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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_decomposeloess.wasp
Title produced by softwareDecomposition by Loess
Date of computationThu, 22 Dec 2011 12:21:01 -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/Dec/22/t1324574474rliei3p27us0dxz.htm/, Retrieved Tue, 25 Aug 2026 21:55:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159755, Retrieved Tue, 25 Aug 2026 21:55:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact382

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Testing Mean with unknown Variance - Critical Value] [] [2010-10-25 13:12:27] [b98453cac15ba1066b407e146608df68]
- RMPD  [Multiple Regression] [] [2011-12-22 13:45:12] [5a05da414fd67612c3b80d44effe0727]
- RM D    [(Partial) Autocorrelation Function] [] [2011-12-22 15:18:49] [5a05da414fd67612c3b80d44effe0727]
- R         [(Partial) Autocorrelation Function] [] [2011-12-22 15:20:17] [5a05da414fd67612c3b80d44effe0727]
-             [(Partial) Autocorrelation Function] [] [2011-12-22 15:29:46] [5a05da414fd67612c3b80d44effe0727]
- RM            [Exponential Smoothing] [] [2011-12-22 16:47:54] [5a05da414fd67612c3b80d44effe0727]
- RM              [Classical Decomposition] [] [2011-12-22 16:54:59] [5a05da414fd67612c3b80d44effe0727]
- RM                  [Decomposition by Loess] [] [2011-12-22 17:21:01] [95610e892c4b5c84ff80f4c898567a9d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.9
7.9
8.0
8.0
7.9
8.0
7.7
7.2
7.5
7.3
7.0
7.0
7.0
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8.0
8.0
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6
8.7
8.5
8.3
8.0
8.0
8.8
8.7
8.5
8.1
7.8
7.6
7.4
7.1
6.9
6.7
6.6
6.5
7.1
7.2
6.9
6.7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159755&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159755&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159755&T=0

As an alternative you can also use a QR Code:  
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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal601061
Trend1912
Low-pass1312

\begin{tabular}{lllllllll}
\hline
Seasonal Decomposition by Loess - Parameters \tabularnewline
Component & Window & Degree & Jump \tabularnewline
Seasonal & 601 & 0 & 61 \tabularnewline
Trend & 19 & 1 & 2 \tabularnewline
Low-pass & 13 & 1 & 2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159755&T=1

[TABLE]
[ROW][C]Seasonal Decomposition by Loess - Parameters[/C][/ROW]
[ROW][C]Component[/C][C]Window[/C][C]Degree[/C][C]Jump[/C][/ROW]
[ROW][C]Seasonal[/C][C]601[/C][C]0[/C][C]61[/C][/ROW]
[ROW][C]Trend[/C][C]19[/C][C]1[/C][C]2[/C][/ROW]
[ROW][C]Low-pass[/C][C]13[/C][C]1[/C][C]2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159755&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159755&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Seasonal Decomposition by Loess - Parameters
ComponentWindowDegreeJump
Seasonal601061
Trend1912
Low-pass1312






Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
17.97.86850921194435-0.2353769722087358.16686776026438-0.031490788055649
27.97.78952029834091-0.06417832256885038.07465802422794-0.110479701659088
387.830531306316390.1870204054921237.98244828819149-0.169468693683614
487.927470291495550.1834196493650157.88911005913943-0.0725297085044492
57.97.964409407376420.03981876253620257.795771830087380.0644094073764201
688.4392434961506-0.1439810562643717.704737560113770.439243496150597
77.78.19407753264411-0.407780822784287.613703290140170.494077532644109
87.27.27470812832812-0.4032038247465987.528495696418480.0747081283281172
97.57.215338750152490.3413731471507217.44328810269679-0.284661249847511
107.36.831769683121080.4140357952150937.35419452166383-0.468230316878923
1176.568200681440520.1666983779286137.26510094063087-0.431799318559483
1276.90823680145689-0.07784488776664127.16960808630975-0.0917631985431058
1377.16126174022011-0.2353769722087357.074115231988620.16126174022011
147.27.44100122489357-0.06417832256885037.023177097675290.241001224893565
157.37.440740631145930.1870204054921236.972238963361950.140740631145931
167.17.039353160019010.1834196493650156.97722719061597-0.0606468399809854
176.86.57796581959380.03981876253620256.98221541786999-0.222034180406197
186.45.95536643617097-0.1439810562643716.9886146200934-0.444633563829032
196.15.61276700046747-0.407780822784286.99501382231681-0.487232999532531
206.56.39605932166913-0.4032038247465987.00714450307747-0.103940678330869
217.78.039351669011160.3413731471507217.019275183838120.339351669011156
227.98.305711795944820.4140357952150937.080252408840090.405711795944819
237.57.692071988229330.1666983779286137.141229633842050.192071988229334
246.96.64756083424665-0.07784488776664127.23028405351999-0.252439165753353
256.66.1160384990108-0.2353769722087357.31933847319794-0.483961500989203
266.96.47235743068467-0.06417832256885037.39182089188418-0.427642569315331
277.77.748676283937450.1870204054921237.464303310570430.0486762839374517
2888.290595502902680.1834196493650157.525984847732310.290595502902675
2988.37251485256960.03981876253620257.58766638489420.372514852569602
307.77.87815356389419-0.1439810562643717.665827492370180.178153563894189
317.37.26379222293811-0.407780822784287.74398859984617-0.0362077770618878
327.47.37938021302504-0.4032038247465987.82382361172155-0.0206197869749563
338.17.954968229252340.3413731471507217.90365862359694-0.145031770747662
348.38.218560745826450.4140357952150937.96740345895846-0.081439254173552
358.18.002153327751410.1666983779286138.03114829431998-0.0978466722485916
367.97.78713048749947-0.07784488776664128.09071440026717-0.112869512500525
377.97.88509646599438-0.2353769722087358.15028050621436-0.0149035340056205
388.38.45670951722863-0.06417832256885038.207468805340220.156709517228627
398.68.748322490041780.1870204054921238.264657104466090.148322490041783
408.78.911711848489480.1834196493650158.30486850214550.211711848489484
418.58.615101337638890.03981876253620258.345079899824910.115101337638892
428.38.39305998234851-0.1439810562643718.350921073915870.093059982348505
4388.05101857477745-0.407780822784288.356762248006830.051018574777455
4488.09843833925975-0.4032038247465988.304765485486850.0984383392597472
458.89.005858129882410.3413731471507218.252768722966870.205858129882406
468.78.843511483549620.4140357952150938.142452721235290.143511483549618
478.58.801164902567690.1666983779286138.03213671950370.301164902567688
488.18.38368955716482-0.07784488776664127.894155330601820.283689557164816
497.88.07920303050878-0.2353769722087357.756173941699950.279203030508784
507.67.65107398396204-0.06417832256885037.613104338606810.0510739839620378
517.47.14294485899420.1870204054921237.47003473551367-0.257055141005796
527.16.662155122445280.1834196493650157.3544252281897-0.437844877554718
536.96.521365516598070.03981876253620257.23881572086573-0.378634483401934
546.76.41705106353596-0.1439810562643717.12692999272842-0.282948936464045
556.66.59273655819318-0.407780822784287.0150442645911-0.00726344180681959
566.56.49538646118618-0.4032038247465986.90781736356042-0.00461353881382287
577.17.058036390319540.3413731471507216.80059046252974-0.0419636096804643
587.27.285583621423180.4140357952150936.700380583361720.0855836214231847
596.97.033130917877690.1666983779286136.60017070419370.133130917877686
606.76.97220456736873-0.07784488776664126.505640320397910.272204567368732

\begin{tabular}{lllllllll}
\hline
Seasonal Decomposition by Loess - Time Series Components \tabularnewline
t & Observed & Fitted & Seasonal & Trend & Remainder \tabularnewline
1 & 7.9 & 7.86850921194435 & -0.235376972208735 & 8.16686776026438 & -0.031490788055649 \tabularnewline
2 & 7.9 & 7.78952029834091 & -0.0641783225688503 & 8.07465802422794 & -0.110479701659088 \tabularnewline
3 & 8 & 7.83053130631639 & 0.187020405492123 & 7.98244828819149 & -0.169468693683614 \tabularnewline
4 & 8 & 7.92747029149555 & 0.183419649365015 & 7.88911005913943 & -0.0725297085044492 \tabularnewline
5 & 7.9 & 7.96440940737642 & 0.0398187625362025 & 7.79577183008738 & 0.0644094073764201 \tabularnewline
6 & 8 & 8.4392434961506 & -0.143981056264371 & 7.70473756011377 & 0.439243496150597 \tabularnewline
7 & 7.7 & 8.19407753264411 & -0.40778082278428 & 7.61370329014017 & 0.494077532644109 \tabularnewline
8 & 7.2 & 7.27470812832812 & -0.403203824746598 & 7.52849569641848 & 0.0747081283281172 \tabularnewline
9 & 7.5 & 7.21533875015249 & 0.341373147150721 & 7.44328810269679 & -0.284661249847511 \tabularnewline
10 & 7.3 & 6.83176968312108 & 0.414035795215093 & 7.35419452166383 & -0.468230316878923 \tabularnewline
11 & 7 & 6.56820068144052 & 0.166698377928613 & 7.26510094063087 & -0.431799318559483 \tabularnewline
12 & 7 & 6.90823680145689 & -0.0778448877666412 & 7.16960808630975 & -0.0917631985431058 \tabularnewline
13 & 7 & 7.16126174022011 & -0.235376972208735 & 7.07411523198862 & 0.16126174022011 \tabularnewline
14 & 7.2 & 7.44100122489357 & -0.0641783225688503 & 7.02317709767529 & 0.241001224893565 \tabularnewline
15 & 7.3 & 7.44074063114593 & 0.187020405492123 & 6.97223896336195 & 0.140740631145931 \tabularnewline
16 & 7.1 & 7.03935316001901 & 0.183419649365015 & 6.97722719061597 & -0.0606468399809854 \tabularnewline
17 & 6.8 & 6.5779658195938 & 0.0398187625362025 & 6.98221541786999 & -0.222034180406197 \tabularnewline
18 & 6.4 & 5.95536643617097 & -0.143981056264371 & 6.9886146200934 & -0.444633563829032 \tabularnewline
19 & 6.1 & 5.61276700046747 & -0.40778082278428 & 6.99501382231681 & -0.487232999532531 \tabularnewline
20 & 6.5 & 6.39605932166913 & -0.403203824746598 & 7.00714450307747 & -0.103940678330869 \tabularnewline
21 & 7.7 & 8.03935166901116 & 0.341373147150721 & 7.01927518383812 & 0.339351669011156 \tabularnewline
22 & 7.9 & 8.30571179594482 & 0.414035795215093 & 7.08025240884009 & 0.405711795944819 \tabularnewline
23 & 7.5 & 7.69207198822933 & 0.166698377928613 & 7.14122963384205 & 0.192071988229334 \tabularnewline
24 & 6.9 & 6.64756083424665 & -0.0778448877666412 & 7.23028405351999 & -0.252439165753353 \tabularnewline
25 & 6.6 & 6.1160384990108 & -0.235376972208735 & 7.31933847319794 & -0.483961500989203 \tabularnewline
26 & 6.9 & 6.47235743068467 & -0.0641783225688503 & 7.39182089188418 & -0.427642569315331 \tabularnewline
27 & 7.7 & 7.74867628393745 & 0.187020405492123 & 7.46430331057043 & 0.0486762839374517 \tabularnewline
28 & 8 & 8.29059550290268 & 0.183419649365015 & 7.52598484773231 & 0.290595502902675 \tabularnewline
29 & 8 & 8.3725148525696 & 0.0398187625362025 & 7.5876663848942 & 0.372514852569602 \tabularnewline
30 & 7.7 & 7.87815356389419 & -0.143981056264371 & 7.66582749237018 & 0.178153563894189 \tabularnewline
31 & 7.3 & 7.26379222293811 & -0.40778082278428 & 7.74398859984617 & -0.0362077770618878 \tabularnewline
32 & 7.4 & 7.37938021302504 & -0.403203824746598 & 7.82382361172155 & -0.0206197869749563 \tabularnewline
33 & 8.1 & 7.95496822925234 & 0.341373147150721 & 7.90365862359694 & -0.145031770747662 \tabularnewline
34 & 8.3 & 8.21856074582645 & 0.414035795215093 & 7.96740345895846 & -0.081439254173552 \tabularnewline
35 & 8.1 & 8.00215332775141 & 0.166698377928613 & 8.03114829431998 & -0.0978466722485916 \tabularnewline
36 & 7.9 & 7.78713048749947 & -0.0778448877666412 & 8.09071440026717 & -0.112869512500525 \tabularnewline
37 & 7.9 & 7.88509646599438 & -0.235376972208735 & 8.15028050621436 & -0.0149035340056205 \tabularnewline
38 & 8.3 & 8.45670951722863 & -0.0641783225688503 & 8.20746880534022 & 0.156709517228627 \tabularnewline
39 & 8.6 & 8.74832249004178 & 0.187020405492123 & 8.26465710446609 & 0.148322490041783 \tabularnewline
40 & 8.7 & 8.91171184848948 & 0.183419649365015 & 8.3048685021455 & 0.211711848489484 \tabularnewline
41 & 8.5 & 8.61510133763889 & 0.0398187625362025 & 8.34507989982491 & 0.115101337638892 \tabularnewline
42 & 8.3 & 8.39305998234851 & -0.143981056264371 & 8.35092107391587 & 0.093059982348505 \tabularnewline
43 & 8 & 8.05101857477745 & -0.40778082278428 & 8.35676224800683 & 0.051018574777455 \tabularnewline
44 & 8 & 8.09843833925975 & -0.403203824746598 & 8.30476548548685 & 0.0984383392597472 \tabularnewline
45 & 8.8 & 9.00585812988241 & 0.341373147150721 & 8.25276872296687 & 0.205858129882406 \tabularnewline
46 & 8.7 & 8.84351148354962 & 0.414035795215093 & 8.14245272123529 & 0.143511483549618 \tabularnewline
47 & 8.5 & 8.80116490256769 & 0.166698377928613 & 8.0321367195037 & 0.301164902567688 \tabularnewline
48 & 8.1 & 8.38368955716482 & -0.0778448877666412 & 7.89415533060182 & 0.283689557164816 \tabularnewline
49 & 7.8 & 8.07920303050878 & -0.235376972208735 & 7.75617394169995 & 0.279203030508784 \tabularnewline
50 & 7.6 & 7.65107398396204 & -0.0641783225688503 & 7.61310433860681 & 0.0510739839620378 \tabularnewline
51 & 7.4 & 7.1429448589942 & 0.187020405492123 & 7.47003473551367 & -0.257055141005796 \tabularnewline
52 & 7.1 & 6.66215512244528 & 0.183419649365015 & 7.3544252281897 & -0.437844877554718 \tabularnewline
53 & 6.9 & 6.52136551659807 & 0.0398187625362025 & 7.23881572086573 & -0.378634483401934 \tabularnewline
54 & 6.7 & 6.41705106353596 & -0.143981056264371 & 7.12692999272842 & -0.282948936464045 \tabularnewline
55 & 6.6 & 6.59273655819318 & -0.40778082278428 & 7.0150442645911 & -0.00726344180681959 \tabularnewline
56 & 6.5 & 6.49538646118618 & -0.403203824746598 & 6.90781736356042 & -0.00461353881382287 \tabularnewline
57 & 7.1 & 7.05803639031954 & 0.341373147150721 & 6.80059046252974 & -0.0419636096804643 \tabularnewline
58 & 7.2 & 7.28558362142318 & 0.414035795215093 & 6.70038058336172 & 0.0855836214231847 \tabularnewline
59 & 6.9 & 7.03313091787769 & 0.166698377928613 & 6.6001707041937 & 0.133130917877686 \tabularnewline
60 & 6.7 & 6.97220456736873 & -0.0778448877666412 & 6.50564032039791 & 0.272204567368732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159755&T=2

[TABLE]
[ROW][C]Seasonal Decomposition by Loess - Time Series Components[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Seasonal[/C][C]Trend[/C][C]Remainder[/C][/ROW]
[ROW][C]1[/C][C]7.9[/C][C]7.86850921194435[/C][C]-0.235376972208735[/C][C]8.16686776026438[/C][C]-0.031490788055649[/C][/ROW]
[ROW][C]2[/C][C]7.9[/C][C]7.78952029834091[/C][C]-0.0641783225688503[/C][C]8.07465802422794[/C][C]-0.110479701659088[/C][/ROW]
[ROW][C]3[/C][C]8[/C][C]7.83053130631639[/C][C]0.187020405492123[/C][C]7.98244828819149[/C][C]-0.169468693683614[/C][/ROW]
[ROW][C]4[/C][C]8[/C][C]7.92747029149555[/C][C]0.183419649365015[/C][C]7.88911005913943[/C][C]-0.0725297085044492[/C][/ROW]
[ROW][C]5[/C][C]7.9[/C][C]7.96440940737642[/C][C]0.0398187625362025[/C][C]7.79577183008738[/C][C]0.0644094073764201[/C][/ROW]
[ROW][C]6[/C][C]8[/C][C]8.4392434961506[/C][C]-0.143981056264371[/C][C]7.70473756011377[/C][C]0.439243496150597[/C][/ROW]
[ROW][C]7[/C][C]7.7[/C][C]8.19407753264411[/C][C]-0.40778082278428[/C][C]7.61370329014017[/C][C]0.494077532644109[/C][/ROW]
[ROW][C]8[/C][C]7.2[/C][C]7.27470812832812[/C][C]-0.403203824746598[/C][C]7.52849569641848[/C][C]0.0747081283281172[/C][/ROW]
[ROW][C]9[/C][C]7.5[/C][C]7.21533875015249[/C][C]0.341373147150721[/C][C]7.44328810269679[/C][C]-0.284661249847511[/C][/ROW]
[ROW][C]10[/C][C]7.3[/C][C]6.83176968312108[/C][C]0.414035795215093[/C][C]7.35419452166383[/C][C]-0.468230316878923[/C][/ROW]
[ROW][C]11[/C][C]7[/C][C]6.56820068144052[/C][C]0.166698377928613[/C][C]7.26510094063087[/C][C]-0.431799318559483[/C][/ROW]
[ROW][C]12[/C][C]7[/C][C]6.90823680145689[/C][C]-0.0778448877666412[/C][C]7.16960808630975[/C][C]-0.0917631985431058[/C][/ROW]
[ROW][C]13[/C][C]7[/C][C]7.16126174022011[/C][C]-0.235376972208735[/C][C]7.07411523198862[/C][C]0.16126174022011[/C][/ROW]
[ROW][C]14[/C][C]7.2[/C][C]7.44100122489357[/C][C]-0.0641783225688503[/C][C]7.02317709767529[/C][C]0.241001224893565[/C][/ROW]
[ROW][C]15[/C][C]7.3[/C][C]7.44074063114593[/C][C]0.187020405492123[/C][C]6.97223896336195[/C][C]0.140740631145931[/C][/ROW]
[ROW][C]16[/C][C]7.1[/C][C]7.03935316001901[/C][C]0.183419649365015[/C][C]6.97722719061597[/C][C]-0.0606468399809854[/C][/ROW]
[ROW][C]17[/C][C]6.8[/C][C]6.5779658195938[/C][C]0.0398187625362025[/C][C]6.98221541786999[/C][C]-0.222034180406197[/C][/ROW]
[ROW][C]18[/C][C]6.4[/C][C]5.95536643617097[/C][C]-0.143981056264371[/C][C]6.9886146200934[/C][C]-0.444633563829032[/C][/ROW]
[ROW][C]19[/C][C]6.1[/C][C]5.61276700046747[/C][C]-0.40778082278428[/C][C]6.99501382231681[/C][C]-0.487232999532531[/C][/ROW]
[ROW][C]20[/C][C]6.5[/C][C]6.39605932166913[/C][C]-0.403203824746598[/C][C]7.00714450307747[/C][C]-0.103940678330869[/C][/ROW]
[ROW][C]21[/C][C]7.7[/C][C]8.03935166901116[/C][C]0.341373147150721[/C][C]7.01927518383812[/C][C]0.339351669011156[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]8.30571179594482[/C][C]0.414035795215093[/C][C]7.08025240884009[/C][C]0.405711795944819[/C][/ROW]
[ROW][C]23[/C][C]7.5[/C][C]7.69207198822933[/C][C]0.166698377928613[/C][C]7.14122963384205[/C][C]0.192071988229334[/C][/ROW]
[ROW][C]24[/C][C]6.9[/C][C]6.64756083424665[/C][C]-0.0778448877666412[/C][C]7.23028405351999[/C][C]-0.252439165753353[/C][/ROW]
[ROW][C]25[/C][C]6.6[/C][C]6.1160384990108[/C][C]-0.235376972208735[/C][C]7.31933847319794[/C][C]-0.483961500989203[/C][/ROW]
[ROW][C]26[/C][C]6.9[/C][C]6.47235743068467[/C][C]-0.0641783225688503[/C][C]7.39182089188418[/C][C]-0.427642569315331[/C][/ROW]
[ROW][C]27[/C][C]7.7[/C][C]7.74867628393745[/C][C]0.187020405492123[/C][C]7.46430331057043[/C][C]0.0486762839374517[/C][/ROW]
[ROW][C]28[/C][C]8[/C][C]8.29059550290268[/C][C]0.183419649365015[/C][C]7.52598484773231[/C][C]0.290595502902675[/C][/ROW]
[ROW][C]29[/C][C]8[/C][C]8.3725148525696[/C][C]0.0398187625362025[/C][C]7.5876663848942[/C][C]0.372514852569602[/C][/ROW]
[ROW][C]30[/C][C]7.7[/C][C]7.87815356389419[/C][C]-0.143981056264371[/C][C]7.66582749237018[/C][C]0.178153563894189[/C][/ROW]
[ROW][C]31[/C][C]7.3[/C][C]7.26379222293811[/C][C]-0.40778082278428[/C][C]7.74398859984617[/C][C]-0.0362077770618878[/C][/ROW]
[ROW][C]32[/C][C]7.4[/C][C]7.37938021302504[/C][C]-0.403203824746598[/C][C]7.82382361172155[/C][C]-0.0206197869749563[/C][/ROW]
[ROW][C]33[/C][C]8.1[/C][C]7.95496822925234[/C][C]0.341373147150721[/C][C]7.90365862359694[/C][C]-0.145031770747662[/C][/ROW]
[ROW][C]34[/C][C]8.3[/C][C]8.21856074582645[/C][C]0.414035795215093[/C][C]7.96740345895846[/C][C]-0.081439254173552[/C][/ROW]
[ROW][C]35[/C][C]8.1[/C][C]8.00215332775141[/C][C]0.166698377928613[/C][C]8.03114829431998[/C][C]-0.0978466722485916[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]7.78713048749947[/C][C]-0.0778448877666412[/C][C]8.09071440026717[/C][C]-0.112869512500525[/C][/ROW]
[ROW][C]37[/C][C]7.9[/C][C]7.88509646599438[/C][C]-0.235376972208735[/C][C]8.15028050621436[/C][C]-0.0149035340056205[/C][/ROW]
[ROW][C]38[/C][C]8.3[/C][C]8.45670951722863[/C][C]-0.0641783225688503[/C][C]8.20746880534022[/C][C]0.156709517228627[/C][/ROW]
[ROW][C]39[/C][C]8.6[/C][C]8.74832249004178[/C][C]0.187020405492123[/C][C]8.26465710446609[/C][C]0.148322490041783[/C][/ROW]
[ROW][C]40[/C][C]8.7[/C][C]8.91171184848948[/C][C]0.183419649365015[/C][C]8.3048685021455[/C][C]0.211711848489484[/C][/ROW]
[ROW][C]41[/C][C]8.5[/C][C]8.61510133763889[/C][C]0.0398187625362025[/C][C]8.34507989982491[/C][C]0.115101337638892[/C][/ROW]
[ROW][C]42[/C][C]8.3[/C][C]8.39305998234851[/C][C]-0.143981056264371[/C][C]8.35092107391587[/C][C]0.093059982348505[/C][/ROW]
[ROW][C]43[/C][C]8[/C][C]8.05101857477745[/C][C]-0.40778082278428[/C][C]8.35676224800683[/C][C]0.051018574777455[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]8.09843833925975[/C][C]-0.403203824746598[/C][C]8.30476548548685[/C][C]0.0984383392597472[/C][/ROW]
[ROW][C]45[/C][C]8.8[/C][C]9.00585812988241[/C][C]0.341373147150721[/C][C]8.25276872296687[/C][C]0.205858129882406[/C][/ROW]
[ROW][C]46[/C][C]8.7[/C][C]8.84351148354962[/C][C]0.414035795215093[/C][C]8.14245272123529[/C][C]0.143511483549618[/C][/ROW]
[ROW][C]47[/C][C]8.5[/C][C]8.80116490256769[/C][C]0.166698377928613[/C][C]8.0321367195037[/C][C]0.301164902567688[/C][/ROW]
[ROW][C]48[/C][C]8.1[/C][C]8.38368955716482[/C][C]-0.0778448877666412[/C][C]7.89415533060182[/C][C]0.283689557164816[/C][/ROW]
[ROW][C]49[/C][C]7.8[/C][C]8.07920303050878[/C][C]-0.235376972208735[/C][C]7.75617394169995[/C][C]0.279203030508784[/C][/ROW]
[ROW][C]50[/C][C]7.6[/C][C]7.65107398396204[/C][C]-0.0641783225688503[/C][C]7.61310433860681[/C][C]0.0510739839620378[/C][/ROW]
[ROW][C]51[/C][C]7.4[/C][C]7.1429448589942[/C][C]0.187020405492123[/C][C]7.47003473551367[/C][C]-0.257055141005796[/C][/ROW]
[ROW][C]52[/C][C]7.1[/C][C]6.66215512244528[/C][C]0.183419649365015[/C][C]7.3544252281897[/C][C]-0.437844877554718[/C][/ROW]
[ROW][C]53[/C][C]6.9[/C][C]6.52136551659807[/C][C]0.0398187625362025[/C][C]7.23881572086573[/C][C]-0.378634483401934[/C][/ROW]
[ROW][C]54[/C][C]6.7[/C][C]6.41705106353596[/C][C]-0.143981056264371[/C][C]7.12692999272842[/C][C]-0.282948936464045[/C][/ROW]
[ROW][C]55[/C][C]6.6[/C][C]6.59273655819318[/C][C]-0.40778082278428[/C][C]7.0150442645911[/C][C]-0.00726344180681959[/C][/ROW]
[ROW][C]56[/C][C]6.5[/C][C]6.49538646118618[/C][C]-0.403203824746598[/C][C]6.90781736356042[/C][C]-0.00461353881382287[/C][/ROW]
[ROW][C]57[/C][C]7.1[/C][C]7.05803639031954[/C][C]0.341373147150721[/C][C]6.80059046252974[/C][C]-0.0419636096804643[/C][/ROW]
[ROW][C]58[/C][C]7.2[/C][C]7.28558362142318[/C][C]0.414035795215093[/C][C]6.70038058336172[/C][C]0.0855836214231847[/C][/ROW]
[ROW][C]59[/C][C]6.9[/C][C]7.03313091787769[/C][C]0.166698377928613[/C][C]6.6001707041937[/C][C]0.133130917877686[/C][/ROW]
[ROW][C]60[/C][C]6.7[/C][C]6.97220456736873[/C][C]-0.0778448877666412[/C][C]6.50564032039791[/C][C]0.272204567368732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159755&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159755&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Seasonal Decomposition by Loess - Time Series Components
tObservedFittedSeasonalTrendRemainder
17.97.86850921194435-0.2353769722087358.16686776026438-0.031490788055649
27.97.78952029834091-0.06417832256885038.07465802422794-0.110479701659088
387.830531306316390.1870204054921237.98244828819149-0.169468693683614
487.927470291495550.1834196493650157.88911005913943-0.0725297085044492
57.97.964409407376420.03981876253620257.795771830087380.0644094073764201
688.4392434961506-0.1439810562643717.704737560113770.439243496150597
77.78.19407753264411-0.407780822784287.613703290140170.494077532644109
87.27.27470812832812-0.4032038247465987.528495696418480.0747081283281172
97.57.215338750152490.3413731471507217.44328810269679-0.284661249847511
107.36.831769683121080.4140357952150937.35419452166383-0.468230316878923
1176.568200681440520.1666983779286137.26510094063087-0.431799318559483
1276.90823680145689-0.07784488776664127.16960808630975-0.0917631985431058
1377.16126174022011-0.2353769722087357.074115231988620.16126174022011
147.27.44100122489357-0.06417832256885037.023177097675290.241001224893565
157.37.440740631145930.1870204054921236.972238963361950.140740631145931
167.17.039353160019010.1834196493650156.97722719061597-0.0606468399809854
176.86.57796581959380.03981876253620256.98221541786999-0.222034180406197
186.45.95536643617097-0.1439810562643716.9886146200934-0.444633563829032
196.15.61276700046747-0.407780822784286.99501382231681-0.487232999532531
206.56.39605932166913-0.4032038247465987.00714450307747-0.103940678330869
217.78.039351669011160.3413731471507217.019275183838120.339351669011156
227.98.305711795944820.4140357952150937.080252408840090.405711795944819
237.57.692071988229330.1666983779286137.141229633842050.192071988229334
246.96.64756083424665-0.07784488776664127.23028405351999-0.252439165753353
256.66.1160384990108-0.2353769722087357.31933847319794-0.483961500989203
266.96.47235743068467-0.06417832256885037.39182089188418-0.427642569315331
277.77.748676283937450.1870204054921237.464303310570430.0486762839374517
2888.290595502902680.1834196493650157.525984847732310.290595502902675
2988.37251485256960.03981876253620257.58766638489420.372514852569602
307.77.87815356389419-0.1439810562643717.665827492370180.178153563894189
317.37.26379222293811-0.407780822784287.74398859984617-0.0362077770618878
327.47.37938021302504-0.4032038247465987.82382361172155-0.0206197869749563
338.17.954968229252340.3413731471507217.90365862359694-0.145031770747662
348.38.218560745826450.4140357952150937.96740345895846-0.081439254173552
358.18.002153327751410.1666983779286138.03114829431998-0.0978466722485916
367.97.78713048749947-0.07784488776664128.09071440026717-0.112869512500525
377.97.88509646599438-0.2353769722087358.15028050621436-0.0149035340056205
388.38.45670951722863-0.06417832256885038.207468805340220.156709517228627
398.68.748322490041780.1870204054921238.264657104466090.148322490041783
408.78.911711848489480.1834196493650158.30486850214550.211711848489484
418.58.615101337638890.03981876253620258.345079899824910.115101337638892
428.38.39305998234851-0.1439810562643718.350921073915870.093059982348505
4388.05101857477745-0.407780822784288.356762248006830.051018574777455
4488.09843833925975-0.4032038247465988.304765485486850.0984383392597472
458.89.005858129882410.3413731471507218.252768722966870.205858129882406
468.78.843511483549620.4140357952150938.142452721235290.143511483549618
478.58.801164902567690.1666983779286138.03213671950370.301164902567688
488.18.38368955716482-0.07784488776664127.894155330601820.283689557164816
497.88.07920303050878-0.2353769722087357.756173941699950.279203030508784
507.67.65107398396204-0.06417832256885037.613104338606810.0510739839620378
517.47.14294485899420.1870204054921237.47003473551367-0.257055141005796
527.16.662155122445280.1834196493650157.3544252281897-0.437844877554718
536.96.521365516598070.03981876253620257.23881572086573-0.378634483401934
546.76.41705106353596-0.1439810562643717.12692999272842-0.282948936464045
556.66.59273655819318-0.407780822784287.0150442645911-0.00726344180681959
566.56.49538646118618-0.4032038247465986.90781736356042-0.00461353881382287
577.17.058036390319540.3413731471507216.80059046252974-0.0419636096804643
587.27.285583621423180.4140357952150936.700380583361720.0855836214231847
596.97.033130917877690.1666983779286136.60017070419370.133130917877686
606.76.97220456736873-0.07784488776664126.505640320397910.272204567368732


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par4 = ; par5 = 1 ; par6 = ; par7 = 1 ; par8 = FALSE ;
R code (references can be found in the software module):
par1 <- as.numeric(par1) #seasonal period
if (par2 != 'periodic') par2 <- as.numeric(par2) #s.window
par3 <- as.numeric(par3) #s.degree
if (par4 == '') par4 <- NULL else par4 <- as.numeric(par4)#t.window
par5 <- as.numeric(par5)#t.degree
if (par6 != '') par6 <- as.numeric(par6)#l.window
par7 <- as.numeric(par7)#l.degree
if (par8 == 'FALSE') par8 <- FALSE else par9 <- TRUE #robust
nx <- length(x)
x <- ts(x,frequency=par1)
if (par6 != '') {
m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.window=par6, l.degree=par7, robust=par8)
} else {
m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.degree=par7, robust=par8)
}
m$time.series
m$win
m$deg
m$jump
m$inner
m$outer
bitmap(file='test1.png')
plot(m,main=main)
dev.off()
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(as.numeric(m$time.series[,'trend']),na.action=na.pass,lag.max = mylagmax,main='Trend')
acf(as.numeric(m$time.series[,'seasonal']),na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(as.numeric(m$time.series[,'remainder']),na.action=na.pass,lag.max = mylagmax,main='Remainder')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')
spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')
spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')
cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')
cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Seasonal Decomposition by Loess - Parameters',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Component',header=TRUE)
a<-table.element(a,'Window',header=TRUE)
a<-table.element(a,'Degree',header=TRUE)
a<-table.element(a,'Jump',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,m$win['s'])
a<-table.element(a,m$deg['s'])
a<-table.element(a,m$jump['s'])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Trend',header=TRUE)
a<-table.element(a,m$win['t'])
a<-table.element(a,m$deg['t'])
a<-table.element(a,m$jump['t'])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Low-pass',header=TRUE)
a<-table.element(a,m$win['l'])
a<-table.element(a,m$deg['l'])
a<-table.element(a,m$jump['l'])
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,'Seasonal Decomposition by Loess - Time Series Components',6,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,'Seasonal',header=TRUE)
a<-table.element(a,'Trend',header=TRUE)
a<-table.element(a,'Remainder',header=TRUE)
a<-table.row.end(a)
for (i in 1:nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]+m$time.series[i,'remainder'])
a<-table.element(a,m$time.series[i,'seasonal'])
a<-table.element(a,m$time.series[i,'trend'])
a<-table.element(a,m$time.series[i,'remainder'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')