61507805585558
24324329.789760748247-5.78976074824709
25324324.320486854875-0.320486854874673
26323322.6777830829070.322216917092931
27309314.84304297509-5.84304297508982
28306307.891442956404-1.89144295640426
29305305.013988640077-0.0139886400766613
30300295.9278081801454.07219181985499
31301302.704413151525-1.70441315152510
32302302.935014611050-0.935014611050349
33308303.5533128361164.44668716388401
34311304.3665532853186.6334467146819
35301299.6367434707041.36325652929582
36301304.73505460785-3.73505460784980
37308303.6521274245384.34787257546185
38302305.460460076231-3.46046007623073
39290292.983127039852-2.98312703985152
40286290.469578026091-4.46957802609114
41286288.124271799635-2.12427179963527
42275280.710765506475-5.71076550647479
43284278.7140877448695.28591225513105
44289282.1551208893266.84487911067407
45292290.1738293477771.82617065222286
46293291.7185125834541.2814874165461
47285281.4460790193053.55392098069547
48280284.651445795878-4.65144579587849
49281287.779429210233-6.77942921023282
50280278.6020690943621.39793090563762
51265267.456032914919-2.45603291491886
52260263.383595893848-3.38359589384788
53254262.085855751082-8.0858557510823
54238248.389388125163-10.3893881251626
55247248.304942615342-1.30494261534224
56246246.403636761513-0.403636761512843
57247243.8999855218633.10001447813656
58237241.317437649324-4.31743764932361
59222224.741569532128-2.7415695321279
60216214.355082749051.64491725095002
61212213.717909759354-1.71790975935434
62209206.9512273706282.04877262937214
63185189.53018209015-4.53018209014994
64186179.3814730301816.61852696981944
65178176.5316158121721.46838418782789
66158163.949963007576-5.94996300757555
67166170.02938663195-4.02938663195002
68162166.120700569598-4.12070056959837
69164162.1054167798961.89458322010435
70147152.622906454693-5.62290645469275
71132134.066268925489-2.06626892548874
72124124.260915470249-0.260915470249202
73117118.360849366858-1.36084936685826
74120111.4439435790268.55605642097385
758991.5590134459976-2.55901344599764
768187.4997715210797-6.49977152107968
777172.9230202749146-1.92302027491462
785250.928230955811.07176904419001
796358.47872781405514.52127218594491
806256.86164882476145.13835117523861
817460.380594725183513.6194052748165
826753.528131000233413.4718689997666
835350.05687058987652.94312941012345
844249.1099877428014-7.1099877428014

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 335 & 339.209935897436 & -4.20993589743614 \tabularnewline
14 & 333 & 334.806502608273 & -1.80650260827315 \tabularnewline
15 & 325 & 324.938209144871 & 0.0617908551287769 \tabularnewline
16 & 322 & 320.583324454149 & 1.41667554585115 \tabularnewline
17 & 322 & 320.358159862371 & 1.64184013762895 \tabularnewline
18 & 315 & 313.941576409506 & 1.05842359049399 \tabularnewline
19 & 321 & 321.482230754680 & -0.482230754679506 \tabularnewline
20 & 324 & 322.375508777505 & 1.62449122249456 \tabularnewline
21 & 329 & 323.750829690947 & 5.2491703090534 \tabularnewline
22 & 332 & 326.8161070501 & 5.18389294990021 \tabularnewline
23 & 322 & 331.615078055856 & -9.61507805585558 \tabularnewline
24 & 324 & 329.789760748247 & -5.78976074824709 \tabularnewline
25 & 324 & 324.320486854875 & -0.320486854874673 \tabularnewline
26 & 323 & 322.677783082907 & 0.322216917092931 \tabularnewline
27 & 309 & 314.84304297509 & -5.84304297508982 \tabularnewline
28 & 306 & 307.891442956404 & -1.89144295640426 \tabularnewline
29 & 305 & 305.013988640077 & -0.0139886400766613 \tabularnewline
30 & 300 & 295.927808180145 & 4.07219181985499 \tabularnewline
31 & 301 & 302.704413151525 & -1.70441315152510 \tabularnewline
32 & 302 & 302.935014611050 & -0.935014611050349 \tabularnewline
33 & 308 & 303.553312836116 & 4.44668716388401 \tabularnewline
34 & 311 & 304.366553285318 & 6.6334467146819 \tabularnewline
35 & 301 & 299.636743470704 & 1.36325652929582 \tabularnewline
36 & 301 & 304.73505460785 & -3.73505460784980 \tabularnewline
37 & 308 & 303.652127424538 & 4.34787257546185 \tabularnewline
38 & 302 & 305.460460076231 & -3.46046007623073 \tabularnewline
39 & 290 & 292.983127039852 & -2.98312703985152 \tabularnewline
40 & 286 & 290.469578026091 & -4.46957802609114 \tabularnewline
41 & 286 & 288.124271799635 & -2.12427179963527 \tabularnewline
42 & 275 & 280.710765506475 & -5.71076550647479 \tabularnewline
43 & 284 & 278.714087744869 & 5.28591225513105 \tabularnewline
44 & 289 & 282.155120889326 & 6.84487911067407 \tabularnewline
45 & 292 & 290.173829347777 & 1.82617065222286 \tabularnewline
46 & 293 & 291.718512583454 & 1.2814874165461 \tabularnewline
47 & 285 & 281.446079019305 & 3.55392098069547 \tabularnewline
48 & 280 & 284.651445795878 & -4.65144579587849 \tabularnewline
49 & 281 & 287.779429210233 & -6.77942921023282 \tabularnewline
50 & 280 & 278.602069094362 & 1.39793090563762 \tabularnewline
51 & 265 & 267.456032914919 & -2.45603291491886 \tabularnewline
52 & 260 & 263.383595893848 & -3.38359589384788 \tabularnewline
53 & 254 & 262.085855751082 & -8.0858557510823 \tabularnewline
54 & 238 & 248.389388125163 & -10.3893881251626 \tabularnewline
55 & 247 & 248.304942615342 & -1.30494261534224 \tabularnewline
56 & 246 & 246.403636761513 & -0.403636761512843 \tabularnewline
57 & 247 & 243.899985521863 & 3.10001447813656 \tabularnewline
58 & 237 & 241.317437649324 & -4.31743764932361 \tabularnewline
59 & 222 & 224.741569532128 & -2.7415695321279 \tabularnewline
60 & 216 & 214.35508274905 & 1.64491725095002 \tabularnewline
61 & 212 & 213.717909759354 & -1.71790975935434 \tabularnewline
62 & 209 & 206.951227370628 & 2.04877262937214 \tabularnewline
63 & 185 & 189.53018209015 & -4.53018209014994 \tabularnewline
64 & 186 & 179.381473030181 & 6.61852696981944 \tabularnewline
65 & 178 & 176.531615812172 & 1.46838418782789 \tabularnewline
66 & 158 & 163.949963007576 & -5.94996300757555 \tabularnewline
67 & 166 & 170.02938663195 & -4.02938663195002 \tabularnewline
68 & 162 & 166.120700569598 & -4.12070056959837 \tabularnewline
69 & 164 & 162.105416779896 & 1.89458322010435 \tabularnewline
70 & 147 & 152.622906454693 & -5.62290645469275 \tabularnewline
71 & 132 & 134.066268925489 & -2.06626892548874 \tabularnewline
72 & 124 & 124.260915470249 & -0.260915470249202 \tabularnewline
73 & 117 & 118.360849366858 & -1.36084936685826 \tabularnewline
74 & 120 & 111.443943579026 & 8.55605642097385 \tabularnewline
75 & 89 & 91.5590134459976 & -2.55901344599764 \tabularnewline
76 & 81 & 87.4997715210797 & -6.49977152107968 \tabularnewline
77 & 71 & 72.9230202749146 & -1.92302027491462 \tabularnewline
78 & 52 & 50.92823095581 & 1.07176904419001 \tabularnewline
79 & 63 & 58.4787278140551 & 4.52127218594491 \tabularnewline
80 & 62 & 56.8616488247614 & 5.13835117523861 \tabularnewline
81 & 74 & 60.3805947251835 & 13.6194052748165 \tabularnewline
82 & 67 & 53.5281310002334 & 13.4718689997666 \tabularnewline
83 & 53 & 50.0568705898765 & 2.94312941012345 \tabularnewline
84 & 42 & 49.1099877428014 & -7.1099877428014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78875&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]-4.20993589743614[/C][/ROW]
[ROW][C]14[/C][C]333[/C][C]334.806502608273[/C][C]-1.80650260827315[/C][/ROW]
[ROW][C]15[/C][C]325[/C][C]324.938209144871[/C][C]0.0617908551287769[/C][/ROW]
[ROW][C]16[/C][C]322[/C][C]320.583324454149[/C][C]1.41667554585115[/C][/ROW]
[ROW][C]17[/C][C]322[/C][C]320.358159862371[/C][C]1.64184013762895[/C][/ROW]
[ROW][C]18[/C][C]315[/C][C]313.941576409506[/C][C]1.05842359049399[/C][/ROW]
[ROW][C]19[/C][C]321[/C][C]321.482230754680[/C][C]-0.482230754679506[/C][/ROW]
[ROW][C]20[/C][C]324[/C][C]322.375508777505[/C][C]1.62449122249456[/C][/ROW]
[ROW][C]21[/C][C]329[/C][C]323.750829690947[/C][C]5.2491703090534[/C][/ROW]
[ROW][C]22[/C][C]332[/C][C]326.8161070501[/C][C]5.18389294990021[/C][/ROW]
[ROW][C]23[/C][C]322[/C][C]331.615078055856[/C][C]-9.61507805585558[/C][/ROW]
[ROW][C]24[/C][C]324[/C][C]329.789760748247[/C][C]-5.78976074824709[/C][/ROW]
[ROW][C]25[/C][C]324[/C][C]324.320486854875[/C][C]-0.320486854874673[/C][/ROW]
[ROW][C]26[/C][C]323[/C][C]322.677783082907[/C][C]0.322216917092931[/C][/ROW]
[ROW][C]27[/C][C]309[/C][C]314.84304297509[/C][C]-5.84304297508982[/C][/ROW]
[ROW][C]28[/C][C]306[/C][C]307.891442956404[/C][C]-1.89144295640426[/C][/ROW]
[ROW][C]29[/C][C]305[/C][C]305.013988640077[/C][C]-0.0139886400766613[/C][/ROW]
[ROW][C]30[/C][C]300[/C][C]295.927808180145[/C][C]4.07219181985499[/C][/ROW]
[ROW][C]31[/C][C]301[/C][C]302.704413151525[/C][C]-1.70441315152510[/C][/ROW]
[ROW][C]32[/C][C]302[/C][C]302.935014611050[/C][C]-0.935014611050349[/C][/ROW]
[ROW][C]33[/C][C]308[/C][C]303.553312836116[/C][C]4.44668716388401[/C][/ROW]
[ROW][C]34[/C][C]311[/C][C]304.366553285318[/C][C]6.6334467146819[/C][/ROW]
[ROW][C]35[/C][C]301[/C][C]299.636743470704[/C][C]1.36325652929582[/C][/ROW]
[ROW][C]36[/C][C]301[/C][C]304.73505460785[/C][C]-3.73505460784980[/C][/ROW]
[ROW][C]37[/C][C]308[/C][C]303.652127424538[/C][C]4.34787257546185[/C][/ROW]
[ROW][C]38[/C][C]302[/C][C]305.460460076231[/C][C]-3.46046007623073[/C][/ROW]
[ROW][C]39[/C][C]290[/C][C]292.983127039852[/C][C]-2.98312703985152[/C][/ROW]
[ROW][C]40[/C][C]286[/C][C]290.469578026091[/C][C]-4.46957802609114[/C][/ROW]
[ROW][C]41[/C][C]286[/C][C]288.124271799635[/C][C]-2.12427179963527[/C][/ROW]
[ROW][C]42[/C][C]275[/C][C]280.710765506475[/C][C]-5.71076550647479[/C][/ROW]
[ROW][C]43[/C][C]284[/C][C]278.714087744869[/C][C]5.28591225513105[/C][/ROW]
[ROW][C]44[/C][C]289[/C][C]282.155120889326[/C][C]6.84487911067407[/C][/ROW]
[ROW][C]45[/C][C]292[/C][C]290.173829347777[/C][C]1.82617065222286[/C][/ROW]
[ROW][C]46[/C][C]293[/C][C]291.718512583454[/C][C]1.2814874165461[/C][/ROW]
[ROW][C]47[/C][C]285[/C][C]281.446079019305[/C][C]3.55392098069547[/C][/ROW]
[ROW][C]48[/C][C]280[/C][C]284.651445795878[/C][C]-4.65144579587849[/C][/ROW]
[ROW][C]49[/C][C]281[/C][C]287.779429210233[/C][C]-6.77942921023282[/C][/ROW]
[ROW][C]50[/C][C]280[/C][C]278.602069094362[/C][C]1.39793090563762[/C][/ROW]
[ROW][C]51[/C][C]265[/C][C]267.456032914919[/C][C]-2.45603291491886[/C][/ROW]
[ROW][C]52[/C][C]260[/C][C]263.383595893848[/C][C]-3.38359589384788[/C][/ROW]
[ROW][C]53[/C][C]254[/C][C]262.085855751082[/C][C]-8.0858557510823[/C][/ROW]
[ROW][C]54[/C][C]238[/C][C]248.389388125163[/C][C]-10.3893881251626[/C][/ROW]
[ROW][C]55[/C][C]247[/C][C]248.304942615342[/C][C]-1.30494261534224[/C][/ROW]
[ROW][C]56[/C][C]246[/C][C]246.403636761513[/C][C]-0.403636761512843[/C][/ROW]
[ROW][C]57[/C][C]247[/C][C]243.899985521863[/C][C]3.10001447813656[/C][/ROW]
[ROW][C]58[/C][C]237[/C][C]241.317437649324[/C][C]-4.31743764932361[/C][/ROW]
[ROW][C]59[/C][C]222[/C][C]224.741569532128[/C][C]-2.7415695321279[/C][/ROW]
[ROW][C]60[/C][C]216[/C][C]214.35508274905[/C][C]1.64491725095002[/C][/ROW]
[ROW][C]61[/C][C]212[/C][C]213.717909759354[/C][C]-1.71790975935434[/C][/ROW]
[ROW][C]62[/C][C]209[/C][C]206.951227370628[/C][C]2.04877262937214[/C][/ROW]
[ROW][C]63[/C][C]185[/C][C]189.53018209015[/C][C]-4.53018209014994[/C][/ROW]
[ROW][C]64[/C][C]186[/C][C]179.381473030181[/C][C]6.61852696981944[/C][/ROW]
[ROW][C]65[/C][C]178[/C][C]176.531615812172[/C][C]1.46838418782789[/C][/ROW]
[ROW][C]66[/C][C]158[/C][C]163.949963007576[/C][C]-5.94996300757555[/C][/ROW]
[ROW][C]67[/C][C]166[/C][C]170.02938663195[/C][C]-4.02938663195002[/C][/ROW]
[ROW][C]68[/C][C]162[/C][C]166.120700569598[/C][C]-4.12070056959837[/C][/ROW]
[ROW][C]69[/C][C]164[/C][C]162.105416779896[/C][C]1.89458322010435[/C][/ROW]
[ROW][C]70[/C][C]147[/C][C]152.622906454693[/C][C]-5.62290645469275[/C][/ROW]
[ROW][C]71[/C][C]132[/C][C]134.066268925489[/C][C]-2.06626892548874[/C][/ROW]
[ROW][C]72[/C][C]124[/C][C]124.260915470249[/C][C]-0.260915470249202[/C][/ROW]
[ROW][C]73[/C][C]117[/C][C]118.360849366858[/C][C]-1.36084936685826[/C][/ROW]
[ROW][C]74[/C][C]120[/C][C]111.443943579026[/C][C]8.55605642097385[/C][/ROW]
[ROW][C]75[/C][C]89[/C][C]91.5590134459976[/C][C]-2.55901344599764[/C][/ROW]
[ROW][C]76[/C][C]81[/C][C]87.4997715210797[/C][C]-6.49977152107968[/C][/ROW]
[ROW][C]77[/C][C]71[/C][C]72.9230202749146[/C][C]-1.92302027491462[/C][/ROW]
[ROW][C]78[/C][C]52[/C][C]50.92823095581[/C][C]1.07176904419001[/C][/ROW]
[ROW][C]79[/C][C]63[/C][C]58.4787278140551[/C][C]4.52127218594491[/C][/ROW]
[ROW][C]80[/C][C]62[/C][C]56.8616488247614[/C][C]5.13835117523861[/C][/ROW]
[ROW][C]81[/C][C]74[/C][C]60.3805947251835[/C][C]13.6194052748165[/C][/ROW]
[ROW][C]82[/C][C]67[/C][C]53.5281310002334[/C][C]13.4718689997666[/C][/ROW]
[ROW][C]83[/C][C]53[/C][C]50.0568705898765[/C][C]2.94312941012345[/C][/ROW]
[ROW][C]84[/C][C]42[/C][C]49.1099877428014[/C][C]-7.1099877428014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78875&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78875&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
13335339.209935897436-4.20993589743614
14333334.806502608273-1.80650260827315
15325324.9382091448710.0617908551287769
16322320.5833244541491.41667554585115
17322320.3581598623711.64184013762895
18315313.9415764095061.05842359049399
19321321.482230754680-0.482230754679506
20324322.3755087775051.62449122249456
21329323.7508296909475.2491703090534
22332326.81610705015.18389294990021
23322331.615078055856-9.61507805585558
24324329.789760748247-5.78976074824709
25324324.320486854875-0.320486854874673
26323322.6777830829070.322216917092931
27309314.84304297509-5.84304297508982
28306307.891442956404-1.89144295640426
29305305.013988640077-0.0139886400766613
30300295.9278081801454.07219181985499
31301302.704413151525-1.70441315152510
32302302.935014611050-0.935014611050349
33308303.5533128361164.44668716388401
34311304.3665532853186.6334467146819
35301299.6367434707041.36325652929582
36301304.73505460785-3.73505460784980
37308303.6521274245384.34787257546185
38302305.460460076231-3.46046007623073
39290292.983127039852-2.98312703985152
40286290.469578026091-4.46957802609114
41286288.124271799635-2.12427179963527
42275280.710765506475-5.71076550647479
43284278.7140877448695.28591225513105
44289282.1551208893266.84487911067407
45292290.1738293477771.82617065222286
46293291.7185125834541.2814874165461
47285281.4460790193053.55392098069547
48280284.651445795878-4.65144579587849
49281287.779429210233-6.77942921023282
50280278.6020690943621.39793090563762
51265267.456032914919-2.45603291491886
52260263.383595893848-3.38359589384788
53254262.085855751082-8.0858557510823
54238248.389388125163-10.3893881251626
55247248.304942615342-1.30494261534224
56246246.403636761513-0.403636761512843
57247243.8999855218633.10001447813656
58237241.317437649324-4.31743764932361
59222224.741569532128-2.7415695321279
60216214.355082749051.64491725095002
61212213.717909759354-1.71790975935434
62209206.9512273706282.04877262937214
63185189.53018209015-4.53018209014994
64186179.3814730301816.61852696981944
65178176.5316158121721.46838418782789
66158163.949963007576-5.94996300757555
67166170.02938663195-4.02938663195002
68162166.120700569598-4.12070056959837
69164162.1054167798961.89458322010435
70147152.622906454693-5.62290645469275
71132134.066268925489-2.06626892548874
72124124.260915470249-0.260915470249202
73117118.360849366858-1.36084936685826
74120111.4439435790268.55605642097385
758991.5590134459976-2.55901344599764
768187.4997715210797-6.49977152107968
777172.9230202749146-1.92302027491462
785250.928230955811.07176904419001
796358.47872781405514.52127218594491
806256.86164882476145.13835117523861
817460.380594725183513.6194052748165
826753.528131000233413.4718689997666
835350.05687058987652.94312941012345
844249.1099877428014-7.1099877428014







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8544.289776960115934.945858221541453.6336956986905
8648.485246671474637.680024741005159.2904686019442
8722.08779656578269.281411960842934.8941811707223
8820.76475966219205.4921579278167836.0373613965673
8916.5000120637975-1.6298252637479934.6298493913431
902.25804980161506-19.06121259894323.5773122021731
9116.3812689970629-8.4159840034923641.1785219976181
9217.5412485401203-10.990505209470746.0730022897114
9327.2939750888859-5.2048578987778759.7928080765497
9415.9994292583440-20.680740128761852.6795986454499
950.100689245159970-40.960661967901641.1620404582215
96-8.97351395682509-54.604259144492836.6572312308426

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 44.2897769601159 & 34.9458582215414 & 53.6336956986905 \tabularnewline
86 & 48.4852466714746 & 37.6800247410051 & 59.2904686019442 \tabularnewline
87 & 22.0877965657826 & 9.2814119608429 & 34.8941811707223 \tabularnewline
88 & 20.7647596621920 & 5.49215792781678 & 36.0373613965673 \tabularnewline
89 & 16.5000120637975 & -1.62982526374799 & 34.6298493913431 \tabularnewline
90 & 2.25804980161506 & -19.061212598943 & 23.5773122021731 \tabularnewline
91 & 16.3812689970629 & -8.41598400349236 & 41.1785219976181 \tabularnewline
92 & 17.5412485401203 & -10.9905052094707 & 46.0730022897114 \tabularnewline
93 & 27.2939750888859 & -5.20485789877787 & 59.7928080765497 \tabularnewline
94 & 15.9994292583440 & -20.6807401287618 & 52.6795986454499 \tabularnewline
95 & 0.100689245159970 & -40.9606619679016 & 41.1620404582215 \tabularnewline
96 & -8.97351395682509 & -54.6042591444928 & 36.6572312308426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78875&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]44.2897769601159[/C][C]34.9458582215414[/C][C]53.6336956986905[/C][/ROW]
[ROW][C]86[/C][C]48.4852466714746[/C][C]37.6800247410051[/C][C]59.2904686019442[/C][/ROW]
[ROW][C]87[/C][C]22.0877965657826[/C][C]9.2814119608429[/C][C]34.8941811707223[/C][/ROW]
[ROW][C]88[/C][C]20.7647596621920[/C][C]5.49215792781678[/C][C]36.0373613965673[/C][/ROW]
[ROW][C]89[/C][C]16.5000120637975[/C][C]-1.62982526374799[/C][C]34.6298493913431[/C][/ROW]
[ROW][C]90[/C][C]2.25804980161506[/C][C]-19.061212598943[/C][C]23.5773122021731[/C][/ROW]
[ROW][C]91[/C][C]16.3812689970629[/C][C]-8.41598400349236[/C][C]41.1785219976181[/C][/ROW]
[ROW][C]92[/C][C]17.5412485401203[/C][C]-10.9905052094707[/C][C]46.0730022897114[/C][/ROW]
[ROW][C]93[/C][C]27.2939750888859[/C][C]-5.20485789877787[/C][C]59.7928080765497[/C][/ROW]
[ROW][C]94[/C][C]15.9994292583440[/C][C]-20.6807401287618[/C][C]52.6795986454499[/C][/ROW]
[ROW][C]95[/C][C]0.100689245159970[/C][C]-40.9606619679016[/C][C]41.1620404582215[/C][/ROW]
[ROW][C]96[/C][C]-8.97351395682509[/C][C]-54.6042591444928[/C][C]36.6572312308426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78875&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78875&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
8544.289776960115934.945858221541453.6336956986905
8648.485246671474637.680024741005159.2904686019442
8722.08779656578269.281411960842934.8941811707223
8820.76475966219205.4921579278167836.0373613965673
8916.5000120637975-1.6298252637479934.6298493913431
902.25804980161506-19.06121259894323.5773122021731
9116.3812689970629-8.4159840034923641.1785219976181
9217.5412485401203-10.990505209470746.0730022897114
9327.2939750888859-5.2048578987778759.7928080765497
9415.9994292583440-20.680740128761852.6795986454499
950.100689245159970-40.960661967901641.1620404582215
96-8.97351395682509-54.604259144492836.6572312308426



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')