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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, 04 Dec 2009 06:54:20 -0700
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/Dec/04/t12599349138rjqaxg5ntb9lvs.htm/, Retrieved Sat, 27 Apr 2024 23:32:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63523, Retrieved Sat, 27 Apr 2024 23:32:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [workshop 9] [2009-12-04 13:54:20] [e81f30a5c3daacfe71a556c99a478849] [Current]
-    D        [Exponential Smoothing] [verbetering] [2009-12-10 17:13:00] [7d268329e554b8694908ba13e6e6f258]
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Dataseries X:
6.9
6.8
6.7
6.6
6.5
6.5
7.0
7.5
7.6
7.6
7.6
7.8
8.0
8.0
8.0
7.9
7.9
8.0
8.5
9.2
9.4
9.5
9.5
9.6
9.7
9.7
9.6
9.5
9.4
9.3
9.6
10.2
10.2
10.1
9.9
9.8
9.8
9.7
9.5
9.3
9.1
9.0
9.5
10.0
10.2
10.1
10.0
9.9
10.0
9.9
9.7
9.5
9.2
9.0
9.3
9.8
9.8
9.6
9.4
9.3
9.2
9.2
9.0
8.8
8.7
8.7
9.1
9.7
9.8
9.6
9.4
9.4
9.5
9.4
9.3
9.2
9.0
8.9
9.2
9.8
9.9
9.6
9.2
9.1
9.1
9.0
8.9
8.7
8.5
8.3
8.5
8.7
8.4
8.1
7.8
7.7
7.5
7.2
6.8
6.7
6.4
6.3
6.8
7.3
7.1
7.0
6.8
6.6
6.3
6.1
6.1
6.3
6.3
6.0
6.2
6.4
6.8
7.5
7.5
7.6
7.6
7.4
7.3
7.1
6.9
6.8
7.5
7.6
7.8
8.0
8.1
8.2
8.3
8.2
8.0
7.9
7.6
7.6
8.3
8.4
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.0
8.2
8.1
8.1
8.0
7.9
7.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63523&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63523&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63523&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.971904589472015
beta0.0881653247099089
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.971904589472015 \tabularnewline
beta & 0.0881653247099089 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63523&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]0.971904589472015[/C][/ROW]
[ROW][C]beta[/C][C]0.0881653247099089[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63523&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63523&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
alpha0.971904589472015
beta0.0881653247099089
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1387.282317406027360.717682593972644
1488.0362665291793-0.0362665291793043
1588.04065730690637-0.0406573069063718
167.97.9281672157671-0.0281672157671071
177.97.92103776925931-0.021037769259312
1888.02284163251019-0.0228416325101879
198.58.55843247582171-0.058432475821709
209.29.16526775157090.0347322484291013
219.49.369177917514890.0308220824851144
229.59.442202345944140.0577976540558627
239.59.53902370006006-0.0390237000600600
249.69.77818546511985-0.178185465119855
259.79.88516467844754-0.185164678447546
269.79.66528217086590.0347178291341006
279.69.67250712157846-0.0725071215784592
289.59.442943066004420.0570569339955789
299.49.45969820114468-0.0596982011446823
309.39.48328436836337-0.183284368363370
319.69.87650622595427-0.276506225954272
3210.210.2671018501516-0.0671018501515608
3310.210.2915578581767-0.0915578581767136
3410.110.1462867132607-0.0462867132606632
359.910.0341740098443-0.134174009844285
369.810.0756990401418-0.275699040141788
379.89.97525673006184-0.175256730061840
389.79.657392412603580.0426075873964216
399.59.56018102582917-0.0601810258291717
409.39.244491886457170.0555081135428352
419.19.15745212963164-0.0574521296316384
4299.07937646480935-0.0793764648093536
439.59.45891035556550.041089644434491
441010.0836438004482-0.0836438004481508
4510.210.01568658841490.184313411585148
4610.110.08841211245120.0115878875488455
47109.98424535781430.0157546421857049
489.910.1349752300051-0.234975230005077
491010.0479909007913-0.047990900791314
509.99.837381403627430.0626185963725678
519.79.73616193857853-0.0361619385785339
529.59.426625741619640.0733742583803583
539.29.33732990375902-0.137329903759021
5499.16105490811093-0.161054908110930
559.39.43723300816736-0.137233008167355
569.89.8284582381197-0.0284582381197023
579.89.781065939008610.0189340609913859
589.69.64018769879226-0.0401876987922645
599.49.4360099541609-0.0360099541609031
609.39.46160601444997-0.161606014449967
619.29.38679364012027-0.186793640120275
629.28.991008882744440.208991117255561
6398.988661007757480.0113389922425178
648.88.700896279878830.0991037201211693
658.78.599503704085290.100496295914711
668.78.631958999561630.0680410004383649
679.19.11146593223397-0.0114659322339694
689.79.622070257205620.0779297427943799
699.89.694255702270110.105744297729890
709.69.65805465071792-0.058054650717919
719.49.45668213410107-0.0566821341010648
729.49.4770555350279-0.0770555350278972
739.59.51090376552828-0.0109037655282762
749.49.332449959890220.0675500401097775
759.39.210927657074050.0890723429259488
769.29.025682924092970.174317075907030
7799.02844268097739-0.0284426809773919
788.98.96055111177748-0.0605511117774817
799.29.34007926671461-0.140079266714608
809.89.741171365603070.0588286343969315
819.99.800802880464990.0991971195350114
829.69.75676581130148-0.156765811301476
839.29.4556575709228-0.255657570922789
849.19.25949851228236-0.159498512282362
859.19.18292435657468-0.0829243565746776
8698.909195594477210.0908044055227872
878.98.787299325567850.112700674432155
888.78.610670131916410.0893298680835883
898.58.50049891896919-0.000498918969190854
908.38.4295699778362-0.129569977836194
918.58.67105757501595-0.171057575015951
928.78.9611488807578-0.261148880757801
938.48.63816607288297-0.238166072882972
948.18.18307903223375-0.0830790322337478
957.87.8818531815114-0.081853181511403
967.77.76733169349048-0.067331693490484
977.57.69329636364513-0.193296363645126
987.27.26325261952877-0.0632526195287735
996.86.93639945251404-0.136399452514040
1006.76.470019575500460.229980424499538
1016.46.441561651945-0.0415616519450044
1026.36.243762244306650.0562377556933535
1036.86.483828898619120.316171101380883
1047.37.09794525975970.202054740240297
1057.17.2190224618741-0.119022461874098
10676.907920089923670.0920799100763281
1076.86.81250621937214-0.0125062193721384
1086.66.78163892406428-0.181638924064285
1096.36.59396813272725-0.293968132727254
1106.16.094150132556250.00584986744375282
1116.15.865721467408720.234278532591275
1126.35.831708937220290.468291062779715
1136.36.09765079865970.202349201340303
11466.22196450180906-0.221964501809063
1156.26.24486287082672-0.0448628708267229
1166.46.50124236330985-0.101242363309847
1176.86.324977856129640.47502214387036
1187.56.657217821484550.842782178515454
1197.57.398619553018920.101380446981081
1207.67.60756432175886-0.00756432175886079
1217.67.74264888465131-0.142648884651314
1227.47.53580327153147-0.135803271531470
1237.37.292603534181220.00739646581877818
1247.17.12964522861433-0.0296452286143323
1256.96.9591415971558-0.0591415971558034
1266.86.86315668382605-0.0631566838260511
1277.57.152883752864550.347116247135451
1287.67.97063370996198-0.370633709961984
1297.87.633439022258930.166560977741066
13087.716938641670400.283061358329603
1318.17.89276756684350.207232433156492
1328.28.22368496904067-0.0236849690406729
1338.38.36265630921508-0.0626563092150825
1348.28.24687170493134-0.0468717049313376
13588.1097455751538-0.109745575153797
1367.97.83238018710110.067619812898907
1377.67.7641174856201-0.164117485620098
1387.67.578235451959360.0217645480406423
1398.38.029213178881770.270786821118232
1408.48.81703316351684-0.417033163516837
1418.48.46950483167575-0.0695048316757507
1428.48.315614077947680.0843859220523164
1438.48.268841213809010.131158786190989
1448.68.494953519572740.105046480427259
1458.98.746936228586420.153063771413583
1468.88.83584461365424-0.0358446136542394
1478.38.70044001488269-0.400440014882685
1487.58.11674836326688-0.616748363266876
1497.27.30878384413295-0.108783844132947
1507.47.112971596590890.287028403409114
1518.87.765888166159861.03411183384014
1529.39.31484844905075-0.0148484490507474
1539.39.420749066177-0.120749066176991
1548.79.2537902441492-0.553790244149202
1558.28.5715355439778-0.371535543977798
1568.38.253148286925110.0468517130748882
1578.58.386816699087640.113183300912356
1588.68.375464610424960.224535389575037
1598.58.447387873952590.0526121260474106
1608.28.29088745303601-0.0908874530360073
1618.18.036203182069550.0637968179304504
1627.98.07159710384127-0.171597103841272
1638.68.343757944015630.256242055984373
1648.79.04760945095619-0.347609450956186
1658.78.74649310803348-0.0464931080334825
1668.58.57619532644035-0.0761953264403452
1678.48.336957803245880.0630421967541217
1688.58.462038976169680.0379610238303165
1698.78.598303869731910.101696130268092
1708.78.581964356830230.118035643169767
1718.68.54054450699830.059455493001705
1728.58.3814936082080.118506391792002
1738.38.3433611518528-0.0433611518527997
17488.2724765068037-0.272476506803693
1758.28.46160505340703-0.261605053407033
1768.18.5768582038509-0.476858203850897
1778.18.094831830982230.00516816901776984
17887.926842880449150.0731571195508538
1797.97.803658010780550.0963419892194537
1807.97.91694966441791-0.0169496644179112

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8 & 7.28231740602736 & 0.717682593972644 \tabularnewline
14 & 8 & 8.0362665291793 & -0.0362665291793043 \tabularnewline
15 & 8 & 8.04065730690637 & -0.0406573069063718 \tabularnewline
16 & 7.9 & 7.9281672157671 & -0.0281672157671071 \tabularnewline
17 & 7.9 & 7.92103776925931 & -0.021037769259312 \tabularnewline
18 & 8 & 8.02284163251019 & -0.0228416325101879 \tabularnewline
19 & 8.5 & 8.55843247582171 & -0.058432475821709 \tabularnewline
20 & 9.2 & 9.1652677515709 & 0.0347322484291013 \tabularnewline
21 & 9.4 & 9.36917791751489 & 0.0308220824851144 \tabularnewline
22 & 9.5 & 9.44220234594414 & 0.0577976540558627 \tabularnewline
23 & 9.5 & 9.53902370006006 & -0.0390237000600600 \tabularnewline
24 & 9.6 & 9.77818546511985 & -0.178185465119855 \tabularnewline
25 & 9.7 & 9.88516467844754 & -0.185164678447546 \tabularnewline
26 & 9.7 & 9.6652821708659 & 0.0347178291341006 \tabularnewline
27 & 9.6 & 9.67250712157846 & -0.0725071215784592 \tabularnewline
28 & 9.5 & 9.44294306600442 & 0.0570569339955789 \tabularnewline
29 & 9.4 & 9.45969820114468 & -0.0596982011446823 \tabularnewline
30 & 9.3 & 9.48328436836337 & -0.183284368363370 \tabularnewline
31 & 9.6 & 9.87650622595427 & -0.276506225954272 \tabularnewline
32 & 10.2 & 10.2671018501516 & -0.0671018501515608 \tabularnewline
33 & 10.2 & 10.2915578581767 & -0.0915578581767136 \tabularnewline
34 & 10.1 & 10.1462867132607 & -0.0462867132606632 \tabularnewline
35 & 9.9 & 10.0341740098443 & -0.134174009844285 \tabularnewline
36 & 9.8 & 10.0756990401418 & -0.275699040141788 \tabularnewline
37 & 9.8 & 9.97525673006184 & -0.175256730061840 \tabularnewline
38 & 9.7 & 9.65739241260358 & 0.0426075873964216 \tabularnewline
39 & 9.5 & 9.56018102582917 & -0.0601810258291717 \tabularnewline
40 & 9.3 & 9.24449188645717 & 0.0555081135428352 \tabularnewline
41 & 9.1 & 9.15745212963164 & -0.0574521296316384 \tabularnewline
42 & 9 & 9.07937646480935 & -0.0793764648093536 \tabularnewline
43 & 9.5 & 9.4589103555655 & 0.041089644434491 \tabularnewline
44 & 10 & 10.0836438004482 & -0.0836438004481508 \tabularnewline
45 & 10.2 & 10.0156865884149 & 0.184313411585148 \tabularnewline
46 & 10.1 & 10.0884121124512 & 0.0115878875488455 \tabularnewline
47 & 10 & 9.9842453578143 & 0.0157546421857049 \tabularnewline
48 & 9.9 & 10.1349752300051 & -0.234975230005077 \tabularnewline
49 & 10 & 10.0479909007913 & -0.047990900791314 \tabularnewline
50 & 9.9 & 9.83738140362743 & 0.0626185963725678 \tabularnewline
51 & 9.7 & 9.73616193857853 & -0.0361619385785339 \tabularnewline
52 & 9.5 & 9.42662574161964 & 0.0733742583803583 \tabularnewline
53 & 9.2 & 9.33732990375902 & -0.137329903759021 \tabularnewline
54 & 9 & 9.16105490811093 & -0.161054908110930 \tabularnewline
55 & 9.3 & 9.43723300816736 & -0.137233008167355 \tabularnewline
56 & 9.8 & 9.8284582381197 & -0.0284582381197023 \tabularnewline
57 & 9.8 & 9.78106593900861 & 0.0189340609913859 \tabularnewline
58 & 9.6 & 9.64018769879226 & -0.0401876987922645 \tabularnewline
59 & 9.4 & 9.4360099541609 & -0.0360099541609031 \tabularnewline
60 & 9.3 & 9.46160601444997 & -0.161606014449967 \tabularnewline
61 & 9.2 & 9.38679364012027 & -0.186793640120275 \tabularnewline
62 & 9.2 & 8.99100888274444 & 0.208991117255561 \tabularnewline
63 & 9 & 8.98866100775748 & 0.0113389922425178 \tabularnewline
64 & 8.8 & 8.70089627987883 & 0.0991037201211693 \tabularnewline
65 & 8.7 & 8.59950370408529 & 0.100496295914711 \tabularnewline
66 & 8.7 & 8.63195899956163 & 0.0680410004383649 \tabularnewline
67 & 9.1 & 9.11146593223397 & -0.0114659322339694 \tabularnewline
68 & 9.7 & 9.62207025720562 & 0.0779297427943799 \tabularnewline
69 & 9.8 & 9.69425570227011 & 0.105744297729890 \tabularnewline
70 & 9.6 & 9.65805465071792 & -0.058054650717919 \tabularnewline
71 & 9.4 & 9.45668213410107 & -0.0566821341010648 \tabularnewline
72 & 9.4 & 9.4770555350279 & -0.0770555350278972 \tabularnewline
73 & 9.5 & 9.51090376552828 & -0.0109037655282762 \tabularnewline
74 & 9.4 & 9.33244995989022 & 0.0675500401097775 \tabularnewline
75 & 9.3 & 9.21092765707405 & 0.0890723429259488 \tabularnewline
76 & 9.2 & 9.02568292409297 & 0.174317075907030 \tabularnewline
77 & 9 & 9.02844268097739 & -0.0284426809773919 \tabularnewline
78 & 8.9 & 8.96055111177748 & -0.0605511117774817 \tabularnewline
79 & 9.2 & 9.34007926671461 & -0.140079266714608 \tabularnewline
80 & 9.8 & 9.74117136560307 & 0.0588286343969315 \tabularnewline
81 & 9.9 & 9.80080288046499 & 0.0991971195350114 \tabularnewline
82 & 9.6 & 9.75676581130148 & -0.156765811301476 \tabularnewline
83 & 9.2 & 9.4556575709228 & -0.255657570922789 \tabularnewline
84 & 9.1 & 9.25949851228236 & -0.159498512282362 \tabularnewline
85 & 9.1 & 9.18292435657468 & -0.0829243565746776 \tabularnewline
86 & 9 & 8.90919559447721 & 0.0908044055227872 \tabularnewline
87 & 8.9 & 8.78729932556785 & 0.112700674432155 \tabularnewline
88 & 8.7 & 8.61067013191641 & 0.0893298680835883 \tabularnewline
89 & 8.5 & 8.50049891896919 & -0.000498918969190854 \tabularnewline
90 & 8.3 & 8.4295699778362 & -0.129569977836194 \tabularnewline
91 & 8.5 & 8.67105757501595 & -0.171057575015951 \tabularnewline
92 & 8.7 & 8.9611488807578 & -0.261148880757801 \tabularnewline
93 & 8.4 & 8.63816607288297 & -0.238166072882972 \tabularnewline
94 & 8.1 & 8.18307903223375 & -0.0830790322337478 \tabularnewline
95 & 7.8 & 7.8818531815114 & -0.081853181511403 \tabularnewline
96 & 7.7 & 7.76733169349048 & -0.067331693490484 \tabularnewline
97 & 7.5 & 7.69329636364513 & -0.193296363645126 \tabularnewline
98 & 7.2 & 7.26325261952877 & -0.0632526195287735 \tabularnewline
99 & 6.8 & 6.93639945251404 & -0.136399452514040 \tabularnewline
100 & 6.7 & 6.47001957550046 & 0.229980424499538 \tabularnewline
101 & 6.4 & 6.441561651945 & -0.0415616519450044 \tabularnewline
102 & 6.3 & 6.24376224430665 & 0.0562377556933535 \tabularnewline
103 & 6.8 & 6.48382889861912 & 0.316171101380883 \tabularnewline
104 & 7.3 & 7.0979452597597 & 0.202054740240297 \tabularnewline
105 & 7.1 & 7.2190224618741 & -0.119022461874098 \tabularnewline
106 & 7 & 6.90792008992367 & 0.0920799100763281 \tabularnewline
107 & 6.8 & 6.81250621937214 & -0.0125062193721384 \tabularnewline
108 & 6.6 & 6.78163892406428 & -0.181638924064285 \tabularnewline
109 & 6.3 & 6.59396813272725 & -0.293968132727254 \tabularnewline
110 & 6.1 & 6.09415013255625 & 0.00584986744375282 \tabularnewline
111 & 6.1 & 5.86572146740872 & 0.234278532591275 \tabularnewline
112 & 6.3 & 5.83170893722029 & 0.468291062779715 \tabularnewline
113 & 6.3 & 6.0976507986597 & 0.202349201340303 \tabularnewline
114 & 6 & 6.22196450180906 & -0.221964501809063 \tabularnewline
115 & 6.2 & 6.24486287082672 & -0.0448628708267229 \tabularnewline
116 & 6.4 & 6.50124236330985 & -0.101242363309847 \tabularnewline
117 & 6.8 & 6.32497785612964 & 0.47502214387036 \tabularnewline
118 & 7.5 & 6.65721782148455 & 0.842782178515454 \tabularnewline
119 & 7.5 & 7.39861955301892 & 0.101380446981081 \tabularnewline
120 & 7.6 & 7.60756432175886 & -0.00756432175886079 \tabularnewline
121 & 7.6 & 7.74264888465131 & -0.142648884651314 \tabularnewline
122 & 7.4 & 7.53580327153147 & -0.135803271531470 \tabularnewline
123 & 7.3 & 7.29260353418122 & 0.00739646581877818 \tabularnewline
124 & 7.1 & 7.12964522861433 & -0.0296452286143323 \tabularnewline
125 & 6.9 & 6.9591415971558 & -0.0591415971558034 \tabularnewline
126 & 6.8 & 6.86315668382605 & -0.0631566838260511 \tabularnewline
127 & 7.5 & 7.15288375286455 & 0.347116247135451 \tabularnewline
128 & 7.6 & 7.97063370996198 & -0.370633709961984 \tabularnewline
129 & 7.8 & 7.63343902225893 & 0.166560977741066 \tabularnewline
130 & 8 & 7.71693864167040 & 0.283061358329603 \tabularnewline
131 & 8.1 & 7.8927675668435 & 0.207232433156492 \tabularnewline
132 & 8.2 & 8.22368496904067 & -0.0236849690406729 \tabularnewline
133 & 8.3 & 8.36265630921508 & -0.0626563092150825 \tabularnewline
134 & 8.2 & 8.24687170493134 & -0.0468717049313376 \tabularnewline
135 & 8 & 8.1097455751538 & -0.109745575153797 \tabularnewline
136 & 7.9 & 7.8323801871011 & 0.067619812898907 \tabularnewline
137 & 7.6 & 7.7641174856201 & -0.164117485620098 \tabularnewline
138 & 7.6 & 7.57823545195936 & 0.0217645480406423 \tabularnewline
139 & 8.3 & 8.02921317888177 & 0.270786821118232 \tabularnewline
140 & 8.4 & 8.81703316351684 & -0.417033163516837 \tabularnewline
141 & 8.4 & 8.46950483167575 & -0.0695048316757507 \tabularnewline
142 & 8.4 & 8.31561407794768 & 0.0843859220523164 \tabularnewline
143 & 8.4 & 8.26884121380901 & 0.131158786190989 \tabularnewline
144 & 8.6 & 8.49495351957274 & 0.105046480427259 \tabularnewline
145 & 8.9 & 8.74693622858642 & 0.153063771413583 \tabularnewline
146 & 8.8 & 8.83584461365424 & -0.0358446136542394 \tabularnewline
147 & 8.3 & 8.70044001488269 & -0.400440014882685 \tabularnewline
148 & 7.5 & 8.11674836326688 & -0.616748363266876 \tabularnewline
149 & 7.2 & 7.30878384413295 & -0.108783844132947 \tabularnewline
150 & 7.4 & 7.11297159659089 & 0.287028403409114 \tabularnewline
151 & 8.8 & 7.76588816615986 & 1.03411183384014 \tabularnewline
152 & 9.3 & 9.31484844905075 & -0.0148484490507474 \tabularnewline
153 & 9.3 & 9.420749066177 & -0.120749066176991 \tabularnewline
154 & 8.7 & 9.2537902441492 & -0.553790244149202 \tabularnewline
155 & 8.2 & 8.5715355439778 & -0.371535543977798 \tabularnewline
156 & 8.3 & 8.25314828692511 & 0.0468517130748882 \tabularnewline
157 & 8.5 & 8.38681669908764 & 0.113183300912356 \tabularnewline
158 & 8.6 & 8.37546461042496 & 0.224535389575037 \tabularnewline
159 & 8.5 & 8.44738787395259 & 0.0526121260474106 \tabularnewline
160 & 8.2 & 8.29088745303601 & -0.0908874530360073 \tabularnewline
161 & 8.1 & 8.03620318206955 & 0.0637968179304504 \tabularnewline
162 & 7.9 & 8.07159710384127 & -0.171597103841272 \tabularnewline
163 & 8.6 & 8.34375794401563 & 0.256242055984373 \tabularnewline
164 & 8.7 & 9.04760945095619 & -0.347609450956186 \tabularnewline
165 & 8.7 & 8.74649310803348 & -0.0464931080334825 \tabularnewline
166 & 8.5 & 8.57619532644035 & -0.0761953264403452 \tabularnewline
167 & 8.4 & 8.33695780324588 & 0.0630421967541217 \tabularnewline
168 & 8.5 & 8.46203897616968 & 0.0379610238303165 \tabularnewline
169 & 8.7 & 8.59830386973191 & 0.101696130268092 \tabularnewline
170 & 8.7 & 8.58196435683023 & 0.118035643169767 \tabularnewline
171 & 8.6 & 8.5405445069983 & 0.059455493001705 \tabularnewline
172 & 8.5 & 8.381493608208 & 0.118506391792002 \tabularnewline
173 & 8.3 & 8.3433611518528 & -0.0433611518527997 \tabularnewline
174 & 8 & 8.2724765068037 & -0.272476506803693 \tabularnewline
175 & 8.2 & 8.46160505340703 & -0.261605053407033 \tabularnewline
176 & 8.1 & 8.5768582038509 & -0.476858203850897 \tabularnewline
177 & 8.1 & 8.09483183098223 & 0.00516816901776984 \tabularnewline
178 & 8 & 7.92684288044915 & 0.0731571195508538 \tabularnewline
179 & 7.9 & 7.80365801078055 & 0.0963419892194537 \tabularnewline
180 & 7.9 & 7.91694966441791 & -0.0169496644179112 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63523&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]8[/C][C]7.28231740602736[/C][C]0.717682593972644[/C][/ROW]
[ROW][C]14[/C][C]8[/C][C]8.0362665291793[/C][C]-0.0362665291793043[/C][/ROW]
[ROW][C]15[/C][C]8[/C][C]8.04065730690637[/C][C]-0.0406573069063718[/C][/ROW]
[ROW][C]16[/C][C]7.9[/C][C]7.9281672157671[/C][C]-0.0281672157671071[/C][/ROW]
[ROW][C]17[/C][C]7.9[/C][C]7.92103776925931[/C][C]-0.021037769259312[/C][/ROW]
[ROW][C]18[/C][C]8[/C][C]8.02284163251019[/C][C]-0.0228416325101879[/C][/ROW]
[ROW][C]19[/C][C]8.5[/C][C]8.55843247582171[/C][C]-0.058432475821709[/C][/ROW]
[ROW][C]20[/C][C]9.2[/C][C]9.1652677515709[/C][C]0.0347322484291013[/C][/ROW]
[ROW][C]21[/C][C]9.4[/C][C]9.36917791751489[/C][C]0.0308220824851144[/C][/ROW]
[ROW][C]22[/C][C]9.5[/C][C]9.44220234594414[/C][C]0.0577976540558627[/C][/ROW]
[ROW][C]23[/C][C]9.5[/C][C]9.53902370006006[/C][C]-0.0390237000600600[/C][/ROW]
[ROW][C]24[/C][C]9.6[/C][C]9.77818546511985[/C][C]-0.178185465119855[/C][/ROW]
[ROW][C]25[/C][C]9.7[/C][C]9.88516467844754[/C][C]-0.185164678447546[/C][/ROW]
[ROW][C]26[/C][C]9.7[/C][C]9.6652821708659[/C][C]0.0347178291341006[/C][/ROW]
[ROW][C]27[/C][C]9.6[/C][C]9.67250712157846[/C][C]-0.0725071215784592[/C][/ROW]
[ROW][C]28[/C][C]9.5[/C][C]9.44294306600442[/C][C]0.0570569339955789[/C][/ROW]
[ROW][C]29[/C][C]9.4[/C][C]9.45969820114468[/C][C]-0.0596982011446823[/C][/ROW]
[ROW][C]30[/C][C]9.3[/C][C]9.48328436836337[/C][C]-0.183284368363370[/C][/ROW]
[ROW][C]31[/C][C]9.6[/C][C]9.87650622595427[/C][C]-0.276506225954272[/C][/ROW]
[ROW][C]32[/C][C]10.2[/C][C]10.2671018501516[/C][C]-0.0671018501515608[/C][/ROW]
[ROW][C]33[/C][C]10.2[/C][C]10.2915578581767[/C][C]-0.0915578581767136[/C][/ROW]
[ROW][C]34[/C][C]10.1[/C][C]10.1462867132607[/C][C]-0.0462867132606632[/C][/ROW]
[ROW][C]35[/C][C]9.9[/C][C]10.0341740098443[/C][C]-0.134174009844285[/C][/ROW]
[ROW][C]36[/C][C]9.8[/C][C]10.0756990401418[/C][C]-0.275699040141788[/C][/ROW]
[ROW][C]37[/C][C]9.8[/C][C]9.97525673006184[/C][C]-0.175256730061840[/C][/ROW]
[ROW][C]38[/C][C]9.7[/C][C]9.65739241260358[/C][C]0.0426075873964216[/C][/ROW]
[ROW][C]39[/C][C]9.5[/C][C]9.56018102582917[/C][C]-0.0601810258291717[/C][/ROW]
[ROW][C]40[/C][C]9.3[/C][C]9.24449188645717[/C][C]0.0555081135428352[/C][/ROW]
[ROW][C]41[/C][C]9.1[/C][C]9.15745212963164[/C][C]-0.0574521296316384[/C][/ROW]
[ROW][C]42[/C][C]9[/C][C]9.07937646480935[/C][C]-0.0793764648093536[/C][/ROW]
[ROW][C]43[/C][C]9.5[/C][C]9.4589103555655[/C][C]0.041089644434491[/C][/ROW]
[ROW][C]44[/C][C]10[/C][C]10.0836438004482[/C][C]-0.0836438004481508[/C][/ROW]
[ROW][C]45[/C][C]10.2[/C][C]10.0156865884149[/C][C]0.184313411585148[/C][/ROW]
[ROW][C]46[/C][C]10.1[/C][C]10.0884121124512[/C][C]0.0115878875488455[/C][/ROW]
[ROW][C]47[/C][C]10[/C][C]9.9842453578143[/C][C]0.0157546421857049[/C][/ROW]
[ROW][C]48[/C][C]9.9[/C][C]10.1349752300051[/C][C]-0.234975230005077[/C][/ROW]
[ROW][C]49[/C][C]10[/C][C]10.0479909007913[/C][C]-0.047990900791314[/C][/ROW]
[ROW][C]50[/C][C]9.9[/C][C]9.83738140362743[/C][C]0.0626185963725678[/C][/ROW]
[ROW][C]51[/C][C]9.7[/C][C]9.73616193857853[/C][C]-0.0361619385785339[/C][/ROW]
[ROW][C]52[/C][C]9.5[/C][C]9.42662574161964[/C][C]0.0733742583803583[/C][/ROW]
[ROW][C]53[/C][C]9.2[/C][C]9.33732990375902[/C][C]-0.137329903759021[/C][/ROW]
[ROW][C]54[/C][C]9[/C][C]9.16105490811093[/C][C]-0.161054908110930[/C][/ROW]
[ROW][C]55[/C][C]9.3[/C][C]9.43723300816736[/C][C]-0.137233008167355[/C][/ROW]
[ROW][C]56[/C][C]9.8[/C][C]9.8284582381197[/C][C]-0.0284582381197023[/C][/ROW]
[ROW][C]57[/C][C]9.8[/C][C]9.78106593900861[/C][C]0.0189340609913859[/C][/ROW]
[ROW][C]58[/C][C]9.6[/C][C]9.64018769879226[/C][C]-0.0401876987922645[/C][/ROW]
[ROW][C]59[/C][C]9.4[/C][C]9.4360099541609[/C][C]-0.0360099541609031[/C][/ROW]
[ROW][C]60[/C][C]9.3[/C][C]9.46160601444997[/C][C]-0.161606014449967[/C][/ROW]
[ROW][C]61[/C][C]9.2[/C][C]9.38679364012027[/C][C]-0.186793640120275[/C][/ROW]
[ROW][C]62[/C][C]9.2[/C][C]8.99100888274444[/C][C]0.208991117255561[/C][/ROW]
[ROW][C]63[/C][C]9[/C][C]8.98866100775748[/C][C]0.0113389922425178[/C][/ROW]
[ROW][C]64[/C][C]8.8[/C][C]8.70089627987883[/C][C]0.0991037201211693[/C][/ROW]
[ROW][C]65[/C][C]8.7[/C][C]8.59950370408529[/C][C]0.100496295914711[/C][/ROW]
[ROW][C]66[/C][C]8.7[/C][C]8.63195899956163[/C][C]0.0680410004383649[/C][/ROW]
[ROW][C]67[/C][C]9.1[/C][C]9.11146593223397[/C][C]-0.0114659322339694[/C][/ROW]
[ROW][C]68[/C][C]9.7[/C][C]9.62207025720562[/C][C]0.0779297427943799[/C][/ROW]
[ROW][C]69[/C][C]9.8[/C][C]9.69425570227011[/C][C]0.105744297729890[/C][/ROW]
[ROW][C]70[/C][C]9.6[/C][C]9.65805465071792[/C][C]-0.058054650717919[/C][/ROW]
[ROW][C]71[/C][C]9.4[/C][C]9.45668213410107[/C][C]-0.0566821341010648[/C][/ROW]
[ROW][C]72[/C][C]9.4[/C][C]9.4770555350279[/C][C]-0.0770555350278972[/C][/ROW]
[ROW][C]73[/C][C]9.5[/C][C]9.51090376552828[/C][C]-0.0109037655282762[/C][/ROW]
[ROW][C]74[/C][C]9.4[/C][C]9.33244995989022[/C][C]0.0675500401097775[/C][/ROW]
[ROW][C]75[/C][C]9.3[/C][C]9.21092765707405[/C][C]0.0890723429259488[/C][/ROW]
[ROW][C]76[/C][C]9.2[/C][C]9.02568292409297[/C][C]0.174317075907030[/C][/ROW]
[ROW][C]77[/C][C]9[/C][C]9.02844268097739[/C][C]-0.0284426809773919[/C][/ROW]
[ROW][C]78[/C][C]8.9[/C][C]8.96055111177748[/C][C]-0.0605511117774817[/C][/ROW]
[ROW][C]79[/C][C]9.2[/C][C]9.34007926671461[/C][C]-0.140079266714608[/C][/ROW]
[ROW][C]80[/C][C]9.8[/C][C]9.74117136560307[/C][C]0.0588286343969315[/C][/ROW]
[ROW][C]81[/C][C]9.9[/C][C]9.80080288046499[/C][C]0.0991971195350114[/C][/ROW]
[ROW][C]82[/C][C]9.6[/C][C]9.75676581130148[/C][C]-0.156765811301476[/C][/ROW]
[ROW][C]83[/C][C]9.2[/C][C]9.4556575709228[/C][C]-0.255657570922789[/C][/ROW]
[ROW][C]84[/C][C]9.1[/C][C]9.25949851228236[/C][C]-0.159498512282362[/C][/ROW]
[ROW][C]85[/C][C]9.1[/C][C]9.18292435657468[/C][C]-0.0829243565746776[/C][/ROW]
[ROW][C]86[/C][C]9[/C][C]8.90919559447721[/C][C]0.0908044055227872[/C][/ROW]
[ROW][C]87[/C][C]8.9[/C][C]8.78729932556785[/C][C]0.112700674432155[/C][/ROW]
[ROW][C]88[/C][C]8.7[/C][C]8.61067013191641[/C][C]0.0893298680835883[/C][/ROW]
[ROW][C]89[/C][C]8.5[/C][C]8.50049891896919[/C][C]-0.000498918969190854[/C][/ROW]
[ROW][C]90[/C][C]8.3[/C][C]8.4295699778362[/C][C]-0.129569977836194[/C][/ROW]
[ROW][C]91[/C][C]8.5[/C][C]8.67105757501595[/C][C]-0.171057575015951[/C][/ROW]
[ROW][C]92[/C][C]8.7[/C][C]8.9611488807578[/C][C]-0.261148880757801[/C][/ROW]
[ROW][C]93[/C][C]8.4[/C][C]8.63816607288297[/C][C]-0.238166072882972[/C][/ROW]
[ROW][C]94[/C][C]8.1[/C][C]8.18307903223375[/C][C]-0.0830790322337478[/C][/ROW]
[ROW][C]95[/C][C]7.8[/C][C]7.8818531815114[/C][C]-0.081853181511403[/C][/ROW]
[ROW][C]96[/C][C]7.7[/C][C]7.76733169349048[/C][C]-0.067331693490484[/C][/ROW]
[ROW][C]97[/C][C]7.5[/C][C]7.69329636364513[/C][C]-0.193296363645126[/C][/ROW]
[ROW][C]98[/C][C]7.2[/C][C]7.26325261952877[/C][C]-0.0632526195287735[/C][/ROW]
[ROW][C]99[/C][C]6.8[/C][C]6.93639945251404[/C][C]-0.136399452514040[/C][/ROW]
[ROW][C]100[/C][C]6.7[/C][C]6.47001957550046[/C][C]0.229980424499538[/C][/ROW]
[ROW][C]101[/C][C]6.4[/C][C]6.441561651945[/C][C]-0.0415616519450044[/C][/ROW]
[ROW][C]102[/C][C]6.3[/C][C]6.24376224430665[/C][C]0.0562377556933535[/C][/ROW]
[ROW][C]103[/C][C]6.8[/C][C]6.48382889861912[/C][C]0.316171101380883[/C][/ROW]
[ROW][C]104[/C][C]7.3[/C][C]7.0979452597597[/C][C]0.202054740240297[/C][/ROW]
[ROW][C]105[/C][C]7.1[/C][C]7.2190224618741[/C][C]-0.119022461874098[/C][/ROW]
[ROW][C]106[/C][C]7[/C][C]6.90792008992367[/C][C]0.0920799100763281[/C][/ROW]
[ROW][C]107[/C][C]6.8[/C][C]6.81250621937214[/C][C]-0.0125062193721384[/C][/ROW]
[ROW][C]108[/C][C]6.6[/C][C]6.78163892406428[/C][C]-0.181638924064285[/C][/ROW]
[ROW][C]109[/C][C]6.3[/C][C]6.59396813272725[/C][C]-0.293968132727254[/C][/ROW]
[ROW][C]110[/C][C]6.1[/C][C]6.09415013255625[/C][C]0.00584986744375282[/C][/ROW]
[ROW][C]111[/C][C]6.1[/C][C]5.86572146740872[/C][C]0.234278532591275[/C][/ROW]
[ROW][C]112[/C][C]6.3[/C][C]5.83170893722029[/C][C]0.468291062779715[/C][/ROW]
[ROW][C]113[/C][C]6.3[/C][C]6.0976507986597[/C][C]0.202349201340303[/C][/ROW]
[ROW][C]114[/C][C]6[/C][C]6.22196450180906[/C][C]-0.221964501809063[/C][/ROW]
[ROW][C]115[/C][C]6.2[/C][C]6.24486287082672[/C][C]-0.0448628708267229[/C][/ROW]
[ROW][C]116[/C][C]6.4[/C][C]6.50124236330985[/C][C]-0.101242363309847[/C][/ROW]
[ROW][C]117[/C][C]6.8[/C][C]6.32497785612964[/C][C]0.47502214387036[/C][/ROW]
[ROW][C]118[/C][C]7.5[/C][C]6.65721782148455[/C][C]0.842782178515454[/C][/ROW]
[ROW][C]119[/C][C]7.5[/C][C]7.39861955301892[/C][C]0.101380446981081[/C][/ROW]
[ROW][C]120[/C][C]7.6[/C][C]7.60756432175886[/C][C]-0.00756432175886079[/C][/ROW]
[ROW][C]121[/C][C]7.6[/C][C]7.74264888465131[/C][C]-0.142648884651314[/C][/ROW]
[ROW][C]122[/C][C]7.4[/C][C]7.53580327153147[/C][C]-0.135803271531470[/C][/ROW]
[ROW][C]123[/C][C]7.3[/C][C]7.29260353418122[/C][C]0.00739646581877818[/C][/ROW]
[ROW][C]124[/C][C]7.1[/C][C]7.12964522861433[/C][C]-0.0296452286143323[/C][/ROW]
[ROW][C]125[/C][C]6.9[/C][C]6.9591415971558[/C][C]-0.0591415971558034[/C][/ROW]
[ROW][C]126[/C][C]6.8[/C][C]6.86315668382605[/C][C]-0.0631566838260511[/C][/ROW]
[ROW][C]127[/C][C]7.5[/C][C]7.15288375286455[/C][C]0.347116247135451[/C][/ROW]
[ROW][C]128[/C][C]7.6[/C][C]7.97063370996198[/C][C]-0.370633709961984[/C][/ROW]
[ROW][C]129[/C][C]7.8[/C][C]7.63343902225893[/C][C]0.166560977741066[/C][/ROW]
[ROW][C]130[/C][C]8[/C][C]7.71693864167040[/C][C]0.283061358329603[/C][/ROW]
[ROW][C]131[/C][C]8.1[/C][C]7.8927675668435[/C][C]0.207232433156492[/C][/ROW]
[ROW][C]132[/C][C]8.2[/C][C]8.22368496904067[/C][C]-0.0236849690406729[/C][/ROW]
[ROW][C]133[/C][C]8.3[/C][C]8.36265630921508[/C][C]-0.0626563092150825[/C][/ROW]
[ROW][C]134[/C][C]8.2[/C][C]8.24687170493134[/C][C]-0.0468717049313376[/C][/ROW]
[ROW][C]135[/C][C]8[/C][C]8.1097455751538[/C][C]-0.109745575153797[/C][/ROW]
[ROW][C]136[/C][C]7.9[/C][C]7.8323801871011[/C][C]0.067619812898907[/C][/ROW]
[ROW][C]137[/C][C]7.6[/C][C]7.7641174856201[/C][C]-0.164117485620098[/C][/ROW]
[ROW][C]138[/C][C]7.6[/C][C]7.57823545195936[/C][C]0.0217645480406423[/C][/ROW]
[ROW][C]139[/C][C]8.3[/C][C]8.02921317888177[/C][C]0.270786821118232[/C][/ROW]
[ROW][C]140[/C][C]8.4[/C][C]8.81703316351684[/C][C]-0.417033163516837[/C][/ROW]
[ROW][C]141[/C][C]8.4[/C][C]8.46950483167575[/C][C]-0.0695048316757507[/C][/ROW]
[ROW][C]142[/C][C]8.4[/C][C]8.31561407794768[/C][C]0.0843859220523164[/C][/ROW]
[ROW][C]143[/C][C]8.4[/C][C]8.26884121380901[/C][C]0.131158786190989[/C][/ROW]
[ROW][C]144[/C][C]8.6[/C][C]8.49495351957274[/C][C]0.105046480427259[/C][/ROW]
[ROW][C]145[/C][C]8.9[/C][C]8.74693622858642[/C][C]0.153063771413583[/C][/ROW]
[ROW][C]146[/C][C]8.8[/C][C]8.83584461365424[/C][C]-0.0358446136542394[/C][/ROW]
[ROW][C]147[/C][C]8.3[/C][C]8.70044001488269[/C][C]-0.400440014882685[/C][/ROW]
[ROW][C]148[/C][C]7.5[/C][C]8.11674836326688[/C][C]-0.616748363266876[/C][/ROW]
[ROW][C]149[/C][C]7.2[/C][C]7.30878384413295[/C][C]-0.108783844132947[/C][/ROW]
[ROW][C]150[/C][C]7.4[/C][C]7.11297159659089[/C][C]0.287028403409114[/C][/ROW]
[ROW][C]151[/C][C]8.8[/C][C]7.76588816615986[/C][C]1.03411183384014[/C][/ROW]
[ROW][C]152[/C][C]9.3[/C][C]9.31484844905075[/C][C]-0.0148484490507474[/C][/ROW]
[ROW][C]153[/C][C]9.3[/C][C]9.420749066177[/C][C]-0.120749066176991[/C][/ROW]
[ROW][C]154[/C][C]8.7[/C][C]9.2537902441492[/C][C]-0.553790244149202[/C][/ROW]
[ROW][C]155[/C][C]8.2[/C][C]8.5715355439778[/C][C]-0.371535543977798[/C][/ROW]
[ROW][C]156[/C][C]8.3[/C][C]8.25314828692511[/C][C]0.0468517130748882[/C][/ROW]
[ROW][C]157[/C][C]8.5[/C][C]8.38681669908764[/C][C]0.113183300912356[/C][/ROW]
[ROW][C]158[/C][C]8.6[/C][C]8.37546461042496[/C][C]0.224535389575037[/C][/ROW]
[ROW][C]159[/C][C]8.5[/C][C]8.44738787395259[/C][C]0.0526121260474106[/C][/ROW]
[ROW][C]160[/C][C]8.2[/C][C]8.29088745303601[/C][C]-0.0908874530360073[/C][/ROW]
[ROW][C]161[/C][C]8.1[/C][C]8.03620318206955[/C][C]0.0637968179304504[/C][/ROW]
[ROW][C]162[/C][C]7.9[/C][C]8.07159710384127[/C][C]-0.171597103841272[/C][/ROW]
[ROW][C]163[/C][C]8.6[/C][C]8.34375794401563[/C][C]0.256242055984373[/C][/ROW]
[ROW][C]164[/C][C]8.7[/C][C]9.04760945095619[/C][C]-0.347609450956186[/C][/ROW]
[ROW][C]165[/C][C]8.7[/C][C]8.74649310803348[/C][C]-0.0464931080334825[/C][/ROW]
[ROW][C]166[/C][C]8.5[/C][C]8.57619532644035[/C][C]-0.0761953264403452[/C][/ROW]
[ROW][C]167[/C][C]8.4[/C][C]8.33695780324588[/C][C]0.0630421967541217[/C][/ROW]
[ROW][C]168[/C][C]8.5[/C][C]8.46203897616968[/C][C]0.0379610238303165[/C][/ROW]
[ROW][C]169[/C][C]8.7[/C][C]8.59830386973191[/C][C]0.101696130268092[/C][/ROW]
[ROW][C]170[/C][C]8.7[/C][C]8.58196435683023[/C][C]0.118035643169767[/C][/ROW]
[ROW][C]171[/C][C]8.6[/C][C]8.5405445069983[/C][C]0.059455493001705[/C][/ROW]
[ROW][C]172[/C][C]8.5[/C][C]8.381493608208[/C][C]0.118506391792002[/C][/ROW]
[ROW][C]173[/C][C]8.3[/C][C]8.3433611518528[/C][C]-0.0433611518527997[/C][/ROW]
[ROW][C]174[/C][C]8[/C][C]8.2724765068037[/C][C]-0.272476506803693[/C][/ROW]
[ROW][C]175[/C][C]8.2[/C][C]8.46160505340703[/C][C]-0.261605053407033[/C][/ROW]
[ROW][C]176[/C][C]8.1[/C][C]8.5768582038509[/C][C]-0.476858203850897[/C][/ROW]
[ROW][C]177[/C][C]8.1[/C][C]8.09483183098223[/C][C]0.00516816901776984[/C][/ROW]
[ROW][C]178[/C][C]8[/C][C]7.92684288044915[/C][C]0.0731571195508538[/C][/ROW]
[ROW][C]179[/C][C]7.9[/C][C]7.80365801078055[/C][C]0.0963419892194537[/C][/ROW]
[ROW][C]180[/C][C]7.9[/C][C]7.91694966441791[/C][C]-0.0169496644179112[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63523&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63523&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
1387.282317406027360.717682593972644
1488.0362665291793-0.0362665291793043
1588.04065730690637-0.0406573069063718
167.97.9281672157671-0.0281672157671071
177.97.92103776925931-0.021037769259312
1888.02284163251019-0.0228416325101879
198.58.55843247582171-0.058432475821709
209.29.16526775157090.0347322484291013
219.49.369177917514890.0308220824851144
229.59.442202345944140.0577976540558627
239.59.53902370006006-0.0390237000600600
249.69.77818546511985-0.178185465119855
259.79.88516467844754-0.185164678447546
269.79.66528217086590.0347178291341006
279.69.67250712157846-0.0725071215784592
289.59.442943066004420.0570569339955789
299.49.45969820114468-0.0596982011446823
309.39.48328436836337-0.183284368363370
319.69.87650622595427-0.276506225954272
3210.210.2671018501516-0.0671018501515608
3310.210.2915578581767-0.0915578581767136
3410.110.1462867132607-0.0462867132606632
359.910.0341740098443-0.134174009844285
369.810.0756990401418-0.275699040141788
379.89.97525673006184-0.175256730061840
389.79.657392412603580.0426075873964216
399.59.56018102582917-0.0601810258291717
409.39.244491886457170.0555081135428352
419.19.15745212963164-0.0574521296316384
4299.07937646480935-0.0793764648093536
439.59.45891035556550.041089644434491
441010.0836438004482-0.0836438004481508
4510.210.01568658841490.184313411585148
4610.110.08841211245120.0115878875488455
47109.98424535781430.0157546421857049
489.910.1349752300051-0.234975230005077
491010.0479909007913-0.047990900791314
509.99.837381403627430.0626185963725678
519.79.73616193857853-0.0361619385785339
529.59.426625741619640.0733742583803583
539.29.33732990375902-0.137329903759021
5499.16105490811093-0.161054908110930
559.39.43723300816736-0.137233008167355
569.89.8284582381197-0.0284582381197023
579.89.781065939008610.0189340609913859
589.69.64018769879226-0.0401876987922645
599.49.4360099541609-0.0360099541609031
609.39.46160601444997-0.161606014449967
619.29.38679364012027-0.186793640120275
629.28.991008882744440.208991117255561
6398.988661007757480.0113389922425178
648.88.700896279878830.0991037201211693
658.78.599503704085290.100496295914711
668.78.631958999561630.0680410004383649
679.19.11146593223397-0.0114659322339694
689.79.622070257205620.0779297427943799
699.89.694255702270110.105744297729890
709.69.65805465071792-0.058054650717919
719.49.45668213410107-0.0566821341010648
729.49.4770555350279-0.0770555350278972
739.59.51090376552828-0.0109037655282762
749.49.332449959890220.0675500401097775
759.39.210927657074050.0890723429259488
769.29.025682924092970.174317075907030
7799.02844268097739-0.0284426809773919
788.98.96055111177748-0.0605511117774817
799.29.34007926671461-0.140079266714608
809.89.741171365603070.0588286343969315
819.99.800802880464990.0991971195350114
829.69.75676581130148-0.156765811301476
839.29.4556575709228-0.255657570922789
849.19.25949851228236-0.159498512282362
859.19.18292435657468-0.0829243565746776
8698.909195594477210.0908044055227872
878.98.787299325567850.112700674432155
888.78.610670131916410.0893298680835883
898.58.50049891896919-0.000498918969190854
908.38.4295699778362-0.129569977836194
918.58.67105757501595-0.171057575015951
928.78.9611488807578-0.261148880757801
938.48.63816607288297-0.238166072882972
948.18.18307903223375-0.0830790322337478
957.87.8818531815114-0.081853181511403
967.77.76733169349048-0.067331693490484
977.57.69329636364513-0.193296363645126
987.27.26325261952877-0.0632526195287735
996.86.93639945251404-0.136399452514040
1006.76.470019575500460.229980424499538
1016.46.441561651945-0.0415616519450044
1026.36.243762244306650.0562377556933535
1036.86.483828898619120.316171101380883
1047.37.09794525975970.202054740240297
1057.17.2190224618741-0.119022461874098
10676.907920089923670.0920799100763281
1076.86.81250621937214-0.0125062193721384
1086.66.78163892406428-0.181638924064285
1096.36.59396813272725-0.293968132727254
1106.16.094150132556250.00584986744375282
1116.15.865721467408720.234278532591275
1126.35.831708937220290.468291062779715
1136.36.09765079865970.202349201340303
11466.22196450180906-0.221964501809063
1156.26.24486287082672-0.0448628708267229
1166.46.50124236330985-0.101242363309847
1176.86.324977856129640.47502214387036
1187.56.657217821484550.842782178515454
1197.57.398619553018920.101380446981081
1207.67.60756432175886-0.00756432175886079
1217.67.74264888465131-0.142648884651314
1227.47.53580327153147-0.135803271531470
1237.37.292603534181220.00739646581877818
1247.17.12964522861433-0.0296452286143323
1256.96.9591415971558-0.0591415971558034
1266.86.86315668382605-0.0631566838260511
1277.57.152883752864550.347116247135451
1287.67.97063370996198-0.370633709961984
1297.87.633439022258930.166560977741066
13087.716938641670400.283061358329603
1318.17.89276756684350.207232433156492
1328.28.22368496904067-0.0236849690406729
1338.38.36265630921508-0.0626563092150825
1348.28.24687170493134-0.0468717049313376
13588.1097455751538-0.109745575153797
1367.97.83238018710110.067619812898907
1377.67.7641174856201-0.164117485620098
1387.67.578235451959360.0217645480406423
1398.38.029213178881770.270786821118232
1408.48.81703316351684-0.417033163516837
1418.48.46950483167575-0.0695048316757507
1428.48.315614077947680.0843859220523164
1438.48.268841213809010.131158786190989
1448.68.494953519572740.105046480427259
1458.98.746936228586420.153063771413583
1468.88.83584461365424-0.0358446136542394
1478.38.70044001488269-0.400440014882685
1487.58.11674836326688-0.616748363266876
1497.27.30878384413295-0.108783844132947
1507.47.112971596590890.287028403409114
1518.87.765888166159861.03411183384014
1529.39.31484844905075-0.0148484490507474
1539.39.420749066177-0.120749066176991
1548.79.2537902441492-0.553790244149202
1558.28.5715355439778-0.371535543977798
1568.38.253148286925110.0468517130748882
1578.58.386816699087640.113183300912356
1588.68.375464610424960.224535389575037
1598.58.447387873952590.0526121260474106
1608.28.29088745303601-0.0908874530360073
1618.18.036203182069550.0637968179304504
1627.98.07159710384127-0.171597103841272
1638.68.343757944015630.256242055984373
1648.79.04760945095619-0.347609450956186
1658.78.74649310803348-0.0464931080334825
1668.58.57619532644035-0.0761953264403452
1678.48.336957803245880.0630421967541217
1688.58.462038976169680.0379610238303165
1698.78.598303869731910.101696130268092
1708.78.581964356830230.118035643169767
1718.68.54054450699830.059455493001705
1728.58.3814936082080.118506391792002
1738.38.3433611518528-0.0433611518527997
17488.2724765068037-0.272476506803693
1758.28.46160505340703-0.261605053407033
1768.18.5768582038509-0.476858203850897
1778.18.094831830982230.00516816901776984
17887.926842880449150.0731571195508538
1797.97.803658010780550.0963419892194537
1807.97.91694966441791-0.0169496644179112







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1817.949775882289657.546885588045968.35266617653335
1827.793005869955867.21098975019528.37502198971652
1837.592092625689156.861024924065678.32316032731262
1847.340042331087366.478302594687338.20178206748738
1857.134923982947176.146769033728218.12307893216613
1867.039495132494865.91595131310878.16303895188102
1877.391458158146086.061799946268848.72111637002332
1887.68962914572556.152513359279289.22674493217172
1897.695733330691346.000755340141369.39071132124132
1907.543502586611175.723864532177169.36314064104518
1917.364840113878385.428828683269419.30085154448734
1927.3758840739992-2.364430887937317.1161990359357

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
181 & 7.94977588228965 & 7.54688558804596 & 8.35266617653335 \tabularnewline
182 & 7.79300586995586 & 7.2109897501952 & 8.37502198971652 \tabularnewline
183 & 7.59209262568915 & 6.86102492406567 & 8.32316032731262 \tabularnewline
184 & 7.34004233108736 & 6.47830259468733 & 8.20178206748738 \tabularnewline
185 & 7.13492398294717 & 6.14676903372821 & 8.12307893216613 \tabularnewline
186 & 7.03949513249486 & 5.9159513131087 & 8.16303895188102 \tabularnewline
187 & 7.39145815814608 & 6.06179994626884 & 8.72111637002332 \tabularnewline
188 & 7.6896291457255 & 6.15251335927928 & 9.22674493217172 \tabularnewline
189 & 7.69573333069134 & 6.00075534014136 & 9.39071132124132 \tabularnewline
190 & 7.54350258661117 & 5.72386453217716 & 9.36314064104518 \tabularnewline
191 & 7.36484011387838 & 5.42882868326941 & 9.30085154448734 \tabularnewline
192 & 7.3758840739992 & -2.3644308879373 & 17.1161990359357 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63523&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]181[/C][C]7.94977588228965[/C][C]7.54688558804596[/C][C]8.35266617653335[/C][/ROW]
[ROW][C]182[/C][C]7.79300586995586[/C][C]7.2109897501952[/C][C]8.37502198971652[/C][/ROW]
[ROW][C]183[/C][C]7.59209262568915[/C][C]6.86102492406567[/C][C]8.32316032731262[/C][/ROW]
[ROW][C]184[/C][C]7.34004233108736[/C][C]6.47830259468733[/C][C]8.20178206748738[/C][/ROW]
[ROW][C]185[/C][C]7.13492398294717[/C][C]6.14676903372821[/C][C]8.12307893216613[/C][/ROW]
[ROW][C]186[/C][C]7.03949513249486[/C][C]5.9159513131087[/C][C]8.16303895188102[/C][/ROW]
[ROW][C]187[/C][C]7.39145815814608[/C][C]6.06179994626884[/C][C]8.72111637002332[/C][/ROW]
[ROW][C]188[/C][C]7.6896291457255[/C][C]6.15251335927928[/C][C]9.22674493217172[/C][/ROW]
[ROW][C]189[/C][C]7.69573333069134[/C][C]6.00075534014136[/C][C]9.39071132124132[/C][/ROW]
[ROW][C]190[/C][C]7.54350258661117[/C][C]5.72386453217716[/C][C]9.36314064104518[/C][/ROW]
[ROW][C]191[/C][C]7.36484011387838[/C][C]5.42882868326941[/C][C]9.30085154448734[/C][/ROW]
[ROW][C]192[/C][C]7.3758840739992[/C][C]-2.3644308879373[/C][C]17.1161990359357[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63523&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63523&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
1817.949775882289657.546885588045968.35266617653335
1827.793005869955867.21098975019528.37502198971652
1837.592092625689156.861024924065678.32316032731262
1847.340042331087366.478302594687338.20178206748738
1857.134923982947176.146769033728218.12307893216613
1867.039495132494865.91595131310878.16303895188102
1877.391458158146086.061799946268848.72111637002332
1887.68962914572556.152513359279289.22674493217172
1897.695733330691346.000755340141369.39071132124132
1907.543502586611175.723864532177169.36314064104518
1917.364840113878385.428828683269419.30085154448734
1927.3758840739992-2.364430887937317.1161990359357



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')