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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 12 Dec 2015 15:35:13 +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/2015/Dec/12/t1449934523ioqzyrkon7o87pj.htm/, Retrieved Thu, 16 May 2024 20:54:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286102, Retrieved Thu, 16 May 2024 20:54:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Double exponential] [2015-12-12 15:35:13] [d42bb29750b9700c1c3b9062bc539f05] [Current]
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Dataseries X:
325.87
302.25
294
285.43
286.19
276.7
267.77
267.03
257.87
257.19
275.6
305.68
358.06
320.07
295.9
291.27
272.87
269.27
271.32
267.45
260.33
277.94
277.07
312.65
319.71
318.39
304.9
303.73
273.29
274.33
270.45
278.23
274.03
279
287.5
336.87
334.1
296.07
286.84
277.63
261.32
264.07
261.94
252.84
257.83
271.16
273.63
304.87
323.9
336.11
335.65
282.23
273.03
270.07
246.03
242.35
250.33
267.45
268.8
302.68
313.1
306.39
305.61
277.27
264.94
268.63
293.9
248.65
256
258.52
266.9
281.23
306
325.46
291.13
282.53
256.52
258.63
252.74
245.16
255.03
268.35
293.73
278.39




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286102&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286102&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286102&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.112415546747099
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.112415546747099 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286102&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]0.112415546747099[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286102&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286102&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
beta0.112415546747099
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3294278.6315.37
4285.43272.10782695350313.3221730464971
5286.19265.03544632038421.1545536796156
6276.7268.1735470384698.52645296153077
7267.77259.6420529099538.12794709004686
8267.03251.62576052601215.4042394739878
9257.87252.6174365287045.25256347129624
10257.19244.04790632315313.1420936768466
11275.6244.84528196923830.7547180307623
12305.68266.71259041171938.9674095882813
13358.06301.17313306590456.8868669340965
14320.07359.948101315029-39.8781013150295
15295.9317.475182752464-21.5751827524642
16291.27290.8797967871770.390203212822655
17272.87286.293661694689-13.4236616946893
18269.27266.3846334259332.88536657406729
19271.32263.1089934869228.21100651307773
20267.45266.0820382734341.36796172656608
21260.33262.365818438855-2.03581843885496
22277.94255.01696079597322.9230392040268
23277.07275.2038667811991.86613321880088
24312.65274.54364916729338.1063508327065
25319.71314.4073954306895.30260456931103
26318.39322.063490622532-3.67349062253174
27304.9320.330533165729-15.4305331657295
28303.73305.105901343305-1.37590134330475
29273.29303.781228641527-30.4912286415271
30274.33269.9135405027994.41645949720095
31270.45271.450019211863-1.00001921186328
32278.23267.45760150540410.772398494596
33274.03276.448586571952-2.41858657195178
34279271.9766998401117.02330015988946
35287.5277.7362279675549.76377203244647
36336.87287.33382773889549.536172261105
37334.1342.272463627386-8.17246362738564
38296.07338.583751660442-42.5137516604423
39286.84295.774545023263-8.9345450232633
40277.63285.540163259537-7.91016325953655
41261.32275.440937931857-14.1209379318569
42264.07257.5435249736656.52647502633459
43261.94261.0272022320820.912797767917937
44252.84258.999814892232-6.15981489223211
45257.83249.2073559332618.62264406673907
46271.16255.16667518042915.993324819571
47273.63270.2945735343253.33542646567491
48304.87273.13952732409931.7304726759014
49323.9307.94652575850415.953474241496
50336.11328.7699442878777.34005571212253
51335.65341.80508066391-6.15508066390998
52282.23340.653153905804-58.4231539058039
53273.03280.665483116793-7.63548311679318
54270.07270.607136107541-0.537136107540562
55246.03267.586753658334-21.5567536583338
56242.35241.123439409741.22656059026033
57250.33237.58132388911212.7486761108878
58267.45246.99447328441920.4555267155806
59268.8266.4139925041512.38600749584879
60302.68268.0322168413434.6477831586602
61313.1305.8071663286957.29283367130455
62306.39317.046994213191-10.6569942131909
63305.61309.138982382034-3.52898238203431
64277.27307.962269898097-30.6922698980971
65264.94276.171981596593-11.2319815965929
66268.63262.5793322443596.05066775564143
67293.9266.94952136829426.9504786317059
68248.65295.249174158773-46.5991741587733
69256244.76070251775111.2392974822485
70258.52253.3741742892725.14582571072822
71266.9256.47264510000910.4273548999914
72281.23266.02484190221715.2051580977829
73306282.06413806315523.9358619368445
74325.46309.52490106964915.935098930351
75291.13330.776253928373-39.6462539283734
76282.53291.989398616541-9.45939861654108
77256.52282.326015149164-25.8060151491638
78258.63253.4150178468075.21498215319338
79252.74256.111262916834-3.37126291683421
80245.16249.84228055281-4.68228055281011
81255.03241.73591942444313.2940805755574
82268.35253.10038076084415.2496192391561
83293.73268.13467504529925.5953249547013
84278.39296.391987494251-18.0019874942512

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 294 & 278.63 & 15.37 \tabularnewline
4 & 285.43 & 272.107826953503 & 13.3221730464971 \tabularnewline
5 & 286.19 & 265.035446320384 & 21.1545536796156 \tabularnewline
6 & 276.7 & 268.173547038469 & 8.52645296153077 \tabularnewline
7 & 267.77 & 259.642052909953 & 8.12794709004686 \tabularnewline
8 & 267.03 & 251.625760526012 & 15.4042394739878 \tabularnewline
9 & 257.87 & 252.617436528704 & 5.25256347129624 \tabularnewline
10 & 257.19 & 244.047906323153 & 13.1420936768466 \tabularnewline
11 & 275.6 & 244.845281969238 & 30.7547180307623 \tabularnewline
12 & 305.68 & 266.712590411719 & 38.9674095882813 \tabularnewline
13 & 358.06 & 301.173133065904 & 56.8868669340965 \tabularnewline
14 & 320.07 & 359.948101315029 & -39.8781013150295 \tabularnewline
15 & 295.9 & 317.475182752464 & -21.5751827524642 \tabularnewline
16 & 291.27 & 290.879796787177 & 0.390203212822655 \tabularnewline
17 & 272.87 & 286.293661694689 & -13.4236616946893 \tabularnewline
18 & 269.27 & 266.384633425933 & 2.88536657406729 \tabularnewline
19 & 271.32 & 263.108993486922 & 8.21100651307773 \tabularnewline
20 & 267.45 & 266.082038273434 & 1.36796172656608 \tabularnewline
21 & 260.33 & 262.365818438855 & -2.03581843885496 \tabularnewline
22 & 277.94 & 255.016960795973 & 22.9230392040268 \tabularnewline
23 & 277.07 & 275.203866781199 & 1.86613321880088 \tabularnewline
24 & 312.65 & 274.543649167293 & 38.1063508327065 \tabularnewline
25 & 319.71 & 314.407395430689 & 5.30260456931103 \tabularnewline
26 & 318.39 & 322.063490622532 & -3.67349062253174 \tabularnewline
27 & 304.9 & 320.330533165729 & -15.4305331657295 \tabularnewline
28 & 303.73 & 305.105901343305 & -1.37590134330475 \tabularnewline
29 & 273.29 & 303.781228641527 & -30.4912286415271 \tabularnewline
30 & 274.33 & 269.913540502799 & 4.41645949720095 \tabularnewline
31 & 270.45 & 271.450019211863 & -1.00001921186328 \tabularnewline
32 & 278.23 & 267.457601505404 & 10.772398494596 \tabularnewline
33 & 274.03 & 276.448586571952 & -2.41858657195178 \tabularnewline
34 & 279 & 271.976699840111 & 7.02330015988946 \tabularnewline
35 & 287.5 & 277.736227967554 & 9.76377203244647 \tabularnewline
36 & 336.87 & 287.333827738895 & 49.536172261105 \tabularnewline
37 & 334.1 & 342.272463627386 & -8.17246362738564 \tabularnewline
38 & 296.07 & 338.583751660442 & -42.5137516604423 \tabularnewline
39 & 286.84 & 295.774545023263 & -8.9345450232633 \tabularnewline
40 & 277.63 & 285.540163259537 & -7.91016325953655 \tabularnewline
41 & 261.32 & 275.440937931857 & -14.1209379318569 \tabularnewline
42 & 264.07 & 257.543524973665 & 6.52647502633459 \tabularnewline
43 & 261.94 & 261.027202232082 & 0.912797767917937 \tabularnewline
44 & 252.84 & 258.999814892232 & -6.15981489223211 \tabularnewline
45 & 257.83 & 249.207355933261 & 8.62264406673907 \tabularnewline
46 & 271.16 & 255.166675180429 & 15.993324819571 \tabularnewline
47 & 273.63 & 270.294573534325 & 3.33542646567491 \tabularnewline
48 & 304.87 & 273.139527324099 & 31.7304726759014 \tabularnewline
49 & 323.9 & 307.946525758504 & 15.953474241496 \tabularnewline
50 & 336.11 & 328.769944287877 & 7.34005571212253 \tabularnewline
51 & 335.65 & 341.80508066391 & -6.15508066390998 \tabularnewline
52 & 282.23 & 340.653153905804 & -58.4231539058039 \tabularnewline
53 & 273.03 & 280.665483116793 & -7.63548311679318 \tabularnewline
54 & 270.07 & 270.607136107541 & -0.537136107540562 \tabularnewline
55 & 246.03 & 267.586753658334 & -21.5567536583338 \tabularnewline
56 & 242.35 & 241.12343940974 & 1.22656059026033 \tabularnewline
57 & 250.33 & 237.581323889112 & 12.7486761108878 \tabularnewline
58 & 267.45 & 246.994473284419 & 20.4555267155806 \tabularnewline
59 & 268.8 & 266.413992504151 & 2.38600749584879 \tabularnewline
60 & 302.68 & 268.03221684134 & 34.6477831586602 \tabularnewline
61 & 313.1 & 305.807166328695 & 7.29283367130455 \tabularnewline
62 & 306.39 & 317.046994213191 & -10.6569942131909 \tabularnewline
63 & 305.61 & 309.138982382034 & -3.52898238203431 \tabularnewline
64 & 277.27 & 307.962269898097 & -30.6922698980971 \tabularnewline
65 & 264.94 & 276.171981596593 & -11.2319815965929 \tabularnewline
66 & 268.63 & 262.579332244359 & 6.05066775564143 \tabularnewline
67 & 293.9 & 266.949521368294 & 26.9504786317059 \tabularnewline
68 & 248.65 & 295.249174158773 & -46.5991741587733 \tabularnewline
69 & 256 & 244.760702517751 & 11.2392974822485 \tabularnewline
70 & 258.52 & 253.374174289272 & 5.14582571072822 \tabularnewline
71 & 266.9 & 256.472645100009 & 10.4273548999914 \tabularnewline
72 & 281.23 & 266.024841902217 & 15.2051580977829 \tabularnewline
73 & 306 & 282.064138063155 & 23.9358619368445 \tabularnewline
74 & 325.46 & 309.524901069649 & 15.935098930351 \tabularnewline
75 & 291.13 & 330.776253928373 & -39.6462539283734 \tabularnewline
76 & 282.53 & 291.989398616541 & -9.45939861654108 \tabularnewline
77 & 256.52 & 282.326015149164 & -25.8060151491638 \tabularnewline
78 & 258.63 & 253.415017846807 & 5.21498215319338 \tabularnewline
79 & 252.74 & 256.111262916834 & -3.37126291683421 \tabularnewline
80 & 245.16 & 249.84228055281 & -4.68228055281011 \tabularnewline
81 & 255.03 & 241.735919424443 & 13.2940805755574 \tabularnewline
82 & 268.35 & 253.100380760844 & 15.2496192391561 \tabularnewline
83 & 293.73 & 268.134675045299 & 25.5953249547013 \tabularnewline
84 & 278.39 & 296.391987494251 & -18.0019874942512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286102&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]294[/C][C]278.63[/C][C]15.37[/C][/ROW]
[ROW][C]4[/C][C]285.43[/C][C]272.107826953503[/C][C]13.3221730464971[/C][/ROW]
[ROW][C]5[/C][C]286.19[/C][C]265.035446320384[/C][C]21.1545536796156[/C][/ROW]
[ROW][C]6[/C][C]276.7[/C][C]268.173547038469[/C][C]8.52645296153077[/C][/ROW]
[ROW][C]7[/C][C]267.77[/C][C]259.642052909953[/C][C]8.12794709004686[/C][/ROW]
[ROW][C]8[/C][C]267.03[/C][C]251.625760526012[/C][C]15.4042394739878[/C][/ROW]
[ROW][C]9[/C][C]257.87[/C][C]252.617436528704[/C][C]5.25256347129624[/C][/ROW]
[ROW][C]10[/C][C]257.19[/C][C]244.047906323153[/C][C]13.1420936768466[/C][/ROW]
[ROW][C]11[/C][C]275.6[/C][C]244.845281969238[/C][C]30.7547180307623[/C][/ROW]
[ROW][C]12[/C][C]305.68[/C][C]266.712590411719[/C][C]38.9674095882813[/C][/ROW]
[ROW][C]13[/C][C]358.06[/C][C]301.173133065904[/C][C]56.8868669340965[/C][/ROW]
[ROW][C]14[/C][C]320.07[/C][C]359.948101315029[/C][C]-39.8781013150295[/C][/ROW]
[ROW][C]15[/C][C]295.9[/C][C]317.475182752464[/C][C]-21.5751827524642[/C][/ROW]
[ROW][C]16[/C][C]291.27[/C][C]290.879796787177[/C][C]0.390203212822655[/C][/ROW]
[ROW][C]17[/C][C]272.87[/C][C]286.293661694689[/C][C]-13.4236616946893[/C][/ROW]
[ROW][C]18[/C][C]269.27[/C][C]266.384633425933[/C][C]2.88536657406729[/C][/ROW]
[ROW][C]19[/C][C]271.32[/C][C]263.108993486922[/C][C]8.21100651307773[/C][/ROW]
[ROW][C]20[/C][C]267.45[/C][C]266.082038273434[/C][C]1.36796172656608[/C][/ROW]
[ROW][C]21[/C][C]260.33[/C][C]262.365818438855[/C][C]-2.03581843885496[/C][/ROW]
[ROW][C]22[/C][C]277.94[/C][C]255.016960795973[/C][C]22.9230392040268[/C][/ROW]
[ROW][C]23[/C][C]277.07[/C][C]275.203866781199[/C][C]1.86613321880088[/C][/ROW]
[ROW][C]24[/C][C]312.65[/C][C]274.543649167293[/C][C]38.1063508327065[/C][/ROW]
[ROW][C]25[/C][C]319.71[/C][C]314.407395430689[/C][C]5.30260456931103[/C][/ROW]
[ROW][C]26[/C][C]318.39[/C][C]322.063490622532[/C][C]-3.67349062253174[/C][/ROW]
[ROW][C]27[/C][C]304.9[/C][C]320.330533165729[/C][C]-15.4305331657295[/C][/ROW]
[ROW][C]28[/C][C]303.73[/C][C]305.105901343305[/C][C]-1.37590134330475[/C][/ROW]
[ROW][C]29[/C][C]273.29[/C][C]303.781228641527[/C][C]-30.4912286415271[/C][/ROW]
[ROW][C]30[/C][C]274.33[/C][C]269.913540502799[/C][C]4.41645949720095[/C][/ROW]
[ROW][C]31[/C][C]270.45[/C][C]271.450019211863[/C][C]-1.00001921186328[/C][/ROW]
[ROW][C]32[/C][C]278.23[/C][C]267.457601505404[/C][C]10.772398494596[/C][/ROW]
[ROW][C]33[/C][C]274.03[/C][C]276.448586571952[/C][C]-2.41858657195178[/C][/ROW]
[ROW][C]34[/C][C]279[/C][C]271.976699840111[/C][C]7.02330015988946[/C][/ROW]
[ROW][C]35[/C][C]287.5[/C][C]277.736227967554[/C][C]9.76377203244647[/C][/ROW]
[ROW][C]36[/C][C]336.87[/C][C]287.333827738895[/C][C]49.536172261105[/C][/ROW]
[ROW][C]37[/C][C]334.1[/C][C]342.272463627386[/C][C]-8.17246362738564[/C][/ROW]
[ROW][C]38[/C][C]296.07[/C][C]338.583751660442[/C][C]-42.5137516604423[/C][/ROW]
[ROW][C]39[/C][C]286.84[/C][C]295.774545023263[/C][C]-8.9345450232633[/C][/ROW]
[ROW][C]40[/C][C]277.63[/C][C]285.540163259537[/C][C]-7.91016325953655[/C][/ROW]
[ROW][C]41[/C][C]261.32[/C][C]275.440937931857[/C][C]-14.1209379318569[/C][/ROW]
[ROW][C]42[/C][C]264.07[/C][C]257.543524973665[/C][C]6.52647502633459[/C][/ROW]
[ROW][C]43[/C][C]261.94[/C][C]261.027202232082[/C][C]0.912797767917937[/C][/ROW]
[ROW][C]44[/C][C]252.84[/C][C]258.999814892232[/C][C]-6.15981489223211[/C][/ROW]
[ROW][C]45[/C][C]257.83[/C][C]249.207355933261[/C][C]8.62264406673907[/C][/ROW]
[ROW][C]46[/C][C]271.16[/C][C]255.166675180429[/C][C]15.993324819571[/C][/ROW]
[ROW][C]47[/C][C]273.63[/C][C]270.294573534325[/C][C]3.33542646567491[/C][/ROW]
[ROW][C]48[/C][C]304.87[/C][C]273.139527324099[/C][C]31.7304726759014[/C][/ROW]
[ROW][C]49[/C][C]323.9[/C][C]307.946525758504[/C][C]15.953474241496[/C][/ROW]
[ROW][C]50[/C][C]336.11[/C][C]328.769944287877[/C][C]7.34005571212253[/C][/ROW]
[ROW][C]51[/C][C]335.65[/C][C]341.80508066391[/C][C]-6.15508066390998[/C][/ROW]
[ROW][C]52[/C][C]282.23[/C][C]340.653153905804[/C][C]-58.4231539058039[/C][/ROW]
[ROW][C]53[/C][C]273.03[/C][C]280.665483116793[/C][C]-7.63548311679318[/C][/ROW]
[ROW][C]54[/C][C]270.07[/C][C]270.607136107541[/C][C]-0.537136107540562[/C][/ROW]
[ROW][C]55[/C][C]246.03[/C][C]267.586753658334[/C][C]-21.5567536583338[/C][/ROW]
[ROW][C]56[/C][C]242.35[/C][C]241.12343940974[/C][C]1.22656059026033[/C][/ROW]
[ROW][C]57[/C][C]250.33[/C][C]237.581323889112[/C][C]12.7486761108878[/C][/ROW]
[ROW][C]58[/C][C]267.45[/C][C]246.994473284419[/C][C]20.4555267155806[/C][/ROW]
[ROW][C]59[/C][C]268.8[/C][C]266.413992504151[/C][C]2.38600749584879[/C][/ROW]
[ROW][C]60[/C][C]302.68[/C][C]268.03221684134[/C][C]34.6477831586602[/C][/ROW]
[ROW][C]61[/C][C]313.1[/C][C]305.807166328695[/C][C]7.29283367130455[/C][/ROW]
[ROW][C]62[/C][C]306.39[/C][C]317.046994213191[/C][C]-10.6569942131909[/C][/ROW]
[ROW][C]63[/C][C]305.61[/C][C]309.138982382034[/C][C]-3.52898238203431[/C][/ROW]
[ROW][C]64[/C][C]277.27[/C][C]307.962269898097[/C][C]-30.6922698980971[/C][/ROW]
[ROW][C]65[/C][C]264.94[/C][C]276.171981596593[/C][C]-11.2319815965929[/C][/ROW]
[ROW][C]66[/C][C]268.63[/C][C]262.579332244359[/C][C]6.05066775564143[/C][/ROW]
[ROW][C]67[/C][C]293.9[/C][C]266.949521368294[/C][C]26.9504786317059[/C][/ROW]
[ROW][C]68[/C][C]248.65[/C][C]295.249174158773[/C][C]-46.5991741587733[/C][/ROW]
[ROW][C]69[/C][C]256[/C][C]244.760702517751[/C][C]11.2392974822485[/C][/ROW]
[ROW][C]70[/C][C]258.52[/C][C]253.374174289272[/C][C]5.14582571072822[/C][/ROW]
[ROW][C]71[/C][C]266.9[/C][C]256.472645100009[/C][C]10.4273548999914[/C][/ROW]
[ROW][C]72[/C][C]281.23[/C][C]266.024841902217[/C][C]15.2051580977829[/C][/ROW]
[ROW][C]73[/C][C]306[/C][C]282.064138063155[/C][C]23.9358619368445[/C][/ROW]
[ROW][C]74[/C][C]325.46[/C][C]309.524901069649[/C][C]15.935098930351[/C][/ROW]
[ROW][C]75[/C][C]291.13[/C][C]330.776253928373[/C][C]-39.6462539283734[/C][/ROW]
[ROW][C]76[/C][C]282.53[/C][C]291.989398616541[/C][C]-9.45939861654108[/C][/ROW]
[ROW][C]77[/C][C]256.52[/C][C]282.326015149164[/C][C]-25.8060151491638[/C][/ROW]
[ROW][C]78[/C][C]258.63[/C][C]253.415017846807[/C][C]5.21498215319338[/C][/ROW]
[ROW][C]79[/C][C]252.74[/C][C]256.111262916834[/C][C]-3.37126291683421[/C][/ROW]
[ROW][C]80[/C][C]245.16[/C][C]249.84228055281[/C][C]-4.68228055281011[/C][/ROW]
[ROW][C]81[/C][C]255.03[/C][C]241.735919424443[/C][C]13.2940805755574[/C][/ROW]
[ROW][C]82[/C][C]268.35[/C][C]253.100380760844[/C][C]15.2496192391561[/C][/ROW]
[ROW][C]83[/C][C]293.73[/C][C]268.134675045299[/C][C]25.5953249547013[/C][/ROW]
[ROW][C]84[/C][C]278.39[/C][C]296.391987494251[/C][C]-18.0019874942512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286102&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286102&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
3294278.6315.37
4285.43272.10782695350313.3221730464971
5286.19265.03544632038421.1545536796156
6276.7268.1735470384698.52645296153077
7267.77259.6420529099538.12794709004686
8267.03251.62576052601215.4042394739878
9257.87252.6174365287045.25256347129624
10257.19244.04790632315313.1420936768466
11275.6244.84528196923830.7547180307623
12305.68266.71259041171938.9674095882813
13358.06301.17313306590456.8868669340965
14320.07359.948101315029-39.8781013150295
15295.9317.475182752464-21.5751827524642
16291.27290.8797967871770.390203212822655
17272.87286.293661694689-13.4236616946893
18269.27266.3846334259332.88536657406729
19271.32263.1089934869228.21100651307773
20267.45266.0820382734341.36796172656608
21260.33262.365818438855-2.03581843885496
22277.94255.01696079597322.9230392040268
23277.07275.2038667811991.86613321880088
24312.65274.54364916729338.1063508327065
25319.71314.4073954306895.30260456931103
26318.39322.063490622532-3.67349062253174
27304.9320.330533165729-15.4305331657295
28303.73305.105901343305-1.37590134330475
29273.29303.781228641527-30.4912286415271
30274.33269.9135405027994.41645949720095
31270.45271.450019211863-1.00001921186328
32278.23267.45760150540410.772398494596
33274.03276.448586571952-2.41858657195178
34279271.9766998401117.02330015988946
35287.5277.7362279675549.76377203244647
36336.87287.33382773889549.536172261105
37334.1342.272463627386-8.17246362738564
38296.07338.583751660442-42.5137516604423
39286.84295.774545023263-8.9345450232633
40277.63285.540163259537-7.91016325953655
41261.32275.440937931857-14.1209379318569
42264.07257.5435249736656.52647502633459
43261.94261.0272022320820.912797767917937
44252.84258.999814892232-6.15981489223211
45257.83249.2073559332618.62264406673907
46271.16255.16667518042915.993324819571
47273.63270.2945735343253.33542646567491
48304.87273.13952732409931.7304726759014
49323.9307.94652575850415.953474241496
50336.11328.7699442878777.34005571212253
51335.65341.80508066391-6.15508066390998
52282.23340.653153905804-58.4231539058039
53273.03280.665483116793-7.63548311679318
54270.07270.607136107541-0.537136107540562
55246.03267.586753658334-21.5567536583338
56242.35241.123439409741.22656059026033
57250.33237.58132388911212.7486761108878
58267.45246.99447328441920.4555267155806
59268.8266.4139925041512.38600749584879
60302.68268.0322168413434.6477831586602
61313.1305.8071663286957.29283367130455
62306.39317.046994213191-10.6569942131909
63305.61309.138982382034-3.52898238203431
64277.27307.962269898097-30.6922698980971
65264.94276.171981596593-11.2319815965929
66268.63262.5793322443596.05066775564143
67293.9266.94952136829426.9504786317059
68248.65295.249174158773-46.5991741587733
69256244.76070251775111.2392974822485
70258.52253.3741742892725.14582571072822
71266.9256.47264510000910.4273548999914
72281.23266.02484190221715.2051580977829
73306282.06413806315523.9358619368445
74325.46309.52490106964915.935098930351
75291.13330.776253928373-39.6462539283734
76282.53291.989398616541-9.45939861654108
77256.52282.326015149164-25.8060151491638
78258.63253.4150178468075.21498215319338
79252.74256.111262916834-3.37126291683421
80245.16249.84228055281-4.68228055281011
81255.03241.73591942444313.2940805755574
82268.35253.10038076084415.2496192391561
83293.73268.13467504529925.5953249547013
84278.39296.391987494251-18.0019874942512







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85279.02828422755238.981725562558319.074842892543
86279.666568455101219.764247204966339.568889705236
87280.304852682651202.882523204632357.727182160671
88280.943136910202186.804689377218375.081584443186
89281.581421137752170.981637645322392.181204630182
90282.219705365303155.154584553866409.284826176739
91282.857989592853139.183777676644426.532201509062
92283.496273820404122.987556772404444.004990868404
93284.134558047954106.515905947889461.75321014802
94284.77284227550589.7373979143392479.80828663667
95285.41112650305572.6321364467053498.190116559405
96286.04941073060555.1876747464047516.911146714806

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 279.02828422755 & 238.981725562558 & 319.074842892543 \tabularnewline
86 & 279.666568455101 & 219.764247204966 & 339.568889705236 \tabularnewline
87 & 280.304852682651 & 202.882523204632 & 357.727182160671 \tabularnewline
88 & 280.943136910202 & 186.804689377218 & 375.081584443186 \tabularnewline
89 & 281.581421137752 & 170.981637645322 & 392.181204630182 \tabularnewline
90 & 282.219705365303 & 155.154584553866 & 409.284826176739 \tabularnewline
91 & 282.857989592853 & 139.183777676644 & 426.532201509062 \tabularnewline
92 & 283.496273820404 & 122.987556772404 & 444.004990868404 \tabularnewline
93 & 284.134558047954 & 106.515905947889 & 461.75321014802 \tabularnewline
94 & 284.772842275505 & 89.7373979143392 & 479.80828663667 \tabularnewline
95 & 285.411126503055 & 72.6321364467053 & 498.190116559405 \tabularnewline
96 & 286.049410730605 & 55.1876747464047 & 516.911146714806 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286102&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]279.02828422755[/C][C]238.981725562558[/C][C]319.074842892543[/C][/ROW]
[ROW][C]86[/C][C]279.666568455101[/C][C]219.764247204966[/C][C]339.568889705236[/C][/ROW]
[ROW][C]87[/C][C]280.304852682651[/C][C]202.882523204632[/C][C]357.727182160671[/C][/ROW]
[ROW][C]88[/C][C]280.943136910202[/C][C]186.804689377218[/C][C]375.081584443186[/C][/ROW]
[ROW][C]89[/C][C]281.581421137752[/C][C]170.981637645322[/C][C]392.181204630182[/C][/ROW]
[ROW][C]90[/C][C]282.219705365303[/C][C]155.154584553866[/C][C]409.284826176739[/C][/ROW]
[ROW][C]91[/C][C]282.857989592853[/C][C]139.183777676644[/C][C]426.532201509062[/C][/ROW]
[ROW][C]92[/C][C]283.496273820404[/C][C]122.987556772404[/C][C]444.004990868404[/C][/ROW]
[ROW][C]93[/C][C]284.134558047954[/C][C]106.515905947889[/C][C]461.75321014802[/C][/ROW]
[ROW][C]94[/C][C]284.772842275505[/C][C]89.7373979143392[/C][C]479.80828663667[/C][/ROW]
[ROW][C]95[/C][C]285.411126503055[/C][C]72.6321364467053[/C][C]498.190116559405[/C][/ROW]
[ROW][C]96[/C][C]286.049410730605[/C][C]55.1876747464047[/C][C]516.911146714806[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286102&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286102&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
85279.02828422755238.981725562558319.074842892543
86279.666568455101219.764247204966339.568889705236
87280.304852682651202.882523204632357.727182160671
88280.943136910202186.804689377218375.081584443186
89281.581421137752170.981637645322392.181204630182
90282.219705365303155.154584553866409.284826176739
91282.857989592853139.183777676644426.532201509062
92283.496273820404122.987556772404444.004990868404
93284.134558047954106.515905947889461.75321014802
94284.77284227550589.7373979143392479.80828663667
95285.41112650305572.6321364467053498.190116559405
96286.04941073060555.1876747464047516.911146714806



Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; par6 = 0.0 ;
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')