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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 11 May 2014 11:56:36 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/11/t1399823825hkg19e51ii781h0.htm/, Retrieved Tue, 14 May 2024 10:03:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234793, Retrieved Tue, 14 May 2024 10:03:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 oefening 2] [2014-05-11 15:56:36] [4e14f87d0dfb5763171576624afe788b] [Current]
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Dataseries X:
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538
27561
25985
34670
32066
27186
29586
21359
21553
19573
24256
22380
16167
27297
28287
33474
28229
28785
25597
18130
20198
22849
23118
21925
20801
18785
20659
29367
23992
20645
22356
17902
15879
16963
21035
17988
10437




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234793&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234793&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234793&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.34398945285136
beta0
gamma0.911295332780041

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.34398945285136 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.911295332780041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234793&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]0.34398945285136[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.911295332780041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234793&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234793&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
alpha0.34398945285136
beta0
gamma0.911295332780041







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133156630657.2978098291908.702190170945
143011129597.1698035063513.830196493684
153001929751.3349961322267.665003867787
163193431884.446958835749.5530411643231
172582626100.2807068284-274.280706828442
182683527278.8440610344-443.844061034364
192020520984.8294098034-779.829409803355
201778918855.7810089499-1066.78100894989
212052020138.7742845112381.225715488818
222251824431.0749342706-1913.07493427058
231557218563.5770255094-2991.57702550938
241150910420.16910581721088.83089418276
252544730166.7432263847-4719.74322638473
262409026934.4272422748-2844.42724227483
272778625786.22498058821999.77501941175
282619528384.7729680746-2189.77296807456
292051621636.7081067021-1120.70810670209
302275922422.7411085737336.25889142626
311902816196.21510236012831.78489763988
321697115137.9787125881833.02128741204
332003618284.11983206471751.88016793525
342248521676.3338341216808.666165878381
351873016100.33673818482629.66326181521
361453812329.92299903442208.07700096556
372756128989.0279710448-1428.02797104478
382598528010.1274989851-2025.12749898509
393467030039.71355443934630.28644556072
403206631038.53687399321027.46312600675
412718626036.27495671311149.72504328688
422958628474.31607918971111.68392081029
432135924006.401839182-2647.40183918204
442155320466.30278959881086.69721040118
451957323307.2085668814-3734.20856688143
462425624248.39432525587.60567474420532
472238019485.46816928292894.53183071712
481616715554.1339998509612.866000149081
492729729490.7693020779-2193.76930207786
502828727891.5042369289395.495763071147
513347434732.4944013081-1258.49440130805
522822931551.8017247901-3322.8017247901
532878525126.18512162823658.81487837176
542559728404.5849645233-2807.58496452327
551813020341.2293599243-2211.22935992426
562019819183.48570900561014.51429099436
572284919117.53056577173731.46943422833
582311824863.759772179-1745.75977217904
592192521223.5547131599701.445286840066
602080115173.79791999095627.20208000912
611878529157.4510550393-10372.4510550393
622065926292.7184865348-5633.71848653485
632936730070.9352153062-703.935215306195
642399225846.9221876967-1854.92218769666
652064524099.9861621023-3454.98616210234
662235621065.57452730561290.42547269443
671790214768.40421061763133.59578938243
681587917377.6360106379-1498.63601063794
691696318071.4320275691-1108.43202756914
702103518878.39257500922156.6074249908
711798818043.5472103536-55.5472103535576
721043714678.1057059775-4241.10570597745

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 31566 & 30657.2978098291 & 908.702190170945 \tabularnewline
14 & 30111 & 29597.1698035063 & 513.830196493684 \tabularnewline
15 & 30019 & 29751.3349961322 & 267.665003867787 \tabularnewline
16 & 31934 & 31884.4469588357 & 49.5530411643231 \tabularnewline
17 & 25826 & 26100.2807068284 & -274.280706828442 \tabularnewline
18 & 26835 & 27278.8440610344 & -443.844061034364 \tabularnewline
19 & 20205 & 20984.8294098034 & -779.829409803355 \tabularnewline
20 & 17789 & 18855.7810089499 & -1066.78100894989 \tabularnewline
21 & 20520 & 20138.7742845112 & 381.225715488818 \tabularnewline
22 & 22518 & 24431.0749342706 & -1913.07493427058 \tabularnewline
23 & 15572 & 18563.5770255094 & -2991.57702550938 \tabularnewline
24 & 11509 & 10420.1691058172 & 1088.83089418276 \tabularnewline
25 & 25447 & 30166.7432263847 & -4719.74322638473 \tabularnewline
26 & 24090 & 26934.4272422748 & -2844.42724227483 \tabularnewline
27 & 27786 & 25786.2249805882 & 1999.77501941175 \tabularnewline
28 & 26195 & 28384.7729680746 & -2189.77296807456 \tabularnewline
29 & 20516 & 21636.7081067021 & -1120.70810670209 \tabularnewline
30 & 22759 & 22422.7411085737 & 336.25889142626 \tabularnewline
31 & 19028 & 16196.2151023601 & 2831.78489763988 \tabularnewline
32 & 16971 & 15137.978712588 & 1833.02128741204 \tabularnewline
33 & 20036 & 18284.1198320647 & 1751.88016793525 \tabularnewline
34 & 22485 & 21676.3338341216 & 808.666165878381 \tabularnewline
35 & 18730 & 16100.3367381848 & 2629.66326181521 \tabularnewline
36 & 14538 & 12329.9229990344 & 2208.07700096556 \tabularnewline
37 & 27561 & 28989.0279710448 & -1428.02797104478 \tabularnewline
38 & 25985 & 28010.1274989851 & -2025.12749898509 \tabularnewline
39 & 34670 & 30039.7135544393 & 4630.28644556072 \tabularnewline
40 & 32066 & 31038.5368739932 & 1027.46312600675 \tabularnewline
41 & 27186 & 26036.2749567131 & 1149.72504328688 \tabularnewline
42 & 29586 & 28474.3160791897 & 1111.68392081029 \tabularnewline
43 & 21359 & 24006.401839182 & -2647.40183918204 \tabularnewline
44 & 21553 & 20466.3027895988 & 1086.69721040118 \tabularnewline
45 & 19573 & 23307.2085668814 & -3734.20856688143 \tabularnewline
46 & 24256 & 24248.3943252558 & 7.60567474420532 \tabularnewline
47 & 22380 & 19485.4681692829 & 2894.53183071712 \tabularnewline
48 & 16167 & 15554.1339998509 & 612.866000149081 \tabularnewline
49 & 27297 & 29490.7693020779 & -2193.76930207786 \tabularnewline
50 & 28287 & 27891.5042369289 & 395.495763071147 \tabularnewline
51 & 33474 & 34732.4944013081 & -1258.49440130805 \tabularnewline
52 & 28229 & 31551.8017247901 & -3322.8017247901 \tabularnewline
53 & 28785 & 25126.1851216282 & 3658.81487837176 \tabularnewline
54 & 25597 & 28404.5849645233 & -2807.58496452327 \tabularnewline
55 & 18130 & 20341.2293599243 & -2211.22935992426 \tabularnewline
56 & 20198 & 19183.4857090056 & 1014.51429099436 \tabularnewline
57 & 22849 & 19117.5305657717 & 3731.46943422833 \tabularnewline
58 & 23118 & 24863.759772179 & -1745.75977217904 \tabularnewline
59 & 21925 & 21223.5547131599 & 701.445286840066 \tabularnewline
60 & 20801 & 15173.7979199909 & 5627.20208000912 \tabularnewline
61 & 18785 & 29157.4510550393 & -10372.4510550393 \tabularnewline
62 & 20659 & 26292.7184865348 & -5633.71848653485 \tabularnewline
63 & 29367 & 30070.9352153062 & -703.935215306195 \tabularnewline
64 & 23992 & 25846.9221876967 & -1854.92218769666 \tabularnewline
65 & 20645 & 24099.9861621023 & -3454.98616210234 \tabularnewline
66 & 22356 & 21065.5745273056 & 1290.42547269443 \tabularnewline
67 & 17902 & 14768.4042106176 & 3133.59578938243 \tabularnewline
68 & 15879 & 17377.6360106379 & -1498.63601063794 \tabularnewline
69 & 16963 & 18071.4320275691 & -1108.43202756914 \tabularnewline
70 & 21035 & 18878.3925750092 & 2156.6074249908 \tabularnewline
71 & 17988 & 18043.5472103536 & -55.5472103535576 \tabularnewline
72 & 10437 & 14678.1057059775 & -4241.10570597745 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234793&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]31566[/C][C]30657.2978098291[/C][C]908.702190170945[/C][/ROW]
[ROW][C]14[/C][C]30111[/C][C]29597.1698035063[/C][C]513.830196493684[/C][/ROW]
[ROW][C]15[/C][C]30019[/C][C]29751.3349961322[/C][C]267.665003867787[/C][/ROW]
[ROW][C]16[/C][C]31934[/C][C]31884.4469588357[/C][C]49.5530411643231[/C][/ROW]
[ROW][C]17[/C][C]25826[/C][C]26100.2807068284[/C][C]-274.280706828442[/C][/ROW]
[ROW][C]18[/C][C]26835[/C][C]27278.8440610344[/C][C]-443.844061034364[/C][/ROW]
[ROW][C]19[/C][C]20205[/C][C]20984.8294098034[/C][C]-779.829409803355[/C][/ROW]
[ROW][C]20[/C][C]17789[/C][C]18855.7810089499[/C][C]-1066.78100894989[/C][/ROW]
[ROW][C]21[/C][C]20520[/C][C]20138.7742845112[/C][C]381.225715488818[/C][/ROW]
[ROW][C]22[/C][C]22518[/C][C]24431.0749342706[/C][C]-1913.07493427058[/C][/ROW]
[ROW][C]23[/C][C]15572[/C][C]18563.5770255094[/C][C]-2991.57702550938[/C][/ROW]
[ROW][C]24[/C][C]11509[/C][C]10420.1691058172[/C][C]1088.83089418276[/C][/ROW]
[ROW][C]25[/C][C]25447[/C][C]30166.7432263847[/C][C]-4719.74322638473[/C][/ROW]
[ROW][C]26[/C][C]24090[/C][C]26934.4272422748[/C][C]-2844.42724227483[/C][/ROW]
[ROW][C]27[/C][C]27786[/C][C]25786.2249805882[/C][C]1999.77501941175[/C][/ROW]
[ROW][C]28[/C][C]26195[/C][C]28384.7729680746[/C][C]-2189.77296807456[/C][/ROW]
[ROW][C]29[/C][C]20516[/C][C]21636.7081067021[/C][C]-1120.70810670209[/C][/ROW]
[ROW][C]30[/C][C]22759[/C][C]22422.7411085737[/C][C]336.25889142626[/C][/ROW]
[ROW][C]31[/C][C]19028[/C][C]16196.2151023601[/C][C]2831.78489763988[/C][/ROW]
[ROW][C]32[/C][C]16971[/C][C]15137.978712588[/C][C]1833.02128741204[/C][/ROW]
[ROW][C]33[/C][C]20036[/C][C]18284.1198320647[/C][C]1751.88016793525[/C][/ROW]
[ROW][C]34[/C][C]22485[/C][C]21676.3338341216[/C][C]808.666165878381[/C][/ROW]
[ROW][C]35[/C][C]18730[/C][C]16100.3367381848[/C][C]2629.66326181521[/C][/ROW]
[ROW][C]36[/C][C]14538[/C][C]12329.9229990344[/C][C]2208.07700096556[/C][/ROW]
[ROW][C]37[/C][C]27561[/C][C]28989.0279710448[/C][C]-1428.02797104478[/C][/ROW]
[ROW][C]38[/C][C]25985[/C][C]28010.1274989851[/C][C]-2025.12749898509[/C][/ROW]
[ROW][C]39[/C][C]34670[/C][C]30039.7135544393[/C][C]4630.28644556072[/C][/ROW]
[ROW][C]40[/C][C]32066[/C][C]31038.5368739932[/C][C]1027.46312600675[/C][/ROW]
[ROW][C]41[/C][C]27186[/C][C]26036.2749567131[/C][C]1149.72504328688[/C][/ROW]
[ROW][C]42[/C][C]29586[/C][C]28474.3160791897[/C][C]1111.68392081029[/C][/ROW]
[ROW][C]43[/C][C]21359[/C][C]24006.401839182[/C][C]-2647.40183918204[/C][/ROW]
[ROW][C]44[/C][C]21553[/C][C]20466.3027895988[/C][C]1086.69721040118[/C][/ROW]
[ROW][C]45[/C][C]19573[/C][C]23307.2085668814[/C][C]-3734.20856688143[/C][/ROW]
[ROW][C]46[/C][C]24256[/C][C]24248.3943252558[/C][C]7.60567474420532[/C][/ROW]
[ROW][C]47[/C][C]22380[/C][C]19485.4681692829[/C][C]2894.53183071712[/C][/ROW]
[ROW][C]48[/C][C]16167[/C][C]15554.1339998509[/C][C]612.866000149081[/C][/ROW]
[ROW][C]49[/C][C]27297[/C][C]29490.7693020779[/C][C]-2193.76930207786[/C][/ROW]
[ROW][C]50[/C][C]28287[/C][C]27891.5042369289[/C][C]395.495763071147[/C][/ROW]
[ROW][C]51[/C][C]33474[/C][C]34732.4944013081[/C][C]-1258.49440130805[/C][/ROW]
[ROW][C]52[/C][C]28229[/C][C]31551.8017247901[/C][C]-3322.8017247901[/C][/ROW]
[ROW][C]53[/C][C]28785[/C][C]25126.1851216282[/C][C]3658.81487837176[/C][/ROW]
[ROW][C]54[/C][C]25597[/C][C]28404.5849645233[/C][C]-2807.58496452327[/C][/ROW]
[ROW][C]55[/C][C]18130[/C][C]20341.2293599243[/C][C]-2211.22935992426[/C][/ROW]
[ROW][C]56[/C][C]20198[/C][C]19183.4857090056[/C][C]1014.51429099436[/C][/ROW]
[ROW][C]57[/C][C]22849[/C][C]19117.5305657717[/C][C]3731.46943422833[/C][/ROW]
[ROW][C]58[/C][C]23118[/C][C]24863.759772179[/C][C]-1745.75977217904[/C][/ROW]
[ROW][C]59[/C][C]21925[/C][C]21223.5547131599[/C][C]701.445286840066[/C][/ROW]
[ROW][C]60[/C][C]20801[/C][C]15173.7979199909[/C][C]5627.20208000912[/C][/ROW]
[ROW][C]61[/C][C]18785[/C][C]29157.4510550393[/C][C]-10372.4510550393[/C][/ROW]
[ROW][C]62[/C][C]20659[/C][C]26292.7184865348[/C][C]-5633.71848653485[/C][/ROW]
[ROW][C]63[/C][C]29367[/C][C]30070.9352153062[/C][C]-703.935215306195[/C][/ROW]
[ROW][C]64[/C][C]23992[/C][C]25846.9221876967[/C][C]-1854.92218769666[/C][/ROW]
[ROW][C]65[/C][C]20645[/C][C]24099.9861621023[/C][C]-3454.98616210234[/C][/ROW]
[ROW][C]66[/C][C]22356[/C][C]21065.5745273056[/C][C]1290.42547269443[/C][/ROW]
[ROW][C]67[/C][C]17902[/C][C]14768.4042106176[/C][C]3133.59578938243[/C][/ROW]
[ROW][C]68[/C][C]15879[/C][C]17377.6360106379[/C][C]-1498.63601063794[/C][/ROW]
[ROW][C]69[/C][C]16963[/C][C]18071.4320275691[/C][C]-1108.43202756914[/C][/ROW]
[ROW][C]70[/C][C]21035[/C][C]18878.3925750092[/C][C]2156.6074249908[/C][/ROW]
[ROW][C]71[/C][C]17988[/C][C]18043.5472103536[/C][C]-55.5472103535576[/C][/ROW]
[ROW][C]72[/C][C]10437[/C][C]14678.1057059775[/C][C]-4241.10570597745[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234793&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234793&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
133156630657.2978098291908.702190170945
143011129597.1698035063513.830196493684
153001929751.3349961322267.665003867787
163193431884.446958835749.5530411643231
172582626100.2807068284-274.280706828442
182683527278.8440610344-443.844061034364
192020520984.8294098034-779.829409803355
201778918855.7810089499-1066.78100894989
212052020138.7742845112381.225715488818
222251824431.0749342706-1913.07493427058
231557218563.5770255094-2991.57702550938
241150910420.16910581721088.83089418276
252544730166.7432263847-4719.74322638473
262409026934.4272422748-2844.42724227483
272778625786.22498058821999.77501941175
282619528384.7729680746-2189.77296807456
292051621636.7081067021-1120.70810670209
302275922422.7411085737336.25889142626
311902816196.21510236012831.78489763988
321697115137.9787125881833.02128741204
332003618284.11983206471751.88016793525
342248521676.3338341216808.666165878381
351873016100.33673818482629.66326181521
361453812329.92299903442208.07700096556
372756128989.0279710448-1428.02797104478
382598528010.1274989851-2025.12749898509
393467030039.71355443934630.28644556072
403206631038.53687399321027.46312600675
412718626036.27495671311149.72504328688
422958628474.31607918971111.68392081029
432135924006.401839182-2647.40183918204
442155320466.30278959881086.69721040118
451957323307.2085668814-3734.20856688143
462425624248.39432525587.60567474420532
472238019485.46816928292894.53183071712
481616715554.1339998509612.866000149081
492729729490.7693020779-2193.76930207786
502828727891.5042369289395.495763071147
513347434732.4944013081-1258.49440130805
522822931551.8017247901-3322.8017247901
532878525126.18512162823658.81487837176
542559728404.5849645233-2807.58496452327
551813020341.2293599243-2211.22935992426
562019819183.48570900561014.51429099436
572284919117.53056577173731.46943422833
582311824863.759772179-1745.75977217904
592192521223.5547131599701.445286840066
602080115173.79791999095627.20208000912
611878529157.4510550393-10372.4510550393
622065926292.7184865348-5633.71848653485
632936730070.9352153062-703.935215306195
642399225846.9221876967-1854.92218769666
652064524099.9861621023-3454.98616210234
662235621065.57452730561290.42547269443
671790214768.40421061763133.59578938243
681587917377.6360106379-1498.63601063794
691696318071.4320275691-1108.43202756914
702103518878.39257500922156.6074249908
711798818043.5472103536-55.5472103535576
721043714678.1057059775-4241.10570597745







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7315702.262809798810426.779711105220977.7459084924
7419238.450027760913659.570544795524817.3295107262
7527901.72632644522035.11992697533768.3327259149
7623231.777304846917090.910508770629372.6441009232
7721166.365742748914762.974503100827569.7569823971
7822157.331805847415501.76318033928812.9004313559
7916518.15161728589619.6178535282923416.6853810433
8015280.22171311918146.9936605083522413.4497657298
8116722.80420284839362.3614979966724083.2469076998
8219862.957439807412282.10714632127443.8077332938
8316963.79302109829168.7647637342524758.8212784622
8411115.2513125183111.7745746275719118.7280504084

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 15702.2628097988 & 10426.7797111052 & 20977.7459084924 \tabularnewline
74 & 19238.4500277609 & 13659.5705447955 & 24817.3295107262 \tabularnewline
75 & 27901.726326445 & 22035.119926975 & 33768.3327259149 \tabularnewline
76 & 23231.7773048469 & 17090.9105087706 & 29372.6441009232 \tabularnewline
77 & 21166.3657427489 & 14762.9745031008 & 27569.7569823971 \tabularnewline
78 & 22157.3318058474 & 15501.763180339 & 28812.9004313559 \tabularnewline
79 & 16518.1516172858 & 9619.61785352829 & 23416.6853810433 \tabularnewline
80 & 15280.2217131191 & 8146.99366050835 & 22413.4497657298 \tabularnewline
81 & 16722.8042028483 & 9362.36149799667 & 24083.2469076998 \tabularnewline
82 & 19862.9574398074 & 12282.107146321 & 27443.8077332938 \tabularnewline
83 & 16963.7930210982 & 9168.76476373425 & 24758.8212784622 \tabularnewline
84 & 11115.251312518 & 3111.77457462757 & 19118.7280504084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234793&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]73[/C][C]15702.2628097988[/C][C]10426.7797111052[/C][C]20977.7459084924[/C][/ROW]
[ROW][C]74[/C][C]19238.4500277609[/C][C]13659.5705447955[/C][C]24817.3295107262[/C][/ROW]
[ROW][C]75[/C][C]27901.726326445[/C][C]22035.119926975[/C][C]33768.3327259149[/C][/ROW]
[ROW][C]76[/C][C]23231.7773048469[/C][C]17090.9105087706[/C][C]29372.6441009232[/C][/ROW]
[ROW][C]77[/C][C]21166.3657427489[/C][C]14762.9745031008[/C][C]27569.7569823971[/C][/ROW]
[ROW][C]78[/C][C]22157.3318058474[/C][C]15501.763180339[/C][C]28812.9004313559[/C][/ROW]
[ROW][C]79[/C][C]16518.1516172858[/C][C]9619.61785352829[/C][C]23416.6853810433[/C][/ROW]
[ROW][C]80[/C][C]15280.2217131191[/C][C]8146.99366050835[/C][C]22413.4497657298[/C][/ROW]
[ROW][C]81[/C][C]16722.8042028483[/C][C]9362.36149799667[/C][C]24083.2469076998[/C][/ROW]
[ROW][C]82[/C][C]19862.9574398074[/C][C]12282.107146321[/C][C]27443.8077332938[/C][/ROW]
[ROW][C]83[/C][C]16963.7930210982[/C][C]9168.76476373425[/C][C]24758.8212784622[/C][/ROW]
[ROW][C]84[/C][C]11115.251312518[/C][C]3111.77457462757[/C][C]19118.7280504084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234793&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234793&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
7315702.262809798810426.779711105220977.7459084924
7419238.450027760913659.570544795524817.3295107262
7527901.72632644522035.11992697533768.3327259149
7623231.777304846917090.910508770629372.6441009232
7721166.365742748914762.974503100827569.7569823971
7822157.331805847415501.76318033928812.9004313559
7916518.15161728589619.6178535282923416.6853810433
8015280.22171311918146.9936605083522413.4497657298
8116722.80420284839362.3614979966724083.2469076998
8219862.957439807412282.10714632127443.8077332938
8316963.79302109829168.7647637342524758.8212784622
8411115.2513125183111.7745746275719118.7280504084



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')