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 Aug 2010 22:18:46 +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/2010/Aug/20/t1282256333tlfum57ade5gja1.htm/, Retrieved Wed, 08 May 2024 09:50:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79403, Retrieved Wed, 08 May 2024 09:50:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Boxel Dieter
Estimated Impact162
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A - Sta...] [2010-08-19 22:18:46] [f91e4cd4d3d1892f3fcf702e4827e40c] [Current]
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Dataseries X:
356
355
354
352
372
371
356
346
347
347
348
350
353
350
343
346
373
363
349
350
353
356
355
346
349
348
342
342
379
375
363
361
363
373
367
360
358
367
357
346
386
383
367
354
363
370
361
354
363
366
353
351
389
385
364
348
347
352
342
338
343
354
329
320
353
345
324
310
314
313
310
301
294
296
274
269
292
287
271
256
260
265
263
256
246
245
220
224
240
238
222
203
209
214
216
214
206
196
169
177
193
183
164
142
141
137
140
146
136
124
105
114
135
123
100
74
64
57
62
64




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79403&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79403&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79403&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.604067171997709
beta0.0703089588431605
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.604067171997709 \tabularnewline
beta & 0.0703089588431605 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79403&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]0.604067171997709[/C][/ROW]
[ROW][C]beta[/C][C]0.0703089588431605[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79403&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79403&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
alpha0.604067171997709
beta0.0703089588431605
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13353355.767282849865-2.76728284986484
14350350.972607223685-0.972607223685145
15343342.6967265586560.303273441344231
16346345.0025982606930.997401739307008
17373371.6335488269251.36645117307523
18363362.1707761809860.829223819013862
19349354.412772362754-5.4127723627538
20350341.2447946699718.75520533002879
21353348.2065916057174.79340839428289
22356352.0272200409093.97277995909059
23355356.048526761376-1.04852676137563
24346358.101527882073-12.1015278820725
25349353.163049124451-4.16304912445094
26348348.14586671249-0.145866712490204
27342340.8454724961731.15452750382741
28342343.896945517829-1.89694551782912
29379368.51022025702710.4897797429729
30375364.50931922199110.4906807780089
31363360.4737424036072.52625759639295
32361358.4419025449332.55809745506747
33363360.7433636632732.25663633672707
34373363.2626101278599.7373898721409
35367369.548773316264-2.54877331626426
36360366.872520210674-6.8725202106736
37358369.459801567944-11.4598015679443
38367362.2533221920324.74667780796767
39357358.951708187976-1.95170818797573
40346359.695540552882-13.695540552882
41386383.1009638304522.89903616954751
42383374.1891649435078.81083505649275
43367365.6491816747831.35081832521655
44354362.664797879166-8.6647978791657
45363357.376387061775.62361293823028
46370364.2594890993635.74051090063733
47361362.628920802497-1.62892080249725
48354358.155358793036-4.1553587930357
49363359.871590989483.1284090105197
50366367.994159890913-1.99415989091261
51353357.74376080876-4.74376080876027
52351351.699854617891-0.699854617890765
53389390.328664004253-1.3286640042528
54385381.1199987826893.88000121731147
55364366.461864237559-2.46186423755927
56348356.884978325654-8.88497832565406
57347356.723802955268-9.7238029552684
58352353.252208419052-1.25220841905212
59342343.611797838406-1.61179783840635
60338337.1357889034840.864211096516442
61343343.386242183586-0.386242183586432
62354345.9247021186198.07529788138129
63329340.31550124668-11.3155012466801
64320330.948138572574-10.9481385725744
65353358.547533529034-5.54753352903435
66345347.600449935565-2.60044993556534
67324326.538974496149-2.53897449614863
68310313.558180460462-3.55818046046221
69314313.9647750780030.035224921996587
70313317.794813879693-4.79481387969338
71310305.2954295120834.70457048791684
72301302.816092223163-1.81609222316257
73294305.002581965368-11.0025819653684
74296301.745160956462-5.74516095646209
75274280.558513439322-6.55851343932233
76269272.311739771828-3.31173977182817
77292298.815311980841-6.81531198084105
78287287.062628017994-0.0626280179935748
79271268.7565717868572.24342821314326
80256258.400939301071-2.40093930107082
81260258.4039496791111.59605032088905
82265259.1137990233465.88620097665410
83263256.4091400396366.59085996036379
84256252.5428274251693.45717257483091
85246253.26125691526-7.26125691525982
86245252.552456822219-7.55245682221889
87220231.830451932749-11.8304519327494
88224220.8757508672493.12424913275075
89240243.998508396941-3.99850839694082
90238236.3578859959891.64211400401120
91222221.9945229130740.00547708692633364
92203209.830381508620-6.83038150861972
93209206.7833320188902.21666798110974
94214207.8981497504576.10185024954319
95216205.48555644549810.5144435545020
96214203.48308445411610.5169155458839
97206204.5431326710381.45686732896226
98196208.052531955809-12.0525319558091
99169185.455340566486-16.4553405664857
100177176.2267482669720.773251733028019
101193190.0277253696282.97227463037163
102183188.548670045437-5.54867004543664
103164171.547067692069-7.54706769206913
104142154.219947267134-12.2199472671343
105141148.160059889812-7.16005988981192
106137142.079166652793-5.07916665279262
107140132.9296809157407.07031908426043
108146128.67024956170117.3297504382987
109136130.7842861957675.21571380423288
110124129.657060689831-5.6570606898311
111105112.851974654600-7.85197465459972
112114110.7061915241763.29380847582370
113135119.39669685770215.6033031422985
114123122.7561413786090.243858621390601
115100111.812161686028-11.8121616860280
1167493.5276024625379-19.5276024625379
1176480.9839341426352-16.9839341426352
1185766.5668433464246-9.56684334642462
1196255.74687047346176.25312952653834
1206452.973876867528211.0261231324718

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 353 & 355.767282849865 & -2.76728284986484 \tabularnewline
14 & 350 & 350.972607223685 & -0.972607223685145 \tabularnewline
15 & 343 & 342.696726558656 & 0.303273441344231 \tabularnewline
16 & 346 & 345.002598260693 & 0.997401739307008 \tabularnewline
17 & 373 & 371.633548826925 & 1.36645117307523 \tabularnewline
18 & 363 & 362.170776180986 & 0.829223819013862 \tabularnewline
19 & 349 & 354.412772362754 & -5.4127723627538 \tabularnewline
20 & 350 & 341.244794669971 & 8.75520533002879 \tabularnewline
21 & 353 & 348.206591605717 & 4.79340839428289 \tabularnewline
22 & 356 & 352.027220040909 & 3.97277995909059 \tabularnewline
23 & 355 & 356.048526761376 & -1.04852676137563 \tabularnewline
24 & 346 & 358.101527882073 & -12.1015278820725 \tabularnewline
25 & 349 & 353.163049124451 & -4.16304912445094 \tabularnewline
26 & 348 & 348.14586671249 & -0.145866712490204 \tabularnewline
27 & 342 & 340.845472496173 & 1.15452750382741 \tabularnewline
28 & 342 & 343.896945517829 & -1.89694551782912 \tabularnewline
29 & 379 & 368.510220257027 & 10.4897797429729 \tabularnewline
30 & 375 & 364.509319221991 & 10.4906807780089 \tabularnewline
31 & 363 & 360.473742403607 & 2.52625759639295 \tabularnewline
32 & 361 & 358.441902544933 & 2.55809745506747 \tabularnewline
33 & 363 & 360.743363663273 & 2.25663633672707 \tabularnewline
34 & 373 & 363.262610127859 & 9.7373898721409 \tabularnewline
35 & 367 & 369.548773316264 & -2.54877331626426 \tabularnewline
36 & 360 & 366.872520210674 & -6.8725202106736 \tabularnewline
37 & 358 & 369.459801567944 & -11.4598015679443 \tabularnewline
38 & 367 & 362.253322192032 & 4.74667780796767 \tabularnewline
39 & 357 & 358.951708187976 & -1.95170818797573 \tabularnewline
40 & 346 & 359.695540552882 & -13.695540552882 \tabularnewline
41 & 386 & 383.100963830452 & 2.89903616954751 \tabularnewline
42 & 383 & 374.189164943507 & 8.81083505649275 \tabularnewline
43 & 367 & 365.649181674783 & 1.35081832521655 \tabularnewline
44 & 354 & 362.664797879166 & -8.6647978791657 \tabularnewline
45 & 363 & 357.37638706177 & 5.62361293823028 \tabularnewline
46 & 370 & 364.259489099363 & 5.74051090063733 \tabularnewline
47 & 361 & 362.628920802497 & -1.62892080249725 \tabularnewline
48 & 354 & 358.155358793036 & -4.1553587930357 \tabularnewline
49 & 363 & 359.87159098948 & 3.1284090105197 \tabularnewline
50 & 366 & 367.994159890913 & -1.99415989091261 \tabularnewline
51 & 353 & 357.74376080876 & -4.74376080876027 \tabularnewline
52 & 351 & 351.699854617891 & -0.699854617890765 \tabularnewline
53 & 389 & 390.328664004253 & -1.3286640042528 \tabularnewline
54 & 385 & 381.119998782689 & 3.88000121731147 \tabularnewline
55 & 364 & 366.461864237559 & -2.46186423755927 \tabularnewline
56 & 348 & 356.884978325654 & -8.88497832565406 \tabularnewline
57 & 347 & 356.723802955268 & -9.7238029552684 \tabularnewline
58 & 352 & 353.252208419052 & -1.25220841905212 \tabularnewline
59 & 342 & 343.611797838406 & -1.61179783840635 \tabularnewline
60 & 338 & 337.135788903484 & 0.864211096516442 \tabularnewline
61 & 343 & 343.386242183586 & -0.386242183586432 \tabularnewline
62 & 354 & 345.924702118619 & 8.07529788138129 \tabularnewline
63 & 329 & 340.31550124668 & -11.3155012466801 \tabularnewline
64 & 320 & 330.948138572574 & -10.9481385725744 \tabularnewline
65 & 353 & 358.547533529034 & -5.54753352903435 \tabularnewline
66 & 345 & 347.600449935565 & -2.60044993556534 \tabularnewline
67 & 324 & 326.538974496149 & -2.53897449614863 \tabularnewline
68 & 310 & 313.558180460462 & -3.55818046046221 \tabularnewline
69 & 314 & 313.964775078003 & 0.035224921996587 \tabularnewline
70 & 313 & 317.794813879693 & -4.79481387969338 \tabularnewline
71 & 310 & 305.295429512083 & 4.70457048791684 \tabularnewline
72 & 301 & 302.816092223163 & -1.81609222316257 \tabularnewline
73 & 294 & 305.002581965368 & -11.0025819653684 \tabularnewline
74 & 296 & 301.745160956462 & -5.74516095646209 \tabularnewline
75 & 274 & 280.558513439322 & -6.55851343932233 \tabularnewline
76 & 269 & 272.311739771828 & -3.31173977182817 \tabularnewline
77 & 292 & 298.815311980841 & -6.81531198084105 \tabularnewline
78 & 287 & 287.062628017994 & -0.0626280179935748 \tabularnewline
79 & 271 & 268.756571786857 & 2.24342821314326 \tabularnewline
80 & 256 & 258.400939301071 & -2.40093930107082 \tabularnewline
81 & 260 & 258.403949679111 & 1.59605032088905 \tabularnewline
82 & 265 & 259.113799023346 & 5.88620097665410 \tabularnewline
83 & 263 & 256.409140039636 & 6.59085996036379 \tabularnewline
84 & 256 & 252.542827425169 & 3.45717257483091 \tabularnewline
85 & 246 & 253.26125691526 & -7.26125691525982 \tabularnewline
86 & 245 & 252.552456822219 & -7.55245682221889 \tabularnewline
87 & 220 & 231.830451932749 & -11.8304519327494 \tabularnewline
88 & 224 & 220.875750867249 & 3.12424913275075 \tabularnewline
89 & 240 & 243.998508396941 & -3.99850839694082 \tabularnewline
90 & 238 & 236.357885995989 & 1.64211400401120 \tabularnewline
91 & 222 & 221.994522913074 & 0.00547708692633364 \tabularnewline
92 & 203 & 209.830381508620 & -6.83038150861972 \tabularnewline
93 & 209 & 206.783332018890 & 2.21666798110974 \tabularnewline
94 & 214 & 207.898149750457 & 6.10185024954319 \tabularnewline
95 & 216 & 205.485556445498 & 10.5144435545020 \tabularnewline
96 & 214 & 203.483084454116 & 10.5169155458839 \tabularnewline
97 & 206 & 204.543132671038 & 1.45686732896226 \tabularnewline
98 & 196 & 208.052531955809 & -12.0525319558091 \tabularnewline
99 & 169 & 185.455340566486 & -16.4553405664857 \tabularnewline
100 & 177 & 176.226748266972 & 0.773251733028019 \tabularnewline
101 & 193 & 190.027725369628 & 2.97227463037163 \tabularnewline
102 & 183 & 188.548670045437 & -5.54867004543664 \tabularnewline
103 & 164 & 171.547067692069 & -7.54706769206913 \tabularnewline
104 & 142 & 154.219947267134 & -12.2199472671343 \tabularnewline
105 & 141 & 148.160059889812 & -7.16005988981192 \tabularnewline
106 & 137 & 142.079166652793 & -5.07916665279262 \tabularnewline
107 & 140 & 132.929680915740 & 7.07031908426043 \tabularnewline
108 & 146 & 128.670249561701 & 17.3297504382987 \tabularnewline
109 & 136 & 130.784286195767 & 5.21571380423288 \tabularnewline
110 & 124 & 129.657060689831 & -5.6570606898311 \tabularnewline
111 & 105 & 112.851974654600 & -7.85197465459972 \tabularnewline
112 & 114 & 110.706191524176 & 3.29380847582370 \tabularnewline
113 & 135 & 119.396696857702 & 15.6033031422985 \tabularnewline
114 & 123 & 122.756141378609 & 0.243858621390601 \tabularnewline
115 & 100 & 111.812161686028 & -11.8121616860280 \tabularnewline
116 & 74 & 93.5276024625379 & -19.5276024625379 \tabularnewline
117 & 64 & 80.9839341426352 & -16.9839341426352 \tabularnewline
118 & 57 & 66.5668433464246 & -9.56684334642462 \tabularnewline
119 & 62 & 55.7468704734617 & 6.25312952653834 \tabularnewline
120 & 64 & 52.9738768675282 & 11.0261231324718 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79403&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]353[/C][C]355.767282849865[/C][C]-2.76728284986484[/C][/ROW]
[ROW][C]14[/C][C]350[/C][C]350.972607223685[/C][C]-0.972607223685145[/C][/ROW]
[ROW][C]15[/C][C]343[/C][C]342.696726558656[/C][C]0.303273441344231[/C][/ROW]
[ROW][C]16[/C][C]346[/C][C]345.002598260693[/C][C]0.997401739307008[/C][/ROW]
[ROW][C]17[/C][C]373[/C][C]371.633548826925[/C][C]1.36645117307523[/C][/ROW]
[ROW][C]18[/C][C]363[/C][C]362.170776180986[/C][C]0.829223819013862[/C][/ROW]
[ROW][C]19[/C][C]349[/C][C]354.412772362754[/C][C]-5.4127723627538[/C][/ROW]
[ROW][C]20[/C][C]350[/C][C]341.244794669971[/C][C]8.75520533002879[/C][/ROW]
[ROW][C]21[/C][C]353[/C][C]348.206591605717[/C][C]4.79340839428289[/C][/ROW]
[ROW][C]22[/C][C]356[/C][C]352.027220040909[/C][C]3.97277995909059[/C][/ROW]
[ROW][C]23[/C][C]355[/C][C]356.048526761376[/C][C]-1.04852676137563[/C][/ROW]
[ROW][C]24[/C][C]346[/C][C]358.101527882073[/C][C]-12.1015278820725[/C][/ROW]
[ROW][C]25[/C][C]349[/C][C]353.163049124451[/C][C]-4.16304912445094[/C][/ROW]
[ROW][C]26[/C][C]348[/C][C]348.14586671249[/C][C]-0.145866712490204[/C][/ROW]
[ROW][C]27[/C][C]342[/C][C]340.845472496173[/C][C]1.15452750382741[/C][/ROW]
[ROW][C]28[/C][C]342[/C][C]343.896945517829[/C][C]-1.89694551782912[/C][/ROW]
[ROW][C]29[/C][C]379[/C][C]368.510220257027[/C][C]10.4897797429729[/C][/ROW]
[ROW][C]30[/C][C]375[/C][C]364.509319221991[/C][C]10.4906807780089[/C][/ROW]
[ROW][C]31[/C][C]363[/C][C]360.473742403607[/C][C]2.52625759639295[/C][/ROW]
[ROW][C]32[/C][C]361[/C][C]358.441902544933[/C][C]2.55809745506747[/C][/ROW]
[ROW][C]33[/C][C]363[/C][C]360.743363663273[/C][C]2.25663633672707[/C][/ROW]
[ROW][C]34[/C][C]373[/C][C]363.262610127859[/C][C]9.7373898721409[/C][/ROW]
[ROW][C]35[/C][C]367[/C][C]369.548773316264[/C][C]-2.54877331626426[/C][/ROW]
[ROW][C]36[/C][C]360[/C][C]366.872520210674[/C][C]-6.8725202106736[/C][/ROW]
[ROW][C]37[/C][C]358[/C][C]369.459801567944[/C][C]-11.4598015679443[/C][/ROW]
[ROW][C]38[/C][C]367[/C][C]362.253322192032[/C][C]4.74667780796767[/C][/ROW]
[ROW][C]39[/C][C]357[/C][C]358.951708187976[/C][C]-1.95170818797573[/C][/ROW]
[ROW][C]40[/C][C]346[/C][C]359.695540552882[/C][C]-13.695540552882[/C][/ROW]
[ROW][C]41[/C][C]386[/C][C]383.100963830452[/C][C]2.89903616954751[/C][/ROW]
[ROW][C]42[/C][C]383[/C][C]374.189164943507[/C][C]8.81083505649275[/C][/ROW]
[ROW][C]43[/C][C]367[/C][C]365.649181674783[/C][C]1.35081832521655[/C][/ROW]
[ROW][C]44[/C][C]354[/C][C]362.664797879166[/C][C]-8.6647978791657[/C][/ROW]
[ROW][C]45[/C][C]363[/C][C]357.37638706177[/C][C]5.62361293823028[/C][/ROW]
[ROW][C]46[/C][C]370[/C][C]364.259489099363[/C][C]5.74051090063733[/C][/ROW]
[ROW][C]47[/C][C]361[/C][C]362.628920802497[/C][C]-1.62892080249725[/C][/ROW]
[ROW][C]48[/C][C]354[/C][C]358.155358793036[/C][C]-4.1553587930357[/C][/ROW]
[ROW][C]49[/C][C]363[/C][C]359.87159098948[/C][C]3.1284090105197[/C][/ROW]
[ROW][C]50[/C][C]366[/C][C]367.994159890913[/C][C]-1.99415989091261[/C][/ROW]
[ROW][C]51[/C][C]353[/C][C]357.74376080876[/C][C]-4.74376080876027[/C][/ROW]
[ROW][C]52[/C][C]351[/C][C]351.699854617891[/C][C]-0.699854617890765[/C][/ROW]
[ROW][C]53[/C][C]389[/C][C]390.328664004253[/C][C]-1.3286640042528[/C][/ROW]
[ROW][C]54[/C][C]385[/C][C]381.119998782689[/C][C]3.88000121731147[/C][/ROW]
[ROW][C]55[/C][C]364[/C][C]366.461864237559[/C][C]-2.46186423755927[/C][/ROW]
[ROW][C]56[/C][C]348[/C][C]356.884978325654[/C][C]-8.88497832565406[/C][/ROW]
[ROW][C]57[/C][C]347[/C][C]356.723802955268[/C][C]-9.7238029552684[/C][/ROW]
[ROW][C]58[/C][C]352[/C][C]353.252208419052[/C][C]-1.25220841905212[/C][/ROW]
[ROW][C]59[/C][C]342[/C][C]343.611797838406[/C][C]-1.61179783840635[/C][/ROW]
[ROW][C]60[/C][C]338[/C][C]337.135788903484[/C][C]0.864211096516442[/C][/ROW]
[ROW][C]61[/C][C]343[/C][C]343.386242183586[/C][C]-0.386242183586432[/C][/ROW]
[ROW][C]62[/C][C]354[/C][C]345.924702118619[/C][C]8.07529788138129[/C][/ROW]
[ROW][C]63[/C][C]329[/C][C]340.31550124668[/C][C]-11.3155012466801[/C][/ROW]
[ROW][C]64[/C][C]320[/C][C]330.948138572574[/C][C]-10.9481385725744[/C][/ROW]
[ROW][C]65[/C][C]353[/C][C]358.547533529034[/C][C]-5.54753352903435[/C][/ROW]
[ROW][C]66[/C][C]345[/C][C]347.600449935565[/C][C]-2.60044993556534[/C][/ROW]
[ROW][C]67[/C][C]324[/C][C]326.538974496149[/C][C]-2.53897449614863[/C][/ROW]
[ROW][C]68[/C][C]310[/C][C]313.558180460462[/C][C]-3.55818046046221[/C][/ROW]
[ROW][C]69[/C][C]314[/C][C]313.964775078003[/C][C]0.035224921996587[/C][/ROW]
[ROW][C]70[/C][C]313[/C][C]317.794813879693[/C][C]-4.79481387969338[/C][/ROW]
[ROW][C]71[/C][C]310[/C][C]305.295429512083[/C][C]4.70457048791684[/C][/ROW]
[ROW][C]72[/C][C]301[/C][C]302.816092223163[/C][C]-1.81609222316257[/C][/ROW]
[ROW][C]73[/C][C]294[/C][C]305.002581965368[/C][C]-11.0025819653684[/C][/ROW]
[ROW][C]74[/C][C]296[/C][C]301.745160956462[/C][C]-5.74516095646209[/C][/ROW]
[ROW][C]75[/C][C]274[/C][C]280.558513439322[/C][C]-6.55851343932233[/C][/ROW]
[ROW][C]76[/C][C]269[/C][C]272.311739771828[/C][C]-3.31173977182817[/C][/ROW]
[ROW][C]77[/C][C]292[/C][C]298.815311980841[/C][C]-6.81531198084105[/C][/ROW]
[ROW][C]78[/C][C]287[/C][C]287.062628017994[/C][C]-0.0626280179935748[/C][/ROW]
[ROW][C]79[/C][C]271[/C][C]268.756571786857[/C][C]2.24342821314326[/C][/ROW]
[ROW][C]80[/C][C]256[/C][C]258.400939301071[/C][C]-2.40093930107082[/C][/ROW]
[ROW][C]81[/C][C]260[/C][C]258.403949679111[/C][C]1.59605032088905[/C][/ROW]
[ROW][C]82[/C][C]265[/C][C]259.113799023346[/C][C]5.88620097665410[/C][/ROW]
[ROW][C]83[/C][C]263[/C][C]256.409140039636[/C][C]6.59085996036379[/C][/ROW]
[ROW][C]84[/C][C]256[/C][C]252.542827425169[/C][C]3.45717257483091[/C][/ROW]
[ROW][C]85[/C][C]246[/C][C]253.26125691526[/C][C]-7.26125691525982[/C][/ROW]
[ROW][C]86[/C][C]245[/C][C]252.552456822219[/C][C]-7.55245682221889[/C][/ROW]
[ROW][C]87[/C][C]220[/C][C]231.830451932749[/C][C]-11.8304519327494[/C][/ROW]
[ROW][C]88[/C][C]224[/C][C]220.875750867249[/C][C]3.12424913275075[/C][/ROW]
[ROW][C]89[/C][C]240[/C][C]243.998508396941[/C][C]-3.99850839694082[/C][/ROW]
[ROW][C]90[/C][C]238[/C][C]236.357885995989[/C][C]1.64211400401120[/C][/ROW]
[ROW][C]91[/C][C]222[/C][C]221.994522913074[/C][C]0.00547708692633364[/C][/ROW]
[ROW][C]92[/C][C]203[/C][C]209.830381508620[/C][C]-6.83038150861972[/C][/ROW]
[ROW][C]93[/C][C]209[/C][C]206.783332018890[/C][C]2.21666798110974[/C][/ROW]
[ROW][C]94[/C][C]214[/C][C]207.898149750457[/C][C]6.10185024954319[/C][/ROW]
[ROW][C]95[/C][C]216[/C][C]205.485556445498[/C][C]10.5144435545020[/C][/ROW]
[ROW][C]96[/C][C]214[/C][C]203.483084454116[/C][C]10.5169155458839[/C][/ROW]
[ROW][C]97[/C][C]206[/C][C]204.543132671038[/C][C]1.45686732896226[/C][/ROW]
[ROW][C]98[/C][C]196[/C][C]208.052531955809[/C][C]-12.0525319558091[/C][/ROW]
[ROW][C]99[/C][C]169[/C][C]185.455340566486[/C][C]-16.4553405664857[/C][/ROW]
[ROW][C]100[/C][C]177[/C][C]176.226748266972[/C][C]0.773251733028019[/C][/ROW]
[ROW][C]101[/C][C]193[/C][C]190.027725369628[/C][C]2.97227463037163[/C][/ROW]
[ROW][C]102[/C][C]183[/C][C]188.548670045437[/C][C]-5.54867004543664[/C][/ROW]
[ROW][C]103[/C][C]164[/C][C]171.547067692069[/C][C]-7.54706769206913[/C][/ROW]
[ROW][C]104[/C][C]142[/C][C]154.219947267134[/C][C]-12.2199472671343[/C][/ROW]
[ROW][C]105[/C][C]141[/C][C]148.160059889812[/C][C]-7.16005988981192[/C][/ROW]
[ROW][C]106[/C][C]137[/C][C]142.079166652793[/C][C]-5.07916665279262[/C][/ROW]
[ROW][C]107[/C][C]140[/C][C]132.929680915740[/C][C]7.07031908426043[/C][/ROW]
[ROW][C]108[/C][C]146[/C][C]128.670249561701[/C][C]17.3297504382987[/C][/ROW]
[ROW][C]109[/C][C]136[/C][C]130.784286195767[/C][C]5.21571380423288[/C][/ROW]
[ROW][C]110[/C][C]124[/C][C]129.657060689831[/C][C]-5.6570606898311[/C][/ROW]
[ROW][C]111[/C][C]105[/C][C]112.851974654600[/C][C]-7.85197465459972[/C][/ROW]
[ROW][C]112[/C][C]114[/C][C]110.706191524176[/C][C]3.29380847582370[/C][/ROW]
[ROW][C]113[/C][C]135[/C][C]119.396696857702[/C][C]15.6033031422985[/C][/ROW]
[ROW][C]114[/C][C]123[/C][C]122.756141378609[/C][C]0.243858621390601[/C][/ROW]
[ROW][C]115[/C][C]100[/C][C]111.812161686028[/C][C]-11.8121616860280[/C][/ROW]
[ROW][C]116[/C][C]74[/C][C]93.5276024625379[/C][C]-19.5276024625379[/C][/ROW]
[ROW][C]117[/C][C]64[/C][C]80.9839341426352[/C][C]-16.9839341426352[/C][/ROW]
[ROW][C]118[/C][C]57[/C][C]66.5668433464246[/C][C]-9.56684334642462[/C][/ROW]
[ROW][C]119[/C][C]62[/C][C]55.7468704734617[/C][C]6.25312952653834[/C][/ROW]
[ROW][C]120[/C][C]64[/C][C]52.9738768675282[/C][C]11.0261231324718[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79403&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79403&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
13353355.767282849865-2.76728284986484
14350350.972607223685-0.972607223685145
15343342.6967265586560.303273441344231
16346345.0025982606930.997401739307008
17373371.6335488269251.36645117307523
18363362.1707761809860.829223819013862
19349354.412772362754-5.4127723627538
20350341.2447946699718.75520533002879
21353348.2065916057174.79340839428289
22356352.0272200409093.97277995909059
23355356.048526761376-1.04852676137563
24346358.101527882073-12.1015278820725
25349353.163049124451-4.16304912445094
26348348.14586671249-0.145866712490204
27342340.8454724961731.15452750382741
28342343.896945517829-1.89694551782912
29379368.51022025702710.4897797429729
30375364.50931922199110.4906807780089
31363360.4737424036072.52625759639295
32361358.4419025449332.55809745506747
33363360.7433636632732.25663633672707
34373363.2626101278599.7373898721409
35367369.548773316264-2.54877331626426
36360366.872520210674-6.8725202106736
37358369.459801567944-11.4598015679443
38367362.2533221920324.74667780796767
39357358.951708187976-1.95170818797573
40346359.695540552882-13.695540552882
41386383.1009638304522.89903616954751
42383374.1891649435078.81083505649275
43367365.6491816747831.35081832521655
44354362.664797879166-8.6647978791657
45363357.376387061775.62361293823028
46370364.2594890993635.74051090063733
47361362.628920802497-1.62892080249725
48354358.155358793036-4.1553587930357
49363359.871590989483.1284090105197
50366367.994159890913-1.99415989091261
51353357.74376080876-4.74376080876027
52351351.699854617891-0.699854617890765
53389390.328664004253-1.3286640042528
54385381.1199987826893.88000121731147
55364366.461864237559-2.46186423755927
56348356.884978325654-8.88497832565406
57347356.723802955268-9.7238029552684
58352353.252208419052-1.25220841905212
59342343.611797838406-1.61179783840635
60338337.1357889034840.864211096516442
61343343.386242183586-0.386242183586432
62354345.9247021186198.07529788138129
63329340.31550124668-11.3155012466801
64320330.948138572574-10.9481385725744
65353358.547533529034-5.54753352903435
66345347.600449935565-2.60044993556534
67324326.538974496149-2.53897449614863
68310313.558180460462-3.55818046046221
69314313.9647750780030.035224921996587
70313317.794813879693-4.79481387969338
71310305.2954295120834.70457048791684
72301302.816092223163-1.81609222316257
73294305.002581965368-11.0025819653684
74296301.745160956462-5.74516095646209
75274280.558513439322-6.55851343932233
76269272.311739771828-3.31173977182817
77292298.815311980841-6.81531198084105
78287287.062628017994-0.0626280179935748
79271268.7565717868572.24342821314326
80256258.400939301071-2.40093930107082
81260258.4039496791111.59605032088905
82265259.1137990233465.88620097665410
83263256.4091400396366.59085996036379
84256252.5428274251693.45717257483091
85246253.26125691526-7.26125691525982
86245252.552456822219-7.55245682221889
87220231.830451932749-11.8304519327494
88224220.8757508672493.12424913275075
89240243.998508396941-3.99850839694082
90238236.3578859959891.64211400401120
91222221.9945229130740.00547708692633364
92203209.830381508620-6.83038150861972
93209206.7833320188902.21666798110974
94214207.8981497504576.10185024954319
95216205.48555644549810.5144435545020
96214203.48308445411610.5169155458839
97206204.5431326710381.45686732896226
98196208.052531955809-12.0525319558091
99169185.455340566486-16.4553405664857
100177176.2267482669720.773251733028019
101193190.0277253696282.97227463037163
102183188.548670045437-5.54867004543664
103164171.547067692069-7.54706769206913
104142154.219947267134-12.2199472671343
105141148.160059889812-7.16005988981192
106137142.079166652793-5.07916665279262
107140132.9296809157407.07031908426043
108146128.67024956170117.3297504382987
109136130.7842861957675.21571380423288
110124129.657060689831-5.6570606898311
111105112.851974654600-7.85197465459972
112114110.7061915241763.29380847582370
113135119.39669685770215.6033031422985
114123122.7561413786090.243858621390601
115100111.812161686028-11.8121616860280
1167493.5276024625379-19.5276024625379
1176480.9839341426352-16.9839341426352
1185766.5668433464246-9.56684334642462
1196255.74687047346176.25312952653834
1206452.973876867528211.0261231324718







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12150.131002250578536.365989432547163.89601506861
12242.713432293229226.479247831865258.9476167545932
12333.859797452271215.786261151769251.9333337527731
12431.79572819471649.8940895729900953.6973668164428
12529.66830220815742.7962481456111856.5403562707036
12621.623822752465-6.5099954432288849.7576409481589
12713.7602879246225-14.522701047689142.0432768969341
1287.12817126818914-20.906598233129135.1629407695074
1292.17906971793759-29.743800889283534.1019403251587
130-3.40015302711963-39.88754180677933.0872357525397
131-10.4762434400666-54.699434964018533.7469480838852
132-17.6446353131815-64.294776088185129.0055054618220

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 50.1310022505785 & 36.3659894325471 & 63.89601506861 \tabularnewline
122 & 42.7134322932292 & 26.4792478318652 & 58.9476167545932 \tabularnewline
123 & 33.8597974522712 & 15.7862611517692 & 51.9333337527731 \tabularnewline
124 & 31.7957281947164 & 9.89408957299009 & 53.6973668164428 \tabularnewline
125 & 29.6683022081574 & 2.79624814561118 & 56.5403562707036 \tabularnewline
126 & 21.623822752465 & -6.50999544322888 & 49.7576409481589 \tabularnewline
127 & 13.7602879246225 & -14.5227010476891 & 42.0432768969341 \tabularnewline
128 & 7.12817126818914 & -20.9065982331291 & 35.1629407695074 \tabularnewline
129 & 2.17906971793759 & -29.7438008892835 & 34.1019403251587 \tabularnewline
130 & -3.40015302711963 & -39.887541806779 & 33.0872357525397 \tabularnewline
131 & -10.4762434400666 & -54.6994349640185 & 33.7469480838852 \tabularnewline
132 & -17.6446353131815 & -64.2947760881851 & 29.0055054618220 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79403&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]121[/C][C]50.1310022505785[/C][C]36.3659894325471[/C][C]63.89601506861[/C][/ROW]
[ROW][C]122[/C][C]42.7134322932292[/C][C]26.4792478318652[/C][C]58.9476167545932[/C][/ROW]
[ROW][C]123[/C][C]33.8597974522712[/C][C]15.7862611517692[/C][C]51.9333337527731[/C][/ROW]
[ROW][C]124[/C][C]31.7957281947164[/C][C]9.89408957299009[/C][C]53.6973668164428[/C][/ROW]
[ROW][C]125[/C][C]29.6683022081574[/C][C]2.79624814561118[/C][C]56.5403562707036[/C][/ROW]
[ROW][C]126[/C][C]21.623822752465[/C][C]-6.50999544322888[/C][C]49.7576409481589[/C][/ROW]
[ROW][C]127[/C][C]13.7602879246225[/C][C]-14.5227010476891[/C][C]42.0432768969341[/C][/ROW]
[ROW][C]128[/C][C]7.12817126818914[/C][C]-20.9065982331291[/C][C]35.1629407695074[/C][/ROW]
[ROW][C]129[/C][C]2.17906971793759[/C][C]-29.7438008892835[/C][C]34.1019403251587[/C][/ROW]
[ROW][C]130[/C][C]-3.40015302711963[/C][C]-39.887541806779[/C][C]33.0872357525397[/C][/ROW]
[ROW][C]131[/C][C]-10.4762434400666[/C][C]-54.6994349640185[/C][C]33.7469480838852[/C][/ROW]
[ROW][C]132[/C][C]-17.6446353131815[/C][C]-64.2947760881851[/C][C]29.0055054618220[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79403&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79403&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
12150.131002250578536.365989432547163.89601506861
12242.713432293229226.479247831865258.9476167545932
12333.859797452271215.786261151769251.9333337527731
12431.79572819471649.8940895729900953.6973668164428
12529.66830220815742.7962481456111856.5403562707036
12621.623822752465-6.5099954432288849.7576409481589
12713.7602879246225-14.522701047689142.0432768969341
1287.12817126818914-20.906598233129135.1629407695074
1292.17906971793759-29.743800889283534.1019403251587
130-3.40015302711963-39.88754180677933.0872357525397
131-10.4762434400666-54.699434964018533.7469480838852
132-17.6446353131815-64.294776088185129.0055054618220



Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
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')