Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Aug 2010 15:24:14 +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/16/t12819722302x93dh1yxkw668t.htm/, Retrieved Thu, 16 May 2024 17:09:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79019, Retrieved Thu, 16 May 2024 17:09:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJeroen_Kinne
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential_Smoot...] [2010-08-16 15:24:14] [6fe3b5976049c9b6736c06f51fce3033] [Current]
Feedback Forum

Post a new message
Dataseries X:
430
429
428
426
424
423
424
426
427
427
428
430
432
435
426
411
405
403
402
399
392
387
380
379
386
385
365
356
338
338
343
338
320
316
317
315
317
321
303
303
290
285
300
291
278
273
277
269
275
278
255
254
245
240
261
247
229
213
218
206
217
219
196
193
188
171
190
180
149
135
151
134
145
151
137
124
125
109
131
133
103
85
104
82




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=79019&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=79019&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79019&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
alpha0.289075319272455
beta0.279089476738451
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.289075319272455 \tabularnewline
beta & 0.279089476738451 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79019&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]0.289075319272455[/C][/ROW]
[ROW][C]beta[/C][C]0.279089476738451[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79019&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79019&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
alpha0.289075319272455
beta0.279089476738451
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13432438.898544293284-6.89854429328369
14435439.588191700283-4.58819170028295
15426429.033615688526-3.03361568852637
16411413.220559235091-2.2205592350914
17405407.049203980354-2.04920398035432
18403405.234879262218-2.23487926221816
19402401.6841459104290.315854089571133
20399399.861758086254-0.86175808625353
21392396.82409187658-4.82409187658021
22387392.119785790203-5.11978579020285
23380388.454794455973-8.45479445597346
24379384.172393304825-5.17239330482471
25386376.1851886861419.81481131385937
26385380.1617678934334.83823210656709
27365372.519373653186-7.51937365318588
28356355.5947798725740.405220127426162
29338348.950662500551-10.9506625005515
30338341.754564225453-3.75456422545290
31343336.6769208925766.32307910742367
32338333.5907229019754.40927709802457
33320327.969073031903-7.96907303190301
34316320.192986655638-4.19298665563781
35317312.6327428745204.36725712548042
36315312.6215222504192.37847774958055
37317315.5438764139731.45612358602699
38321312.2283493305388.77165066946162
39303298.8308684005474.16913159945295
40303292.06098344030910.9390165596913
41290283.2604741755896.73952582441069
42285287.890663970284-2.89066397028449
43300291.6047067488578.39529325114307
44291290.7972499820950.202750017904634
45278279.135422883107-1.13542288310725
46273278.724118657224-5.72411865722393
47277279.089544421879-2.08954442187934
48269277.929911950002-8.92991195000207
49275277.642399308342-2.64239930834185
50278278.721962385085-0.721962385084964
51255261.734565583615-6.73456558361477
52254256.010769194701-2.01076919470103
53245240.889438751544.11056124845996
54240236.5348606522663.46513934773409
55261246.29287510485114.7071248951487
56247241.9351519236815.06484807631912
57229232.176420030279-3.17642003027919
58213227.642466677343-14.6424666773428
59218225.470770073857-7.47077007385678
60206216.702300550868-10.7023005508676
61217216.3355590004850.664440999514909
62219216.5376735685242.46232643147644
63196198.609369711206-2.60936971120603
64193195.512785156476-2.51278515647567
65188184.8683782332403.13162176676028
66171179.088920736665-8.08892073666513
67190185.5944167781494.40558322185075
68180171.9809842396288.01901576037173
69149158.962083943998-9.96208394399758
70135144.113000044135-9.1130000441351
71151142.1448524275818.85514757241899
72134135.826386053537-1.82638605353671
73145139.6645637340485.33543626595227
74151139.58790821100511.4120917889950
75137126.84188722817710.1581127718226
76124127.743624201119-3.74362420111891
77125122.0498199588142.95018004118644
78109112.628086561266-3.62808656126597
79131122.5287862507088.4712137492922
80133116.70795228859916.2920477114015
81103103.103878543786-0.103878543786308
828596.424073755864-11.4240737558641
83104103.2916716242550.70832837574494
848292.6595025076693-10.6595025076693

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 432 & 438.898544293284 & -6.89854429328369 \tabularnewline
14 & 435 & 439.588191700283 & -4.58819170028295 \tabularnewline
15 & 426 & 429.033615688526 & -3.03361568852637 \tabularnewline
16 & 411 & 413.220559235091 & -2.2205592350914 \tabularnewline
17 & 405 & 407.049203980354 & -2.04920398035432 \tabularnewline
18 & 403 & 405.234879262218 & -2.23487926221816 \tabularnewline
19 & 402 & 401.684145910429 & 0.315854089571133 \tabularnewline
20 & 399 & 399.861758086254 & -0.86175808625353 \tabularnewline
21 & 392 & 396.82409187658 & -4.82409187658021 \tabularnewline
22 & 387 & 392.119785790203 & -5.11978579020285 \tabularnewline
23 & 380 & 388.454794455973 & -8.45479445597346 \tabularnewline
24 & 379 & 384.172393304825 & -5.17239330482471 \tabularnewline
25 & 386 & 376.185188686141 & 9.81481131385937 \tabularnewline
26 & 385 & 380.161767893433 & 4.83823210656709 \tabularnewline
27 & 365 & 372.519373653186 & -7.51937365318588 \tabularnewline
28 & 356 & 355.594779872574 & 0.405220127426162 \tabularnewline
29 & 338 & 348.950662500551 & -10.9506625005515 \tabularnewline
30 & 338 & 341.754564225453 & -3.75456422545290 \tabularnewline
31 & 343 & 336.676920892576 & 6.32307910742367 \tabularnewline
32 & 338 & 333.590722901975 & 4.40927709802457 \tabularnewline
33 & 320 & 327.969073031903 & -7.96907303190301 \tabularnewline
34 & 316 & 320.192986655638 & -4.19298665563781 \tabularnewline
35 & 317 & 312.632742874520 & 4.36725712548042 \tabularnewline
36 & 315 & 312.621522250419 & 2.37847774958055 \tabularnewline
37 & 317 & 315.543876413973 & 1.45612358602699 \tabularnewline
38 & 321 & 312.228349330538 & 8.77165066946162 \tabularnewline
39 & 303 & 298.830868400547 & 4.16913159945295 \tabularnewline
40 & 303 & 292.060983440309 & 10.9390165596913 \tabularnewline
41 & 290 & 283.260474175589 & 6.73952582441069 \tabularnewline
42 & 285 & 287.890663970284 & -2.89066397028449 \tabularnewline
43 & 300 & 291.604706748857 & 8.39529325114307 \tabularnewline
44 & 291 & 290.797249982095 & 0.202750017904634 \tabularnewline
45 & 278 & 279.135422883107 & -1.13542288310725 \tabularnewline
46 & 273 & 278.724118657224 & -5.72411865722393 \tabularnewline
47 & 277 & 279.089544421879 & -2.08954442187934 \tabularnewline
48 & 269 & 277.929911950002 & -8.92991195000207 \tabularnewline
49 & 275 & 277.642399308342 & -2.64239930834185 \tabularnewline
50 & 278 & 278.721962385085 & -0.721962385084964 \tabularnewline
51 & 255 & 261.734565583615 & -6.73456558361477 \tabularnewline
52 & 254 & 256.010769194701 & -2.01076919470103 \tabularnewline
53 & 245 & 240.88943875154 & 4.11056124845996 \tabularnewline
54 & 240 & 236.534860652266 & 3.46513934773409 \tabularnewline
55 & 261 & 246.292875104851 & 14.7071248951487 \tabularnewline
56 & 247 & 241.935151923681 & 5.06484807631912 \tabularnewline
57 & 229 & 232.176420030279 & -3.17642003027919 \tabularnewline
58 & 213 & 227.642466677343 & -14.6424666773428 \tabularnewline
59 & 218 & 225.470770073857 & -7.47077007385678 \tabularnewline
60 & 206 & 216.702300550868 & -10.7023005508676 \tabularnewline
61 & 217 & 216.335559000485 & 0.664440999514909 \tabularnewline
62 & 219 & 216.537673568524 & 2.46232643147644 \tabularnewline
63 & 196 & 198.609369711206 & -2.60936971120603 \tabularnewline
64 & 193 & 195.512785156476 & -2.51278515647567 \tabularnewline
65 & 188 & 184.868378233240 & 3.13162176676028 \tabularnewline
66 & 171 & 179.088920736665 & -8.08892073666513 \tabularnewline
67 & 190 & 185.594416778149 & 4.40558322185075 \tabularnewline
68 & 180 & 171.980984239628 & 8.01901576037173 \tabularnewline
69 & 149 & 158.962083943998 & -9.96208394399758 \tabularnewline
70 & 135 & 144.113000044135 & -9.1130000441351 \tabularnewline
71 & 151 & 142.144852427581 & 8.85514757241899 \tabularnewline
72 & 134 & 135.826386053537 & -1.82638605353671 \tabularnewline
73 & 145 & 139.664563734048 & 5.33543626595227 \tabularnewline
74 & 151 & 139.587908211005 & 11.4120917889950 \tabularnewline
75 & 137 & 126.841887228177 & 10.1581127718226 \tabularnewline
76 & 124 & 127.743624201119 & -3.74362420111891 \tabularnewline
77 & 125 & 122.049819958814 & 2.95018004118644 \tabularnewline
78 & 109 & 112.628086561266 & -3.62808656126597 \tabularnewline
79 & 131 & 122.528786250708 & 8.4712137492922 \tabularnewline
80 & 133 & 116.707952288599 & 16.2920477114015 \tabularnewline
81 & 103 & 103.103878543786 & -0.103878543786308 \tabularnewline
82 & 85 & 96.424073755864 & -11.4240737558641 \tabularnewline
83 & 104 & 103.291671624255 & 0.70832837574494 \tabularnewline
84 & 82 & 92.6595025076693 & -10.6595025076693 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79019&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]432[/C][C]438.898544293284[/C][C]-6.89854429328369[/C][/ROW]
[ROW][C]14[/C][C]435[/C][C]439.588191700283[/C][C]-4.58819170028295[/C][/ROW]
[ROW][C]15[/C][C]426[/C][C]429.033615688526[/C][C]-3.03361568852637[/C][/ROW]
[ROW][C]16[/C][C]411[/C][C]413.220559235091[/C][C]-2.2205592350914[/C][/ROW]
[ROW][C]17[/C][C]405[/C][C]407.049203980354[/C][C]-2.04920398035432[/C][/ROW]
[ROW][C]18[/C][C]403[/C][C]405.234879262218[/C][C]-2.23487926221816[/C][/ROW]
[ROW][C]19[/C][C]402[/C][C]401.684145910429[/C][C]0.315854089571133[/C][/ROW]
[ROW][C]20[/C][C]399[/C][C]399.861758086254[/C][C]-0.86175808625353[/C][/ROW]
[ROW][C]21[/C][C]392[/C][C]396.82409187658[/C][C]-4.82409187658021[/C][/ROW]
[ROW][C]22[/C][C]387[/C][C]392.119785790203[/C][C]-5.11978579020285[/C][/ROW]
[ROW][C]23[/C][C]380[/C][C]388.454794455973[/C][C]-8.45479445597346[/C][/ROW]
[ROW][C]24[/C][C]379[/C][C]384.172393304825[/C][C]-5.17239330482471[/C][/ROW]
[ROW][C]25[/C][C]386[/C][C]376.185188686141[/C][C]9.81481131385937[/C][/ROW]
[ROW][C]26[/C][C]385[/C][C]380.161767893433[/C][C]4.83823210656709[/C][/ROW]
[ROW][C]27[/C][C]365[/C][C]372.519373653186[/C][C]-7.51937365318588[/C][/ROW]
[ROW][C]28[/C][C]356[/C][C]355.594779872574[/C][C]0.405220127426162[/C][/ROW]
[ROW][C]29[/C][C]338[/C][C]348.950662500551[/C][C]-10.9506625005515[/C][/ROW]
[ROW][C]30[/C][C]338[/C][C]341.754564225453[/C][C]-3.75456422545290[/C][/ROW]
[ROW][C]31[/C][C]343[/C][C]336.676920892576[/C][C]6.32307910742367[/C][/ROW]
[ROW][C]32[/C][C]338[/C][C]333.590722901975[/C][C]4.40927709802457[/C][/ROW]
[ROW][C]33[/C][C]320[/C][C]327.969073031903[/C][C]-7.96907303190301[/C][/ROW]
[ROW][C]34[/C][C]316[/C][C]320.192986655638[/C][C]-4.19298665563781[/C][/ROW]
[ROW][C]35[/C][C]317[/C][C]312.632742874520[/C][C]4.36725712548042[/C][/ROW]
[ROW][C]36[/C][C]315[/C][C]312.621522250419[/C][C]2.37847774958055[/C][/ROW]
[ROW][C]37[/C][C]317[/C][C]315.543876413973[/C][C]1.45612358602699[/C][/ROW]
[ROW][C]38[/C][C]321[/C][C]312.228349330538[/C][C]8.77165066946162[/C][/ROW]
[ROW][C]39[/C][C]303[/C][C]298.830868400547[/C][C]4.16913159945295[/C][/ROW]
[ROW][C]40[/C][C]303[/C][C]292.060983440309[/C][C]10.9390165596913[/C][/ROW]
[ROW][C]41[/C][C]290[/C][C]283.260474175589[/C][C]6.73952582441069[/C][/ROW]
[ROW][C]42[/C][C]285[/C][C]287.890663970284[/C][C]-2.89066397028449[/C][/ROW]
[ROW][C]43[/C][C]300[/C][C]291.604706748857[/C][C]8.39529325114307[/C][/ROW]
[ROW][C]44[/C][C]291[/C][C]290.797249982095[/C][C]0.202750017904634[/C][/ROW]
[ROW][C]45[/C][C]278[/C][C]279.135422883107[/C][C]-1.13542288310725[/C][/ROW]
[ROW][C]46[/C][C]273[/C][C]278.724118657224[/C][C]-5.72411865722393[/C][/ROW]
[ROW][C]47[/C][C]277[/C][C]279.089544421879[/C][C]-2.08954442187934[/C][/ROW]
[ROW][C]48[/C][C]269[/C][C]277.929911950002[/C][C]-8.92991195000207[/C][/ROW]
[ROW][C]49[/C][C]275[/C][C]277.642399308342[/C][C]-2.64239930834185[/C][/ROW]
[ROW][C]50[/C][C]278[/C][C]278.721962385085[/C][C]-0.721962385084964[/C][/ROW]
[ROW][C]51[/C][C]255[/C][C]261.734565583615[/C][C]-6.73456558361477[/C][/ROW]
[ROW][C]52[/C][C]254[/C][C]256.010769194701[/C][C]-2.01076919470103[/C][/ROW]
[ROW][C]53[/C][C]245[/C][C]240.88943875154[/C][C]4.11056124845996[/C][/ROW]
[ROW][C]54[/C][C]240[/C][C]236.534860652266[/C][C]3.46513934773409[/C][/ROW]
[ROW][C]55[/C][C]261[/C][C]246.292875104851[/C][C]14.7071248951487[/C][/ROW]
[ROW][C]56[/C][C]247[/C][C]241.935151923681[/C][C]5.06484807631912[/C][/ROW]
[ROW][C]57[/C][C]229[/C][C]232.176420030279[/C][C]-3.17642003027919[/C][/ROW]
[ROW][C]58[/C][C]213[/C][C]227.642466677343[/C][C]-14.6424666773428[/C][/ROW]
[ROW][C]59[/C][C]218[/C][C]225.470770073857[/C][C]-7.47077007385678[/C][/ROW]
[ROW][C]60[/C][C]206[/C][C]216.702300550868[/C][C]-10.7023005508676[/C][/ROW]
[ROW][C]61[/C][C]217[/C][C]216.335559000485[/C][C]0.664440999514909[/C][/ROW]
[ROW][C]62[/C][C]219[/C][C]216.537673568524[/C][C]2.46232643147644[/C][/ROW]
[ROW][C]63[/C][C]196[/C][C]198.609369711206[/C][C]-2.60936971120603[/C][/ROW]
[ROW][C]64[/C][C]193[/C][C]195.512785156476[/C][C]-2.51278515647567[/C][/ROW]
[ROW][C]65[/C][C]188[/C][C]184.868378233240[/C][C]3.13162176676028[/C][/ROW]
[ROW][C]66[/C][C]171[/C][C]179.088920736665[/C][C]-8.08892073666513[/C][/ROW]
[ROW][C]67[/C][C]190[/C][C]185.594416778149[/C][C]4.40558322185075[/C][/ROW]
[ROW][C]68[/C][C]180[/C][C]171.980984239628[/C][C]8.01901576037173[/C][/ROW]
[ROW][C]69[/C][C]149[/C][C]158.962083943998[/C][C]-9.96208394399758[/C][/ROW]
[ROW][C]70[/C][C]135[/C][C]144.113000044135[/C][C]-9.1130000441351[/C][/ROW]
[ROW][C]71[/C][C]151[/C][C]142.144852427581[/C][C]8.85514757241899[/C][/ROW]
[ROW][C]72[/C][C]134[/C][C]135.826386053537[/C][C]-1.82638605353671[/C][/ROW]
[ROW][C]73[/C][C]145[/C][C]139.664563734048[/C][C]5.33543626595227[/C][/ROW]
[ROW][C]74[/C][C]151[/C][C]139.587908211005[/C][C]11.4120917889950[/C][/ROW]
[ROW][C]75[/C][C]137[/C][C]126.841887228177[/C][C]10.1581127718226[/C][/ROW]
[ROW][C]76[/C][C]124[/C][C]127.743624201119[/C][C]-3.74362420111891[/C][/ROW]
[ROW][C]77[/C][C]125[/C][C]122.049819958814[/C][C]2.95018004118644[/C][/ROW]
[ROW][C]78[/C][C]109[/C][C]112.628086561266[/C][C]-3.62808656126597[/C][/ROW]
[ROW][C]79[/C][C]131[/C][C]122.528786250708[/C][C]8.4712137492922[/C][/ROW]
[ROW][C]80[/C][C]133[/C][C]116.707952288599[/C][C]16.2920477114015[/C][/ROW]
[ROW][C]81[/C][C]103[/C][C]103.103878543786[/C][C]-0.103878543786308[/C][/ROW]
[ROW][C]82[/C][C]85[/C][C]96.424073755864[/C][C]-11.4240737558641[/C][/ROW]
[ROW][C]83[/C][C]104[/C][C]103.291671624255[/C][C]0.70832837574494[/C][/ROW]
[ROW][C]84[/C][C]82[/C][C]92.6595025076693[/C][C]-10.6595025076693[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79019&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79019&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
13432438.898544293284-6.89854429328369
14435439.588191700283-4.58819170028295
15426429.033615688526-3.03361568852637
16411413.220559235091-2.2205592350914
17405407.049203980354-2.04920398035432
18403405.234879262218-2.23487926221816
19402401.6841459104290.315854089571133
20399399.861758086254-0.86175808625353
21392396.82409187658-4.82409187658021
22387392.119785790203-5.11978579020285
23380388.454794455973-8.45479445597346
24379384.172393304825-5.17239330482471
25386376.1851886861419.81481131385937
26385380.1617678934334.83823210656709
27365372.519373653186-7.51937365318588
28356355.5947798725740.405220127426162
29338348.950662500551-10.9506625005515
30338341.754564225453-3.75456422545290
31343336.6769208925766.32307910742367
32338333.5907229019754.40927709802457
33320327.969073031903-7.96907303190301
34316320.192986655638-4.19298665563781
35317312.6327428745204.36725712548042
36315312.6215222504192.37847774958055
37317315.5438764139731.45612358602699
38321312.2283493305388.77165066946162
39303298.8308684005474.16913159945295
40303292.06098344030910.9390165596913
41290283.2604741755896.73952582441069
42285287.890663970284-2.89066397028449
43300291.6047067488578.39529325114307
44291290.7972499820950.202750017904634
45278279.135422883107-1.13542288310725
46273278.724118657224-5.72411865722393
47277279.089544421879-2.08954442187934
48269277.929911950002-8.92991195000207
49275277.642399308342-2.64239930834185
50278278.721962385085-0.721962385084964
51255261.734565583615-6.73456558361477
52254256.010769194701-2.01076919470103
53245240.889438751544.11056124845996
54240236.5348606522663.46513934773409
55261246.29287510485114.7071248951487
56247241.9351519236815.06484807631912
57229232.176420030279-3.17642003027919
58213227.642466677343-14.6424666773428
59218225.470770073857-7.47077007385678
60206216.702300550868-10.7023005508676
61217216.3355590004850.664440999514909
62219216.5376735685242.46232643147644
63196198.609369711206-2.60936971120603
64193195.512785156476-2.51278515647567
65188184.8683782332403.13162176676028
66171179.088920736665-8.08892073666513
67190185.5944167781494.40558322185075
68180171.9809842396288.01901576037173
69149158.962083943998-9.96208394399758
70135144.113000044135-9.1130000441351
71151142.1448524275818.85514757241899
72134135.826386053537-1.82638605353671
73145139.6645637340485.33543626595227
74151139.58790821100511.4120917889950
75137126.84188722817710.1581127718226
76124127.743624201119-3.74362420111891
77125122.0498199588142.95018004118644
78109112.628086561266-3.62808656126597
79131122.5287862507088.4712137492922
80133116.70795228859916.2920477114015
81103103.103878543786-0.103878543786308
828596.424073755864-11.4240737558641
83104103.2916716242550.70832837574494
848292.6595025076693-10.6595025076693







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8595.417236817122782.2422049101686108.592268724077
8696.20124311758482.0429725652299110.359513669938
8783.80151352171868.712003184882998.891023858553
8874.448473716501458.217984432158390.6789630008445
8972.533345339886654.275301412464990.7913892673083
9061.807565959298142.497060045277681.1180718733186
9170.460289593298645.868601841843895.0519773447533
9265.818055164847738.100348361724893.5357619679706
9347.922595971093422.166707717916873.67848422427
9438.200001522714712.509040844712963.8909622007166
9543.59315578672839.354576686278177.8317348871784
9632.84462951852822.9154864050661362.7737726319902

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 95.4172368171227 & 82.2422049101686 & 108.592268724077 \tabularnewline
86 & 96.201243117584 & 82.0429725652299 & 110.359513669938 \tabularnewline
87 & 83.801513521718 & 68.7120031848829 & 98.891023858553 \tabularnewline
88 & 74.4484737165014 & 58.2179844321583 & 90.6789630008445 \tabularnewline
89 & 72.5333453398866 & 54.2753014124649 & 90.7913892673083 \tabularnewline
90 & 61.8075659592981 & 42.4970600452776 & 81.1180718733186 \tabularnewline
91 & 70.4602895932986 & 45.8686018418438 & 95.0519773447533 \tabularnewline
92 & 65.8180551648477 & 38.1003483617248 & 93.5357619679706 \tabularnewline
93 & 47.9225959710934 & 22.1667077179168 & 73.67848422427 \tabularnewline
94 & 38.2000015227147 & 12.5090408447129 & 63.8909622007166 \tabularnewline
95 & 43.5931557867283 & 9.3545766862781 & 77.8317348871784 \tabularnewline
96 & 32.8446295185282 & 2.91548640506613 & 62.7737726319902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79019&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]85[/C][C]95.4172368171227[/C][C]82.2422049101686[/C][C]108.592268724077[/C][/ROW]
[ROW][C]86[/C][C]96.201243117584[/C][C]82.0429725652299[/C][C]110.359513669938[/C][/ROW]
[ROW][C]87[/C][C]83.801513521718[/C][C]68.7120031848829[/C][C]98.891023858553[/C][/ROW]
[ROW][C]88[/C][C]74.4484737165014[/C][C]58.2179844321583[/C][C]90.6789630008445[/C][/ROW]
[ROW][C]89[/C][C]72.5333453398866[/C][C]54.2753014124649[/C][C]90.7913892673083[/C][/ROW]
[ROW][C]90[/C][C]61.8075659592981[/C][C]42.4970600452776[/C][C]81.1180718733186[/C][/ROW]
[ROW][C]91[/C][C]70.4602895932986[/C][C]45.8686018418438[/C][C]95.0519773447533[/C][/ROW]
[ROW][C]92[/C][C]65.8180551648477[/C][C]38.1003483617248[/C][C]93.5357619679706[/C][/ROW]
[ROW][C]93[/C][C]47.9225959710934[/C][C]22.1667077179168[/C][C]73.67848422427[/C][/ROW]
[ROW][C]94[/C][C]38.2000015227147[/C][C]12.5090408447129[/C][C]63.8909622007166[/C][/ROW]
[ROW][C]95[/C][C]43.5931557867283[/C][C]9.3545766862781[/C][C]77.8317348871784[/C][/ROW]
[ROW][C]96[/C][C]32.8446295185282[/C][C]2.91548640506613[/C][C]62.7737726319902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79019&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79019&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
8595.417236817122782.2422049101686108.592268724077
8696.20124311758482.0429725652299110.359513669938
8783.80151352171868.712003184882998.891023858553
8874.448473716501458.217984432158390.6789630008445
8972.533345339886654.275301412464990.7913892673083
9061.807565959298142.497060045277681.1180718733186
9170.460289593298645.868601841843895.0519773447533
9265.818055164847738.100348361724893.5357619679706
9347.922595971093422.166707717916873.67848422427
9438.200001522714712.509040844712963.8909622007166
9543.59315578672839.354576686278177.8317348871784
9632.84462951852822.9154864050661362.7737726319902



Parameters (Session):
par1 = 4 ;
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')