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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 05 Jun 2010 09:58:01 +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/Jun/05/t1275731938empp36giexmc5aa.htm/, Retrieved Fri, 03 May 2024 12:08:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77503, Retrieved Fri, 03 May 2024 12:08:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact172
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-06-05 09:58:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
8027,7
8059,6
8059,5
7988,9
7950,2
8003,8
8037,5
8069
8157,6
8244,3
8329,4
8417
8432,5
8486,4
8531,1
8643,8
8727,9
8847,3
8904,3
9003,2
9025,3
9044,7
9120,7
9184,3
9247,2
9407,1
9488,9
9592,5
9666,2
9809,6
9932,7
10008,9
10103,4
10194,3
10328,8
10507,6
10601,2
10684
10819,9
11014,3
11043
11258,5
11267,9
11334,5
11297,2
11371,3
11340,1
11380,1
11477,9
11538,8
11596,4
11598,8
11645,8
11738,7
11935,5
12042,8
12127,6
12213,8
12303,5
12410,3
12534,1
12587,5
12683,2
12748,7
12915,9
12962,5
12965,9
13060,7
13099,9
13204
13321,1
13391,2
13366,9
13415,3
13324,6
13141,9
12925,4
12901,5
12973
13155




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77503&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77503&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77503&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.517785522407035
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.517785522407035 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77503&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.517785522407035[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77503&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77503&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.517785522407035
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38059.58091.5-32.0000000000009
47988.98074.83086328297-85.9308632829752
57950.27959.73710634711-9.53710634711206
68003.87916.0989307549287.7010692450795
78037.58015.1092747096422.39072529036
880698060.402868101188.59713189881859
98157.68096.3543385326161.2456614673874
108244.38216.6664553506727.6335446493304
118329.48317.6747047028811.7252952971194
1284178408.845892853688.15410714632344
138432.58500.6679714822-68.1679714821985
148486.48480.871582756865.52841724313839
158531.18537.63411716718-6.53411716718256
168643.88578.950845896364.8491541036947
178727.98725.228799031542.67120096845974
188847.38810.7119082204536.5880917795512
198904.38949.0566924364-44.7566924364
209003.28982.88232506220.3176749379945
219025.39092.30252299387-67.0025229938747
229044.79079.7095866229-35.0095866228985
239120.79080.9821295241139.7178704758917
249184.39177.547467837366.75253216263627
259247.29244.643831230762.55616876923887
269407.19308.867378412398.2326215876965
279488.99519.6308076985-30.7308076985028
289592.59585.518840380346.98115961965777
299666.29692.73358376101-26.5335837610128
309809.69752.6948782319956.9051217680135
319932.79925.559526434277.140473565727
3210008.910052.3567602697-43.4567602697389
3310103.410106.0554789514-2.65547895135387
3410194.310199.1805103953-4.88051039528546
3510328.810287.553452770641.2465472293497
3610507.610443.410317775364.1896822247163
3710601.210655.4468059192-54.2468059191506
381068410720.9585951774-36.9585951773915
3910819.910784.62196966635.2780303339641
4011014.310938.78842303275.5115769680015
411104311172.2872243602-129.287224360152
4211258.511134.0441713543124.455828645723
4311267.911413.9855976062-146.085597606203
4411334.511347.7445901335-13.2445901335304
4511297.211407.4867331122-110.286733112172
4611371.311313.081859393158.2181406068757
4711340.111417.3263697408-77.226369740818
4811380.111346.13967354133.9603264590296
4911477.911403.723838917774.1761610823269
5011538.811539.9311812338-1.13118123383356
5111596.411600.2454719677-3.84547196773565
5211598.811655.854342256-57.0543422560204
5311645.811628.712429845417.0875701546029
5411738.711684.560126284654.1398737154359
5511935.511805.4929690794130.007030920637
5612042.812069.6087275012-26.8087275011931
5712127.612163.0275565269-35.4275565269181
5812213.812229.483680663-15.6836806630254
5912303.512307.5628978777-4.06289787765309
6012410.312395.159188177615.1408118224117
6112534.112509.798881336724.3011186632793
6212587.512646.1816487589-58.681648758864
6312683.212669.197140600514.0028593994521
6412748.712772.1476184699-23.4476184698869
6512915.912825.506781091390.3932189087427
6612962.513039.511081166-77.0110811659724
6712965.913046.2358582733-80.3358582733199
6813060.713008.039113929252.6608860707511
6913099.913130.1061583338-30.2061583338127
701320413153.66584686150.3341531389724
7113321.113283.82814263937.2718573609927
7213391.213420.2269707738-29.0269707737498
7313366.913475.2972255478-108.397225547771
7413415.313394.8707114920.4292885099549
7513324.613453.8487013136-129.248701313574
7613141.913296.2255949835-154.325594983497
7712925.413033.6180361642-108.218036164189
7812901.512761.0843037751140.415696224949
791297312809.889518399163.110481600967
801315512965.8457643249189.154235675147

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8059.5 & 8091.5 & -32.0000000000009 \tabularnewline
4 & 7988.9 & 8074.83086328297 & -85.9308632829752 \tabularnewline
5 & 7950.2 & 7959.73710634711 & -9.53710634711206 \tabularnewline
6 & 8003.8 & 7916.09893075492 & 87.7010692450795 \tabularnewline
7 & 8037.5 & 8015.10927470964 & 22.39072529036 \tabularnewline
8 & 8069 & 8060.40286810118 & 8.59713189881859 \tabularnewline
9 & 8157.6 & 8096.35433853261 & 61.2456614673874 \tabularnewline
10 & 8244.3 & 8216.66645535067 & 27.6335446493304 \tabularnewline
11 & 8329.4 & 8317.67470470288 & 11.7252952971194 \tabularnewline
12 & 8417 & 8408.84589285368 & 8.15410714632344 \tabularnewline
13 & 8432.5 & 8500.6679714822 & -68.1679714821985 \tabularnewline
14 & 8486.4 & 8480.87158275686 & 5.52841724313839 \tabularnewline
15 & 8531.1 & 8537.63411716718 & -6.53411716718256 \tabularnewline
16 & 8643.8 & 8578.9508458963 & 64.8491541036947 \tabularnewline
17 & 8727.9 & 8725.22879903154 & 2.67120096845974 \tabularnewline
18 & 8847.3 & 8810.71190822045 & 36.5880917795512 \tabularnewline
19 & 8904.3 & 8949.0566924364 & -44.7566924364 \tabularnewline
20 & 9003.2 & 8982.882325062 & 20.3176749379945 \tabularnewline
21 & 9025.3 & 9092.30252299387 & -67.0025229938747 \tabularnewline
22 & 9044.7 & 9079.7095866229 & -35.0095866228985 \tabularnewline
23 & 9120.7 & 9080.98212952411 & 39.7178704758917 \tabularnewline
24 & 9184.3 & 9177.54746783736 & 6.75253216263627 \tabularnewline
25 & 9247.2 & 9244.64383123076 & 2.55616876923887 \tabularnewline
26 & 9407.1 & 9308.8673784123 & 98.2326215876965 \tabularnewline
27 & 9488.9 & 9519.6308076985 & -30.7308076985028 \tabularnewline
28 & 9592.5 & 9585.51884038034 & 6.98115961965777 \tabularnewline
29 & 9666.2 & 9692.73358376101 & -26.5335837610128 \tabularnewline
30 & 9809.6 & 9752.69487823199 & 56.9051217680135 \tabularnewline
31 & 9932.7 & 9925.55952643427 & 7.140473565727 \tabularnewline
32 & 10008.9 & 10052.3567602697 & -43.4567602697389 \tabularnewline
33 & 10103.4 & 10106.0554789514 & -2.65547895135387 \tabularnewline
34 & 10194.3 & 10199.1805103953 & -4.88051039528546 \tabularnewline
35 & 10328.8 & 10287.5534527706 & 41.2465472293497 \tabularnewline
36 & 10507.6 & 10443.4103177753 & 64.1896822247163 \tabularnewline
37 & 10601.2 & 10655.4468059192 & -54.2468059191506 \tabularnewline
38 & 10684 & 10720.9585951774 & -36.9585951773915 \tabularnewline
39 & 10819.9 & 10784.621969666 & 35.2780303339641 \tabularnewline
40 & 11014.3 & 10938.788423032 & 75.5115769680015 \tabularnewline
41 & 11043 & 11172.2872243602 & -129.287224360152 \tabularnewline
42 & 11258.5 & 11134.0441713543 & 124.455828645723 \tabularnewline
43 & 11267.9 & 11413.9855976062 & -146.085597606203 \tabularnewline
44 & 11334.5 & 11347.7445901335 & -13.2445901335304 \tabularnewline
45 & 11297.2 & 11407.4867331122 & -110.286733112172 \tabularnewline
46 & 11371.3 & 11313.0818593931 & 58.2181406068757 \tabularnewline
47 & 11340.1 & 11417.3263697408 & -77.226369740818 \tabularnewline
48 & 11380.1 & 11346.139673541 & 33.9603264590296 \tabularnewline
49 & 11477.9 & 11403.7238389177 & 74.1761610823269 \tabularnewline
50 & 11538.8 & 11539.9311812338 & -1.13118123383356 \tabularnewline
51 & 11596.4 & 11600.2454719677 & -3.84547196773565 \tabularnewline
52 & 11598.8 & 11655.854342256 & -57.0543422560204 \tabularnewline
53 & 11645.8 & 11628.7124298454 & 17.0875701546029 \tabularnewline
54 & 11738.7 & 11684.5601262846 & 54.1398737154359 \tabularnewline
55 & 11935.5 & 11805.4929690794 & 130.007030920637 \tabularnewline
56 & 12042.8 & 12069.6087275012 & -26.8087275011931 \tabularnewline
57 & 12127.6 & 12163.0275565269 & -35.4275565269181 \tabularnewline
58 & 12213.8 & 12229.483680663 & -15.6836806630254 \tabularnewline
59 & 12303.5 & 12307.5628978777 & -4.06289787765309 \tabularnewline
60 & 12410.3 & 12395.1591881776 & 15.1408118224117 \tabularnewline
61 & 12534.1 & 12509.7988813367 & 24.3011186632793 \tabularnewline
62 & 12587.5 & 12646.1816487589 & -58.681648758864 \tabularnewline
63 & 12683.2 & 12669.1971406005 & 14.0028593994521 \tabularnewline
64 & 12748.7 & 12772.1476184699 & -23.4476184698869 \tabularnewline
65 & 12915.9 & 12825.5067810913 & 90.3932189087427 \tabularnewline
66 & 12962.5 & 13039.511081166 & -77.0110811659724 \tabularnewline
67 & 12965.9 & 13046.2358582733 & -80.3358582733199 \tabularnewline
68 & 13060.7 & 13008.0391139292 & 52.6608860707511 \tabularnewline
69 & 13099.9 & 13130.1061583338 & -30.2061583338127 \tabularnewline
70 & 13204 & 13153.665846861 & 50.3341531389724 \tabularnewline
71 & 13321.1 & 13283.828142639 & 37.2718573609927 \tabularnewline
72 & 13391.2 & 13420.2269707738 & -29.0269707737498 \tabularnewline
73 & 13366.9 & 13475.2972255478 & -108.397225547771 \tabularnewline
74 & 13415.3 & 13394.87071149 & 20.4292885099549 \tabularnewline
75 & 13324.6 & 13453.8487013136 & -129.248701313574 \tabularnewline
76 & 13141.9 & 13296.2255949835 & -154.325594983497 \tabularnewline
77 & 12925.4 & 13033.6180361642 & -108.218036164189 \tabularnewline
78 & 12901.5 & 12761.0843037751 & 140.415696224949 \tabularnewline
79 & 12973 & 12809.889518399 & 163.110481600967 \tabularnewline
80 & 13155 & 12965.8457643249 & 189.154235675147 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77503&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]8059.5[/C][C]8091.5[/C][C]-32.0000000000009[/C][/ROW]
[ROW][C]4[/C][C]7988.9[/C][C]8074.83086328297[/C][C]-85.9308632829752[/C][/ROW]
[ROW][C]5[/C][C]7950.2[/C][C]7959.73710634711[/C][C]-9.53710634711206[/C][/ROW]
[ROW][C]6[/C][C]8003.8[/C][C]7916.09893075492[/C][C]87.7010692450795[/C][/ROW]
[ROW][C]7[/C][C]8037.5[/C][C]8015.10927470964[/C][C]22.39072529036[/C][/ROW]
[ROW][C]8[/C][C]8069[/C][C]8060.40286810118[/C][C]8.59713189881859[/C][/ROW]
[ROW][C]9[/C][C]8157.6[/C][C]8096.35433853261[/C][C]61.2456614673874[/C][/ROW]
[ROW][C]10[/C][C]8244.3[/C][C]8216.66645535067[/C][C]27.6335446493304[/C][/ROW]
[ROW][C]11[/C][C]8329.4[/C][C]8317.67470470288[/C][C]11.7252952971194[/C][/ROW]
[ROW][C]12[/C][C]8417[/C][C]8408.84589285368[/C][C]8.15410714632344[/C][/ROW]
[ROW][C]13[/C][C]8432.5[/C][C]8500.6679714822[/C][C]-68.1679714821985[/C][/ROW]
[ROW][C]14[/C][C]8486.4[/C][C]8480.87158275686[/C][C]5.52841724313839[/C][/ROW]
[ROW][C]15[/C][C]8531.1[/C][C]8537.63411716718[/C][C]-6.53411716718256[/C][/ROW]
[ROW][C]16[/C][C]8643.8[/C][C]8578.9508458963[/C][C]64.8491541036947[/C][/ROW]
[ROW][C]17[/C][C]8727.9[/C][C]8725.22879903154[/C][C]2.67120096845974[/C][/ROW]
[ROW][C]18[/C][C]8847.3[/C][C]8810.71190822045[/C][C]36.5880917795512[/C][/ROW]
[ROW][C]19[/C][C]8904.3[/C][C]8949.0566924364[/C][C]-44.7566924364[/C][/ROW]
[ROW][C]20[/C][C]9003.2[/C][C]8982.882325062[/C][C]20.3176749379945[/C][/ROW]
[ROW][C]21[/C][C]9025.3[/C][C]9092.30252299387[/C][C]-67.0025229938747[/C][/ROW]
[ROW][C]22[/C][C]9044.7[/C][C]9079.7095866229[/C][C]-35.0095866228985[/C][/ROW]
[ROW][C]23[/C][C]9120.7[/C][C]9080.98212952411[/C][C]39.7178704758917[/C][/ROW]
[ROW][C]24[/C][C]9184.3[/C][C]9177.54746783736[/C][C]6.75253216263627[/C][/ROW]
[ROW][C]25[/C][C]9247.2[/C][C]9244.64383123076[/C][C]2.55616876923887[/C][/ROW]
[ROW][C]26[/C][C]9407.1[/C][C]9308.8673784123[/C][C]98.2326215876965[/C][/ROW]
[ROW][C]27[/C][C]9488.9[/C][C]9519.6308076985[/C][C]-30.7308076985028[/C][/ROW]
[ROW][C]28[/C][C]9592.5[/C][C]9585.51884038034[/C][C]6.98115961965777[/C][/ROW]
[ROW][C]29[/C][C]9666.2[/C][C]9692.73358376101[/C][C]-26.5335837610128[/C][/ROW]
[ROW][C]30[/C][C]9809.6[/C][C]9752.69487823199[/C][C]56.9051217680135[/C][/ROW]
[ROW][C]31[/C][C]9932.7[/C][C]9925.55952643427[/C][C]7.140473565727[/C][/ROW]
[ROW][C]32[/C][C]10008.9[/C][C]10052.3567602697[/C][C]-43.4567602697389[/C][/ROW]
[ROW][C]33[/C][C]10103.4[/C][C]10106.0554789514[/C][C]-2.65547895135387[/C][/ROW]
[ROW][C]34[/C][C]10194.3[/C][C]10199.1805103953[/C][C]-4.88051039528546[/C][/ROW]
[ROW][C]35[/C][C]10328.8[/C][C]10287.5534527706[/C][C]41.2465472293497[/C][/ROW]
[ROW][C]36[/C][C]10507.6[/C][C]10443.4103177753[/C][C]64.1896822247163[/C][/ROW]
[ROW][C]37[/C][C]10601.2[/C][C]10655.4468059192[/C][C]-54.2468059191506[/C][/ROW]
[ROW][C]38[/C][C]10684[/C][C]10720.9585951774[/C][C]-36.9585951773915[/C][/ROW]
[ROW][C]39[/C][C]10819.9[/C][C]10784.621969666[/C][C]35.2780303339641[/C][/ROW]
[ROW][C]40[/C][C]11014.3[/C][C]10938.788423032[/C][C]75.5115769680015[/C][/ROW]
[ROW][C]41[/C][C]11043[/C][C]11172.2872243602[/C][C]-129.287224360152[/C][/ROW]
[ROW][C]42[/C][C]11258.5[/C][C]11134.0441713543[/C][C]124.455828645723[/C][/ROW]
[ROW][C]43[/C][C]11267.9[/C][C]11413.9855976062[/C][C]-146.085597606203[/C][/ROW]
[ROW][C]44[/C][C]11334.5[/C][C]11347.7445901335[/C][C]-13.2445901335304[/C][/ROW]
[ROW][C]45[/C][C]11297.2[/C][C]11407.4867331122[/C][C]-110.286733112172[/C][/ROW]
[ROW][C]46[/C][C]11371.3[/C][C]11313.0818593931[/C][C]58.2181406068757[/C][/ROW]
[ROW][C]47[/C][C]11340.1[/C][C]11417.3263697408[/C][C]-77.226369740818[/C][/ROW]
[ROW][C]48[/C][C]11380.1[/C][C]11346.139673541[/C][C]33.9603264590296[/C][/ROW]
[ROW][C]49[/C][C]11477.9[/C][C]11403.7238389177[/C][C]74.1761610823269[/C][/ROW]
[ROW][C]50[/C][C]11538.8[/C][C]11539.9311812338[/C][C]-1.13118123383356[/C][/ROW]
[ROW][C]51[/C][C]11596.4[/C][C]11600.2454719677[/C][C]-3.84547196773565[/C][/ROW]
[ROW][C]52[/C][C]11598.8[/C][C]11655.854342256[/C][C]-57.0543422560204[/C][/ROW]
[ROW][C]53[/C][C]11645.8[/C][C]11628.7124298454[/C][C]17.0875701546029[/C][/ROW]
[ROW][C]54[/C][C]11738.7[/C][C]11684.5601262846[/C][C]54.1398737154359[/C][/ROW]
[ROW][C]55[/C][C]11935.5[/C][C]11805.4929690794[/C][C]130.007030920637[/C][/ROW]
[ROW][C]56[/C][C]12042.8[/C][C]12069.6087275012[/C][C]-26.8087275011931[/C][/ROW]
[ROW][C]57[/C][C]12127.6[/C][C]12163.0275565269[/C][C]-35.4275565269181[/C][/ROW]
[ROW][C]58[/C][C]12213.8[/C][C]12229.483680663[/C][C]-15.6836806630254[/C][/ROW]
[ROW][C]59[/C][C]12303.5[/C][C]12307.5628978777[/C][C]-4.06289787765309[/C][/ROW]
[ROW][C]60[/C][C]12410.3[/C][C]12395.1591881776[/C][C]15.1408118224117[/C][/ROW]
[ROW][C]61[/C][C]12534.1[/C][C]12509.7988813367[/C][C]24.3011186632793[/C][/ROW]
[ROW][C]62[/C][C]12587.5[/C][C]12646.1816487589[/C][C]-58.681648758864[/C][/ROW]
[ROW][C]63[/C][C]12683.2[/C][C]12669.1971406005[/C][C]14.0028593994521[/C][/ROW]
[ROW][C]64[/C][C]12748.7[/C][C]12772.1476184699[/C][C]-23.4476184698869[/C][/ROW]
[ROW][C]65[/C][C]12915.9[/C][C]12825.5067810913[/C][C]90.3932189087427[/C][/ROW]
[ROW][C]66[/C][C]12962.5[/C][C]13039.511081166[/C][C]-77.0110811659724[/C][/ROW]
[ROW][C]67[/C][C]12965.9[/C][C]13046.2358582733[/C][C]-80.3358582733199[/C][/ROW]
[ROW][C]68[/C][C]13060.7[/C][C]13008.0391139292[/C][C]52.6608860707511[/C][/ROW]
[ROW][C]69[/C][C]13099.9[/C][C]13130.1061583338[/C][C]-30.2061583338127[/C][/ROW]
[ROW][C]70[/C][C]13204[/C][C]13153.665846861[/C][C]50.3341531389724[/C][/ROW]
[ROW][C]71[/C][C]13321.1[/C][C]13283.828142639[/C][C]37.2718573609927[/C][/ROW]
[ROW][C]72[/C][C]13391.2[/C][C]13420.2269707738[/C][C]-29.0269707737498[/C][/ROW]
[ROW][C]73[/C][C]13366.9[/C][C]13475.2972255478[/C][C]-108.397225547771[/C][/ROW]
[ROW][C]74[/C][C]13415.3[/C][C]13394.87071149[/C][C]20.4292885099549[/C][/ROW]
[ROW][C]75[/C][C]13324.6[/C][C]13453.8487013136[/C][C]-129.248701313574[/C][/ROW]
[ROW][C]76[/C][C]13141.9[/C][C]13296.2255949835[/C][C]-154.325594983497[/C][/ROW]
[ROW][C]77[/C][C]12925.4[/C][C]13033.6180361642[/C][C]-108.218036164189[/C][/ROW]
[ROW][C]78[/C][C]12901.5[/C][C]12761.0843037751[/C][C]140.415696224949[/C][/ROW]
[ROW][C]79[/C][C]12973[/C][C]12809.889518399[/C][C]163.110481600967[/C][/ROW]
[ROW][C]80[/C][C]13155[/C][C]12965.8457643249[/C][C]189.154235675147[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77503&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77503&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
38059.58091.5-32.0000000000009
47988.98074.83086328297-85.9308632829752
57950.27959.73710634711-9.53710634711206
68003.87916.0989307549287.7010692450795
78037.58015.1092747096422.39072529036
880698060.402868101188.59713189881859
98157.68096.3543385326161.2456614673874
108244.38216.6664553506727.6335446493304
118329.48317.6747047028811.7252952971194
1284178408.845892853688.15410714632344
138432.58500.6679714822-68.1679714821985
148486.48480.871582756865.52841724313839
158531.18537.63411716718-6.53411716718256
168643.88578.950845896364.8491541036947
178727.98725.228799031542.67120096845974
188847.38810.7119082204536.5880917795512
198904.38949.0566924364-44.7566924364
209003.28982.88232506220.3176749379945
219025.39092.30252299387-67.0025229938747
229044.79079.7095866229-35.0095866228985
239120.79080.9821295241139.7178704758917
249184.39177.547467837366.75253216263627
259247.29244.643831230762.55616876923887
269407.19308.867378412398.2326215876965
279488.99519.6308076985-30.7308076985028
289592.59585.518840380346.98115961965777
299666.29692.73358376101-26.5335837610128
309809.69752.6948782319956.9051217680135
319932.79925.559526434277.140473565727
3210008.910052.3567602697-43.4567602697389
3310103.410106.0554789514-2.65547895135387
3410194.310199.1805103953-4.88051039528546
3510328.810287.553452770641.2465472293497
3610507.610443.410317775364.1896822247163
3710601.210655.4468059192-54.2468059191506
381068410720.9585951774-36.9585951773915
3910819.910784.62196966635.2780303339641
4011014.310938.78842303275.5115769680015
411104311172.2872243602-129.287224360152
4211258.511134.0441713543124.455828645723
4311267.911413.9855976062-146.085597606203
4411334.511347.7445901335-13.2445901335304
4511297.211407.4867331122-110.286733112172
4611371.311313.081859393158.2181406068757
4711340.111417.3263697408-77.226369740818
4811380.111346.13967354133.9603264590296
4911477.911403.723838917774.1761610823269
5011538.811539.9311812338-1.13118123383356
5111596.411600.2454719677-3.84547196773565
5211598.811655.854342256-57.0543422560204
5311645.811628.712429845417.0875701546029
5411738.711684.560126284654.1398737154359
5511935.511805.4929690794130.007030920637
5612042.812069.6087275012-26.8087275011931
5712127.612163.0275565269-35.4275565269181
5812213.812229.483680663-15.6836806630254
5912303.512307.5628978777-4.06289787765309
6012410.312395.159188177615.1408118224117
6112534.112509.798881336724.3011186632793
6212587.512646.1816487589-58.681648758864
6312683.212669.197140600514.0028593994521
6412748.712772.1476184699-23.4476184698869
6512915.912825.506781091390.3932189087427
6612962.513039.511081166-77.0110811659724
6712965.913046.2358582733-80.3358582733199
6813060.713008.039113929252.6608860707511
6913099.913130.1061583338-30.2061583338127
701320413153.66584686150.3341531389724
7113321.113283.82814263937.2718573609927
7213391.213420.2269707738-29.0269707737498
7313366.913475.2972255478-108.397225547771
7413415.313394.8707114920.4292885099549
7513324.613453.8487013136-129.248701313574
7613141.913296.2255949835-154.325594983497
7712925.413033.6180361642-108.218036164189
7812901.512761.0843037751140.415696224949
791297312809.889518399163.110481600967
801315512965.8457643249189.154235675147







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8113245.787089059413111.210143131613380.3640349872
8213336.574178118813091.967005251113581.1813509865
8313427.361267178213060.106172489513794.6163618669
8413518.148356237613015.204003758814021.0927087165

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 13245.7870890594 & 13111.2101431316 & 13380.3640349872 \tabularnewline
82 & 13336.5741781188 & 13091.9670052511 & 13581.1813509865 \tabularnewline
83 & 13427.3612671782 & 13060.1061724895 & 13794.6163618669 \tabularnewline
84 & 13518.1483562376 & 13015.2040037588 & 14021.0927087165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77503&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]81[/C][C]13245.7870890594[/C][C]13111.2101431316[/C][C]13380.3640349872[/C][/ROW]
[ROW][C]82[/C][C]13336.5741781188[/C][C]13091.9670052511[/C][C]13581.1813509865[/C][/ROW]
[ROW][C]83[/C][C]13427.3612671782[/C][C]13060.1061724895[/C][C]13794.6163618669[/C][/ROW]
[ROW][C]84[/C][C]13518.1483562376[/C][C]13015.2040037588[/C][C]14021.0927087165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77503&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77503&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
8113245.787089059413111.210143131613380.3640349872
8213336.574178118813091.967005251113581.1813509865
8313427.361267178213060.106172489513794.6163618669
8413518.148356237613015.204003758814021.0927087165



Parameters (Session):
par1 = 4 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 4 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')