Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 27 Nov 2016 12:56:14 +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/2016/Nov/27/t14802516260xgbmzray3z8jog.htm/, Retrieved Mon, 29 Apr 2024 23:18:27 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 23:18:27 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
272 567
266 674
301 601
322 421
313 776
300 156
315 745
299 214
295 184
340 003
332 748
316 337
293 572
308 713
354 188
334 540
313 285
337 881
356 955
323 661
296 034
377 623
342 590
300 905
309 470
271 492
307 759
326 106
335 576
310 485
335 173
298 344
288 269
319 410
327 692
315 401
277 720
260 573
318 025
300 264
317 640
303 273
315 089
275 840
292 823
339 759
328 032
344 675
260 952
275 466
331 940
347 644
338 063
384 283
398 482
347 062
350 731
368 799
387 710
362 988




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.345911531677233
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.345911531677233 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.345911531677233[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.345911531677233
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2266674272567-5893
3301601270528.54334382631072.4566561739
4322421281276.86441873841144.1355812624
5313776295509.09537718818266.9046228122
6300156301827.828334267-1671.82833426673
7315745301249.52363445914495.4763655409
8299214306263.676066454-7049.6760664545
9295184303825.111820479-8641.11182047887
10340003300836.05159526339166.9484047372
11332748314384.35070906918363.6492909314
12316337320736.548762478-4399.54876247817
13293572319214.694111361-25642.6941113606
14308713310344.590514969-1631.59051496908
15354188309780.20454086644407.7954591339
16334540325141.3730865449398.62691345566
17313285328392.466517841-15107.4665178406
18337881323166.61963489214714.3803651081
19356955328256.49348466828698.5065153322
20323661338183.637830235-14522.6378302354
21296034333160.089934385-37126.0899343849
22377623320317.74729999557305.2527000049
23342590340140.2950346052449.70496539533
24300905340987.676231342-40082.6762313418
25309470327122.616302436-17652.6163024358
26271492321016.37275915-49524.3727591497
27307759303885.3211226783873.678877322
28326106305225.27131635820880.7286836418
29335576312448.15615785323127.8438421466
30310485320448.344045682-9963.34404568223
31335173317001.90844621318171.091553787
32298344323287.498557831-24943.4985578307
33288269314659.254766303-26390.2547663026
34319410305530.56131873913879.4386812615
35327692310331.61921179417360.3807882061
36315401316336.775120742-935.77512074227
37277720316013.079715421-38293.0797154208
38260573302767.061858421-42194.0618584212
39318025288171.64929329129853.3507067092
40300264298498.2675619461765.73243805382
41317640299109.05477412618530.9452258744
42303273305519.122420635-2246.12242063473
43315089304742.16277377810346.8372262216
44275840308321.253086716-32481.2530867157
45292823297085.613080694-4262.61308069399
46339759295611.12606100444147.8739389963
47328032310882.38475553517149.6152444647
48344675316814.63443242327860.3655675767
49260952326451.856158991-65499.8561589913
50275466303794.700590396-28328.7005903962
51331940293995.47637874637944.5236212536
52347644307120.92466333740523.0753366628
53338063321138.32372131416924.6762786859
54384283326992.76441601657290.2355839844
55398482346810.11755702151671.8824429788
56347062364684.017557518-17622.0175575179
57350731358588.358472954-7857.35847295378
58368799355870.40756863712928.5924313628
59387710360342.55677900127367.4432209994
60362988369809.270981666-6821.27098166622

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 266674 & 272567 & -5893 \tabularnewline
3 & 301601 & 270528.543343826 & 31072.4566561739 \tabularnewline
4 & 322421 & 281276.864418738 & 41144.1355812624 \tabularnewline
5 & 313776 & 295509.095377188 & 18266.9046228122 \tabularnewline
6 & 300156 & 301827.828334267 & -1671.82833426673 \tabularnewline
7 & 315745 & 301249.523634459 & 14495.4763655409 \tabularnewline
8 & 299214 & 306263.676066454 & -7049.6760664545 \tabularnewline
9 & 295184 & 303825.111820479 & -8641.11182047887 \tabularnewline
10 & 340003 & 300836.051595263 & 39166.9484047372 \tabularnewline
11 & 332748 & 314384.350709069 & 18363.6492909314 \tabularnewline
12 & 316337 & 320736.548762478 & -4399.54876247817 \tabularnewline
13 & 293572 & 319214.694111361 & -25642.6941113606 \tabularnewline
14 & 308713 & 310344.590514969 & -1631.59051496908 \tabularnewline
15 & 354188 & 309780.204540866 & 44407.7954591339 \tabularnewline
16 & 334540 & 325141.373086544 & 9398.62691345566 \tabularnewline
17 & 313285 & 328392.466517841 & -15107.4665178406 \tabularnewline
18 & 337881 & 323166.619634892 & 14714.3803651081 \tabularnewline
19 & 356955 & 328256.493484668 & 28698.5065153322 \tabularnewline
20 & 323661 & 338183.637830235 & -14522.6378302354 \tabularnewline
21 & 296034 & 333160.089934385 & -37126.0899343849 \tabularnewline
22 & 377623 & 320317.747299995 & 57305.2527000049 \tabularnewline
23 & 342590 & 340140.295034605 & 2449.70496539533 \tabularnewline
24 & 300905 & 340987.676231342 & -40082.6762313418 \tabularnewline
25 & 309470 & 327122.616302436 & -17652.6163024358 \tabularnewline
26 & 271492 & 321016.37275915 & -49524.3727591497 \tabularnewline
27 & 307759 & 303885.321122678 & 3873.678877322 \tabularnewline
28 & 326106 & 305225.271316358 & 20880.7286836418 \tabularnewline
29 & 335576 & 312448.156157853 & 23127.8438421466 \tabularnewline
30 & 310485 & 320448.344045682 & -9963.34404568223 \tabularnewline
31 & 335173 & 317001.908446213 & 18171.091553787 \tabularnewline
32 & 298344 & 323287.498557831 & -24943.4985578307 \tabularnewline
33 & 288269 & 314659.254766303 & -26390.2547663026 \tabularnewline
34 & 319410 & 305530.561318739 & 13879.4386812615 \tabularnewline
35 & 327692 & 310331.619211794 & 17360.3807882061 \tabularnewline
36 & 315401 & 316336.775120742 & -935.77512074227 \tabularnewline
37 & 277720 & 316013.079715421 & -38293.0797154208 \tabularnewline
38 & 260573 & 302767.061858421 & -42194.0618584212 \tabularnewline
39 & 318025 & 288171.649293291 & 29853.3507067092 \tabularnewline
40 & 300264 & 298498.267561946 & 1765.73243805382 \tabularnewline
41 & 317640 & 299109.054774126 & 18530.9452258744 \tabularnewline
42 & 303273 & 305519.122420635 & -2246.12242063473 \tabularnewline
43 & 315089 & 304742.162773778 & 10346.8372262216 \tabularnewline
44 & 275840 & 308321.253086716 & -32481.2530867157 \tabularnewline
45 & 292823 & 297085.613080694 & -4262.61308069399 \tabularnewline
46 & 339759 & 295611.126061004 & 44147.8739389963 \tabularnewline
47 & 328032 & 310882.384755535 & 17149.6152444647 \tabularnewline
48 & 344675 & 316814.634432423 & 27860.3655675767 \tabularnewline
49 & 260952 & 326451.856158991 & -65499.8561589913 \tabularnewline
50 & 275466 & 303794.700590396 & -28328.7005903962 \tabularnewline
51 & 331940 & 293995.476378746 & 37944.5236212536 \tabularnewline
52 & 347644 & 307120.924663337 & 40523.0753366628 \tabularnewline
53 & 338063 & 321138.323721314 & 16924.6762786859 \tabularnewline
54 & 384283 & 326992.764416016 & 57290.2355839844 \tabularnewline
55 & 398482 & 346810.117557021 & 51671.8824429788 \tabularnewline
56 & 347062 & 364684.017557518 & -17622.0175575179 \tabularnewline
57 & 350731 & 358588.358472954 & -7857.35847295378 \tabularnewline
58 & 368799 & 355870.407568637 & 12928.5924313628 \tabularnewline
59 & 387710 & 360342.556779001 & 27367.4432209994 \tabularnewline
60 & 362988 & 369809.270981666 & -6821.27098166622 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]2[/C][C]266674[/C][C]272567[/C][C]-5893[/C][/ROW]
[ROW][C]3[/C][C]301601[/C][C]270528.543343826[/C][C]31072.4566561739[/C][/ROW]
[ROW][C]4[/C][C]322421[/C][C]281276.864418738[/C][C]41144.1355812624[/C][/ROW]
[ROW][C]5[/C][C]313776[/C][C]295509.095377188[/C][C]18266.9046228122[/C][/ROW]
[ROW][C]6[/C][C]300156[/C][C]301827.828334267[/C][C]-1671.82833426673[/C][/ROW]
[ROW][C]7[/C][C]315745[/C][C]301249.523634459[/C][C]14495.4763655409[/C][/ROW]
[ROW][C]8[/C][C]299214[/C][C]306263.676066454[/C][C]-7049.6760664545[/C][/ROW]
[ROW][C]9[/C][C]295184[/C][C]303825.111820479[/C][C]-8641.11182047887[/C][/ROW]
[ROW][C]10[/C][C]340003[/C][C]300836.051595263[/C][C]39166.9484047372[/C][/ROW]
[ROW][C]11[/C][C]332748[/C][C]314384.350709069[/C][C]18363.6492909314[/C][/ROW]
[ROW][C]12[/C][C]316337[/C][C]320736.548762478[/C][C]-4399.54876247817[/C][/ROW]
[ROW][C]13[/C][C]293572[/C][C]319214.694111361[/C][C]-25642.6941113606[/C][/ROW]
[ROW][C]14[/C][C]308713[/C][C]310344.590514969[/C][C]-1631.59051496908[/C][/ROW]
[ROW][C]15[/C][C]354188[/C][C]309780.204540866[/C][C]44407.7954591339[/C][/ROW]
[ROW][C]16[/C][C]334540[/C][C]325141.373086544[/C][C]9398.62691345566[/C][/ROW]
[ROW][C]17[/C][C]313285[/C][C]328392.466517841[/C][C]-15107.4665178406[/C][/ROW]
[ROW][C]18[/C][C]337881[/C][C]323166.619634892[/C][C]14714.3803651081[/C][/ROW]
[ROW][C]19[/C][C]356955[/C][C]328256.493484668[/C][C]28698.5065153322[/C][/ROW]
[ROW][C]20[/C][C]323661[/C][C]338183.637830235[/C][C]-14522.6378302354[/C][/ROW]
[ROW][C]21[/C][C]296034[/C][C]333160.089934385[/C][C]-37126.0899343849[/C][/ROW]
[ROW][C]22[/C][C]377623[/C][C]320317.747299995[/C][C]57305.2527000049[/C][/ROW]
[ROW][C]23[/C][C]342590[/C][C]340140.295034605[/C][C]2449.70496539533[/C][/ROW]
[ROW][C]24[/C][C]300905[/C][C]340987.676231342[/C][C]-40082.6762313418[/C][/ROW]
[ROW][C]25[/C][C]309470[/C][C]327122.616302436[/C][C]-17652.6163024358[/C][/ROW]
[ROW][C]26[/C][C]271492[/C][C]321016.37275915[/C][C]-49524.3727591497[/C][/ROW]
[ROW][C]27[/C][C]307759[/C][C]303885.321122678[/C][C]3873.678877322[/C][/ROW]
[ROW][C]28[/C][C]326106[/C][C]305225.271316358[/C][C]20880.7286836418[/C][/ROW]
[ROW][C]29[/C][C]335576[/C][C]312448.156157853[/C][C]23127.8438421466[/C][/ROW]
[ROW][C]30[/C][C]310485[/C][C]320448.344045682[/C][C]-9963.34404568223[/C][/ROW]
[ROW][C]31[/C][C]335173[/C][C]317001.908446213[/C][C]18171.091553787[/C][/ROW]
[ROW][C]32[/C][C]298344[/C][C]323287.498557831[/C][C]-24943.4985578307[/C][/ROW]
[ROW][C]33[/C][C]288269[/C][C]314659.254766303[/C][C]-26390.2547663026[/C][/ROW]
[ROW][C]34[/C][C]319410[/C][C]305530.561318739[/C][C]13879.4386812615[/C][/ROW]
[ROW][C]35[/C][C]327692[/C][C]310331.619211794[/C][C]17360.3807882061[/C][/ROW]
[ROW][C]36[/C][C]315401[/C][C]316336.775120742[/C][C]-935.77512074227[/C][/ROW]
[ROW][C]37[/C][C]277720[/C][C]316013.079715421[/C][C]-38293.0797154208[/C][/ROW]
[ROW][C]38[/C][C]260573[/C][C]302767.061858421[/C][C]-42194.0618584212[/C][/ROW]
[ROW][C]39[/C][C]318025[/C][C]288171.649293291[/C][C]29853.3507067092[/C][/ROW]
[ROW][C]40[/C][C]300264[/C][C]298498.267561946[/C][C]1765.73243805382[/C][/ROW]
[ROW][C]41[/C][C]317640[/C][C]299109.054774126[/C][C]18530.9452258744[/C][/ROW]
[ROW][C]42[/C][C]303273[/C][C]305519.122420635[/C][C]-2246.12242063473[/C][/ROW]
[ROW][C]43[/C][C]315089[/C][C]304742.162773778[/C][C]10346.8372262216[/C][/ROW]
[ROW][C]44[/C][C]275840[/C][C]308321.253086716[/C][C]-32481.2530867157[/C][/ROW]
[ROW][C]45[/C][C]292823[/C][C]297085.613080694[/C][C]-4262.61308069399[/C][/ROW]
[ROW][C]46[/C][C]339759[/C][C]295611.126061004[/C][C]44147.8739389963[/C][/ROW]
[ROW][C]47[/C][C]328032[/C][C]310882.384755535[/C][C]17149.6152444647[/C][/ROW]
[ROW][C]48[/C][C]344675[/C][C]316814.634432423[/C][C]27860.3655675767[/C][/ROW]
[ROW][C]49[/C][C]260952[/C][C]326451.856158991[/C][C]-65499.8561589913[/C][/ROW]
[ROW][C]50[/C][C]275466[/C][C]303794.700590396[/C][C]-28328.7005903962[/C][/ROW]
[ROW][C]51[/C][C]331940[/C][C]293995.476378746[/C][C]37944.5236212536[/C][/ROW]
[ROW][C]52[/C][C]347644[/C][C]307120.924663337[/C][C]40523.0753366628[/C][/ROW]
[ROW][C]53[/C][C]338063[/C][C]321138.323721314[/C][C]16924.6762786859[/C][/ROW]
[ROW][C]54[/C][C]384283[/C][C]326992.764416016[/C][C]57290.2355839844[/C][/ROW]
[ROW][C]55[/C][C]398482[/C][C]346810.117557021[/C][C]51671.8824429788[/C][/ROW]
[ROW][C]56[/C][C]347062[/C][C]364684.017557518[/C][C]-17622.0175575179[/C][/ROW]
[ROW][C]57[/C][C]350731[/C][C]358588.358472954[/C][C]-7857.35847295378[/C][/ROW]
[ROW][C]58[/C][C]368799[/C][C]355870.407568637[/C][C]12928.5924313628[/C][/ROW]
[ROW][C]59[/C][C]387710[/C][C]360342.556779001[/C][C]27367.4432209994[/C][/ROW]
[ROW][C]60[/C][C]362988[/C][C]369809.270981666[/C][C]-6821.27098166622[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
2266674272567-5893
3301601270528.54334382631072.4566561739
4322421281276.86441873841144.1355812624
5313776295509.09537718818266.9046228122
6300156301827.828334267-1671.82833426673
7315745301249.52363445914495.4763655409
8299214306263.676066454-7049.6760664545
9295184303825.111820479-8641.11182047887
10340003300836.05159526339166.9484047372
11332748314384.35070906918363.6492909314
12316337320736.548762478-4399.54876247817
13293572319214.694111361-25642.6941113606
14308713310344.590514969-1631.59051496908
15354188309780.20454086644407.7954591339
16334540325141.3730865449398.62691345566
17313285328392.466517841-15107.4665178406
18337881323166.61963489214714.3803651081
19356955328256.49348466828698.5065153322
20323661338183.637830235-14522.6378302354
21296034333160.089934385-37126.0899343849
22377623320317.74729999557305.2527000049
23342590340140.2950346052449.70496539533
24300905340987.676231342-40082.6762313418
25309470327122.616302436-17652.6163024358
26271492321016.37275915-49524.3727591497
27307759303885.3211226783873.678877322
28326106305225.27131635820880.7286836418
29335576312448.15615785323127.8438421466
30310485320448.344045682-9963.34404568223
31335173317001.90844621318171.091553787
32298344323287.498557831-24943.4985578307
33288269314659.254766303-26390.2547663026
34319410305530.56131873913879.4386812615
35327692310331.61921179417360.3807882061
36315401316336.775120742-935.77512074227
37277720316013.079715421-38293.0797154208
38260573302767.061858421-42194.0618584212
39318025288171.64929329129853.3507067092
40300264298498.2675619461765.73243805382
41317640299109.05477412618530.9452258744
42303273305519.122420635-2246.12242063473
43315089304742.16277377810346.8372262216
44275840308321.253086716-32481.2530867157
45292823297085.613080694-4262.61308069399
46339759295611.12606100444147.8739389963
47328032310882.38475553517149.6152444647
48344675316814.63443242327860.3655675767
49260952326451.856158991-65499.8561589913
50275466303794.700590396-28328.7005903962
51331940293995.47637874637944.5236212536
52347644307120.92466333740523.0753366628
53338063321138.32372131416924.6762786859
54384283326992.76441601657290.2355839844
55398482346810.11755702151671.8824429788
56347062364684.017557518-17622.0175575179
57350731358588.358472954-7857.35847295378
58368799355870.40756863712928.5924313628
59387710360342.55677900127367.4432209994
60362988369809.270981666-6821.27098166622







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61367449.714688413312926.359628448421973.069748377
62367449.714688413309756.512740999425142.916635826
63367449.714688413306751.981164869428147.448211957
64367449.714688413303889.316964317431010.112412509
65367449.714688413301150.141063876433749.28831295
66367449.714688413298519.730162479436379.699214347
67367449.714688413295986.073088676438913.356288149
68367449.714688413293539.218988237441360.210388589
69367449.714688413291170.814076278443728.615300547
70367449.714688413288873.76428025446025.665096575
71367449.714688413286641.984324938448257.445051888
72367449.714688413284470.207637297450429.221739529

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 367449.714688413 & 312926.359628448 & 421973.069748377 \tabularnewline
62 & 367449.714688413 & 309756.512740999 & 425142.916635826 \tabularnewline
63 & 367449.714688413 & 306751.981164869 & 428147.448211957 \tabularnewline
64 & 367449.714688413 & 303889.316964317 & 431010.112412509 \tabularnewline
65 & 367449.714688413 & 301150.141063876 & 433749.28831295 \tabularnewline
66 & 367449.714688413 & 298519.730162479 & 436379.699214347 \tabularnewline
67 & 367449.714688413 & 295986.073088676 & 438913.356288149 \tabularnewline
68 & 367449.714688413 & 293539.218988237 & 441360.210388589 \tabularnewline
69 & 367449.714688413 & 291170.814076278 & 443728.615300547 \tabularnewline
70 & 367449.714688413 & 288873.76428025 & 446025.665096575 \tabularnewline
71 & 367449.714688413 & 286641.984324938 & 448257.445051888 \tabularnewline
72 & 367449.714688413 & 284470.207637297 & 450429.221739529 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]61[/C][C]367449.714688413[/C][C]312926.359628448[/C][C]421973.069748377[/C][/ROW]
[ROW][C]62[/C][C]367449.714688413[/C][C]309756.512740999[/C][C]425142.916635826[/C][/ROW]
[ROW][C]63[/C][C]367449.714688413[/C][C]306751.981164869[/C][C]428147.448211957[/C][/ROW]
[ROW][C]64[/C][C]367449.714688413[/C][C]303889.316964317[/C][C]431010.112412509[/C][/ROW]
[ROW][C]65[/C][C]367449.714688413[/C][C]301150.141063876[/C][C]433749.28831295[/C][/ROW]
[ROW][C]66[/C][C]367449.714688413[/C][C]298519.730162479[/C][C]436379.699214347[/C][/ROW]
[ROW][C]67[/C][C]367449.714688413[/C][C]295986.073088676[/C][C]438913.356288149[/C][/ROW]
[ROW][C]68[/C][C]367449.714688413[/C][C]293539.218988237[/C][C]441360.210388589[/C][/ROW]
[ROW][C]69[/C][C]367449.714688413[/C][C]291170.814076278[/C][C]443728.615300547[/C][/ROW]
[ROW][C]70[/C][C]367449.714688413[/C][C]288873.76428025[/C][C]446025.665096575[/C][/ROW]
[ROW][C]71[/C][C]367449.714688413[/C][C]286641.984324938[/C][C]448257.445051888[/C][/ROW]
[ROW][C]72[/C][C]367449.714688413[/C][C]284470.207637297[/C][C]450429.221739529[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61367449.714688413312926.359628448421973.069748377
62367449.714688413309756.512740999425142.916635826
63367449.714688413306751.981164869428147.448211957
64367449.714688413303889.316964317431010.112412509
65367449.714688413301150.141063876433749.28831295
66367449.714688413298519.730162479436379.699214347
67367449.714688413295986.073088676438913.356288149
68367449.714688413293539.218988237441360.210388589
69367449.714688413291170.814076278443728.615300547
70367449.714688413288873.76428025446025.665096575
71367449.714688413286641.984324938448257.445051888
72367449.714688413284470.207637297450429.221739529



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