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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 17 Nov 2013 08:55:56 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/17/t1384696575q25jmdioasjh44w.htm/, Retrieved Sun, 28 Apr 2024 21:48:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=225744, Retrieved Sun, 28 Apr 2024 21:48:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-11-17 13:55:56] [a6c86ecfac1c17167d9b343b3a96f19f] [Current]
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Dataseries X:
41
39
50
40
43
38
44
35
39
35
29
49
50
59
63
32
39
47
53
60
57
52
70
90
74
62
55
84
94
70
108
139
120
97
126
149
158
124
140
109
114
77
120
133
110
92
97
78
99
107
112
90
98
125
155
190
236
189
174
178
136
161
171
149
184
155
276
224
213
279
268
287
238
213
257
293
212
246
353
339
308
247
257
322
298
273
312
249
286
279
309
401
309
328
353
354
327
324
285
243
241
287
355
460
364
487
452
391
500
451
375
372
302
316
398
394
431
431




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225744&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225744&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225744&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.213143664571784
beta0.00645020019309324
gamma0.424943606209404

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.213143664571784 \tabularnewline
beta & 0.00645020019309324 \tabularnewline
gamma & 0.424943606209404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225744&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]0.213143664571784[/C][/ROW]
[ROW][C]beta[/C][C]0.00645020019309324[/C][/ROW]
[ROW][C]gamma[/C][C]0.424943606209404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225744&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225744&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
alpha0.213143664571784
beta0.00645020019309324
gamma0.424943606209404







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135047.10543991015492.89456008984506
145955.96233342379513.03766657620488
156359.6005878986163.39941210138404
163230.43937366267471.56062633732526
173936.56040094510452.43959905489554
184742.82510943552454.17489056447554
195356.0035962549122-3.00359625491225
206043.687488354030416.3125116459696
215751.89885109767775.10114890232234
225248.24019090219993.75980909780009
237041.881904574986328.1180954250137
249081.86586557226558.13413442773454
257486.9533818199799-12.9533818199799
266297.5989383758822-35.5989383758822
275594.1112419276594-39.1112419276594
288442.929253022433941.0707469775661
299461.235481075664632.7645189243354
307078.9123828735172-8.91238287351722
3110893.191244531291614.8087554687084
3213985.74516824033453.254831759666
3312098.16111810263221.838881897368
349792.38268778488184.6173122151182
3512692.41333415975733.586665840243
36149146.1903153237172.80968467628333
37158139.58302505972518.4169749402755
38124151.40690084049-27.4069008404896
39140147.812296583395-7.81229658339493
40109108.5353212094310.464678790568755
41114117.503833288207-3.50383328820688
4277111.491890235352-34.4918902353522
43120137.392741457317-17.3927414573171
44133133.550538091545-0.550538091545462
45110121.870273958659-11.8702739586587
4692101.636565226354-9.63656522635388
4797107.771493254875-10.7714932548753
4878139.96193181665-61.9619318166498
4999124.886206798657-25.8862067986565
50107113.177831745115-6.17783174511507
51112119.061002171171-7.06100217117134
529089.02511348040280.974886519597192
539895.41996297598742.58003702401257
5412582.320232669807742.6797673301923
55155129.63084923444225.3691507655582
56190140.70015487820849.2998451217921
57236133.52953175825102.47046824175
58189132.20975747218556.7902425278149
59174155.57070228571718.4292977142827
60178182.91427237436-4.91427237435985
61136198.150377986202-62.1503779862019
62161185.047759625672-24.0477596256715
63171190.702749040377-19.7027490403766
64149144.299472155174.70052784483045
65184155.81958896549728.1804110345027
66155158.658606313425-3.658606313425
67276205.40654058262470.593459417376
68224239.226122351414-15.2261223514139
69213228.97946822359-15.9794682235899
70279177.769152238654101.230847761346
71268197.04525974419770.9547402558033
72287231.90942291166455.0905770883356
73238237.5203557885680.479644211431577
74213255.630083725721-42.6300837257214
75257263.551451392396-6.55145139239562
76293212.26466516524980.7353348347509
77212257.289537670057-45.289537670057
78246227.38623846700618.6137615329943
79353335.43591869760217.5640813023978
80339324.95676728060814.0432327193918
81308317.200424013298-9.2004240132984
82247297.35309743694-50.3530974369401
83257269.048143450586-12.0481434505858
84322281.58562500722840.4143749927717
85298263.01824072364234.9817592763578
86273273.783458765981-0.783458765981436
87312307.6340368082344.36596319176562
88249281.393544546959-32.3935445469594
89286258.37636111754327.6236388824571
90279265.2471902105113.7528097894896
91309384.965513568952-75.9655135689516
92401352.06668663173748.9333133682632
93309342.098302816728-33.0983028167284
94328300.23275821301927.7672417869809
95353300.52637748454952.4736225154508
96354349.8066004467274.19339955327297
97327316.66835967606610.3316403239343
98324308.931172358715.0688276413005
99285352.763567038032-67.7635670380317
100243294.805200411894-51.8052004118941
101241287.64632500351-46.6463250035102
102287273.79882701988313.2011729801171
103355363.304616749653-8.30461674965301
104460387.21980598328472.780194016716
105364351.47134467329412.5286553267057
106487337.976115293891149.023884706109
107452371.92643091763180.0735690823693
108391414.75027036822-23.7502703682199
109500372.29416944829127.70583055171
110451388.94363921966462.0563607803361
111375417.178199639255-42.1781996392548
112372357.81512560495214.1848743950485
113302367.547487313144-65.5474873131442
114316375.106366255881-59.1063662558813
115398464.864989196214-66.8649891962139
116394515.546883764626-121.546883764626
117431407.55404299828923.4459570017113
118431441.367396683966-10.3673966839662

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 50 & 47.1054399101549 & 2.89456008984506 \tabularnewline
14 & 59 & 55.9623334237951 & 3.03766657620488 \tabularnewline
15 & 63 & 59.600587898616 & 3.39941210138404 \tabularnewline
16 & 32 & 30.4393736626747 & 1.56062633732526 \tabularnewline
17 & 39 & 36.5604009451045 & 2.43959905489554 \tabularnewline
18 & 47 & 42.8251094355245 & 4.17489056447554 \tabularnewline
19 & 53 & 56.0035962549122 & -3.00359625491225 \tabularnewline
20 & 60 & 43.6874883540304 & 16.3125116459696 \tabularnewline
21 & 57 & 51.8988510976777 & 5.10114890232234 \tabularnewline
22 & 52 & 48.2401909021999 & 3.75980909780009 \tabularnewline
23 & 70 & 41.8819045749863 & 28.1180954250137 \tabularnewline
24 & 90 & 81.8658655722655 & 8.13413442773454 \tabularnewline
25 & 74 & 86.9533818199799 & -12.9533818199799 \tabularnewline
26 & 62 & 97.5989383758822 & -35.5989383758822 \tabularnewline
27 & 55 & 94.1112419276594 & -39.1112419276594 \tabularnewline
28 & 84 & 42.9292530224339 & 41.0707469775661 \tabularnewline
29 & 94 & 61.2354810756646 & 32.7645189243354 \tabularnewline
30 & 70 & 78.9123828735172 & -8.91238287351722 \tabularnewline
31 & 108 & 93.1912445312916 & 14.8087554687084 \tabularnewline
32 & 139 & 85.745168240334 & 53.254831759666 \tabularnewline
33 & 120 & 98.161118102632 & 21.838881897368 \tabularnewline
34 & 97 & 92.3826877848818 & 4.6173122151182 \tabularnewline
35 & 126 & 92.413334159757 & 33.586665840243 \tabularnewline
36 & 149 & 146.190315323717 & 2.80968467628333 \tabularnewline
37 & 158 & 139.583025059725 & 18.4169749402755 \tabularnewline
38 & 124 & 151.40690084049 & -27.4069008404896 \tabularnewline
39 & 140 & 147.812296583395 & -7.81229658339493 \tabularnewline
40 & 109 & 108.535321209431 & 0.464678790568755 \tabularnewline
41 & 114 & 117.503833288207 & -3.50383328820688 \tabularnewline
42 & 77 & 111.491890235352 & -34.4918902353522 \tabularnewline
43 & 120 & 137.392741457317 & -17.3927414573171 \tabularnewline
44 & 133 & 133.550538091545 & -0.550538091545462 \tabularnewline
45 & 110 & 121.870273958659 & -11.8702739586587 \tabularnewline
46 & 92 & 101.636565226354 & -9.63656522635388 \tabularnewline
47 & 97 & 107.771493254875 & -10.7714932548753 \tabularnewline
48 & 78 & 139.96193181665 & -61.9619318166498 \tabularnewline
49 & 99 & 124.886206798657 & -25.8862067986565 \tabularnewline
50 & 107 & 113.177831745115 & -6.17783174511507 \tabularnewline
51 & 112 & 119.061002171171 & -7.06100217117134 \tabularnewline
52 & 90 & 89.0251134804028 & 0.974886519597192 \tabularnewline
53 & 98 & 95.4199629759874 & 2.58003702401257 \tabularnewline
54 & 125 & 82.3202326698077 & 42.6797673301923 \tabularnewline
55 & 155 & 129.630849234442 & 25.3691507655582 \tabularnewline
56 & 190 & 140.700154878208 & 49.2998451217921 \tabularnewline
57 & 236 & 133.52953175825 & 102.47046824175 \tabularnewline
58 & 189 & 132.209757472185 & 56.7902425278149 \tabularnewline
59 & 174 & 155.570702285717 & 18.4292977142827 \tabularnewline
60 & 178 & 182.91427237436 & -4.91427237435985 \tabularnewline
61 & 136 & 198.150377986202 & -62.1503779862019 \tabularnewline
62 & 161 & 185.047759625672 & -24.0477596256715 \tabularnewline
63 & 171 & 190.702749040377 & -19.7027490403766 \tabularnewline
64 & 149 & 144.29947215517 & 4.70052784483045 \tabularnewline
65 & 184 & 155.819588965497 & 28.1804110345027 \tabularnewline
66 & 155 & 158.658606313425 & -3.658606313425 \tabularnewline
67 & 276 & 205.406540582624 & 70.593459417376 \tabularnewline
68 & 224 & 239.226122351414 & -15.2261223514139 \tabularnewline
69 & 213 & 228.97946822359 & -15.9794682235899 \tabularnewline
70 & 279 & 177.769152238654 & 101.230847761346 \tabularnewline
71 & 268 & 197.045259744197 & 70.9547402558033 \tabularnewline
72 & 287 & 231.909422911664 & 55.0905770883356 \tabularnewline
73 & 238 & 237.520355788568 & 0.479644211431577 \tabularnewline
74 & 213 & 255.630083725721 & -42.6300837257214 \tabularnewline
75 & 257 & 263.551451392396 & -6.55145139239562 \tabularnewline
76 & 293 & 212.264665165249 & 80.7353348347509 \tabularnewline
77 & 212 & 257.289537670057 & -45.289537670057 \tabularnewline
78 & 246 & 227.386238467006 & 18.6137615329943 \tabularnewline
79 & 353 & 335.435918697602 & 17.5640813023978 \tabularnewline
80 & 339 & 324.956767280608 & 14.0432327193918 \tabularnewline
81 & 308 & 317.200424013298 & -9.2004240132984 \tabularnewline
82 & 247 & 297.35309743694 & -50.3530974369401 \tabularnewline
83 & 257 & 269.048143450586 & -12.0481434505858 \tabularnewline
84 & 322 & 281.585625007228 & 40.4143749927717 \tabularnewline
85 & 298 & 263.018240723642 & 34.9817592763578 \tabularnewline
86 & 273 & 273.783458765981 & -0.783458765981436 \tabularnewline
87 & 312 & 307.634036808234 & 4.36596319176562 \tabularnewline
88 & 249 & 281.393544546959 & -32.3935445469594 \tabularnewline
89 & 286 & 258.376361117543 & 27.6236388824571 \tabularnewline
90 & 279 & 265.24719021051 & 13.7528097894896 \tabularnewline
91 & 309 & 384.965513568952 & -75.9655135689516 \tabularnewline
92 & 401 & 352.066686631737 & 48.9333133682632 \tabularnewline
93 & 309 & 342.098302816728 & -33.0983028167284 \tabularnewline
94 & 328 & 300.232758213019 & 27.7672417869809 \tabularnewline
95 & 353 & 300.526377484549 & 52.4736225154508 \tabularnewline
96 & 354 & 349.806600446727 & 4.19339955327297 \tabularnewline
97 & 327 & 316.668359676066 & 10.3316403239343 \tabularnewline
98 & 324 & 308.9311723587 & 15.0688276413005 \tabularnewline
99 & 285 & 352.763567038032 & -67.7635670380317 \tabularnewline
100 & 243 & 294.805200411894 & -51.8052004118941 \tabularnewline
101 & 241 & 287.64632500351 & -46.6463250035102 \tabularnewline
102 & 287 & 273.798827019883 & 13.2011729801171 \tabularnewline
103 & 355 & 363.304616749653 & -8.30461674965301 \tabularnewline
104 & 460 & 387.219805983284 & 72.780194016716 \tabularnewline
105 & 364 & 351.471344673294 & 12.5286553267057 \tabularnewline
106 & 487 & 337.976115293891 & 149.023884706109 \tabularnewline
107 & 452 & 371.926430917631 & 80.0735690823693 \tabularnewline
108 & 391 & 414.75027036822 & -23.7502703682199 \tabularnewline
109 & 500 & 372.29416944829 & 127.70583055171 \tabularnewline
110 & 451 & 388.943639219664 & 62.0563607803361 \tabularnewline
111 & 375 & 417.178199639255 & -42.1781996392548 \tabularnewline
112 & 372 & 357.815125604952 & 14.1848743950485 \tabularnewline
113 & 302 & 367.547487313144 & -65.5474873131442 \tabularnewline
114 & 316 & 375.106366255881 & -59.1063662558813 \tabularnewline
115 & 398 & 464.864989196214 & -66.8649891962139 \tabularnewline
116 & 394 & 515.546883764626 & -121.546883764626 \tabularnewline
117 & 431 & 407.554042998289 & 23.4459570017113 \tabularnewline
118 & 431 & 441.367396683966 & -10.3673966839662 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225744&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]50[/C][C]47.1054399101549[/C][C]2.89456008984506[/C][/ROW]
[ROW][C]14[/C][C]59[/C][C]55.9623334237951[/C][C]3.03766657620488[/C][/ROW]
[ROW][C]15[/C][C]63[/C][C]59.600587898616[/C][C]3.39941210138404[/C][/ROW]
[ROW][C]16[/C][C]32[/C][C]30.4393736626747[/C][C]1.56062633732526[/C][/ROW]
[ROW][C]17[/C][C]39[/C][C]36.5604009451045[/C][C]2.43959905489554[/C][/ROW]
[ROW][C]18[/C][C]47[/C][C]42.8251094355245[/C][C]4.17489056447554[/C][/ROW]
[ROW][C]19[/C][C]53[/C][C]56.0035962549122[/C][C]-3.00359625491225[/C][/ROW]
[ROW][C]20[/C][C]60[/C][C]43.6874883540304[/C][C]16.3125116459696[/C][/ROW]
[ROW][C]21[/C][C]57[/C][C]51.8988510976777[/C][C]5.10114890232234[/C][/ROW]
[ROW][C]22[/C][C]52[/C][C]48.2401909021999[/C][C]3.75980909780009[/C][/ROW]
[ROW][C]23[/C][C]70[/C][C]41.8819045749863[/C][C]28.1180954250137[/C][/ROW]
[ROW][C]24[/C][C]90[/C][C]81.8658655722655[/C][C]8.13413442773454[/C][/ROW]
[ROW][C]25[/C][C]74[/C][C]86.9533818199799[/C][C]-12.9533818199799[/C][/ROW]
[ROW][C]26[/C][C]62[/C][C]97.5989383758822[/C][C]-35.5989383758822[/C][/ROW]
[ROW][C]27[/C][C]55[/C][C]94.1112419276594[/C][C]-39.1112419276594[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]42.9292530224339[/C][C]41.0707469775661[/C][/ROW]
[ROW][C]29[/C][C]94[/C][C]61.2354810756646[/C][C]32.7645189243354[/C][/ROW]
[ROW][C]30[/C][C]70[/C][C]78.9123828735172[/C][C]-8.91238287351722[/C][/ROW]
[ROW][C]31[/C][C]108[/C][C]93.1912445312916[/C][C]14.8087554687084[/C][/ROW]
[ROW][C]32[/C][C]139[/C][C]85.745168240334[/C][C]53.254831759666[/C][/ROW]
[ROW][C]33[/C][C]120[/C][C]98.161118102632[/C][C]21.838881897368[/C][/ROW]
[ROW][C]34[/C][C]97[/C][C]92.3826877848818[/C][C]4.6173122151182[/C][/ROW]
[ROW][C]35[/C][C]126[/C][C]92.413334159757[/C][C]33.586665840243[/C][/ROW]
[ROW][C]36[/C][C]149[/C][C]146.190315323717[/C][C]2.80968467628333[/C][/ROW]
[ROW][C]37[/C][C]158[/C][C]139.583025059725[/C][C]18.4169749402755[/C][/ROW]
[ROW][C]38[/C][C]124[/C][C]151.40690084049[/C][C]-27.4069008404896[/C][/ROW]
[ROW][C]39[/C][C]140[/C][C]147.812296583395[/C][C]-7.81229658339493[/C][/ROW]
[ROW][C]40[/C][C]109[/C][C]108.535321209431[/C][C]0.464678790568755[/C][/ROW]
[ROW][C]41[/C][C]114[/C][C]117.503833288207[/C][C]-3.50383328820688[/C][/ROW]
[ROW][C]42[/C][C]77[/C][C]111.491890235352[/C][C]-34.4918902353522[/C][/ROW]
[ROW][C]43[/C][C]120[/C][C]137.392741457317[/C][C]-17.3927414573171[/C][/ROW]
[ROW][C]44[/C][C]133[/C][C]133.550538091545[/C][C]-0.550538091545462[/C][/ROW]
[ROW][C]45[/C][C]110[/C][C]121.870273958659[/C][C]-11.8702739586587[/C][/ROW]
[ROW][C]46[/C][C]92[/C][C]101.636565226354[/C][C]-9.63656522635388[/C][/ROW]
[ROW][C]47[/C][C]97[/C][C]107.771493254875[/C][C]-10.7714932548753[/C][/ROW]
[ROW][C]48[/C][C]78[/C][C]139.96193181665[/C][C]-61.9619318166498[/C][/ROW]
[ROW][C]49[/C][C]99[/C][C]124.886206798657[/C][C]-25.8862067986565[/C][/ROW]
[ROW][C]50[/C][C]107[/C][C]113.177831745115[/C][C]-6.17783174511507[/C][/ROW]
[ROW][C]51[/C][C]112[/C][C]119.061002171171[/C][C]-7.06100217117134[/C][/ROW]
[ROW][C]52[/C][C]90[/C][C]89.0251134804028[/C][C]0.974886519597192[/C][/ROW]
[ROW][C]53[/C][C]98[/C][C]95.4199629759874[/C][C]2.58003702401257[/C][/ROW]
[ROW][C]54[/C][C]125[/C][C]82.3202326698077[/C][C]42.6797673301923[/C][/ROW]
[ROW][C]55[/C][C]155[/C][C]129.630849234442[/C][C]25.3691507655582[/C][/ROW]
[ROW][C]56[/C][C]190[/C][C]140.700154878208[/C][C]49.2998451217921[/C][/ROW]
[ROW][C]57[/C][C]236[/C][C]133.52953175825[/C][C]102.47046824175[/C][/ROW]
[ROW][C]58[/C][C]189[/C][C]132.209757472185[/C][C]56.7902425278149[/C][/ROW]
[ROW][C]59[/C][C]174[/C][C]155.570702285717[/C][C]18.4292977142827[/C][/ROW]
[ROW][C]60[/C][C]178[/C][C]182.91427237436[/C][C]-4.91427237435985[/C][/ROW]
[ROW][C]61[/C][C]136[/C][C]198.150377986202[/C][C]-62.1503779862019[/C][/ROW]
[ROW][C]62[/C][C]161[/C][C]185.047759625672[/C][C]-24.0477596256715[/C][/ROW]
[ROW][C]63[/C][C]171[/C][C]190.702749040377[/C][C]-19.7027490403766[/C][/ROW]
[ROW][C]64[/C][C]149[/C][C]144.29947215517[/C][C]4.70052784483045[/C][/ROW]
[ROW][C]65[/C][C]184[/C][C]155.819588965497[/C][C]28.1804110345027[/C][/ROW]
[ROW][C]66[/C][C]155[/C][C]158.658606313425[/C][C]-3.658606313425[/C][/ROW]
[ROW][C]67[/C][C]276[/C][C]205.406540582624[/C][C]70.593459417376[/C][/ROW]
[ROW][C]68[/C][C]224[/C][C]239.226122351414[/C][C]-15.2261223514139[/C][/ROW]
[ROW][C]69[/C][C]213[/C][C]228.97946822359[/C][C]-15.9794682235899[/C][/ROW]
[ROW][C]70[/C][C]279[/C][C]177.769152238654[/C][C]101.230847761346[/C][/ROW]
[ROW][C]71[/C][C]268[/C][C]197.045259744197[/C][C]70.9547402558033[/C][/ROW]
[ROW][C]72[/C][C]287[/C][C]231.909422911664[/C][C]55.0905770883356[/C][/ROW]
[ROW][C]73[/C][C]238[/C][C]237.520355788568[/C][C]0.479644211431577[/C][/ROW]
[ROW][C]74[/C][C]213[/C][C]255.630083725721[/C][C]-42.6300837257214[/C][/ROW]
[ROW][C]75[/C][C]257[/C][C]263.551451392396[/C][C]-6.55145139239562[/C][/ROW]
[ROW][C]76[/C][C]293[/C][C]212.264665165249[/C][C]80.7353348347509[/C][/ROW]
[ROW][C]77[/C][C]212[/C][C]257.289537670057[/C][C]-45.289537670057[/C][/ROW]
[ROW][C]78[/C][C]246[/C][C]227.386238467006[/C][C]18.6137615329943[/C][/ROW]
[ROW][C]79[/C][C]353[/C][C]335.435918697602[/C][C]17.5640813023978[/C][/ROW]
[ROW][C]80[/C][C]339[/C][C]324.956767280608[/C][C]14.0432327193918[/C][/ROW]
[ROW][C]81[/C][C]308[/C][C]317.200424013298[/C][C]-9.2004240132984[/C][/ROW]
[ROW][C]82[/C][C]247[/C][C]297.35309743694[/C][C]-50.3530974369401[/C][/ROW]
[ROW][C]83[/C][C]257[/C][C]269.048143450586[/C][C]-12.0481434505858[/C][/ROW]
[ROW][C]84[/C][C]322[/C][C]281.585625007228[/C][C]40.4143749927717[/C][/ROW]
[ROW][C]85[/C][C]298[/C][C]263.018240723642[/C][C]34.9817592763578[/C][/ROW]
[ROW][C]86[/C][C]273[/C][C]273.783458765981[/C][C]-0.783458765981436[/C][/ROW]
[ROW][C]87[/C][C]312[/C][C]307.634036808234[/C][C]4.36596319176562[/C][/ROW]
[ROW][C]88[/C][C]249[/C][C]281.393544546959[/C][C]-32.3935445469594[/C][/ROW]
[ROW][C]89[/C][C]286[/C][C]258.376361117543[/C][C]27.6236388824571[/C][/ROW]
[ROW][C]90[/C][C]279[/C][C]265.24719021051[/C][C]13.7528097894896[/C][/ROW]
[ROW][C]91[/C][C]309[/C][C]384.965513568952[/C][C]-75.9655135689516[/C][/ROW]
[ROW][C]92[/C][C]401[/C][C]352.066686631737[/C][C]48.9333133682632[/C][/ROW]
[ROW][C]93[/C][C]309[/C][C]342.098302816728[/C][C]-33.0983028167284[/C][/ROW]
[ROW][C]94[/C][C]328[/C][C]300.232758213019[/C][C]27.7672417869809[/C][/ROW]
[ROW][C]95[/C][C]353[/C][C]300.526377484549[/C][C]52.4736225154508[/C][/ROW]
[ROW][C]96[/C][C]354[/C][C]349.806600446727[/C][C]4.19339955327297[/C][/ROW]
[ROW][C]97[/C][C]327[/C][C]316.668359676066[/C][C]10.3316403239343[/C][/ROW]
[ROW][C]98[/C][C]324[/C][C]308.9311723587[/C][C]15.0688276413005[/C][/ROW]
[ROW][C]99[/C][C]285[/C][C]352.763567038032[/C][C]-67.7635670380317[/C][/ROW]
[ROW][C]100[/C][C]243[/C][C]294.805200411894[/C][C]-51.8052004118941[/C][/ROW]
[ROW][C]101[/C][C]241[/C][C]287.64632500351[/C][C]-46.6463250035102[/C][/ROW]
[ROW][C]102[/C][C]287[/C][C]273.798827019883[/C][C]13.2011729801171[/C][/ROW]
[ROW][C]103[/C][C]355[/C][C]363.304616749653[/C][C]-8.30461674965301[/C][/ROW]
[ROW][C]104[/C][C]460[/C][C]387.219805983284[/C][C]72.780194016716[/C][/ROW]
[ROW][C]105[/C][C]364[/C][C]351.471344673294[/C][C]12.5286553267057[/C][/ROW]
[ROW][C]106[/C][C]487[/C][C]337.976115293891[/C][C]149.023884706109[/C][/ROW]
[ROW][C]107[/C][C]452[/C][C]371.926430917631[/C][C]80.0735690823693[/C][/ROW]
[ROW][C]108[/C][C]391[/C][C]414.75027036822[/C][C]-23.7502703682199[/C][/ROW]
[ROW][C]109[/C][C]500[/C][C]372.29416944829[/C][C]127.70583055171[/C][/ROW]
[ROW][C]110[/C][C]451[/C][C]388.943639219664[/C][C]62.0563607803361[/C][/ROW]
[ROW][C]111[/C][C]375[/C][C]417.178199639255[/C][C]-42.1781996392548[/C][/ROW]
[ROW][C]112[/C][C]372[/C][C]357.815125604952[/C][C]14.1848743950485[/C][/ROW]
[ROW][C]113[/C][C]302[/C][C]367.547487313144[/C][C]-65.5474873131442[/C][/ROW]
[ROW][C]114[/C][C]316[/C][C]375.106366255881[/C][C]-59.1063662558813[/C][/ROW]
[ROW][C]115[/C][C]398[/C][C]464.864989196214[/C][C]-66.8649891962139[/C][/ROW]
[ROW][C]116[/C][C]394[/C][C]515.546883764626[/C][C]-121.546883764626[/C][/ROW]
[ROW][C]117[/C][C]431[/C][C]407.554042998289[/C][C]23.4459570017113[/C][/ROW]
[ROW][C]118[/C][C]431[/C][C]441.367396683966[/C][C]-10.3673966839662[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225744&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225744&T=2

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135047.10543991015492.89456008984506
145955.96233342379513.03766657620488
156359.6005878986163.39941210138404
163230.43937366267471.56062633732526
173936.56040094510452.43959905489554
184742.82510943552454.17489056447554
195356.0035962549122-3.00359625491225
206043.687488354030416.3125116459696
215751.89885109767775.10114890232234
225248.24019090219993.75980909780009
237041.881904574986328.1180954250137
249081.86586557226558.13413442773454
257486.9533818199799-12.9533818199799
266297.5989383758822-35.5989383758822
275594.1112419276594-39.1112419276594
288442.929253022433941.0707469775661
299461.235481075664632.7645189243354
307078.9123828735172-8.91238287351722
3110893.191244531291614.8087554687084
3213985.74516824033453.254831759666
3312098.16111810263221.838881897368
349792.38268778488184.6173122151182
3512692.41333415975733.586665840243
36149146.1903153237172.80968467628333
37158139.58302505972518.4169749402755
38124151.40690084049-27.4069008404896
39140147.812296583395-7.81229658339493
40109108.5353212094310.464678790568755
41114117.503833288207-3.50383328820688
4277111.491890235352-34.4918902353522
43120137.392741457317-17.3927414573171
44133133.550538091545-0.550538091545462
45110121.870273958659-11.8702739586587
4692101.636565226354-9.63656522635388
4797107.771493254875-10.7714932548753
4878139.96193181665-61.9619318166498
4999124.886206798657-25.8862067986565
50107113.177831745115-6.17783174511507
51112119.061002171171-7.06100217117134
529089.02511348040280.974886519597192
539895.41996297598742.58003702401257
5412582.320232669807742.6797673301923
55155129.63084923444225.3691507655582
56190140.70015487820849.2998451217921
57236133.52953175825102.47046824175
58189132.20975747218556.7902425278149
59174155.57070228571718.4292977142827
60178182.91427237436-4.91427237435985
61136198.150377986202-62.1503779862019
62161185.047759625672-24.0477596256715
63171190.702749040377-19.7027490403766
64149144.299472155174.70052784483045
65184155.81958896549728.1804110345027
66155158.658606313425-3.658606313425
67276205.40654058262470.593459417376
68224239.226122351414-15.2261223514139
69213228.97946822359-15.9794682235899
70279177.769152238654101.230847761346
71268197.04525974419770.9547402558033
72287231.90942291166455.0905770883356
73238237.5203557885680.479644211431577
74213255.630083725721-42.6300837257214
75257263.551451392396-6.55145139239562
76293212.26466516524980.7353348347509
77212257.289537670057-45.289537670057
78246227.38623846700618.6137615329943
79353335.43591869760217.5640813023978
80339324.95676728060814.0432327193918
81308317.200424013298-9.2004240132984
82247297.35309743694-50.3530974369401
83257269.048143450586-12.0481434505858
84322281.58562500722840.4143749927717
85298263.01824072364234.9817592763578
86273273.783458765981-0.783458765981436
87312307.6340368082344.36596319176562
88249281.393544546959-32.3935445469594
89286258.37636111754327.6236388824571
90279265.2471902105113.7528097894896
91309384.965513568952-75.9655135689516
92401352.06668663173748.9333133682632
93309342.098302816728-33.0983028167284
94328300.23275821301927.7672417869809
95353300.52637748454952.4736225154508
96354349.8066004467274.19339955327297
97327316.66835967606610.3316403239343
98324308.931172358715.0688276413005
99285352.763567038032-67.7635670380317
100243294.805200411894-51.8052004118941
101241287.64632500351-46.6463250035102
102287273.79882701988313.2011729801171
103355363.304616749653-8.30461674965301
104460387.21980598328472.780194016716
105364351.47134467329412.5286553267057
106487337.976115293891149.023884706109
107452371.92643091763180.0735690823693
108391414.75027036822-23.7502703682199
109500372.29416944829127.70583055171
110451388.94363921966462.0563607803361
111375417.178199639255-42.1781996392548
112372357.81512560495214.1848743950485
113302367.547487313144-65.5474873131442
114316375.106366255881-59.1063662558813
115398464.864989196214-66.8649891962139
116394515.546883764626-121.546883764626
117431407.55404299828923.4459570017113
118431441.367396683966-10.3673966839662







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
119415.894057518486370.11725471943461.670860317541
120406.642333118463357.656358905085455.628307331841
121416.914953425485364.473432897229469.35647395374
122385.423295300715331.314231281698439.532359319733
123366.8727400694310.844594442423422.900885696377
124337.324017241972280.330013889305394.318020594638
125317.963806162532259.617461655594376.310150669469
126339.857506927654276.953324752298402.761689103011
127437.892047535499362.264104046392513.519991024607
128483.19937256445400.109727283811566.28901784509
129446.772591109982366.23781730235527.307364917615
130465.193408486709388.40960019872541.977216774697

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
119 & 415.894057518486 & 370.11725471943 & 461.670860317541 \tabularnewline
120 & 406.642333118463 & 357.656358905085 & 455.628307331841 \tabularnewline
121 & 416.914953425485 & 364.473432897229 & 469.35647395374 \tabularnewline
122 & 385.423295300715 & 331.314231281698 & 439.532359319733 \tabularnewline
123 & 366.8727400694 & 310.844594442423 & 422.900885696377 \tabularnewline
124 & 337.324017241972 & 280.330013889305 & 394.318020594638 \tabularnewline
125 & 317.963806162532 & 259.617461655594 & 376.310150669469 \tabularnewline
126 & 339.857506927654 & 276.953324752298 & 402.761689103011 \tabularnewline
127 & 437.892047535499 & 362.264104046392 & 513.519991024607 \tabularnewline
128 & 483.19937256445 & 400.109727283811 & 566.28901784509 \tabularnewline
129 & 446.772591109982 & 366.23781730235 & 527.307364917615 \tabularnewline
130 & 465.193408486709 & 388.40960019872 & 541.977216774697 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225744&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]119[/C][C]415.894057518486[/C][C]370.11725471943[/C][C]461.670860317541[/C][/ROW]
[ROW][C]120[/C][C]406.642333118463[/C][C]357.656358905085[/C][C]455.628307331841[/C][/ROW]
[ROW][C]121[/C][C]416.914953425485[/C][C]364.473432897229[/C][C]469.35647395374[/C][/ROW]
[ROW][C]122[/C][C]385.423295300715[/C][C]331.314231281698[/C][C]439.532359319733[/C][/ROW]
[ROW][C]123[/C][C]366.8727400694[/C][C]310.844594442423[/C][C]422.900885696377[/C][/ROW]
[ROW][C]124[/C][C]337.324017241972[/C][C]280.330013889305[/C][C]394.318020594638[/C][/ROW]
[ROW][C]125[/C][C]317.963806162532[/C][C]259.617461655594[/C][C]376.310150669469[/C][/ROW]
[ROW][C]126[/C][C]339.857506927654[/C][C]276.953324752298[/C][C]402.761689103011[/C][/ROW]
[ROW][C]127[/C][C]437.892047535499[/C][C]362.264104046392[/C][C]513.519991024607[/C][/ROW]
[ROW][C]128[/C][C]483.19937256445[/C][C]400.109727283811[/C][C]566.28901784509[/C][/ROW]
[ROW][C]129[/C][C]446.772591109982[/C][C]366.23781730235[/C][C]527.307364917615[/C][/ROW]
[ROW][C]130[/C][C]465.193408486709[/C][C]388.40960019872[/C][C]541.977216774697[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225744&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225744&T=3

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
119415.894057518486370.11725471943461.670860317541
120406.642333118463357.656358905085455.628307331841
121416.914953425485364.473432897229469.35647395374
122385.423295300715331.314231281698439.532359319733
123366.8727400694310.844594442423422.900885696377
124337.324017241972280.330013889305394.318020594638
125317.963806162532259.617461655594376.310150669469
126339.857506927654276.953324752298402.761689103011
127437.892047535499362.264104046392513.519991024607
128483.19937256445400.109727283811566.28901784509
129446.772591109982366.23781730235527.307364917615
130465.193408486709388.40960019872541.977216774697



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')