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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 Dec 2011 08:26:46 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/26/t1324906062v2nd2lo5wdke72u.htm/, Retrieved Fri, 03 May 2024 15:10:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160810, Retrieved Fri, 03 May 2024 15:10:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential tripl...] [2011-12-26 13:26:46] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
293896
295705
339828
336278
346017
351623
352478
356391
333962
336828
344530
406516
319235
314750
362781
352440
374399
367418
362980
376600
346981
349571
357797
419221
329877
324252
375221
359533
392530
377686
373303
388904
354829
369553
378740
427251
343705
345062
374186
370241
399458
379886
385254
384375
352107
351566
337330
386331
311953
301261
330481
331632
349725
346615
350251
355782
326844
341207
342127
403845
318619
315067
365498
362038
371518
364774
368462
369199
351696
361750
372533
434288




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=160810&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=160810&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160810&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
alpha0.681011770747198
beta0.172412788822592
gamma0.448573760141997

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.681011770747198 \tabularnewline
beta & 0.172412788822592 \tabularnewline
gamma & 0.448573760141997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160810&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]0.681011770747198[/C][/ROW]
[ROW][C]beta[/C][C]0.172412788822592[/C][/ROW]
[ROW][C]gamma[/C][C]0.448573760141997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160810&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160810&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
alpha0.681011770747198
beta0.172412788822592
gamma0.448573760141997







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13319235309200.33680555610034.6631944445
14314750312896.1171536651853.88284633547
15362781363649.488702193-868.488702193426
16352440354386.002793806-1946.00279380608
17374399376449.89358477-2050.89358477021
18367418369263.129891237-1845.12989123666
19362980371047.930846382-8067.93084638205
20376600368726.3838853887873.61611461209
21346981351943.116442919-4962.11644291948
22349571351251.061452637-1680.06145263708
23357797357206.651561299590.348438700719
24419221419077.025040812143.974959188432
25329877333574.175208594-3697.17520859436
26324252325026.992640253-774.992640252516
27375221371571.0222763993649.97772360098
28359533363731.5170306-4198.5170306004
29392530382482.96410646810047.0358935316
30377686383221.509322268-5535.50932226825
31373303380826.426862041-7523.42686204094
32388904380444.4259398378459.5740601627
33354829361580.001789303-6751.00178930338
34369553359285.7418162510267.25818375
35378740374251.6843682684488.31563173194
36427251439719.643036797-12468.6430367972
37343705344603.805501929-898.805501929484
38345062338235.0338088596826.96619114099
39374186391336.393635105-17150.3936351046
40370241366513.4118684963727.58813150373
41399458391936.527548957521.47245105018
42379886387664.397554958-7778.39755495818
43385254382133.0478652173120.95213478309
44384375391212.425844828-6837.42584482773
45352107357883.415766012-5776.41576601227
46351566356931.758606069-5365.75860606856
47337330356832.732141042-19502.7321410425
48386331397127.432587779-10796.4325877786
49311953298593.55269853313359.4473014669
50301261298502.0699527432758.93004725705
51330481340386.258065864-9905.25806586351
52331632319319.53587383412312.4641261657
53349725347974.7253101781750.27468982193
54346615333748.26735523412866.7326447664
55350251342425.3105917127825.68940828805
56355782352425.3666375383356.63336246239
57326844326529.025826373314.974173626571
58341207330838.23442924510368.7655707554
59342127342333.016155686-206.016155685822
60403845402181.7841499211663.21585007932
61318619322219.476258547-3600.47625854739
62315067313699.8547554371367.14524456288
63365498357299.2831019458198.71689805499
64362038358341.5675593533696.43244064669
65371518385207.002706283-13689.0027062834
66364774365833.26714608-1059.26714607998
67368462366446.4966460782015.50335392152
68369199373309.345341995-4110.34534199513
69351696342475.0114035139220.98859648692
70361750355915.9535822155834.04641778511
71372533363904.9890744478628.01092555339
72434288432170.143701312117.85629869043

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 319235 & 309200.336805556 & 10034.6631944445 \tabularnewline
14 & 314750 & 312896.117153665 & 1853.88284633547 \tabularnewline
15 & 362781 & 363649.488702193 & -868.488702193426 \tabularnewline
16 & 352440 & 354386.002793806 & -1946.00279380608 \tabularnewline
17 & 374399 & 376449.89358477 & -2050.89358477021 \tabularnewline
18 & 367418 & 369263.129891237 & -1845.12989123666 \tabularnewline
19 & 362980 & 371047.930846382 & -8067.93084638205 \tabularnewline
20 & 376600 & 368726.383885388 & 7873.61611461209 \tabularnewline
21 & 346981 & 351943.116442919 & -4962.11644291948 \tabularnewline
22 & 349571 & 351251.061452637 & -1680.06145263708 \tabularnewline
23 & 357797 & 357206.651561299 & 590.348438700719 \tabularnewline
24 & 419221 & 419077.025040812 & 143.974959188432 \tabularnewline
25 & 329877 & 333574.175208594 & -3697.17520859436 \tabularnewline
26 & 324252 & 325026.992640253 & -774.992640252516 \tabularnewline
27 & 375221 & 371571.022276399 & 3649.97772360098 \tabularnewline
28 & 359533 & 363731.5170306 & -4198.5170306004 \tabularnewline
29 & 392530 & 382482.964106468 & 10047.0358935316 \tabularnewline
30 & 377686 & 383221.509322268 & -5535.50932226825 \tabularnewline
31 & 373303 & 380826.426862041 & -7523.42686204094 \tabularnewline
32 & 388904 & 380444.425939837 & 8459.5740601627 \tabularnewline
33 & 354829 & 361580.001789303 & -6751.00178930338 \tabularnewline
34 & 369553 & 359285.74181625 & 10267.25818375 \tabularnewline
35 & 378740 & 374251.684368268 & 4488.31563173194 \tabularnewline
36 & 427251 & 439719.643036797 & -12468.6430367972 \tabularnewline
37 & 343705 & 344603.805501929 & -898.805501929484 \tabularnewline
38 & 345062 & 338235.033808859 & 6826.96619114099 \tabularnewline
39 & 374186 & 391336.393635105 & -17150.3936351046 \tabularnewline
40 & 370241 & 366513.411868496 & 3727.58813150373 \tabularnewline
41 & 399458 & 391936.52754895 & 7521.47245105018 \tabularnewline
42 & 379886 & 387664.397554958 & -7778.39755495818 \tabularnewline
43 & 385254 & 382133.047865217 & 3120.95213478309 \tabularnewline
44 & 384375 & 391212.425844828 & -6837.42584482773 \tabularnewline
45 & 352107 & 357883.415766012 & -5776.41576601227 \tabularnewline
46 & 351566 & 356931.758606069 & -5365.75860606856 \tabularnewline
47 & 337330 & 356832.732141042 & -19502.7321410425 \tabularnewline
48 & 386331 & 397127.432587779 & -10796.4325877786 \tabularnewline
49 & 311953 & 298593.552698533 & 13359.4473014669 \tabularnewline
50 & 301261 & 298502.069952743 & 2758.93004725705 \tabularnewline
51 & 330481 & 340386.258065864 & -9905.25806586351 \tabularnewline
52 & 331632 & 319319.535873834 & 12312.4641261657 \tabularnewline
53 & 349725 & 347974.725310178 & 1750.27468982193 \tabularnewline
54 & 346615 & 333748.267355234 & 12866.7326447664 \tabularnewline
55 & 350251 & 342425.310591712 & 7825.68940828805 \tabularnewline
56 & 355782 & 352425.366637538 & 3356.63336246239 \tabularnewline
57 & 326844 & 326529.025826373 & 314.974173626571 \tabularnewline
58 & 341207 & 330838.234429245 & 10368.7655707554 \tabularnewline
59 & 342127 & 342333.016155686 & -206.016155685822 \tabularnewline
60 & 403845 & 402181.784149921 & 1663.21585007932 \tabularnewline
61 & 318619 & 322219.476258547 & -3600.47625854739 \tabularnewline
62 & 315067 & 313699.854755437 & 1367.14524456288 \tabularnewline
63 & 365498 & 357299.283101945 & 8198.71689805499 \tabularnewline
64 & 362038 & 358341.567559353 & 3696.43244064669 \tabularnewline
65 & 371518 & 385207.002706283 & -13689.0027062834 \tabularnewline
66 & 364774 & 365833.26714608 & -1059.26714607998 \tabularnewline
67 & 368462 & 366446.496646078 & 2015.50335392152 \tabularnewline
68 & 369199 & 373309.345341995 & -4110.34534199513 \tabularnewline
69 & 351696 & 342475.011403513 & 9220.98859648692 \tabularnewline
70 & 361750 & 355915.953582215 & 5834.04641778511 \tabularnewline
71 & 372533 & 363904.989074447 & 8628.01092555339 \tabularnewline
72 & 434288 & 432170.14370131 & 2117.85629869043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160810&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]319235[/C][C]309200.336805556[/C][C]10034.6631944445[/C][/ROW]
[ROW][C]14[/C][C]314750[/C][C]312896.117153665[/C][C]1853.88284633547[/C][/ROW]
[ROW][C]15[/C][C]362781[/C][C]363649.488702193[/C][C]-868.488702193426[/C][/ROW]
[ROW][C]16[/C][C]352440[/C][C]354386.002793806[/C][C]-1946.00279380608[/C][/ROW]
[ROW][C]17[/C][C]374399[/C][C]376449.89358477[/C][C]-2050.89358477021[/C][/ROW]
[ROW][C]18[/C][C]367418[/C][C]369263.129891237[/C][C]-1845.12989123666[/C][/ROW]
[ROW][C]19[/C][C]362980[/C][C]371047.930846382[/C][C]-8067.93084638205[/C][/ROW]
[ROW][C]20[/C][C]376600[/C][C]368726.383885388[/C][C]7873.61611461209[/C][/ROW]
[ROW][C]21[/C][C]346981[/C][C]351943.116442919[/C][C]-4962.11644291948[/C][/ROW]
[ROW][C]22[/C][C]349571[/C][C]351251.061452637[/C][C]-1680.06145263708[/C][/ROW]
[ROW][C]23[/C][C]357797[/C][C]357206.651561299[/C][C]590.348438700719[/C][/ROW]
[ROW][C]24[/C][C]419221[/C][C]419077.025040812[/C][C]143.974959188432[/C][/ROW]
[ROW][C]25[/C][C]329877[/C][C]333574.175208594[/C][C]-3697.17520859436[/C][/ROW]
[ROW][C]26[/C][C]324252[/C][C]325026.992640253[/C][C]-774.992640252516[/C][/ROW]
[ROW][C]27[/C][C]375221[/C][C]371571.022276399[/C][C]3649.97772360098[/C][/ROW]
[ROW][C]28[/C][C]359533[/C][C]363731.5170306[/C][C]-4198.5170306004[/C][/ROW]
[ROW][C]29[/C][C]392530[/C][C]382482.964106468[/C][C]10047.0358935316[/C][/ROW]
[ROW][C]30[/C][C]377686[/C][C]383221.509322268[/C][C]-5535.50932226825[/C][/ROW]
[ROW][C]31[/C][C]373303[/C][C]380826.426862041[/C][C]-7523.42686204094[/C][/ROW]
[ROW][C]32[/C][C]388904[/C][C]380444.425939837[/C][C]8459.5740601627[/C][/ROW]
[ROW][C]33[/C][C]354829[/C][C]361580.001789303[/C][C]-6751.00178930338[/C][/ROW]
[ROW][C]34[/C][C]369553[/C][C]359285.74181625[/C][C]10267.25818375[/C][/ROW]
[ROW][C]35[/C][C]378740[/C][C]374251.684368268[/C][C]4488.31563173194[/C][/ROW]
[ROW][C]36[/C][C]427251[/C][C]439719.643036797[/C][C]-12468.6430367972[/C][/ROW]
[ROW][C]37[/C][C]343705[/C][C]344603.805501929[/C][C]-898.805501929484[/C][/ROW]
[ROW][C]38[/C][C]345062[/C][C]338235.033808859[/C][C]6826.96619114099[/C][/ROW]
[ROW][C]39[/C][C]374186[/C][C]391336.393635105[/C][C]-17150.3936351046[/C][/ROW]
[ROW][C]40[/C][C]370241[/C][C]366513.411868496[/C][C]3727.58813150373[/C][/ROW]
[ROW][C]41[/C][C]399458[/C][C]391936.52754895[/C][C]7521.47245105018[/C][/ROW]
[ROW][C]42[/C][C]379886[/C][C]387664.397554958[/C][C]-7778.39755495818[/C][/ROW]
[ROW][C]43[/C][C]385254[/C][C]382133.047865217[/C][C]3120.95213478309[/C][/ROW]
[ROW][C]44[/C][C]384375[/C][C]391212.425844828[/C][C]-6837.42584482773[/C][/ROW]
[ROW][C]45[/C][C]352107[/C][C]357883.415766012[/C][C]-5776.41576601227[/C][/ROW]
[ROW][C]46[/C][C]351566[/C][C]356931.758606069[/C][C]-5365.75860606856[/C][/ROW]
[ROW][C]47[/C][C]337330[/C][C]356832.732141042[/C][C]-19502.7321410425[/C][/ROW]
[ROW][C]48[/C][C]386331[/C][C]397127.432587779[/C][C]-10796.4325877786[/C][/ROW]
[ROW][C]49[/C][C]311953[/C][C]298593.552698533[/C][C]13359.4473014669[/C][/ROW]
[ROW][C]50[/C][C]301261[/C][C]298502.069952743[/C][C]2758.93004725705[/C][/ROW]
[ROW][C]51[/C][C]330481[/C][C]340386.258065864[/C][C]-9905.25806586351[/C][/ROW]
[ROW][C]52[/C][C]331632[/C][C]319319.535873834[/C][C]12312.4641261657[/C][/ROW]
[ROW][C]53[/C][C]349725[/C][C]347974.725310178[/C][C]1750.27468982193[/C][/ROW]
[ROW][C]54[/C][C]346615[/C][C]333748.267355234[/C][C]12866.7326447664[/C][/ROW]
[ROW][C]55[/C][C]350251[/C][C]342425.310591712[/C][C]7825.68940828805[/C][/ROW]
[ROW][C]56[/C][C]355782[/C][C]352425.366637538[/C][C]3356.63336246239[/C][/ROW]
[ROW][C]57[/C][C]326844[/C][C]326529.025826373[/C][C]314.974173626571[/C][/ROW]
[ROW][C]58[/C][C]341207[/C][C]330838.234429245[/C][C]10368.7655707554[/C][/ROW]
[ROW][C]59[/C][C]342127[/C][C]342333.016155686[/C][C]-206.016155685822[/C][/ROW]
[ROW][C]60[/C][C]403845[/C][C]402181.784149921[/C][C]1663.21585007932[/C][/ROW]
[ROW][C]61[/C][C]318619[/C][C]322219.476258547[/C][C]-3600.47625854739[/C][/ROW]
[ROW][C]62[/C][C]315067[/C][C]313699.854755437[/C][C]1367.14524456288[/C][/ROW]
[ROW][C]63[/C][C]365498[/C][C]357299.283101945[/C][C]8198.71689805499[/C][/ROW]
[ROW][C]64[/C][C]362038[/C][C]358341.567559353[/C][C]3696.43244064669[/C][/ROW]
[ROW][C]65[/C][C]371518[/C][C]385207.002706283[/C][C]-13689.0027062834[/C][/ROW]
[ROW][C]66[/C][C]364774[/C][C]365833.26714608[/C][C]-1059.26714607998[/C][/ROW]
[ROW][C]67[/C][C]368462[/C][C]366446.496646078[/C][C]2015.50335392152[/C][/ROW]
[ROW][C]68[/C][C]369199[/C][C]373309.345341995[/C][C]-4110.34534199513[/C][/ROW]
[ROW][C]69[/C][C]351696[/C][C]342475.011403513[/C][C]9220.98859648692[/C][/ROW]
[ROW][C]70[/C][C]361750[/C][C]355915.953582215[/C][C]5834.04641778511[/C][/ROW]
[ROW][C]71[/C][C]372533[/C][C]363904.989074447[/C][C]8628.01092555339[/C][/ROW]
[ROW][C]72[/C][C]434288[/C][C]432170.14370131[/C][C]2117.85629869043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160810&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160810&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
13319235309200.33680555610034.6631944445
14314750312896.1171536651853.88284633547
15362781363649.488702193-868.488702193426
16352440354386.002793806-1946.00279380608
17374399376449.89358477-2050.89358477021
18367418369263.129891237-1845.12989123666
19362980371047.930846382-8067.93084638205
20376600368726.3838853887873.61611461209
21346981351943.116442919-4962.11644291948
22349571351251.061452637-1680.06145263708
23357797357206.651561299590.348438700719
24419221419077.025040812143.974959188432
25329877333574.175208594-3697.17520859436
26324252325026.992640253-774.992640252516
27375221371571.0222763993649.97772360098
28359533363731.5170306-4198.5170306004
29392530382482.96410646810047.0358935316
30377686383221.509322268-5535.50932226825
31373303380826.426862041-7523.42686204094
32388904380444.4259398378459.5740601627
33354829361580.001789303-6751.00178930338
34369553359285.7418162510267.25818375
35378740374251.6843682684488.31563173194
36427251439719.643036797-12468.6430367972
37343705344603.805501929-898.805501929484
38345062338235.0338088596826.96619114099
39374186391336.393635105-17150.3936351046
40370241366513.4118684963727.58813150373
41399458391936.527548957521.47245105018
42379886387664.397554958-7778.39755495818
43385254382133.0478652173120.95213478309
44384375391212.425844828-6837.42584482773
45352107357883.415766012-5776.41576601227
46351566356931.758606069-5365.75860606856
47337330356832.732141042-19502.7321410425
48386331397127.432587779-10796.4325877786
49311953298593.55269853313359.4473014669
50301261298502.0699527432758.93004725705
51330481340386.258065864-9905.25806586351
52331632319319.53587383412312.4641261657
53349725347974.7253101781750.27468982193
54346615333748.26735523412866.7326447664
55350251342425.3105917127825.68940828805
56355782352425.3666375383356.63336246239
57326844326529.025826373314.974173626571
58341207330838.23442924510368.7655707554
59342127342333.016155686-206.016155685822
60403845402181.7841499211663.21585007932
61318619322219.476258547-3600.47625854739
62315067313699.8547554371367.14524456288
63365498357299.2831019458198.71689805499
64362038358341.5675593533696.43244064669
65371518385207.002706283-13689.0027062834
66364774365833.26714608-1059.26714607998
67368462366446.4966460782015.50335392152
68369199373309.345341995-4110.34534199513
69351696342475.0114035139220.98859648692
70361750355915.9535822155834.04641778511
71372533363904.9890744478628.01092555339
72434288432170.143701312117.85629869043







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73353950.494861116339344.800427027368556.189295204
74351202.630144683332512.559370439369892.700918927
75397296.995173217374313.310931568420280.679414866
76393597.423491802366101.946326652421092.900656952
77416509.647279133384284.57501356448734.719544705
78410924.545740009373756.094567238448092.996912781
79415482.567125609373162.374876047457802.759375172
80422643.08790319374968.650536717470317.525269664
81399544.941270102346319.612258354452770.270281851
82408168.377827475349201.169567681467135.586087269
83413845.874209141348951.175271851478740.573146431
84475552.383834091404549.647856184546555.119811999

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 353950.494861116 & 339344.800427027 & 368556.189295204 \tabularnewline
74 & 351202.630144683 & 332512.559370439 & 369892.700918927 \tabularnewline
75 & 397296.995173217 & 374313.310931568 & 420280.679414866 \tabularnewline
76 & 393597.423491802 & 366101.946326652 & 421092.900656952 \tabularnewline
77 & 416509.647279133 & 384284.57501356 & 448734.719544705 \tabularnewline
78 & 410924.545740009 & 373756.094567238 & 448092.996912781 \tabularnewline
79 & 415482.567125609 & 373162.374876047 & 457802.759375172 \tabularnewline
80 & 422643.08790319 & 374968.650536717 & 470317.525269664 \tabularnewline
81 & 399544.941270102 & 346319.612258354 & 452770.270281851 \tabularnewline
82 & 408168.377827475 & 349201.169567681 & 467135.586087269 \tabularnewline
83 & 413845.874209141 & 348951.175271851 & 478740.573146431 \tabularnewline
84 & 475552.383834091 & 404549.647856184 & 546555.119811999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160810&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]353950.494861116[/C][C]339344.800427027[/C][C]368556.189295204[/C][/ROW]
[ROW][C]74[/C][C]351202.630144683[/C][C]332512.559370439[/C][C]369892.700918927[/C][/ROW]
[ROW][C]75[/C][C]397296.995173217[/C][C]374313.310931568[/C][C]420280.679414866[/C][/ROW]
[ROW][C]76[/C][C]393597.423491802[/C][C]366101.946326652[/C][C]421092.900656952[/C][/ROW]
[ROW][C]77[/C][C]416509.647279133[/C][C]384284.57501356[/C][C]448734.719544705[/C][/ROW]
[ROW][C]78[/C][C]410924.545740009[/C][C]373756.094567238[/C][C]448092.996912781[/C][/ROW]
[ROW][C]79[/C][C]415482.567125609[/C][C]373162.374876047[/C][C]457802.759375172[/C][/ROW]
[ROW][C]80[/C][C]422643.08790319[/C][C]374968.650536717[/C][C]470317.525269664[/C][/ROW]
[ROW][C]81[/C][C]399544.941270102[/C][C]346319.612258354[/C][C]452770.270281851[/C][/ROW]
[ROW][C]82[/C][C]408168.377827475[/C][C]349201.169567681[/C][C]467135.586087269[/C][/ROW]
[ROW][C]83[/C][C]413845.874209141[/C][C]348951.175271851[/C][C]478740.573146431[/C][/ROW]
[ROW][C]84[/C][C]475552.383834091[/C][C]404549.647856184[/C][C]546555.119811999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160810&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160810&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
73353950.494861116339344.800427027368556.189295204
74351202.630144683332512.559370439369892.700918927
75397296.995173217374313.310931568420280.679414866
76393597.423491802366101.946326652421092.900656952
77416509.647279133384284.57501356448734.719544705
78410924.545740009373756.094567238448092.996912781
79415482.567125609373162.374876047457802.759375172
80422643.08790319374968.650536717470317.525269664
81399544.941270102346319.612258354452770.270281851
82408168.377827475349201.169567681467135.586087269
83413845.874209141348951.175271851478740.573146431
84475552.383834091404549.647856184546555.119811999



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')