Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 Jul 2010 15:48:44 +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/26/t1280159334cud36wf2rskay6s.htm/, Retrieved Sat, 04 May 2024 09:09:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78124, Retrieved Sat, 04 May 2024 09:09:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact198
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Kelly Janbroers -...] [2010-07-26 15:48:44] [413e0fefcf22560c5655fbc122c1a3c2] [Current]
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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 time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78124&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78124&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78124&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.116508597215365
beta0.113960080374117
gamma0.923119969726914

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.116508597215365 \tabularnewline
beta & 0.113960080374117 \tabularnewline
gamma & 0.923119969726914 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78124&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]0.116508597215365[/C][/ROW]
[ROW][C]beta[/C][C]0.113960080374117[/C][/ROW]
[ROW][C]gamma[/C][C]0.923119969726914[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78124&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78124&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
alpha0.116508597215365
beta0.113960080374117
gamma0.923119969726914







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132426.4444669311186-2.44446693111864
142122.7999103475503-1.79991034755028
151515.5071479699010-0.507147969901043
162120.48639043327280.513609566727155
174945.13584072224323.86415927775681
184841.83805251667436.16194748332573
193536.3824260342733-1.38242603427332
203626.40117712165979.5988228783403
215130.461879939621720.5381200603783
225034.964458720263315.0355412797367
236139.908889188661521.0911108113385
246347.359079512626915.6409204873731
256141.747448840777619.2525511592224
266239.612406558976522.3875934410235
275830.924810308435627.0751896915644
286548.839665261101816.1603347388982
2993120.376007733544-27.3760077335443
3094115.441865223909-21.4418652239095
318685.48186431547910.518135684520871
328884.38681820173083.61318179826920
33102112.134675530090-10.1346755300897
34107105.1407632408391.85923675916068
35121121.118271453613-0.118271453613005
36127121.0771150270695.92288497293131
37125110.94539262437814.0546073756224
38128106.35233614866321.6476638513365
3911790.964998862566126.0350011374339
40127101.77286738347125.2271326165286
41160157.8922126708982.10778732910242
42162161.2869357592470.713064240753056
43153144.3172252481308.68277475187034
44160146.83494888252313.1650511174767
45177174.6759060405622.32409395943776
46178181.105546752881-3.10554675288139
47196203.976018348845-7.97601834884512
48212210.4728699302121.52713006978769
49212202.6466102111889.35338978881151
50211202.1487833227878.85121667721307
51204178.10541478294425.8945852170555
52216190.2158564970725.7841435029301
53248244.5102368255743.48976317442575
54250246.4507833250213.54921667497905
55240229.37289088386310.6271091161367
56249236.93756378876612.0624362112345
57275263.04238536772711.9576146322730
58277265.71255214223411.2874478577659
59286294.649798731673-8.64979873167329
60302315.135086901385-13.1350869013848
61290309.893093353792-19.8930933537925
62290303.117698760301-13.1176987603006
63277283.486602623844-6.4866026238443
64285292.823866971079-7.82386697107933
65311334.270974687350-23.2709746873496
66300330.791503884563-30.7915038845633
67291308.866917739733-17.8669177397330
68299313.146783649465-14.1467836494645
69332338.698860574392-6.69886057439152
70337335.0988643722961.90113562770421
71343345.341446975476-2.34144697547589
72360362.791377332174-2.79137733217431
73353348.0038375339574.99616246604324
74351346.9450060116184.05499398838157
75341329.82148483705511.1785151629454
76348339.6589700725088.34102992749234
77381373.8410835032577.1589164967433
78358364.443136986266-6.4431369862657
79353352.9522578797940.0477421202064647
80358363.236019478418-5.23601947841757
81399401.904778684521-2.90477868452052
82409405.7752366898113.22476331018885
83407413.224574255489-6.22457425548936
84419432.469211640472-13.4692116404721
85418420.232241543497-2.23224154349737
86421416.0844032743914.91559672560919
87414401.66233554937712.3376644506232
88424409.49363141732714.5063685826732
89463448.37587503461614.6241249653841
90437424.03234811269612.9676518873035
91430418.53176411050511.4682358894946
92436426.5528249270839.44717507291728
93474476.553445223035-2.553445223035
94489487.0091468959821.99085310401750
95482486.231795117647-4.23179511764693
96492502.246427752703-10.2464277527030
97502499.1173532096862.88264679031357
98500501.693261568068-1.69326156806761
99493490.6373778357572.36262216424342
100504500.2478274204123.75217257958786
101538544.266158879228-6.26615887922787
102516510.5395158400275.46048415997313
103502500.6877092950271.31229070497284
104501505.760629563508-4.76062956350842
105541549.401803617438-8.40180361743785
106571563.8869245502487.11307544975182
107559556.528108034362.47189196563954
108569569.123138142177-0.123138142176572
109576578.319365692353-2.31936569235324
110573575.369278243249-2.36927824324903
111562565.481496797421-3.48149679742119
112570576.077233259365-6.07723325936456
113597614.63374958803-17.6337495880302
114573584.699471116764-11.6994711167645
115562566.285335599852-4.28533559985181
116556564.350268451656-8.35026845165567
117600608.180435407701-8.18043540770122
118630637.202970029505-7.20297002950474
119624621.3565148055792.64348519442080
120634631.3552942288842.64470577111581

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 24 & 26.4444669311186 & -2.44446693111864 \tabularnewline
14 & 21 & 22.7999103475503 & -1.79991034755028 \tabularnewline
15 & 15 & 15.5071479699010 & -0.507147969901043 \tabularnewline
16 & 21 & 20.4863904332728 & 0.513609566727155 \tabularnewline
17 & 49 & 45.1358407222432 & 3.86415927775681 \tabularnewline
18 & 48 & 41.8380525166743 & 6.16194748332573 \tabularnewline
19 & 35 & 36.3824260342733 & -1.38242603427332 \tabularnewline
20 & 36 & 26.4011771216597 & 9.5988228783403 \tabularnewline
21 & 51 & 30.4618799396217 & 20.5381200603783 \tabularnewline
22 & 50 & 34.9644587202633 & 15.0355412797367 \tabularnewline
23 & 61 & 39.9088891886615 & 21.0911108113385 \tabularnewline
24 & 63 & 47.3590795126269 & 15.6409204873731 \tabularnewline
25 & 61 & 41.7474488407776 & 19.2525511592224 \tabularnewline
26 & 62 & 39.6124065589765 & 22.3875934410235 \tabularnewline
27 & 58 & 30.9248103084356 & 27.0751896915644 \tabularnewline
28 & 65 & 48.8396652611018 & 16.1603347388982 \tabularnewline
29 & 93 & 120.376007733544 & -27.3760077335443 \tabularnewline
30 & 94 & 115.441865223909 & -21.4418652239095 \tabularnewline
31 & 86 & 85.4818643154791 & 0.518135684520871 \tabularnewline
32 & 88 & 84.3868182017308 & 3.61318179826920 \tabularnewline
33 & 102 & 112.134675530090 & -10.1346755300897 \tabularnewline
34 & 107 & 105.140763240839 & 1.85923675916068 \tabularnewline
35 & 121 & 121.118271453613 & -0.118271453613005 \tabularnewline
36 & 127 & 121.077115027069 & 5.92288497293131 \tabularnewline
37 & 125 & 110.945392624378 & 14.0546073756224 \tabularnewline
38 & 128 & 106.352336148663 & 21.6476638513365 \tabularnewline
39 & 117 & 90.9649988625661 & 26.0350011374339 \tabularnewline
40 & 127 & 101.772867383471 & 25.2271326165286 \tabularnewline
41 & 160 & 157.892212670898 & 2.10778732910242 \tabularnewline
42 & 162 & 161.286935759247 & 0.713064240753056 \tabularnewline
43 & 153 & 144.317225248130 & 8.68277475187034 \tabularnewline
44 & 160 & 146.834948882523 & 13.1650511174767 \tabularnewline
45 & 177 & 174.675906040562 & 2.32409395943776 \tabularnewline
46 & 178 & 181.105546752881 & -3.10554675288139 \tabularnewline
47 & 196 & 203.976018348845 & -7.97601834884512 \tabularnewline
48 & 212 & 210.472869930212 & 1.52713006978769 \tabularnewline
49 & 212 & 202.646610211188 & 9.35338978881151 \tabularnewline
50 & 211 & 202.148783322787 & 8.85121667721307 \tabularnewline
51 & 204 & 178.105414782944 & 25.8945852170555 \tabularnewline
52 & 216 & 190.21585649707 & 25.7841435029301 \tabularnewline
53 & 248 & 244.510236825574 & 3.48976317442575 \tabularnewline
54 & 250 & 246.450783325021 & 3.54921667497905 \tabularnewline
55 & 240 & 229.372890883863 & 10.6271091161367 \tabularnewline
56 & 249 & 236.937563788766 & 12.0624362112345 \tabularnewline
57 & 275 & 263.042385367727 & 11.9576146322730 \tabularnewline
58 & 277 & 265.712552142234 & 11.2874478577659 \tabularnewline
59 & 286 & 294.649798731673 & -8.64979873167329 \tabularnewline
60 & 302 & 315.135086901385 & -13.1350869013848 \tabularnewline
61 & 290 & 309.893093353792 & -19.8930933537925 \tabularnewline
62 & 290 & 303.117698760301 & -13.1176987603006 \tabularnewline
63 & 277 & 283.486602623844 & -6.4866026238443 \tabularnewline
64 & 285 & 292.823866971079 & -7.82386697107933 \tabularnewline
65 & 311 & 334.270974687350 & -23.2709746873496 \tabularnewline
66 & 300 & 330.791503884563 & -30.7915038845633 \tabularnewline
67 & 291 & 308.866917739733 & -17.8669177397330 \tabularnewline
68 & 299 & 313.146783649465 & -14.1467836494645 \tabularnewline
69 & 332 & 338.698860574392 & -6.69886057439152 \tabularnewline
70 & 337 & 335.098864372296 & 1.90113562770421 \tabularnewline
71 & 343 & 345.341446975476 & -2.34144697547589 \tabularnewline
72 & 360 & 362.791377332174 & -2.79137733217431 \tabularnewline
73 & 353 & 348.003837533957 & 4.99616246604324 \tabularnewline
74 & 351 & 346.945006011618 & 4.05499398838157 \tabularnewline
75 & 341 & 329.821484837055 & 11.1785151629454 \tabularnewline
76 & 348 & 339.658970072508 & 8.34102992749234 \tabularnewline
77 & 381 & 373.841083503257 & 7.1589164967433 \tabularnewline
78 & 358 & 364.443136986266 & -6.4431369862657 \tabularnewline
79 & 353 & 352.952257879794 & 0.0477421202064647 \tabularnewline
80 & 358 & 363.236019478418 & -5.23601947841757 \tabularnewline
81 & 399 & 401.904778684521 & -2.90477868452052 \tabularnewline
82 & 409 & 405.775236689811 & 3.22476331018885 \tabularnewline
83 & 407 & 413.224574255489 & -6.22457425548936 \tabularnewline
84 & 419 & 432.469211640472 & -13.4692116404721 \tabularnewline
85 & 418 & 420.232241543497 & -2.23224154349737 \tabularnewline
86 & 421 & 416.084403274391 & 4.91559672560919 \tabularnewline
87 & 414 & 401.662335549377 & 12.3376644506232 \tabularnewline
88 & 424 & 409.493631417327 & 14.5063685826732 \tabularnewline
89 & 463 & 448.375875034616 & 14.6241249653841 \tabularnewline
90 & 437 & 424.032348112696 & 12.9676518873035 \tabularnewline
91 & 430 & 418.531764110505 & 11.4682358894946 \tabularnewline
92 & 436 & 426.552824927083 & 9.44717507291728 \tabularnewline
93 & 474 & 476.553445223035 & -2.553445223035 \tabularnewline
94 & 489 & 487.009146895982 & 1.99085310401750 \tabularnewline
95 & 482 & 486.231795117647 & -4.23179511764693 \tabularnewline
96 & 492 & 502.246427752703 & -10.2464277527030 \tabularnewline
97 & 502 & 499.117353209686 & 2.88264679031357 \tabularnewline
98 & 500 & 501.693261568068 & -1.69326156806761 \tabularnewline
99 & 493 & 490.637377835757 & 2.36262216424342 \tabularnewline
100 & 504 & 500.247827420412 & 3.75217257958786 \tabularnewline
101 & 538 & 544.266158879228 & -6.26615887922787 \tabularnewline
102 & 516 & 510.539515840027 & 5.46048415997313 \tabularnewline
103 & 502 & 500.687709295027 & 1.31229070497284 \tabularnewline
104 & 501 & 505.760629563508 & -4.76062956350842 \tabularnewline
105 & 541 & 549.401803617438 & -8.40180361743785 \tabularnewline
106 & 571 & 563.886924550248 & 7.11307544975182 \tabularnewline
107 & 559 & 556.52810803436 & 2.47189196563954 \tabularnewline
108 & 569 & 569.123138142177 & -0.123138142176572 \tabularnewline
109 & 576 & 578.319365692353 & -2.31936569235324 \tabularnewline
110 & 573 & 575.369278243249 & -2.36927824324903 \tabularnewline
111 & 562 & 565.481496797421 & -3.48149679742119 \tabularnewline
112 & 570 & 576.077233259365 & -6.07723325936456 \tabularnewline
113 & 597 & 614.63374958803 & -17.6337495880302 \tabularnewline
114 & 573 & 584.699471116764 & -11.6994711167645 \tabularnewline
115 & 562 & 566.285335599852 & -4.28533559985181 \tabularnewline
116 & 556 & 564.350268451656 & -8.35026845165567 \tabularnewline
117 & 600 & 608.180435407701 & -8.18043540770122 \tabularnewline
118 & 630 & 637.202970029505 & -7.20297002950474 \tabularnewline
119 & 624 & 621.356514805579 & 2.64348519442080 \tabularnewline
120 & 634 & 631.355294228884 & 2.64470577111581 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78124&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]26.4444669311186[/C][C]-2.44446693111864[/C][/ROW]
[ROW][C]14[/C][C]21[/C][C]22.7999103475503[/C][C]-1.79991034755028[/C][/ROW]
[ROW][C]15[/C][C]15[/C][C]15.5071479699010[/C][C]-0.507147969901043[/C][/ROW]
[ROW][C]16[/C][C]21[/C][C]20.4863904332728[/C][C]0.513609566727155[/C][/ROW]
[ROW][C]17[/C][C]49[/C][C]45.1358407222432[/C][C]3.86415927775681[/C][/ROW]
[ROW][C]18[/C][C]48[/C][C]41.8380525166743[/C][C]6.16194748332573[/C][/ROW]
[ROW][C]19[/C][C]35[/C][C]36.3824260342733[/C][C]-1.38242603427332[/C][/ROW]
[ROW][C]20[/C][C]36[/C][C]26.4011771216597[/C][C]9.5988228783403[/C][/ROW]
[ROW][C]21[/C][C]51[/C][C]30.4618799396217[/C][C]20.5381200603783[/C][/ROW]
[ROW][C]22[/C][C]50[/C][C]34.9644587202633[/C][C]15.0355412797367[/C][/ROW]
[ROW][C]23[/C][C]61[/C][C]39.9088891886615[/C][C]21.0911108113385[/C][/ROW]
[ROW][C]24[/C][C]63[/C][C]47.3590795126269[/C][C]15.6409204873731[/C][/ROW]
[ROW][C]25[/C][C]61[/C][C]41.7474488407776[/C][C]19.2525511592224[/C][/ROW]
[ROW][C]26[/C][C]62[/C][C]39.6124065589765[/C][C]22.3875934410235[/C][/ROW]
[ROW][C]27[/C][C]58[/C][C]30.9248103084356[/C][C]27.0751896915644[/C][/ROW]
[ROW][C]28[/C][C]65[/C][C]48.8396652611018[/C][C]16.1603347388982[/C][/ROW]
[ROW][C]29[/C][C]93[/C][C]120.376007733544[/C][C]-27.3760077335443[/C][/ROW]
[ROW][C]30[/C][C]94[/C][C]115.441865223909[/C][C]-21.4418652239095[/C][/ROW]
[ROW][C]31[/C][C]86[/C][C]85.4818643154791[/C][C]0.518135684520871[/C][/ROW]
[ROW][C]32[/C][C]88[/C][C]84.3868182017308[/C][C]3.61318179826920[/C][/ROW]
[ROW][C]33[/C][C]102[/C][C]112.134675530090[/C][C]-10.1346755300897[/C][/ROW]
[ROW][C]34[/C][C]107[/C][C]105.140763240839[/C][C]1.85923675916068[/C][/ROW]
[ROW][C]35[/C][C]121[/C][C]121.118271453613[/C][C]-0.118271453613005[/C][/ROW]
[ROW][C]36[/C][C]127[/C][C]121.077115027069[/C][C]5.92288497293131[/C][/ROW]
[ROW][C]37[/C][C]125[/C][C]110.945392624378[/C][C]14.0546073756224[/C][/ROW]
[ROW][C]38[/C][C]128[/C][C]106.352336148663[/C][C]21.6476638513365[/C][/ROW]
[ROW][C]39[/C][C]117[/C][C]90.9649988625661[/C][C]26.0350011374339[/C][/ROW]
[ROW][C]40[/C][C]127[/C][C]101.772867383471[/C][C]25.2271326165286[/C][/ROW]
[ROW][C]41[/C][C]160[/C][C]157.892212670898[/C][C]2.10778732910242[/C][/ROW]
[ROW][C]42[/C][C]162[/C][C]161.286935759247[/C][C]0.713064240753056[/C][/ROW]
[ROW][C]43[/C][C]153[/C][C]144.317225248130[/C][C]8.68277475187034[/C][/ROW]
[ROW][C]44[/C][C]160[/C][C]146.834948882523[/C][C]13.1650511174767[/C][/ROW]
[ROW][C]45[/C][C]177[/C][C]174.675906040562[/C][C]2.32409395943776[/C][/ROW]
[ROW][C]46[/C][C]178[/C][C]181.105546752881[/C][C]-3.10554675288139[/C][/ROW]
[ROW][C]47[/C][C]196[/C][C]203.976018348845[/C][C]-7.97601834884512[/C][/ROW]
[ROW][C]48[/C][C]212[/C][C]210.472869930212[/C][C]1.52713006978769[/C][/ROW]
[ROW][C]49[/C][C]212[/C][C]202.646610211188[/C][C]9.35338978881151[/C][/ROW]
[ROW][C]50[/C][C]211[/C][C]202.148783322787[/C][C]8.85121667721307[/C][/ROW]
[ROW][C]51[/C][C]204[/C][C]178.105414782944[/C][C]25.8945852170555[/C][/ROW]
[ROW][C]52[/C][C]216[/C][C]190.21585649707[/C][C]25.7841435029301[/C][/ROW]
[ROW][C]53[/C][C]248[/C][C]244.510236825574[/C][C]3.48976317442575[/C][/ROW]
[ROW][C]54[/C][C]250[/C][C]246.450783325021[/C][C]3.54921667497905[/C][/ROW]
[ROW][C]55[/C][C]240[/C][C]229.372890883863[/C][C]10.6271091161367[/C][/ROW]
[ROW][C]56[/C][C]249[/C][C]236.937563788766[/C][C]12.0624362112345[/C][/ROW]
[ROW][C]57[/C][C]275[/C][C]263.042385367727[/C][C]11.9576146322730[/C][/ROW]
[ROW][C]58[/C][C]277[/C][C]265.712552142234[/C][C]11.2874478577659[/C][/ROW]
[ROW][C]59[/C][C]286[/C][C]294.649798731673[/C][C]-8.64979873167329[/C][/ROW]
[ROW][C]60[/C][C]302[/C][C]315.135086901385[/C][C]-13.1350869013848[/C][/ROW]
[ROW][C]61[/C][C]290[/C][C]309.893093353792[/C][C]-19.8930933537925[/C][/ROW]
[ROW][C]62[/C][C]290[/C][C]303.117698760301[/C][C]-13.1176987603006[/C][/ROW]
[ROW][C]63[/C][C]277[/C][C]283.486602623844[/C][C]-6.4866026238443[/C][/ROW]
[ROW][C]64[/C][C]285[/C][C]292.823866971079[/C][C]-7.82386697107933[/C][/ROW]
[ROW][C]65[/C][C]311[/C][C]334.270974687350[/C][C]-23.2709746873496[/C][/ROW]
[ROW][C]66[/C][C]300[/C][C]330.791503884563[/C][C]-30.7915038845633[/C][/ROW]
[ROW][C]67[/C][C]291[/C][C]308.866917739733[/C][C]-17.8669177397330[/C][/ROW]
[ROW][C]68[/C][C]299[/C][C]313.146783649465[/C][C]-14.1467836494645[/C][/ROW]
[ROW][C]69[/C][C]332[/C][C]338.698860574392[/C][C]-6.69886057439152[/C][/ROW]
[ROW][C]70[/C][C]337[/C][C]335.098864372296[/C][C]1.90113562770421[/C][/ROW]
[ROW][C]71[/C][C]343[/C][C]345.341446975476[/C][C]-2.34144697547589[/C][/ROW]
[ROW][C]72[/C][C]360[/C][C]362.791377332174[/C][C]-2.79137733217431[/C][/ROW]
[ROW][C]73[/C][C]353[/C][C]348.003837533957[/C][C]4.99616246604324[/C][/ROW]
[ROW][C]74[/C][C]351[/C][C]346.945006011618[/C][C]4.05499398838157[/C][/ROW]
[ROW][C]75[/C][C]341[/C][C]329.821484837055[/C][C]11.1785151629454[/C][/ROW]
[ROW][C]76[/C][C]348[/C][C]339.658970072508[/C][C]8.34102992749234[/C][/ROW]
[ROW][C]77[/C][C]381[/C][C]373.841083503257[/C][C]7.1589164967433[/C][/ROW]
[ROW][C]78[/C][C]358[/C][C]364.443136986266[/C][C]-6.4431369862657[/C][/ROW]
[ROW][C]79[/C][C]353[/C][C]352.952257879794[/C][C]0.0477421202064647[/C][/ROW]
[ROW][C]80[/C][C]358[/C][C]363.236019478418[/C][C]-5.23601947841757[/C][/ROW]
[ROW][C]81[/C][C]399[/C][C]401.904778684521[/C][C]-2.90477868452052[/C][/ROW]
[ROW][C]82[/C][C]409[/C][C]405.775236689811[/C][C]3.22476331018885[/C][/ROW]
[ROW][C]83[/C][C]407[/C][C]413.224574255489[/C][C]-6.22457425548936[/C][/ROW]
[ROW][C]84[/C][C]419[/C][C]432.469211640472[/C][C]-13.4692116404721[/C][/ROW]
[ROW][C]85[/C][C]418[/C][C]420.232241543497[/C][C]-2.23224154349737[/C][/ROW]
[ROW][C]86[/C][C]421[/C][C]416.084403274391[/C][C]4.91559672560919[/C][/ROW]
[ROW][C]87[/C][C]414[/C][C]401.662335549377[/C][C]12.3376644506232[/C][/ROW]
[ROW][C]88[/C][C]424[/C][C]409.493631417327[/C][C]14.5063685826732[/C][/ROW]
[ROW][C]89[/C][C]463[/C][C]448.375875034616[/C][C]14.6241249653841[/C][/ROW]
[ROW][C]90[/C][C]437[/C][C]424.032348112696[/C][C]12.9676518873035[/C][/ROW]
[ROW][C]91[/C][C]430[/C][C]418.531764110505[/C][C]11.4682358894946[/C][/ROW]
[ROW][C]92[/C][C]436[/C][C]426.552824927083[/C][C]9.44717507291728[/C][/ROW]
[ROW][C]93[/C][C]474[/C][C]476.553445223035[/C][C]-2.553445223035[/C][/ROW]
[ROW][C]94[/C][C]489[/C][C]487.009146895982[/C][C]1.99085310401750[/C][/ROW]
[ROW][C]95[/C][C]482[/C][C]486.231795117647[/C][C]-4.23179511764693[/C][/ROW]
[ROW][C]96[/C][C]492[/C][C]502.246427752703[/C][C]-10.2464277527030[/C][/ROW]
[ROW][C]97[/C][C]502[/C][C]499.117353209686[/C][C]2.88264679031357[/C][/ROW]
[ROW][C]98[/C][C]500[/C][C]501.693261568068[/C][C]-1.69326156806761[/C][/ROW]
[ROW][C]99[/C][C]493[/C][C]490.637377835757[/C][C]2.36262216424342[/C][/ROW]
[ROW][C]100[/C][C]504[/C][C]500.247827420412[/C][C]3.75217257958786[/C][/ROW]
[ROW][C]101[/C][C]538[/C][C]544.266158879228[/C][C]-6.26615887922787[/C][/ROW]
[ROW][C]102[/C][C]516[/C][C]510.539515840027[/C][C]5.46048415997313[/C][/ROW]
[ROW][C]103[/C][C]502[/C][C]500.687709295027[/C][C]1.31229070497284[/C][/ROW]
[ROW][C]104[/C][C]501[/C][C]505.760629563508[/C][C]-4.76062956350842[/C][/ROW]
[ROW][C]105[/C][C]541[/C][C]549.401803617438[/C][C]-8.40180361743785[/C][/ROW]
[ROW][C]106[/C][C]571[/C][C]563.886924550248[/C][C]7.11307544975182[/C][/ROW]
[ROW][C]107[/C][C]559[/C][C]556.52810803436[/C][C]2.47189196563954[/C][/ROW]
[ROW][C]108[/C][C]569[/C][C]569.123138142177[/C][C]-0.123138142176572[/C][/ROW]
[ROW][C]109[/C][C]576[/C][C]578.319365692353[/C][C]-2.31936569235324[/C][/ROW]
[ROW][C]110[/C][C]573[/C][C]575.369278243249[/C][C]-2.36927824324903[/C][/ROW]
[ROW][C]111[/C][C]562[/C][C]565.481496797421[/C][C]-3.48149679742119[/C][/ROW]
[ROW][C]112[/C][C]570[/C][C]576.077233259365[/C][C]-6.07723325936456[/C][/ROW]
[ROW][C]113[/C][C]597[/C][C]614.63374958803[/C][C]-17.6337495880302[/C][/ROW]
[ROW][C]114[/C][C]573[/C][C]584.699471116764[/C][C]-11.6994711167645[/C][/ROW]
[ROW][C]115[/C][C]562[/C][C]566.285335599852[/C][C]-4.28533559985181[/C][/ROW]
[ROW][C]116[/C][C]556[/C][C]564.350268451656[/C][C]-8.35026845165567[/C][/ROW]
[ROW][C]117[/C][C]600[/C][C]608.180435407701[/C][C]-8.18043540770122[/C][/ROW]
[ROW][C]118[/C][C]630[/C][C]637.202970029505[/C][C]-7.20297002950474[/C][/ROW]
[ROW][C]119[/C][C]624[/C][C]621.356514805579[/C][C]2.64348519442080[/C][/ROW]
[ROW][C]120[/C][C]634[/C][C]631.355294228884[/C][C]2.64470577111581[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78124&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78124&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
132426.4444669311186-2.44446693111864
142122.7999103475503-1.79991034755028
151515.5071479699010-0.507147969901043
162120.48639043327280.513609566727155
174945.13584072224323.86415927775681
184841.83805251667436.16194748332573
193536.3824260342733-1.38242603427332
203626.40117712165979.5988228783403
215130.461879939621720.5381200603783
225034.964458720263315.0355412797367
236139.908889188661521.0911108113385
246347.359079512626915.6409204873731
256141.747448840777619.2525511592224
266239.612406558976522.3875934410235
275830.924810308435627.0751896915644
286548.839665261101816.1603347388982
2993120.376007733544-27.3760077335443
3094115.441865223909-21.4418652239095
318685.48186431547910.518135684520871
328884.38681820173083.61318179826920
33102112.134675530090-10.1346755300897
34107105.1407632408391.85923675916068
35121121.118271453613-0.118271453613005
36127121.0771150270695.92288497293131
37125110.94539262437814.0546073756224
38128106.35233614866321.6476638513365
3911790.964998862566126.0350011374339
40127101.77286738347125.2271326165286
41160157.8922126708982.10778732910242
42162161.2869357592470.713064240753056
43153144.3172252481308.68277475187034
44160146.83494888252313.1650511174767
45177174.6759060405622.32409395943776
46178181.105546752881-3.10554675288139
47196203.976018348845-7.97601834884512
48212210.4728699302121.52713006978769
49212202.6466102111889.35338978881151
50211202.1487833227878.85121667721307
51204178.10541478294425.8945852170555
52216190.2158564970725.7841435029301
53248244.5102368255743.48976317442575
54250246.4507833250213.54921667497905
55240229.37289088386310.6271091161367
56249236.93756378876612.0624362112345
57275263.04238536772711.9576146322730
58277265.71255214223411.2874478577659
59286294.649798731673-8.64979873167329
60302315.135086901385-13.1350869013848
61290309.893093353792-19.8930933537925
62290303.117698760301-13.1176987603006
63277283.486602623844-6.4866026238443
64285292.823866971079-7.82386697107933
65311334.270974687350-23.2709746873496
66300330.791503884563-30.7915038845633
67291308.866917739733-17.8669177397330
68299313.146783649465-14.1467836494645
69332338.698860574392-6.69886057439152
70337335.0988643722961.90113562770421
71343345.341446975476-2.34144697547589
72360362.791377332174-2.79137733217431
73353348.0038375339574.99616246604324
74351346.9450060116184.05499398838157
75341329.82148483705511.1785151629454
76348339.6589700725088.34102992749234
77381373.8410835032577.1589164967433
78358364.443136986266-6.4431369862657
79353352.9522578797940.0477421202064647
80358363.236019478418-5.23601947841757
81399401.904778684521-2.90477868452052
82409405.7752366898113.22476331018885
83407413.224574255489-6.22457425548936
84419432.469211640472-13.4692116404721
85418420.232241543497-2.23224154349737
86421416.0844032743914.91559672560919
87414401.66233554937712.3376644506232
88424409.49363141732714.5063685826732
89463448.37587503461614.6241249653841
90437424.03234811269612.9676518873035
91430418.53176411050511.4682358894946
92436426.5528249270839.44717507291728
93474476.553445223035-2.553445223035
94489487.0091468959821.99085310401750
95482486.231795117647-4.23179511764693
96492502.246427752703-10.2464277527030
97502499.1173532096862.88264679031357
98500501.693261568068-1.69326156806761
99493490.6373778357572.36262216424342
100504500.2478274204123.75217257958786
101538544.266158879228-6.26615887922787
102516510.5395158400275.46048415997313
103502500.6877092950271.31229070497284
104501505.760629563508-4.76062956350842
105541549.401803617438-8.40180361743785
106571563.8869245502487.11307544975182
107559556.528108034362.47189196563954
108569569.123138142177-0.123138142176572
109576578.319365692353-2.31936569235324
110573575.369278243249-2.36927824324903
111562565.481496797421-3.48149679742119
112570576.077233259365-6.07723325936456
113597614.63374958803-17.6337495880302
114573584.699471116764-11.6994711167645
115562566.285335599852-4.28533559985181
116556564.350268451656-8.35026845165567
117600608.180435407701-8.18043540770122
118630637.202970029505-7.20297002950474
119624621.3565148055792.64348519442080
120634631.3552942288842.64470577111581







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121638.301890061408617.075085764316659.528694358501
122633.76228918743612.33697205899655.187606315869
123620.694976661165599.049663884489642.340289437841
124629.116610441239607.17979435738651.053426525099
125660.63537349351638.280785539932682.989961447088
126634.123589831142611.512970567519656.734209094764
127621.106080396055598.169561865774644.042598926336
128615.071615963833591.747445347015638.395786580651
129664.024070526507639.839811170905688.20832988211
130697.4299466292672.366044308721722.493848949679
131689.212738480854663.625475474793714.800001486914
132699.38549502688682.363862116969716.40712793679

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 638.301890061408 & 617.075085764316 & 659.528694358501 \tabularnewline
122 & 633.76228918743 & 612.33697205899 & 655.187606315869 \tabularnewline
123 & 620.694976661165 & 599.049663884489 & 642.340289437841 \tabularnewline
124 & 629.116610441239 & 607.17979435738 & 651.053426525099 \tabularnewline
125 & 660.63537349351 & 638.280785539932 & 682.989961447088 \tabularnewline
126 & 634.123589831142 & 611.512970567519 & 656.734209094764 \tabularnewline
127 & 621.106080396055 & 598.169561865774 & 644.042598926336 \tabularnewline
128 & 615.071615963833 & 591.747445347015 & 638.395786580651 \tabularnewline
129 & 664.024070526507 & 639.839811170905 & 688.20832988211 \tabularnewline
130 & 697.4299466292 & 672.366044308721 & 722.493848949679 \tabularnewline
131 & 689.212738480854 & 663.625475474793 & 714.800001486914 \tabularnewline
132 & 699.38549502688 & 682.363862116969 & 716.40712793679 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78124&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]638.301890061408[/C][C]617.075085764316[/C][C]659.528694358501[/C][/ROW]
[ROW][C]122[/C][C]633.76228918743[/C][C]612.33697205899[/C][C]655.187606315869[/C][/ROW]
[ROW][C]123[/C][C]620.694976661165[/C][C]599.049663884489[/C][C]642.340289437841[/C][/ROW]
[ROW][C]124[/C][C]629.116610441239[/C][C]607.17979435738[/C][C]651.053426525099[/C][/ROW]
[ROW][C]125[/C][C]660.63537349351[/C][C]638.280785539932[/C][C]682.989961447088[/C][/ROW]
[ROW][C]126[/C][C]634.123589831142[/C][C]611.512970567519[/C][C]656.734209094764[/C][/ROW]
[ROW][C]127[/C][C]621.106080396055[/C][C]598.169561865774[/C][C]644.042598926336[/C][/ROW]
[ROW][C]128[/C][C]615.071615963833[/C][C]591.747445347015[/C][C]638.395786580651[/C][/ROW]
[ROW][C]129[/C][C]664.024070526507[/C][C]639.839811170905[/C][C]688.20832988211[/C][/ROW]
[ROW][C]130[/C][C]697.4299466292[/C][C]672.366044308721[/C][C]722.493848949679[/C][/ROW]
[ROW][C]131[/C][C]689.212738480854[/C][C]663.625475474793[/C][C]714.800001486914[/C][/ROW]
[ROW][C]132[/C][C]699.38549502688[/C][C]682.363862116969[/C][C]716.40712793679[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78124&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78124&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
121638.301890061408617.075085764316659.528694358501
122633.76228918743612.33697205899655.187606315869
123620.694976661165599.049663884489642.340289437841
124629.116610441239607.17979435738651.053426525099
125660.63537349351638.280785539932682.989961447088
126634.123589831142611.512970567519656.734209094764
127621.106080396055598.169561865774644.042598926336
128615.071615963833591.747445347015638.395786580651
129664.024070526507639.839811170905688.20832988211
130697.4299466292672.366044308721722.493848949679
131689.212738480854663.625475474793714.800001486914
132699.38549502688682.363862116969716.40712793679



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')