Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 12:08:18 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t124396617481cr5qtq520dxk3.htm/, Retrieved Thu, 09 May 2024 22:35:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41350, Retrieved Thu, 09 May 2024 22:35:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [voorspellen- uitv...] [2009-06-02 18:08:18] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
11025,1
10853,8
12252,6
11839,4
11669,1
11601,4
11178,4
9516,4
12102,8
12989
11610,2
10205,5
11356,2
11307,1
12648,6
11947,2
11714,1
12192,5
11268,8
9097,4
12639,8
13040,1
11687,3
11191,7
11391,9
11793,1
13933,2
12778,1
11810,3
13698,4
11956,6
10723,8
13938,9
13979,8
13807,4
12973,9
12509,8
12934,1
14908,3
13772,1
13012,6
14049,9
11816,5
11593,2
14466,2
13615,9
14733,9
13880,7
13527,5
13584
16170,2
13260,6
14741,9
15486,5
13154,5
12621,2
15031,6
15452,4
15428
13105,9
14716,8
14180
16202,2
14392,4
15140,6
15960,1
14351,3
13230,2
15202,1
17056
16077,7
13348,2
16707,5
16792,6
16831,3
17804,5
16370,2
17602,5
17065,6
14427,9
17818,5
18027,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41350&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41350&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41350&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.151057287538905
beta0.0628426978359442
gamma0.193352917851991

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.151057287538905 \tabularnewline
beta & 0.0628426978359442 \tabularnewline
gamma & 0.193352917851991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41350&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]0.151057287538905[/C][/ROW]
[ROW][C]beta[/C][C]0.0628426978359442[/C][/ROW]
[ROW][C]gamma[/C][C]0.193352917851991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41350&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41350&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
alpha0.151057287538905
beta0.0628426978359442
gamma0.193352917851991







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311356.211204.6067190448151.593280955216
1411307.111209.759269154097.3407308459537
1512648.612571.474990435477.1250095645864
1611947.211880.373350395666.8266496044234
1711714.111673.480431684140.6195683159076
1812192.512131.840871912360.659128087711
1911268.811362.1338650906-93.3338650905916
209097.49650.01594479876-552.615944798756
2112639.812143.7016223049496.098377695094
2213040.113110.1082113040-70.0082113040353
2311687.311720.4306396411-33.1306396411201
2411191.710289.769607038901.93039296201
2511391.911625.4345969344-233.534596934413
2611793.111568.9564158721224.143584127922
2713933.212998.0924885712935.10751142883
2812778.112419.7299668009358.370033199102
2911810.312259.4361990709-449.136199070866
3013698.412680.21495053001018.18504947003
3111956.612005.3393842018-48.7393842018282
3210723.810137.4049372083586.395062791677
3313938.913229.2659696772709.634030322824
3413979.814243.0957945779-263.295794577907
3513807.412748.14028329991059.25971670007
3612973.911543.69284174241430.20715825758
3712509.812934.1037373036-424.303737303582
3812934.112976.3311981753-42.2311981753064
3914908.314702.0251392523206.274860747741
4013772.113869.0434891948-96.9434891948458
4113012.613503.3941589387-490.794158938741
4214049.914270.2858591979-220.385859197915
4311816.513158.4419012346-1341.9419012346
4411593.211064.7514683299528.448531670116
4514466.214416.559264531549.6407354685143
4613615.915227.0817932000-1611.18179320002
4714733.913662.71380818981071.18619181025
4813880.712434.23837477631446.46162522367
4913527.513560.5390884228-33.0390884227636
501358413728.5900635703-144.590063570307
5116170.215573.5724782049596.627521795052
5213260.614690.1934763267-1429.59347632665
5314741.914024.0564018549717.843598145078
5415486.515065.3355466502421.164453349818
5513154.513781.2421626330-626.742162633022
5612621.211990.6411027533630.558897246705
5715031.615531.8147219158-500.214721915792
5815452.416024.4896110769-572.089611076859
591542814996.1070578172431.892942182811
6013105.913634.0929504598-528.192950459772
6114716.814241.1005561881475.699443811862
621418014468.4051771226-288.405177122626
6316202.216510.1751009291-307.975100929085
6414392.415078.8821856548-686.48218565476
6515140.614861.7295627150278.870437284973
6615960.115813.5244853532146.575514646833
6714351.314236.0319698116115.268030188397
6813230.212681.9366631210548.263336879014
6915202.116167.6232390865-965.523239086522
701705616585.9101180026470.089881997425
7116077.715834.0886753871243.611324612908
7213348.214201.6257030140-853.425703013965
7316707.514952.44360046461755.05639953544
7416792.615250.51966268871542.08033731127
7516831.317745.6814828752-914.38148287516
7617804.516067.99416186021736.50583813976
7716370.216414.9668672790-44.7668672789805
7817602.517416.608096819185.891903180993
7917065.615709.88887459401355.71112540598
8014427.914277.5964180937150.303581906297
8117818.517847.9542355833-29.4542355832891
8218027.618794.2166467020-766.61664670198

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 11356.2 & 11204.6067190448 & 151.593280955216 \tabularnewline
14 & 11307.1 & 11209.7592691540 & 97.3407308459537 \tabularnewline
15 & 12648.6 & 12571.4749904354 & 77.1250095645864 \tabularnewline
16 & 11947.2 & 11880.3733503956 & 66.8266496044234 \tabularnewline
17 & 11714.1 & 11673.4804316841 & 40.6195683159076 \tabularnewline
18 & 12192.5 & 12131.8408719123 & 60.659128087711 \tabularnewline
19 & 11268.8 & 11362.1338650906 & -93.3338650905916 \tabularnewline
20 & 9097.4 & 9650.01594479876 & -552.615944798756 \tabularnewline
21 & 12639.8 & 12143.7016223049 & 496.098377695094 \tabularnewline
22 & 13040.1 & 13110.1082113040 & -70.0082113040353 \tabularnewline
23 & 11687.3 & 11720.4306396411 & -33.1306396411201 \tabularnewline
24 & 11191.7 & 10289.769607038 & 901.93039296201 \tabularnewline
25 & 11391.9 & 11625.4345969344 & -233.534596934413 \tabularnewline
26 & 11793.1 & 11568.9564158721 & 224.143584127922 \tabularnewline
27 & 13933.2 & 12998.0924885712 & 935.10751142883 \tabularnewline
28 & 12778.1 & 12419.7299668009 & 358.370033199102 \tabularnewline
29 & 11810.3 & 12259.4361990709 & -449.136199070866 \tabularnewline
30 & 13698.4 & 12680.2149505300 & 1018.18504947003 \tabularnewline
31 & 11956.6 & 12005.3393842018 & -48.7393842018282 \tabularnewline
32 & 10723.8 & 10137.4049372083 & 586.395062791677 \tabularnewline
33 & 13938.9 & 13229.2659696772 & 709.634030322824 \tabularnewline
34 & 13979.8 & 14243.0957945779 & -263.295794577907 \tabularnewline
35 & 13807.4 & 12748.1402832999 & 1059.25971670007 \tabularnewline
36 & 12973.9 & 11543.6928417424 & 1430.20715825758 \tabularnewline
37 & 12509.8 & 12934.1037373036 & -424.303737303582 \tabularnewline
38 & 12934.1 & 12976.3311981753 & -42.2311981753064 \tabularnewline
39 & 14908.3 & 14702.0251392523 & 206.274860747741 \tabularnewline
40 & 13772.1 & 13869.0434891948 & -96.9434891948458 \tabularnewline
41 & 13012.6 & 13503.3941589387 & -490.794158938741 \tabularnewline
42 & 14049.9 & 14270.2858591979 & -220.385859197915 \tabularnewline
43 & 11816.5 & 13158.4419012346 & -1341.9419012346 \tabularnewline
44 & 11593.2 & 11064.7514683299 & 528.448531670116 \tabularnewline
45 & 14466.2 & 14416.5592645315 & 49.6407354685143 \tabularnewline
46 & 13615.9 & 15227.0817932000 & -1611.18179320002 \tabularnewline
47 & 14733.9 & 13662.7138081898 & 1071.18619181025 \tabularnewline
48 & 13880.7 & 12434.2383747763 & 1446.46162522367 \tabularnewline
49 & 13527.5 & 13560.5390884228 & -33.0390884227636 \tabularnewline
50 & 13584 & 13728.5900635703 & -144.590063570307 \tabularnewline
51 & 16170.2 & 15573.5724782049 & 596.627521795052 \tabularnewline
52 & 13260.6 & 14690.1934763267 & -1429.59347632665 \tabularnewline
53 & 14741.9 & 14024.0564018549 & 717.843598145078 \tabularnewline
54 & 15486.5 & 15065.3355466502 & 421.164453349818 \tabularnewline
55 & 13154.5 & 13781.2421626330 & -626.742162633022 \tabularnewline
56 & 12621.2 & 11990.6411027533 & 630.558897246705 \tabularnewline
57 & 15031.6 & 15531.8147219158 & -500.214721915792 \tabularnewline
58 & 15452.4 & 16024.4896110769 & -572.089611076859 \tabularnewline
59 & 15428 & 14996.1070578172 & 431.892942182811 \tabularnewline
60 & 13105.9 & 13634.0929504598 & -528.192950459772 \tabularnewline
61 & 14716.8 & 14241.1005561881 & 475.699443811862 \tabularnewline
62 & 14180 & 14468.4051771226 & -288.405177122626 \tabularnewline
63 & 16202.2 & 16510.1751009291 & -307.975100929085 \tabularnewline
64 & 14392.4 & 15078.8821856548 & -686.48218565476 \tabularnewline
65 & 15140.6 & 14861.7295627150 & 278.870437284973 \tabularnewline
66 & 15960.1 & 15813.5244853532 & 146.575514646833 \tabularnewline
67 & 14351.3 & 14236.0319698116 & 115.268030188397 \tabularnewline
68 & 13230.2 & 12681.9366631210 & 548.263336879014 \tabularnewline
69 & 15202.1 & 16167.6232390865 & -965.523239086522 \tabularnewline
70 & 17056 & 16585.9101180026 & 470.089881997425 \tabularnewline
71 & 16077.7 & 15834.0886753871 & 243.611324612908 \tabularnewline
72 & 13348.2 & 14201.6257030140 & -853.425703013965 \tabularnewline
73 & 16707.5 & 14952.4436004646 & 1755.05639953544 \tabularnewline
74 & 16792.6 & 15250.5196626887 & 1542.08033731127 \tabularnewline
75 & 16831.3 & 17745.6814828752 & -914.38148287516 \tabularnewline
76 & 17804.5 & 16067.9941618602 & 1736.50583813976 \tabularnewline
77 & 16370.2 & 16414.9668672790 & -44.7668672789805 \tabularnewline
78 & 17602.5 & 17416.608096819 & 185.891903180993 \tabularnewline
79 & 17065.6 & 15709.8888745940 & 1355.71112540598 \tabularnewline
80 & 14427.9 & 14277.5964180937 & 150.303581906297 \tabularnewline
81 & 17818.5 & 17847.9542355833 & -29.4542355832891 \tabularnewline
82 & 18027.6 & 18794.2166467020 & -766.61664670198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41350&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]11356.2[/C][C]11204.6067190448[/C][C]151.593280955216[/C][/ROW]
[ROW][C]14[/C][C]11307.1[/C][C]11209.7592691540[/C][C]97.3407308459537[/C][/ROW]
[ROW][C]15[/C][C]12648.6[/C][C]12571.4749904354[/C][C]77.1250095645864[/C][/ROW]
[ROW][C]16[/C][C]11947.2[/C][C]11880.3733503956[/C][C]66.8266496044234[/C][/ROW]
[ROW][C]17[/C][C]11714.1[/C][C]11673.4804316841[/C][C]40.6195683159076[/C][/ROW]
[ROW][C]18[/C][C]12192.5[/C][C]12131.8408719123[/C][C]60.659128087711[/C][/ROW]
[ROW][C]19[/C][C]11268.8[/C][C]11362.1338650906[/C][C]-93.3338650905916[/C][/ROW]
[ROW][C]20[/C][C]9097.4[/C][C]9650.01594479876[/C][C]-552.615944798756[/C][/ROW]
[ROW][C]21[/C][C]12639.8[/C][C]12143.7016223049[/C][C]496.098377695094[/C][/ROW]
[ROW][C]22[/C][C]13040.1[/C][C]13110.1082113040[/C][C]-70.0082113040353[/C][/ROW]
[ROW][C]23[/C][C]11687.3[/C][C]11720.4306396411[/C][C]-33.1306396411201[/C][/ROW]
[ROW][C]24[/C][C]11191.7[/C][C]10289.769607038[/C][C]901.93039296201[/C][/ROW]
[ROW][C]25[/C][C]11391.9[/C][C]11625.4345969344[/C][C]-233.534596934413[/C][/ROW]
[ROW][C]26[/C][C]11793.1[/C][C]11568.9564158721[/C][C]224.143584127922[/C][/ROW]
[ROW][C]27[/C][C]13933.2[/C][C]12998.0924885712[/C][C]935.10751142883[/C][/ROW]
[ROW][C]28[/C][C]12778.1[/C][C]12419.7299668009[/C][C]358.370033199102[/C][/ROW]
[ROW][C]29[/C][C]11810.3[/C][C]12259.4361990709[/C][C]-449.136199070866[/C][/ROW]
[ROW][C]30[/C][C]13698.4[/C][C]12680.2149505300[/C][C]1018.18504947003[/C][/ROW]
[ROW][C]31[/C][C]11956.6[/C][C]12005.3393842018[/C][C]-48.7393842018282[/C][/ROW]
[ROW][C]32[/C][C]10723.8[/C][C]10137.4049372083[/C][C]586.395062791677[/C][/ROW]
[ROW][C]33[/C][C]13938.9[/C][C]13229.2659696772[/C][C]709.634030322824[/C][/ROW]
[ROW][C]34[/C][C]13979.8[/C][C]14243.0957945779[/C][C]-263.295794577907[/C][/ROW]
[ROW][C]35[/C][C]13807.4[/C][C]12748.1402832999[/C][C]1059.25971670007[/C][/ROW]
[ROW][C]36[/C][C]12973.9[/C][C]11543.6928417424[/C][C]1430.20715825758[/C][/ROW]
[ROW][C]37[/C][C]12509.8[/C][C]12934.1037373036[/C][C]-424.303737303582[/C][/ROW]
[ROW][C]38[/C][C]12934.1[/C][C]12976.3311981753[/C][C]-42.2311981753064[/C][/ROW]
[ROW][C]39[/C][C]14908.3[/C][C]14702.0251392523[/C][C]206.274860747741[/C][/ROW]
[ROW][C]40[/C][C]13772.1[/C][C]13869.0434891948[/C][C]-96.9434891948458[/C][/ROW]
[ROW][C]41[/C][C]13012.6[/C][C]13503.3941589387[/C][C]-490.794158938741[/C][/ROW]
[ROW][C]42[/C][C]14049.9[/C][C]14270.2858591979[/C][C]-220.385859197915[/C][/ROW]
[ROW][C]43[/C][C]11816.5[/C][C]13158.4419012346[/C][C]-1341.9419012346[/C][/ROW]
[ROW][C]44[/C][C]11593.2[/C][C]11064.7514683299[/C][C]528.448531670116[/C][/ROW]
[ROW][C]45[/C][C]14466.2[/C][C]14416.5592645315[/C][C]49.6407354685143[/C][/ROW]
[ROW][C]46[/C][C]13615.9[/C][C]15227.0817932000[/C][C]-1611.18179320002[/C][/ROW]
[ROW][C]47[/C][C]14733.9[/C][C]13662.7138081898[/C][C]1071.18619181025[/C][/ROW]
[ROW][C]48[/C][C]13880.7[/C][C]12434.2383747763[/C][C]1446.46162522367[/C][/ROW]
[ROW][C]49[/C][C]13527.5[/C][C]13560.5390884228[/C][C]-33.0390884227636[/C][/ROW]
[ROW][C]50[/C][C]13584[/C][C]13728.5900635703[/C][C]-144.590063570307[/C][/ROW]
[ROW][C]51[/C][C]16170.2[/C][C]15573.5724782049[/C][C]596.627521795052[/C][/ROW]
[ROW][C]52[/C][C]13260.6[/C][C]14690.1934763267[/C][C]-1429.59347632665[/C][/ROW]
[ROW][C]53[/C][C]14741.9[/C][C]14024.0564018549[/C][C]717.843598145078[/C][/ROW]
[ROW][C]54[/C][C]15486.5[/C][C]15065.3355466502[/C][C]421.164453349818[/C][/ROW]
[ROW][C]55[/C][C]13154.5[/C][C]13781.2421626330[/C][C]-626.742162633022[/C][/ROW]
[ROW][C]56[/C][C]12621.2[/C][C]11990.6411027533[/C][C]630.558897246705[/C][/ROW]
[ROW][C]57[/C][C]15031.6[/C][C]15531.8147219158[/C][C]-500.214721915792[/C][/ROW]
[ROW][C]58[/C][C]15452.4[/C][C]16024.4896110769[/C][C]-572.089611076859[/C][/ROW]
[ROW][C]59[/C][C]15428[/C][C]14996.1070578172[/C][C]431.892942182811[/C][/ROW]
[ROW][C]60[/C][C]13105.9[/C][C]13634.0929504598[/C][C]-528.192950459772[/C][/ROW]
[ROW][C]61[/C][C]14716.8[/C][C]14241.1005561881[/C][C]475.699443811862[/C][/ROW]
[ROW][C]62[/C][C]14180[/C][C]14468.4051771226[/C][C]-288.405177122626[/C][/ROW]
[ROW][C]63[/C][C]16202.2[/C][C]16510.1751009291[/C][C]-307.975100929085[/C][/ROW]
[ROW][C]64[/C][C]14392.4[/C][C]15078.8821856548[/C][C]-686.48218565476[/C][/ROW]
[ROW][C]65[/C][C]15140.6[/C][C]14861.7295627150[/C][C]278.870437284973[/C][/ROW]
[ROW][C]66[/C][C]15960.1[/C][C]15813.5244853532[/C][C]146.575514646833[/C][/ROW]
[ROW][C]67[/C][C]14351.3[/C][C]14236.0319698116[/C][C]115.268030188397[/C][/ROW]
[ROW][C]68[/C][C]13230.2[/C][C]12681.9366631210[/C][C]548.263336879014[/C][/ROW]
[ROW][C]69[/C][C]15202.1[/C][C]16167.6232390865[/C][C]-965.523239086522[/C][/ROW]
[ROW][C]70[/C][C]17056[/C][C]16585.9101180026[/C][C]470.089881997425[/C][/ROW]
[ROW][C]71[/C][C]16077.7[/C][C]15834.0886753871[/C][C]243.611324612908[/C][/ROW]
[ROW][C]72[/C][C]13348.2[/C][C]14201.6257030140[/C][C]-853.425703013965[/C][/ROW]
[ROW][C]73[/C][C]16707.5[/C][C]14952.4436004646[/C][C]1755.05639953544[/C][/ROW]
[ROW][C]74[/C][C]16792.6[/C][C]15250.5196626887[/C][C]1542.08033731127[/C][/ROW]
[ROW][C]75[/C][C]16831.3[/C][C]17745.6814828752[/C][C]-914.38148287516[/C][/ROW]
[ROW][C]76[/C][C]17804.5[/C][C]16067.9941618602[/C][C]1736.50583813976[/C][/ROW]
[ROW][C]77[/C][C]16370.2[/C][C]16414.9668672790[/C][C]-44.7668672789805[/C][/ROW]
[ROW][C]78[/C][C]17602.5[/C][C]17416.608096819[/C][C]185.891903180993[/C][/ROW]
[ROW][C]79[/C][C]17065.6[/C][C]15709.8888745940[/C][C]1355.71112540598[/C][/ROW]
[ROW][C]80[/C][C]14427.9[/C][C]14277.5964180937[/C][C]150.303581906297[/C][/ROW]
[ROW][C]81[/C][C]17818.5[/C][C]17847.9542355833[/C][C]-29.4542355832891[/C][/ROW]
[ROW][C]82[/C][C]18027.6[/C][C]18794.2166467020[/C][C]-766.61664670198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41350&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41350&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
1311356.211204.6067190448151.593280955216
1411307.111209.759269154097.3407308459537
1512648.612571.474990435477.1250095645864
1611947.211880.373350395666.8266496044234
1711714.111673.480431684140.6195683159076
1812192.512131.840871912360.659128087711
1911268.811362.1338650906-93.3338650905916
209097.49650.01594479876-552.615944798756
2112639.812143.7016223049496.098377695094
2213040.113110.1082113040-70.0082113040353
2311687.311720.4306396411-33.1306396411201
2411191.710289.769607038901.93039296201
2511391.911625.4345969344-233.534596934413
2611793.111568.9564158721224.143584127922
2713933.212998.0924885712935.10751142883
2812778.112419.7299668009358.370033199102
2911810.312259.4361990709-449.136199070866
3013698.412680.21495053001018.18504947003
3111956.612005.3393842018-48.7393842018282
3210723.810137.4049372083586.395062791677
3313938.913229.2659696772709.634030322824
3413979.814243.0957945779-263.295794577907
3513807.412748.14028329991059.25971670007
3612973.911543.69284174241430.20715825758
3712509.812934.1037373036-424.303737303582
3812934.112976.3311981753-42.2311981753064
3914908.314702.0251392523206.274860747741
4013772.113869.0434891948-96.9434891948458
4113012.613503.3941589387-490.794158938741
4214049.914270.2858591979-220.385859197915
4311816.513158.4419012346-1341.9419012346
4411593.211064.7514683299528.448531670116
4514466.214416.559264531549.6407354685143
4613615.915227.0817932000-1611.18179320002
4714733.913662.71380818981071.18619181025
4813880.712434.23837477631446.46162522367
4913527.513560.5390884228-33.0390884227636
501358413728.5900635703-144.590063570307
5116170.215573.5724782049596.627521795052
5213260.614690.1934763267-1429.59347632665
5314741.914024.0564018549717.843598145078
5415486.515065.3355466502421.164453349818
5513154.513781.2421626330-626.742162633022
5612621.211990.6411027533630.558897246705
5715031.615531.8147219158-500.214721915792
5815452.416024.4896110769-572.089611076859
591542814996.1070578172431.892942182811
6013105.913634.0929504598-528.192950459772
6114716.814241.1005561881475.699443811862
621418014468.4051771226-288.405177122626
6316202.216510.1751009291-307.975100929085
6414392.415078.8821856548-686.48218565476
6515140.614861.7295627150278.870437284973
6615960.115813.5244853532146.575514646833
6714351.314236.0319698116115.268030188397
6813230.212681.9366631210548.263336879014
6915202.116167.6232390865-965.523239086522
701705616585.9101180026470.089881997425
7116077.715834.0886753871243.611324612908
7213348.214201.6257030140-853.425703013965
7316707.514952.44360046461755.05639953544
7416792.615250.51966268871542.08033731127
7516831.317745.6814828752-914.38148287516
7617804.516067.99416186021736.50583813976
7716370.216414.9668672790-44.7668672789805
7817602.517416.608096819185.891903180993
7917065.615709.88887459401355.71112540598
8014427.914277.5964180937150.303581906297
8117818.517847.9542355833-29.4542355832891
8218027.618794.2166467020-766.61664670198







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8317755.926520326117314.645992581618197.2070480707
8415721.480495912915237.910612063916205.0503797620
8517234.208797757916680.35754568117788.0600498349
8617252.294463189516645.055400973717859.5335254054
8719299.456037776318594.522747172320004.3893283803
8818091.13212732417363.077119585418819.1871350626
8917865.78053054217090.403241739918641.1578193441
9019006.758542418718138.889315347819874.6277694896
9117325.260358115416464.313943784218186.2067724465
9215343.688750573414507.523747759216179.8537533876
9319096.211394167918038.663517131020153.7592712048
9419967.526393567818896.664527982821038.3882591529

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
83 & 17755.9265203261 & 17314.6459925816 & 18197.2070480707 \tabularnewline
84 & 15721.4804959129 & 15237.9106120639 & 16205.0503797620 \tabularnewline
85 & 17234.2087977579 & 16680.357545681 & 17788.0600498349 \tabularnewline
86 & 17252.2944631895 & 16645.0554009737 & 17859.5335254054 \tabularnewline
87 & 19299.4560377763 & 18594.5227471723 & 20004.3893283803 \tabularnewline
88 & 18091.132127324 & 17363.0771195854 & 18819.1871350626 \tabularnewline
89 & 17865.780530542 & 17090.4032417399 & 18641.1578193441 \tabularnewline
90 & 19006.7585424187 & 18138.8893153478 & 19874.6277694896 \tabularnewline
91 & 17325.2603581154 & 16464.3139437842 & 18186.2067724465 \tabularnewline
92 & 15343.6887505734 & 14507.5237477592 & 16179.8537533876 \tabularnewline
93 & 19096.2113941679 & 18038.6635171310 & 20153.7592712048 \tabularnewline
94 & 19967.5263935678 & 18896.6645279828 & 21038.3882591529 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41350&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]83[/C][C]17755.9265203261[/C][C]17314.6459925816[/C][C]18197.2070480707[/C][/ROW]
[ROW][C]84[/C][C]15721.4804959129[/C][C]15237.9106120639[/C][C]16205.0503797620[/C][/ROW]
[ROW][C]85[/C][C]17234.2087977579[/C][C]16680.357545681[/C][C]17788.0600498349[/C][/ROW]
[ROW][C]86[/C][C]17252.2944631895[/C][C]16645.0554009737[/C][C]17859.5335254054[/C][/ROW]
[ROW][C]87[/C][C]19299.4560377763[/C][C]18594.5227471723[/C][C]20004.3893283803[/C][/ROW]
[ROW][C]88[/C][C]18091.132127324[/C][C]17363.0771195854[/C][C]18819.1871350626[/C][/ROW]
[ROW][C]89[/C][C]17865.780530542[/C][C]17090.4032417399[/C][C]18641.1578193441[/C][/ROW]
[ROW][C]90[/C][C]19006.7585424187[/C][C]18138.8893153478[/C][C]19874.6277694896[/C][/ROW]
[ROW][C]91[/C][C]17325.2603581154[/C][C]16464.3139437842[/C][C]18186.2067724465[/C][/ROW]
[ROW][C]92[/C][C]15343.6887505734[/C][C]14507.5237477592[/C][C]16179.8537533876[/C][/ROW]
[ROW][C]93[/C][C]19096.2113941679[/C][C]18038.6635171310[/C][C]20153.7592712048[/C][/ROW]
[ROW][C]94[/C][C]19967.5263935678[/C][C]18896.6645279828[/C][C]21038.3882591529[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41350&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41350&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
8317755.926520326117314.645992581618197.2070480707
8415721.480495912915237.910612063916205.0503797620
8517234.208797757916680.35754568117788.0600498349
8617252.294463189516645.055400973717859.5335254054
8719299.456037776318594.522747172320004.3893283803
8818091.13212732417363.077119585418819.1871350626
8917865.78053054217090.403241739918641.1578193441
9019006.758542418718138.889315347819874.6277694896
9117325.260358115416464.313943784218186.2067724465
9215343.688750573414507.523747759216179.8537533876
9319096.211394167918038.663517131020153.7592712048
9419967.526393567818896.664527982821038.3882591529



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')