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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 17:40:55 +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/t1418665271qd84hkdkny9fjp2.htm/, Retrieved Thu, 16 May 2024 05:34:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268799, Retrieved Thu, 16 May 2024 05:34:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact42
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-15 17:40:55] [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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268799&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268799&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268799&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0241602799826075
beta0.190641650124046
gamma0.36287474331864

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0241602799826075 \tabularnewline
beta & 0.190641650124046 \tabularnewline
gamma & 0.36287474331864 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268799&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]0.0241602799826075[/C][/ROW]
[ROW][C]beta[/C][C]0.190641650124046[/C][/ROW]
[ROW][C]gamma[/C][C]0.36287474331864[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268799&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268799&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
alpha0.0241602799826075
beta0.190641650124046
gamma0.36287474331864







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13358.06358.475054365398-0.415054365397566
14320.07320.480826840247-0.410826840246955
15295.9296.36081604815-0.460816048150093
16291.27290.9408552108650.329144789135228
17272.87271.8911121419740.978887858026042
18269.27268.1983268805831.07167311941737
19271.32271.0736617215790.246338278420524
20267.45268.570220949387-1.12022094938749
21260.33258.7813617924111.54863820758862
22277.94258.04436891417819.8956310858217
23277.07277.640463998583-0.57046399858308
24312.65309.1976507461743.45234925382562
25319.71362.752710233936-43.0427102339363
26318.39323.331707753107-4.94170775310732
27304.9298.8123117577836.08768824221693
28303.73293.7580627730159.97193722698512
29273.29275.000306803067-1.71030680306671
30274.33271.2451063380953.08489366190474
31270.45273.918223826227-3.4682238262269
32278.23270.8101410839687.41985891603247
33274.03262.11557787678511.9144221232152
34279268.26524505374110.734754946259
35287.5280.566625814316.93337418569035
36336.87314.20799310058222.6620068994184
37334.1352.418285834802-18.3182858348016
38296.07326.969311981921-30.8993119819209
39286.84305.57331356675-18.7333135667495
40277.63301.275389100714-23.6453891007138
41261.32277.210258113941-15.8902581139411
42264.07274.617033117651-10.5470331176513
43261.94274.404312898828-12.464312898828
44252.84274.657971941337-21.8179719413372
45257.83266.428021912282-8.59802191228158
46271.16271.1461882018540.0138117981464347
47273.63281.218252969967-7.58825296996719
48304.87319.037857923878-14.1678579238775
49323.9340.584722257386-16.6847222573856
50336.11310.27603144953625.8339685504642
51335.65294.19068696495841.4593130350415
52282.23289.34770866427-7.11770866427031
53273.03268.4270238879974.60297611200269
54270.07268.0956915550141.97430844498649
55246.03267.439332657042-21.4093326570423
56242.35264.06838295032-21.7183829503198
57250.33260.440101165685-10.1101011656848
58267.45267.957130492978-0.50713049297832
59268.8275.105795319615-6.30579531961479
60302.68310.045234850555-7.36523485055454
61313.1330.484203426049-17.3842034260492
62306.39315.264408254921-8.87440825492058
63305.61303.7266866240171.88331337598305
64277.27280.751118619097-3.48111861909678
65264.94264.0268797523780.913120247621976
66268.63262.3037493825456.32625061745506
67293.9253.30130290062340.5986970993766
68248.65251.274096888024-2.62409688802427
69256252.1918944092193.80810559078091
70258.52263.318664672632-4.79866467263156
71266.9268.264448139959-1.36444813995939
72281.23302.448178106693-21.2181781066935
73306318.709613881847-12.7096138818468
74325.46306.84068906042818.6193109395716
75291.13300.037443183382-8.90744318338193
76282.53275.3710407352097.15895926479124
77256.52260.80375735461-4.28375735461003
78258.63260.978518762556-2.34851876255624
79252.74263.876667158402-11.1366671584018
80245.16245.473829302976-0.313829302976472
81255.03248.5057879822456.52421201775462
82268.35256.34507905630912.0049209436914
83293.73262.72314116362731.0068588363731
84278.39290.296700804342-11.9067008043423

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 358.06 & 358.475054365398 & -0.415054365397566 \tabularnewline
14 & 320.07 & 320.480826840247 & -0.410826840246955 \tabularnewline
15 & 295.9 & 296.36081604815 & -0.460816048150093 \tabularnewline
16 & 291.27 & 290.940855210865 & 0.329144789135228 \tabularnewline
17 & 272.87 & 271.891112141974 & 0.978887858026042 \tabularnewline
18 & 269.27 & 268.198326880583 & 1.07167311941737 \tabularnewline
19 & 271.32 & 271.073661721579 & 0.246338278420524 \tabularnewline
20 & 267.45 & 268.570220949387 & -1.12022094938749 \tabularnewline
21 & 260.33 & 258.781361792411 & 1.54863820758862 \tabularnewline
22 & 277.94 & 258.044368914178 & 19.8956310858217 \tabularnewline
23 & 277.07 & 277.640463998583 & -0.57046399858308 \tabularnewline
24 & 312.65 & 309.197650746174 & 3.45234925382562 \tabularnewline
25 & 319.71 & 362.752710233936 & -43.0427102339363 \tabularnewline
26 & 318.39 & 323.331707753107 & -4.94170775310732 \tabularnewline
27 & 304.9 & 298.812311757783 & 6.08768824221693 \tabularnewline
28 & 303.73 & 293.758062773015 & 9.97193722698512 \tabularnewline
29 & 273.29 & 275.000306803067 & -1.71030680306671 \tabularnewline
30 & 274.33 & 271.245106338095 & 3.08489366190474 \tabularnewline
31 & 270.45 & 273.918223826227 & -3.4682238262269 \tabularnewline
32 & 278.23 & 270.810141083968 & 7.41985891603247 \tabularnewline
33 & 274.03 & 262.115577876785 & 11.9144221232152 \tabularnewline
34 & 279 & 268.265245053741 & 10.734754946259 \tabularnewline
35 & 287.5 & 280.56662581431 & 6.93337418569035 \tabularnewline
36 & 336.87 & 314.207993100582 & 22.6620068994184 \tabularnewline
37 & 334.1 & 352.418285834802 & -18.3182858348016 \tabularnewline
38 & 296.07 & 326.969311981921 & -30.8993119819209 \tabularnewline
39 & 286.84 & 305.57331356675 & -18.7333135667495 \tabularnewline
40 & 277.63 & 301.275389100714 & -23.6453891007138 \tabularnewline
41 & 261.32 & 277.210258113941 & -15.8902581139411 \tabularnewline
42 & 264.07 & 274.617033117651 & -10.5470331176513 \tabularnewline
43 & 261.94 & 274.404312898828 & -12.464312898828 \tabularnewline
44 & 252.84 & 274.657971941337 & -21.8179719413372 \tabularnewline
45 & 257.83 & 266.428021912282 & -8.59802191228158 \tabularnewline
46 & 271.16 & 271.146188201854 & 0.0138117981464347 \tabularnewline
47 & 273.63 & 281.218252969967 & -7.58825296996719 \tabularnewline
48 & 304.87 & 319.037857923878 & -14.1678579238775 \tabularnewline
49 & 323.9 & 340.584722257386 & -16.6847222573856 \tabularnewline
50 & 336.11 & 310.276031449536 & 25.8339685504642 \tabularnewline
51 & 335.65 & 294.190686964958 & 41.4593130350415 \tabularnewline
52 & 282.23 & 289.34770866427 & -7.11770866427031 \tabularnewline
53 & 273.03 & 268.427023887997 & 4.60297611200269 \tabularnewline
54 & 270.07 & 268.095691555014 & 1.97430844498649 \tabularnewline
55 & 246.03 & 267.439332657042 & -21.4093326570423 \tabularnewline
56 & 242.35 & 264.06838295032 & -21.7183829503198 \tabularnewline
57 & 250.33 & 260.440101165685 & -10.1101011656848 \tabularnewline
58 & 267.45 & 267.957130492978 & -0.50713049297832 \tabularnewline
59 & 268.8 & 275.105795319615 & -6.30579531961479 \tabularnewline
60 & 302.68 & 310.045234850555 & -7.36523485055454 \tabularnewline
61 & 313.1 & 330.484203426049 & -17.3842034260492 \tabularnewline
62 & 306.39 & 315.264408254921 & -8.87440825492058 \tabularnewline
63 & 305.61 & 303.726686624017 & 1.88331337598305 \tabularnewline
64 & 277.27 & 280.751118619097 & -3.48111861909678 \tabularnewline
65 & 264.94 & 264.026879752378 & 0.913120247621976 \tabularnewline
66 & 268.63 & 262.303749382545 & 6.32625061745506 \tabularnewline
67 & 293.9 & 253.301302900623 & 40.5986970993766 \tabularnewline
68 & 248.65 & 251.274096888024 & -2.62409688802427 \tabularnewline
69 & 256 & 252.191894409219 & 3.80810559078091 \tabularnewline
70 & 258.52 & 263.318664672632 & -4.79866467263156 \tabularnewline
71 & 266.9 & 268.264448139959 & -1.36444813995939 \tabularnewline
72 & 281.23 & 302.448178106693 & -21.2181781066935 \tabularnewline
73 & 306 & 318.709613881847 & -12.7096138818468 \tabularnewline
74 & 325.46 & 306.840689060428 & 18.6193109395716 \tabularnewline
75 & 291.13 & 300.037443183382 & -8.90744318338193 \tabularnewline
76 & 282.53 & 275.371040735209 & 7.15895926479124 \tabularnewline
77 & 256.52 & 260.80375735461 & -4.28375735461003 \tabularnewline
78 & 258.63 & 260.978518762556 & -2.34851876255624 \tabularnewline
79 & 252.74 & 263.876667158402 & -11.1366671584018 \tabularnewline
80 & 245.16 & 245.473829302976 & -0.313829302976472 \tabularnewline
81 & 255.03 & 248.505787982245 & 6.52421201775462 \tabularnewline
82 & 268.35 & 256.345079056309 & 12.0049209436914 \tabularnewline
83 & 293.73 & 262.723141163627 & 31.0068588363731 \tabularnewline
84 & 278.39 & 290.296700804342 & -11.9067008043423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268799&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]358.06[/C][C]358.475054365398[/C][C]-0.415054365397566[/C][/ROW]
[ROW][C]14[/C][C]320.07[/C][C]320.480826840247[/C][C]-0.410826840246955[/C][/ROW]
[ROW][C]15[/C][C]295.9[/C][C]296.36081604815[/C][C]-0.460816048150093[/C][/ROW]
[ROW][C]16[/C][C]291.27[/C][C]290.940855210865[/C][C]0.329144789135228[/C][/ROW]
[ROW][C]17[/C][C]272.87[/C][C]271.891112141974[/C][C]0.978887858026042[/C][/ROW]
[ROW][C]18[/C][C]269.27[/C][C]268.198326880583[/C][C]1.07167311941737[/C][/ROW]
[ROW][C]19[/C][C]271.32[/C][C]271.073661721579[/C][C]0.246338278420524[/C][/ROW]
[ROW][C]20[/C][C]267.45[/C][C]268.570220949387[/C][C]-1.12022094938749[/C][/ROW]
[ROW][C]21[/C][C]260.33[/C][C]258.781361792411[/C][C]1.54863820758862[/C][/ROW]
[ROW][C]22[/C][C]277.94[/C][C]258.044368914178[/C][C]19.8956310858217[/C][/ROW]
[ROW][C]23[/C][C]277.07[/C][C]277.640463998583[/C][C]-0.57046399858308[/C][/ROW]
[ROW][C]24[/C][C]312.65[/C][C]309.197650746174[/C][C]3.45234925382562[/C][/ROW]
[ROW][C]25[/C][C]319.71[/C][C]362.752710233936[/C][C]-43.0427102339363[/C][/ROW]
[ROW][C]26[/C][C]318.39[/C][C]323.331707753107[/C][C]-4.94170775310732[/C][/ROW]
[ROW][C]27[/C][C]304.9[/C][C]298.812311757783[/C][C]6.08768824221693[/C][/ROW]
[ROW][C]28[/C][C]303.73[/C][C]293.758062773015[/C][C]9.97193722698512[/C][/ROW]
[ROW][C]29[/C][C]273.29[/C][C]275.000306803067[/C][C]-1.71030680306671[/C][/ROW]
[ROW][C]30[/C][C]274.33[/C][C]271.245106338095[/C][C]3.08489366190474[/C][/ROW]
[ROW][C]31[/C][C]270.45[/C][C]273.918223826227[/C][C]-3.4682238262269[/C][/ROW]
[ROW][C]32[/C][C]278.23[/C][C]270.810141083968[/C][C]7.41985891603247[/C][/ROW]
[ROW][C]33[/C][C]274.03[/C][C]262.115577876785[/C][C]11.9144221232152[/C][/ROW]
[ROW][C]34[/C][C]279[/C][C]268.265245053741[/C][C]10.734754946259[/C][/ROW]
[ROW][C]35[/C][C]287.5[/C][C]280.56662581431[/C][C]6.93337418569035[/C][/ROW]
[ROW][C]36[/C][C]336.87[/C][C]314.207993100582[/C][C]22.6620068994184[/C][/ROW]
[ROW][C]37[/C][C]334.1[/C][C]352.418285834802[/C][C]-18.3182858348016[/C][/ROW]
[ROW][C]38[/C][C]296.07[/C][C]326.969311981921[/C][C]-30.8993119819209[/C][/ROW]
[ROW][C]39[/C][C]286.84[/C][C]305.57331356675[/C][C]-18.7333135667495[/C][/ROW]
[ROW][C]40[/C][C]277.63[/C][C]301.275389100714[/C][C]-23.6453891007138[/C][/ROW]
[ROW][C]41[/C][C]261.32[/C][C]277.210258113941[/C][C]-15.8902581139411[/C][/ROW]
[ROW][C]42[/C][C]264.07[/C][C]274.617033117651[/C][C]-10.5470331176513[/C][/ROW]
[ROW][C]43[/C][C]261.94[/C][C]274.404312898828[/C][C]-12.464312898828[/C][/ROW]
[ROW][C]44[/C][C]252.84[/C][C]274.657971941337[/C][C]-21.8179719413372[/C][/ROW]
[ROW][C]45[/C][C]257.83[/C][C]266.428021912282[/C][C]-8.59802191228158[/C][/ROW]
[ROW][C]46[/C][C]271.16[/C][C]271.146188201854[/C][C]0.0138117981464347[/C][/ROW]
[ROW][C]47[/C][C]273.63[/C][C]281.218252969967[/C][C]-7.58825296996719[/C][/ROW]
[ROW][C]48[/C][C]304.87[/C][C]319.037857923878[/C][C]-14.1678579238775[/C][/ROW]
[ROW][C]49[/C][C]323.9[/C][C]340.584722257386[/C][C]-16.6847222573856[/C][/ROW]
[ROW][C]50[/C][C]336.11[/C][C]310.276031449536[/C][C]25.8339685504642[/C][/ROW]
[ROW][C]51[/C][C]335.65[/C][C]294.190686964958[/C][C]41.4593130350415[/C][/ROW]
[ROW][C]52[/C][C]282.23[/C][C]289.34770866427[/C][C]-7.11770866427031[/C][/ROW]
[ROW][C]53[/C][C]273.03[/C][C]268.427023887997[/C][C]4.60297611200269[/C][/ROW]
[ROW][C]54[/C][C]270.07[/C][C]268.095691555014[/C][C]1.97430844498649[/C][/ROW]
[ROW][C]55[/C][C]246.03[/C][C]267.439332657042[/C][C]-21.4093326570423[/C][/ROW]
[ROW][C]56[/C][C]242.35[/C][C]264.06838295032[/C][C]-21.7183829503198[/C][/ROW]
[ROW][C]57[/C][C]250.33[/C][C]260.440101165685[/C][C]-10.1101011656848[/C][/ROW]
[ROW][C]58[/C][C]267.45[/C][C]267.957130492978[/C][C]-0.50713049297832[/C][/ROW]
[ROW][C]59[/C][C]268.8[/C][C]275.105795319615[/C][C]-6.30579531961479[/C][/ROW]
[ROW][C]60[/C][C]302.68[/C][C]310.045234850555[/C][C]-7.36523485055454[/C][/ROW]
[ROW][C]61[/C][C]313.1[/C][C]330.484203426049[/C][C]-17.3842034260492[/C][/ROW]
[ROW][C]62[/C][C]306.39[/C][C]315.264408254921[/C][C]-8.87440825492058[/C][/ROW]
[ROW][C]63[/C][C]305.61[/C][C]303.726686624017[/C][C]1.88331337598305[/C][/ROW]
[ROW][C]64[/C][C]277.27[/C][C]280.751118619097[/C][C]-3.48111861909678[/C][/ROW]
[ROW][C]65[/C][C]264.94[/C][C]264.026879752378[/C][C]0.913120247621976[/C][/ROW]
[ROW][C]66[/C][C]268.63[/C][C]262.303749382545[/C][C]6.32625061745506[/C][/ROW]
[ROW][C]67[/C][C]293.9[/C][C]253.301302900623[/C][C]40.5986970993766[/C][/ROW]
[ROW][C]68[/C][C]248.65[/C][C]251.274096888024[/C][C]-2.62409688802427[/C][/ROW]
[ROW][C]69[/C][C]256[/C][C]252.191894409219[/C][C]3.80810559078091[/C][/ROW]
[ROW][C]70[/C][C]258.52[/C][C]263.318664672632[/C][C]-4.79866467263156[/C][/ROW]
[ROW][C]71[/C][C]266.9[/C][C]268.264448139959[/C][C]-1.36444813995939[/C][/ROW]
[ROW][C]72[/C][C]281.23[/C][C]302.448178106693[/C][C]-21.2181781066935[/C][/ROW]
[ROW][C]73[/C][C]306[/C][C]318.709613881847[/C][C]-12.7096138818468[/C][/ROW]
[ROW][C]74[/C][C]325.46[/C][C]306.840689060428[/C][C]18.6193109395716[/C][/ROW]
[ROW][C]75[/C][C]291.13[/C][C]300.037443183382[/C][C]-8.90744318338193[/C][/ROW]
[ROW][C]76[/C][C]282.53[/C][C]275.371040735209[/C][C]7.15895926479124[/C][/ROW]
[ROW][C]77[/C][C]256.52[/C][C]260.80375735461[/C][C]-4.28375735461003[/C][/ROW]
[ROW][C]78[/C][C]258.63[/C][C]260.978518762556[/C][C]-2.34851876255624[/C][/ROW]
[ROW][C]79[/C][C]252.74[/C][C]263.876667158402[/C][C]-11.1366671584018[/C][/ROW]
[ROW][C]80[/C][C]245.16[/C][C]245.473829302976[/C][C]-0.313829302976472[/C][/ROW]
[ROW][C]81[/C][C]255.03[/C][C]248.505787982245[/C][C]6.52421201775462[/C][/ROW]
[ROW][C]82[/C][C]268.35[/C][C]256.345079056309[/C][C]12.0049209436914[/C][/ROW]
[ROW][C]83[/C][C]293.73[/C][C]262.723141163627[/C][C]31.0068588363731[/C][/ROW]
[ROW][C]84[/C][C]278.39[/C][C]290.296700804342[/C][C]-11.9067008043423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268799&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268799&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
13358.06358.475054365398-0.415054365397566
14320.07320.480826840247-0.410826840246955
15295.9296.36081604815-0.460816048150093
16291.27290.9408552108650.329144789135228
17272.87271.8911121419740.978887858026042
18269.27268.1983268805831.07167311941737
19271.32271.0736617215790.246338278420524
20267.45268.570220949387-1.12022094938749
21260.33258.7813617924111.54863820758862
22277.94258.04436891417819.8956310858217
23277.07277.640463998583-0.57046399858308
24312.65309.1976507461743.45234925382562
25319.71362.752710233936-43.0427102339363
26318.39323.331707753107-4.94170775310732
27304.9298.8123117577836.08768824221693
28303.73293.7580627730159.97193722698512
29273.29275.000306803067-1.71030680306671
30274.33271.2451063380953.08489366190474
31270.45273.918223826227-3.4682238262269
32278.23270.8101410839687.41985891603247
33274.03262.11557787678511.9144221232152
34279268.26524505374110.734754946259
35287.5280.566625814316.93337418569035
36336.87314.20799310058222.6620068994184
37334.1352.418285834802-18.3182858348016
38296.07326.969311981921-30.8993119819209
39286.84305.57331356675-18.7333135667495
40277.63301.275389100714-23.6453891007138
41261.32277.210258113941-15.8902581139411
42264.07274.617033117651-10.5470331176513
43261.94274.404312898828-12.464312898828
44252.84274.657971941337-21.8179719413372
45257.83266.428021912282-8.59802191228158
46271.16271.1461882018540.0138117981464347
47273.63281.218252969967-7.58825296996719
48304.87319.037857923878-14.1678579238775
49323.9340.584722257386-16.6847222573856
50336.11310.27603144953625.8339685504642
51335.65294.19068696495841.4593130350415
52282.23289.34770866427-7.11770866427031
53273.03268.4270238879974.60297611200269
54270.07268.0956915550141.97430844498649
55246.03267.439332657042-21.4093326570423
56242.35264.06838295032-21.7183829503198
57250.33260.440101165685-10.1101011656848
58267.45267.957130492978-0.50713049297832
59268.8275.105795319615-6.30579531961479
60302.68310.045234850555-7.36523485055454
61313.1330.484203426049-17.3842034260492
62306.39315.264408254921-8.87440825492058
63305.61303.7266866240171.88331337598305
64277.27280.751118619097-3.48111861909678
65264.94264.0268797523780.913120247621976
66268.63262.3037493825456.32625061745506
67293.9253.30130290062340.5986970993766
68248.65251.274096888024-2.62409688802427
69256252.1918944092193.80810559078091
70258.52263.318664672632-4.79866467263156
71266.9268.264448139959-1.36444813995939
72281.23302.448178106693-21.2181781066935
73306318.709613881847-12.7096138818468
74325.46306.84068906042818.6193109395716
75291.13300.037443183382-8.90744318338193
76282.53275.3710407352097.15895926479124
77256.52260.80375735461-4.28375735461003
78258.63260.978518762556-2.34851876255624
79252.74263.876667158402-11.1366671584018
80245.16245.473829302976-0.313829302976472
81255.03248.5057879822456.52421201775462
82268.35256.34507905630912.0049209436914
83293.73262.72314116362731.0068588363731
84278.39290.296700804342-11.9067008043423







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85309.627898936946298.802681359625320.453116514267
86309.346981070011298.49049944575320.203462694272
87292.687983750106281.797087540233303.578879959979
88274.306102993554263.37748319818285.234722788928
89255.858899679972244.890238829699266.827560530245
90256.920722592332245.880307171155267.961138013509
91256.883420600043245.757556587621268.009284612465
92242.898405373457231.712551481957254.084259264957
93248.472063370265237.154281313114259.789845427417
94258.138204780452246.639513589539269.636895971365
95270.882064854562259.141235683963282.622894025161
96282.297957251481242.380951130687322.214963372275

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 309.627898936946 & 298.802681359625 & 320.453116514267 \tabularnewline
86 & 309.346981070011 & 298.49049944575 & 320.203462694272 \tabularnewline
87 & 292.687983750106 & 281.797087540233 & 303.578879959979 \tabularnewline
88 & 274.306102993554 & 263.37748319818 & 285.234722788928 \tabularnewline
89 & 255.858899679972 & 244.890238829699 & 266.827560530245 \tabularnewline
90 & 256.920722592332 & 245.880307171155 & 267.961138013509 \tabularnewline
91 & 256.883420600043 & 245.757556587621 & 268.009284612465 \tabularnewline
92 & 242.898405373457 & 231.712551481957 & 254.084259264957 \tabularnewline
93 & 248.472063370265 & 237.154281313114 & 259.789845427417 \tabularnewline
94 & 258.138204780452 & 246.639513589539 & 269.636895971365 \tabularnewline
95 & 270.882064854562 & 259.141235683963 & 282.622894025161 \tabularnewline
96 & 282.297957251481 & 242.380951130687 & 322.214963372275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268799&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]309.627898936946[/C][C]298.802681359625[/C][C]320.453116514267[/C][/ROW]
[ROW][C]86[/C][C]309.346981070011[/C][C]298.49049944575[/C][C]320.203462694272[/C][/ROW]
[ROW][C]87[/C][C]292.687983750106[/C][C]281.797087540233[/C][C]303.578879959979[/C][/ROW]
[ROW][C]88[/C][C]274.306102993554[/C][C]263.37748319818[/C][C]285.234722788928[/C][/ROW]
[ROW][C]89[/C][C]255.858899679972[/C][C]244.890238829699[/C][C]266.827560530245[/C][/ROW]
[ROW][C]90[/C][C]256.920722592332[/C][C]245.880307171155[/C][C]267.961138013509[/C][/ROW]
[ROW][C]91[/C][C]256.883420600043[/C][C]245.757556587621[/C][C]268.009284612465[/C][/ROW]
[ROW][C]92[/C][C]242.898405373457[/C][C]231.712551481957[/C][C]254.084259264957[/C][/ROW]
[ROW][C]93[/C][C]248.472063370265[/C][C]237.154281313114[/C][C]259.789845427417[/C][/ROW]
[ROW][C]94[/C][C]258.138204780452[/C][C]246.639513589539[/C][C]269.636895971365[/C][/ROW]
[ROW][C]95[/C][C]270.882064854562[/C][C]259.141235683963[/C][C]282.622894025161[/C][/ROW]
[ROW][C]96[/C][C]282.297957251481[/C][C]242.380951130687[/C][C]322.214963372275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268799&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268799&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
85309.627898936946298.802681359625320.453116514267
86309.346981070011298.49049944575320.203462694272
87292.687983750106281.797087540233303.578879959979
88274.306102993554263.37748319818285.234722788928
89255.858899679972244.890238829699266.827560530245
90256.920722592332245.880307171155267.961138013509
91256.883420600043245.757556587621268.009284612465
92242.898405373457231.712551481957254.084259264957
93248.472063370265237.154281313114259.789845427417
94258.138204780452246.639513589539269.636895971365
95270.882064854562259.141235683963282.622894025161
96282.297957251481242.380951130687322.214963372275



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')