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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 17:38:52 +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/t1418665148v0wbomkg0enze3h.htm/, Retrieved Thu, 16 May 2024 09:02:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268794, Retrieved Thu, 16 May 2024 09:02:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact38
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-15 17:38:52] [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'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=268794&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=268794&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268794&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
alpha0.0224935200424173
beta0.191709497844683
gamma0.355127583738585

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0224935200424173 \tabularnewline
beta & 0.191709497844683 \tabularnewline
gamma & 0.355127583738585 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268794&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]0.0224935200424173[/C][/ROW]
[ROW][C]beta[/C][C]0.191709497844683[/C][/ROW]
[ROW][C]gamma[/C][C]0.355127583738585[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268794&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268794&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
alpha0.0224935200424173
beta0.191709497844683
gamma0.355127583738585







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13358.06358.427601495727-0.367601495726547
14320.07320.472590322409-0.402590322409139
15295.9296.380472735268-0.48047273526754
16291.27290.9774480603510.292551939648604
17272.87271.8643229801981.00567701980214
18269.27268.1457419619931.12425803800716
19271.32271.3063429645710.0136570354292189
20267.45268.698271533399-1.24827153339896
21260.33258.8985153967461.43148460325386
22277.94258.14437595371419.7956240462856
23277.07277.612840430247-0.542840430246997
24312.65308.8443970669743.80560293302631
25319.71361.65965043282-41.9496504328203
26318.39322.683190575425-4.29319057542517
27304.9298.3857704721426.51422952785816
28303.73293.34783822958710.382161770413
29273.29274.692136062717-1.40213606271686
30274.33270.9330941649333.39690583506649
31270.45273.741616839373-3.29161683937303
32278.23270.5892151364497.64078486355095
33274.03261.9260682341712.1039317658304
34279267.83934392015311.1606560798467
35287.5280.0684927751927.43150722480846
36336.87313.0385241145923.8314758854104
37334.1350.556716459476-16.4567164594761
38296.07325.47160182061-29.4016018206096
39286.84304.498688913814-17.6586889138141
40277.63300.293096971316-22.663096971316
41261.32276.694158920727-15.3741589207272
42264.07274.11738739636-10.0473873963602
43261.94274.07428858546-12.13428858546
44252.84274.252559633843-21.4125596338434
45257.83266.09445788597-8.26445788597039
46271.16270.7435180143760.416481985623818
47273.63280.911515880722-7.28151588072228
48304.87318.655289111072-13.7852891110725
49323.9340.591125070496-16.6911250704961
50336.11310.25544631305725.8545536869432
51335.65294.08853448215341.5614655178467
52282.23289.219821458304-6.98982145830377
53273.03268.3133325644834.71666743551651
54270.07267.9338670223972.13613297760264
55246.03267.389170340807-21.3591703408073
56242.35264.048104823096-21.6981048230956
57250.33260.355592481623-10.0255924816233
58267.45267.878728010091-0.42872801009139
59268.8275.251982420825-6.45198242082455
60302.68310.656822763135-7.97682276313498
61313.1331.639753151068-18.5397531510684
62306.39315.948978865261-9.55897886526054
63305.61304.2024711447541.40752885524569
64277.27281.167821265465-3.89782126546544
65264.94263.9993373023890.940662697610833
66268.63262.2275177685836.40248223141703
67293.9253.22942268439640.6705773156041
68248.65251.040237562142-2.39023756214209
69256251.7915477588484.2084522411522
70258.52262.985218655796-4.46521865579621
71266.9268.17827305769-1.27827305769023
72281.23303.193970664959-21.9639706649593
73306320.158969323193-14.158969323193
74325.46307.66670580647817.7932941935222
75291.13300.442694106667-9.31269410666675
76282.53275.3793229925327.15067700746795
77256.52260.240742170198-3.72074217019821
78258.63260.341738153278-1.71173815327836
79252.74263.103598799714-10.3635987997143
80245.16244.6449576088410.515042391158858
81255.03247.5914045197227.43859548027839
82268.35255.69980866663712.6501913333633
83293.73262.31101893179131.4189810682087
84278.39290.949222957964-12.5592229579642

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 358.06 & 358.427601495727 & -0.367601495726547 \tabularnewline
14 & 320.07 & 320.472590322409 & -0.402590322409139 \tabularnewline
15 & 295.9 & 296.380472735268 & -0.48047273526754 \tabularnewline
16 & 291.27 & 290.977448060351 & 0.292551939648604 \tabularnewline
17 & 272.87 & 271.864322980198 & 1.00567701980214 \tabularnewline
18 & 269.27 & 268.145741961993 & 1.12425803800716 \tabularnewline
19 & 271.32 & 271.306342964571 & 0.0136570354292189 \tabularnewline
20 & 267.45 & 268.698271533399 & -1.24827153339896 \tabularnewline
21 & 260.33 & 258.898515396746 & 1.43148460325386 \tabularnewline
22 & 277.94 & 258.144375953714 & 19.7956240462856 \tabularnewline
23 & 277.07 & 277.612840430247 & -0.542840430246997 \tabularnewline
24 & 312.65 & 308.844397066974 & 3.80560293302631 \tabularnewline
25 & 319.71 & 361.65965043282 & -41.9496504328203 \tabularnewline
26 & 318.39 & 322.683190575425 & -4.29319057542517 \tabularnewline
27 & 304.9 & 298.385770472142 & 6.51422952785816 \tabularnewline
28 & 303.73 & 293.347838229587 & 10.382161770413 \tabularnewline
29 & 273.29 & 274.692136062717 & -1.40213606271686 \tabularnewline
30 & 274.33 & 270.933094164933 & 3.39690583506649 \tabularnewline
31 & 270.45 & 273.741616839373 & -3.29161683937303 \tabularnewline
32 & 278.23 & 270.589215136449 & 7.64078486355095 \tabularnewline
33 & 274.03 & 261.92606823417 & 12.1039317658304 \tabularnewline
34 & 279 & 267.839343920153 & 11.1606560798467 \tabularnewline
35 & 287.5 & 280.068492775192 & 7.43150722480846 \tabularnewline
36 & 336.87 & 313.03852411459 & 23.8314758854104 \tabularnewline
37 & 334.1 & 350.556716459476 & -16.4567164594761 \tabularnewline
38 & 296.07 & 325.47160182061 & -29.4016018206096 \tabularnewline
39 & 286.84 & 304.498688913814 & -17.6586889138141 \tabularnewline
40 & 277.63 & 300.293096971316 & -22.663096971316 \tabularnewline
41 & 261.32 & 276.694158920727 & -15.3741589207272 \tabularnewline
42 & 264.07 & 274.11738739636 & -10.0473873963602 \tabularnewline
43 & 261.94 & 274.07428858546 & -12.13428858546 \tabularnewline
44 & 252.84 & 274.252559633843 & -21.4125596338434 \tabularnewline
45 & 257.83 & 266.09445788597 & -8.26445788597039 \tabularnewline
46 & 271.16 & 270.743518014376 & 0.416481985623818 \tabularnewline
47 & 273.63 & 280.911515880722 & -7.28151588072228 \tabularnewline
48 & 304.87 & 318.655289111072 & -13.7852891110725 \tabularnewline
49 & 323.9 & 340.591125070496 & -16.6911250704961 \tabularnewline
50 & 336.11 & 310.255446313057 & 25.8545536869432 \tabularnewline
51 & 335.65 & 294.088534482153 & 41.5614655178467 \tabularnewline
52 & 282.23 & 289.219821458304 & -6.98982145830377 \tabularnewline
53 & 273.03 & 268.313332564483 & 4.71666743551651 \tabularnewline
54 & 270.07 & 267.933867022397 & 2.13613297760264 \tabularnewline
55 & 246.03 & 267.389170340807 & -21.3591703408073 \tabularnewline
56 & 242.35 & 264.048104823096 & -21.6981048230956 \tabularnewline
57 & 250.33 & 260.355592481623 & -10.0255924816233 \tabularnewline
58 & 267.45 & 267.878728010091 & -0.42872801009139 \tabularnewline
59 & 268.8 & 275.251982420825 & -6.45198242082455 \tabularnewline
60 & 302.68 & 310.656822763135 & -7.97682276313498 \tabularnewline
61 & 313.1 & 331.639753151068 & -18.5397531510684 \tabularnewline
62 & 306.39 & 315.948978865261 & -9.55897886526054 \tabularnewline
63 & 305.61 & 304.202471144754 & 1.40752885524569 \tabularnewline
64 & 277.27 & 281.167821265465 & -3.89782126546544 \tabularnewline
65 & 264.94 & 263.999337302389 & 0.940662697610833 \tabularnewline
66 & 268.63 & 262.227517768583 & 6.40248223141703 \tabularnewline
67 & 293.9 & 253.229422684396 & 40.6705773156041 \tabularnewline
68 & 248.65 & 251.040237562142 & -2.39023756214209 \tabularnewline
69 & 256 & 251.791547758848 & 4.2084522411522 \tabularnewline
70 & 258.52 & 262.985218655796 & -4.46521865579621 \tabularnewline
71 & 266.9 & 268.17827305769 & -1.27827305769023 \tabularnewline
72 & 281.23 & 303.193970664959 & -21.9639706649593 \tabularnewline
73 & 306 & 320.158969323193 & -14.158969323193 \tabularnewline
74 & 325.46 & 307.666705806478 & 17.7932941935222 \tabularnewline
75 & 291.13 & 300.442694106667 & -9.31269410666675 \tabularnewline
76 & 282.53 & 275.379322992532 & 7.15067700746795 \tabularnewline
77 & 256.52 & 260.240742170198 & -3.72074217019821 \tabularnewline
78 & 258.63 & 260.341738153278 & -1.71173815327836 \tabularnewline
79 & 252.74 & 263.103598799714 & -10.3635987997143 \tabularnewline
80 & 245.16 & 244.644957608841 & 0.515042391158858 \tabularnewline
81 & 255.03 & 247.591404519722 & 7.43859548027839 \tabularnewline
82 & 268.35 & 255.699808666637 & 12.6501913333633 \tabularnewline
83 & 293.73 & 262.311018931791 & 31.4189810682087 \tabularnewline
84 & 278.39 & 290.949222957964 & -12.5592229579642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268794&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]358.427601495727[/C][C]-0.367601495726547[/C][/ROW]
[ROW][C]14[/C][C]320.07[/C][C]320.472590322409[/C][C]-0.402590322409139[/C][/ROW]
[ROW][C]15[/C][C]295.9[/C][C]296.380472735268[/C][C]-0.48047273526754[/C][/ROW]
[ROW][C]16[/C][C]291.27[/C][C]290.977448060351[/C][C]0.292551939648604[/C][/ROW]
[ROW][C]17[/C][C]272.87[/C][C]271.864322980198[/C][C]1.00567701980214[/C][/ROW]
[ROW][C]18[/C][C]269.27[/C][C]268.145741961993[/C][C]1.12425803800716[/C][/ROW]
[ROW][C]19[/C][C]271.32[/C][C]271.306342964571[/C][C]0.0136570354292189[/C][/ROW]
[ROW][C]20[/C][C]267.45[/C][C]268.698271533399[/C][C]-1.24827153339896[/C][/ROW]
[ROW][C]21[/C][C]260.33[/C][C]258.898515396746[/C][C]1.43148460325386[/C][/ROW]
[ROW][C]22[/C][C]277.94[/C][C]258.144375953714[/C][C]19.7956240462856[/C][/ROW]
[ROW][C]23[/C][C]277.07[/C][C]277.612840430247[/C][C]-0.542840430246997[/C][/ROW]
[ROW][C]24[/C][C]312.65[/C][C]308.844397066974[/C][C]3.80560293302631[/C][/ROW]
[ROW][C]25[/C][C]319.71[/C][C]361.65965043282[/C][C]-41.9496504328203[/C][/ROW]
[ROW][C]26[/C][C]318.39[/C][C]322.683190575425[/C][C]-4.29319057542517[/C][/ROW]
[ROW][C]27[/C][C]304.9[/C][C]298.385770472142[/C][C]6.51422952785816[/C][/ROW]
[ROW][C]28[/C][C]303.73[/C][C]293.347838229587[/C][C]10.382161770413[/C][/ROW]
[ROW][C]29[/C][C]273.29[/C][C]274.692136062717[/C][C]-1.40213606271686[/C][/ROW]
[ROW][C]30[/C][C]274.33[/C][C]270.933094164933[/C][C]3.39690583506649[/C][/ROW]
[ROW][C]31[/C][C]270.45[/C][C]273.741616839373[/C][C]-3.29161683937303[/C][/ROW]
[ROW][C]32[/C][C]278.23[/C][C]270.589215136449[/C][C]7.64078486355095[/C][/ROW]
[ROW][C]33[/C][C]274.03[/C][C]261.92606823417[/C][C]12.1039317658304[/C][/ROW]
[ROW][C]34[/C][C]279[/C][C]267.839343920153[/C][C]11.1606560798467[/C][/ROW]
[ROW][C]35[/C][C]287.5[/C][C]280.068492775192[/C][C]7.43150722480846[/C][/ROW]
[ROW][C]36[/C][C]336.87[/C][C]313.03852411459[/C][C]23.8314758854104[/C][/ROW]
[ROW][C]37[/C][C]334.1[/C][C]350.556716459476[/C][C]-16.4567164594761[/C][/ROW]
[ROW][C]38[/C][C]296.07[/C][C]325.47160182061[/C][C]-29.4016018206096[/C][/ROW]
[ROW][C]39[/C][C]286.84[/C][C]304.498688913814[/C][C]-17.6586889138141[/C][/ROW]
[ROW][C]40[/C][C]277.63[/C][C]300.293096971316[/C][C]-22.663096971316[/C][/ROW]
[ROW][C]41[/C][C]261.32[/C][C]276.694158920727[/C][C]-15.3741589207272[/C][/ROW]
[ROW][C]42[/C][C]264.07[/C][C]274.11738739636[/C][C]-10.0473873963602[/C][/ROW]
[ROW][C]43[/C][C]261.94[/C][C]274.07428858546[/C][C]-12.13428858546[/C][/ROW]
[ROW][C]44[/C][C]252.84[/C][C]274.252559633843[/C][C]-21.4125596338434[/C][/ROW]
[ROW][C]45[/C][C]257.83[/C][C]266.09445788597[/C][C]-8.26445788597039[/C][/ROW]
[ROW][C]46[/C][C]271.16[/C][C]270.743518014376[/C][C]0.416481985623818[/C][/ROW]
[ROW][C]47[/C][C]273.63[/C][C]280.911515880722[/C][C]-7.28151588072228[/C][/ROW]
[ROW][C]48[/C][C]304.87[/C][C]318.655289111072[/C][C]-13.7852891110725[/C][/ROW]
[ROW][C]49[/C][C]323.9[/C][C]340.591125070496[/C][C]-16.6911250704961[/C][/ROW]
[ROW][C]50[/C][C]336.11[/C][C]310.255446313057[/C][C]25.8545536869432[/C][/ROW]
[ROW][C]51[/C][C]335.65[/C][C]294.088534482153[/C][C]41.5614655178467[/C][/ROW]
[ROW][C]52[/C][C]282.23[/C][C]289.219821458304[/C][C]-6.98982145830377[/C][/ROW]
[ROW][C]53[/C][C]273.03[/C][C]268.313332564483[/C][C]4.71666743551651[/C][/ROW]
[ROW][C]54[/C][C]270.07[/C][C]267.933867022397[/C][C]2.13613297760264[/C][/ROW]
[ROW][C]55[/C][C]246.03[/C][C]267.389170340807[/C][C]-21.3591703408073[/C][/ROW]
[ROW][C]56[/C][C]242.35[/C][C]264.048104823096[/C][C]-21.6981048230956[/C][/ROW]
[ROW][C]57[/C][C]250.33[/C][C]260.355592481623[/C][C]-10.0255924816233[/C][/ROW]
[ROW][C]58[/C][C]267.45[/C][C]267.878728010091[/C][C]-0.42872801009139[/C][/ROW]
[ROW][C]59[/C][C]268.8[/C][C]275.251982420825[/C][C]-6.45198242082455[/C][/ROW]
[ROW][C]60[/C][C]302.68[/C][C]310.656822763135[/C][C]-7.97682276313498[/C][/ROW]
[ROW][C]61[/C][C]313.1[/C][C]331.639753151068[/C][C]-18.5397531510684[/C][/ROW]
[ROW][C]62[/C][C]306.39[/C][C]315.948978865261[/C][C]-9.55897886526054[/C][/ROW]
[ROW][C]63[/C][C]305.61[/C][C]304.202471144754[/C][C]1.40752885524569[/C][/ROW]
[ROW][C]64[/C][C]277.27[/C][C]281.167821265465[/C][C]-3.89782126546544[/C][/ROW]
[ROW][C]65[/C][C]264.94[/C][C]263.999337302389[/C][C]0.940662697610833[/C][/ROW]
[ROW][C]66[/C][C]268.63[/C][C]262.227517768583[/C][C]6.40248223141703[/C][/ROW]
[ROW][C]67[/C][C]293.9[/C][C]253.229422684396[/C][C]40.6705773156041[/C][/ROW]
[ROW][C]68[/C][C]248.65[/C][C]251.040237562142[/C][C]-2.39023756214209[/C][/ROW]
[ROW][C]69[/C][C]256[/C][C]251.791547758848[/C][C]4.2084522411522[/C][/ROW]
[ROW][C]70[/C][C]258.52[/C][C]262.985218655796[/C][C]-4.46521865579621[/C][/ROW]
[ROW][C]71[/C][C]266.9[/C][C]268.17827305769[/C][C]-1.27827305769023[/C][/ROW]
[ROW][C]72[/C][C]281.23[/C][C]303.193970664959[/C][C]-21.9639706649593[/C][/ROW]
[ROW][C]73[/C][C]306[/C][C]320.158969323193[/C][C]-14.158969323193[/C][/ROW]
[ROW][C]74[/C][C]325.46[/C][C]307.666705806478[/C][C]17.7932941935222[/C][/ROW]
[ROW][C]75[/C][C]291.13[/C][C]300.442694106667[/C][C]-9.31269410666675[/C][/ROW]
[ROW][C]76[/C][C]282.53[/C][C]275.379322992532[/C][C]7.15067700746795[/C][/ROW]
[ROW][C]77[/C][C]256.52[/C][C]260.240742170198[/C][C]-3.72074217019821[/C][/ROW]
[ROW][C]78[/C][C]258.63[/C][C]260.341738153278[/C][C]-1.71173815327836[/C][/ROW]
[ROW][C]79[/C][C]252.74[/C][C]263.103598799714[/C][C]-10.3635987997143[/C][/ROW]
[ROW][C]80[/C][C]245.16[/C][C]244.644957608841[/C][C]0.515042391158858[/C][/ROW]
[ROW][C]81[/C][C]255.03[/C][C]247.591404519722[/C][C]7.43859548027839[/C][/ROW]
[ROW][C]82[/C][C]268.35[/C][C]255.699808666637[/C][C]12.6501913333633[/C][/ROW]
[ROW][C]83[/C][C]293.73[/C][C]262.311018931791[/C][C]31.4189810682087[/C][/ROW]
[ROW][C]84[/C][C]278.39[/C][C]290.949222957964[/C][C]-12.5592229579642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268794&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268794&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
13358.06358.427601495727-0.367601495726547
14320.07320.472590322409-0.402590322409139
15295.9296.380472735268-0.48047273526754
16291.27290.9774480603510.292551939648604
17272.87271.8643229801981.00567701980214
18269.27268.1457419619931.12425803800716
19271.32271.3063429645710.0136570354292189
20267.45268.698271533399-1.24827153339896
21260.33258.8985153967461.43148460325386
22277.94258.14437595371419.7956240462856
23277.07277.612840430247-0.542840430246997
24312.65308.8443970669743.80560293302631
25319.71361.65965043282-41.9496504328203
26318.39322.683190575425-4.29319057542517
27304.9298.3857704721426.51422952785816
28303.73293.34783822958710.382161770413
29273.29274.692136062717-1.40213606271686
30274.33270.9330941649333.39690583506649
31270.45273.741616839373-3.29161683937303
32278.23270.5892151364497.64078486355095
33274.03261.9260682341712.1039317658304
34279267.83934392015311.1606560798467
35287.5280.0684927751927.43150722480846
36336.87313.0385241145923.8314758854104
37334.1350.556716459476-16.4567164594761
38296.07325.47160182061-29.4016018206096
39286.84304.498688913814-17.6586889138141
40277.63300.293096971316-22.663096971316
41261.32276.694158920727-15.3741589207272
42264.07274.11738739636-10.0473873963602
43261.94274.07428858546-12.13428858546
44252.84274.252559633843-21.4125596338434
45257.83266.09445788597-8.26445788597039
46271.16270.7435180143760.416481985623818
47273.63280.911515880722-7.28151588072228
48304.87318.655289111072-13.7852891110725
49323.9340.591125070496-16.6911250704961
50336.11310.25544631305725.8545536869432
51335.65294.08853448215341.5614655178467
52282.23289.219821458304-6.98982145830377
53273.03268.3133325644834.71666743551651
54270.07267.9338670223972.13613297760264
55246.03267.389170340807-21.3591703408073
56242.35264.048104823096-21.6981048230956
57250.33260.355592481623-10.0255924816233
58267.45267.878728010091-0.42872801009139
59268.8275.251982420825-6.45198242082455
60302.68310.656822763135-7.97682276313498
61313.1331.639753151068-18.5397531510684
62306.39315.948978865261-9.55897886526054
63305.61304.2024711447541.40752885524569
64277.27281.167821265465-3.89782126546544
65264.94263.9993373023890.940662697610833
66268.63262.2275177685836.40248223141703
67293.9253.22942268439640.6705773156041
68248.65251.040237562142-2.39023756214209
69256251.7915477588484.2084522411522
70258.52262.985218655796-4.46521865579621
71266.9268.17827305769-1.27827305769023
72281.23303.193970664959-21.9639706649593
73306320.158969323193-14.158969323193
74325.46307.66670580647817.7932941935222
75291.13300.442694106667-9.31269410666675
76282.53275.3793229925327.15067700746795
77256.52260.240742170198-3.72074217019821
78258.63260.341738153278-1.71173815327836
79252.74263.103598799714-10.3635987997143
80245.16244.6449576088410.515042391158858
81255.03247.5914045197227.43859548027839
82268.35255.69980866663712.6501913333633
83293.73262.31101893179131.4189810682087
84278.39290.949222957964-12.5592229579642







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85310.943600325451282.421095336281339.466105314621
86310.031180171647281.498429631363338.563930711931
87293.090111478284264.543559669953321.636663286615
88274.084197126968245.519763878119302.648630375818
89255.112932770857226.526016372674283.69984916904
90256.113130221407227.498611129734284.727649313079
91256.035576775715227.387822175802284.683331375629
92241.756631348582213.069500659368270.443762037796
93247.262886749982218.529738136351275.996035363614
94257.148999432941228.362697385758285.935301480124
95270.072378371782241.225302405719298.919454337845
96282.683128381033253.767182889154311.599073872912

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 310.943600325451 & 282.421095336281 & 339.466105314621 \tabularnewline
86 & 310.031180171647 & 281.498429631363 & 338.563930711931 \tabularnewline
87 & 293.090111478284 & 264.543559669953 & 321.636663286615 \tabularnewline
88 & 274.084197126968 & 245.519763878119 & 302.648630375818 \tabularnewline
89 & 255.112932770857 & 226.526016372674 & 283.69984916904 \tabularnewline
90 & 256.113130221407 & 227.498611129734 & 284.727649313079 \tabularnewline
91 & 256.035576775715 & 227.387822175802 & 284.683331375629 \tabularnewline
92 & 241.756631348582 & 213.069500659368 & 270.443762037796 \tabularnewline
93 & 247.262886749982 & 218.529738136351 & 275.996035363614 \tabularnewline
94 & 257.148999432941 & 228.362697385758 & 285.935301480124 \tabularnewline
95 & 270.072378371782 & 241.225302405719 & 298.919454337845 \tabularnewline
96 & 282.683128381033 & 253.767182889154 & 311.599073872912 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268794&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]310.943600325451[/C][C]282.421095336281[/C][C]339.466105314621[/C][/ROW]
[ROW][C]86[/C][C]310.031180171647[/C][C]281.498429631363[/C][C]338.563930711931[/C][/ROW]
[ROW][C]87[/C][C]293.090111478284[/C][C]264.543559669953[/C][C]321.636663286615[/C][/ROW]
[ROW][C]88[/C][C]274.084197126968[/C][C]245.519763878119[/C][C]302.648630375818[/C][/ROW]
[ROW][C]89[/C][C]255.112932770857[/C][C]226.526016372674[/C][C]283.69984916904[/C][/ROW]
[ROW][C]90[/C][C]256.113130221407[/C][C]227.498611129734[/C][C]284.727649313079[/C][/ROW]
[ROW][C]91[/C][C]256.035576775715[/C][C]227.387822175802[/C][C]284.683331375629[/C][/ROW]
[ROW][C]92[/C][C]241.756631348582[/C][C]213.069500659368[/C][C]270.443762037796[/C][/ROW]
[ROW][C]93[/C][C]247.262886749982[/C][C]218.529738136351[/C][C]275.996035363614[/C][/ROW]
[ROW][C]94[/C][C]257.148999432941[/C][C]228.362697385758[/C][C]285.935301480124[/C][/ROW]
[ROW][C]95[/C][C]270.072378371782[/C][C]241.225302405719[/C][C]298.919454337845[/C][/ROW]
[ROW][C]96[/C][C]282.683128381033[/C][C]253.767182889154[/C][C]311.599073872912[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268794&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268794&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
85310.943600325451282.421095336281339.466105314621
86310.031180171647281.498429631363338.563930711931
87293.090111478284264.543559669953321.636663286615
88274.084197126968245.519763878119302.648630375818
89255.112932770857226.526016372674283.69984916904
90256.113130221407227.498611129734284.727649313079
91256.035576775715227.387822175802284.683331375629
92241.756631348582213.069500659368270.443762037796
93247.262886749982218.529738136351275.996035363614
94257.148999432941228.362697385758285.935301480124
95270.072378371782241.225302405719298.919454337845
96282.683128381033253.767182889154311.599073872912



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')