Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 Aug 2013 04:13:21 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/21/t13770729518hs560gh17ahqqr.htm/, Retrieved Sat, 27 Apr 2024 07:55:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211303, Retrieved Sat, 27 Apr 2024 07:55:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJoris Claus
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A - Sta...] [2013-08-21 08:13:21] [5b48cba8ffed7710e2defc0d8d22bd89] [Current]
Feedback Forum

Post a new message
Dataseries X:
865911
858030
850038
833499
997113
988455
865911
784437
792318
792318
801087
816849
865911
850038
874569
914862
1144188
1144188
1095237
1046175
1086468
1135530
1144188
1168719
1242312
1193250
1193250
1266843
1470861
1487400
1446330
1348206
1421799
1421799
1429680
1470861
1503273
1519812
1519812
1568874
1757130
1806081
1813962
1691418
1757130
1732599
1683537
1789542
1813962
1772892
1781550
1838493
2051280
2157174
2157174
2108223
2181705
2108223
2067042
2222886
2247306
2189586
2336661
2394381
2565987
2679873
2664111
2655342
2721054
2713062
2615049
2762124
2811186
2762124
2966142
3064266
3292704
3382836
3358416
3309354
3350424
3399486
3235761
3366297
3448548
3415359
3628035
3701517
4012317
4069260
3995778
4036848
4061379
4085910
3930066
4077141
4158615
4077141
4314459
4387941
4706622
4755684
4771446
4853697
4853697
4886109
4739034
4812627
4861578
4771446
5033184
5082246
5408808
5466528
5548002
5621595
5629476
5638134
5491059
5638134




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211303&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211303&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211303&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.214229733832505
beta0.107869753887267
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.214229733832505 \tabularnewline
beta & 0.107869753887267 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211303&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]0.214229733832505[/C][/ROW]
[ROW][C]beta[/C][C]0.107869753887267[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211303&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211303&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
alpha0.214229733832505
beta0.107869753887267
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13865911816579.60643253649331.3935674642
14850038810021.75327846540016.2467215352
15874569838608.46107419635960.5389258041
16914862879266.04881200135595.9511879993
1711441881100546.4278620643641.5721379353
1811441881102050.3664976642137.6335023411
1910952371031186.8610238664050.1389761432
201046175968464.45840644777710.5415935531
2110864681017720.4277946168747.572205389
2211355301052115.9131822583414.0868177502
2311441881096866.8361605447321.1638394594
2411687191140751.0239673927967.976032607
2512423121281188.81344969-38876.8134496922
2611932501240799.93118894-47549.9311889368
2711932501256841.1211785-63591.1211784952
2812668431289326.3240663-22483.3240663002
2914708611591300.44340944-120439.44340944
3014874001547916.18917266-60516.1891726558
3114463301443555.631547292774.36845271289
3213482061348910.81070484-704.810704835458
3314217991371685.2508715250113.7491284807
3414217991411092.2642789710706.7357210263
3514296801400222.9057822229457.0942177828
3614708611418104.8361009252756.1638990818
3715032731518412.76778444-15139.7677844365
3815198121457806.7729621562005.2270378454
3915198121480096.1521441639715.8478558357
4015688741581299.98878164-12425.988781641
4117571301857698.24555015-100568.245550151
4218060811867972.06802645-61891.0680264502
4318139621798734.4773744815227.5226255185
4416914181676515.9660195814902.0339804241
4517571301754501.972195492628.02780451439
4617325991748019.04107473-15420.0410747339
4716835371741906.75662924-58369.756629244
4817895421758754.6933605730787.3066394278
4918139621801115.9459353612846.0540646366
5017728921801063.83844784-28171.838447839
5117815501776855.977939634694.02206037147
5218384931829610.897595788882.10240422096
5320512802066296.81955504-15016.819555037
5421571742128583.7905624528590.2094375533
5521571742135155.9846435522018.0153564466
5621082231987088.55742878121134.442571217
5721817052088213.3243929693491.6756070412
5821082232082231.4799696925991.5200303062
5920670422043715.2107727823326.7892272212
6022228862171888.9926681350997.0073318686
6122473062211765.1866537435540.8133462612
6221895862179232.0600290510353.939970952
6323366612194502.42950116142158.570498839
6423943812300156.4431947394224.5568052693
6525659872601839.12537863-35852.1253786292
6626798732728992.84608298-49119.8460829807
6726641112719261.7912728-55150.7912727962
6826553422616666.0977162638675.9022837398
6927210542692938.5147620428115.4852379584
7027130622601504.78412663111557.215873365
7126150492569744.8762098745304.1237901291
7227621242762357.69684806-233.69684805721
7328111862784050.9488609827135.0511390241
7427621242716033.4982821946090.5017178087
7529661422870475.7882882695666.2117117424
7630642662936102.46677908128163.533220921
7732927043184994.35709175107709.642908255
7833828363366127.428140316708.571859695
7933584163368630.07491094-10214.0749109411
8033093543349881.37232018-40527.372320184
8133504243419510.1049249-69086.1049248991
8233994863364908.8669301434577.1330698631
8332357613237228.68938609-1467.68938608794
8433662973416769.6837878-50472.6837878013
8534485483456014.68548473-7466.68548472598
8634153593377990.5821002437368.4178997567
8736280353605929.2818252822105.7181747244
8837015173689249.3825157812267.6174842203
8940123173928998.6982371883318.3017628156
9040692604040100.2734054429159.7265945645
9139957784009852.92578276-14074.925782762
9240368483949064.5419732387783.4580267677
9340613794027896.0707588833482.9292411185
9440859104080881.233118585028.76688142167
9539300663881098.7811669948967.2188330111
9640771414057770.5029263919370.4970736117
9741586154161051.16612882-2436.16612881748
9840771414108911.68779596-31770.6877959576
9943144594348316.6558885-33857.655888495
10043879414421129.15211169-33188.1521116905
10147066224757044.26975436-50422.2697543632
10247556844797267.50519041-41583.5051904116
10347714464695442.2750663776003.724933628
10448536974729672.28919557124024.710804425
10548536974769278.0763415484418.9236584622
10648861094808702.0481873977406.9518126138
10747390344624206.7425048114827.257495199
10848126274814454.20382262-1827.20382261928
10948615784907005.27840535-45427.278405345
11047714464804761.64980539-33315.6498053931
11150331845080766.55700692-47582.5570069188
11250822465160514.92226235-78268.9222623538
11354088085524070.48694524-115262.486945244
11454665285560147.36810164-93619.3681016443
11555480025531594.8210075816407.1789924214
11656215955590018.5048693131576.4951306935
11756294765564531.3783057664944.6216942389
11856381345584852.5534760653281.4465239421
11954910595387528.53655974103530.463440265
12056381345482104.10179898156029.898201019

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 865911 & 816579.606432536 & 49331.3935674642 \tabularnewline
14 & 850038 & 810021.753278465 & 40016.2467215352 \tabularnewline
15 & 874569 & 838608.461074196 & 35960.5389258041 \tabularnewline
16 & 914862 & 879266.048812001 & 35595.9511879993 \tabularnewline
17 & 1144188 & 1100546.42786206 & 43641.5721379353 \tabularnewline
18 & 1144188 & 1102050.36649766 & 42137.6335023411 \tabularnewline
19 & 1095237 & 1031186.86102386 & 64050.1389761432 \tabularnewline
20 & 1046175 & 968464.458406447 & 77710.5415935531 \tabularnewline
21 & 1086468 & 1017720.42779461 & 68747.572205389 \tabularnewline
22 & 1135530 & 1052115.91318225 & 83414.0868177502 \tabularnewline
23 & 1144188 & 1096866.83616054 & 47321.1638394594 \tabularnewline
24 & 1168719 & 1140751.02396739 & 27967.976032607 \tabularnewline
25 & 1242312 & 1281188.81344969 & -38876.8134496922 \tabularnewline
26 & 1193250 & 1240799.93118894 & -47549.9311889368 \tabularnewline
27 & 1193250 & 1256841.1211785 & -63591.1211784952 \tabularnewline
28 & 1266843 & 1289326.3240663 & -22483.3240663002 \tabularnewline
29 & 1470861 & 1591300.44340944 & -120439.44340944 \tabularnewline
30 & 1487400 & 1547916.18917266 & -60516.1891726558 \tabularnewline
31 & 1446330 & 1443555.63154729 & 2774.36845271289 \tabularnewline
32 & 1348206 & 1348910.81070484 & -704.810704835458 \tabularnewline
33 & 1421799 & 1371685.25087152 & 50113.7491284807 \tabularnewline
34 & 1421799 & 1411092.26427897 & 10706.7357210263 \tabularnewline
35 & 1429680 & 1400222.90578222 & 29457.0942177828 \tabularnewline
36 & 1470861 & 1418104.83610092 & 52756.1638990818 \tabularnewline
37 & 1503273 & 1518412.76778444 & -15139.7677844365 \tabularnewline
38 & 1519812 & 1457806.77296215 & 62005.2270378454 \tabularnewline
39 & 1519812 & 1480096.15214416 & 39715.8478558357 \tabularnewline
40 & 1568874 & 1581299.98878164 & -12425.988781641 \tabularnewline
41 & 1757130 & 1857698.24555015 & -100568.245550151 \tabularnewline
42 & 1806081 & 1867972.06802645 & -61891.0680264502 \tabularnewline
43 & 1813962 & 1798734.47737448 & 15227.5226255185 \tabularnewline
44 & 1691418 & 1676515.96601958 & 14902.0339804241 \tabularnewline
45 & 1757130 & 1754501.97219549 & 2628.02780451439 \tabularnewline
46 & 1732599 & 1748019.04107473 & -15420.0410747339 \tabularnewline
47 & 1683537 & 1741906.75662924 & -58369.756629244 \tabularnewline
48 & 1789542 & 1758754.69336057 & 30787.3066394278 \tabularnewline
49 & 1813962 & 1801115.94593536 & 12846.0540646366 \tabularnewline
50 & 1772892 & 1801063.83844784 & -28171.838447839 \tabularnewline
51 & 1781550 & 1776855.97793963 & 4694.02206037147 \tabularnewline
52 & 1838493 & 1829610.89759578 & 8882.10240422096 \tabularnewline
53 & 2051280 & 2066296.81955504 & -15016.819555037 \tabularnewline
54 & 2157174 & 2128583.79056245 & 28590.2094375533 \tabularnewline
55 & 2157174 & 2135155.98464355 & 22018.0153564466 \tabularnewline
56 & 2108223 & 1987088.55742878 & 121134.442571217 \tabularnewline
57 & 2181705 & 2088213.32439296 & 93491.6756070412 \tabularnewline
58 & 2108223 & 2082231.47996969 & 25991.5200303062 \tabularnewline
59 & 2067042 & 2043715.21077278 & 23326.7892272212 \tabularnewline
60 & 2222886 & 2171888.99266813 & 50997.0073318686 \tabularnewline
61 & 2247306 & 2211765.18665374 & 35540.8133462612 \tabularnewline
62 & 2189586 & 2179232.06002905 & 10353.939970952 \tabularnewline
63 & 2336661 & 2194502.42950116 & 142158.570498839 \tabularnewline
64 & 2394381 & 2300156.44319473 & 94224.5568052693 \tabularnewline
65 & 2565987 & 2601839.12537863 & -35852.1253786292 \tabularnewline
66 & 2679873 & 2728992.84608298 & -49119.8460829807 \tabularnewline
67 & 2664111 & 2719261.7912728 & -55150.7912727962 \tabularnewline
68 & 2655342 & 2616666.09771626 & 38675.9022837398 \tabularnewline
69 & 2721054 & 2692938.51476204 & 28115.4852379584 \tabularnewline
70 & 2713062 & 2601504.78412663 & 111557.215873365 \tabularnewline
71 & 2615049 & 2569744.87620987 & 45304.1237901291 \tabularnewline
72 & 2762124 & 2762357.69684806 & -233.69684805721 \tabularnewline
73 & 2811186 & 2784050.94886098 & 27135.0511390241 \tabularnewline
74 & 2762124 & 2716033.49828219 & 46090.5017178087 \tabularnewline
75 & 2966142 & 2870475.78828826 & 95666.2117117424 \tabularnewline
76 & 3064266 & 2936102.46677908 & 128163.533220921 \tabularnewline
77 & 3292704 & 3184994.35709175 & 107709.642908255 \tabularnewline
78 & 3382836 & 3366127.4281403 & 16708.571859695 \tabularnewline
79 & 3358416 & 3368630.07491094 & -10214.0749109411 \tabularnewline
80 & 3309354 & 3349881.37232018 & -40527.372320184 \tabularnewline
81 & 3350424 & 3419510.1049249 & -69086.1049248991 \tabularnewline
82 & 3399486 & 3364908.86693014 & 34577.1330698631 \tabularnewline
83 & 3235761 & 3237228.68938609 & -1467.68938608794 \tabularnewline
84 & 3366297 & 3416769.6837878 & -50472.6837878013 \tabularnewline
85 & 3448548 & 3456014.68548473 & -7466.68548472598 \tabularnewline
86 & 3415359 & 3377990.58210024 & 37368.4178997567 \tabularnewline
87 & 3628035 & 3605929.28182528 & 22105.7181747244 \tabularnewline
88 & 3701517 & 3689249.38251578 & 12267.6174842203 \tabularnewline
89 & 4012317 & 3928998.69823718 & 83318.3017628156 \tabularnewline
90 & 4069260 & 4040100.27340544 & 29159.7265945645 \tabularnewline
91 & 3995778 & 4009852.92578276 & -14074.925782762 \tabularnewline
92 & 4036848 & 3949064.54197323 & 87783.4580267677 \tabularnewline
93 & 4061379 & 4027896.07075888 & 33482.9292411185 \tabularnewline
94 & 4085910 & 4080881.23311858 & 5028.76688142167 \tabularnewline
95 & 3930066 & 3881098.78116699 & 48967.2188330111 \tabularnewline
96 & 4077141 & 4057770.50292639 & 19370.4970736117 \tabularnewline
97 & 4158615 & 4161051.16612882 & -2436.16612881748 \tabularnewline
98 & 4077141 & 4108911.68779596 & -31770.6877959576 \tabularnewline
99 & 4314459 & 4348316.6558885 & -33857.655888495 \tabularnewline
100 & 4387941 & 4421129.15211169 & -33188.1521116905 \tabularnewline
101 & 4706622 & 4757044.26975436 & -50422.2697543632 \tabularnewline
102 & 4755684 & 4797267.50519041 & -41583.5051904116 \tabularnewline
103 & 4771446 & 4695442.27506637 & 76003.724933628 \tabularnewline
104 & 4853697 & 4729672.28919557 & 124024.710804425 \tabularnewline
105 & 4853697 & 4769278.07634154 & 84418.9236584622 \tabularnewline
106 & 4886109 & 4808702.04818739 & 77406.9518126138 \tabularnewline
107 & 4739034 & 4624206.7425048 & 114827.257495199 \tabularnewline
108 & 4812627 & 4814454.20382262 & -1827.20382261928 \tabularnewline
109 & 4861578 & 4907005.27840535 & -45427.278405345 \tabularnewline
110 & 4771446 & 4804761.64980539 & -33315.6498053931 \tabularnewline
111 & 5033184 & 5080766.55700692 & -47582.5570069188 \tabularnewline
112 & 5082246 & 5160514.92226235 & -78268.9222623538 \tabularnewline
113 & 5408808 & 5524070.48694524 & -115262.486945244 \tabularnewline
114 & 5466528 & 5560147.36810164 & -93619.3681016443 \tabularnewline
115 & 5548002 & 5531594.82100758 & 16407.1789924214 \tabularnewline
116 & 5621595 & 5590018.50486931 & 31576.4951306935 \tabularnewline
117 & 5629476 & 5564531.37830576 & 64944.6216942389 \tabularnewline
118 & 5638134 & 5584852.55347606 & 53281.4465239421 \tabularnewline
119 & 5491059 & 5387528.53655974 & 103530.463440265 \tabularnewline
120 & 5638134 & 5482104.10179898 & 156029.898201019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211303&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]865911[/C][C]816579.606432536[/C][C]49331.3935674642[/C][/ROW]
[ROW][C]14[/C][C]850038[/C][C]810021.753278465[/C][C]40016.2467215352[/C][/ROW]
[ROW][C]15[/C][C]874569[/C][C]838608.461074196[/C][C]35960.5389258041[/C][/ROW]
[ROW][C]16[/C][C]914862[/C][C]879266.048812001[/C][C]35595.9511879993[/C][/ROW]
[ROW][C]17[/C][C]1144188[/C][C]1100546.42786206[/C][C]43641.5721379353[/C][/ROW]
[ROW][C]18[/C][C]1144188[/C][C]1102050.36649766[/C][C]42137.6335023411[/C][/ROW]
[ROW][C]19[/C][C]1095237[/C][C]1031186.86102386[/C][C]64050.1389761432[/C][/ROW]
[ROW][C]20[/C][C]1046175[/C][C]968464.458406447[/C][C]77710.5415935531[/C][/ROW]
[ROW][C]21[/C][C]1086468[/C][C]1017720.42779461[/C][C]68747.572205389[/C][/ROW]
[ROW][C]22[/C][C]1135530[/C][C]1052115.91318225[/C][C]83414.0868177502[/C][/ROW]
[ROW][C]23[/C][C]1144188[/C][C]1096866.83616054[/C][C]47321.1638394594[/C][/ROW]
[ROW][C]24[/C][C]1168719[/C][C]1140751.02396739[/C][C]27967.976032607[/C][/ROW]
[ROW][C]25[/C][C]1242312[/C][C]1281188.81344969[/C][C]-38876.8134496922[/C][/ROW]
[ROW][C]26[/C][C]1193250[/C][C]1240799.93118894[/C][C]-47549.9311889368[/C][/ROW]
[ROW][C]27[/C][C]1193250[/C][C]1256841.1211785[/C][C]-63591.1211784952[/C][/ROW]
[ROW][C]28[/C][C]1266843[/C][C]1289326.3240663[/C][C]-22483.3240663002[/C][/ROW]
[ROW][C]29[/C][C]1470861[/C][C]1591300.44340944[/C][C]-120439.44340944[/C][/ROW]
[ROW][C]30[/C][C]1487400[/C][C]1547916.18917266[/C][C]-60516.1891726558[/C][/ROW]
[ROW][C]31[/C][C]1446330[/C][C]1443555.63154729[/C][C]2774.36845271289[/C][/ROW]
[ROW][C]32[/C][C]1348206[/C][C]1348910.81070484[/C][C]-704.810704835458[/C][/ROW]
[ROW][C]33[/C][C]1421799[/C][C]1371685.25087152[/C][C]50113.7491284807[/C][/ROW]
[ROW][C]34[/C][C]1421799[/C][C]1411092.26427897[/C][C]10706.7357210263[/C][/ROW]
[ROW][C]35[/C][C]1429680[/C][C]1400222.90578222[/C][C]29457.0942177828[/C][/ROW]
[ROW][C]36[/C][C]1470861[/C][C]1418104.83610092[/C][C]52756.1638990818[/C][/ROW]
[ROW][C]37[/C][C]1503273[/C][C]1518412.76778444[/C][C]-15139.7677844365[/C][/ROW]
[ROW][C]38[/C][C]1519812[/C][C]1457806.77296215[/C][C]62005.2270378454[/C][/ROW]
[ROW][C]39[/C][C]1519812[/C][C]1480096.15214416[/C][C]39715.8478558357[/C][/ROW]
[ROW][C]40[/C][C]1568874[/C][C]1581299.98878164[/C][C]-12425.988781641[/C][/ROW]
[ROW][C]41[/C][C]1757130[/C][C]1857698.24555015[/C][C]-100568.245550151[/C][/ROW]
[ROW][C]42[/C][C]1806081[/C][C]1867972.06802645[/C][C]-61891.0680264502[/C][/ROW]
[ROW][C]43[/C][C]1813962[/C][C]1798734.47737448[/C][C]15227.5226255185[/C][/ROW]
[ROW][C]44[/C][C]1691418[/C][C]1676515.96601958[/C][C]14902.0339804241[/C][/ROW]
[ROW][C]45[/C][C]1757130[/C][C]1754501.97219549[/C][C]2628.02780451439[/C][/ROW]
[ROW][C]46[/C][C]1732599[/C][C]1748019.04107473[/C][C]-15420.0410747339[/C][/ROW]
[ROW][C]47[/C][C]1683537[/C][C]1741906.75662924[/C][C]-58369.756629244[/C][/ROW]
[ROW][C]48[/C][C]1789542[/C][C]1758754.69336057[/C][C]30787.3066394278[/C][/ROW]
[ROW][C]49[/C][C]1813962[/C][C]1801115.94593536[/C][C]12846.0540646366[/C][/ROW]
[ROW][C]50[/C][C]1772892[/C][C]1801063.83844784[/C][C]-28171.838447839[/C][/ROW]
[ROW][C]51[/C][C]1781550[/C][C]1776855.97793963[/C][C]4694.02206037147[/C][/ROW]
[ROW][C]52[/C][C]1838493[/C][C]1829610.89759578[/C][C]8882.10240422096[/C][/ROW]
[ROW][C]53[/C][C]2051280[/C][C]2066296.81955504[/C][C]-15016.819555037[/C][/ROW]
[ROW][C]54[/C][C]2157174[/C][C]2128583.79056245[/C][C]28590.2094375533[/C][/ROW]
[ROW][C]55[/C][C]2157174[/C][C]2135155.98464355[/C][C]22018.0153564466[/C][/ROW]
[ROW][C]56[/C][C]2108223[/C][C]1987088.55742878[/C][C]121134.442571217[/C][/ROW]
[ROW][C]57[/C][C]2181705[/C][C]2088213.32439296[/C][C]93491.6756070412[/C][/ROW]
[ROW][C]58[/C][C]2108223[/C][C]2082231.47996969[/C][C]25991.5200303062[/C][/ROW]
[ROW][C]59[/C][C]2067042[/C][C]2043715.21077278[/C][C]23326.7892272212[/C][/ROW]
[ROW][C]60[/C][C]2222886[/C][C]2171888.99266813[/C][C]50997.0073318686[/C][/ROW]
[ROW][C]61[/C][C]2247306[/C][C]2211765.18665374[/C][C]35540.8133462612[/C][/ROW]
[ROW][C]62[/C][C]2189586[/C][C]2179232.06002905[/C][C]10353.939970952[/C][/ROW]
[ROW][C]63[/C][C]2336661[/C][C]2194502.42950116[/C][C]142158.570498839[/C][/ROW]
[ROW][C]64[/C][C]2394381[/C][C]2300156.44319473[/C][C]94224.5568052693[/C][/ROW]
[ROW][C]65[/C][C]2565987[/C][C]2601839.12537863[/C][C]-35852.1253786292[/C][/ROW]
[ROW][C]66[/C][C]2679873[/C][C]2728992.84608298[/C][C]-49119.8460829807[/C][/ROW]
[ROW][C]67[/C][C]2664111[/C][C]2719261.7912728[/C][C]-55150.7912727962[/C][/ROW]
[ROW][C]68[/C][C]2655342[/C][C]2616666.09771626[/C][C]38675.9022837398[/C][/ROW]
[ROW][C]69[/C][C]2721054[/C][C]2692938.51476204[/C][C]28115.4852379584[/C][/ROW]
[ROW][C]70[/C][C]2713062[/C][C]2601504.78412663[/C][C]111557.215873365[/C][/ROW]
[ROW][C]71[/C][C]2615049[/C][C]2569744.87620987[/C][C]45304.1237901291[/C][/ROW]
[ROW][C]72[/C][C]2762124[/C][C]2762357.69684806[/C][C]-233.69684805721[/C][/ROW]
[ROW][C]73[/C][C]2811186[/C][C]2784050.94886098[/C][C]27135.0511390241[/C][/ROW]
[ROW][C]74[/C][C]2762124[/C][C]2716033.49828219[/C][C]46090.5017178087[/C][/ROW]
[ROW][C]75[/C][C]2966142[/C][C]2870475.78828826[/C][C]95666.2117117424[/C][/ROW]
[ROW][C]76[/C][C]3064266[/C][C]2936102.46677908[/C][C]128163.533220921[/C][/ROW]
[ROW][C]77[/C][C]3292704[/C][C]3184994.35709175[/C][C]107709.642908255[/C][/ROW]
[ROW][C]78[/C][C]3382836[/C][C]3366127.4281403[/C][C]16708.571859695[/C][/ROW]
[ROW][C]79[/C][C]3358416[/C][C]3368630.07491094[/C][C]-10214.0749109411[/C][/ROW]
[ROW][C]80[/C][C]3309354[/C][C]3349881.37232018[/C][C]-40527.372320184[/C][/ROW]
[ROW][C]81[/C][C]3350424[/C][C]3419510.1049249[/C][C]-69086.1049248991[/C][/ROW]
[ROW][C]82[/C][C]3399486[/C][C]3364908.86693014[/C][C]34577.1330698631[/C][/ROW]
[ROW][C]83[/C][C]3235761[/C][C]3237228.68938609[/C][C]-1467.68938608794[/C][/ROW]
[ROW][C]84[/C][C]3366297[/C][C]3416769.6837878[/C][C]-50472.6837878013[/C][/ROW]
[ROW][C]85[/C][C]3448548[/C][C]3456014.68548473[/C][C]-7466.68548472598[/C][/ROW]
[ROW][C]86[/C][C]3415359[/C][C]3377990.58210024[/C][C]37368.4178997567[/C][/ROW]
[ROW][C]87[/C][C]3628035[/C][C]3605929.28182528[/C][C]22105.7181747244[/C][/ROW]
[ROW][C]88[/C][C]3701517[/C][C]3689249.38251578[/C][C]12267.6174842203[/C][/ROW]
[ROW][C]89[/C][C]4012317[/C][C]3928998.69823718[/C][C]83318.3017628156[/C][/ROW]
[ROW][C]90[/C][C]4069260[/C][C]4040100.27340544[/C][C]29159.7265945645[/C][/ROW]
[ROW][C]91[/C][C]3995778[/C][C]4009852.92578276[/C][C]-14074.925782762[/C][/ROW]
[ROW][C]92[/C][C]4036848[/C][C]3949064.54197323[/C][C]87783.4580267677[/C][/ROW]
[ROW][C]93[/C][C]4061379[/C][C]4027896.07075888[/C][C]33482.9292411185[/C][/ROW]
[ROW][C]94[/C][C]4085910[/C][C]4080881.23311858[/C][C]5028.76688142167[/C][/ROW]
[ROW][C]95[/C][C]3930066[/C][C]3881098.78116699[/C][C]48967.2188330111[/C][/ROW]
[ROW][C]96[/C][C]4077141[/C][C]4057770.50292639[/C][C]19370.4970736117[/C][/ROW]
[ROW][C]97[/C][C]4158615[/C][C]4161051.16612882[/C][C]-2436.16612881748[/C][/ROW]
[ROW][C]98[/C][C]4077141[/C][C]4108911.68779596[/C][C]-31770.6877959576[/C][/ROW]
[ROW][C]99[/C][C]4314459[/C][C]4348316.6558885[/C][C]-33857.655888495[/C][/ROW]
[ROW][C]100[/C][C]4387941[/C][C]4421129.15211169[/C][C]-33188.1521116905[/C][/ROW]
[ROW][C]101[/C][C]4706622[/C][C]4757044.26975436[/C][C]-50422.2697543632[/C][/ROW]
[ROW][C]102[/C][C]4755684[/C][C]4797267.50519041[/C][C]-41583.5051904116[/C][/ROW]
[ROW][C]103[/C][C]4771446[/C][C]4695442.27506637[/C][C]76003.724933628[/C][/ROW]
[ROW][C]104[/C][C]4853697[/C][C]4729672.28919557[/C][C]124024.710804425[/C][/ROW]
[ROW][C]105[/C][C]4853697[/C][C]4769278.07634154[/C][C]84418.9236584622[/C][/ROW]
[ROW][C]106[/C][C]4886109[/C][C]4808702.04818739[/C][C]77406.9518126138[/C][/ROW]
[ROW][C]107[/C][C]4739034[/C][C]4624206.7425048[/C][C]114827.257495199[/C][/ROW]
[ROW][C]108[/C][C]4812627[/C][C]4814454.20382262[/C][C]-1827.20382261928[/C][/ROW]
[ROW][C]109[/C][C]4861578[/C][C]4907005.27840535[/C][C]-45427.278405345[/C][/ROW]
[ROW][C]110[/C][C]4771446[/C][C]4804761.64980539[/C][C]-33315.6498053931[/C][/ROW]
[ROW][C]111[/C][C]5033184[/C][C]5080766.55700692[/C][C]-47582.5570069188[/C][/ROW]
[ROW][C]112[/C][C]5082246[/C][C]5160514.92226235[/C][C]-78268.9222623538[/C][/ROW]
[ROW][C]113[/C][C]5408808[/C][C]5524070.48694524[/C][C]-115262.486945244[/C][/ROW]
[ROW][C]114[/C][C]5466528[/C][C]5560147.36810164[/C][C]-93619.3681016443[/C][/ROW]
[ROW][C]115[/C][C]5548002[/C][C]5531594.82100758[/C][C]16407.1789924214[/C][/ROW]
[ROW][C]116[/C][C]5621595[/C][C]5590018.50486931[/C][C]31576.4951306935[/C][/ROW]
[ROW][C]117[/C][C]5629476[/C][C]5564531.37830576[/C][C]64944.6216942389[/C][/ROW]
[ROW][C]118[/C][C]5638134[/C][C]5584852.55347606[/C][C]53281.4465239421[/C][/ROW]
[ROW][C]119[/C][C]5491059[/C][C]5387528.53655974[/C][C]103530.463440265[/C][/ROW]
[ROW][C]120[/C][C]5638134[/C][C]5482104.10179898[/C][C]156029.898201019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211303&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211303&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
13865911816579.60643253649331.3935674642
14850038810021.75327846540016.2467215352
15874569838608.46107419635960.5389258041
16914862879266.04881200135595.9511879993
1711441881100546.4278620643641.5721379353
1811441881102050.3664976642137.6335023411
1910952371031186.8610238664050.1389761432
201046175968464.45840644777710.5415935531
2110864681017720.4277946168747.572205389
2211355301052115.9131822583414.0868177502
2311441881096866.8361605447321.1638394594
2411687191140751.0239673927967.976032607
2512423121281188.81344969-38876.8134496922
2611932501240799.93118894-47549.9311889368
2711932501256841.1211785-63591.1211784952
2812668431289326.3240663-22483.3240663002
2914708611591300.44340944-120439.44340944
3014874001547916.18917266-60516.1891726558
3114463301443555.631547292774.36845271289
3213482061348910.81070484-704.810704835458
3314217991371685.2508715250113.7491284807
3414217991411092.2642789710706.7357210263
3514296801400222.9057822229457.0942177828
3614708611418104.8361009252756.1638990818
3715032731518412.76778444-15139.7677844365
3815198121457806.7729621562005.2270378454
3915198121480096.1521441639715.8478558357
4015688741581299.98878164-12425.988781641
4117571301857698.24555015-100568.245550151
4218060811867972.06802645-61891.0680264502
4318139621798734.4773744815227.5226255185
4416914181676515.9660195814902.0339804241
4517571301754501.972195492628.02780451439
4617325991748019.04107473-15420.0410747339
4716835371741906.75662924-58369.756629244
4817895421758754.6933605730787.3066394278
4918139621801115.9459353612846.0540646366
5017728921801063.83844784-28171.838447839
5117815501776855.977939634694.02206037147
5218384931829610.897595788882.10240422096
5320512802066296.81955504-15016.819555037
5421571742128583.7905624528590.2094375533
5521571742135155.9846435522018.0153564466
5621082231987088.55742878121134.442571217
5721817052088213.3243929693491.6756070412
5821082232082231.4799696925991.5200303062
5920670422043715.2107727823326.7892272212
6022228862171888.9926681350997.0073318686
6122473062211765.1866537435540.8133462612
6221895862179232.0600290510353.939970952
6323366612194502.42950116142158.570498839
6423943812300156.4431947394224.5568052693
6525659872601839.12537863-35852.1253786292
6626798732728992.84608298-49119.8460829807
6726641112719261.7912728-55150.7912727962
6826553422616666.0977162638675.9022837398
6927210542692938.5147620428115.4852379584
7027130622601504.78412663111557.215873365
7126150492569744.8762098745304.1237901291
7227621242762357.69684806-233.69684805721
7328111862784050.9488609827135.0511390241
7427621242716033.4982821946090.5017178087
7529661422870475.7882882695666.2117117424
7630642662936102.46677908128163.533220921
7732927043184994.35709175107709.642908255
7833828363366127.428140316708.571859695
7933584163368630.07491094-10214.0749109411
8033093543349881.37232018-40527.372320184
8133504243419510.1049249-69086.1049248991
8233994863364908.8669301434577.1330698631
8332357613237228.68938609-1467.68938608794
8433662973416769.6837878-50472.6837878013
8534485483456014.68548473-7466.68548472598
8634153593377990.5821002437368.4178997567
8736280353605929.2818252822105.7181747244
8837015173689249.3825157812267.6174842203
8940123173928998.6982371883318.3017628156
9040692604040100.2734054429159.7265945645
9139957784009852.92578276-14074.925782762
9240368483949064.5419732387783.4580267677
9340613794027896.0707588833482.9292411185
9440859104080881.233118585028.76688142167
9539300663881098.7811669948967.2188330111
9640771414057770.5029263919370.4970736117
9741586154161051.16612882-2436.16612881748
9840771414108911.68779596-31770.6877959576
9943144594348316.6558885-33857.655888495
10043879414421129.15211169-33188.1521116905
10147066224757044.26975436-50422.2697543632
10247556844797267.50519041-41583.5051904116
10347714464695442.2750663776003.724933628
10448536974729672.28919557124024.710804425
10548536974769278.0763415484418.9236584622
10648861094808702.0481873977406.9518126138
10747390344624206.7425048114827.257495199
10848126274814454.20382262-1827.20382261928
10948615784907005.27840535-45427.278405345
11047714464804761.64980539-33315.6498053931
11150331845080766.55700692-47582.5570069188
11250822465160514.92226235-78268.9222623538
11354088085524070.48694524-115262.486945244
11454665285560147.36810164-93619.3681016443
11555480025531594.8210075816407.1789924214
11656215955590018.5048693131576.4951306935
11756294765564531.3783057664944.6216942389
11856381345584852.5534760653281.4465239421
11954910595387528.53655974103530.463440265
12056381345482104.10179898156029.898201019







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1215574020.312693375462684.664505455685355.9608813
1225471521.172135255357269.932836765585772.41143374
1235776552.314485325658146.734442955894957.89452768
1245846349.103625355723717.881902375968980.32534832
1256246108.957223676116995.772959836375222.1414875
1266334523.361357356199784.860072346469261.86264235
1276425996.088350476285051.947609856566940.22909109
1286504101.792322136356536.261088996651667.32355527
1296496938.569205266343218.199717186650658.93869334
1306492061.56338066331887.497415556652235.62934565
1316294036.046915116129893.707700166458178.38613006
1326418171.567867566285850.773089056550492.36264608

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 5574020.31269337 & 5462684.66450545 & 5685355.9608813 \tabularnewline
122 & 5471521.17213525 & 5357269.93283676 & 5585772.41143374 \tabularnewline
123 & 5776552.31448532 & 5658146.73444295 & 5894957.89452768 \tabularnewline
124 & 5846349.10362535 & 5723717.88190237 & 5968980.32534832 \tabularnewline
125 & 6246108.95722367 & 6116995.77295983 & 6375222.1414875 \tabularnewline
126 & 6334523.36135735 & 6199784.86007234 & 6469261.86264235 \tabularnewline
127 & 6425996.08835047 & 6285051.94760985 & 6566940.22909109 \tabularnewline
128 & 6504101.79232213 & 6356536.26108899 & 6651667.32355527 \tabularnewline
129 & 6496938.56920526 & 6343218.19971718 & 6650658.93869334 \tabularnewline
130 & 6492061.5633806 & 6331887.49741555 & 6652235.62934565 \tabularnewline
131 & 6294036.04691511 & 6129893.70770016 & 6458178.38613006 \tabularnewline
132 & 6418171.56786756 & 6285850.77308905 & 6550492.36264608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211303&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]121[/C][C]5574020.31269337[/C][C]5462684.66450545[/C][C]5685355.9608813[/C][/ROW]
[ROW][C]122[/C][C]5471521.17213525[/C][C]5357269.93283676[/C][C]5585772.41143374[/C][/ROW]
[ROW][C]123[/C][C]5776552.31448532[/C][C]5658146.73444295[/C][C]5894957.89452768[/C][/ROW]
[ROW][C]124[/C][C]5846349.10362535[/C][C]5723717.88190237[/C][C]5968980.32534832[/C][/ROW]
[ROW][C]125[/C][C]6246108.95722367[/C][C]6116995.77295983[/C][C]6375222.1414875[/C][/ROW]
[ROW][C]126[/C][C]6334523.36135735[/C][C]6199784.86007234[/C][C]6469261.86264235[/C][/ROW]
[ROW][C]127[/C][C]6425996.08835047[/C][C]6285051.94760985[/C][C]6566940.22909109[/C][/ROW]
[ROW][C]128[/C][C]6504101.79232213[/C][C]6356536.26108899[/C][C]6651667.32355527[/C][/ROW]
[ROW][C]129[/C][C]6496938.56920526[/C][C]6343218.19971718[/C][C]6650658.93869334[/C][/ROW]
[ROW][C]130[/C][C]6492061.5633806[/C][C]6331887.49741555[/C][C]6652235.62934565[/C][/ROW]
[ROW][C]131[/C][C]6294036.04691511[/C][C]6129893.70770016[/C][C]6458178.38613006[/C][/ROW]
[ROW][C]132[/C][C]6418171.56786756[/C][C]6285850.77308905[/C][C]6550492.36264608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211303&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211303&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
1215574020.312693375462684.664505455685355.9608813
1225471521.172135255357269.932836765585772.41143374
1235776552.314485325658146.734442955894957.89452768
1245846349.103625355723717.881902375968980.32534832
1256246108.957223676116995.772959836375222.1414875
1266334523.361357356199784.860072346469261.86264235
1276425996.088350476285051.947609856566940.22909109
1286504101.792322136356536.261088996651667.32355527
1296496938.569205266343218.199717186650658.93869334
1306492061.56338066331887.497415556652235.62934565
1316294036.046915116129893.707700166458178.38613006
1326418171.567867566285850.773089056550492.36264608



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=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')