Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 13 Aug 2010 14:29:10 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/13/t1281709825bvw77wtm0kcscyd.htm/, Retrieved Mon, 06 May 2024 04:22:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78753, Retrieved Mon, 06 May 2024 04:22:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCols Julien
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A-Stap 32] [2010-08-13 14:29:10] [de7054811a4039cd82332eb5d7e753fd] [Current]
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Dataseries X:
356
355
354
352
372
371
356
346
347
347
348
350
353
351
348
351
370
370
351
335
330
328
332
334
343
334
336
343
365
364
351
326
320
312
315
316
319
311
315
322
336
339
317
295
291
283
285
289
296
283
285
289
306
306
283
258
255
248
244
249
258
252
246
249
267
284
261
235
229
218
218
229
237
231
229
233
245
256
224
194
192
178
170
187
192
182
178
186
204
224
194
173
178
168
152
163
172
170
156
155
178
194
164
135
139
135
109
121
131
135
119
121
151
169
135
105
112
105
82
81




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78753&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78753&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78753&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0011609542690148
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0011609542690148 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78753&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0011609542690148[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78753&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78753&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
alpha1
beta0.0011609542690148
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33543540
4352353-1
5372350.99883904573121.0011609542690
6371371.023220433195-0.0232204331950925
7356370.023193475334-14.0231934753340
8346355.006913189004-9.00691318900368
9347344.9964565746862.00354342531375
10347345.9987825969791.00121740302097
11348345.9999449645972.00005503540274
12350347.0022669370292.99773306297112
13353349.0057471680263.99425283197428
14351352.010384312902-1.01038431290249
15348350.009211302921-2.00921130292107
16351347.0068787004823.99312129951841
17370350.01151453170119.988485468299
18370369.0347202492370.965279750763443
19351369.035840894884-18.0358408948840
20335350.014902108402-15.0149021084018
21330333.9974704937-3.99747049370023
22328328.992829613265-0.992829613265314
23332326.9916769834875.00832301651263
24334330.9974914174743.00250858252599
25343333.0009771926319.99902280736939
26334342.012585600845-8.01258560084483
27336333.0032833553862.99671664461431
28343335.0067624063677.99323759363273
29365342.01604218967522.9839578103251
30364364.042725513614-0.0427255136136182
31351363.042675911246-12.0426759112462
32326350.028694915237-24.0286949152367
33320325.000798699296-5.00079869929596
34312318.994993000697-6.99499300069749
35315310.9868721337124.01312786628836
36316313.991531191642.00846880835991
37319314.9938629320774.00613706792268
38311317.998513874009-6.99851387400861
39315309.990388919455.0096110805502
40322313.996204848828.0037951511801
41336321.00549688896914.994503111031
42339335.0229048213673.97709517863251
43317338.027522046993-21.0275220469934
44295316.003110055506-21.0031100555061
45291293.978726405225-2.97872640522462
46283289.975268240088-6.97526824008821
47285281.9671702726473.03282972735263
48289283.9706912492675.02930875073343
49296287.9765300467318.02346995326911
50283294.985844928425-11.9858449284255
51285281.9719299105883.02807008941193
52289283.9754453614855.02455463851476
53306287.98127863964318.0187213603573
54306305.0021975511280.997802448871767
55283305.003355954141-22.0033559541409
56258281.977811064113-23.9778110641133
57255256.949973921997-1.94997392199673
58248253.947710091448-5.94771009144753
59244246.940805072026-2.94080507202600
60249242.9373909318236.06260906817673
61258247.94442934370210.0555706562976
62252256.956103401383-4.95610340138319
63246250.950349591982-4.95034959198165
64249244.9446024624904.05539753751029
65267247.94931059357319.0506894064266
66284265.97142757276818.0285724272325
67261282.992357920891-21.9923579208912
68235259.966825799077-24.9668257990772
69229233.937840456082-4.937840456082
70218227.932107849125-9.9321078491248
71218216.9205771261171.07942287388295
72229216.92183028671112.0781697132894
73237227.9358524894019.06414751059893
74231235.946375550149-4.9463755501485
75229229.940633034337-0.940633034337395
76233227.9395410024015.0604589975994
77245231.94541596387713.0545840361229
78256243.96057173894412.039428261056
79224254.97454896458-30.9745489645802
80194222.938588929729-28.9385889297289
81192192.904992551372-0.904992551371691
82178190.903941896406-12.9039418964057
83170176.888961009974-6.888961009974
84187168.88096324128018.1190367587196
85192185.9019986143566.09800138564412
86182190.909078115097-8.90907811509697
87178180.898735082826-2.89873508282628
88186176.8953697839579.10463021604286
89204184.90593984327419.0940601567258
90224202.92810717392621.071892826074
91194222.952570677859-28.9525706778587
92173192.918958067331-19.9189580673313
93178171.8958330679296.10416693207134
94168176.902919726587-8.90291972658724
95152166.892583843924-14.8925838439239
96163150.87529423513412.1247057648663
97172161.88937046405210.1106295359480
98170170.901108442574-0.901108442574156
99156168.900062296881-12.9000622968809
100155154.8850859144870.114914085513220
101178153.88521932448524.1147806755151
102194176.91321548205717.0867845179435
103164192.933052457486-28.9330524574864
104135162.899462506720-27.8994625067202
105139133.8670725066205.13292749338018
106135137.873031600706-2.87303160070579
107109133.869696142404-24.8696961424039
108121107.84082356249813.1591764375017
109131119.8561007645611.1438992354398
110135129.8690383219515.130961678049
111119133.874995133815-14.8749951338153
112121117.8577259447133.14227405528689
113151119.86137398119231.138626018808
114169149.89752450200019.1024754980002
115135167.919701602478-32.9197016024779
116105133.881483334368-28.8814833343679
117112103.8479532529958.15204674700465
118105110.857417406467-5.85741740646749
11982103.850617212724-21.8506172127241
1208180.82524964539030.174750354609671

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 354 & 354 & 0 \tabularnewline
4 & 352 & 353 & -1 \tabularnewline
5 & 372 & 350.998839045731 & 21.0011609542690 \tabularnewline
6 & 371 & 371.023220433195 & -0.0232204331950925 \tabularnewline
7 & 356 & 370.023193475334 & -14.0231934753340 \tabularnewline
8 & 346 & 355.006913189004 & -9.00691318900368 \tabularnewline
9 & 347 & 344.996456574686 & 2.00354342531375 \tabularnewline
10 & 347 & 345.998782596979 & 1.00121740302097 \tabularnewline
11 & 348 & 345.999944964597 & 2.00005503540274 \tabularnewline
12 & 350 & 347.002266937029 & 2.99773306297112 \tabularnewline
13 & 353 & 349.005747168026 & 3.99425283197428 \tabularnewline
14 & 351 & 352.010384312902 & -1.01038431290249 \tabularnewline
15 & 348 & 350.009211302921 & -2.00921130292107 \tabularnewline
16 & 351 & 347.006878700482 & 3.99312129951841 \tabularnewline
17 & 370 & 350.011514531701 & 19.988485468299 \tabularnewline
18 & 370 & 369.034720249237 & 0.965279750763443 \tabularnewline
19 & 351 & 369.035840894884 & -18.0358408948840 \tabularnewline
20 & 335 & 350.014902108402 & -15.0149021084018 \tabularnewline
21 & 330 & 333.9974704937 & -3.99747049370023 \tabularnewline
22 & 328 & 328.992829613265 & -0.992829613265314 \tabularnewline
23 & 332 & 326.991676983487 & 5.00832301651263 \tabularnewline
24 & 334 & 330.997491417474 & 3.00250858252599 \tabularnewline
25 & 343 & 333.000977192631 & 9.99902280736939 \tabularnewline
26 & 334 & 342.012585600845 & -8.01258560084483 \tabularnewline
27 & 336 & 333.003283355386 & 2.99671664461431 \tabularnewline
28 & 343 & 335.006762406367 & 7.99323759363273 \tabularnewline
29 & 365 & 342.016042189675 & 22.9839578103251 \tabularnewline
30 & 364 & 364.042725513614 & -0.0427255136136182 \tabularnewline
31 & 351 & 363.042675911246 & -12.0426759112462 \tabularnewline
32 & 326 & 350.028694915237 & -24.0286949152367 \tabularnewline
33 & 320 & 325.000798699296 & -5.00079869929596 \tabularnewline
34 & 312 & 318.994993000697 & -6.99499300069749 \tabularnewline
35 & 315 & 310.986872133712 & 4.01312786628836 \tabularnewline
36 & 316 & 313.99153119164 & 2.00846880835991 \tabularnewline
37 & 319 & 314.993862932077 & 4.00613706792268 \tabularnewline
38 & 311 & 317.998513874009 & -6.99851387400861 \tabularnewline
39 & 315 & 309.99038891945 & 5.0096110805502 \tabularnewline
40 & 322 & 313.99620484882 & 8.0037951511801 \tabularnewline
41 & 336 & 321.005496888969 & 14.994503111031 \tabularnewline
42 & 339 & 335.022904821367 & 3.97709517863251 \tabularnewline
43 & 317 & 338.027522046993 & -21.0275220469934 \tabularnewline
44 & 295 & 316.003110055506 & -21.0031100555061 \tabularnewline
45 & 291 & 293.978726405225 & -2.97872640522462 \tabularnewline
46 & 283 & 289.975268240088 & -6.97526824008821 \tabularnewline
47 & 285 & 281.967170272647 & 3.03282972735263 \tabularnewline
48 & 289 & 283.970691249267 & 5.02930875073343 \tabularnewline
49 & 296 & 287.976530046731 & 8.02346995326911 \tabularnewline
50 & 283 & 294.985844928425 & -11.9858449284255 \tabularnewline
51 & 285 & 281.971929910588 & 3.02807008941193 \tabularnewline
52 & 289 & 283.975445361485 & 5.02455463851476 \tabularnewline
53 & 306 & 287.981278639643 & 18.0187213603573 \tabularnewline
54 & 306 & 305.002197551128 & 0.997802448871767 \tabularnewline
55 & 283 & 305.003355954141 & -22.0033559541409 \tabularnewline
56 & 258 & 281.977811064113 & -23.9778110641133 \tabularnewline
57 & 255 & 256.949973921997 & -1.94997392199673 \tabularnewline
58 & 248 & 253.947710091448 & -5.94771009144753 \tabularnewline
59 & 244 & 246.940805072026 & -2.94080507202600 \tabularnewline
60 & 249 & 242.937390931823 & 6.06260906817673 \tabularnewline
61 & 258 & 247.944429343702 & 10.0555706562976 \tabularnewline
62 & 252 & 256.956103401383 & -4.95610340138319 \tabularnewline
63 & 246 & 250.950349591982 & -4.95034959198165 \tabularnewline
64 & 249 & 244.944602462490 & 4.05539753751029 \tabularnewline
65 & 267 & 247.949310593573 & 19.0506894064266 \tabularnewline
66 & 284 & 265.971427572768 & 18.0285724272325 \tabularnewline
67 & 261 & 282.992357920891 & -21.9923579208912 \tabularnewline
68 & 235 & 259.966825799077 & -24.9668257990772 \tabularnewline
69 & 229 & 233.937840456082 & -4.937840456082 \tabularnewline
70 & 218 & 227.932107849125 & -9.9321078491248 \tabularnewline
71 & 218 & 216.920577126117 & 1.07942287388295 \tabularnewline
72 & 229 & 216.921830286711 & 12.0781697132894 \tabularnewline
73 & 237 & 227.935852489401 & 9.06414751059893 \tabularnewline
74 & 231 & 235.946375550149 & -4.9463755501485 \tabularnewline
75 & 229 & 229.940633034337 & -0.940633034337395 \tabularnewline
76 & 233 & 227.939541002401 & 5.0604589975994 \tabularnewline
77 & 245 & 231.945415963877 & 13.0545840361229 \tabularnewline
78 & 256 & 243.960571738944 & 12.039428261056 \tabularnewline
79 & 224 & 254.97454896458 & -30.9745489645802 \tabularnewline
80 & 194 & 222.938588929729 & -28.9385889297289 \tabularnewline
81 & 192 & 192.904992551372 & -0.904992551371691 \tabularnewline
82 & 178 & 190.903941896406 & -12.9039418964057 \tabularnewline
83 & 170 & 176.888961009974 & -6.888961009974 \tabularnewline
84 & 187 & 168.880963241280 & 18.1190367587196 \tabularnewline
85 & 192 & 185.901998614356 & 6.09800138564412 \tabularnewline
86 & 182 & 190.909078115097 & -8.90907811509697 \tabularnewline
87 & 178 & 180.898735082826 & -2.89873508282628 \tabularnewline
88 & 186 & 176.895369783957 & 9.10463021604286 \tabularnewline
89 & 204 & 184.905939843274 & 19.0940601567258 \tabularnewline
90 & 224 & 202.928107173926 & 21.071892826074 \tabularnewline
91 & 194 & 222.952570677859 & -28.9525706778587 \tabularnewline
92 & 173 & 192.918958067331 & -19.9189580673313 \tabularnewline
93 & 178 & 171.895833067929 & 6.10416693207134 \tabularnewline
94 & 168 & 176.902919726587 & -8.90291972658724 \tabularnewline
95 & 152 & 166.892583843924 & -14.8925838439239 \tabularnewline
96 & 163 & 150.875294235134 & 12.1247057648663 \tabularnewline
97 & 172 & 161.889370464052 & 10.1106295359480 \tabularnewline
98 & 170 & 170.901108442574 & -0.901108442574156 \tabularnewline
99 & 156 & 168.900062296881 & -12.9000622968809 \tabularnewline
100 & 155 & 154.885085914487 & 0.114914085513220 \tabularnewline
101 & 178 & 153.885219324485 & 24.1147806755151 \tabularnewline
102 & 194 & 176.913215482057 & 17.0867845179435 \tabularnewline
103 & 164 & 192.933052457486 & -28.9330524574864 \tabularnewline
104 & 135 & 162.899462506720 & -27.8994625067202 \tabularnewline
105 & 139 & 133.867072506620 & 5.13292749338018 \tabularnewline
106 & 135 & 137.873031600706 & -2.87303160070579 \tabularnewline
107 & 109 & 133.869696142404 & -24.8696961424039 \tabularnewline
108 & 121 & 107.840823562498 & 13.1591764375017 \tabularnewline
109 & 131 & 119.85610076456 & 11.1438992354398 \tabularnewline
110 & 135 & 129.869038321951 & 5.130961678049 \tabularnewline
111 & 119 & 133.874995133815 & -14.8749951338153 \tabularnewline
112 & 121 & 117.857725944713 & 3.14227405528689 \tabularnewline
113 & 151 & 119.861373981192 & 31.138626018808 \tabularnewline
114 & 169 & 149.897524502000 & 19.1024754980002 \tabularnewline
115 & 135 & 167.919701602478 & -32.9197016024779 \tabularnewline
116 & 105 & 133.881483334368 & -28.8814833343679 \tabularnewline
117 & 112 & 103.847953252995 & 8.15204674700465 \tabularnewline
118 & 105 & 110.857417406467 & -5.85741740646749 \tabularnewline
119 & 82 & 103.850617212724 & -21.8506172127241 \tabularnewline
120 & 81 & 80.8252496453903 & 0.174750354609671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78753&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]3[/C][C]354[/C][C]354[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]352[/C][C]353[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]372[/C][C]350.998839045731[/C][C]21.0011609542690[/C][/ROW]
[ROW][C]6[/C][C]371[/C][C]371.023220433195[/C][C]-0.0232204331950925[/C][/ROW]
[ROW][C]7[/C][C]356[/C][C]370.023193475334[/C][C]-14.0231934753340[/C][/ROW]
[ROW][C]8[/C][C]346[/C][C]355.006913189004[/C][C]-9.00691318900368[/C][/ROW]
[ROW][C]9[/C][C]347[/C][C]344.996456574686[/C][C]2.00354342531375[/C][/ROW]
[ROW][C]10[/C][C]347[/C][C]345.998782596979[/C][C]1.00121740302097[/C][/ROW]
[ROW][C]11[/C][C]348[/C][C]345.999944964597[/C][C]2.00005503540274[/C][/ROW]
[ROW][C]12[/C][C]350[/C][C]347.002266937029[/C][C]2.99773306297112[/C][/ROW]
[ROW][C]13[/C][C]353[/C][C]349.005747168026[/C][C]3.99425283197428[/C][/ROW]
[ROW][C]14[/C][C]351[/C][C]352.010384312902[/C][C]-1.01038431290249[/C][/ROW]
[ROW][C]15[/C][C]348[/C][C]350.009211302921[/C][C]-2.00921130292107[/C][/ROW]
[ROW][C]16[/C][C]351[/C][C]347.006878700482[/C][C]3.99312129951841[/C][/ROW]
[ROW][C]17[/C][C]370[/C][C]350.011514531701[/C][C]19.988485468299[/C][/ROW]
[ROW][C]18[/C][C]370[/C][C]369.034720249237[/C][C]0.965279750763443[/C][/ROW]
[ROW][C]19[/C][C]351[/C][C]369.035840894884[/C][C]-18.0358408948840[/C][/ROW]
[ROW][C]20[/C][C]335[/C][C]350.014902108402[/C][C]-15.0149021084018[/C][/ROW]
[ROW][C]21[/C][C]330[/C][C]333.9974704937[/C][C]-3.99747049370023[/C][/ROW]
[ROW][C]22[/C][C]328[/C][C]328.992829613265[/C][C]-0.992829613265314[/C][/ROW]
[ROW][C]23[/C][C]332[/C][C]326.991676983487[/C][C]5.00832301651263[/C][/ROW]
[ROW][C]24[/C][C]334[/C][C]330.997491417474[/C][C]3.00250858252599[/C][/ROW]
[ROW][C]25[/C][C]343[/C][C]333.000977192631[/C][C]9.99902280736939[/C][/ROW]
[ROW][C]26[/C][C]334[/C][C]342.012585600845[/C][C]-8.01258560084483[/C][/ROW]
[ROW][C]27[/C][C]336[/C][C]333.003283355386[/C][C]2.99671664461431[/C][/ROW]
[ROW][C]28[/C][C]343[/C][C]335.006762406367[/C][C]7.99323759363273[/C][/ROW]
[ROW][C]29[/C][C]365[/C][C]342.016042189675[/C][C]22.9839578103251[/C][/ROW]
[ROW][C]30[/C][C]364[/C][C]364.042725513614[/C][C]-0.0427255136136182[/C][/ROW]
[ROW][C]31[/C][C]351[/C][C]363.042675911246[/C][C]-12.0426759112462[/C][/ROW]
[ROW][C]32[/C][C]326[/C][C]350.028694915237[/C][C]-24.0286949152367[/C][/ROW]
[ROW][C]33[/C][C]320[/C][C]325.000798699296[/C][C]-5.00079869929596[/C][/ROW]
[ROW][C]34[/C][C]312[/C][C]318.994993000697[/C][C]-6.99499300069749[/C][/ROW]
[ROW][C]35[/C][C]315[/C][C]310.986872133712[/C][C]4.01312786628836[/C][/ROW]
[ROW][C]36[/C][C]316[/C][C]313.99153119164[/C][C]2.00846880835991[/C][/ROW]
[ROW][C]37[/C][C]319[/C][C]314.993862932077[/C][C]4.00613706792268[/C][/ROW]
[ROW][C]38[/C][C]311[/C][C]317.998513874009[/C][C]-6.99851387400861[/C][/ROW]
[ROW][C]39[/C][C]315[/C][C]309.99038891945[/C][C]5.0096110805502[/C][/ROW]
[ROW][C]40[/C][C]322[/C][C]313.99620484882[/C][C]8.0037951511801[/C][/ROW]
[ROW][C]41[/C][C]336[/C][C]321.005496888969[/C][C]14.994503111031[/C][/ROW]
[ROW][C]42[/C][C]339[/C][C]335.022904821367[/C][C]3.97709517863251[/C][/ROW]
[ROW][C]43[/C][C]317[/C][C]338.027522046993[/C][C]-21.0275220469934[/C][/ROW]
[ROW][C]44[/C][C]295[/C][C]316.003110055506[/C][C]-21.0031100555061[/C][/ROW]
[ROW][C]45[/C][C]291[/C][C]293.978726405225[/C][C]-2.97872640522462[/C][/ROW]
[ROW][C]46[/C][C]283[/C][C]289.975268240088[/C][C]-6.97526824008821[/C][/ROW]
[ROW][C]47[/C][C]285[/C][C]281.967170272647[/C][C]3.03282972735263[/C][/ROW]
[ROW][C]48[/C][C]289[/C][C]283.970691249267[/C][C]5.02930875073343[/C][/ROW]
[ROW][C]49[/C][C]296[/C][C]287.976530046731[/C][C]8.02346995326911[/C][/ROW]
[ROW][C]50[/C][C]283[/C][C]294.985844928425[/C][C]-11.9858449284255[/C][/ROW]
[ROW][C]51[/C][C]285[/C][C]281.971929910588[/C][C]3.02807008941193[/C][/ROW]
[ROW][C]52[/C][C]289[/C][C]283.975445361485[/C][C]5.02455463851476[/C][/ROW]
[ROW][C]53[/C][C]306[/C][C]287.981278639643[/C][C]18.0187213603573[/C][/ROW]
[ROW][C]54[/C][C]306[/C][C]305.002197551128[/C][C]0.997802448871767[/C][/ROW]
[ROW][C]55[/C][C]283[/C][C]305.003355954141[/C][C]-22.0033559541409[/C][/ROW]
[ROW][C]56[/C][C]258[/C][C]281.977811064113[/C][C]-23.9778110641133[/C][/ROW]
[ROW][C]57[/C][C]255[/C][C]256.949973921997[/C][C]-1.94997392199673[/C][/ROW]
[ROW][C]58[/C][C]248[/C][C]253.947710091448[/C][C]-5.94771009144753[/C][/ROW]
[ROW][C]59[/C][C]244[/C][C]246.940805072026[/C][C]-2.94080507202600[/C][/ROW]
[ROW][C]60[/C][C]249[/C][C]242.937390931823[/C][C]6.06260906817673[/C][/ROW]
[ROW][C]61[/C][C]258[/C][C]247.944429343702[/C][C]10.0555706562976[/C][/ROW]
[ROW][C]62[/C][C]252[/C][C]256.956103401383[/C][C]-4.95610340138319[/C][/ROW]
[ROW][C]63[/C][C]246[/C][C]250.950349591982[/C][C]-4.95034959198165[/C][/ROW]
[ROW][C]64[/C][C]249[/C][C]244.944602462490[/C][C]4.05539753751029[/C][/ROW]
[ROW][C]65[/C][C]267[/C][C]247.949310593573[/C][C]19.0506894064266[/C][/ROW]
[ROW][C]66[/C][C]284[/C][C]265.971427572768[/C][C]18.0285724272325[/C][/ROW]
[ROW][C]67[/C][C]261[/C][C]282.992357920891[/C][C]-21.9923579208912[/C][/ROW]
[ROW][C]68[/C][C]235[/C][C]259.966825799077[/C][C]-24.9668257990772[/C][/ROW]
[ROW][C]69[/C][C]229[/C][C]233.937840456082[/C][C]-4.937840456082[/C][/ROW]
[ROW][C]70[/C][C]218[/C][C]227.932107849125[/C][C]-9.9321078491248[/C][/ROW]
[ROW][C]71[/C][C]218[/C][C]216.920577126117[/C][C]1.07942287388295[/C][/ROW]
[ROW][C]72[/C][C]229[/C][C]216.921830286711[/C][C]12.0781697132894[/C][/ROW]
[ROW][C]73[/C][C]237[/C][C]227.935852489401[/C][C]9.06414751059893[/C][/ROW]
[ROW][C]74[/C][C]231[/C][C]235.946375550149[/C][C]-4.9463755501485[/C][/ROW]
[ROW][C]75[/C][C]229[/C][C]229.940633034337[/C][C]-0.940633034337395[/C][/ROW]
[ROW][C]76[/C][C]233[/C][C]227.939541002401[/C][C]5.0604589975994[/C][/ROW]
[ROW][C]77[/C][C]245[/C][C]231.945415963877[/C][C]13.0545840361229[/C][/ROW]
[ROW][C]78[/C][C]256[/C][C]243.960571738944[/C][C]12.039428261056[/C][/ROW]
[ROW][C]79[/C][C]224[/C][C]254.97454896458[/C][C]-30.9745489645802[/C][/ROW]
[ROW][C]80[/C][C]194[/C][C]222.938588929729[/C][C]-28.9385889297289[/C][/ROW]
[ROW][C]81[/C][C]192[/C][C]192.904992551372[/C][C]-0.904992551371691[/C][/ROW]
[ROW][C]82[/C][C]178[/C][C]190.903941896406[/C][C]-12.9039418964057[/C][/ROW]
[ROW][C]83[/C][C]170[/C][C]176.888961009974[/C][C]-6.888961009974[/C][/ROW]
[ROW][C]84[/C][C]187[/C][C]168.880963241280[/C][C]18.1190367587196[/C][/ROW]
[ROW][C]85[/C][C]192[/C][C]185.901998614356[/C][C]6.09800138564412[/C][/ROW]
[ROW][C]86[/C][C]182[/C][C]190.909078115097[/C][C]-8.90907811509697[/C][/ROW]
[ROW][C]87[/C][C]178[/C][C]180.898735082826[/C][C]-2.89873508282628[/C][/ROW]
[ROW][C]88[/C][C]186[/C][C]176.895369783957[/C][C]9.10463021604286[/C][/ROW]
[ROW][C]89[/C][C]204[/C][C]184.905939843274[/C][C]19.0940601567258[/C][/ROW]
[ROW][C]90[/C][C]224[/C][C]202.928107173926[/C][C]21.071892826074[/C][/ROW]
[ROW][C]91[/C][C]194[/C][C]222.952570677859[/C][C]-28.9525706778587[/C][/ROW]
[ROW][C]92[/C][C]173[/C][C]192.918958067331[/C][C]-19.9189580673313[/C][/ROW]
[ROW][C]93[/C][C]178[/C][C]171.895833067929[/C][C]6.10416693207134[/C][/ROW]
[ROW][C]94[/C][C]168[/C][C]176.902919726587[/C][C]-8.90291972658724[/C][/ROW]
[ROW][C]95[/C][C]152[/C][C]166.892583843924[/C][C]-14.8925838439239[/C][/ROW]
[ROW][C]96[/C][C]163[/C][C]150.875294235134[/C][C]12.1247057648663[/C][/ROW]
[ROW][C]97[/C][C]172[/C][C]161.889370464052[/C][C]10.1106295359480[/C][/ROW]
[ROW][C]98[/C][C]170[/C][C]170.901108442574[/C][C]-0.901108442574156[/C][/ROW]
[ROW][C]99[/C][C]156[/C][C]168.900062296881[/C][C]-12.9000622968809[/C][/ROW]
[ROW][C]100[/C][C]155[/C][C]154.885085914487[/C][C]0.114914085513220[/C][/ROW]
[ROW][C]101[/C][C]178[/C][C]153.885219324485[/C][C]24.1147806755151[/C][/ROW]
[ROW][C]102[/C][C]194[/C][C]176.913215482057[/C][C]17.0867845179435[/C][/ROW]
[ROW][C]103[/C][C]164[/C][C]192.933052457486[/C][C]-28.9330524574864[/C][/ROW]
[ROW][C]104[/C][C]135[/C][C]162.899462506720[/C][C]-27.8994625067202[/C][/ROW]
[ROW][C]105[/C][C]139[/C][C]133.867072506620[/C][C]5.13292749338018[/C][/ROW]
[ROW][C]106[/C][C]135[/C][C]137.873031600706[/C][C]-2.87303160070579[/C][/ROW]
[ROW][C]107[/C][C]109[/C][C]133.869696142404[/C][C]-24.8696961424039[/C][/ROW]
[ROW][C]108[/C][C]121[/C][C]107.840823562498[/C][C]13.1591764375017[/C][/ROW]
[ROW][C]109[/C][C]131[/C][C]119.85610076456[/C][C]11.1438992354398[/C][/ROW]
[ROW][C]110[/C][C]135[/C][C]129.869038321951[/C][C]5.130961678049[/C][/ROW]
[ROW][C]111[/C][C]119[/C][C]133.874995133815[/C][C]-14.8749951338153[/C][/ROW]
[ROW][C]112[/C][C]121[/C][C]117.857725944713[/C][C]3.14227405528689[/C][/ROW]
[ROW][C]113[/C][C]151[/C][C]119.861373981192[/C][C]31.138626018808[/C][/ROW]
[ROW][C]114[/C][C]169[/C][C]149.897524502000[/C][C]19.1024754980002[/C][/ROW]
[ROW][C]115[/C][C]135[/C][C]167.919701602478[/C][C]-32.9197016024779[/C][/ROW]
[ROW][C]116[/C][C]105[/C][C]133.881483334368[/C][C]-28.8814833343679[/C][/ROW]
[ROW][C]117[/C][C]112[/C][C]103.847953252995[/C][C]8.15204674700465[/C][/ROW]
[ROW][C]118[/C][C]105[/C][C]110.857417406467[/C][C]-5.85741740646749[/C][/ROW]
[ROW][C]119[/C][C]82[/C][C]103.850617212724[/C][C]-21.8506172127241[/C][/ROW]
[ROW][C]120[/C][C]81[/C][C]80.8252496453903[/C][C]0.174750354609671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78753&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78753&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
33543540
4352353-1
5372350.99883904573121.0011609542690
6371371.023220433195-0.0232204331950925
7356370.023193475334-14.0231934753340
8346355.006913189004-9.00691318900368
9347344.9964565746862.00354342531375
10347345.9987825969791.00121740302097
11348345.9999449645972.00005503540274
12350347.0022669370292.99773306297112
13353349.0057471680263.99425283197428
14351352.010384312902-1.01038431290249
15348350.009211302921-2.00921130292107
16351347.0068787004823.99312129951841
17370350.01151453170119.988485468299
18370369.0347202492370.965279750763443
19351369.035840894884-18.0358408948840
20335350.014902108402-15.0149021084018
21330333.9974704937-3.99747049370023
22328328.992829613265-0.992829613265314
23332326.9916769834875.00832301651263
24334330.9974914174743.00250858252599
25343333.0009771926319.99902280736939
26334342.012585600845-8.01258560084483
27336333.0032833553862.99671664461431
28343335.0067624063677.99323759363273
29365342.01604218967522.9839578103251
30364364.042725513614-0.0427255136136182
31351363.042675911246-12.0426759112462
32326350.028694915237-24.0286949152367
33320325.000798699296-5.00079869929596
34312318.994993000697-6.99499300069749
35315310.9868721337124.01312786628836
36316313.991531191642.00846880835991
37319314.9938629320774.00613706792268
38311317.998513874009-6.99851387400861
39315309.990388919455.0096110805502
40322313.996204848828.0037951511801
41336321.00549688896914.994503111031
42339335.0229048213673.97709517863251
43317338.027522046993-21.0275220469934
44295316.003110055506-21.0031100555061
45291293.978726405225-2.97872640522462
46283289.975268240088-6.97526824008821
47285281.9671702726473.03282972735263
48289283.9706912492675.02930875073343
49296287.9765300467318.02346995326911
50283294.985844928425-11.9858449284255
51285281.9719299105883.02807008941193
52289283.9754453614855.02455463851476
53306287.98127863964318.0187213603573
54306305.0021975511280.997802448871767
55283305.003355954141-22.0033559541409
56258281.977811064113-23.9778110641133
57255256.949973921997-1.94997392199673
58248253.947710091448-5.94771009144753
59244246.940805072026-2.94080507202600
60249242.9373909318236.06260906817673
61258247.94442934370210.0555706562976
62252256.956103401383-4.95610340138319
63246250.950349591982-4.95034959198165
64249244.9446024624904.05539753751029
65267247.94931059357319.0506894064266
66284265.97142757276818.0285724272325
67261282.992357920891-21.9923579208912
68235259.966825799077-24.9668257990772
69229233.937840456082-4.937840456082
70218227.932107849125-9.9321078491248
71218216.9205771261171.07942287388295
72229216.92183028671112.0781697132894
73237227.9358524894019.06414751059893
74231235.946375550149-4.9463755501485
75229229.940633034337-0.940633034337395
76233227.9395410024015.0604589975994
77245231.94541596387713.0545840361229
78256243.96057173894412.039428261056
79224254.97454896458-30.9745489645802
80194222.938588929729-28.9385889297289
81192192.904992551372-0.904992551371691
82178190.903941896406-12.9039418964057
83170176.888961009974-6.888961009974
84187168.88096324128018.1190367587196
85192185.9019986143566.09800138564412
86182190.909078115097-8.90907811509697
87178180.898735082826-2.89873508282628
88186176.8953697839579.10463021604286
89204184.90593984327419.0940601567258
90224202.92810717392621.071892826074
91194222.952570677859-28.9525706778587
92173192.918958067331-19.9189580673313
93178171.8958330679296.10416693207134
94168176.902919726587-8.90291972658724
95152166.892583843924-14.8925838439239
96163150.87529423513412.1247057648663
97172161.88937046405210.1106295359480
98170170.901108442574-0.901108442574156
99156168.900062296881-12.9000622968809
100155154.8850859144870.114914085513220
101178153.88521932448524.1147806755151
102194176.91321548205717.0867845179435
103164192.933052457486-28.9330524574864
104135162.899462506720-27.8994625067202
105139133.8670725066205.13292749338018
106135137.873031600706-2.87303160070579
107109133.869696142404-24.8696961424039
108121107.84082356249813.1591764375017
109131119.8561007645611.1438992354398
110135129.8690383219515.130961678049
111119133.874995133815-14.8749951338153
112121117.8577259447133.14227405528689
113151119.86137398119231.138626018808
114169149.89752450200019.1024754980002
115135167.919701602478-32.9197016024779
116105133.881483334368-28.8814833343679
117112103.8479532529958.15204674700465
118105110.857417406467-5.85741740646749
11982103.850617212724-21.8506172127241
1208180.82524964539030.174750354609671







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12179.825452522560553.0698731131734106.581031931948
12278.65090504512140.7908312503085116.510978839934
12377.476357567681631.080512879325123.872202256038
12476.301810090242122.6974202604850129.906199919999
12575.127262612802715.1609743212278135.093550904377
12673.95271513536328.22485421333582139.680576057391
12772.77816765792371.74282118542384143.813514130424
12871.6036201804842-4.38035117145721147.587591532426
12970.4290727030448-10.2107685227119151.068913928801
13069.2545252256053-15.7965338487652154.305584299976
13168.0799777481658-21.1739398262426157.333895322574
13266.9054302707264-26.3711658331901160.182026374643

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 79.8254525225605 & 53.0698731131734 & 106.581031931948 \tabularnewline
122 & 78.650905045121 & 40.7908312503085 & 116.510978839934 \tabularnewline
123 & 77.4763575676816 & 31.080512879325 & 123.872202256038 \tabularnewline
124 & 76.3018100902421 & 22.6974202604850 & 129.906199919999 \tabularnewline
125 & 75.1272626128027 & 15.1609743212278 & 135.093550904377 \tabularnewline
126 & 73.9527151353632 & 8.22485421333582 & 139.680576057391 \tabularnewline
127 & 72.7781676579237 & 1.74282118542384 & 143.813514130424 \tabularnewline
128 & 71.6036201804842 & -4.38035117145721 & 147.587591532426 \tabularnewline
129 & 70.4290727030448 & -10.2107685227119 & 151.068913928801 \tabularnewline
130 & 69.2545252256053 & -15.7965338487652 & 154.305584299976 \tabularnewline
131 & 68.0799777481658 & -21.1739398262426 & 157.333895322574 \tabularnewline
132 & 66.9054302707264 & -26.3711658331901 & 160.182026374643 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78753&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]79.8254525225605[/C][C]53.0698731131734[/C][C]106.581031931948[/C][/ROW]
[ROW][C]122[/C][C]78.650905045121[/C][C]40.7908312503085[/C][C]116.510978839934[/C][/ROW]
[ROW][C]123[/C][C]77.4763575676816[/C][C]31.080512879325[/C][C]123.872202256038[/C][/ROW]
[ROW][C]124[/C][C]76.3018100902421[/C][C]22.6974202604850[/C][C]129.906199919999[/C][/ROW]
[ROW][C]125[/C][C]75.1272626128027[/C][C]15.1609743212278[/C][C]135.093550904377[/C][/ROW]
[ROW][C]126[/C][C]73.9527151353632[/C][C]8.22485421333582[/C][C]139.680576057391[/C][/ROW]
[ROW][C]127[/C][C]72.7781676579237[/C][C]1.74282118542384[/C][C]143.813514130424[/C][/ROW]
[ROW][C]128[/C][C]71.6036201804842[/C][C]-4.38035117145721[/C][C]147.587591532426[/C][/ROW]
[ROW][C]129[/C][C]70.4290727030448[/C][C]-10.2107685227119[/C][C]151.068913928801[/C][/ROW]
[ROW][C]130[/C][C]69.2545252256053[/C][C]-15.7965338487652[/C][C]154.305584299976[/C][/ROW]
[ROW][C]131[/C][C]68.0799777481658[/C][C]-21.1739398262426[/C][C]157.333895322574[/C][/ROW]
[ROW][C]132[/C][C]66.9054302707264[/C][C]-26.3711658331901[/C][C]160.182026374643[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78753&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78753&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
12179.825452522560553.0698731131734106.581031931948
12278.65090504512140.7908312503085116.510978839934
12377.476357567681631.080512879325123.872202256038
12476.301810090242122.6974202604850129.906199919999
12575.127262612802715.1609743212278135.093550904377
12673.95271513536328.22485421333582139.680576057391
12772.77816765792371.74282118542384143.813514130424
12871.6036201804842-4.38035117145721147.587591532426
12970.4290727030448-10.2107685227119151.068913928801
13069.2545252256053-15.7965338487652154.305584299976
13168.0799777481658-21.1739398262426157.333895322574
13266.9054302707264-26.3711658331901160.182026374643



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')