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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 10:29:01 -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/t12439602115tjjqtk39vc23b1.htm/, Retrieved Fri, 10 May 2024 02:37:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41310, Retrieved Fri, 10 May 2024 02:37:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Datareeks - Aardo...] [2009-06-02 16:29:01] [900fe54243512ff0c75e5ed1f9ef5c37] [Current]
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Dataseries X:
493395.00
487190.00
519493.00
519453.00
538588.00
438224.00
542034.00
512027.00
619880.00
533737.00
573789.00
589213.00
532168.00
551102.00
593789.00
527106.00
547327.00
601305.00
610872.00
601325.00
642143.00
614216.00
657979.00
673098.00
602297.00
615381.00
703671.00
733852.00
716596.00
745798.00
742027.10
679181.20
739022.70
645410.60
729382.10
671052.70
744954.80
677639.30
778207.20
763316.20
658531.60
831700.10
664156.30
621402.10
683588.70
600023.80
643273.80
653615.90
620177.50
574128.80
599828.00
599369.40
596617.70
616114.60
510226.90
493960.10
634503.30
588556.20
603239.00
617458.20
646543.50
680125.60
731595.80
759600.30
785031.70
849573.30
762342.00
815346.60
929603.20
784057.50
944667.70
1007258.30
664292.70
873207.40
1146510.00
1417266.80
1089387.90
1373379.70
1009397.60
818175.10
1003458.10
961142.70
1121906.60
1141713.30
1042352.60
992223.60
920525.30
1076093.40
967880.40
1236416.10




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41310&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41310&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41310&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.668837108850633
beta0
gamma0.703044343859426

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.668837108850633 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.703044343859426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41310&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]0.668837108850633[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.703044343859426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41310&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41310&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
alpha0.668837108850633
beta0
gamma0.703044343859426







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13532168499791.70847647532376.2915235246
14551102539103.86076577711998.1392342234
15593789590455.1048425133333.89515748725
16527106527271.974943384-165.974943384412
17547327546140.1259675711186.87403242872
18601305599384.5273075531920.47269244655
19610872608483.7321804492388.26781955070
20601325576989.85913815324335.140861847
21642143716926.628860752-74783.6288607515
22614216576047.11006657138168.8899334290
23657979651719.1370249636259.86297503684
24673098670713.5623947682384.437605232
25602297610728.630374213-8431.63037421345
26615381619039.750355153-3658.75035515311
27703671662212.63825827841458.361741722
28733852612127.883262676121724.116737324
29716596717293.380123523-697.38012352318
30745798784016.794608828-38218.7946088276
31742027.1766974.573905942-24947.4739059421
32679181.2714498.114775428-35316.9147754284
33739022.7804449.728749846-65427.0287498465
34645410.6683691.368821074-38280.7688210745
35729382.1703670.01493812225712.0850618776
36671052.7735545.105597858-64492.4055978581
37744954.8626277.833757071118676.966242929
38677639.3722358.702578015-44719.4025780149
39778207.2754405.33278448823801.8672155116
40763316.2701027.80850325562288.3914967446
41658531.6737651.945883853-79120.3458838535
42831700.1740543.71517665991156.3848233406
43664156.3813401.07946849-149244.779468491
44621402.1676910.5401654-55508.4401653998
45683588.7739212.716908837-55624.016908837
46600023.8635439.675750915-35415.8757509151
47643273.8668950.699031645-25676.8990316449
48653615.9645863.1922243827752.70777561842
49620177.5625701.958769171-5524.45876917127
50574128.8604329.101478896-30200.3014788956
51599828651597.175796715-51769.1757967147
52599369.4569440.11922199729929.2807780030
53596617.7559913.55092916636704.1490708342
54616114.6667475.504536375-51360.9045363754
55510226.9596686.845058719-86459.9450587189
56493960.1527542.88488512-33582.7848851199
57634503.3585770.02232874648733.2776712541
58588556.2563108.58212697625447.6178730238
59603239637365.210952478-34126.210952478
60617458.2616585.308318703872.891681296634
61646543.5590578.1075172155965.3924827899
62680125.6604004.44740074276121.152599258
63731595.8724242.2423730127353.55762698816
64759600.3693397.96640489566202.3335951052
65785031.7701432.91687980883598.7831201917
66849573.3834801.36021239814771.9397876016
67762342779240.207694494-16898.2076944942
68815346.6766455.35458378348891.2454162168
69929603.2955007.951241408-25404.7512414085
70784057.5844729.693556326-60672.1935563263
71944667.7861113.04651026283554.6534897379
721007258.3929447.66739931177810.6326006893
73664292.7955073.862868592-290781.162868592
74873207.4735038.697237401138168.702762599
751146510891699.382528233254810.617471767
761417266.81026218.64548934391048.154510665
771089387.91226540.72989738-137152.829897380
781373379.71221902.54560288151477.154397119
791009397.61206666.75808575-197269.158085752
80818175.11091436.31765757-273261.217657573
811003458.11063152.38644291-59694.2864429121
82961142.7910505.32247507750637.3775249226
831121906.61050042.7459777371863.8540222712
841141713.31108996.0242257632717.2757742386
851042352.6983653.03584016458699.5641598356
86992223.61124671.42382884-132447.823828837
87920525.31133535.55347793-213010.253477934
881076093.4971710.947012389104382.452987611
89967880.4901678.34960488466202.0503951164
901236416.11076801.59113149159614.508868511

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 532168 & 499791.708476475 & 32376.2915235246 \tabularnewline
14 & 551102 & 539103.860765777 & 11998.1392342234 \tabularnewline
15 & 593789 & 590455.104842513 & 3333.89515748725 \tabularnewline
16 & 527106 & 527271.974943384 & -165.974943384412 \tabularnewline
17 & 547327 & 546140.125967571 & 1186.87403242872 \tabularnewline
18 & 601305 & 599384.527307553 & 1920.47269244655 \tabularnewline
19 & 610872 & 608483.732180449 & 2388.26781955070 \tabularnewline
20 & 601325 & 576989.859138153 & 24335.140861847 \tabularnewline
21 & 642143 & 716926.628860752 & -74783.6288607515 \tabularnewline
22 & 614216 & 576047.110066571 & 38168.8899334290 \tabularnewline
23 & 657979 & 651719.137024963 & 6259.86297503684 \tabularnewline
24 & 673098 & 670713.562394768 & 2384.437605232 \tabularnewline
25 & 602297 & 610728.630374213 & -8431.63037421345 \tabularnewline
26 & 615381 & 619039.750355153 & -3658.75035515311 \tabularnewline
27 & 703671 & 662212.638258278 & 41458.361741722 \tabularnewline
28 & 733852 & 612127.883262676 & 121724.116737324 \tabularnewline
29 & 716596 & 717293.380123523 & -697.38012352318 \tabularnewline
30 & 745798 & 784016.794608828 & -38218.7946088276 \tabularnewline
31 & 742027.1 & 766974.573905942 & -24947.4739059421 \tabularnewline
32 & 679181.2 & 714498.114775428 & -35316.9147754284 \tabularnewline
33 & 739022.7 & 804449.728749846 & -65427.0287498465 \tabularnewline
34 & 645410.6 & 683691.368821074 & -38280.7688210745 \tabularnewline
35 & 729382.1 & 703670.014938122 & 25712.0850618776 \tabularnewline
36 & 671052.7 & 735545.105597858 & -64492.4055978581 \tabularnewline
37 & 744954.8 & 626277.833757071 & 118676.966242929 \tabularnewline
38 & 677639.3 & 722358.702578015 & -44719.4025780149 \tabularnewline
39 & 778207.2 & 754405.332784488 & 23801.8672155116 \tabularnewline
40 & 763316.2 & 701027.808503255 & 62288.3914967446 \tabularnewline
41 & 658531.6 & 737651.945883853 & -79120.3458838535 \tabularnewline
42 & 831700.1 & 740543.715176659 & 91156.3848233406 \tabularnewline
43 & 664156.3 & 813401.07946849 & -149244.779468491 \tabularnewline
44 & 621402.1 & 676910.5401654 & -55508.4401653998 \tabularnewline
45 & 683588.7 & 739212.716908837 & -55624.016908837 \tabularnewline
46 & 600023.8 & 635439.675750915 & -35415.8757509151 \tabularnewline
47 & 643273.8 & 668950.699031645 & -25676.8990316449 \tabularnewline
48 & 653615.9 & 645863.192224382 & 7752.70777561842 \tabularnewline
49 & 620177.5 & 625701.958769171 & -5524.45876917127 \tabularnewline
50 & 574128.8 & 604329.101478896 & -30200.3014788956 \tabularnewline
51 & 599828 & 651597.175796715 & -51769.1757967147 \tabularnewline
52 & 599369.4 & 569440.119221997 & 29929.2807780030 \tabularnewline
53 & 596617.7 & 559913.550929166 & 36704.1490708342 \tabularnewline
54 & 616114.6 & 667475.504536375 & -51360.9045363754 \tabularnewline
55 & 510226.9 & 596686.845058719 & -86459.9450587189 \tabularnewline
56 & 493960.1 & 527542.88488512 & -33582.7848851199 \tabularnewline
57 & 634503.3 & 585770.022328746 & 48733.2776712541 \tabularnewline
58 & 588556.2 & 563108.582126976 & 25447.6178730238 \tabularnewline
59 & 603239 & 637365.210952478 & -34126.210952478 \tabularnewline
60 & 617458.2 & 616585.308318703 & 872.891681296634 \tabularnewline
61 & 646543.5 & 590578.10751721 & 55965.3924827899 \tabularnewline
62 & 680125.6 & 604004.447400742 & 76121.152599258 \tabularnewline
63 & 731595.8 & 724242.242373012 & 7353.55762698816 \tabularnewline
64 & 759600.3 & 693397.966404895 & 66202.3335951052 \tabularnewline
65 & 785031.7 & 701432.916879808 & 83598.7831201917 \tabularnewline
66 & 849573.3 & 834801.360212398 & 14771.9397876016 \tabularnewline
67 & 762342 & 779240.207694494 & -16898.2076944942 \tabularnewline
68 & 815346.6 & 766455.354583783 & 48891.2454162168 \tabularnewline
69 & 929603.2 & 955007.951241408 & -25404.7512414085 \tabularnewline
70 & 784057.5 & 844729.693556326 & -60672.1935563263 \tabularnewline
71 & 944667.7 & 861113.046510262 & 83554.6534897379 \tabularnewline
72 & 1007258.3 & 929447.667399311 & 77810.6326006893 \tabularnewline
73 & 664292.7 & 955073.862868592 & -290781.162868592 \tabularnewline
74 & 873207.4 & 735038.697237401 & 138168.702762599 \tabularnewline
75 & 1146510 & 891699.382528233 & 254810.617471767 \tabularnewline
76 & 1417266.8 & 1026218.64548934 & 391048.154510665 \tabularnewline
77 & 1089387.9 & 1226540.72989738 & -137152.829897380 \tabularnewline
78 & 1373379.7 & 1221902.54560288 & 151477.154397119 \tabularnewline
79 & 1009397.6 & 1206666.75808575 & -197269.158085752 \tabularnewline
80 & 818175.1 & 1091436.31765757 & -273261.217657573 \tabularnewline
81 & 1003458.1 & 1063152.38644291 & -59694.2864429121 \tabularnewline
82 & 961142.7 & 910505.322475077 & 50637.3775249226 \tabularnewline
83 & 1121906.6 & 1050042.74597773 & 71863.8540222712 \tabularnewline
84 & 1141713.3 & 1108996.02422576 & 32717.2757742386 \tabularnewline
85 & 1042352.6 & 983653.035840164 & 58699.5641598356 \tabularnewline
86 & 992223.6 & 1124671.42382884 & -132447.823828837 \tabularnewline
87 & 920525.3 & 1133535.55347793 & -213010.253477934 \tabularnewline
88 & 1076093.4 & 971710.947012389 & 104382.452987611 \tabularnewline
89 & 967880.4 & 901678.349604884 & 66202.0503951164 \tabularnewline
90 & 1236416.1 & 1076801.59113149 & 159614.508868511 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41310&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]532168[/C][C]499791.708476475[/C][C]32376.2915235246[/C][/ROW]
[ROW][C]14[/C][C]551102[/C][C]539103.860765777[/C][C]11998.1392342234[/C][/ROW]
[ROW][C]15[/C][C]593789[/C][C]590455.104842513[/C][C]3333.89515748725[/C][/ROW]
[ROW][C]16[/C][C]527106[/C][C]527271.974943384[/C][C]-165.974943384412[/C][/ROW]
[ROW][C]17[/C][C]547327[/C][C]546140.125967571[/C][C]1186.87403242872[/C][/ROW]
[ROW][C]18[/C][C]601305[/C][C]599384.527307553[/C][C]1920.47269244655[/C][/ROW]
[ROW][C]19[/C][C]610872[/C][C]608483.732180449[/C][C]2388.26781955070[/C][/ROW]
[ROW][C]20[/C][C]601325[/C][C]576989.859138153[/C][C]24335.140861847[/C][/ROW]
[ROW][C]21[/C][C]642143[/C][C]716926.628860752[/C][C]-74783.6288607515[/C][/ROW]
[ROW][C]22[/C][C]614216[/C][C]576047.110066571[/C][C]38168.8899334290[/C][/ROW]
[ROW][C]23[/C][C]657979[/C][C]651719.137024963[/C][C]6259.86297503684[/C][/ROW]
[ROW][C]24[/C][C]673098[/C][C]670713.562394768[/C][C]2384.437605232[/C][/ROW]
[ROW][C]25[/C][C]602297[/C][C]610728.630374213[/C][C]-8431.63037421345[/C][/ROW]
[ROW][C]26[/C][C]615381[/C][C]619039.750355153[/C][C]-3658.75035515311[/C][/ROW]
[ROW][C]27[/C][C]703671[/C][C]662212.638258278[/C][C]41458.361741722[/C][/ROW]
[ROW][C]28[/C][C]733852[/C][C]612127.883262676[/C][C]121724.116737324[/C][/ROW]
[ROW][C]29[/C][C]716596[/C][C]717293.380123523[/C][C]-697.38012352318[/C][/ROW]
[ROW][C]30[/C][C]745798[/C][C]784016.794608828[/C][C]-38218.7946088276[/C][/ROW]
[ROW][C]31[/C][C]742027.1[/C][C]766974.573905942[/C][C]-24947.4739059421[/C][/ROW]
[ROW][C]32[/C][C]679181.2[/C][C]714498.114775428[/C][C]-35316.9147754284[/C][/ROW]
[ROW][C]33[/C][C]739022.7[/C][C]804449.728749846[/C][C]-65427.0287498465[/C][/ROW]
[ROW][C]34[/C][C]645410.6[/C][C]683691.368821074[/C][C]-38280.7688210745[/C][/ROW]
[ROW][C]35[/C][C]729382.1[/C][C]703670.014938122[/C][C]25712.0850618776[/C][/ROW]
[ROW][C]36[/C][C]671052.7[/C][C]735545.105597858[/C][C]-64492.4055978581[/C][/ROW]
[ROW][C]37[/C][C]744954.8[/C][C]626277.833757071[/C][C]118676.966242929[/C][/ROW]
[ROW][C]38[/C][C]677639.3[/C][C]722358.702578015[/C][C]-44719.4025780149[/C][/ROW]
[ROW][C]39[/C][C]778207.2[/C][C]754405.332784488[/C][C]23801.8672155116[/C][/ROW]
[ROW][C]40[/C][C]763316.2[/C][C]701027.808503255[/C][C]62288.3914967446[/C][/ROW]
[ROW][C]41[/C][C]658531.6[/C][C]737651.945883853[/C][C]-79120.3458838535[/C][/ROW]
[ROW][C]42[/C][C]831700.1[/C][C]740543.715176659[/C][C]91156.3848233406[/C][/ROW]
[ROW][C]43[/C][C]664156.3[/C][C]813401.07946849[/C][C]-149244.779468491[/C][/ROW]
[ROW][C]44[/C][C]621402.1[/C][C]676910.5401654[/C][C]-55508.4401653998[/C][/ROW]
[ROW][C]45[/C][C]683588.7[/C][C]739212.716908837[/C][C]-55624.016908837[/C][/ROW]
[ROW][C]46[/C][C]600023.8[/C][C]635439.675750915[/C][C]-35415.8757509151[/C][/ROW]
[ROW][C]47[/C][C]643273.8[/C][C]668950.699031645[/C][C]-25676.8990316449[/C][/ROW]
[ROW][C]48[/C][C]653615.9[/C][C]645863.192224382[/C][C]7752.70777561842[/C][/ROW]
[ROW][C]49[/C][C]620177.5[/C][C]625701.958769171[/C][C]-5524.45876917127[/C][/ROW]
[ROW][C]50[/C][C]574128.8[/C][C]604329.101478896[/C][C]-30200.3014788956[/C][/ROW]
[ROW][C]51[/C][C]599828[/C][C]651597.175796715[/C][C]-51769.1757967147[/C][/ROW]
[ROW][C]52[/C][C]599369.4[/C][C]569440.119221997[/C][C]29929.2807780030[/C][/ROW]
[ROW][C]53[/C][C]596617.7[/C][C]559913.550929166[/C][C]36704.1490708342[/C][/ROW]
[ROW][C]54[/C][C]616114.6[/C][C]667475.504536375[/C][C]-51360.9045363754[/C][/ROW]
[ROW][C]55[/C][C]510226.9[/C][C]596686.845058719[/C][C]-86459.9450587189[/C][/ROW]
[ROW][C]56[/C][C]493960.1[/C][C]527542.88488512[/C][C]-33582.7848851199[/C][/ROW]
[ROW][C]57[/C][C]634503.3[/C][C]585770.022328746[/C][C]48733.2776712541[/C][/ROW]
[ROW][C]58[/C][C]588556.2[/C][C]563108.582126976[/C][C]25447.6178730238[/C][/ROW]
[ROW][C]59[/C][C]603239[/C][C]637365.210952478[/C][C]-34126.210952478[/C][/ROW]
[ROW][C]60[/C][C]617458.2[/C][C]616585.308318703[/C][C]872.891681296634[/C][/ROW]
[ROW][C]61[/C][C]646543.5[/C][C]590578.10751721[/C][C]55965.3924827899[/C][/ROW]
[ROW][C]62[/C][C]680125.6[/C][C]604004.447400742[/C][C]76121.152599258[/C][/ROW]
[ROW][C]63[/C][C]731595.8[/C][C]724242.242373012[/C][C]7353.55762698816[/C][/ROW]
[ROW][C]64[/C][C]759600.3[/C][C]693397.966404895[/C][C]66202.3335951052[/C][/ROW]
[ROW][C]65[/C][C]785031.7[/C][C]701432.916879808[/C][C]83598.7831201917[/C][/ROW]
[ROW][C]66[/C][C]849573.3[/C][C]834801.360212398[/C][C]14771.9397876016[/C][/ROW]
[ROW][C]67[/C][C]762342[/C][C]779240.207694494[/C][C]-16898.2076944942[/C][/ROW]
[ROW][C]68[/C][C]815346.6[/C][C]766455.354583783[/C][C]48891.2454162168[/C][/ROW]
[ROW][C]69[/C][C]929603.2[/C][C]955007.951241408[/C][C]-25404.7512414085[/C][/ROW]
[ROW][C]70[/C][C]784057.5[/C][C]844729.693556326[/C][C]-60672.1935563263[/C][/ROW]
[ROW][C]71[/C][C]944667.7[/C][C]861113.046510262[/C][C]83554.6534897379[/C][/ROW]
[ROW][C]72[/C][C]1007258.3[/C][C]929447.667399311[/C][C]77810.6326006893[/C][/ROW]
[ROW][C]73[/C][C]664292.7[/C][C]955073.862868592[/C][C]-290781.162868592[/C][/ROW]
[ROW][C]74[/C][C]873207.4[/C][C]735038.697237401[/C][C]138168.702762599[/C][/ROW]
[ROW][C]75[/C][C]1146510[/C][C]891699.382528233[/C][C]254810.617471767[/C][/ROW]
[ROW][C]76[/C][C]1417266.8[/C][C]1026218.64548934[/C][C]391048.154510665[/C][/ROW]
[ROW][C]77[/C][C]1089387.9[/C][C]1226540.72989738[/C][C]-137152.829897380[/C][/ROW]
[ROW][C]78[/C][C]1373379.7[/C][C]1221902.54560288[/C][C]151477.154397119[/C][/ROW]
[ROW][C]79[/C][C]1009397.6[/C][C]1206666.75808575[/C][C]-197269.158085752[/C][/ROW]
[ROW][C]80[/C][C]818175.1[/C][C]1091436.31765757[/C][C]-273261.217657573[/C][/ROW]
[ROW][C]81[/C][C]1003458.1[/C][C]1063152.38644291[/C][C]-59694.2864429121[/C][/ROW]
[ROW][C]82[/C][C]961142.7[/C][C]910505.322475077[/C][C]50637.3775249226[/C][/ROW]
[ROW][C]83[/C][C]1121906.6[/C][C]1050042.74597773[/C][C]71863.8540222712[/C][/ROW]
[ROW][C]84[/C][C]1141713.3[/C][C]1108996.02422576[/C][C]32717.2757742386[/C][/ROW]
[ROW][C]85[/C][C]1042352.6[/C][C]983653.035840164[/C][C]58699.5641598356[/C][/ROW]
[ROW][C]86[/C][C]992223.6[/C][C]1124671.42382884[/C][C]-132447.823828837[/C][/ROW]
[ROW][C]87[/C][C]920525.3[/C][C]1133535.55347793[/C][C]-213010.253477934[/C][/ROW]
[ROW][C]88[/C][C]1076093.4[/C][C]971710.947012389[/C][C]104382.452987611[/C][/ROW]
[ROW][C]89[/C][C]967880.4[/C][C]901678.349604884[/C][C]66202.0503951164[/C][/ROW]
[ROW][C]90[/C][C]1236416.1[/C][C]1076801.59113149[/C][C]159614.508868511[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41310&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41310&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
13532168499791.70847647532376.2915235246
14551102539103.86076577711998.1392342234
15593789590455.1048425133333.89515748725
16527106527271.974943384-165.974943384412
17547327546140.1259675711186.87403242872
18601305599384.5273075531920.47269244655
19610872608483.7321804492388.26781955070
20601325576989.85913815324335.140861847
21642143716926.628860752-74783.6288607515
22614216576047.11006657138168.8899334290
23657979651719.1370249636259.86297503684
24673098670713.5623947682384.437605232
25602297610728.630374213-8431.63037421345
26615381619039.750355153-3658.75035515311
27703671662212.63825827841458.361741722
28733852612127.883262676121724.116737324
29716596717293.380123523-697.38012352318
30745798784016.794608828-38218.7946088276
31742027.1766974.573905942-24947.4739059421
32679181.2714498.114775428-35316.9147754284
33739022.7804449.728749846-65427.0287498465
34645410.6683691.368821074-38280.7688210745
35729382.1703670.01493812225712.0850618776
36671052.7735545.105597858-64492.4055978581
37744954.8626277.833757071118676.966242929
38677639.3722358.702578015-44719.4025780149
39778207.2754405.33278448823801.8672155116
40763316.2701027.80850325562288.3914967446
41658531.6737651.945883853-79120.3458838535
42831700.1740543.71517665991156.3848233406
43664156.3813401.07946849-149244.779468491
44621402.1676910.5401654-55508.4401653998
45683588.7739212.716908837-55624.016908837
46600023.8635439.675750915-35415.8757509151
47643273.8668950.699031645-25676.8990316449
48653615.9645863.1922243827752.70777561842
49620177.5625701.958769171-5524.45876917127
50574128.8604329.101478896-30200.3014788956
51599828651597.175796715-51769.1757967147
52599369.4569440.11922199729929.2807780030
53596617.7559913.55092916636704.1490708342
54616114.6667475.504536375-51360.9045363754
55510226.9596686.845058719-86459.9450587189
56493960.1527542.88488512-33582.7848851199
57634503.3585770.02232874648733.2776712541
58588556.2563108.58212697625447.6178730238
59603239637365.210952478-34126.210952478
60617458.2616585.308318703872.891681296634
61646543.5590578.1075172155965.3924827899
62680125.6604004.44740074276121.152599258
63731595.8724242.2423730127353.55762698816
64759600.3693397.96640489566202.3335951052
65785031.7701432.91687980883598.7831201917
66849573.3834801.36021239814771.9397876016
67762342779240.207694494-16898.2076944942
68815346.6766455.35458378348891.2454162168
69929603.2955007.951241408-25404.7512414085
70784057.5844729.693556326-60672.1935563263
71944667.7861113.04651026283554.6534897379
721007258.3929447.66739931177810.6326006893
73664292.7955073.862868592-290781.162868592
74873207.4735038.697237401138168.702762599
751146510891699.382528233254810.617471767
761417266.81026218.64548934391048.154510665
771089387.91226540.72989738-137152.829897380
781373379.71221902.54560288151477.154397119
791009397.61206666.75808575-197269.158085752
80818175.11091436.31765757-273261.217657573
811003458.11063152.38644291-59694.2864429121
82961142.7910505.32247507750637.3775249226
831121906.61050042.7459777371863.8540222712
841141713.31108996.0242257632717.2757742386
851042352.6983653.03584016458699.5641598356
86992223.61124671.42382884-132447.823828837
87920525.31133535.55347793-213010.253477934
881076093.4971710.947012389104382.452987611
89967880.4901678.34960488466202.0503951164
901236416.11076801.59113149159614.508868511







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
911006991.05379214831150.7757842121182831.33180006
92993605.904937146776063.7169422581211148.09293203
931232034.45041535946012.3220013961518056.57882931
941124096.3014259829296.6547368941418895.94811490
951252228.08112224904878.5220846281599577.64015985
961253324.27861662883401.6548339151623246.90239933
971096810.67582455744412.4457430951449208.90590600
981154287.95037287764523.0356278181544052.86511792
991235607.78165482802492.4435931421668723.11971649
1001303159.64685823831648.8882217381774670.40549472
1011119269.30958045691194.065801291547344.55335962
1021292046.43721176819196.404880351764896.46954317

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
91 & 1006991.05379214 & 831150.775784212 & 1182831.33180006 \tabularnewline
92 & 993605.904937146 & 776063.716942258 & 1211148.09293203 \tabularnewline
93 & 1232034.45041535 & 946012.322001396 & 1518056.57882931 \tabularnewline
94 & 1124096.3014259 & 829296.654736894 & 1418895.94811490 \tabularnewline
95 & 1252228.08112224 & 904878.522084628 & 1599577.64015985 \tabularnewline
96 & 1253324.27861662 & 883401.654833915 & 1623246.90239933 \tabularnewline
97 & 1096810.67582455 & 744412.445743095 & 1449208.90590600 \tabularnewline
98 & 1154287.95037287 & 764523.035627818 & 1544052.86511792 \tabularnewline
99 & 1235607.78165482 & 802492.443593142 & 1668723.11971649 \tabularnewline
100 & 1303159.64685823 & 831648.888221738 & 1774670.40549472 \tabularnewline
101 & 1119269.30958045 & 691194.06580129 & 1547344.55335962 \tabularnewline
102 & 1292046.43721176 & 819196.40488035 & 1764896.46954317 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41310&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]91[/C][C]1006991.05379214[/C][C]831150.775784212[/C][C]1182831.33180006[/C][/ROW]
[ROW][C]92[/C][C]993605.904937146[/C][C]776063.716942258[/C][C]1211148.09293203[/C][/ROW]
[ROW][C]93[/C][C]1232034.45041535[/C][C]946012.322001396[/C][C]1518056.57882931[/C][/ROW]
[ROW][C]94[/C][C]1124096.3014259[/C][C]829296.654736894[/C][C]1418895.94811490[/C][/ROW]
[ROW][C]95[/C][C]1252228.08112224[/C][C]904878.522084628[/C][C]1599577.64015985[/C][/ROW]
[ROW][C]96[/C][C]1253324.27861662[/C][C]883401.654833915[/C][C]1623246.90239933[/C][/ROW]
[ROW][C]97[/C][C]1096810.67582455[/C][C]744412.445743095[/C][C]1449208.90590600[/C][/ROW]
[ROW][C]98[/C][C]1154287.95037287[/C][C]764523.035627818[/C][C]1544052.86511792[/C][/ROW]
[ROW][C]99[/C][C]1235607.78165482[/C][C]802492.443593142[/C][C]1668723.11971649[/C][/ROW]
[ROW][C]100[/C][C]1303159.64685823[/C][C]831648.888221738[/C][C]1774670.40549472[/C][/ROW]
[ROW][C]101[/C][C]1119269.30958045[/C][C]691194.06580129[/C][C]1547344.55335962[/C][/ROW]
[ROW][C]102[/C][C]1292046.43721176[/C][C]819196.40488035[/C][C]1764896.46954317[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41310&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41310&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
911006991.05379214831150.7757842121182831.33180006
92993605.904937146776063.7169422581211148.09293203
931232034.45041535946012.3220013961518056.57882931
941124096.3014259829296.6547368941418895.94811490
951252228.08112224904878.5220846281599577.64015985
961253324.27861662883401.6548339151623246.90239933
971096810.67582455744412.4457430951449208.90590600
981154287.95037287764523.0356278181544052.86511792
991235607.78165482802492.4435931421668723.11971649
1001303159.64685823831648.8882217381774670.40549472
1011119269.30958045691194.065801291547344.55335962
1021292046.43721176819196.404880351764896.46954317



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')