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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 computationMon, 15 Dec 2014 17:37:06 +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/2014/Dec/15/t1418665046pfhg5c06ghvz2e7.htm/, Retrieved Thu, 16 May 2024 17:38:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268792, Retrieved Thu, 16 May 2024 17:38:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact44
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-15 17:37:06] [578aae52f3152e8435e37fe3b2f57a45] [Current]
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Dataseries X:
325.87
302.25
294.00
285.43
286.19
276.70
267.77
267.03
257.87
257.19
275.60
305.68
358.06
320.07
295.90
291.27
272.87
269.27
271.32
267.45
260.33
277.94
277.07
312.65
319.71
318.39
304.90
303.73
273.29
274.33
270.45
278.23
274.03
279.00
287.50
336.87
334.10
296.07
286.84
277.63
261.32
264.07
261.94
252.84
257.83
271.16
273.63
304.87
323.90
336.11
335.65
282.23
273.03
270.07
246.03
242.35
250.33
267.45
268.80
302.68
313.10
306.39
305.61
277.27
264.94
268.63
293.90
248.65
256.00
258.52
266.90
281.23
306.00
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'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268792&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268792&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268792&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'Herman Ole Andreas Wold' @ wold.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=268792&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=268792&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268792&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=268792&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=268792&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268792&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=268792&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=268792&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268792&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 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')