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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 25 Nov 2011 09:57:22 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/25/t13222330740k3fz2ykkqwm7qp.htm/, Retrieved Thu, 28 Mar 2024 18:24:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147329, Retrieved Thu, 28 Mar 2024 18:24:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Nyrstar ] [2011-11-25 09:39:56] [25b6caf3839c2bdc14961e5bff2d6373]
- RMPD  [Decomposition by Loess] [loess] [2011-11-25 14:47:30] [25b6caf3839c2bdc14961e5bff2d6373]
- RMPD      [Exponential Smoothing] [exp. smoothing] [2011-11-25 14:57:22] [2adf2d2c11e011c12275478b9efd18e5] [Current]
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Dataseries X:
9.82
9.94
9.9
9.8
9.86
10.5
10.33
10.16
9.91
9.96
10.03
9.55
9.51
9.8
10.08
10.2
10.23
10.2
10.07
10.01
10.05
9.92
10.03
10.18
10.1
10.16
10.15
10.13
10.09
10.18
10.06
9.65
9.74
9.53
9.5
9
9.15
9.32
9.62
9.59
9.37
9.35
9.32
9.49
9.52
9.59
9.35
9.2
9.57
9.78
9.79
9.57
9.53
9.65
9.36
9.4
9.32
9.31
9.19
9.39
9.28
9.28
9.31
9.28
9.31
9.35
9.19
9.07
8.96
8.69
8.58
8.56
8.47
8.46
8.75
8.95
9.33
9.51
9.561
9.94
9.9
9.275
9.56
9.779
9.746
9.991
9.98
10.195
10.31
10.25
9.871
10.06
9.894
9.59
9.64
9.89
9.53
9.388
9.16
9.418
9.57
9.857
9.877
9.76
9.76
9.695
9.475
9.262
9.097
8.55
8.16
7.532
7.325
6.749
7.13
6.995
7.346
7.73
7.837
7.514
7.58
6.83
6.617
6.715
6.63
6.891
7.002
7.09
7.36
7.477
7.826
7.79
7.578
7.204
7.198
7.685
7.795
7.46
7.274
7.33
7.655
7.767
7.84
7.424
7.54
7.351
6.735
6.777
6.679
7.34
6.978
6.92
6.628
6.385
5.984
6.268
6.596
6.395
6.715
6.804
6.929
6.846
6.992
6.774
6.75
6.485
6.27
6.47
6.78
6.71
6.141
6.72
6.68
6.371
6.097
6.27
6.447
6.37
6.446
6.54
6.374
6.33
6.63




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147329&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147329&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147329&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0347340612933478
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0347340612933478 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147329&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0347340612933478[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147329&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147329&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0347340612933478
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
39.910.06-0.159999999999998
49.810.0144425501931-0.214442550193063
59.869.90699408951076-0.0469940895107577
610.59.965361793925260.534638206074737
710.3310.6239319501448-0.293931950144829
810.1610.4437224997724-0.283722499772425
99.9110.263867665075-0.353867665075029
109.9610.0015764039066-0.0415764039065785
1110.0310.0501322865449-0.020132286544932
129.5510.1194330104701-0.569433010470103
139.519.61965428938198-0.109654289381981
149.89.57584555057350.224154449426493
1510.089.873631344959070.206368655040935
1610.210.16079936647230.0392006335277184
1710.2310.28216096368-0.0521609636799703
1810.210.3103492015704-0.110349201570392
1910.0710.2765163256394-0.206516325639372
2010.0110.1393431749265-0.129343174926539
2110.0510.0748505611608-0.024850561160763
229.9210.1139874002462-0.193987400246233
2310.039.977249429995940.0527505700040578
2410.1810.08908167152770.090918328472279
2510.110.2422396343216-0.142239634321566
2610.1610.15729907414470.00270092585530257
2710.1510.2173928882689-0.0673928882689054
2810.1310.205052059557-0.0750520595570361
2910.0910.1824451967202-0.0924451967201918
3010.1810.1392341995910.0407658004089644
3110.0610.2306501614011-0.170650161401113
329.6510.1047227882353-0.454722788235287
339.749.678928419037240.0610715809627589
349.539.77104968307368-0.241049683073683
359.59.55267704860706-0.0526770486070589
3699.520847360772-0.52084736077199
379.159.002756216618460.147243783381544
389.329.15787059121550.162129408784505
399.629.333502004037670.286497995962328
409.599.64345324298985-0.0534532429898462
419.379.61159659477151-0.241596594771512
429.359.38320496384045-0.0332049638404524
439.329.36205162059117-0.0420516205911738
449.499.330590997024080.159409002975924
459.529.506127919104150.0138720808958457
469.599.536609752812260.0533902471877443
479.359.60846421293054-0.258464212930543
489.29.35948670111648-0.159486701116476
499.579.203947080264420.366052919735578
509.789.586661584815130.193338415184872
519.799.80337701317852-0.0133770131785163
529.579.81291237518285-0.242912375182851
539.539.58447504185434-0.0544750418543387
549.659.542582902411610.107417097588389
559.369.6663139344632-0.306313934463201
569.49.365674407488550.0343255925114523
579.329.40686667472277-0.0868666747227724
589.319.3238494423186-0.0138494423186017
599.199.31336839494023-0.123368394940231
609.399.189083309548710.200916690451287
619.289.3960619621897-0.116061962189706
629.289.28203065888118-0.00203065888118203
639.319.281960125851140.028039874148865
649.289.31293406455848-0.0329340645584821
659.319.281790130741470.028209869258534
669.359.312769974069370.0372300259306275
679.199.354063124072-0.164063124071999
689.079.1883645454645-0.118364545464503
698.969.06425326408738-0.104253264087379
708.698.95063212482254-0.260632124822539
718.588.67157931262394-0.091579312623935
728.568.558398391166050.00160160883394589
738.478.53845402154546-0.0684540215454597
748.468.446076335365320.0139236646346763
758.758.436559960786170.313440039213827
768.958.737447006320010.212552993679985
779.338.944829835030580.38517016496942
789.519.3382083591490.171791640851003
799.5619.5241753805320.0368246194679998
809.949.57645444912170.363545550878293
819.99.96808186256884-0.0680818625688353
829.2759.9257171029814-0.650717102981405
839.569.278115055241820.281884944758181
849.7799.572906064190720.206093935809276
859.7469.7990645435893-0.0530645435893078
869.9919.764221396479770.226778603520225
879.9810.0170983383945-0.0370983383944647
8810.19510.00480976243480.19019023756521
8910.3110.22641584180380.0835841581962224
9010.2510.3443190590777-0.0943190590777174
919.87110.2810429750986-0.41004297509858
9210.069.88780051726860.172199482731399
939.89410.0827817046565-0.188781704656476
949.599.91022454935588-0.320224549355876
959.649.595101850230910.0448981497690877
969.899.646661345316950.243338654683049
979.539.90511348506375-0.375113485063753
989.3889.53208427028159-0.144084270281587
999.169.38507963840622-0.225079638406219
1009.4189.149261708449930.268738291550067
1019.579.41659608074050.153403919259498
1029.8579.57392442187470.283075578125297
1039.8779.870756786355950.00624321364404601
1049.769.89097363852134-0.130973638521336
1059.769.76942439213312-0.00942439213312163
1069.6959.76909704471912-0.0740970447191174
1079.4759.70152335342619-0.226523353426188
1089.2629.4736552773839-0.211655277383908
1099.0979.2533036300062-0.156303630006196
1108.559.08287457014119-0.532874570141185
1118.168.51736567216024-0.357365672160238
1127.5328.11495291099929-0.582952910999285
1137.3257.4667045888575-0.1417045888575
1146.7497.25478261298258-0.505782612982576
1157.136.661214728702130.468785271297872
1166.9957.0584975450488-0.0634975450488078
1177.3466.92129201742710.424707982572895
1187.737.287043850525570.442956149474434
1197.8377.686429516571680.150570483428322
1207.5147.79865944097204-0.284659440972044
1217.587.465772062501590.114227937498408
1226.837.53573966268407-0.705739662684074
1236.6176.76122645798326-0.144226457983259
1246.7156.543216887351550.171783112648454
1256.636.64718361251544-0.0171836125154394
1266.8916.561586755865090.329413244134913
1277.0026.834028615677710.16797138432229
1287.096.950862944036290.139137055963712
1297.367.043695739066310.316304260933692
1307.4777.324682270652930.152317729347074
1317.8267.446972884000130.379027115999868
1327.797.80913803507911-0.019138035079111
1337.5787.77247329339564-0.194473293395639
1347.2047.55371844610292-0.349718446102917
1357.1987.167571304160560.0304286958394382
1367.6857.162628216346930.522371783653073
1377.7957.667772309898250.127227690101753
1387.467.78219144428445-0.322191444284453
1397.2747.43600042691048-0.162000426910485
1407.337.244373494152630.0856265058473724
1417.6557.303347650455070.351652349544935
1427.7677.640561964718110.126438035281891
1437.847.75695367118540.0830463288145991
1447.4247.83283820746063-0.408838207460634
1457.547.402637596103630.137362403896366
1467.3517.52340875025997-0.172408750259972
1476.7357.32842029416093-0.593420294160932
1486.7776.691808397290830.0851916027091697
1496.6796.73676744764101-0.0577674476410088
1507.346.636760949573890.703239050426114
1516.9787.32218729785526-0.344187297855263
1526.926.94823227515517-0.0282322751551662
1536.6286.88925165357948-0.261251653579476
1546.3856.58817732263106-0.203177322631058
1555.9846.33812014905337-0.354120149053372
1566.2685.924820118090940.343179881909057
1576.5966.220740149143820.375259850856184
1586.3956.56177444780439-0.166774447804388
1596.7156.354981693912190.360018306087815
1606.8046.687486591822570.116513408177433
1616.9296.78053357568370.148466424316301
1626.8466.9106904175659-0.0646904175659051
1636.9926.825443456637080.166556543362921
1646.7746.97722864182305-0.203228641823054
1656.756.75216968572141-0.00216968572140885
1666.4856.72809432372457-0.243094323724574
1676.276.45465067058426-0.184650670584261
1686.476.233237002874330.236762997125672
1696.786.441460743328490.338539256671512
1706.716.76321958661992-0.053219586619921
1716.1416.69137105423626-0.550371054236258
1726.726.103254432304330.616745567695668
1736.686.70367651065507-0.0236765106550729
1746.3716.66285412928277-0.291854129282767
1756.0976.34371685006754-0.246716850067543
1766.276.06114737187520.208852628124804
1776.4476.241401671861760.205598328138241
1786.376.42554293679312-0.0555429367931222
1796.4466.346613705022140.0993862949778617
1806.546.426065794683620.113934205316383
1816.3746.52402319235449-0.150023192354486
1826.336.35281227759582-0.0228122775958211
1836.636.308019914547570.321980085452433

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 9.9 & 10.06 & -0.159999999999998 \tabularnewline
4 & 9.8 & 10.0144425501931 & -0.214442550193063 \tabularnewline
5 & 9.86 & 9.90699408951076 & -0.0469940895107577 \tabularnewline
6 & 10.5 & 9.96536179392526 & 0.534638206074737 \tabularnewline
7 & 10.33 & 10.6239319501448 & -0.293931950144829 \tabularnewline
8 & 10.16 & 10.4437224997724 & -0.283722499772425 \tabularnewline
9 & 9.91 & 10.263867665075 & -0.353867665075029 \tabularnewline
10 & 9.96 & 10.0015764039066 & -0.0415764039065785 \tabularnewline
11 & 10.03 & 10.0501322865449 & -0.020132286544932 \tabularnewline
12 & 9.55 & 10.1194330104701 & -0.569433010470103 \tabularnewline
13 & 9.51 & 9.61965428938198 & -0.109654289381981 \tabularnewline
14 & 9.8 & 9.5758455505735 & 0.224154449426493 \tabularnewline
15 & 10.08 & 9.87363134495907 & 0.206368655040935 \tabularnewline
16 & 10.2 & 10.1607993664723 & 0.0392006335277184 \tabularnewline
17 & 10.23 & 10.28216096368 & -0.0521609636799703 \tabularnewline
18 & 10.2 & 10.3103492015704 & -0.110349201570392 \tabularnewline
19 & 10.07 & 10.2765163256394 & -0.206516325639372 \tabularnewline
20 & 10.01 & 10.1393431749265 & -0.129343174926539 \tabularnewline
21 & 10.05 & 10.0748505611608 & -0.024850561160763 \tabularnewline
22 & 9.92 & 10.1139874002462 & -0.193987400246233 \tabularnewline
23 & 10.03 & 9.97724942999594 & 0.0527505700040578 \tabularnewline
24 & 10.18 & 10.0890816715277 & 0.090918328472279 \tabularnewline
25 & 10.1 & 10.2422396343216 & -0.142239634321566 \tabularnewline
26 & 10.16 & 10.1572990741447 & 0.00270092585530257 \tabularnewline
27 & 10.15 & 10.2173928882689 & -0.0673928882689054 \tabularnewline
28 & 10.13 & 10.205052059557 & -0.0750520595570361 \tabularnewline
29 & 10.09 & 10.1824451967202 & -0.0924451967201918 \tabularnewline
30 & 10.18 & 10.139234199591 & 0.0407658004089644 \tabularnewline
31 & 10.06 & 10.2306501614011 & -0.170650161401113 \tabularnewline
32 & 9.65 & 10.1047227882353 & -0.454722788235287 \tabularnewline
33 & 9.74 & 9.67892841903724 & 0.0610715809627589 \tabularnewline
34 & 9.53 & 9.77104968307368 & -0.241049683073683 \tabularnewline
35 & 9.5 & 9.55267704860706 & -0.0526770486070589 \tabularnewline
36 & 9 & 9.520847360772 & -0.52084736077199 \tabularnewline
37 & 9.15 & 9.00275621661846 & 0.147243783381544 \tabularnewline
38 & 9.32 & 9.1578705912155 & 0.162129408784505 \tabularnewline
39 & 9.62 & 9.33350200403767 & 0.286497995962328 \tabularnewline
40 & 9.59 & 9.64345324298985 & -0.0534532429898462 \tabularnewline
41 & 9.37 & 9.61159659477151 & -0.241596594771512 \tabularnewline
42 & 9.35 & 9.38320496384045 & -0.0332049638404524 \tabularnewline
43 & 9.32 & 9.36205162059117 & -0.0420516205911738 \tabularnewline
44 & 9.49 & 9.33059099702408 & 0.159409002975924 \tabularnewline
45 & 9.52 & 9.50612791910415 & 0.0138720808958457 \tabularnewline
46 & 9.59 & 9.53660975281226 & 0.0533902471877443 \tabularnewline
47 & 9.35 & 9.60846421293054 & -0.258464212930543 \tabularnewline
48 & 9.2 & 9.35948670111648 & -0.159486701116476 \tabularnewline
49 & 9.57 & 9.20394708026442 & 0.366052919735578 \tabularnewline
50 & 9.78 & 9.58666158481513 & 0.193338415184872 \tabularnewline
51 & 9.79 & 9.80337701317852 & -0.0133770131785163 \tabularnewline
52 & 9.57 & 9.81291237518285 & -0.242912375182851 \tabularnewline
53 & 9.53 & 9.58447504185434 & -0.0544750418543387 \tabularnewline
54 & 9.65 & 9.54258290241161 & 0.107417097588389 \tabularnewline
55 & 9.36 & 9.6663139344632 & -0.306313934463201 \tabularnewline
56 & 9.4 & 9.36567440748855 & 0.0343255925114523 \tabularnewline
57 & 9.32 & 9.40686667472277 & -0.0868666747227724 \tabularnewline
58 & 9.31 & 9.3238494423186 & -0.0138494423186017 \tabularnewline
59 & 9.19 & 9.31336839494023 & -0.123368394940231 \tabularnewline
60 & 9.39 & 9.18908330954871 & 0.200916690451287 \tabularnewline
61 & 9.28 & 9.3960619621897 & -0.116061962189706 \tabularnewline
62 & 9.28 & 9.28203065888118 & -0.00203065888118203 \tabularnewline
63 & 9.31 & 9.28196012585114 & 0.028039874148865 \tabularnewline
64 & 9.28 & 9.31293406455848 & -0.0329340645584821 \tabularnewline
65 & 9.31 & 9.28179013074147 & 0.028209869258534 \tabularnewline
66 & 9.35 & 9.31276997406937 & 0.0372300259306275 \tabularnewline
67 & 9.19 & 9.354063124072 & -0.164063124071999 \tabularnewline
68 & 9.07 & 9.1883645454645 & -0.118364545464503 \tabularnewline
69 & 8.96 & 9.06425326408738 & -0.104253264087379 \tabularnewline
70 & 8.69 & 8.95063212482254 & -0.260632124822539 \tabularnewline
71 & 8.58 & 8.67157931262394 & -0.091579312623935 \tabularnewline
72 & 8.56 & 8.55839839116605 & 0.00160160883394589 \tabularnewline
73 & 8.47 & 8.53845402154546 & -0.0684540215454597 \tabularnewline
74 & 8.46 & 8.44607633536532 & 0.0139236646346763 \tabularnewline
75 & 8.75 & 8.43655996078617 & 0.313440039213827 \tabularnewline
76 & 8.95 & 8.73744700632001 & 0.212552993679985 \tabularnewline
77 & 9.33 & 8.94482983503058 & 0.38517016496942 \tabularnewline
78 & 9.51 & 9.338208359149 & 0.171791640851003 \tabularnewline
79 & 9.561 & 9.524175380532 & 0.0368246194679998 \tabularnewline
80 & 9.94 & 9.5764544491217 & 0.363545550878293 \tabularnewline
81 & 9.9 & 9.96808186256884 & -0.0680818625688353 \tabularnewline
82 & 9.275 & 9.9257171029814 & -0.650717102981405 \tabularnewline
83 & 9.56 & 9.27811505524182 & 0.281884944758181 \tabularnewline
84 & 9.779 & 9.57290606419072 & 0.206093935809276 \tabularnewline
85 & 9.746 & 9.7990645435893 & -0.0530645435893078 \tabularnewline
86 & 9.991 & 9.76422139647977 & 0.226778603520225 \tabularnewline
87 & 9.98 & 10.0170983383945 & -0.0370983383944647 \tabularnewline
88 & 10.195 & 10.0048097624348 & 0.19019023756521 \tabularnewline
89 & 10.31 & 10.2264158418038 & 0.0835841581962224 \tabularnewline
90 & 10.25 & 10.3443190590777 & -0.0943190590777174 \tabularnewline
91 & 9.871 & 10.2810429750986 & -0.41004297509858 \tabularnewline
92 & 10.06 & 9.8878005172686 & 0.172199482731399 \tabularnewline
93 & 9.894 & 10.0827817046565 & -0.188781704656476 \tabularnewline
94 & 9.59 & 9.91022454935588 & -0.320224549355876 \tabularnewline
95 & 9.64 & 9.59510185023091 & 0.0448981497690877 \tabularnewline
96 & 9.89 & 9.64666134531695 & 0.243338654683049 \tabularnewline
97 & 9.53 & 9.90511348506375 & -0.375113485063753 \tabularnewline
98 & 9.388 & 9.53208427028159 & -0.144084270281587 \tabularnewline
99 & 9.16 & 9.38507963840622 & -0.225079638406219 \tabularnewline
100 & 9.418 & 9.14926170844993 & 0.268738291550067 \tabularnewline
101 & 9.57 & 9.4165960807405 & 0.153403919259498 \tabularnewline
102 & 9.857 & 9.5739244218747 & 0.283075578125297 \tabularnewline
103 & 9.877 & 9.87075678635595 & 0.00624321364404601 \tabularnewline
104 & 9.76 & 9.89097363852134 & -0.130973638521336 \tabularnewline
105 & 9.76 & 9.76942439213312 & -0.00942439213312163 \tabularnewline
106 & 9.695 & 9.76909704471912 & -0.0740970447191174 \tabularnewline
107 & 9.475 & 9.70152335342619 & -0.226523353426188 \tabularnewline
108 & 9.262 & 9.4736552773839 & -0.211655277383908 \tabularnewline
109 & 9.097 & 9.2533036300062 & -0.156303630006196 \tabularnewline
110 & 8.55 & 9.08287457014119 & -0.532874570141185 \tabularnewline
111 & 8.16 & 8.51736567216024 & -0.357365672160238 \tabularnewline
112 & 7.532 & 8.11495291099929 & -0.582952910999285 \tabularnewline
113 & 7.325 & 7.4667045888575 & -0.1417045888575 \tabularnewline
114 & 6.749 & 7.25478261298258 & -0.505782612982576 \tabularnewline
115 & 7.13 & 6.66121472870213 & 0.468785271297872 \tabularnewline
116 & 6.995 & 7.0584975450488 & -0.0634975450488078 \tabularnewline
117 & 7.346 & 6.9212920174271 & 0.424707982572895 \tabularnewline
118 & 7.73 & 7.28704385052557 & 0.442956149474434 \tabularnewline
119 & 7.837 & 7.68642951657168 & 0.150570483428322 \tabularnewline
120 & 7.514 & 7.79865944097204 & -0.284659440972044 \tabularnewline
121 & 7.58 & 7.46577206250159 & 0.114227937498408 \tabularnewline
122 & 6.83 & 7.53573966268407 & -0.705739662684074 \tabularnewline
123 & 6.617 & 6.76122645798326 & -0.144226457983259 \tabularnewline
124 & 6.715 & 6.54321688735155 & 0.171783112648454 \tabularnewline
125 & 6.63 & 6.64718361251544 & -0.0171836125154394 \tabularnewline
126 & 6.891 & 6.56158675586509 & 0.329413244134913 \tabularnewline
127 & 7.002 & 6.83402861567771 & 0.16797138432229 \tabularnewline
128 & 7.09 & 6.95086294403629 & 0.139137055963712 \tabularnewline
129 & 7.36 & 7.04369573906631 & 0.316304260933692 \tabularnewline
130 & 7.477 & 7.32468227065293 & 0.152317729347074 \tabularnewline
131 & 7.826 & 7.44697288400013 & 0.379027115999868 \tabularnewline
132 & 7.79 & 7.80913803507911 & -0.019138035079111 \tabularnewline
133 & 7.578 & 7.77247329339564 & -0.194473293395639 \tabularnewline
134 & 7.204 & 7.55371844610292 & -0.349718446102917 \tabularnewline
135 & 7.198 & 7.16757130416056 & 0.0304286958394382 \tabularnewline
136 & 7.685 & 7.16262821634693 & 0.522371783653073 \tabularnewline
137 & 7.795 & 7.66777230989825 & 0.127227690101753 \tabularnewline
138 & 7.46 & 7.78219144428445 & -0.322191444284453 \tabularnewline
139 & 7.274 & 7.43600042691048 & -0.162000426910485 \tabularnewline
140 & 7.33 & 7.24437349415263 & 0.0856265058473724 \tabularnewline
141 & 7.655 & 7.30334765045507 & 0.351652349544935 \tabularnewline
142 & 7.767 & 7.64056196471811 & 0.126438035281891 \tabularnewline
143 & 7.84 & 7.7569536711854 & 0.0830463288145991 \tabularnewline
144 & 7.424 & 7.83283820746063 & -0.408838207460634 \tabularnewline
145 & 7.54 & 7.40263759610363 & 0.137362403896366 \tabularnewline
146 & 7.351 & 7.52340875025997 & -0.172408750259972 \tabularnewline
147 & 6.735 & 7.32842029416093 & -0.593420294160932 \tabularnewline
148 & 6.777 & 6.69180839729083 & 0.0851916027091697 \tabularnewline
149 & 6.679 & 6.73676744764101 & -0.0577674476410088 \tabularnewline
150 & 7.34 & 6.63676094957389 & 0.703239050426114 \tabularnewline
151 & 6.978 & 7.32218729785526 & -0.344187297855263 \tabularnewline
152 & 6.92 & 6.94823227515517 & -0.0282322751551662 \tabularnewline
153 & 6.628 & 6.88925165357948 & -0.261251653579476 \tabularnewline
154 & 6.385 & 6.58817732263106 & -0.203177322631058 \tabularnewline
155 & 5.984 & 6.33812014905337 & -0.354120149053372 \tabularnewline
156 & 6.268 & 5.92482011809094 & 0.343179881909057 \tabularnewline
157 & 6.596 & 6.22074014914382 & 0.375259850856184 \tabularnewline
158 & 6.395 & 6.56177444780439 & -0.166774447804388 \tabularnewline
159 & 6.715 & 6.35498169391219 & 0.360018306087815 \tabularnewline
160 & 6.804 & 6.68748659182257 & 0.116513408177433 \tabularnewline
161 & 6.929 & 6.7805335756837 & 0.148466424316301 \tabularnewline
162 & 6.846 & 6.9106904175659 & -0.0646904175659051 \tabularnewline
163 & 6.992 & 6.82544345663708 & 0.166556543362921 \tabularnewline
164 & 6.774 & 6.97722864182305 & -0.203228641823054 \tabularnewline
165 & 6.75 & 6.75216968572141 & -0.00216968572140885 \tabularnewline
166 & 6.485 & 6.72809432372457 & -0.243094323724574 \tabularnewline
167 & 6.27 & 6.45465067058426 & -0.184650670584261 \tabularnewline
168 & 6.47 & 6.23323700287433 & 0.236762997125672 \tabularnewline
169 & 6.78 & 6.44146074332849 & 0.338539256671512 \tabularnewline
170 & 6.71 & 6.76321958661992 & -0.053219586619921 \tabularnewline
171 & 6.141 & 6.69137105423626 & -0.550371054236258 \tabularnewline
172 & 6.72 & 6.10325443230433 & 0.616745567695668 \tabularnewline
173 & 6.68 & 6.70367651065507 & -0.0236765106550729 \tabularnewline
174 & 6.371 & 6.66285412928277 & -0.291854129282767 \tabularnewline
175 & 6.097 & 6.34371685006754 & -0.246716850067543 \tabularnewline
176 & 6.27 & 6.0611473718752 & 0.208852628124804 \tabularnewline
177 & 6.447 & 6.24140167186176 & 0.205598328138241 \tabularnewline
178 & 6.37 & 6.42554293679312 & -0.0555429367931222 \tabularnewline
179 & 6.446 & 6.34661370502214 & 0.0993862949778617 \tabularnewline
180 & 6.54 & 6.42606579468362 & 0.113934205316383 \tabularnewline
181 & 6.374 & 6.52402319235449 & -0.150023192354486 \tabularnewline
182 & 6.33 & 6.35281227759582 & -0.0228122775958211 \tabularnewline
183 & 6.63 & 6.30801991454757 & 0.321980085452433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147329&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]9.9[/C][C]10.06[/C][C]-0.159999999999998[/C][/ROW]
[ROW][C]4[/C][C]9.8[/C][C]10.0144425501931[/C][C]-0.214442550193063[/C][/ROW]
[ROW][C]5[/C][C]9.86[/C][C]9.90699408951076[/C][C]-0.0469940895107577[/C][/ROW]
[ROW][C]6[/C][C]10.5[/C][C]9.96536179392526[/C][C]0.534638206074737[/C][/ROW]
[ROW][C]7[/C][C]10.33[/C][C]10.6239319501448[/C][C]-0.293931950144829[/C][/ROW]
[ROW][C]8[/C][C]10.16[/C][C]10.4437224997724[/C][C]-0.283722499772425[/C][/ROW]
[ROW][C]9[/C][C]9.91[/C][C]10.263867665075[/C][C]-0.353867665075029[/C][/ROW]
[ROW][C]10[/C][C]9.96[/C][C]10.0015764039066[/C][C]-0.0415764039065785[/C][/ROW]
[ROW][C]11[/C][C]10.03[/C][C]10.0501322865449[/C][C]-0.020132286544932[/C][/ROW]
[ROW][C]12[/C][C]9.55[/C][C]10.1194330104701[/C][C]-0.569433010470103[/C][/ROW]
[ROW][C]13[/C][C]9.51[/C][C]9.61965428938198[/C][C]-0.109654289381981[/C][/ROW]
[ROW][C]14[/C][C]9.8[/C][C]9.5758455505735[/C][C]0.224154449426493[/C][/ROW]
[ROW][C]15[/C][C]10.08[/C][C]9.87363134495907[/C][C]0.206368655040935[/C][/ROW]
[ROW][C]16[/C][C]10.2[/C][C]10.1607993664723[/C][C]0.0392006335277184[/C][/ROW]
[ROW][C]17[/C][C]10.23[/C][C]10.28216096368[/C][C]-0.0521609636799703[/C][/ROW]
[ROW][C]18[/C][C]10.2[/C][C]10.3103492015704[/C][C]-0.110349201570392[/C][/ROW]
[ROW][C]19[/C][C]10.07[/C][C]10.2765163256394[/C][C]-0.206516325639372[/C][/ROW]
[ROW][C]20[/C][C]10.01[/C][C]10.1393431749265[/C][C]-0.129343174926539[/C][/ROW]
[ROW][C]21[/C][C]10.05[/C][C]10.0748505611608[/C][C]-0.024850561160763[/C][/ROW]
[ROW][C]22[/C][C]9.92[/C][C]10.1139874002462[/C][C]-0.193987400246233[/C][/ROW]
[ROW][C]23[/C][C]10.03[/C][C]9.97724942999594[/C][C]0.0527505700040578[/C][/ROW]
[ROW][C]24[/C][C]10.18[/C][C]10.0890816715277[/C][C]0.090918328472279[/C][/ROW]
[ROW][C]25[/C][C]10.1[/C][C]10.2422396343216[/C][C]-0.142239634321566[/C][/ROW]
[ROW][C]26[/C][C]10.16[/C][C]10.1572990741447[/C][C]0.00270092585530257[/C][/ROW]
[ROW][C]27[/C][C]10.15[/C][C]10.2173928882689[/C][C]-0.0673928882689054[/C][/ROW]
[ROW][C]28[/C][C]10.13[/C][C]10.205052059557[/C][C]-0.0750520595570361[/C][/ROW]
[ROW][C]29[/C][C]10.09[/C][C]10.1824451967202[/C][C]-0.0924451967201918[/C][/ROW]
[ROW][C]30[/C][C]10.18[/C][C]10.139234199591[/C][C]0.0407658004089644[/C][/ROW]
[ROW][C]31[/C][C]10.06[/C][C]10.2306501614011[/C][C]-0.170650161401113[/C][/ROW]
[ROW][C]32[/C][C]9.65[/C][C]10.1047227882353[/C][C]-0.454722788235287[/C][/ROW]
[ROW][C]33[/C][C]9.74[/C][C]9.67892841903724[/C][C]0.0610715809627589[/C][/ROW]
[ROW][C]34[/C][C]9.53[/C][C]9.77104968307368[/C][C]-0.241049683073683[/C][/ROW]
[ROW][C]35[/C][C]9.5[/C][C]9.55267704860706[/C][C]-0.0526770486070589[/C][/ROW]
[ROW][C]36[/C][C]9[/C][C]9.520847360772[/C][C]-0.52084736077199[/C][/ROW]
[ROW][C]37[/C][C]9.15[/C][C]9.00275621661846[/C][C]0.147243783381544[/C][/ROW]
[ROW][C]38[/C][C]9.32[/C][C]9.1578705912155[/C][C]0.162129408784505[/C][/ROW]
[ROW][C]39[/C][C]9.62[/C][C]9.33350200403767[/C][C]0.286497995962328[/C][/ROW]
[ROW][C]40[/C][C]9.59[/C][C]9.64345324298985[/C][C]-0.0534532429898462[/C][/ROW]
[ROW][C]41[/C][C]9.37[/C][C]9.61159659477151[/C][C]-0.241596594771512[/C][/ROW]
[ROW][C]42[/C][C]9.35[/C][C]9.38320496384045[/C][C]-0.0332049638404524[/C][/ROW]
[ROW][C]43[/C][C]9.32[/C][C]9.36205162059117[/C][C]-0.0420516205911738[/C][/ROW]
[ROW][C]44[/C][C]9.49[/C][C]9.33059099702408[/C][C]0.159409002975924[/C][/ROW]
[ROW][C]45[/C][C]9.52[/C][C]9.50612791910415[/C][C]0.0138720808958457[/C][/ROW]
[ROW][C]46[/C][C]9.59[/C][C]9.53660975281226[/C][C]0.0533902471877443[/C][/ROW]
[ROW][C]47[/C][C]9.35[/C][C]9.60846421293054[/C][C]-0.258464212930543[/C][/ROW]
[ROW][C]48[/C][C]9.2[/C][C]9.35948670111648[/C][C]-0.159486701116476[/C][/ROW]
[ROW][C]49[/C][C]9.57[/C][C]9.20394708026442[/C][C]0.366052919735578[/C][/ROW]
[ROW][C]50[/C][C]9.78[/C][C]9.58666158481513[/C][C]0.193338415184872[/C][/ROW]
[ROW][C]51[/C][C]9.79[/C][C]9.80337701317852[/C][C]-0.0133770131785163[/C][/ROW]
[ROW][C]52[/C][C]9.57[/C][C]9.81291237518285[/C][C]-0.242912375182851[/C][/ROW]
[ROW][C]53[/C][C]9.53[/C][C]9.58447504185434[/C][C]-0.0544750418543387[/C][/ROW]
[ROW][C]54[/C][C]9.65[/C][C]9.54258290241161[/C][C]0.107417097588389[/C][/ROW]
[ROW][C]55[/C][C]9.36[/C][C]9.6663139344632[/C][C]-0.306313934463201[/C][/ROW]
[ROW][C]56[/C][C]9.4[/C][C]9.36567440748855[/C][C]0.0343255925114523[/C][/ROW]
[ROW][C]57[/C][C]9.32[/C][C]9.40686667472277[/C][C]-0.0868666747227724[/C][/ROW]
[ROW][C]58[/C][C]9.31[/C][C]9.3238494423186[/C][C]-0.0138494423186017[/C][/ROW]
[ROW][C]59[/C][C]9.19[/C][C]9.31336839494023[/C][C]-0.123368394940231[/C][/ROW]
[ROW][C]60[/C][C]9.39[/C][C]9.18908330954871[/C][C]0.200916690451287[/C][/ROW]
[ROW][C]61[/C][C]9.28[/C][C]9.3960619621897[/C][C]-0.116061962189706[/C][/ROW]
[ROW][C]62[/C][C]9.28[/C][C]9.28203065888118[/C][C]-0.00203065888118203[/C][/ROW]
[ROW][C]63[/C][C]9.31[/C][C]9.28196012585114[/C][C]0.028039874148865[/C][/ROW]
[ROW][C]64[/C][C]9.28[/C][C]9.31293406455848[/C][C]-0.0329340645584821[/C][/ROW]
[ROW][C]65[/C][C]9.31[/C][C]9.28179013074147[/C][C]0.028209869258534[/C][/ROW]
[ROW][C]66[/C][C]9.35[/C][C]9.31276997406937[/C][C]0.0372300259306275[/C][/ROW]
[ROW][C]67[/C][C]9.19[/C][C]9.354063124072[/C][C]-0.164063124071999[/C][/ROW]
[ROW][C]68[/C][C]9.07[/C][C]9.1883645454645[/C][C]-0.118364545464503[/C][/ROW]
[ROW][C]69[/C][C]8.96[/C][C]9.06425326408738[/C][C]-0.104253264087379[/C][/ROW]
[ROW][C]70[/C][C]8.69[/C][C]8.95063212482254[/C][C]-0.260632124822539[/C][/ROW]
[ROW][C]71[/C][C]8.58[/C][C]8.67157931262394[/C][C]-0.091579312623935[/C][/ROW]
[ROW][C]72[/C][C]8.56[/C][C]8.55839839116605[/C][C]0.00160160883394589[/C][/ROW]
[ROW][C]73[/C][C]8.47[/C][C]8.53845402154546[/C][C]-0.0684540215454597[/C][/ROW]
[ROW][C]74[/C][C]8.46[/C][C]8.44607633536532[/C][C]0.0139236646346763[/C][/ROW]
[ROW][C]75[/C][C]8.75[/C][C]8.43655996078617[/C][C]0.313440039213827[/C][/ROW]
[ROW][C]76[/C][C]8.95[/C][C]8.73744700632001[/C][C]0.212552993679985[/C][/ROW]
[ROW][C]77[/C][C]9.33[/C][C]8.94482983503058[/C][C]0.38517016496942[/C][/ROW]
[ROW][C]78[/C][C]9.51[/C][C]9.338208359149[/C][C]0.171791640851003[/C][/ROW]
[ROW][C]79[/C][C]9.561[/C][C]9.524175380532[/C][C]0.0368246194679998[/C][/ROW]
[ROW][C]80[/C][C]9.94[/C][C]9.5764544491217[/C][C]0.363545550878293[/C][/ROW]
[ROW][C]81[/C][C]9.9[/C][C]9.96808186256884[/C][C]-0.0680818625688353[/C][/ROW]
[ROW][C]82[/C][C]9.275[/C][C]9.9257171029814[/C][C]-0.650717102981405[/C][/ROW]
[ROW][C]83[/C][C]9.56[/C][C]9.27811505524182[/C][C]0.281884944758181[/C][/ROW]
[ROW][C]84[/C][C]9.779[/C][C]9.57290606419072[/C][C]0.206093935809276[/C][/ROW]
[ROW][C]85[/C][C]9.746[/C][C]9.7990645435893[/C][C]-0.0530645435893078[/C][/ROW]
[ROW][C]86[/C][C]9.991[/C][C]9.76422139647977[/C][C]0.226778603520225[/C][/ROW]
[ROW][C]87[/C][C]9.98[/C][C]10.0170983383945[/C][C]-0.0370983383944647[/C][/ROW]
[ROW][C]88[/C][C]10.195[/C][C]10.0048097624348[/C][C]0.19019023756521[/C][/ROW]
[ROW][C]89[/C][C]10.31[/C][C]10.2264158418038[/C][C]0.0835841581962224[/C][/ROW]
[ROW][C]90[/C][C]10.25[/C][C]10.3443190590777[/C][C]-0.0943190590777174[/C][/ROW]
[ROW][C]91[/C][C]9.871[/C][C]10.2810429750986[/C][C]-0.41004297509858[/C][/ROW]
[ROW][C]92[/C][C]10.06[/C][C]9.8878005172686[/C][C]0.172199482731399[/C][/ROW]
[ROW][C]93[/C][C]9.894[/C][C]10.0827817046565[/C][C]-0.188781704656476[/C][/ROW]
[ROW][C]94[/C][C]9.59[/C][C]9.91022454935588[/C][C]-0.320224549355876[/C][/ROW]
[ROW][C]95[/C][C]9.64[/C][C]9.59510185023091[/C][C]0.0448981497690877[/C][/ROW]
[ROW][C]96[/C][C]9.89[/C][C]9.64666134531695[/C][C]0.243338654683049[/C][/ROW]
[ROW][C]97[/C][C]9.53[/C][C]9.90511348506375[/C][C]-0.375113485063753[/C][/ROW]
[ROW][C]98[/C][C]9.388[/C][C]9.53208427028159[/C][C]-0.144084270281587[/C][/ROW]
[ROW][C]99[/C][C]9.16[/C][C]9.38507963840622[/C][C]-0.225079638406219[/C][/ROW]
[ROW][C]100[/C][C]9.418[/C][C]9.14926170844993[/C][C]0.268738291550067[/C][/ROW]
[ROW][C]101[/C][C]9.57[/C][C]9.4165960807405[/C][C]0.153403919259498[/C][/ROW]
[ROW][C]102[/C][C]9.857[/C][C]9.5739244218747[/C][C]0.283075578125297[/C][/ROW]
[ROW][C]103[/C][C]9.877[/C][C]9.87075678635595[/C][C]0.00624321364404601[/C][/ROW]
[ROW][C]104[/C][C]9.76[/C][C]9.89097363852134[/C][C]-0.130973638521336[/C][/ROW]
[ROW][C]105[/C][C]9.76[/C][C]9.76942439213312[/C][C]-0.00942439213312163[/C][/ROW]
[ROW][C]106[/C][C]9.695[/C][C]9.76909704471912[/C][C]-0.0740970447191174[/C][/ROW]
[ROW][C]107[/C][C]9.475[/C][C]9.70152335342619[/C][C]-0.226523353426188[/C][/ROW]
[ROW][C]108[/C][C]9.262[/C][C]9.4736552773839[/C][C]-0.211655277383908[/C][/ROW]
[ROW][C]109[/C][C]9.097[/C][C]9.2533036300062[/C][C]-0.156303630006196[/C][/ROW]
[ROW][C]110[/C][C]8.55[/C][C]9.08287457014119[/C][C]-0.532874570141185[/C][/ROW]
[ROW][C]111[/C][C]8.16[/C][C]8.51736567216024[/C][C]-0.357365672160238[/C][/ROW]
[ROW][C]112[/C][C]7.532[/C][C]8.11495291099929[/C][C]-0.582952910999285[/C][/ROW]
[ROW][C]113[/C][C]7.325[/C][C]7.4667045888575[/C][C]-0.1417045888575[/C][/ROW]
[ROW][C]114[/C][C]6.749[/C][C]7.25478261298258[/C][C]-0.505782612982576[/C][/ROW]
[ROW][C]115[/C][C]7.13[/C][C]6.66121472870213[/C][C]0.468785271297872[/C][/ROW]
[ROW][C]116[/C][C]6.995[/C][C]7.0584975450488[/C][C]-0.0634975450488078[/C][/ROW]
[ROW][C]117[/C][C]7.346[/C][C]6.9212920174271[/C][C]0.424707982572895[/C][/ROW]
[ROW][C]118[/C][C]7.73[/C][C]7.28704385052557[/C][C]0.442956149474434[/C][/ROW]
[ROW][C]119[/C][C]7.837[/C][C]7.68642951657168[/C][C]0.150570483428322[/C][/ROW]
[ROW][C]120[/C][C]7.514[/C][C]7.79865944097204[/C][C]-0.284659440972044[/C][/ROW]
[ROW][C]121[/C][C]7.58[/C][C]7.46577206250159[/C][C]0.114227937498408[/C][/ROW]
[ROW][C]122[/C][C]6.83[/C][C]7.53573966268407[/C][C]-0.705739662684074[/C][/ROW]
[ROW][C]123[/C][C]6.617[/C][C]6.76122645798326[/C][C]-0.144226457983259[/C][/ROW]
[ROW][C]124[/C][C]6.715[/C][C]6.54321688735155[/C][C]0.171783112648454[/C][/ROW]
[ROW][C]125[/C][C]6.63[/C][C]6.64718361251544[/C][C]-0.0171836125154394[/C][/ROW]
[ROW][C]126[/C][C]6.891[/C][C]6.56158675586509[/C][C]0.329413244134913[/C][/ROW]
[ROW][C]127[/C][C]7.002[/C][C]6.83402861567771[/C][C]0.16797138432229[/C][/ROW]
[ROW][C]128[/C][C]7.09[/C][C]6.95086294403629[/C][C]0.139137055963712[/C][/ROW]
[ROW][C]129[/C][C]7.36[/C][C]7.04369573906631[/C][C]0.316304260933692[/C][/ROW]
[ROW][C]130[/C][C]7.477[/C][C]7.32468227065293[/C][C]0.152317729347074[/C][/ROW]
[ROW][C]131[/C][C]7.826[/C][C]7.44697288400013[/C][C]0.379027115999868[/C][/ROW]
[ROW][C]132[/C][C]7.79[/C][C]7.80913803507911[/C][C]-0.019138035079111[/C][/ROW]
[ROW][C]133[/C][C]7.578[/C][C]7.77247329339564[/C][C]-0.194473293395639[/C][/ROW]
[ROW][C]134[/C][C]7.204[/C][C]7.55371844610292[/C][C]-0.349718446102917[/C][/ROW]
[ROW][C]135[/C][C]7.198[/C][C]7.16757130416056[/C][C]0.0304286958394382[/C][/ROW]
[ROW][C]136[/C][C]7.685[/C][C]7.16262821634693[/C][C]0.522371783653073[/C][/ROW]
[ROW][C]137[/C][C]7.795[/C][C]7.66777230989825[/C][C]0.127227690101753[/C][/ROW]
[ROW][C]138[/C][C]7.46[/C][C]7.78219144428445[/C][C]-0.322191444284453[/C][/ROW]
[ROW][C]139[/C][C]7.274[/C][C]7.43600042691048[/C][C]-0.162000426910485[/C][/ROW]
[ROW][C]140[/C][C]7.33[/C][C]7.24437349415263[/C][C]0.0856265058473724[/C][/ROW]
[ROW][C]141[/C][C]7.655[/C][C]7.30334765045507[/C][C]0.351652349544935[/C][/ROW]
[ROW][C]142[/C][C]7.767[/C][C]7.64056196471811[/C][C]0.126438035281891[/C][/ROW]
[ROW][C]143[/C][C]7.84[/C][C]7.7569536711854[/C][C]0.0830463288145991[/C][/ROW]
[ROW][C]144[/C][C]7.424[/C][C]7.83283820746063[/C][C]-0.408838207460634[/C][/ROW]
[ROW][C]145[/C][C]7.54[/C][C]7.40263759610363[/C][C]0.137362403896366[/C][/ROW]
[ROW][C]146[/C][C]7.351[/C][C]7.52340875025997[/C][C]-0.172408750259972[/C][/ROW]
[ROW][C]147[/C][C]6.735[/C][C]7.32842029416093[/C][C]-0.593420294160932[/C][/ROW]
[ROW][C]148[/C][C]6.777[/C][C]6.69180839729083[/C][C]0.0851916027091697[/C][/ROW]
[ROW][C]149[/C][C]6.679[/C][C]6.73676744764101[/C][C]-0.0577674476410088[/C][/ROW]
[ROW][C]150[/C][C]7.34[/C][C]6.63676094957389[/C][C]0.703239050426114[/C][/ROW]
[ROW][C]151[/C][C]6.978[/C][C]7.32218729785526[/C][C]-0.344187297855263[/C][/ROW]
[ROW][C]152[/C][C]6.92[/C][C]6.94823227515517[/C][C]-0.0282322751551662[/C][/ROW]
[ROW][C]153[/C][C]6.628[/C][C]6.88925165357948[/C][C]-0.261251653579476[/C][/ROW]
[ROW][C]154[/C][C]6.385[/C][C]6.58817732263106[/C][C]-0.203177322631058[/C][/ROW]
[ROW][C]155[/C][C]5.984[/C][C]6.33812014905337[/C][C]-0.354120149053372[/C][/ROW]
[ROW][C]156[/C][C]6.268[/C][C]5.92482011809094[/C][C]0.343179881909057[/C][/ROW]
[ROW][C]157[/C][C]6.596[/C][C]6.22074014914382[/C][C]0.375259850856184[/C][/ROW]
[ROW][C]158[/C][C]6.395[/C][C]6.56177444780439[/C][C]-0.166774447804388[/C][/ROW]
[ROW][C]159[/C][C]6.715[/C][C]6.35498169391219[/C][C]0.360018306087815[/C][/ROW]
[ROW][C]160[/C][C]6.804[/C][C]6.68748659182257[/C][C]0.116513408177433[/C][/ROW]
[ROW][C]161[/C][C]6.929[/C][C]6.7805335756837[/C][C]0.148466424316301[/C][/ROW]
[ROW][C]162[/C][C]6.846[/C][C]6.9106904175659[/C][C]-0.0646904175659051[/C][/ROW]
[ROW][C]163[/C][C]6.992[/C][C]6.82544345663708[/C][C]0.166556543362921[/C][/ROW]
[ROW][C]164[/C][C]6.774[/C][C]6.97722864182305[/C][C]-0.203228641823054[/C][/ROW]
[ROW][C]165[/C][C]6.75[/C][C]6.75216968572141[/C][C]-0.00216968572140885[/C][/ROW]
[ROW][C]166[/C][C]6.485[/C][C]6.72809432372457[/C][C]-0.243094323724574[/C][/ROW]
[ROW][C]167[/C][C]6.27[/C][C]6.45465067058426[/C][C]-0.184650670584261[/C][/ROW]
[ROW][C]168[/C][C]6.47[/C][C]6.23323700287433[/C][C]0.236762997125672[/C][/ROW]
[ROW][C]169[/C][C]6.78[/C][C]6.44146074332849[/C][C]0.338539256671512[/C][/ROW]
[ROW][C]170[/C][C]6.71[/C][C]6.76321958661992[/C][C]-0.053219586619921[/C][/ROW]
[ROW][C]171[/C][C]6.141[/C][C]6.69137105423626[/C][C]-0.550371054236258[/C][/ROW]
[ROW][C]172[/C][C]6.72[/C][C]6.10325443230433[/C][C]0.616745567695668[/C][/ROW]
[ROW][C]173[/C][C]6.68[/C][C]6.70367651065507[/C][C]-0.0236765106550729[/C][/ROW]
[ROW][C]174[/C][C]6.371[/C][C]6.66285412928277[/C][C]-0.291854129282767[/C][/ROW]
[ROW][C]175[/C][C]6.097[/C][C]6.34371685006754[/C][C]-0.246716850067543[/C][/ROW]
[ROW][C]176[/C][C]6.27[/C][C]6.0611473718752[/C][C]0.208852628124804[/C][/ROW]
[ROW][C]177[/C][C]6.447[/C][C]6.24140167186176[/C][C]0.205598328138241[/C][/ROW]
[ROW][C]178[/C][C]6.37[/C][C]6.42554293679312[/C][C]-0.0555429367931222[/C][/ROW]
[ROW][C]179[/C][C]6.446[/C][C]6.34661370502214[/C][C]0.0993862949778617[/C][/ROW]
[ROW][C]180[/C][C]6.54[/C][C]6.42606579468362[/C][C]0.113934205316383[/C][/ROW]
[ROW][C]181[/C][C]6.374[/C][C]6.52402319235449[/C][C]-0.150023192354486[/C][/ROW]
[ROW][C]182[/C][C]6.33[/C][C]6.35281227759582[/C][C]-0.0228122775958211[/C][/ROW]
[ROW][C]183[/C][C]6.63[/C][C]6.30801991454757[/C][C]0.321980085452433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147329&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147329&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
39.910.06-0.159999999999998
49.810.0144425501931-0.214442550193063
59.869.90699408951076-0.0469940895107577
610.59.965361793925260.534638206074737
710.3310.6239319501448-0.293931950144829
810.1610.4437224997724-0.283722499772425
99.9110.263867665075-0.353867665075029
109.9610.0015764039066-0.0415764039065785
1110.0310.0501322865449-0.020132286544932
129.5510.1194330104701-0.569433010470103
139.519.61965428938198-0.109654289381981
149.89.57584555057350.224154449426493
1510.089.873631344959070.206368655040935
1610.210.16079936647230.0392006335277184
1710.2310.28216096368-0.0521609636799703
1810.210.3103492015704-0.110349201570392
1910.0710.2765163256394-0.206516325639372
2010.0110.1393431749265-0.129343174926539
2110.0510.0748505611608-0.024850561160763
229.9210.1139874002462-0.193987400246233
2310.039.977249429995940.0527505700040578
2410.1810.08908167152770.090918328472279
2510.110.2422396343216-0.142239634321566
2610.1610.15729907414470.00270092585530257
2710.1510.2173928882689-0.0673928882689054
2810.1310.205052059557-0.0750520595570361
2910.0910.1824451967202-0.0924451967201918
3010.1810.1392341995910.0407658004089644
3110.0610.2306501614011-0.170650161401113
329.6510.1047227882353-0.454722788235287
339.749.678928419037240.0610715809627589
349.539.77104968307368-0.241049683073683
359.59.55267704860706-0.0526770486070589
3699.520847360772-0.52084736077199
379.159.002756216618460.147243783381544
389.329.15787059121550.162129408784505
399.629.333502004037670.286497995962328
409.599.64345324298985-0.0534532429898462
419.379.61159659477151-0.241596594771512
429.359.38320496384045-0.0332049638404524
439.329.36205162059117-0.0420516205911738
449.499.330590997024080.159409002975924
459.529.506127919104150.0138720808958457
469.599.536609752812260.0533902471877443
479.359.60846421293054-0.258464212930543
489.29.35948670111648-0.159486701116476
499.579.203947080264420.366052919735578
509.789.586661584815130.193338415184872
519.799.80337701317852-0.0133770131785163
529.579.81291237518285-0.242912375182851
539.539.58447504185434-0.0544750418543387
549.659.542582902411610.107417097588389
559.369.6663139344632-0.306313934463201
569.49.365674407488550.0343255925114523
579.329.40686667472277-0.0868666747227724
589.319.3238494423186-0.0138494423186017
599.199.31336839494023-0.123368394940231
609.399.189083309548710.200916690451287
619.289.3960619621897-0.116061962189706
629.289.28203065888118-0.00203065888118203
639.319.281960125851140.028039874148865
649.289.31293406455848-0.0329340645584821
659.319.281790130741470.028209869258534
669.359.312769974069370.0372300259306275
679.199.354063124072-0.164063124071999
689.079.1883645454645-0.118364545464503
698.969.06425326408738-0.104253264087379
708.698.95063212482254-0.260632124822539
718.588.67157931262394-0.091579312623935
728.568.558398391166050.00160160883394589
738.478.53845402154546-0.0684540215454597
748.468.446076335365320.0139236646346763
758.758.436559960786170.313440039213827
768.958.737447006320010.212552993679985
779.338.944829835030580.38517016496942
789.519.3382083591490.171791640851003
799.5619.5241753805320.0368246194679998
809.949.57645444912170.363545550878293
819.99.96808186256884-0.0680818625688353
829.2759.9257171029814-0.650717102981405
839.569.278115055241820.281884944758181
849.7799.572906064190720.206093935809276
859.7469.7990645435893-0.0530645435893078
869.9919.764221396479770.226778603520225
879.9810.0170983383945-0.0370983383944647
8810.19510.00480976243480.19019023756521
8910.3110.22641584180380.0835841581962224
9010.2510.3443190590777-0.0943190590777174
919.87110.2810429750986-0.41004297509858
9210.069.88780051726860.172199482731399
939.89410.0827817046565-0.188781704656476
949.599.91022454935588-0.320224549355876
959.649.595101850230910.0448981497690877
969.899.646661345316950.243338654683049
979.539.90511348506375-0.375113485063753
989.3889.53208427028159-0.144084270281587
999.169.38507963840622-0.225079638406219
1009.4189.149261708449930.268738291550067
1019.579.41659608074050.153403919259498
1029.8579.57392442187470.283075578125297
1039.8779.870756786355950.00624321364404601
1049.769.89097363852134-0.130973638521336
1059.769.76942439213312-0.00942439213312163
1069.6959.76909704471912-0.0740970447191174
1079.4759.70152335342619-0.226523353426188
1089.2629.4736552773839-0.211655277383908
1099.0979.2533036300062-0.156303630006196
1108.559.08287457014119-0.532874570141185
1118.168.51736567216024-0.357365672160238
1127.5328.11495291099929-0.582952910999285
1137.3257.4667045888575-0.1417045888575
1146.7497.25478261298258-0.505782612982576
1157.136.661214728702130.468785271297872
1166.9957.0584975450488-0.0634975450488078
1177.3466.92129201742710.424707982572895
1187.737.287043850525570.442956149474434
1197.8377.686429516571680.150570483428322
1207.5147.79865944097204-0.284659440972044
1217.587.465772062501590.114227937498408
1226.837.53573966268407-0.705739662684074
1236.6176.76122645798326-0.144226457983259
1246.7156.543216887351550.171783112648454
1256.636.64718361251544-0.0171836125154394
1266.8916.561586755865090.329413244134913
1277.0026.834028615677710.16797138432229
1287.096.950862944036290.139137055963712
1297.367.043695739066310.316304260933692
1307.4777.324682270652930.152317729347074
1317.8267.446972884000130.379027115999868
1327.797.80913803507911-0.019138035079111
1337.5787.77247329339564-0.194473293395639
1347.2047.55371844610292-0.349718446102917
1357.1987.167571304160560.0304286958394382
1367.6857.162628216346930.522371783653073
1377.7957.667772309898250.127227690101753
1387.467.78219144428445-0.322191444284453
1397.2747.43600042691048-0.162000426910485
1407.337.244373494152630.0856265058473724
1417.6557.303347650455070.351652349544935
1427.7677.640561964718110.126438035281891
1437.847.75695367118540.0830463288145991
1447.4247.83283820746063-0.408838207460634
1457.547.402637596103630.137362403896366
1467.3517.52340875025997-0.172408750259972
1476.7357.32842029416093-0.593420294160932
1486.7776.691808397290830.0851916027091697
1496.6796.73676744764101-0.0577674476410088
1507.346.636760949573890.703239050426114
1516.9787.32218729785526-0.344187297855263
1526.926.94823227515517-0.0282322751551662
1536.6286.88925165357948-0.261251653579476
1546.3856.58817732263106-0.203177322631058
1555.9846.33812014905337-0.354120149053372
1566.2685.924820118090940.343179881909057
1576.5966.220740149143820.375259850856184
1586.3956.56177444780439-0.166774447804388
1596.7156.354981693912190.360018306087815
1606.8046.687486591822570.116513408177433
1616.9296.78053357568370.148466424316301
1626.8466.9106904175659-0.0646904175659051
1636.9926.825443456637080.166556543362921
1646.7746.97722864182305-0.203228641823054
1656.756.75216968572141-0.00216968572140885
1666.4856.72809432372457-0.243094323724574
1676.276.45465067058426-0.184650670584261
1686.476.233237002874330.236762997125672
1696.786.441460743328490.338539256671512
1706.716.76321958661992-0.053219586619921
1716.1416.69137105423626-0.550371054236258
1726.726.103254432304330.616745567695668
1736.686.70367651065507-0.0236765106550729
1746.3716.66285412928277-0.291854129282767
1756.0976.34371685006754-0.246716850067543
1766.276.06114737187520.208852628124804
1776.4476.241401671861760.205598328138241
1786.376.42554293679312-0.0555429367931222
1796.4466.346613705022140.0993862949778617
1806.546.426065794683620.113934205316383
1816.3746.52402319235449-0.150023192354486
1826.336.35281227759582-0.0228122775958211
1836.636.308019914547570.321980085452433







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1846.619203590570916.12617857325687.11222860788502
1856.608407181141825.898952133809357.31786222847429
1866.597610771712735.713673610849977.48154793257549
1876.586814362283645.548683588684447.62494513588284
1886.576017952854555.395753247250567.75628265845854

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
184 & 6.61920359057091 & 6.1261785732568 & 7.11222860788502 \tabularnewline
185 & 6.60840718114182 & 5.89895213380935 & 7.31786222847429 \tabularnewline
186 & 6.59761077171273 & 5.71367361084997 & 7.48154793257549 \tabularnewline
187 & 6.58681436228364 & 5.54868358868444 & 7.62494513588284 \tabularnewline
188 & 6.57601795285455 & 5.39575324725056 & 7.75628265845854 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147329&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]184[/C][C]6.61920359057091[/C][C]6.1261785732568[/C][C]7.11222860788502[/C][/ROW]
[ROW][C]185[/C][C]6.60840718114182[/C][C]5.89895213380935[/C][C]7.31786222847429[/C][/ROW]
[ROW][C]186[/C][C]6.59761077171273[/C][C]5.71367361084997[/C][C]7.48154793257549[/C][/ROW]
[ROW][C]187[/C][C]6.58681436228364[/C][C]5.54868358868444[/C][C]7.62494513588284[/C][/ROW]
[ROW][C]188[/C][C]6.57601795285455[/C][C]5.39575324725056[/C][C]7.75628265845854[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147329&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147329&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
1846.619203590570916.12617857325687.11222860788502
1856.608407181141825.898952133809357.31786222847429
1866.597610771712735.713673610849977.48154793257549
1876.586814362283645.548683588684447.62494513588284
1886.576017952854555.395753247250567.75628265845854



Parameters (Session):
par1 = 5 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 5 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')