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Workshop 5 STSM

*The author of this computation has been verified*
R Software Module: /rwasp_structuraltimeseries.wasp (opens new window with default values)
Title produced by software: Structural Time Series Models
Date of computation: Thu, 09 Dec 2010 21:00:28 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/09/t1291928338jutmioltg9yu2sb.htm/, Retrieved Thu, 09 Dec 2010 21:59:00 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/09/t1291928338jutmioltg9yu2sb.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
235.1 280.7 264.6 240.7 201.4 240.8 241.1 223.8 206.1 174.7 203.3 220.5 299.5 347.4 338.3 327.7 351.6 396.6 438.8 395.6 363.5 378.8 357 369 464.8 479.1 431.3 366.5 326.3 355.1 331.6 261.3 249 205.5 235.6 240.9 264.9 253.8 232.3 193.8 177 213.2 207.2 180.6 188.6 175.4 199 179.6 225.8 234 200.2 183.6 178.2 203.2 208.5 191.8 172.8 148 159.4 154.5 213.2 196.4 182.8 176.4 153.6 173.2 171 151.2 161.9 157.2 201.7 236.4 356.1 398.3 403.7 384.6 365.8 368.1 367.9 347 343.3 292.9 311.5 300.9 366.9 356.9 329.7 316.2 269 289.3 266.2 253.6 233.8 228.4 253.6 260.1 306.6 309.2 309.5 271 279.9 317.9 298.4 246.7 227.3 209.1 259.9 266 320.6 308.5 282.2 262.7 263.5 313.1 284.3 252.6 250.3 246.5 312.7 333.2 446.4 511.6 515.5 506.4 483.2 522.3 509.8 460.7 405.8 375 378.5 406.8 467.8 469.8 429.8 355.8 332.7 378 360.5 334.7 319.5 323.1 363.6 352.1 411.9 388.6 416.4 360.7 338 417.2 388. etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk


Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
1235.1235.1000
2280.7276.8962159840493.229142343321673.803784015951331.42067327615987
3264.6265.9633201403961.50309127397057-1.36332014039577-0.734903192958745
4240.7241.861842741856-2.61710346036254-1.16184274185618-1.29364989904452
5201.4203.400455149288-9.37559126835787-2.00045514928794-1.77273304652696
6240.8231.511772808939-1.64208960797519.288227191061361.83019827593514
7241.1239.5350833739170.4562231279348541.564916626082540.467980148529886
8223.8224.505103417909-3.00538545782006-0.705103417909013-0.745971474683479
9206.1205.645999774034-6.609310772724370.454000225966415-0.761334374530572
10174.7175.353810704195-12.0456383068053-0.65381070419474-1.13525469491882
11203.3195.560601946487-4.600406182776817.739398053513371.54440221573735
12220.5216.3859713222091.288087493612064.114028677791271.21675230904754
13299.5288.87254456233517.209513344792710.62745543766463.83219960998184
14347.4340.17739381595424.9132391109217.222606184045911.44303742849705
15338.3345.19425405707520.4090352307895-6.89425405707475-0.929072821568613
16327.7331.37657441297612.5503943633847-3.67657441297638-1.61859605212461
17351.6356.28800676917315.3924508213383-4.688006769172850.582409305042532
18396.6388.49409915585619.25627326527068.105900844143970.792935002200693
19438.8433.77054896329825.23508108221385.029451036702281.22812014074052
20395.6408.5169055312413.6337983669419-12.9169055312398-2.38378341413936
21363.5368.9621620118751.41159881306686-5.46216201187509-2.51169632903526
22378.8379.1977112418023.43952619022249-0.3977112418022330.416792784636876
23357357.765285038778-2.27634517251773-0.765285038777964-1.17473270601674
24369371.855259463871.47449629863266-2.855259463870370.771879025320205
25464.8442.46148308564817.234438401111122.33851691435193.4117209536275
26479.1468.28823301739419.188623493124810.81176698260630.388213812438684
27431.3443.035075151899.1400507178128-11.7350751518903-2.05885241871944
28366.5386.564804798826-5.83260001733276-20.0648047988257-3.09038381940777
29326.3341.660008402259-14.7727639916897-15.3600084022588-1.83378993070821
30355.1347.79168941766-9.991513734516787.30831058234020.980733492263645
31331.6323.128774312177-13.34619534527828.47122568782341-0.688870068685405
32261.3273.488344198205-21.6449056852575-12.1883441982049-1.70503372567286
33249254.649361643-21.0032743657798-5.649361642999750.131859692847288
34205.5206.688813597959-27.168084689437-1.18881359795922-1.2670300476127
35235.6227.556103822911-16.18946017100928.043896177088742.25584881901562
36240.9250.46830142074-7.27600246058865-9.568301420739681.83821737957645
37264.9245.283822097189-6.799067295818619.61617790281050.10034546424882
38253.8235.072839631174-7.5756931975431318.7271603688258-0.157150743104033
39232.3230.443514645116-6.90896530401261.856485354884030.136375546710108
40193.8210.141365097372-9.95540616317708-16.3413650973722-0.628827805859645
41177197.819192874448-10.4953704767714-20.8191928744483-0.110924937508902
42213.2200.35707732516-7.5220060445456112.84292267483980.610000848877979
43207.2192.275651393618-7.6495900949393114.9243486063823-0.0261952868917168
44180.6190.866778731357-6.22633714019595-10.26677873135710.292406567209551
45188.6187.584013478576-5.554959887118081.015986521424480.137973466188811
46175.4185.610863452006-4.73806044633742-10.21086345200590.167877215024977
47199195.823843130338-1.331239570894643.176156869661890.70007784371653
48179.6191.06618117599-2.11066455335522-11.4661811759904-0.160872735729458
49225.8202.3105987922750.93176473539575223.48940120772490.632937421976381
50234213.7964587103473.3329753218407320.20354128965260.489354069051082
51200.2199.727031612065-0.6080216347426430.47296838793541-0.806261681339022
52183.6199.096879149368-0.613047031768081-15.4968791493683-0.00103643468153373
53178.2201.034695009284-0.0322039165814644-22.83469500928380.119450128127895
54203.2192.235798131419-2.0289928374447910.9642018685807-0.409822128080191
55208.5193.600127038433-1.2563228882328414.89987296156720.158636795187237
56191.8200.603077582190.624220609016814-8.803077582190220.386330310210544
57172.8178.115069897703-4.63848947719295-5.31506989770331-1.08145253276541
58148162.738610257627-7.08307311058334-14.7386102576272-0.50231501975224
59159.4155.131289339597-7.202312270551034.26871066040273-0.0245097552895159
60154.5164.759390746273-3.37772265968249-10.25939074627290.789316206707382
61213.2186.039781773952.2340121286924827.16021822604981.16139028433382
62196.4175.902303783159-0.57873006516221520.4976962168407-0.575047304191518
63182.8181.0093700954330.7094709146317621.790629904567390.263721973449956
64176.4190.7086133455892.74893556525058-14.30861334558930.420232391066356
65153.6178.752626317997-0.594849645427055-25.1526263179969-0.688062521856649
66173.2166.070741477084-3.344740409325777.12925852291571-0.564668589694088
67171158.40057872575-4.3285769667869312.5994212742502-0.202001847211485
68151.2154.440203472066-4.24483720702611-3.240203472066410.0172017297249659
69161.9161.654956591226-1.638633858559040.2450434087744220.535496614754551
70157.2169.7023295531730.563568513641495-12.50232955317270.452479655042817
71201.7195.7486400560696.352672126543045.951359943930691.19031423612303
72236.4242.92564845946615.6238341500401-6.525648459466451.91251169690664
73356.1314.58700196274828.365952149513641.51299803725222.6300278186262
74398.3374.37144210513335.504440070054723.92855789486681.46178562383185
75403.7406.42367341741534.7221399269876-2.72367341741525-0.1602633755443
76384.6404.93001418759226.5106428767748-20.3300141875923-1.69072930752133
77365.8396.01686268980318.4637197321816-30.2168626898025-1.65629623517769
78368.1369.1593103783788.1619960080138-1.05931037837805-2.11635450116838
79367.9357.5608927846233.6710691239779810.3391072153768-0.92218286621996
80347352.2865554549141.63837443067688-5.28655545491393-0.41752192936498
81343.3344.988753074349-0.392019535478827-1.68875307434873-0.417134711091808
82292.9315.881150396055-6.91424991865418-22.9811503960554-1.3400877682447
83311.5312.540614500108-6.10305232631274-1.040614500108370.166831223380639
84300.9317.600856424373-3.56909730586194-16.70085642437290.5224469699542
85366.9329.8230162705220.019013933548547937.07698372947810.739492254440025
86356.9332.8217150923570.6956242134377524.07828490764250.13868162873354
87329.7327.120036693707-0.754098508173882.57996330629309-0.297164279069231
88316.2328.622031535509-0.242749852758556-12.42203153550940.105228728562402
89269297.270828810991-7.30392108533563-28.2708288109913-1.45350587736807
90289.3286.49499975008-8.092527805437352.80500024991978-0.162070175819587
91266.2258.525736491102-12.60695474036137.67426350889833-0.927139055112284
92253.6253.761435802791-10.8260607728523-0.161435802790850.365778903903948
93233.8231.656901358636-13.38669648996042.14309864136418-0.526015622446123
94228.4245.34601008598-7.24172263696368-16.94601008597981.26260847586195
95253.6254.264875251032-3.5756666031157-0.6648752510320.754074024833554
96260.1275.2110925447711.98827374606546-15.1110925447711.14661143984645
97306.6272.3602562169610.88939653017779534.2397437830386-0.226270215873147
98309.2282.3331273387252.950973792133226.86687266127520.422799169395268
99309.5303.5742890340387.095489745583225.925710965962360.849933313532326
100271283.8362214891561.01536152543458-12.8362214891561-1.25073620794936
101279.9302.3119747858874.97620343440834-22.41197478588670.81528969727925
102317.9310.435492339675.690646040818247.464507660329840.146870054402445
103298.4296.2011340535191.167717125867432.19886594648052-0.929020423728182
104246.7253.758856214014-8.72955288375521-7.05885621401353-2.03272507762966
105227.3232.35202431047-11.6059590927862-5.05202431047011-0.590836849929565
106209.1227.511218212879-10.0715398774057-18.41121821287920.315291180210988
107259.9256.357126394254-1.247277654143283.542873605746261.81521019901855
108266276.1129338803083.51649622328926-10.11293388030760.981309010413292
109320.6287.5232194719375.3080920206842833.07678052806330.368699890985314
110308.5286.9884747354223.9826007375146721.5115252645784-0.271947340365475
111282.2275.0992863054710.3865709025550417.10071369452903-0.737718951207992
112262.7279.1337566799571.21293470604772-16.43375667995710.169945974469197
113263.5285.7946184520172.44817122260959-22.29461845201710.25423506176644
114313.1298.3054734424794.7312124384148814.7945265575210.469424479402792
115284.3277.938396137119-0.9633572192326176.36160386288088-1.16983665463459
116252.6259.63284649214-4.89726553018469-7.03284649213967-0.807941019271879
117250.3256.296264700931-4.54334169718862-5.996264700930810.0726952627189273
118246.5269.49538053881-0.521196001365975-22.99538053880970.82650671571776
119312.7305.7989756361427.8252790870366.90102436385811.71697019410385
120333.2339.81638852882713.763968248979-6.616388528826971.22291576402563
121446.4401.3663372747424.604581621579345.03366272526032.23010970798248
122511.6476.67166202168136.101833295618634.92833797831882.35954297488421
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140334.7336.36567627074-10.549639059427-1.665676270740430.145477502398077
141319.5334.186060232562-8.65310647509646-14.68606023256230.38953473458784
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189347372.859076668305-7.94035576291835-25.85907666830520.100219612058782
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267373.3355.07363010256411.954258651832718.22636989743620.773741340943312
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270466.9407.89459578018515.243511173118859.00540421981520.442733746928631
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278544.2502.83770847496810.557033364425241.362291525032-0.803458897786442
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285484510.3236112938042.99772804150825-26.3236112938038-1.01726430684308
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290541.2498.6112211157950.12798826156207942.5887788842051-0.265283357179425
291521.5501.3718821654710.7232320640039320.12811783452920.122310140916831
292469.7492.602495554141-1.42286962392015-22.9024955541415-0.441089103578256
293434.4485.888526368785-2.61915456905406-51.4885263687847-0.245935079281457
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295517.3493.249097155067-0.0017139790214251724.05090284493240.327520184540218
296485.7497.7211134601391.00989237087422-12.02111346013940.20787151105551
297465.8489.646761440512-1.04399266905306-23.8467614405117-0.422040868938342
298447483.626342984323-2.16904612688595-36.6263429843231-0.231231348610256
299426.6447.742758592431-9.79145089388926-21.1427585924314-1.56699895244569
300411.6437.480076883278-9.89800180128586-25.8800768832779-0.0219050034854646
301467.5425.219535870052-10.43223299384342.2804641299481-0.109804530771417
302484.5437.164400908261-5.372488094963347.33559909173951.0397180430236
303451.2429.921095829785-5.7954507366662921.2789041702151-0.0869124960250366
304417.4436.425486883686-3.01483986153748-19.02548688368650.571499290781554
305379.9433.083681673421-3.08876013982479-53.1836816734208-0.0151962522193725
306484.7431.39341320277-2.7725550897731953.30658679722960.0650046260456113
307455431.319674752053-2.1623076194437723.6803252479470.125427098866942
308420.8430.550652700283-1.84727957158363-9.75065270028280.0647356040975572
309416.5436.59973540718-0.0620761777347292-20.09973540718020.366840086900792
310376.3411.316885978149-5.76359896079783-35.0168859781491-1.17182991131375
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312405.8429.7658908304540.1744042629687-23.96589083045360.457743138666963
313500.8457.2404258022096.3471893792371643.55957419779111.26873320377439
314514466.4734670417086.999670830717747.52653295829250.134080520808731
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317414.4464.7966283957363.89079356810105-50.39662839573650.566041000253799
318538482.4301291932656.9978703017816955.56987080673470.638728727117662
319526500.4672045435989.4938363136831625.53279545640210.513007367274292
320488.5501.3437041775117.54554813006338-12.8437041775111-0.400365489478426
321520.2529.85779131781612.2858420310775-9.657791317815780.974101048327822
322504.4543.33677423934412.5555562275857-38.93677423934390.0554341826858219
323568.5581.68432208738718.3861423841292-13.18432208738691.19858014076295
324610.6633.51158268906925.9465705924424-22.91158268906851.554204763842
325818753.71631035648647.257650159958964.28368964351444.38019067492865
326830.9785.53758070782343.767755077098545.3624192921772-0.717165226717225
327835.9819.1352649332241.468702562812916.7647350667795-0.472443810559123
328782815.85502794659831.3532811022132-33.8550279465982-2.07902069311339
329762.3820.46173952625925.3070424561573-58.161739526259-1.24290107983364
330856.9810.48884498002217.331106620200746.4111550199783-1.63959361534514
331820.9799.15540031913410.850466561585221.7445996808659-1.331994090164
332769.6790.3669653698536.41058181413785-20.7669653698532-0.912396432210983
333752.2768.396405904683-0.00514977843458075-16.1964059046828-1.31841946953571
334724.4769.0019468260040.13289355305447-44.60194682600440.0283719627758471
335723.1750.735158447819-4.02638481088778-27.6351584478188-0.854995157238647
336719.5760.062281274294-1.00756705107642-40.56228127429380.620566966080307
337817.4752.366698082443-2.5195863510519965.0333019175572-0.310773193205168
338803.3754.309623674517-1.5107465494093448.99037632548280.207318142825319
339752.5731.135446562391-6.4077798564707721.3645534376088-1.00633615685973
340689717.801076152114-7.97346467108881-28.8010761521144-0.321794784145955
341630.4685.967178176686-13.3670435478787-55.5671781766857-1.10871350201951
342765.5704.741960438096-6.100940058378460.75803956190441.49364454435257
343757.7725.833874711420.046618478643722931.86612528858061.26353271058102
344732.2743.4857382267584.02653445169656-11.28573822675780.817886996934446
345702.6724.251883540317-1.23139788011076-21.6518835403167-1.08051348136091
346683.3723.511601059781-1.12038793827162-40.2116010597810.0228158115402887
347709.5736.7508097155442.12549274710293-27.25080971554390.66722151245832
348702.2741.2668222692442.66588934031043-39.06682226924360.111085007264783
349784.8724.598225091963-1.7049943080814160.201774908037-0.89836804964076
350810.9750.0377673361384.4312682174626560.86223266386151.26103261341379
351755.6736.610844318140.39456894387541618.9891556818599-0.829553026871376
352656.8690.936619765033-10.0184617582312-34.1366197650326-2.14018694834425
353615.1677.887201252419-10.7035746482339-62.7872012524187-0.14083043040418
354745.3686.59812287992-6.3148632096091758.70187712008080.902141683747534
355694.1668.763917713994-8.9189385975389425.3360822860063-0.535225474307013
356675.7677.598628150278-4.90565904532996-1.89862815027780.824756020118442
357643.7667.598287407262-6.05725179787488-23.8982874072619-0.236657934113607
358622.1664.791180428142-5.32262439452072-42.69118042814160.150987592836333
359634.6661.701122527669-4.81798703155171-27.10112252766870.103731253752732
360588629.977435629836-10.8999776624606-41.9774356298365-1.25020351835166
361689.7631.650604219498-8.0577433552688558.0493957805020.584176279916867
362673.9611.229891090379-10.852380752875662.670108909621-0.574320454980166
363647.9615.009993292321-7.5449405150595432.89000670767860.679698956762823
364568.8603.910763760614-8.34830055751754-35.1107637606144-0.16511432083326
365545.7609.211258201661-5.26324968720423-63.51125820166140.634146633960423
366632.6578.102016445458-11.105583173661354.4979835545422-1.20092798993762
367643.8611.440792185754-1.0588909798290232.35920781424582.06493189125259
368593.1598.040100528621-3.84868795468285-4.9401005286213-0.573329920163594
369579.7602.167858315385-2.04576550743587-22.46785831538520.370514652778008
370546590.820048941927-4.14823910504888-44.8200489419272-0.432120406922654
371562.9584.542809172381-4.62945204417866-21.6428091723814-0.098914755294593
372572.5609.9050332669252.1498594765344-37.40503326692451.39352127176385
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291928338jutmioltg9yu2sb/15ih41291928418.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291928338jutmioltg9yu2sb/15ih41291928418.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291928338jutmioltg9yu2sb/2y9y71291928418.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291928338jutmioltg9yu2sb/2y9y71291928418.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291928338jutmioltg9yu2sb/3y9y71291928418.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291928338jutmioltg9yu2sb/3y9y71291928418.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291928338jutmioltg9yu2sb/48iya1291928418.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291928338jutmioltg9yu2sb/48iya1291928418.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291928338jutmioltg9yu2sb/58iya1291928418.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291928338jutmioltg9yu2sb/58iya1291928418.ps (open in new window)


 
Parameters (Session):
par1 = 12 ;
 
Parameters (R input):
par1 = 12 ;
 
R code (references can be found in the software module):
par1 <- as.numeric(par1)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
m$coef
m$fitted
m$resid
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time')
grid()
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(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel,main='Level')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test5.png')
op <- par(mfrow = c(2,2))
hist(m$resid,main='Residual Histogram')
plot(density(m$resid),main='Residual Kernel Density')
qqnorm(m$resid,main='Residual Normal QQ Plot')
qqline(m$resid)
plot(m$resid^2, myfit^2,main='Sq.Resid vs. Sq.Fit',xlab='Squared residuals',ylab='Squared Fit')
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model',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,'Level',header=TRUE)
a<-table.element(a,'Slope',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,'Stand. Residuals',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,mylevel[i])
a<-table.element(a,myslope[i])
a<-table.element(a,myseas[i])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
 





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