Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 14:52:25 +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/2011/May/19/t1305816593tuc4c0reaud4cdg.htm/, Retrieved Sun, 12 May 2024 11:41:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122070, Retrieved Sun, 12 May 2024 11:41:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oefenin...] [2011-05-19 14:52:25] [ab2f1cf8b83b48d30fb4cac56e306499] [Current]
Feedback Forum

Post a new message
Dataseries X:
41
39
50
40
43
38
44
35
39
35
29
49
50
59
63
32
39
47
53
60
57
52
70
90
74
62
55
84
94
70
108
139
120
97
126
149
158
124
140
109
114
77
120
133
110
92
97
78
99
107
112
90
98
125
155
190
236
189
174
178
136
161
171
149
184
155
276
224
213
279
268
287
238
213
257
293
212
246
353
339
308
247
257
322
298
273
312
249
286
279
309
401
309
328
353
354
327
324
285
243
241
287
355
460
364
487
452
391
500
451
375
372
302
316
398
394
431
431




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122070&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122070&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122070&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 time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.213143664571728
beta0.00645020019309578
gamma0.424943606209328

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.213143664571728 \tabularnewline
beta & 0.00645020019309578 \tabularnewline
gamma & 0.424943606209328 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122070&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]0.213143664571728[/C][/ROW]
[ROW][C]beta[/C][C]0.00645020019309578[/C][/ROW]
[ROW][C]gamma[/C][C]0.424943606209328[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122070&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122070&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
alpha0.213143664571728
beta0.00645020019309578
gamma0.424943606209328







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135047.10543991015492.89456008984506
145955.96233342379493.03766657620507
156359.60058789861573.39941210138434
163230.43937366267451.56062633732548
173936.56040094510422.43959905489584
184742.82510943552414.17489056447594
195356.0035962549115-3.00359625491154
206043.687488354030216.3125116459698
215751.89885109767645.10114890232358
225248.24019090219883.7598090978012
237041.881904574985428.1180954250146
249081.86586557226168.13413442773837
257486.9533818199762-12.9533818199762
266297.59893837588-35.5989383758799
275594.1112419276597-39.1112419276597
288442.929253022435241.0707469775648
299461.235481075663132.7645189243369
307078.9123828735137-8.91238287351375
3110893.191244531289614.8087554687104
3213985.745168240330853.2548317596692
3312098.161118102627721.8388818973723
349792.38268778487784.61731221512221
3512692.413334159752833.5866658402472
36149146.1903153237122.80968467628821
37158139.58302505972218.4169749402784
38124151.406900840488-27.4069008404876
39140147.812296583395-7.81229658339467
40109108.5353212094270.464678790573487
41114117.503833288205-3.50383328820544
4277111.491890235354-34.4918902353538
43120137.39274145732-17.39274145732
44133133.550538091547-0.55053809154694
45110121.870273958662-11.8702739586622
4692101.636565226357-9.6365652263573
4797107.771493254877-10.7714932548772
4878139.961931816656-61.9619318166555
4999124.886206798664-25.8862067986642
50107113.177831745124-6.1778317451242
51112119.061002171178-7.06100217117785
529089.0251134804040.974886519596055
539895.41996297598952.58003702401052
5412582.320232669811342.6797673301887
55155129.63084923443925.3691507655606
56190140.70015487820249.2998451217977
57236133.529531758246102.470468241754
58189132.20975747217856.790242527822
59174155.57070228570618.4292977142937
60178182.914272374356-4.91427237435593
61136198.150377986194-62.1503779861937
62161185.047759625669-24.0477596256693
63171190.702749040376-19.7027490403756
64149144.2994721551674.70052784483343
65184155.81958896549628.1804110345041
66155158.658606313424-3.65860631342397
67276205.40654058262470.5934594173757
68224239.226122351407-15.2261223514072
69213228.979468223588-15.9794682235881
70279177.769152238656101.230847761344
71268197.04525974419370.9547402558069
72287231.90942291166355.0905770883368
73238237.5203557885630.479644211436948
74213255.630083725713-42.630083725713
75257263.55145139239-6.5514513923896
76293212.26466516524180.7353348347592
77212257.289537670045-45.289537670045
78246227.38623846700318.6137615329972
79353335.43591869759517.5640813024049
80339324.95676728060514.0432327193946
81308317.200424013297-9.20042401329687
82247297.353097436938-50.3530974369376
83257269.048143450591-12.0481434505908
84322281.5856250072440.41437499276
85298263.0182407236534.9817592763499
86273273.783458765984-0.783458765984278
87312307.6340368082324.36596319176772
88249281.39354454695-32.3935445469503
89286258.37636111754327.6236388824572
90279265.24719021050713.7528097894926
91309384.965513568946-75.9655135689458
92401352.06668663173948.9333133682611
93309342.098302816729-33.0983028167292
94328300.23275821302227.7672417869783
95353300.5263774845552.4736225154502
96354349.8066004467284.19339955327212
97327316.66835967606910.3316403239307
98324308.93117235870415.0688276412964
99285352.763567038031-67.7635670380308
100243294.805200411893-51.8052004118931
101241287.646325003512-46.6463250035125
102287273.79882701988713.2011729801129
103355363.304616749659-8.30461674965943
104460387.21980598328572.7801940167154
105364351.47134467329612.5286553267037
106487337.976115293889149.023884706111
107452371.92643091762180.073569082379
108391414.750270368213-23.7502703682132
109500372.294169448289127.705830551711
110451388.94363921965862.0563607803422
111375417.178199639249-42.1781996392486
112372357.81512560494514.1848743950554
113302367.547487313136-65.5474873131365
114316375.106366255874-59.1063662558744
115398464.864989196216-66.8649891962161
116394515.546883764625-121.546883764625
117431407.55404299830123.4459570016993
118431441.367396683969-10.367396683969

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 50 & 47.1054399101549 & 2.89456008984506 \tabularnewline
14 & 59 & 55.9623334237949 & 3.03766657620507 \tabularnewline
15 & 63 & 59.6005878986157 & 3.39941210138434 \tabularnewline
16 & 32 & 30.4393736626745 & 1.56062633732548 \tabularnewline
17 & 39 & 36.5604009451042 & 2.43959905489584 \tabularnewline
18 & 47 & 42.8251094355241 & 4.17489056447594 \tabularnewline
19 & 53 & 56.0035962549115 & -3.00359625491154 \tabularnewline
20 & 60 & 43.6874883540302 & 16.3125116459698 \tabularnewline
21 & 57 & 51.8988510976764 & 5.10114890232358 \tabularnewline
22 & 52 & 48.2401909021988 & 3.7598090978012 \tabularnewline
23 & 70 & 41.8819045749854 & 28.1180954250146 \tabularnewline
24 & 90 & 81.8658655722616 & 8.13413442773837 \tabularnewline
25 & 74 & 86.9533818199762 & -12.9533818199762 \tabularnewline
26 & 62 & 97.59893837588 & -35.5989383758799 \tabularnewline
27 & 55 & 94.1112419276597 & -39.1112419276597 \tabularnewline
28 & 84 & 42.9292530224352 & 41.0707469775648 \tabularnewline
29 & 94 & 61.2354810756631 & 32.7645189243369 \tabularnewline
30 & 70 & 78.9123828735137 & -8.91238287351375 \tabularnewline
31 & 108 & 93.1912445312896 & 14.8087554687104 \tabularnewline
32 & 139 & 85.7451682403308 & 53.2548317596692 \tabularnewline
33 & 120 & 98.1611181026277 & 21.8388818973723 \tabularnewline
34 & 97 & 92.3826877848778 & 4.61731221512221 \tabularnewline
35 & 126 & 92.4133341597528 & 33.5866658402472 \tabularnewline
36 & 149 & 146.190315323712 & 2.80968467628821 \tabularnewline
37 & 158 & 139.583025059722 & 18.4169749402784 \tabularnewline
38 & 124 & 151.406900840488 & -27.4069008404876 \tabularnewline
39 & 140 & 147.812296583395 & -7.81229658339467 \tabularnewline
40 & 109 & 108.535321209427 & 0.464678790573487 \tabularnewline
41 & 114 & 117.503833288205 & -3.50383328820544 \tabularnewline
42 & 77 & 111.491890235354 & -34.4918902353538 \tabularnewline
43 & 120 & 137.39274145732 & -17.39274145732 \tabularnewline
44 & 133 & 133.550538091547 & -0.55053809154694 \tabularnewline
45 & 110 & 121.870273958662 & -11.8702739586622 \tabularnewline
46 & 92 & 101.636565226357 & -9.6365652263573 \tabularnewline
47 & 97 & 107.771493254877 & -10.7714932548772 \tabularnewline
48 & 78 & 139.961931816656 & -61.9619318166555 \tabularnewline
49 & 99 & 124.886206798664 & -25.8862067986642 \tabularnewline
50 & 107 & 113.177831745124 & -6.1778317451242 \tabularnewline
51 & 112 & 119.061002171178 & -7.06100217117785 \tabularnewline
52 & 90 & 89.025113480404 & 0.974886519596055 \tabularnewline
53 & 98 & 95.4199629759895 & 2.58003702401052 \tabularnewline
54 & 125 & 82.3202326698113 & 42.6797673301887 \tabularnewline
55 & 155 & 129.630849234439 & 25.3691507655606 \tabularnewline
56 & 190 & 140.700154878202 & 49.2998451217977 \tabularnewline
57 & 236 & 133.529531758246 & 102.470468241754 \tabularnewline
58 & 189 & 132.209757472178 & 56.790242527822 \tabularnewline
59 & 174 & 155.570702285706 & 18.4292977142937 \tabularnewline
60 & 178 & 182.914272374356 & -4.91427237435593 \tabularnewline
61 & 136 & 198.150377986194 & -62.1503779861937 \tabularnewline
62 & 161 & 185.047759625669 & -24.0477596256693 \tabularnewline
63 & 171 & 190.702749040376 & -19.7027490403756 \tabularnewline
64 & 149 & 144.299472155167 & 4.70052784483343 \tabularnewline
65 & 184 & 155.819588965496 & 28.1804110345041 \tabularnewline
66 & 155 & 158.658606313424 & -3.65860631342397 \tabularnewline
67 & 276 & 205.406540582624 & 70.5934594173757 \tabularnewline
68 & 224 & 239.226122351407 & -15.2261223514072 \tabularnewline
69 & 213 & 228.979468223588 & -15.9794682235881 \tabularnewline
70 & 279 & 177.769152238656 & 101.230847761344 \tabularnewline
71 & 268 & 197.045259744193 & 70.9547402558069 \tabularnewline
72 & 287 & 231.909422911663 & 55.0905770883368 \tabularnewline
73 & 238 & 237.520355788563 & 0.479644211436948 \tabularnewline
74 & 213 & 255.630083725713 & -42.630083725713 \tabularnewline
75 & 257 & 263.55145139239 & -6.5514513923896 \tabularnewline
76 & 293 & 212.264665165241 & 80.7353348347592 \tabularnewline
77 & 212 & 257.289537670045 & -45.289537670045 \tabularnewline
78 & 246 & 227.386238467003 & 18.6137615329972 \tabularnewline
79 & 353 & 335.435918697595 & 17.5640813024049 \tabularnewline
80 & 339 & 324.956767280605 & 14.0432327193946 \tabularnewline
81 & 308 & 317.200424013297 & -9.20042401329687 \tabularnewline
82 & 247 & 297.353097436938 & -50.3530974369376 \tabularnewline
83 & 257 & 269.048143450591 & -12.0481434505908 \tabularnewline
84 & 322 & 281.58562500724 & 40.41437499276 \tabularnewline
85 & 298 & 263.01824072365 & 34.9817592763499 \tabularnewline
86 & 273 & 273.783458765984 & -0.783458765984278 \tabularnewline
87 & 312 & 307.634036808232 & 4.36596319176772 \tabularnewline
88 & 249 & 281.39354454695 & -32.3935445469503 \tabularnewline
89 & 286 & 258.376361117543 & 27.6236388824572 \tabularnewline
90 & 279 & 265.247190210507 & 13.7528097894926 \tabularnewline
91 & 309 & 384.965513568946 & -75.9655135689458 \tabularnewline
92 & 401 & 352.066686631739 & 48.9333133682611 \tabularnewline
93 & 309 & 342.098302816729 & -33.0983028167292 \tabularnewline
94 & 328 & 300.232758213022 & 27.7672417869783 \tabularnewline
95 & 353 & 300.52637748455 & 52.4736225154502 \tabularnewline
96 & 354 & 349.806600446728 & 4.19339955327212 \tabularnewline
97 & 327 & 316.668359676069 & 10.3316403239307 \tabularnewline
98 & 324 & 308.931172358704 & 15.0688276412964 \tabularnewline
99 & 285 & 352.763567038031 & -67.7635670380308 \tabularnewline
100 & 243 & 294.805200411893 & -51.8052004118931 \tabularnewline
101 & 241 & 287.646325003512 & -46.6463250035125 \tabularnewline
102 & 287 & 273.798827019887 & 13.2011729801129 \tabularnewline
103 & 355 & 363.304616749659 & -8.30461674965943 \tabularnewline
104 & 460 & 387.219805983285 & 72.7801940167154 \tabularnewline
105 & 364 & 351.471344673296 & 12.5286553267037 \tabularnewline
106 & 487 & 337.976115293889 & 149.023884706111 \tabularnewline
107 & 452 & 371.926430917621 & 80.073569082379 \tabularnewline
108 & 391 & 414.750270368213 & -23.7502703682132 \tabularnewline
109 & 500 & 372.294169448289 & 127.705830551711 \tabularnewline
110 & 451 & 388.943639219658 & 62.0563607803422 \tabularnewline
111 & 375 & 417.178199639249 & -42.1781996392486 \tabularnewline
112 & 372 & 357.815125604945 & 14.1848743950554 \tabularnewline
113 & 302 & 367.547487313136 & -65.5474873131365 \tabularnewline
114 & 316 & 375.106366255874 & -59.1063662558744 \tabularnewline
115 & 398 & 464.864989196216 & -66.8649891962161 \tabularnewline
116 & 394 & 515.546883764625 & -121.546883764625 \tabularnewline
117 & 431 & 407.554042998301 & 23.4459570016993 \tabularnewline
118 & 431 & 441.367396683969 & -10.367396683969 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122070&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]50[/C][C]47.1054399101549[/C][C]2.89456008984506[/C][/ROW]
[ROW][C]14[/C][C]59[/C][C]55.9623334237949[/C][C]3.03766657620507[/C][/ROW]
[ROW][C]15[/C][C]63[/C][C]59.6005878986157[/C][C]3.39941210138434[/C][/ROW]
[ROW][C]16[/C][C]32[/C][C]30.4393736626745[/C][C]1.56062633732548[/C][/ROW]
[ROW][C]17[/C][C]39[/C][C]36.5604009451042[/C][C]2.43959905489584[/C][/ROW]
[ROW][C]18[/C][C]47[/C][C]42.8251094355241[/C][C]4.17489056447594[/C][/ROW]
[ROW][C]19[/C][C]53[/C][C]56.0035962549115[/C][C]-3.00359625491154[/C][/ROW]
[ROW][C]20[/C][C]60[/C][C]43.6874883540302[/C][C]16.3125116459698[/C][/ROW]
[ROW][C]21[/C][C]57[/C][C]51.8988510976764[/C][C]5.10114890232358[/C][/ROW]
[ROW][C]22[/C][C]52[/C][C]48.2401909021988[/C][C]3.7598090978012[/C][/ROW]
[ROW][C]23[/C][C]70[/C][C]41.8819045749854[/C][C]28.1180954250146[/C][/ROW]
[ROW][C]24[/C][C]90[/C][C]81.8658655722616[/C][C]8.13413442773837[/C][/ROW]
[ROW][C]25[/C][C]74[/C][C]86.9533818199762[/C][C]-12.9533818199762[/C][/ROW]
[ROW][C]26[/C][C]62[/C][C]97.59893837588[/C][C]-35.5989383758799[/C][/ROW]
[ROW][C]27[/C][C]55[/C][C]94.1112419276597[/C][C]-39.1112419276597[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]42.9292530224352[/C][C]41.0707469775648[/C][/ROW]
[ROW][C]29[/C][C]94[/C][C]61.2354810756631[/C][C]32.7645189243369[/C][/ROW]
[ROW][C]30[/C][C]70[/C][C]78.9123828735137[/C][C]-8.91238287351375[/C][/ROW]
[ROW][C]31[/C][C]108[/C][C]93.1912445312896[/C][C]14.8087554687104[/C][/ROW]
[ROW][C]32[/C][C]139[/C][C]85.7451682403308[/C][C]53.2548317596692[/C][/ROW]
[ROW][C]33[/C][C]120[/C][C]98.1611181026277[/C][C]21.8388818973723[/C][/ROW]
[ROW][C]34[/C][C]97[/C][C]92.3826877848778[/C][C]4.61731221512221[/C][/ROW]
[ROW][C]35[/C][C]126[/C][C]92.4133341597528[/C][C]33.5866658402472[/C][/ROW]
[ROW][C]36[/C][C]149[/C][C]146.190315323712[/C][C]2.80968467628821[/C][/ROW]
[ROW][C]37[/C][C]158[/C][C]139.583025059722[/C][C]18.4169749402784[/C][/ROW]
[ROW][C]38[/C][C]124[/C][C]151.406900840488[/C][C]-27.4069008404876[/C][/ROW]
[ROW][C]39[/C][C]140[/C][C]147.812296583395[/C][C]-7.81229658339467[/C][/ROW]
[ROW][C]40[/C][C]109[/C][C]108.535321209427[/C][C]0.464678790573487[/C][/ROW]
[ROW][C]41[/C][C]114[/C][C]117.503833288205[/C][C]-3.50383328820544[/C][/ROW]
[ROW][C]42[/C][C]77[/C][C]111.491890235354[/C][C]-34.4918902353538[/C][/ROW]
[ROW][C]43[/C][C]120[/C][C]137.39274145732[/C][C]-17.39274145732[/C][/ROW]
[ROW][C]44[/C][C]133[/C][C]133.550538091547[/C][C]-0.55053809154694[/C][/ROW]
[ROW][C]45[/C][C]110[/C][C]121.870273958662[/C][C]-11.8702739586622[/C][/ROW]
[ROW][C]46[/C][C]92[/C][C]101.636565226357[/C][C]-9.6365652263573[/C][/ROW]
[ROW][C]47[/C][C]97[/C][C]107.771493254877[/C][C]-10.7714932548772[/C][/ROW]
[ROW][C]48[/C][C]78[/C][C]139.961931816656[/C][C]-61.9619318166555[/C][/ROW]
[ROW][C]49[/C][C]99[/C][C]124.886206798664[/C][C]-25.8862067986642[/C][/ROW]
[ROW][C]50[/C][C]107[/C][C]113.177831745124[/C][C]-6.1778317451242[/C][/ROW]
[ROW][C]51[/C][C]112[/C][C]119.061002171178[/C][C]-7.06100217117785[/C][/ROW]
[ROW][C]52[/C][C]90[/C][C]89.025113480404[/C][C]0.974886519596055[/C][/ROW]
[ROW][C]53[/C][C]98[/C][C]95.4199629759895[/C][C]2.58003702401052[/C][/ROW]
[ROW][C]54[/C][C]125[/C][C]82.3202326698113[/C][C]42.6797673301887[/C][/ROW]
[ROW][C]55[/C][C]155[/C][C]129.630849234439[/C][C]25.3691507655606[/C][/ROW]
[ROW][C]56[/C][C]190[/C][C]140.700154878202[/C][C]49.2998451217977[/C][/ROW]
[ROW][C]57[/C][C]236[/C][C]133.529531758246[/C][C]102.470468241754[/C][/ROW]
[ROW][C]58[/C][C]189[/C][C]132.209757472178[/C][C]56.790242527822[/C][/ROW]
[ROW][C]59[/C][C]174[/C][C]155.570702285706[/C][C]18.4292977142937[/C][/ROW]
[ROW][C]60[/C][C]178[/C][C]182.914272374356[/C][C]-4.91427237435593[/C][/ROW]
[ROW][C]61[/C][C]136[/C][C]198.150377986194[/C][C]-62.1503779861937[/C][/ROW]
[ROW][C]62[/C][C]161[/C][C]185.047759625669[/C][C]-24.0477596256693[/C][/ROW]
[ROW][C]63[/C][C]171[/C][C]190.702749040376[/C][C]-19.7027490403756[/C][/ROW]
[ROW][C]64[/C][C]149[/C][C]144.299472155167[/C][C]4.70052784483343[/C][/ROW]
[ROW][C]65[/C][C]184[/C][C]155.819588965496[/C][C]28.1804110345041[/C][/ROW]
[ROW][C]66[/C][C]155[/C][C]158.658606313424[/C][C]-3.65860631342397[/C][/ROW]
[ROW][C]67[/C][C]276[/C][C]205.406540582624[/C][C]70.5934594173757[/C][/ROW]
[ROW][C]68[/C][C]224[/C][C]239.226122351407[/C][C]-15.2261223514072[/C][/ROW]
[ROW][C]69[/C][C]213[/C][C]228.979468223588[/C][C]-15.9794682235881[/C][/ROW]
[ROW][C]70[/C][C]279[/C][C]177.769152238656[/C][C]101.230847761344[/C][/ROW]
[ROW][C]71[/C][C]268[/C][C]197.045259744193[/C][C]70.9547402558069[/C][/ROW]
[ROW][C]72[/C][C]287[/C][C]231.909422911663[/C][C]55.0905770883368[/C][/ROW]
[ROW][C]73[/C][C]238[/C][C]237.520355788563[/C][C]0.479644211436948[/C][/ROW]
[ROW][C]74[/C][C]213[/C][C]255.630083725713[/C][C]-42.630083725713[/C][/ROW]
[ROW][C]75[/C][C]257[/C][C]263.55145139239[/C][C]-6.5514513923896[/C][/ROW]
[ROW][C]76[/C][C]293[/C][C]212.264665165241[/C][C]80.7353348347592[/C][/ROW]
[ROW][C]77[/C][C]212[/C][C]257.289537670045[/C][C]-45.289537670045[/C][/ROW]
[ROW][C]78[/C][C]246[/C][C]227.386238467003[/C][C]18.6137615329972[/C][/ROW]
[ROW][C]79[/C][C]353[/C][C]335.435918697595[/C][C]17.5640813024049[/C][/ROW]
[ROW][C]80[/C][C]339[/C][C]324.956767280605[/C][C]14.0432327193946[/C][/ROW]
[ROW][C]81[/C][C]308[/C][C]317.200424013297[/C][C]-9.20042401329687[/C][/ROW]
[ROW][C]82[/C][C]247[/C][C]297.353097436938[/C][C]-50.3530974369376[/C][/ROW]
[ROW][C]83[/C][C]257[/C][C]269.048143450591[/C][C]-12.0481434505908[/C][/ROW]
[ROW][C]84[/C][C]322[/C][C]281.58562500724[/C][C]40.41437499276[/C][/ROW]
[ROW][C]85[/C][C]298[/C][C]263.01824072365[/C][C]34.9817592763499[/C][/ROW]
[ROW][C]86[/C][C]273[/C][C]273.783458765984[/C][C]-0.783458765984278[/C][/ROW]
[ROW][C]87[/C][C]312[/C][C]307.634036808232[/C][C]4.36596319176772[/C][/ROW]
[ROW][C]88[/C][C]249[/C][C]281.39354454695[/C][C]-32.3935445469503[/C][/ROW]
[ROW][C]89[/C][C]286[/C][C]258.376361117543[/C][C]27.6236388824572[/C][/ROW]
[ROW][C]90[/C][C]279[/C][C]265.247190210507[/C][C]13.7528097894926[/C][/ROW]
[ROW][C]91[/C][C]309[/C][C]384.965513568946[/C][C]-75.9655135689458[/C][/ROW]
[ROW][C]92[/C][C]401[/C][C]352.066686631739[/C][C]48.9333133682611[/C][/ROW]
[ROW][C]93[/C][C]309[/C][C]342.098302816729[/C][C]-33.0983028167292[/C][/ROW]
[ROW][C]94[/C][C]328[/C][C]300.232758213022[/C][C]27.7672417869783[/C][/ROW]
[ROW][C]95[/C][C]353[/C][C]300.52637748455[/C][C]52.4736225154502[/C][/ROW]
[ROW][C]96[/C][C]354[/C][C]349.806600446728[/C][C]4.19339955327212[/C][/ROW]
[ROW][C]97[/C][C]327[/C][C]316.668359676069[/C][C]10.3316403239307[/C][/ROW]
[ROW][C]98[/C][C]324[/C][C]308.931172358704[/C][C]15.0688276412964[/C][/ROW]
[ROW][C]99[/C][C]285[/C][C]352.763567038031[/C][C]-67.7635670380308[/C][/ROW]
[ROW][C]100[/C][C]243[/C][C]294.805200411893[/C][C]-51.8052004118931[/C][/ROW]
[ROW][C]101[/C][C]241[/C][C]287.646325003512[/C][C]-46.6463250035125[/C][/ROW]
[ROW][C]102[/C][C]287[/C][C]273.798827019887[/C][C]13.2011729801129[/C][/ROW]
[ROW][C]103[/C][C]355[/C][C]363.304616749659[/C][C]-8.30461674965943[/C][/ROW]
[ROW][C]104[/C][C]460[/C][C]387.219805983285[/C][C]72.7801940167154[/C][/ROW]
[ROW][C]105[/C][C]364[/C][C]351.471344673296[/C][C]12.5286553267037[/C][/ROW]
[ROW][C]106[/C][C]487[/C][C]337.976115293889[/C][C]149.023884706111[/C][/ROW]
[ROW][C]107[/C][C]452[/C][C]371.926430917621[/C][C]80.073569082379[/C][/ROW]
[ROW][C]108[/C][C]391[/C][C]414.750270368213[/C][C]-23.7502703682132[/C][/ROW]
[ROW][C]109[/C][C]500[/C][C]372.294169448289[/C][C]127.705830551711[/C][/ROW]
[ROW][C]110[/C][C]451[/C][C]388.943639219658[/C][C]62.0563607803422[/C][/ROW]
[ROW][C]111[/C][C]375[/C][C]417.178199639249[/C][C]-42.1781996392486[/C][/ROW]
[ROW][C]112[/C][C]372[/C][C]357.815125604945[/C][C]14.1848743950554[/C][/ROW]
[ROW][C]113[/C][C]302[/C][C]367.547487313136[/C][C]-65.5474873131365[/C][/ROW]
[ROW][C]114[/C][C]316[/C][C]375.106366255874[/C][C]-59.1063662558744[/C][/ROW]
[ROW][C]115[/C][C]398[/C][C]464.864989196216[/C][C]-66.8649891962161[/C][/ROW]
[ROW][C]116[/C][C]394[/C][C]515.546883764625[/C][C]-121.546883764625[/C][/ROW]
[ROW][C]117[/C][C]431[/C][C]407.554042998301[/C][C]23.4459570016993[/C][/ROW]
[ROW][C]118[/C][C]431[/C][C]441.367396683969[/C][C]-10.367396683969[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122070&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122070&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
135047.10543991015492.89456008984506
145955.96233342379493.03766657620507
156359.60058789861573.39941210138434
163230.43937366267451.56062633732548
173936.56040094510422.43959905489584
184742.82510943552414.17489056447594
195356.0035962549115-3.00359625491154
206043.687488354030216.3125116459698
215751.89885109767645.10114890232358
225248.24019090219883.7598090978012
237041.881904574985428.1180954250146
249081.86586557226168.13413442773837
257486.9533818199762-12.9533818199762
266297.59893837588-35.5989383758799
275594.1112419276597-39.1112419276597
288442.929253022435241.0707469775648
299461.235481075663132.7645189243369
307078.9123828735137-8.91238287351375
3110893.191244531289614.8087554687104
3213985.745168240330853.2548317596692
3312098.161118102627721.8388818973723
349792.38268778487784.61731221512221
3512692.413334159752833.5866658402472
36149146.1903153237122.80968467628821
37158139.58302505972218.4169749402784
38124151.406900840488-27.4069008404876
39140147.812296583395-7.81229658339467
40109108.5353212094270.464678790573487
41114117.503833288205-3.50383328820544
4277111.491890235354-34.4918902353538
43120137.39274145732-17.39274145732
44133133.550538091547-0.55053809154694
45110121.870273958662-11.8702739586622
4692101.636565226357-9.6365652263573
4797107.771493254877-10.7714932548772
4878139.961931816656-61.9619318166555
4999124.886206798664-25.8862067986642
50107113.177831745124-6.1778317451242
51112119.061002171178-7.06100217117785
529089.0251134804040.974886519596055
539895.41996297598952.58003702401052
5412582.320232669811342.6797673301887
55155129.63084923443925.3691507655606
56190140.70015487820249.2998451217977
57236133.529531758246102.470468241754
58189132.20975747217856.790242527822
59174155.57070228570618.4292977142937
60178182.914272374356-4.91427237435593
61136198.150377986194-62.1503779861937
62161185.047759625669-24.0477596256693
63171190.702749040376-19.7027490403756
64149144.2994721551674.70052784483343
65184155.81958896549628.1804110345041
66155158.658606313424-3.65860631342397
67276205.40654058262470.5934594173757
68224239.226122351407-15.2261223514072
69213228.979468223588-15.9794682235881
70279177.769152238656101.230847761344
71268197.04525974419370.9547402558069
72287231.90942291166355.0905770883368
73238237.5203557885630.479644211436948
74213255.630083725713-42.630083725713
75257263.55145139239-6.5514513923896
76293212.26466516524180.7353348347592
77212257.289537670045-45.289537670045
78246227.38623846700318.6137615329972
79353335.43591869759517.5640813024049
80339324.95676728060514.0432327193946
81308317.200424013297-9.20042401329687
82247297.353097436938-50.3530974369376
83257269.048143450591-12.0481434505908
84322281.5856250072440.41437499276
85298263.0182407236534.9817592763499
86273273.783458765984-0.783458765984278
87312307.6340368082324.36596319176772
88249281.39354454695-32.3935445469503
89286258.37636111754327.6236388824572
90279265.24719021050713.7528097894926
91309384.965513568946-75.9655135689458
92401352.06668663173948.9333133682611
93309342.098302816729-33.0983028167292
94328300.23275821302227.7672417869783
95353300.5263774845552.4736225154502
96354349.8066004467284.19339955327212
97327316.66835967606910.3316403239307
98324308.93117235870415.0688276412964
99285352.763567038031-67.7635670380308
100243294.805200411893-51.8052004118931
101241287.646325003512-46.6463250035125
102287273.79882701988713.2011729801129
103355363.304616749659-8.30461674965943
104460387.21980598328572.7801940167154
105364351.47134467329612.5286553267037
106487337.976115293889149.023884706111
107452371.92643091762180.073569082379
108391414.750270368213-23.7502703682132
109500372.294169448289127.705830551711
110451388.94363921965862.0563607803422
111375417.178199639249-42.1781996392486
112372357.81512560494514.1848743950554
113302367.547487313136-65.5474873131365
114316375.106366255874-59.1063662558744
115398464.864989196216-66.8649891962161
116394515.546883764625-121.546883764625
117431407.55404299830123.4459570016993
118431441.367396683969-10.367396683969







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
119415.894057518493370.117254719446461.67086031754
120406.642333118478357.656358905109455.628307331848
121416.914953425497364.473432897251469.356473953742
122385.423295300731331.314231281724439.532359319739
123366.87274006942310.844594442455422.900885696386
124337.324017241984280.33001388933394.318020594639
125317.963806162545259.61746165562376.310150669471
126339.857506927664276.953324752322402.761689103007
127437.892047535513362.264104046423513.519991024603
128483.199372564462400.109727283842566.289017845081
129446.77259110999366.237817302377527.307364917603
130465.193408486715388.409600198748541.977216774682

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
119 & 415.894057518493 & 370.117254719446 & 461.67086031754 \tabularnewline
120 & 406.642333118478 & 357.656358905109 & 455.628307331848 \tabularnewline
121 & 416.914953425497 & 364.473432897251 & 469.356473953742 \tabularnewline
122 & 385.423295300731 & 331.314231281724 & 439.532359319739 \tabularnewline
123 & 366.87274006942 & 310.844594442455 & 422.900885696386 \tabularnewline
124 & 337.324017241984 & 280.33001388933 & 394.318020594639 \tabularnewline
125 & 317.963806162545 & 259.61746165562 & 376.310150669471 \tabularnewline
126 & 339.857506927664 & 276.953324752322 & 402.761689103007 \tabularnewline
127 & 437.892047535513 & 362.264104046423 & 513.519991024603 \tabularnewline
128 & 483.199372564462 & 400.109727283842 & 566.289017845081 \tabularnewline
129 & 446.77259110999 & 366.237817302377 & 527.307364917603 \tabularnewline
130 & 465.193408486715 & 388.409600198748 & 541.977216774682 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122070&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]119[/C][C]415.894057518493[/C][C]370.117254719446[/C][C]461.67086031754[/C][/ROW]
[ROW][C]120[/C][C]406.642333118478[/C][C]357.656358905109[/C][C]455.628307331848[/C][/ROW]
[ROW][C]121[/C][C]416.914953425497[/C][C]364.473432897251[/C][C]469.356473953742[/C][/ROW]
[ROW][C]122[/C][C]385.423295300731[/C][C]331.314231281724[/C][C]439.532359319739[/C][/ROW]
[ROW][C]123[/C][C]366.87274006942[/C][C]310.844594442455[/C][C]422.900885696386[/C][/ROW]
[ROW][C]124[/C][C]337.324017241984[/C][C]280.33001388933[/C][C]394.318020594639[/C][/ROW]
[ROW][C]125[/C][C]317.963806162545[/C][C]259.61746165562[/C][C]376.310150669471[/C][/ROW]
[ROW][C]126[/C][C]339.857506927664[/C][C]276.953324752322[/C][C]402.761689103007[/C][/ROW]
[ROW][C]127[/C][C]437.892047535513[/C][C]362.264104046423[/C][C]513.519991024603[/C][/ROW]
[ROW][C]128[/C][C]483.199372564462[/C][C]400.109727283842[/C][C]566.289017845081[/C][/ROW]
[ROW][C]129[/C][C]446.77259110999[/C][C]366.237817302377[/C][C]527.307364917603[/C][/ROW]
[ROW][C]130[/C][C]465.193408486715[/C][C]388.409600198748[/C][C]541.977216774682[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122070&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122070&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
119415.894057518493370.117254719446461.67086031754
120406.642333118478357.656358905109455.628307331848
121416.914953425497364.473432897251469.356473953742
122385.423295300731331.314231281724439.532359319739
123366.87274006942310.844594442455422.900885696386
124337.324017241984280.33001388933394.318020594639
125317.963806162545259.61746165562376.310150669471
126339.857506927664276.953324752322402.761689103007
127437.892047535513362.264104046423513.519991024603
128483.199372564462400.109727283842566.289017845081
129446.77259110999366.237817302377527.307364917603
130465.193408486715388.409600198748541.977216774682



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')