Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 12 Dec 2013 10:06:38 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/12/t1386860865tlm0mi4is0dpoj6.htm/, Retrieved Tue, 07 Dec 2021 11:16:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232253, Retrieved Tue, 07 Dec 2021 11:16:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Reserve positie I...] [2013-12-12 15:06:38] [0b006450a16a8f41725aee2d0d1bc384] [Current]
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Dataseries X:
679
687
638
628
604
713
712
693
697
555
486
470
465
426
384
379
381
380
351
346
339
336
333
324
324
321
304
343
407
389
361
353
361
387
692
704
742
721
843
847
945
946
946
945
1082
1075
820
832
851
1090
1203
1239
1535
1527
1480
1452
1383
1381
1429
1376
1602
1597
2003
1958
1997
1986
2129
2115
2297
2250
2309
2648
2627
2711
2732
2825
2932
2910
2969
2999
2965
2846
2847
2751




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232253&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232253&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232253&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.972448439053752
beta0.065187907046855
gamma0.74672997962751

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.972448439053752 \tabularnewline
beta & 0.065187907046855 \tabularnewline
gamma & 0.74672997962751 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232253&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]0.972448439053752[/C][/ROW]
[ROW][C]beta[/C][C]0.065187907046855[/C][/ROW]
[ROW][C]gamma[/C][C]0.74672997962751[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232253&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232253&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
alpha0.972448439053752
beta0.065187907046855
gamma0.74672997962751







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13465598.841346153846-133.841346153846
14426427.057687387933-1.05768738793273
15384381.2072415304412.79275846955909
16379370.9448606088458.05513939115468
17381364.768837550716.2311624492999
18380361.53083256358418.4691674364157
19351437.348300583373-86.3483005833725
20346319.38740446655626.6125955334442
21339337.6288445406891.37115545931061
22336184.91120573548151.08879426452
23333259.07238690015473.927613099846
24324319.3847081496354.61529185036505
25324326.583347633008-2.58334763300775
26321298.68668140893122.3133185910689
27304290.63760524725813.362394752742
28343306.42699969570436.5730003042963
29407345.6242198450561.3757801549499
30389406.667757603921-17.6677576039215
31361463.23135747429-102.23135747429
32353349.1860587070813.81394129291914
33361360.3294684223690.670531577630754
34387225.558114524396161.441885475604
35692324.403341714789367.596658285211
36704703.6875777293210.31242227067878
37742741.100942183470.899057816529762
38721751.870850931602-30.8708509316018
39843723.315216968909119.684783031091
40847881.111610370015-34.1116103700145
41945885.73757611037559.2624238896245
42946976.621408986575-30.6214089865755
439461051.5489521942-105.548952194195
44945968.949363229427-23.9493632294269
451082983.75992013076498.2400798692356
461075984.09288038183190.907119618169
478201051.0320117677-231.032011767702
48832835.12017193719-3.12017193719021
49851863.485776372315-12.4857763723148
501090854.015705244088235.984294755912
5112031098.40655986511104.593440134886
5212391247.75274082413-8.75274082412693
5315351289.95696615997245.043033840028
5415271582.42764176637-55.427641766368
5514801652.89237188301-172.892371883008
5614521523.41604587531-71.4160458753065
5713831508.50504393868-125.505043938681
5813811290.8463876325890.1536123674177
5914291350.1214115212478.8785884787642
6013761459.60850674546-83.6085067454574
6116021423.74625883426178.253741165736
6215971631.19937532074-34.1993753207355
6320031619.3468350314383.653164968603
6419582064.62186675377-106.621866753769
6519972037.56038568516-40.5603856851599
6619862048.69525362652-62.6952536265158
6721292111.7957770346317.2042229653739
6821152183.43673986894-68.4367398689442
6922972184.66944002179112.330559978208
7022502232.1666458202317.8333541797674
7123092245.7335933898663.2664066101388
7226482360.55763393382287.44236606618
7326272738.29421082749-111.294210827492
7427112688.8345040620822.1654959379221
7527322772.99224228452-40.9922422845234
7628252800.9173558543224.0826441456752
7729322916.2865539676115.7134460323941
7829102999.22489286576-89.2248928657636
7929693054.02422888183-85.0242288818295
8029993033.86459966967-34.8645996696705
8129653082.96495334939-117.964953349386
8228462901.47008431983-55.4700843198329
8328472836.9436783867210.05632161328
8427512893.51840931585-142.518409315852

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 465 & 598.841346153846 & -133.841346153846 \tabularnewline
14 & 426 & 427.057687387933 & -1.05768738793273 \tabularnewline
15 & 384 & 381.207241530441 & 2.79275846955909 \tabularnewline
16 & 379 & 370.944860608845 & 8.05513939115468 \tabularnewline
17 & 381 & 364.7688375507 & 16.2311624492999 \tabularnewline
18 & 380 & 361.530832563584 & 18.4691674364157 \tabularnewline
19 & 351 & 437.348300583373 & -86.3483005833725 \tabularnewline
20 & 346 & 319.387404466556 & 26.6125955334442 \tabularnewline
21 & 339 & 337.628844540689 & 1.37115545931061 \tabularnewline
22 & 336 & 184.91120573548 & 151.08879426452 \tabularnewline
23 & 333 & 259.072386900154 & 73.927613099846 \tabularnewline
24 & 324 & 319.384708149635 & 4.61529185036505 \tabularnewline
25 & 324 & 326.583347633008 & -2.58334763300775 \tabularnewline
26 & 321 & 298.686681408931 & 22.3133185910689 \tabularnewline
27 & 304 & 290.637605247258 & 13.362394752742 \tabularnewline
28 & 343 & 306.426999695704 & 36.5730003042963 \tabularnewline
29 & 407 & 345.62421984505 & 61.3757801549499 \tabularnewline
30 & 389 & 406.667757603921 & -17.6677576039215 \tabularnewline
31 & 361 & 463.23135747429 & -102.23135747429 \tabularnewline
32 & 353 & 349.186058707081 & 3.81394129291914 \tabularnewline
33 & 361 & 360.329468422369 & 0.670531577630754 \tabularnewline
34 & 387 & 225.558114524396 & 161.441885475604 \tabularnewline
35 & 692 & 324.403341714789 & 367.596658285211 \tabularnewline
36 & 704 & 703.687577729321 & 0.31242227067878 \tabularnewline
37 & 742 & 741.10094218347 & 0.899057816529762 \tabularnewline
38 & 721 & 751.870850931602 & -30.8708509316018 \tabularnewline
39 & 843 & 723.315216968909 & 119.684783031091 \tabularnewline
40 & 847 & 881.111610370015 & -34.1116103700145 \tabularnewline
41 & 945 & 885.737576110375 & 59.2624238896245 \tabularnewline
42 & 946 & 976.621408986575 & -30.6214089865755 \tabularnewline
43 & 946 & 1051.5489521942 & -105.548952194195 \tabularnewline
44 & 945 & 968.949363229427 & -23.9493632294269 \tabularnewline
45 & 1082 & 983.759920130764 & 98.2400798692356 \tabularnewline
46 & 1075 & 984.092880381831 & 90.907119618169 \tabularnewline
47 & 820 & 1051.0320117677 & -231.032011767702 \tabularnewline
48 & 832 & 835.12017193719 & -3.12017193719021 \tabularnewline
49 & 851 & 863.485776372315 & -12.4857763723148 \tabularnewline
50 & 1090 & 854.015705244088 & 235.984294755912 \tabularnewline
51 & 1203 & 1098.40655986511 & 104.593440134886 \tabularnewline
52 & 1239 & 1247.75274082413 & -8.75274082412693 \tabularnewline
53 & 1535 & 1289.95696615997 & 245.043033840028 \tabularnewline
54 & 1527 & 1582.42764176637 & -55.427641766368 \tabularnewline
55 & 1480 & 1652.89237188301 & -172.892371883008 \tabularnewline
56 & 1452 & 1523.41604587531 & -71.4160458753065 \tabularnewline
57 & 1383 & 1508.50504393868 & -125.505043938681 \tabularnewline
58 & 1381 & 1290.84638763258 & 90.1536123674177 \tabularnewline
59 & 1429 & 1350.12141152124 & 78.8785884787642 \tabularnewline
60 & 1376 & 1459.60850674546 & -83.6085067454574 \tabularnewline
61 & 1602 & 1423.74625883426 & 178.253741165736 \tabularnewline
62 & 1597 & 1631.19937532074 & -34.1993753207355 \tabularnewline
63 & 2003 & 1619.3468350314 & 383.653164968603 \tabularnewline
64 & 1958 & 2064.62186675377 & -106.621866753769 \tabularnewline
65 & 1997 & 2037.56038568516 & -40.5603856851599 \tabularnewline
66 & 1986 & 2048.69525362652 & -62.6952536265158 \tabularnewline
67 & 2129 & 2111.79577703463 & 17.2042229653739 \tabularnewline
68 & 2115 & 2183.43673986894 & -68.4367398689442 \tabularnewline
69 & 2297 & 2184.66944002179 & 112.330559978208 \tabularnewline
70 & 2250 & 2232.16664582023 & 17.8333541797674 \tabularnewline
71 & 2309 & 2245.73359338986 & 63.2664066101388 \tabularnewline
72 & 2648 & 2360.55763393382 & 287.44236606618 \tabularnewline
73 & 2627 & 2738.29421082749 & -111.294210827492 \tabularnewline
74 & 2711 & 2688.83450406208 & 22.1654959379221 \tabularnewline
75 & 2732 & 2772.99224228452 & -40.9922422845234 \tabularnewline
76 & 2825 & 2800.91735585432 & 24.0826441456752 \tabularnewline
77 & 2932 & 2916.28655396761 & 15.7134460323941 \tabularnewline
78 & 2910 & 2999.22489286576 & -89.2248928657636 \tabularnewline
79 & 2969 & 3054.02422888183 & -85.0242288818295 \tabularnewline
80 & 2999 & 3033.86459966967 & -34.8645996696705 \tabularnewline
81 & 2965 & 3082.96495334939 & -117.964953349386 \tabularnewline
82 & 2846 & 2901.47008431983 & -55.4700843198329 \tabularnewline
83 & 2847 & 2836.94367838672 & 10.05632161328 \tabularnewline
84 & 2751 & 2893.51840931585 & -142.518409315852 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232253&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]465[/C][C]598.841346153846[/C][C]-133.841346153846[/C][/ROW]
[ROW][C]14[/C][C]426[/C][C]427.057687387933[/C][C]-1.05768738793273[/C][/ROW]
[ROW][C]15[/C][C]384[/C][C]381.207241530441[/C][C]2.79275846955909[/C][/ROW]
[ROW][C]16[/C][C]379[/C][C]370.944860608845[/C][C]8.05513939115468[/C][/ROW]
[ROW][C]17[/C][C]381[/C][C]364.7688375507[/C][C]16.2311624492999[/C][/ROW]
[ROW][C]18[/C][C]380[/C][C]361.530832563584[/C][C]18.4691674364157[/C][/ROW]
[ROW][C]19[/C][C]351[/C][C]437.348300583373[/C][C]-86.3483005833725[/C][/ROW]
[ROW][C]20[/C][C]346[/C][C]319.387404466556[/C][C]26.6125955334442[/C][/ROW]
[ROW][C]21[/C][C]339[/C][C]337.628844540689[/C][C]1.37115545931061[/C][/ROW]
[ROW][C]22[/C][C]336[/C][C]184.91120573548[/C][C]151.08879426452[/C][/ROW]
[ROW][C]23[/C][C]333[/C][C]259.072386900154[/C][C]73.927613099846[/C][/ROW]
[ROW][C]24[/C][C]324[/C][C]319.384708149635[/C][C]4.61529185036505[/C][/ROW]
[ROW][C]25[/C][C]324[/C][C]326.583347633008[/C][C]-2.58334763300775[/C][/ROW]
[ROW][C]26[/C][C]321[/C][C]298.686681408931[/C][C]22.3133185910689[/C][/ROW]
[ROW][C]27[/C][C]304[/C][C]290.637605247258[/C][C]13.362394752742[/C][/ROW]
[ROW][C]28[/C][C]343[/C][C]306.426999695704[/C][C]36.5730003042963[/C][/ROW]
[ROW][C]29[/C][C]407[/C][C]345.62421984505[/C][C]61.3757801549499[/C][/ROW]
[ROW][C]30[/C][C]389[/C][C]406.667757603921[/C][C]-17.6677576039215[/C][/ROW]
[ROW][C]31[/C][C]361[/C][C]463.23135747429[/C][C]-102.23135747429[/C][/ROW]
[ROW][C]32[/C][C]353[/C][C]349.186058707081[/C][C]3.81394129291914[/C][/ROW]
[ROW][C]33[/C][C]361[/C][C]360.329468422369[/C][C]0.670531577630754[/C][/ROW]
[ROW][C]34[/C][C]387[/C][C]225.558114524396[/C][C]161.441885475604[/C][/ROW]
[ROW][C]35[/C][C]692[/C][C]324.403341714789[/C][C]367.596658285211[/C][/ROW]
[ROW][C]36[/C][C]704[/C][C]703.687577729321[/C][C]0.31242227067878[/C][/ROW]
[ROW][C]37[/C][C]742[/C][C]741.10094218347[/C][C]0.899057816529762[/C][/ROW]
[ROW][C]38[/C][C]721[/C][C]751.870850931602[/C][C]-30.8708509316018[/C][/ROW]
[ROW][C]39[/C][C]843[/C][C]723.315216968909[/C][C]119.684783031091[/C][/ROW]
[ROW][C]40[/C][C]847[/C][C]881.111610370015[/C][C]-34.1116103700145[/C][/ROW]
[ROW][C]41[/C][C]945[/C][C]885.737576110375[/C][C]59.2624238896245[/C][/ROW]
[ROW][C]42[/C][C]946[/C][C]976.621408986575[/C][C]-30.6214089865755[/C][/ROW]
[ROW][C]43[/C][C]946[/C][C]1051.5489521942[/C][C]-105.548952194195[/C][/ROW]
[ROW][C]44[/C][C]945[/C][C]968.949363229427[/C][C]-23.9493632294269[/C][/ROW]
[ROW][C]45[/C][C]1082[/C][C]983.759920130764[/C][C]98.2400798692356[/C][/ROW]
[ROW][C]46[/C][C]1075[/C][C]984.092880381831[/C][C]90.907119618169[/C][/ROW]
[ROW][C]47[/C][C]820[/C][C]1051.0320117677[/C][C]-231.032011767702[/C][/ROW]
[ROW][C]48[/C][C]832[/C][C]835.12017193719[/C][C]-3.12017193719021[/C][/ROW]
[ROW][C]49[/C][C]851[/C][C]863.485776372315[/C][C]-12.4857763723148[/C][/ROW]
[ROW][C]50[/C][C]1090[/C][C]854.015705244088[/C][C]235.984294755912[/C][/ROW]
[ROW][C]51[/C][C]1203[/C][C]1098.40655986511[/C][C]104.593440134886[/C][/ROW]
[ROW][C]52[/C][C]1239[/C][C]1247.75274082413[/C][C]-8.75274082412693[/C][/ROW]
[ROW][C]53[/C][C]1535[/C][C]1289.95696615997[/C][C]245.043033840028[/C][/ROW]
[ROW][C]54[/C][C]1527[/C][C]1582.42764176637[/C][C]-55.427641766368[/C][/ROW]
[ROW][C]55[/C][C]1480[/C][C]1652.89237188301[/C][C]-172.892371883008[/C][/ROW]
[ROW][C]56[/C][C]1452[/C][C]1523.41604587531[/C][C]-71.4160458753065[/C][/ROW]
[ROW][C]57[/C][C]1383[/C][C]1508.50504393868[/C][C]-125.505043938681[/C][/ROW]
[ROW][C]58[/C][C]1381[/C][C]1290.84638763258[/C][C]90.1536123674177[/C][/ROW]
[ROW][C]59[/C][C]1429[/C][C]1350.12141152124[/C][C]78.8785884787642[/C][/ROW]
[ROW][C]60[/C][C]1376[/C][C]1459.60850674546[/C][C]-83.6085067454574[/C][/ROW]
[ROW][C]61[/C][C]1602[/C][C]1423.74625883426[/C][C]178.253741165736[/C][/ROW]
[ROW][C]62[/C][C]1597[/C][C]1631.19937532074[/C][C]-34.1993753207355[/C][/ROW]
[ROW][C]63[/C][C]2003[/C][C]1619.3468350314[/C][C]383.653164968603[/C][/ROW]
[ROW][C]64[/C][C]1958[/C][C]2064.62186675377[/C][C]-106.621866753769[/C][/ROW]
[ROW][C]65[/C][C]1997[/C][C]2037.56038568516[/C][C]-40.5603856851599[/C][/ROW]
[ROW][C]66[/C][C]1986[/C][C]2048.69525362652[/C][C]-62.6952536265158[/C][/ROW]
[ROW][C]67[/C][C]2129[/C][C]2111.79577703463[/C][C]17.2042229653739[/C][/ROW]
[ROW][C]68[/C][C]2115[/C][C]2183.43673986894[/C][C]-68.4367398689442[/C][/ROW]
[ROW][C]69[/C][C]2297[/C][C]2184.66944002179[/C][C]112.330559978208[/C][/ROW]
[ROW][C]70[/C][C]2250[/C][C]2232.16664582023[/C][C]17.8333541797674[/C][/ROW]
[ROW][C]71[/C][C]2309[/C][C]2245.73359338986[/C][C]63.2664066101388[/C][/ROW]
[ROW][C]72[/C][C]2648[/C][C]2360.55763393382[/C][C]287.44236606618[/C][/ROW]
[ROW][C]73[/C][C]2627[/C][C]2738.29421082749[/C][C]-111.294210827492[/C][/ROW]
[ROW][C]74[/C][C]2711[/C][C]2688.83450406208[/C][C]22.1654959379221[/C][/ROW]
[ROW][C]75[/C][C]2732[/C][C]2772.99224228452[/C][C]-40.9922422845234[/C][/ROW]
[ROW][C]76[/C][C]2825[/C][C]2800.91735585432[/C][C]24.0826441456752[/C][/ROW]
[ROW][C]77[/C][C]2932[/C][C]2916.28655396761[/C][C]15.7134460323941[/C][/ROW]
[ROW][C]78[/C][C]2910[/C][C]2999.22489286576[/C][C]-89.2248928657636[/C][/ROW]
[ROW][C]79[/C][C]2969[/C][C]3054.02422888183[/C][C]-85.0242288818295[/C][/ROW]
[ROW][C]80[/C][C]2999[/C][C]3033.86459966967[/C][C]-34.8645996696705[/C][/ROW]
[ROW][C]81[/C][C]2965[/C][C]3082.96495334939[/C][C]-117.964953349386[/C][/ROW]
[ROW][C]82[/C][C]2846[/C][C]2901.47008431983[/C][C]-55.4700843198329[/C][/ROW]
[ROW][C]83[/C][C]2847[/C][C]2836.94367838672[/C][C]10.05632161328[/C][/ROW]
[ROW][C]84[/C][C]2751[/C][C]2893.51840931585[/C][C]-142.518409315852[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232253&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232253&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
13465598.841346153846-133.841346153846
14426427.057687387933-1.05768738793273
15384381.2072415304412.79275846955909
16379370.9448606088458.05513939115468
17381364.768837550716.2311624492999
18380361.53083256358418.4691674364157
19351437.348300583373-86.3483005833725
20346319.38740446655626.6125955334442
21339337.6288445406891.37115545931061
22336184.91120573548151.08879426452
23333259.07238690015473.927613099846
24324319.3847081496354.61529185036505
25324326.583347633008-2.58334763300775
26321298.68668140893122.3133185910689
27304290.63760524725813.362394752742
28343306.42699969570436.5730003042963
29407345.6242198450561.3757801549499
30389406.667757603921-17.6677576039215
31361463.23135747429-102.23135747429
32353349.1860587070813.81394129291914
33361360.3294684223690.670531577630754
34387225.558114524396161.441885475604
35692324.403341714789367.596658285211
36704703.6875777293210.31242227067878
37742741.100942183470.899057816529762
38721751.870850931602-30.8708509316018
39843723.315216968909119.684783031091
40847881.111610370015-34.1116103700145
41945885.73757611037559.2624238896245
42946976.621408986575-30.6214089865755
439461051.5489521942-105.548952194195
44945968.949363229427-23.9493632294269
451082983.75992013076498.2400798692356
461075984.09288038183190.907119618169
478201051.0320117677-231.032011767702
48832835.12017193719-3.12017193719021
49851863.485776372315-12.4857763723148
501090854.015705244088235.984294755912
5112031098.40655986511104.593440134886
5212391247.75274082413-8.75274082412693
5315351289.95696615997245.043033840028
5415271582.42764176637-55.427641766368
5514801652.89237188301-172.892371883008
5614521523.41604587531-71.4160458753065
5713831508.50504393868-125.505043938681
5813811290.8463876325890.1536123674177
5914291350.1214115212478.8785884787642
6013761459.60850674546-83.6085067454574
6116021423.74625883426178.253741165736
6215971631.19937532074-34.1993753207355
6320031619.3468350314383.653164968603
6419582064.62186675377-106.621866753769
6519972037.56038568516-40.5603856851599
6619862048.69525362652-62.6952536265158
6721292111.7957770346317.2042229653739
6821152183.43673986894-68.4367398689442
6922972184.66944002179112.330559978208
7022502232.1666458202317.8333541797674
7123092245.7335933898663.2664066101388
7226482360.55763393382287.44236606618
7326272738.29421082749-111.294210827492
7427112688.8345040620822.1654959379221
7527322772.99224228452-40.9922422845234
7628252800.9173558543224.0826441456752
7729322916.2865539676115.7134460323941
7829102999.22489286576-89.2248928657636
7929693054.02422888183-85.0242288818295
8029993033.86459966967-34.8645996696705
8129653082.96495334939-117.964953349386
8228462901.47008431983-55.4700843198329
8328472836.9436783867210.05632161328
8427512893.51840931585-142.518409315852







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
852806.563495857812586.10600545053027.02098626513
862836.759195273832519.34900811623154.16938243146
872865.33941967842465.996233238953264.68260611785
882904.341442338062429.821285499333378.8615991768
892964.467926264992418.369916544713510.56593598526
902997.319287147482381.667953424223612.97062087075
913111.980282199552427.896531502553796.06403289656
923153.932768761072401.97154022943905.89399729274
933215.836083089862396.176085472674035.49608070705
943138.428418373332250.987345038544025.86949170812
953120.794901316082165.303539086524076.28626354564
963155.416860403642131.468922815034179.36479799225

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 2806.56349585781 & 2586.1060054505 & 3027.02098626513 \tabularnewline
86 & 2836.75919527383 & 2519.3490081162 & 3154.16938243146 \tabularnewline
87 & 2865.3394196784 & 2465.99623323895 & 3264.68260611785 \tabularnewline
88 & 2904.34144233806 & 2429.82128549933 & 3378.8615991768 \tabularnewline
89 & 2964.46792626499 & 2418.36991654471 & 3510.56593598526 \tabularnewline
90 & 2997.31928714748 & 2381.66795342422 & 3612.97062087075 \tabularnewline
91 & 3111.98028219955 & 2427.89653150255 & 3796.06403289656 \tabularnewline
92 & 3153.93276876107 & 2401.9715402294 & 3905.89399729274 \tabularnewline
93 & 3215.83608308986 & 2396.17608547267 & 4035.49608070705 \tabularnewline
94 & 3138.42841837333 & 2250.98734503854 & 4025.86949170812 \tabularnewline
95 & 3120.79490131608 & 2165.30353908652 & 4076.28626354564 \tabularnewline
96 & 3155.41686040364 & 2131.46892281503 & 4179.36479799225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232253&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]2806.56349585781[/C][C]2586.1060054505[/C][C]3027.02098626513[/C][/ROW]
[ROW][C]86[/C][C]2836.75919527383[/C][C]2519.3490081162[/C][C]3154.16938243146[/C][/ROW]
[ROW][C]87[/C][C]2865.3394196784[/C][C]2465.99623323895[/C][C]3264.68260611785[/C][/ROW]
[ROW][C]88[/C][C]2904.34144233806[/C][C]2429.82128549933[/C][C]3378.8615991768[/C][/ROW]
[ROW][C]89[/C][C]2964.46792626499[/C][C]2418.36991654471[/C][C]3510.56593598526[/C][/ROW]
[ROW][C]90[/C][C]2997.31928714748[/C][C]2381.66795342422[/C][C]3612.97062087075[/C][/ROW]
[ROW][C]91[/C][C]3111.98028219955[/C][C]2427.89653150255[/C][C]3796.06403289656[/C][/ROW]
[ROW][C]92[/C][C]3153.93276876107[/C][C]2401.9715402294[/C][C]3905.89399729274[/C][/ROW]
[ROW][C]93[/C][C]3215.83608308986[/C][C]2396.17608547267[/C][C]4035.49608070705[/C][/ROW]
[ROW][C]94[/C][C]3138.42841837333[/C][C]2250.98734503854[/C][C]4025.86949170812[/C][/ROW]
[ROW][C]95[/C][C]3120.79490131608[/C][C]2165.30353908652[/C][C]4076.28626354564[/C][/ROW]
[ROW][C]96[/C][C]3155.41686040364[/C][C]2131.46892281503[/C][C]4179.36479799225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232253&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232253&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
852806.563495857812586.10600545053027.02098626513
862836.759195273832519.34900811623154.16938243146
872865.33941967842465.996233238953264.68260611785
882904.341442338062429.821285499333378.8615991768
892964.467926264992418.369916544713510.56593598526
902997.319287147482381.667953424223612.97062087075
913111.980282199552427.896531502553796.06403289656
923153.932768761072401.97154022943905.89399729274
933215.836083089862396.176085472674035.49608070705
943138.428418373332250.987345038544025.86949170812
953120.794901316082165.303539086524076.28626354564
963155.416860403642131.468922815034179.36479799225



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')