Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 10 Jul 2010 07:31:40 +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/Jul/10/t1278747263zum1hf3yu1chdrk.htm/, Retrieved Sun, 28 Apr 2024 23:08:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77975, Retrieved Sun, 28 Apr 2024 23:08:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact233
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Kelly Janbroers -...] [2010-07-10 07:31:40] [413e0fefcf22560c5655fbc122c1a3c2] [Current]
Feedback Forum

Post a new message
Dataseries X:
33
32
31
29
49
48
33
23
24
24
25
27
24
21
15
21
49
48
35
36
51
50
61
63
61
62
58
65
93
94
86
88
102
107
121
127
125
128
117
127
160
162
153
160
177
178
196
212
212
211
204
216
248
250
240
249
275
277
286
302
290
290
277
285
311
300
291
299
332
337
343
360
353
351
341
348
381
358
353
358
399
409
407
419
418
421
414
424
463
437
430
436
474
489
482
492
502
500
493
504
538
516
502
501
541
571
559
569
576
573
562
570
597
573
562
556
600
630
624
634




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77975&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77975&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77975&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.312591008980173
beta0.140711984725360
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.312591008980173 \tabularnewline
beta & 0.140711984725360 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77975&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]0.312591008980173[/C][/ROW]
[ROW][C]beta[/C][C]0.140711984725360[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77975&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77975&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
alpha0.312591008980173
beta0.140711984725360
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132426.3878205128205-2.38782051282053
142122.4469280703411-1.44692807034106
151514.69483991202560.305160087974350
162118.96219465068212.03780534931794
174945.48579220202823.51420779797183
184843.20880670655064.79119329344939
193537.4167374760649-2.41673747606485
203628.22356630100927.77643369899084
215133.850404234079517.1495957659205
225042.03653849159587.96346150840424
236148.034778359947112.9652216400529
246356.83346932120536.16653067879469
256157.05344470211643.94655529788356
266258.49958670992733.50041329007271
275856.47619203241541.52380796758464
286565.3469215664832-0.346921566483189
299395.066474805018-2.06647480501803
309494.6038689715942-0.603868971594153
318684.6142914841251.38570851587494
328886.22759610114971.77240389885026
3310298.76772297061173.23227702938829
3410798.02353857346728.97646142653278
35121109.55598643316211.4440135668382
36127114.91806777801912.0819322219815
37125117.4336918222387.56630817776154
38128121.8364482916546.16355170834557
39117121.535723698735-4.5357236987348
40127129.208744717578-2.20874471757821
41160159.0647824736130.935217526386936
42162162.578427468024-0.578427468023733
43153155.998115664341-2.99811566434119
44160158.3477297586931.65227024130724
45177173.6893853454593.31061465454076
46178178.757289793167-0.757289793167416
47196190.3541272918905.64587270810952
48212195.49809520895316.5019047910471
49212197.64151844960314.3584815503967
50211204.8521717090636.14782829093696
51204198.8400542773665.15994572263395
52216213.2182078699132.78179213008718
53248249.089707968217-1.08970796821694
54250253.135096802614-3.13509680261444
55240246.185032381257-6.18503238125749
56249252.687739205703-3.68773920570348
57275269.2178119458765.78218805412376
58277274.088402059532.91159794047019
59286293.221477618580-7.22147761857957
60302303.227572561421-1.22757256142074
61290298.997486764376-8.9974867643757
62290292.877852730668-2.87785273066805
63277282.582967183926-5.58296718392558
64285290.713346351007-5.71334635100698
65311319.639505059182-8.63950505918217
66300317.958262924178-17.9582629241781
67291301.665441877772-10.6654418777717
68299305.674587565542-6.67458756554169
69332324.8396468873587.16035311264159
70337325.28732394025811.7126760597415
71343337.7126426021455.28735739785526
72360353.8060284678156.19397153218483
73353344.9380579338098.06194206619085
74351347.491419733383.50858026662013
75341336.7479452096184.25205479038237
76348347.7102258974210.289774102578519
77381376.6126732319634.38732676803681
78358373.281927734667-15.2819277346667
79353363.640799246914-10.6407992469138
80358371.204024533344-13.2040245333438
81399398.3541313232480.645868676752343
82409400.1240334221238.87596657787685
83407407.350313450249-0.350313450248791
84419422.161167217467-3.16116721746681
85418411.0979739790966.90202602090386
86421409.55276517113711.4472348288627
87414401.54512843163512.4548715683648
88424412.45184656261411.5481534373855
89463448.28947784310214.7105221568984
90437435.7181381226371.28186187736293
91430436.226908175786-6.22690817578598
92436445.383891728934-9.3838917289342
93474485.392708207393-11.3927082073935
94489490.671411677834-1.6714116778345
95482489.40902761187-7.40902761187016
96492500.921284338081-8.92128433808057
97502495.56179899356.43820100650044
98500497.5623577798922.43764222010827
99493487.601110028365.39888997163956
100504495.538594158388.46140584162049
101538532.3090936624365.690906337564
102516507.0145078779218.985492122079
103502504.435800492344-2.43580049234362
104501512.440497412423-11.4404974124232
105541550.167884585948-9.1678845859476
106571562.6647397424378.33526025756282
107559560.866594239744-1.86659423974424
108569573.595944203855-4.59594420385486
109576580.861138276491-4.86113827649149
110573576.796968931272-3.79696893127243
111562566.865558683047-4.86555868304686
112570573.191317093755-3.19131709375461
113597603.393913078432-6.39391307843232
114573575.033994035413-2.03399403541266
115562559.1224444487252.87755555127546
116556560.794697965195-4.79469796519504
117600600.65059316829-0.650593168289788
118630626.7052081933133.29479180668727
119624614.9604165558529.03958344414764
120634628.3442769031175.65572309688298

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 24 & 26.3878205128205 & -2.38782051282053 \tabularnewline
14 & 21 & 22.4469280703411 & -1.44692807034106 \tabularnewline
15 & 15 & 14.6948399120256 & 0.305160087974350 \tabularnewline
16 & 21 & 18.9621946506821 & 2.03780534931794 \tabularnewline
17 & 49 & 45.4857922020282 & 3.51420779797183 \tabularnewline
18 & 48 & 43.2088067065506 & 4.79119329344939 \tabularnewline
19 & 35 & 37.4167374760649 & -2.41673747606485 \tabularnewline
20 & 36 & 28.2235663010092 & 7.77643369899084 \tabularnewline
21 & 51 & 33.8504042340795 & 17.1495957659205 \tabularnewline
22 & 50 & 42.0365384915958 & 7.96346150840424 \tabularnewline
23 & 61 & 48.0347783599471 & 12.9652216400529 \tabularnewline
24 & 63 & 56.8334693212053 & 6.16653067879469 \tabularnewline
25 & 61 & 57.0534447021164 & 3.94655529788356 \tabularnewline
26 & 62 & 58.4995867099273 & 3.50041329007271 \tabularnewline
27 & 58 & 56.4761920324154 & 1.52380796758464 \tabularnewline
28 & 65 & 65.3469215664832 & -0.346921566483189 \tabularnewline
29 & 93 & 95.066474805018 & -2.06647480501803 \tabularnewline
30 & 94 & 94.6038689715942 & -0.603868971594153 \tabularnewline
31 & 86 & 84.614291484125 & 1.38570851587494 \tabularnewline
32 & 88 & 86.2275961011497 & 1.77240389885026 \tabularnewline
33 & 102 & 98.7677229706117 & 3.23227702938829 \tabularnewline
34 & 107 & 98.0235385734672 & 8.97646142653278 \tabularnewline
35 & 121 & 109.555986433162 & 11.4440135668382 \tabularnewline
36 & 127 & 114.918067778019 & 12.0819322219815 \tabularnewline
37 & 125 & 117.433691822238 & 7.56630817776154 \tabularnewline
38 & 128 & 121.836448291654 & 6.16355170834557 \tabularnewline
39 & 117 & 121.535723698735 & -4.5357236987348 \tabularnewline
40 & 127 & 129.208744717578 & -2.20874471757821 \tabularnewline
41 & 160 & 159.064782473613 & 0.935217526386936 \tabularnewline
42 & 162 & 162.578427468024 & -0.578427468023733 \tabularnewline
43 & 153 & 155.998115664341 & -2.99811566434119 \tabularnewline
44 & 160 & 158.347729758693 & 1.65227024130724 \tabularnewline
45 & 177 & 173.689385345459 & 3.31061465454076 \tabularnewline
46 & 178 & 178.757289793167 & -0.757289793167416 \tabularnewline
47 & 196 & 190.354127291890 & 5.64587270810952 \tabularnewline
48 & 212 & 195.498095208953 & 16.5019047910471 \tabularnewline
49 & 212 & 197.641518449603 & 14.3584815503967 \tabularnewline
50 & 211 & 204.852171709063 & 6.14782829093696 \tabularnewline
51 & 204 & 198.840054277366 & 5.15994572263395 \tabularnewline
52 & 216 & 213.218207869913 & 2.78179213008718 \tabularnewline
53 & 248 & 249.089707968217 & -1.08970796821694 \tabularnewline
54 & 250 & 253.135096802614 & -3.13509680261444 \tabularnewline
55 & 240 & 246.185032381257 & -6.18503238125749 \tabularnewline
56 & 249 & 252.687739205703 & -3.68773920570348 \tabularnewline
57 & 275 & 269.217811945876 & 5.78218805412376 \tabularnewline
58 & 277 & 274.08840205953 & 2.91159794047019 \tabularnewline
59 & 286 & 293.221477618580 & -7.22147761857957 \tabularnewline
60 & 302 & 303.227572561421 & -1.22757256142074 \tabularnewline
61 & 290 & 298.997486764376 & -8.9974867643757 \tabularnewline
62 & 290 & 292.877852730668 & -2.87785273066805 \tabularnewline
63 & 277 & 282.582967183926 & -5.58296718392558 \tabularnewline
64 & 285 & 290.713346351007 & -5.71334635100698 \tabularnewline
65 & 311 & 319.639505059182 & -8.63950505918217 \tabularnewline
66 & 300 & 317.958262924178 & -17.9582629241781 \tabularnewline
67 & 291 & 301.665441877772 & -10.6654418777717 \tabularnewline
68 & 299 & 305.674587565542 & -6.67458756554169 \tabularnewline
69 & 332 & 324.839646887358 & 7.16035311264159 \tabularnewline
70 & 337 & 325.287323940258 & 11.7126760597415 \tabularnewline
71 & 343 & 337.712642602145 & 5.28735739785526 \tabularnewline
72 & 360 & 353.806028467815 & 6.19397153218483 \tabularnewline
73 & 353 & 344.938057933809 & 8.06194206619085 \tabularnewline
74 & 351 & 347.49141973338 & 3.50858026662013 \tabularnewline
75 & 341 & 336.747945209618 & 4.25205479038237 \tabularnewline
76 & 348 & 347.710225897421 & 0.289774102578519 \tabularnewline
77 & 381 & 376.612673231963 & 4.38732676803681 \tabularnewline
78 & 358 & 373.281927734667 & -15.2819277346667 \tabularnewline
79 & 353 & 363.640799246914 & -10.6407992469138 \tabularnewline
80 & 358 & 371.204024533344 & -13.2040245333438 \tabularnewline
81 & 399 & 398.354131323248 & 0.645868676752343 \tabularnewline
82 & 409 & 400.124033422123 & 8.87596657787685 \tabularnewline
83 & 407 & 407.350313450249 & -0.350313450248791 \tabularnewline
84 & 419 & 422.161167217467 & -3.16116721746681 \tabularnewline
85 & 418 & 411.097973979096 & 6.90202602090386 \tabularnewline
86 & 421 & 409.552765171137 & 11.4472348288627 \tabularnewline
87 & 414 & 401.545128431635 & 12.4548715683648 \tabularnewline
88 & 424 & 412.451846562614 & 11.5481534373855 \tabularnewline
89 & 463 & 448.289477843102 & 14.7105221568984 \tabularnewline
90 & 437 & 435.718138122637 & 1.28186187736293 \tabularnewline
91 & 430 & 436.226908175786 & -6.22690817578598 \tabularnewline
92 & 436 & 445.383891728934 & -9.3838917289342 \tabularnewline
93 & 474 & 485.392708207393 & -11.3927082073935 \tabularnewline
94 & 489 & 490.671411677834 & -1.6714116778345 \tabularnewline
95 & 482 & 489.40902761187 & -7.40902761187016 \tabularnewline
96 & 492 & 500.921284338081 & -8.92128433808057 \tabularnewline
97 & 502 & 495.5617989935 & 6.43820100650044 \tabularnewline
98 & 500 & 497.562357779892 & 2.43764222010827 \tabularnewline
99 & 493 & 487.60111002836 & 5.39888997163956 \tabularnewline
100 & 504 & 495.53859415838 & 8.46140584162049 \tabularnewline
101 & 538 & 532.309093662436 & 5.690906337564 \tabularnewline
102 & 516 & 507.014507877921 & 8.985492122079 \tabularnewline
103 & 502 & 504.435800492344 & -2.43580049234362 \tabularnewline
104 & 501 & 512.440497412423 & -11.4404974124232 \tabularnewline
105 & 541 & 550.167884585948 & -9.1678845859476 \tabularnewline
106 & 571 & 562.664739742437 & 8.33526025756282 \tabularnewline
107 & 559 & 560.866594239744 & -1.86659423974424 \tabularnewline
108 & 569 & 573.595944203855 & -4.59594420385486 \tabularnewline
109 & 576 & 580.861138276491 & -4.86113827649149 \tabularnewline
110 & 573 & 576.796968931272 & -3.79696893127243 \tabularnewline
111 & 562 & 566.865558683047 & -4.86555868304686 \tabularnewline
112 & 570 & 573.191317093755 & -3.19131709375461 \tabularnewline
113 & 597 & 603.393913078432 & -6.39391307843232 \tabularnewline
114 & 573 & 575.033994035413 & -2.03399403541266 \tabularnewline
115 & 562 & 559.122444448725 & 2.87755555127546 \tabularnewline
116 & 556 & 560.794697965195 & -4.79469796519504 \tabularnewline
117 & 600 & 600.65059316829 & -0.650593168289788 \tabularnewline
118 & 630 & 626.705208193313 & 3.29479180668727 \tabularnewline
119 & 624 & 614.960416555852 & 9.03958344414764 \tabularnewline
120 & 634 & 628.344276903117 & 5.65572309688298 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77975&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]24[/C][C]26.3878205128205[/C][C]-2.38782051282053[/C][/ROW]
[ROW][C]14[/C][C]21[/C][C]22.4469280703411[/C][C]-1.44692807034106[/C][/ROW]
[ROW][C]15[/C][C]15[/C][C]14.6948399120256[/C][C]0.305160087974350[/C][/ROW]
[ROW][C]16[/C][C]21[/C][C]18.9621946506821[/C][C]2.03780534931794[/C][/ROW]
[ROW][C]17[/C][C]49[/C][C]45.4857922020282[/C][C]3.51420779797183[/C][/ROW]
[ROW][C]18[/C][C]48[/C][C]43.2088067065506[/C][C]4.79119329344939[/C][/ROW]
[ROW][C]19[/C][C]35[/C][C]37.4167374760649[/C][C]-2.41673747606485[/C][/ROW]
[ROW][C]20[/C][C]36[/C][C]28.2235663010092[/C][C]7.77643369899084[/C][/ROW]
[ROW][C]21[/C][C]51[/C][C]33.8504042340795[/C][C]17.1495957659205[/C][/ROW]
[ROW][C]22[/C][C]50[/C][C]42.0365384915958[/C][C]7.96346150840424[/C][/ROW]
[ROW][C]23[/C][C]61[/C][C]48.0347783599471[/C][C]12.9652216400529[/C][/ROW]
[ROW][C]24[/C][C]63[/C][C]56.8334693212053[/C][C]6.16653067879469[/C][/ROW]
[ROW][C]25[/C][C]61[/C][C]57.0534447021164[/C][C]3.94655529788356[/C][/ROW]
[ROW][C]26[/C][C]62[/C][C]58.4995867099273[/C][C]3.50041329007271[/C][/ROW]
[ROW][C]27[/C][C]58[/C][C]56.4761920324154[/C][C]1.52380796758464[/C][/ROW]
[ROW][C]28[/C][C]65[/C][C]65.3469215664832[/C][C]-0.346921566483189[/C][/ROW]
[ROW][C]29[/C][C]93[/C][C]95.066474805018[/C][C]-2.06647480501803[/C][/ROW]
[ROW][C]30[/C][C]94[/C][C]94.6038689715942[/C][C]-0.603868971594153[/C][/ROW]
[ROW][C]31[/C][C]86[/C][C]84.614291484125[/C][C]1.38570851587494[/C][/ROW]
[ROW][C]32[/C][C]88[/C][C]86.2275961011497[/C][C]1.77240389885026[/C][/ROW]
[ROW][C]33[/C][C]102[/C][C]98.7677229706117[/C][C]3.23227702938829[/C][/ROW]
[ROW][C]34[/C][C]107[/C][C]98.0235385734672[/C][C]8.97646142653278[/C][/ROW]
[ROW][C]35[/C][C]121[/C][C]109.555986433162[/C][C]11.4440135668382[/C][/ROW]
[ROW][C]36[/C][C]127[/C][C]114.918067778019[/C][C]12.0819322219815[/C][/ROW]
[ROW][C]37[/C][C]125[/C][C]117.433691822238[/C][C]7.56630817776154[/C][/ROW]
[ROW][C]38[/C][C]128[/C][C]121.836448291654[/C][C]6.16355170834557[/C][/ROW]
[ROW][C]39[/C][C]117[/C][C]121.535723698735[/C][C]-4.5357236987348[/C][/ROW]
[ROW][C]40[/C][C]127[/C][C]129.208744717578[/C][C]-2.20874471757821[/C][/ROW]
[ROW][C]41[/C][C]160[/C][C]159.064782473613[/C][C]0.935217526386936[/C][/ROW]
[ROW][C]42[/C][C]162[/C][C]162.578427468024[/C][C]-0.578427468023733[/C][/ROW]
[ROW][C]43[/C][C]153[/C][C]155.998115664341[/C][C]-2.99811566434119[/C][/ROW]
[ROW][C]44[/C][C]160[/C][C]158.347729758693[/C][C]1.65227024130724[/C][/ROW]
[ROW][C]45[/C][C]177[/C][C]173.689385345459[/C][C]3.31061465454076[/C][/ROW]
[ROW][C]46[/C][C]178[/C][C]178.757289793167[/C][C]-0.757289793167416[/C][/ROW]
[ROW][C]47[/C][C]196[/C][C]190.354127291890[/C][C]5.64587270810952[/C][/ROW]
[ROW][C]48[/C][C]212[/C][C]195.498095208953[/C][C]16.5019047910471[/C][/ROW]
[ROW][C]49[/C][C]212[/C][C]197.641518449603[/C][C]14.3584815503967[/C][/ROW]
[ROW][C]50[/C][C]211[/C][C]204.852171709063[/C][C]6.14782829093696[/C][/ROW]
[ROW][C]51[/C][C]204[/C][C]198.840054277366[/C][C]5.15994572263395[/C][/ROW]
[ROW][C]52[/C][C]216[/C][C]213.218207869913[/C][C]2.78179213008718[/C][/ROW]
[ROW][C]53[/C][C]248[/C][C]249.089707968217[/C][C]-1.08970796821694[/C][/ROW]
[ROW][C]54[/C][C]250[/C][C]253.135096802614[/C][C]-3.13509680261444[/C][/ROW]
[ROW][C]55[/C][C]240[/C][C]246.185032381257[/C][C]-6.18503238125749[/C][/ROW]
[ROW][C]56[/C][C]249[/C][C]252.687739205703[/C][C]-3.68773920570348[/C][/ROW]
[ROW][C]57[/C][C]275[/C][C]269.217811945876[/C][C]5.78218805412376[/C][/ROW]
[ROW][C]58[/C][C]277[/C][C]274.08840205953[/C][C]2.91159794047019[/C][/ROW]
[ROW][C]59[/C][C]286[/C][C]293.221477618580[/C][C]-7.22147761857957[/C][/ROW]
[ROW][C]60[/C][C]302[/C][C]303.227572561421[/C][C]-1.22757256142074[/C][/ROW]
[ROW][C]61[/C][C]290[/C][C]298.997486764376[/C][C]-8.9974867643757[/C][/ROW]
[ROW][C]62[/C][C]290[/C][C]292.877852730668[/C][C]-2.87785273066805[/C][/ROW]
[ROW][C]63[/C][C]277[/C][C]282.582967183926[/C][C]-5.58296718392558[/C][/ROW]
[ROW][C]64[/C][C]285[/C][C]290.713346351007[/C][C]-5.71334635100698[/C][/ROW]
[ROW][C]65[/C][C]311[/C][C]319.639505059182[/C][C]-8.63950505918217[/C][/ROW]
[ROW][C]66[/C][C]300[/C][C]317.958262924178[/C][C]-17.9582629241781[/C][/ROW]
[ROW][C]67[/C][C]291[/C][C]301.665441877772[/C][C]-10.6654418777717[/C][/ROW]
[ROW][C]68[/C][C]299[/C][C]305.674587565542[/C][C]-6.67458756554169[/C][/ROW]
[ROW][C]69[/C][C]332[/C][C]324.839646887358[/C][C]7.16035311264159[/C][/ROW]
[ROW][C]70[/C][C]337[/C][C]325.287323940258[/C][C]11.7126760597415[/C][/ROW]
[ROW][C]71[/C][C]343[/C][C]337.712642602145[/C][C]5.28735739785526[/C][/ROW]
[ROW][C]72[/C][C]360[/C][C]353.806028467815[/C][C]6.19397153218483[/C][/ROW]
[ROW][C]73[/C][C]353[/C][C]344.938057933809[/C][C]8.06194206619085[/C][/ROW]
[ROW][C]74[/C][C]351[/C][C]347.49141973338[/C][C]3.50858026662013[/C][/ROW]
[ROW][C]75[/C][C]341[/C][C]336.747945209618[/C][C]4.25205479038237[/C][/ROW]
[ROW][C]76[/C][C]348[/C][C]347.710225897421[/C][C]0.289774102578519[/C][/ROW]
[ROW][C]77[/C][C]381[/C][C]376.612673231963[/C][C]4.38732676803681[/C][/ROW]
[ROW][C]78[/C][C]358[/C][C]373.281927734667[/C][C]-15.2819277346667[/C][/ROW]
[ROW][C]79[/C][C]353[/C][C]363.640799246914[/C][C]-10.6407992469138[/C][/ROW]
[ROW][C]80[/C][C]358[/C][C]371.204024533344[/C][C]-13.2040245333438[/C][/ROW]
[ROW][C]81[/C][C]399[/C][C]398.354131323248[/C][C]0.645868676752343[/C][/ROW]
[ROW][C]82[/C][C]409[/C][C]400.124033422123[/C][C]8.87596657787685[/C][/ROW]
[ROW][C]83[/C][C]407[/C][C]407.350313450249[/C][C]-0.350313450248791[/C][/ROW]
[ROW][C]84[/C][C]419[/C][C]422.161167217467[/C][C]-3.16116721746681[/C][/ROW]
[ROW][C]85[/C][C]418[/C][C]411.097973979096[/C][C]6.90202602090386[/C][/ROW]
[ROW][C]86[/C][C]421[/C][C]409.552765171137[/C][C]11.4472348288627[/C][/ROW]
[ROW][C]87[/C][C]414[/C][C]401.545128431635[/C][C]12.4548715683648[/C][/ROW]
[ROW][C]88[/C][C]424[/C][C]412.451846562614[/C][C]11.5481534373855[/C][/ROW]
[ROW][C]89[/C][C]463[/C][C]448.289477843102[/C][C]14.7105221568984[/C][/ROW]
[ROW][C]90[/C][C]437[/C][C]435.718138122637[/C][C]1.28186187736293[/C][/ROW]
[ROW][C]91[/C][C]430[/C][C]436.226908175786[/C][C]-6.22690817578598[/C][/ROW]
[ROW][C]92[/C][C]436[/C][C]445.383891728934[/C][C]-9.3838917289342[/C][/ROW]
[ROW][C]93[/C][C]474[/C][C]485.392708207393[/C][C]-11.3927082073935[/C][/ROW]
[ROW][C]94[/C][C]489[/C][C]490.671411677834[/C][C]-1.6714116778345[/C][/ROW]
[ROW][C]95[/C][C]482[/C][C]489.40902761187[/C][C]-7.40902761187016[/C][/ROW]
[ROW][C]96[/C][C]492[/C][C]500.921284338081[/C][C]-8.92128433808057[/C][/ROW]
[ROW][C]97[/C][C]502[/C][C]495.5617989935[/C][C]6.43820100650044[/C][/ROW]
[ROW][C]98[/C][C]500[/C][C]497.562357779892[/C][C]2.43764222010827[/C][/ROW]
[ROW][C]99[/C][C]493[/C][C]487.60111002836[/C][C]5.39888997163956[/C][/ROW]
[ROW][C]100[/C][C]504[/C][C]495.53859415838[/C][C]8.46140584162049[/C][/ROW]
[ROW][C]101[/C][C]538[/C][C]532.309093662436[/C][C]5.690906337564[/C][/ROW]
[ROW][C]102[/C][C]516[/C][C]507.014507877921[/C][C]8.985492122079[/C][/ROW]
[ROW][C]103[/C][C]502[/C][C]504.435800492344[/C][C]-2.43580049234362[/C][/ROW]
[ROW][C]104[/C][C]501[/C][C]512.440497412423[/C][C]-11.4404974124232[/C][/ROW]
[ROW][C]105[/C][C]541[/C][C]550.167884585948[/C][C]-9.1678845859476[/C][/ROW]
[ROW][C]106[/C][C]571[/C][C]562.664739742437[/C][C]8.33526025756282[/C][/ROW]
[ROW][C]107[/C][C]559[/C][C]560.866594239744[/C][C]-1.86659423974424[/C][/ROW]
[ROW][C]108[/C][C]569[/C][C]573.595944203855[/C][C]-4.59594420385486[/C][/ROW]
[ROW][C]109[/C][C]576[/C][C]580.861138276491[/C][C]-4.86113827649149[/C][/ROW]
[ROW][C]110[/C][C]573[/C][C]576.796968931272[/C][C]-3.79696893127243[/C][/ROW]
[ROW][C]111[/C][C]562[/C][C]566.865558683047[/C][C]-4.86555868304686[/C][/ROW]
[ROW][C]112[/C][C]570[/C][C]573.191317093755[/C][C]-3.19131709375461[/C][/ROW]
[ROW][C]113[/C][C]597[/C][C]603.393913078432[/C][C]-6.39391307843232[/C][/ROW]
[ROW][C]114[/C][C]573[/C][C]575.033994035413[/C][C]-2.03399403541266[/C][/ROW]
[ROW][C]115[/C][C]562[/C][C]559.122444448725[/C][C]2.87755555127546[/C][/ROW]
[ROW][C]116[/C][C]556[/C][C]560.794697965195[/C][C]-4.79469796519504[/C][/ROW]
[ROW][C]117[/C][C]600[/C][C]600.65059316829[/C][C]-0.650593168289788[/C][/ROW]
[ROW][C]118[/C][C]630[/C][C]626.705208193313[/C][C]3.29479180668727[/C][/ROW]
[ROW][C]119[/C][C]624[/C][C]614.960416555852[/C][C]9.03958344414764[/C][/ROW]
[ROW][C]120[/C][C]634[/C][C]628.344276903117[/C][C]5.65572309688298[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77975&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77975&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
132426.3878205128205-2.38782051282053
142122.4469280703411-1.44692807034106
151514.69483991202560.305160087974350
162118.96219465068212.03780534931794
174945.48579220202823.51420779797183
184843.20880670655064.79119329344939
193537.4167374760649-2.41673747606485
203628.22356630100927.77643369899084
215133.850404234079517.1495957659205
225042.03653849159587.96346150840424
236148.034778359947112.9652216400529
246356.83346932120536.16653067879469
256157.05344470211643.94655529788356
266258.49958670992733.50041329007271
275856.47619203241541.52380796758464
286565.3469215664832-0.346921566483189
299395.066474805018-2.06647480501803
309494.6038689715942-0.603868971594153
318684.6142914841251.38570851587494
328886.22759610114971.77240389885026
3310298.76772297061173.23227702938829
3410798.02353857346728.97646142653278
35121109.55598643316211.4440135668382
36127114.91806777801912.0819322219815
37125117.4336918222387.56630817776154
38128121.8364482916546.16355170834557
39117121.535723698735-4.5357236987348
40127129.208744717578-2.20874471757821
41160159.0647824736130.935217526386936
42162162.578427468024-0.578427468023733
43153155.998115664341-2.99811566434119
44160158.3477297586931.65227024130724
45177173.6893853454593.31061465454076
46178178.757289793167-0.757289793167416
47196190.3541272918905.64587270810952
48212195.49809520895316.5019047910471
49212197.64151844960314.3584815503967
50211204.8521717090636.14782829093696
51204198.8400542773665.15994572263395
52216213.2182078699132.78179213008718
53248249.089707968217-1.08970796821694
54250253.135096802614-3.13509680261444
55240246.185032381257-6.18503238125749
56249252.687739205703-3.68773920570348
57275269.2178119458765.78218805412376
58277274.088402059532.91159794047019
59286293.221477618580-7.22147761857957
60302303.227572561421-1.22757256142074
61290298.997486764376-8.9974867643757
62290292.877852730668-2.87785273066805
63277282.582967183926-5.58296718392558
64285290.713346351007-5.71334635100698
65311319.639505059182-8.63950505918217
66300317.958262924178-17.9582629241781
67291301.665441877772-10.6654418777717
68299305.674587565542-6.67458756554169
69332324.8396468873587.16035311264159
70337325.28732394025811.7126760597415
71343337.7126426021455.28735739785526
72360353.8060284678156.19397153218483
73353344.9380579338098.06194206619085
74351347.491419733383.50858026662013
75341336.7479452096184.25205479038237
76348347.7102258974210.289774102578519
77381376.6126732319634.38732676803681
78358373.281927734667-15.2819277346667
79353363.640799246914-10.6407992469138
80358371.204024533344-13.2040245333438
81399398.3541313232480.645868676752343
82409400.1240334221238.87596657787685
83407407.350313450249-0.350313450248791
84419422.161167217467-3.16116721746681
85418411.0979739790966.90202602090386
86421409.55276517113711.4472348288627
87414401.54512843163512.4548715683648
88424412.45184656261411.5481534373855
89463448.28947784310214.7105221568984
90437435.7181381226371.28186187736293
91430436.226908175786-6.22690817578598
92436445.383891728934-9.3838917289342
93474485.392708207393-11.3927082073935
94489490.671411677834-1.6714116778345
95482489.40902761187-7.40902761187016
96492500.921284338081-8.92128433808057
97502495.56179899356.43820100650044
98500497.5623577798922.43764222010827
99493487.601110028365.39888997163956
100504495.538594158388.46140584162049
101538532.3090936624365.690906337564
102516507.0145078779218.985492122079
103502504.435800492344-2.43580049234362
104501512.440497412423-11.4404974124232
105541550.167884585948-9.1678845859476
106571562.6647397424378.33526025756282
107559560.866594239744-1.86659423974424
108569573.595944203855-4.59594420385486
109576580.861138276491-4.86113827649149
110573576.796968931272-3.79696893127243
111562566.865558683047-4.86555868304686
112570573.191317093755-3.19131709375461
113597603.393913078432-6.39391307843232
114573575.033994035413-2.03399403541266
115562559.1224444487252.87755555127546
116556560.794697965195-4.79469796519504
117600600.65059316829-0.650593168289788
118630626.7052081933133.29479180668727
119624614.9604165558529.03958344414764
120634628.3442769031175.65572309688298







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121638.204192887778624.201608526867652.206777248689
122636.177349545383621.311202883193651.043496207573
123626.651548574078610.762494145502642.540603002654
124635.816407799673618.751524090595652.881291508752
125665.122740779326646.737811686329683.507669872324
126642.347440459369622.507913727433662.186967191304
127631.126299738903609.707323324408652.545276153399
128627.176866338428604.062769083514650.29096359334
129672.142919272718647.22641209767697.059426447765
130701.904296873383675.085576743761728.723017003005
131693.724981849439664.910845809426722.539117889452
132702.20582234445671.308847186826733.102797502074

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 638.204192887778 & 624.201608526867 & 652.206777248689 \tabularnewline
122 & 636.177349545383 & 621.311202883193 & 651.043496207573 \tabularnewline
123 & 626.651548574078 & 610.762494145502 & 642.540603002654 \tabularnewline
124 & 635.816407799673 & 618.751524090595 & 652.881291508752 \tabularnewline
125 & 665.122740779326 & 646.737811686329 & 683.507669872324 \tabularnewline
126 & 642.347440459369 & 622.507913727433 & 662.186967191304 \tabularnewline
127 & 631.126299738903 & 609.707323324408 & 652.545276153399 \tabularnewline
128 & 627.176866338428 & 604.062769083514 & 650.29096359334 \tabularnewline
129 & 672.142919272718 & 647.22641209767 & 697.059426447765 \tabularnewline
130 & 701.904296873383 & 675.085576743761 & 728.723017003005 \tabularnewline
131 & 693.724981849439 & 664.910845809426 & 722.539117889452 \tabularnewline
132 & 702.20582234445 & 671.308847186826 & 733.102797502074 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77975&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]638.204192887778[/C][C]624.201608526867[/C][C]652.206777248689[/C][/ROW]
[ROW][C]122[/C][C]636.177349545383[/C][C]621.311202883193[/C][C]651.043496207573[/C][/ROW]
[ROW][C]123[/C][C]626.651548574078[/C][C]610.762494145502[/C][C]642.540603002654[/C][/ROW]
[ROW][C]124[/C][C]635.816407799673[/C][C]618.751524090595[/C][C]652.881291508752[/C][/ROW]
[ROW][C]125[/C][C]665.122740779326[/C][C]646.737811686329[/C][C]683.507669872324[/C][/ROW]
[ROW][C]126[/C][C]642.347440459369[/C][C]622.507913727433[/C][C]662.186967191304[/C][/ROW]
[ROW][C]127[/C][C]631.126299738903[/C][C]609.707323324408[/C][C]652.545276153399[/C][/ROW]
[ROW][C]128[/C][C]627.176866338428[/C][C]604.062769083514[/C][C]650.29096359334[/C][/ROW]
[ROW][C]129[/C][C]672.142919272718[/C][C]647.22641209767[/C][C]697.059426447765[/C][/ROW]
[ROW][C]130[/C][C]701.904296873383[/C][C]675.085576743761[/C][C]728.723017003005[/C][/ROW]
[ROW][C]131[/C][C]693.724981849439[/C][C]664.910845809426[/C][C]722.539117889452[/C][/ROW]
[ROW][C]132[/C][C]702.20582234445[/C][C]671.308847186826[/C][C]733.102797502074[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77975&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77975&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
121638.204192887778624.201608526867652.206777248689
122636.177349545383621.311202883193651.043496207573
123626.651548574078610.762494145502642.540603002654
124635.816407799673618.751524090595652.881291508752
125665.122740779326646.737811686329683.507669872324
126642.347440459369622.507913727433662.186967191304
127631.126299738903609.707323324408652.545276153399
128627.176866338428604.062769083514650.29096359334
129672.142919272718647.22641209767697.059426447765
130701.904296873383675.085576743761728.723017003005
131693.724981849439664.910845809426722.539117889452
132702.20582234445671.308847186826733.102797502074



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')