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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 20:45:19 +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/19/t12822507590s3cwrgfwvxl1pa.htm/, Retrieved Fri, 03 May 2024 05:36:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79381, Retrieved Fri, 03 May 2024 05:36:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Boxel Dieter
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdsreeks A - St...] [2010-08-19 20:45:19] [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=79381&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=79381&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79381&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
alpha0.658681111002325
beta0.0625489335806356
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.658681111002325 \tabularnewline
beta & 0.0625489335806356 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79381&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]0.658681111002325[/C][/ROW]
[ROW][C]beta[/C][C]0.0625489335806356[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79381&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79381&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
alpha0.658681111002325
beta0.0625489335806356
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13353355.748664529915-2.74866452991461
14350350.827694757025-0.82769475702463
15343342.5962639623470.403736037653118
16346344.984253882731.01574611727017
17373371.7755451535951.22445484640519
18363362.2964228847910.703577115208532
19349354.503195530486-5.50319553048615
20350340.8532870464439.1467129535572
21353348.5631726461514.43682735384903
22356352.3952086373453.60479136265491
23355356.327714924480-1.32771492448035
24346358.039904232956-12.0399042329558
25349352.595297336999-3.59529733699878
26348347.6587023504610.341297649539058
27342340.5521101738561.44788982614432
28342343.814308810741-1.81430881074141
29379368.67368862755910.3263113724408
30375365.2479526357509.75204736425047
31363361.9050388652061.09496113479446
32361358.482090664642.51790933536017
33363360.8256188548762.17438114512356
34373363.3977055724669.60229442753405
35367370.358463117726-3.35846311772599
36360367.754464817046-7.75446481704563
37358368.869159432285-10.8691594322851
38367361.0396211073425.96037889265807
39357358.797995448988-1.79799544898844
40346359.461093954553-13.4610939545531
41386380.9652873572805.03471264272036
42383373.8125632383379.18743676166332
43367367.074157386902-0.0741573869016179
44354363.249877859877-9.24987785987696
45363357.1231696160775.87683038392254
46370364.2200523629095.7799476370912
47361363.632646526404-2.63264652640419
48354359.429490602323-5.42949060232343
49363360.5314852997382.46851470026229
50366367.299957423934-1.29995742393447
51353357.397378361618-4.39737836161828
52351352.029755257315-1.02975525731483
53389388.2096521236870.790347876313376
54385379.678228623895.32177137611029
55364367.07274066793-3.07274066792979
56348357.858278913217-9.8582789132165
57347356.185568294151-9.18556829415104
58352352.399206459288-0.399206459287768
59342343.686892149996-1.68689214999563
60338338.007596854715-0.00759685471535931
61343344.455535686608-1.45553568660756
62354346.2702958702937.7297041297071
63329340.547432945162-11.5474329451620
64320330.614313400402-10.6143134004017
65353359.702072631114-6.70207263111399
66345346.073301658595-1.07330165859537
67324324.417926586511-0.417926586511101
68310312.773118377198-2.7731183771981
69314314.425795249205-0.425795249205464
70313318.198099858792-5.19809985879226
71310304.4774383540915.52256164590949
72301303.009182051353-2.00918205135287
73294306.45117348886-12.4511734888599
74296302.512060348188-6.51206034818756
75274278.595657051527-4.5956570515267
76269271.61333597285-2.61333597284994
77292305.68945192654-13.6894519265402
78287287.474495763584-0.474495763584343
79271264.5569691110376.44303088896265
80256255.0298770277820.970122972217894
81260258.5059672706111.49403272938935
82265260.5496704074354.45032959256486
83263255.8766465899177.1233534100827
84256251.9912626787824.00873732121761
85246255.180219583985-9.18021958398452
86245254.904640710207-9.90464071020656
87220228.749827035597-8.74982703559684
88224218.8787988877885.12120111221154
89240253.758644722309-13.7586447223085
90238239.495399990311-1.49539999031083
91222217.7112177309454.28878226905451
92203204.253113520854-1.25311352085350
93209205.7079808726573.29201912734322
94214209.2834610264484.71653897355239
95216205.04754297086410.9524570291362
96214202.12840344136511.871596558635
97206205.825948781970.174051218029859
98196211.681098570010-15.6810985700105
99169182.094117811691-13.0941178116913
100177173.8955642665263.10443573347391
101193200.719399464561-7.71939946456064
102183194.585026907671-11.5850269076714
103164167.6788163532-3.67881635320
104142146.302355948336-4.30235594833587
105141146.395760586422-5.39576058642174
106137143.472721131887-6.47272113188671
107140132.2718313854037.7281686145974
108146125.68653958664920.3134604133506
109136129.4436970445526.55630295544839
110124132.845709923259-8.84570992325857
111105107.680329139749-2.68032913974920
112114111.3353329963092.66466700369078
113135133.62232226031.37767773969989
114123131.982609556056-8.98260955605616
115100109.418318830872-9.41831883087198
1167483.741282029476-9.741282029476
1176479.3476377788613-15.3476377788613
1185768.5605511026289-11.5605511026289
1196257.70447146768714.29552853231285
1206451.861373910028312.1386260899717

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 353 & 355.748664529915 & -2.74866452991461 \tabularnewline
14 & 350 & 350.827694757025 & -0.82769475702463 \tabularnewline
15 & 343 & 342.596263962347 & 0.403736037653118 \tabularnewline
16 & 346 & 344.98425388273 & 1.01574611727017 \tabularnewline
17 & 373 & 371.775545153595 & 1.22445484640519 \tabularnewline
18 & 363 & 362.296422884791 & 0.703577115208532 \tabularnewline
19 & 349 & 354.503195530486 & -5.50319553048615 \tabularnewline
20 & 350 & 340.853287046443 & 9.1467129535572 \tabularnewline
21 & 353 & 348.563172646151 & 4.43682735384903 \tabularnewline
22 & 356 & 352.395208637345 & 3.60479136265491 \tabularnewline
23 & 355 & 356.327714924480 & -1.32771492448035 \tabularnewline
24 & 346 & 358.039904232956 & -12.0399042329558 \tabularnewline
25 & 349 & 352.595297336999 & -3.59529733699878 \tabularnewline
26 & 348 & 347.658702350461 & 0.341297649539058 \tabularnewline
27 & 342 & 340.552110173856 & 1.44788982614432 \tabularnewline
28 & 342 & 343.814308810741 & -1.81430881074141 \tabularnewline
29 & 379 & 368.673688627559 & 10.3263113724408 \tabularnewline
30 & 375 & 365.247952635750 & 9.75204736425047 \tabularnewline
31 & 363 & 361.905038865206 & 1.09496113479446 \tabularnewline
32 & 361 & 358.48209066464 & 2.51790933536017 \tabularnewline
33 & 363 & 360.825618854876 & 2.17438114512356 \tabularnewline
34 & 373 & 363.397705572466 & 9.60229442753405 \tabularnewline
35 & 367 & 370.358463117726 & -3.35846311772599 \tabularnewline
36 & 360 & 367.754464817046 & -7.75446481704563 \tabularnewline
37 & 358 & 368.869159432285 & -10.8691594322851 \tabularnewline
38 & 367 & 361.039621107342 & 5.96037889265807 \tabularnewline
39 & 357 & 358.797995448988 & -1.79799544898844 \tabularnewline
40 & 346 & 359.461093954553 & -13.4610939545531 \tabularnewline
41 & 386 & 380.965287357280 & 5.03471264272036 \tabularnewline
42 & 383 & 373.812563238337 & 9.18743676166332 \tabularnewline
43 & 367 & 367.074157386902 & -0.0741573869016179 \tabularnewline
44 & 354 & 363.249877859877 & -9.24987785987696 \tabularnewline
45 & 363 & 357.123169616077 & 5.87683038392254 \tabularnewline
46 & 370 & 364.220052362909 & 5.7799476370912 \tabularnewline
47 & 361 & 363.632646526404 & -2.63264652640419 \tabularnewline
48 & 354 & 359.429490602323 & -5.42949060232343 \tabularnewline
49 & 363 & 360.531485299738 & 2.46851470026229 \tabularnewline
50 & 366 & 367.299957423934 & -1.29995742393447 \tabularnewline
51 & 353 & 357.397378361618 & -4.39737836161828 \tabularnewline
52 & 351 & 352.029755257315 & -1.02975525731483 \tabularnewline
53 & 389 & 388.209652123687 & 0.790347876313376 \tabularnewline
54 & 385 & 379.67822862389 & 5.32177137611029 \tabularnewline
55 & 364 & 367.07274066793 & -3.07274066792979 \tabularnewline
56 & 348 & 357.858278913217 & -9.8582789132165 \tabularnewline
57 & 347 & 356.185568294151 & -9.18556829415104 \tabularnewline
58 & 352 & 352.399206459288 & -0.399206459287768 \tabularnewline
59 & 342 & 343.686892149996 & -1.68689214999563 \tabularnewline
60 & 338 & 338.007596854715 & -0.00759685471535931 \tabularnewline
61 & 343 & 344.455535686608 & -1.45553568660756 \tabularnewline
62 & 354 & 346.270295870293 & 7.7297041297071 \tabularnewline
63 & 329 & 340.547432945162 & -11.5474329451620 \tabularnewline
64 & 320 & 330.614313400402 & -10.6143134004017 \tabularnewline
65 & 353 & 359.702072631114 & -6.70207263111399 \tabularnewline
66 & 345 & 346.073301658595 & -1.07330165859537 \tabularnewline
67 & 324 & 324.417926586511 & -0.417926586511101 \tabularnewline
68 & 310 & 312.773118377198 & -2.7731183771981 \tabularnewline
69 & 314 & 314.425795249205 & -0.425795249205464 \tabularnewline
70 & 313 & 318.198099858792 & -5.19809985879226 \tabularnewline
71 & 310 & 304.477438354091 & 5.52256164590949 \tabularnewline
72 & 301 & 303.009182051353 & -2.00918205135287 \tabularnewline
73 & 294 & 306.45117348886 & -12.4511734888599 \tabularnewline
74 & 296 & 302.512060348188 & -6.51206034818756 \tabularnewline
75 & 274 & 278.595657051527 & -4.5956570515267 \tabularnewline
76 & 269 & 271.61333597285 & -2.61333597284994 \tabularnewline
77 & 292 & 305.68945192654 & -13.6894519265402 \tabularnewline
78 & 287 & 287.474495763584 & -0.474495763584343 \tabularnewline
79 & 271 & 264.556969111037 & 6.44303088896265 \tabularnewline
80 & 256 & 255.029877027782 & 0.970122972217894 \tabularnewline
81 & 260 & 258.505967270611 & 1.49403272938935 \tabularnewline
82 & 265 & 260.549670407435 & 4.45032959256486 \tabularnewline
83 & 263 & 255.876646589917 & 7.1233534100827 \tabularnewline
84 & 256 & 251.991262678782 & 4.00873732121761 \tabularnewline
85 & 246 & 255.180219583985 & -9.18021958398452 \tabularnewline
86 & 245 & 254.904640710207 & -9.90464071020656 \tabularnewline
87 & 220 & 228.749827035597 & -8.74982703559684 \tabularnewline
88 & 224 & 218.878798887788 & 5.12120111221154 \tabularnewline
89 & 240 & 253.758644722309 & -13.7586447223085 \tabularnewline
90 & 238 & 239.495399990311 & -1.49539999031083 \tabularnewline
91 & 222 & 217.711217730945 & 4.28878226905451 \tabularnewline
92 & 203 & 204.253113520854 & -1.25311352085350 \tabularnewline
93 & 209 & 205.707980872657 & 3.29201912734322 \tabularnewline
94 & 214 & 209.283461026448 & 4.71653897355239 \tabularnewline
95 & 216 & 205.047542970864 & 10.9524570291362 \tabularnewline
96 & 214 & 202.128403441365 & 11.871596558635 \tabularnewline
97 & 206 & 205.82594878197 & 0.174051218029859 \tabularnewline
98 & 196 & 211.681098570010 & -15.6810985700105 \tabularnewline
99 & 169 & 182.094117811691 & -13.0941178116913 \tabularnewline
100 & 177 & 173.895564266526 & 3.10443573347391 \tabularnewline
101 & 193 & 200.719399464561 & -7.71939946456064 \tabularnewline
102 & 183 & 194.585026907671 & -11.5850269076714 \tabularnewline
103 & 164 & 167.6788163532 & -3.67881635320 \tabularnewline
104 & 142 & 146.302355948336 & -4.30235594833587 \tabularnewline
105 & 141 & 146.395760586422 & -5.39576058642174 \tabularnewline
106 & 137 & 143.472721131887 & -6.47272113188671 \tabularnewline
107 & 140 & 132.271831385403 & 7.7281686145974 \tabularnewline
108 & 146 & 125.686539586649 & 20.3134604133506 \tabularnewline
109 & 136 & 129.443697044552 & 6.55630295544839 \tabularnewline
110 & 124 & 132.845709923259 & -8.84570992325857 \tabularnewline
111 & 105 & 107.680329139749 & -2.68032913974920 \tabularnewline
112 & 114 & 111.335332996309 & 2.66466700369078 \tabularnewline
113 & 135 & 133.6223222603 & 1.37767773969989 \tabularnewline
114 & 123 & 131.982609556056 & -8.98260955605616 \tabularnewline
115 & 100 & 109.418318830872 & -9.41831883087198 \tabularnewline
116 & 74 & 83.741282029476 & -9.741282029476 \tabularnewline
117 & 64 & 79.3476377788613 & -15.3476377788613 \tabularnewline
118 & 57 & 68.5605511026289 & -11.5605511026289 \tabularnewline
119 & 62 & 57.7044714676871 & 4.29552853231285 \tabularnewline
120 & 64 & 51.8613739100283 & 12.1386260899717 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79381&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]355.748664529915[/C][C]-2.74866452991461[/C][/ROW]
[ROW][C]14[/C][C]350[/C][C]350.827694757025[/C][C]-0.82769475702463[/C][/ROW]
[ROW][C]15[/C][C]343[/C][C]342.596263962347[/C][C]0.403736037653118[/C][/ROW]
[ROW][C]16[/C][C]346[/C][C]344.98425388273[/C][C]1.01574611727017[/C][/ROW]
[ROW][C]17[/C][C]373[/C][C]371.775545153595[/C][C]1.22445484640519[/C][/ROW]
[ROW][C]18[/C][C]363[/C][C]362.296422884791[/C][C]0.703577115208532[/C][/ROW]
[ROW][C]19[/C][C]349[/C][C]354.503195530486[/C][C]-5.50319553048615[/C][/ROW]
[ROW][C]20[/C][C]350[/C][C]340.853287046443[/C][C]9.1467129535572[/C][/ROW]
[ROW][C]21[/C][C]353[/C][C]348.563172646151[/C][C]4.43682735384903[/C][/ROW]
[ROW][C]22[/C][C]356[/C][C]352.395208637345[/C][C]3.60479136265491[/C][/ROW]
[ROW][C]23[/C][C]355[/C][C]356.327714924480[/C][C]-1.32771492448035[/C][/ROW]
[ROW][C]24[/C][C]346[/C][C]358.039904232956[/C][C]-12.0399042329558[/C][/ROW]
[ROW][C]25[/C][C]349[/C][C]352.595297336999[/C][C]-3.59529733699878[/C][/ROW]
[ROW][C]26[/C][C]348[/C][C]347.658702350461[/C][C]0.341297649539058[/C][/ROW]
[ROW][C]27[/C][C]342[/C][C]340.552110173856[/C][C]1.44788982614432[/C][/ROW]
[ROW][C]28[/C][C]342[/C][C]343.814308810741[/C][C]-1.81430881074141[/C][/ROW]
[ROW][C]29[/C][C]379[/C][C]368.673688627559[/C][C]10.3263113724408[/C][/ROW]
[ROW][C]30[/C][C]375[/C][C]365.247952635750[/C][C]9.75204736425047[/C][/ROW]
[ROW][C]31[/C][C]363[/C][C]361.905038865206[/C][C]1.09496113479446[/C][/ROW]
[ROW][C]32[/C][C]361[/C][C]358.48209066464[/C][C]2.51790933536017[/C][/ROW]
[ROW][C]33[/C][C]363[/C][C]360.825618854876[/C][C]2.17438114512356[/C][/ROW]
[ROW][C]34[/C][C]373[/C][C]363.397705572466[/C][C]9.60229442753405[/C][/ROW]
[ROW][C]35[/C][C]367[/C][C]370.358463117726[/C][C]-3.35846311772599[/C][/ROW]
[ROW][C]36[/C][C]360[/C][C]367.754464817046[/C][C]-7.75446481704563[/C][/ROW]
[ROW][C]37[/C][C]358[/C][C]368.869159432285[/C][C]-10.8691594322851[/C][/ROW]
[ROW][C]38[/C][C]367[/C][C]361.039621107342[/C][C]5.96037889265807[/C][/ROW]
[ROW][C]39[/C][C]357[/C][C]358.797995448988[/C][C]-1.79799544898844[/C][/ROW]
[ROW][C]40[/C][C]346[/C][C]359.461093954553[/C][C]-13.4610939545531[/C][/ROW]
[ROW][C]41[/C][C]386[/C][C]380.965287357280[/C][C]5.03471264272036[/C][/ROW]
[ROW][C]42[/C][C]383[/C][C]373.812563238337[/C][C]9.18743676166332[/C][/ROW]
[ROW][C]43[/C][C]367[/C][C]367.074157386902[/C][C]-0.0741573869016179[/C][/ROW]
[ROW][C]44[/C][C]354[/C][C]363.249877859877[/C][C]-9.24987785987696[/C][/ROW]
[ROW][C]45[/C][C]363[/C][C]357.123169616077[/C][C]5.87683038392254[/C][/ROW]
[ROW][C]46[/C][C]370[/C][C]364.220052362909[/C][C]5.7799476370912[/C][/ROW]
[ROW][C]47[/C][C]361[/C][C]363.632646526404[/C][C]-2.63264652640419[/C][/ROW]
[ROW][C]48[/C][C]354[/C][C]359.429490602323[/C][C]-5.42949060232343[/C][/ROW]
[ROW][C]49[/C][C]363[/C][C]360.531485299738[/C][C]2.46851470026229[/C][/ROW]
[ROW][C]50[/C][C]366[/C][C]367.299957423934[/C][C]-1.29995742393447[/C][/ROW]
[ROW][C]51[/C][C]353[/C][C]357.397378361618[/C][C]-4.39737836161828[/C][/ROW]
[ROW][C]52[/C][C]351[/C][C]352.029755257315[/C][C]-1.02975525731483[/C][/ROW]
[ROW][C]53[/C][C]389[/C][C]388.209652123687[/C][C]0.790347876313376[/C][/ROW]
[ROW][C]54[/C][C]385[/C][C]379.67822862389[/C][C]5.32177137611029[/C][/ROW]
[ROW][C]55[/C][C]364[/C][C]367.07274066793[/C][C]-3.07274066792979[/C][/ROW]
[ROW][C]56[/C][C]348[/C][C]357.858278913217[/C][C]-9.8582789132165[/C][/ROW]
[ROW][C]57[/C][C]347[/C][C]356.185568294151[/C][C]-9.18556829415104[/C][/ROW]
[ROW][C]58[/C][C]352[/C][C]352.399206459288[/C][C]-0.399206459287768[/C][/ROW]
[ROW][C]59[/C][C]342[/C][C]343.686892149996[/C][C]-1.68689214999563[/C][/ROW]
[ROW][C]60[/C][C]338[/C][C]338.007596854715[/C][C]-0.00759685471535931[/C][/ROW]
[ROW][C]61[/C][C]343[/C][C]344.455535686608[/C][C]-1.45553568660756[/C][/ROW]
[ROW][C]62[/C][C]354[/C][C]346.270295870293[/C][C]7.7297041297071[/C][/ROW]
[ROW][C]63[/C][C]329[/C][C]340.547432945162[/C][C]-11.5474329451620[/C][/ROW]
[ROW][C]64[/C][C]320[/C][C]330.614313400402[/C][C]-10.6143134004017[/C][/ROW]
[ROW][C]65[/C][C]353[/C][C]359.702072631114[/C][C]-6.70207263111399[/C][/ROW]
[ROW][C]66[/C][C]345[/C][C]346.073301658595[/C][C]-1.07330165859537[/C][/ROW]
[ROW][C]67[/C][C]324[/C][C]324.417926586511[/C][C]-0.417926586511101[/C][/ROW]
[ROW][C]68[/C][C]310[/C][C]312.773118377198[/C][C]-2.7731183771981[/C][/ROW]
[ROW][C]69[/C][C]314[/C][C]314.425795249205[/C][C]-0.425795249205464[/C][/ROW]
[ROW][C]70[/C][C]313[/C][C]318.198099858792[/C][C]-5.19809985879226[/C][/ROW]
[ROW][C]71[/C][C]310[/C][C]304.477438354091[/C][C]5.52256164590949[/C][/ROW]
[ROW][C]72[/C][C]301[/C][C]303.009182051353[/C][C]-2.00918205135287[/C][/ROW]
[ROW][C]73[/C][C]294[/C][C]306.45117348886[/C][C]-12.4511734888599[/C][/ROW]
[ROW][C]74[/C][C]296[/C][C]302.512060348188[/C][C]-6.51206034818756[/C][/ROW]
[ROW][C]75[/C][C]274[/C][C]278.595657051527[/C][C]-4.5956570515267[/C][/ROW]
[ROW][C]76[/C][C]269[/C][C]271.61333597285[/C][C]-2.61333597284994[/C][/ROW]
[ROW][C]77[/C][C]292[/C][C]305.68945192654[/C][C]-13.6894519265402[/C][/ROW]
[ROW][C]78[/C][C]287[/C][C]287.474495763584[/C][C]-0.474495763584343[/C][/ROW]
[ROW][C]79[/C][C]271[/C][C]264.556969111037[/C][C]6.44303088896265[/C][/ROW]
[ROW][C]80[/C][C]256[/C][C]255.029877027782[/C][C]0.970122972217894[/C][/ROW]
[ROW][C]81[/C][C]260[/C][C]258.505967270611[/C][C]1.49403272938935[/C][/ROW]
[ROW][C]82[/C][C]265[/C][C]260.549670407435[/C][C]4.45032959256486[/C][/ROW]
[ROW][C]83[/C][C]263[/C][C]255.876646589917[/C][C]7.1233534100827[/C][/ROW]
[ROW][C]84[/C][C]256[/C][C]251.991262678782[/C][C]4.00873732121761[/C][/ROW]
[ROW][C]85[/C][C]246[/C][C]255.180219583985[/C][C]-9.18021958398452[/C][/ROW]
[ROW][C]86[/C][C]245[/C][C]254.904640710207[/C][C]-9.90464071020656[/C][/ROW]
[ROW][C]87[/C][C]220[/C][C]228.749827035597[/C][C]-8.74982703559684[/C][/ROW]
[ROW][C]88[/C][C]224[/C][C]218.878798887788[/C][C]5.12120111221154[/C][/ROW]
[ROW][C]89[/C][C]240[/C][C]253.758644722309[/C][C]-13.7586447223085[/C][/ROW]
[ROW][C]90[/C][C]238[/C][C]239.495399990311[/C][C]-1.49539999031083[/C][/ROW]
[ROW][C]91[/C][C]222[/C][C]217.711217730945[/C][C]4.28878226905451[/C][/ROW]
[ROW][C]92[/C][C]203[/C][C]204.253113520854[/C][C]-1.25311352085350[/C][/ROW]
[ROW][C]93[/C][C]209[/C][C]205.707980872657[/C][C]3.29201912734322[/C][/ROW]
[ROW][C]94[/C][C]214[/C][C]209.283461026448[/C][C]4.71653897355239[/C][/ROW]
[ROW][C]95[/C][C]216[/C][C]205.047542970864[/C][C]10.9524570291362[/C][/ROW]
[ROW][C]96[/C][C]214[/C][C]202.128403441365[/C][C]11.871596558635[/C][/ROW]
[ROW][C]97[/C][C]206[/C][C]205.82594878197[/C][C]0.174051218029859[/C][/ROW]
[ROW][C]98[/C][C]196[/C][C]211.681098570010[/C][C]-15.6810985700105[/C][/ROW]
[ROW][C]99[/C][C]169[/C][C]182.094117811691[/C][C]-13.0941178116913[/C][/ROW]
[ROW][C]100[/C][C]177[/C][C]173.895564266526[/C][C]3.10443573347391[/C][/ROW]
[ROW][C]101[/C][C]193[/C][C]200.719399464561[/C][C]-7.71939946456064[/C][/ROW]
[ROW][C]102[/C][C]183[/C][C]194.585026907671[/C][C]-11.5850269076714[/C][/ROW]
[ROW][C]103[/C][C]164[/C][C]167.6788163532[/C][C]-3.67881635320[/C][/ROW]
[ROW][C]104[/C][C]142[/C][C]146.302355948336[/C][C]-4.30235594833587[/C][/ROW]
[ROW][C]105[/C][C]141[/C][C]146.395760586422[/C][C]-5.39576058642174[/C][/ROW]
[ROW][C]106[/C][C]137[/C][C]143.472721131887[/C][C]-6.47272113188671[/C][/ROW]
[ROW][C]107[/C][C]140[/C][C]132.271831385403[/C][C]7.7281686145974[/C][/ROW]
[ROW][C]108[/C][C]146[/C][C]125.686539586649[/C][C]20.3134604133506[/C][/ROW]
[ROW][C]109[/C][C]136[/C][C]129.443697044552[/C][C]6.55630295544839[/C][/ROW]
[ROW][C]110[/C][C]124[/C][C]132.845709923259[/C][C]-8.84570992325857[/C][/ROW]
[ROW][C]111[/C][C]105[/C][C]107.680329139749[/C][C]-2.68032913974920[/C][/ROW]
[ROW][C]112[/C][C]114[/C][C]111.335332996309[/C][C]2.66466700369078[/C][/ROW]
[ROW][C]113[/C][C]135[/C][C]133.6223222603[/C][C]1.37767773969989[/C][/ROW]
[ROW][C]114[/C][C]123[/C][C]131.982609556056[/C][C]-8.98260955605616[/C][/ROW]
[ROW][C]115[/C][C]100[/C][C]109.418318830872[/C][C]-9.41831883087198[/C][/ROW]
[ROW][C]116[/C][C]74[/C][C]83.741282029476[/C][C]-9.741282029476[/C][/ROW]
[ROW][C]117[/C][C]64[/C][C]79.3476377788613[/C][C]-15.3476377788613[/C][/ROW]
[ROW][C]118[/C][C]57[/C][C]68.5605511026289[/C][C]-11.5605511026289[/C][/ROW]
[ROW][C]119[/C][C]62[/C][C]57.7044714676871[/C][C]4.29552853231285[/C][/ROW]
[ROW][C]120[/C][C]64[/C][C]51.8613739100283[/C][C]12.1386260899717[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79381&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79381&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
13353355.748664529915-2.74866452991461
14350350.827694757025-0.82769475702463
15343342.5962639623470.403736037653118
16346344.984253882731.01574611727017
17373371.7755451535951.22445484640519
18363362.2964228847910.703577115208532
19349354.503195530486-5.50319553048615
20350340.8532870464439.1467129535572
21353348.5631726461514.43682735384903
22356352.3952086373453.60479136265491
23355356.327714924480-1.32771492448035
24346358.039904232956-12.0399042329558
25349352.595297336999-3.59529733699878
26348347.6587023504610.341297649539058
27342340.5521101738561.44788982614432
28342343.814308810741-1.81430881074141
29379368.67368862755910.3263113724408
30375365.2479526357509.75204736425047
31363361.9050388652061.09496113479446
32361358.482090664642.51790933536017
33363360.8256188548762.17438114512356
34373363.3977055724669.60229442753405
35367370.358463117726-3.35846311772599
36360367.754464817046-7.75446481704563
37358368.869159432285-10.8691594322851
38367361.0396211073425.96037889265807
39357358.797995448988-1.79799544898844
40346359.461093954553-13.4610939545531
41386380.9652873572805.03471264272036
42383373.8125632383379.18743676166332
43367367.074157386902-0.0741573869016179
44354363.249877859877-9.24987785987696
45363357.1231696160775.87683038392254
46370364.2200523629095.7799476370912
47361363.632646526404-2.63264652640419
48354359.429490602323-5.42949060232343
49363360.5314852997382.46851470026229
50366367.299957423934-1.29995742393447
51353357.397378361618-4.39737836161828
52351352.029755257315-1.02975525731483
53389388.2096521236870.790347876313376
54385379.678228623895.32177137611029
55364367.07274066793-3.07274066792979
56348357.858278913217-9.8582789132165
57347356.185568294151-9.18556829415104
58352352.399206459288-0.399206459287768
59342343.686892149996-1.68689214999563
60338338.007596854715-0.00759685471535931
61343344.455535686608-1.45553568660756
62354346.2702958702937.7297041297071
63329340.547432945162-11.5474329451620
64320330.614313400402-10.6143134004017
65353359.702072631114-6.70207263111399
66345346.073301658595-1.07330165859537
67324324.417926586511-0.417926586511101
68310312.773118377198-2.7731183771981
69314314.425795249205-0.425795249205464
70313318.198099858792-5.19809985879226
71310304.4774383540915.52256164590949
72301303.009182051353-2.00918205135287
73294306.45117348886-12.4511734888599
74296302.512060348188-6.51206034818756
75274278.595657051527-4.5956570515267
76269271.61333597285-2.61333597284994
77292305.68945192654-13.6894519265402
78287287.474495763584-0.474495763584343
79271264.5569691110376.44303088896265
80256255.0298770277820.970122972217894
81260258.5059672706111.49403272938935
82265260.5496704074354.45032959256486
83263255.8766465899177.1233534100827
84256251.9912626787824.00873732121761
85246255.180219583985-9.18021958398452
86245254.904640710207-9.90464071020656
87220228.749827035597-8.74982703559684
88224218.8787988877885.12120111221154
89240253.758644722309-13.7586447223085
90238239.495399990311-1.49539999031083
91222217.7112177309454.28878226905451
92203204.253113520854-1.25311352085350
93209205.7079808726573.29201912734322
94214209.2834610264484.71653897355239
95216205.04754297086410.9524570291362
96214202.12840344136511.871596558635
97206205.825948781970.174051218029859
98196211.681098570010-15.6810985700105
99169182.094117811691-13.0941178116913
100177173.8955642665263.10443573347391
101193200.719399464561-7.71939946456064
102183194.585026907671-11.5850269076714
103164167.6788163532-3.67881635320
104142146.302355948336-4.30235594833587
105141146.395760586422-5.39576058642174
106137143.472721131887-6.47272113188671
107140132.2718313854037.7281686145974
108146125.68653958664920.3134604133506
109136129.4436970445526.55630295544839
110124132.845709923259-8.84570992325857
111105107.680329139749-2.68032913974920
112114111.3353329963092.66466700369078
113135133.62232226031.37767773969989
114123131.982609556056-8.98260955605616
115100109.418318830872-9.41831883087198
1167483.741282029476-9.741282029476
1176479.3476377788613-15.3476377788613
1185768.5605511026289-11.5605511026289
1196257.70447146768714.29552853231285
1206451.861373910028312.1386260899717







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12143.909154776107330.116352463759657.7019570884551
12235.836348500348219.001029538531852.6716674621646
12317.0669638494532-2.6284330141694236.7623607130758
12422.88736022783480.43008267003235945.3446377856372
12541.44568837401916.279525017321066.6118517307169
12633.77138201767065.9222548060099261.6205092293313
12715.7541508572672-14.769438067466246.2777397820005
128-4.66231768248794-37.863649007492228.5390136425163
129-4.98464670685161-40.875265113940230.905971700237
130-4.16913856730358-42.766542430645134.4282652960379
131-1.32143817223447-42.647501718921440.0046253744524
132-6.81681291113506-50.896674071762237.2630482494921

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 43.9091547761073 & 30.1163524637596 & 57.7019570884551 \tabularnewline
122 & 35.8363485003482 & 19.0010295385318 & 52.6716674621646 \tabularnewline
123 & 17.0669638494532 & -2.62843301416942 & 36.7623607130758 \tabularnewline
124 & 22.8873602278348 & 0.430082670032359 & 45.3446377856372 \tabularnewline
125 & 41.445688374019 & 16.2795250173210 & 66.6118517307169 \tabularnewline
126 & 33.7713820176706 & 5.92225480600992 & 61.6205092293313 \tabularnewline
127 & 15.7541508572672 & -14.7694380674662 & 46.2777397820005 \tabularnewline
128 & -4.66231768248794 & -37.8636490074922 & 28.5390136425163 \tabularnewline
129 & -4.98464670685161 & -40.8752651139402 & 30.905971700237 \tabularnewline
130 & -4.16913856730358 & -42.7665424306451 & 34.4282652960379 \tabularnewline
131 & -1.32143817223447 & -42.6475017189214 & 40.0046253744524 \tabularnewline
132 & -6.81681291113506 & -50.8966740717622 & 37.2630482494921 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79381&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]43.9091547761073[/C][C]30.1163524637596[/C][C]57.7019570884551[/C][/ROW]
[ROW][C]122[/C][C]35.8363485003482[/C][C]19.0010295385318[/C][C]52.6716674621646[/C][/ROW]
[ROW][C]123[/C][C]17.0669638494532[/C][C]-2.62843301416942[/C][C]36.7623607130758[/C][/ROW]
[ROW][C]124[/C][C]22.8873602278348[/C][C]0.430082670032359[/C][C]45.3446377856372[/C][/ROW]
[ROW][C]125[/C][C]41.445688374019[/C][C]16.2795250173210[/C][C]66.6118517307169[/C][/ROW]
[ROW][C]126[/C][C]33.7713820176706[/C][C]5.92225480600992[/C][C]61.6205092293313[/C][/ROW]
[ROW][C]127[/C][C]15.7541508572672[/C][C]-14.7694380674662[/C][C]46.2777397820005[/C][/ROW]
[ROW][C]128[/C][C]-4.66231768248794[/C][C]-37.8636490074922[/C][C]28.5390136425163[/C][/ROW]
[ROW][C]129[/C][C]-4.98464670685161[/C][C]-40.8752651139402[/C][C]30.905971700237[/C][/ROW]
[ROW][C]130[/C][C]-4.16913856730358[/C][C]-42.7665424306451[/C][C]34.4282652960379[/C][/ROW]
[ROW][C]131[/C][C]-1.32143817223447[/C][C]-42.6475017189214[/C][C]40.0046253744524[/C][/ROW]
[ROW][C]132[/C][C]-6.81681291113506[/C][C]-50.8966740717622[/C][C]37.2630482494921[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79381&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79381&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
12143.909154776107330.116352463759657.7019570884551
12235.836348500348219.001029538531852.6716674621646
12317.0669638494532-2.6284330141694236.7623607130758
12422.88736022783480.43008267003235945.3446377856372
12541.44568837401916.279525017321066.6118517307169
12633.77138201767065.9222548060099261.6205092293313
12715.7541508572672-14.769438067466246.2777397820005
128-4.66231768248794-37.863649007492228.5390136425163
129-4.98464670685161-40.875265113940230.905971700237
130-4.16913856730358-42.766542430645134.4282652960379
131-1.32143817223447-42.647501718921440.0046253744524
132-6.81681291113506-50.896674071762237.2630482494921



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')