Time Series Analysis Multiple Linear Regression (verleden)

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 17 Dec 2010 12:25:38 +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/17/t12925886525esubilo0lalgu9.htm/, Retrieved Fri, 17 Dec 2010 13:24:24 +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/17/t12925886525esubilo0lalgu9.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 «

40399 44164 44496 43110 43880 36763 40399 44164 44496 43110 37903 36763 40399 44164 44496 35532 37903 36763 40399 44164 35533 35532 37903 36763 40399 32110 35533 35532 37903 36763 33374 32110 35533 35532 37903 35462 33374 32110 35533 35532 33508 35462 33374 32110 35533 36080 33508 35462 33374 32110 34560 36080 33508 35462 33374 38737 34560 36080 33508 35462 38144 38737 34560 36080 33508 37594 38144 38737 34560 36080 36424 37594 38144 38737 34560 36843 36424 37594 38144 38737 37246 36843 36424 37594 38144 38661 37246 36843 36424 37594 40454 38661 37246 36843 36424 44928 40454 38661 37246 36843 48441 44928 40454 38661 37246 48140 48441 44928 40454 38661 45998 48140 48441 44928 40454 47369 45998 48140 48441 44928 49554 47369 45998 48140 48441 47510 49554 47369 45998 48140 44873 47510 49554 47369 45998 45344 44873 47510 49554 47369 42413 45344 44873 47510 49554 36912 42413 45344 44873 47510 43452 36912 42413 45344 44873 42142 43452 36912 42413 45344 44382 42142 43452 36912 42413 4 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 9 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation OPENVAC[t] = + 1842.18557079189 + 1.17683534632143Y1[t] -0.0681417804041687Y2[t] -0.194231091231271Y3[t] + 0.0268886495538088Y4[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 1842.18557079189 832.191319 2.2137 0.028743 0.014371 Y1 1.17683534632143 0.09136 12.8813 0 0 Y2 -0.0681417804041687 0.139838 -0.4873 0.626941 0.313471 Y3 -0.194231091231271 0.139921 -1.3881 0.167663 0.083832 Y4 0.0268886495538088 0.091044 0.2953 0.768247 0.384123 Multiple Linear Regression - Regression Statistics Multiple R 0.965335002681266 R-squared 0.93187166740164 Adjusted R-squared 0.929600722981695 F-TEST (value) 410.345431273955 F-TEST (DF numerator) 4 F-TEST (DF denominator) 120 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2074.32861480789 Sum Squared Residuals 516340704.265297 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 40399 43590.476744309 -3191.47674430903 2 36763 38892.4061838999 -2129.40618389993 3 37903 34971.7390584672 2931.26094153278 4 35532 37283.4478936571 -1751.44789365708 5 35533 35020.478140015 512.521859984981 6 32110 34864.0285629183 -2754.02856291833 7 33374 31326.8280084803 2047.17199151966 8 35462 32983.6499813708 2478.35001862921 9 33508 36019.6308879933 -2511.63088799327 10 36080 33240.2666370583 2839.73336294173 11 34560 36028.6689212519 -1468.66892125186 12 38737 34500.289588178 4236.71041182198 13 38144 38967.403548102 -823.403548102015 14 37594 38349.3008363091 -755.30083630912 15 36424 36890.2754562172 -466.275456217195 16 36843 35778.3490065298 1064.65099347019 17 37246 36442.0510307032 803.94896929684 18 38661 37100.2258887673 1560.77411123266 19 40454 38625.1442191054 1828.85578089456 20 44928 40571.7805901847 4356.21940981529 21 48441 45450.7628490401 2990.23715095993 22 48140 48969.91018768 -829.910187679996 23 45998 47555.5221203587 -1557.52212035867 24 47369 44493.2174790481 2875.7825209519 25 49554 46405.5418168237 3148.45818317634 26 47510 49291.4541815036 -1781.45418150357 27 44873 46413.2266300171 -1540.22663001711 28 45344 43061.6630251116 2282.33697488845 29 42413 44251.4023979065 -1838.40239790653 30 36912 41227.2302071569 -4315.23020715692 31 43452 34790.794312564 8661.205687436 32 42142 43444.1012938482 -1302.10129384822 33 44382 42446.4543473449 1935.54565265512 34 43636 43753.6454575863 -117.645457586344 35 44167 43153.3831987201 1013.61680127991 36 44423 43358.8147605247 1064.18523947525 37 42868 43829.0282928475 -961.02829284748 38 43908 41858.4093915232 2049.59060847676 39 42013 43152.8333337839 -1139.83333378388 40 38846 41160.7757420348 -2314.77574203482 41 35087 37319.0546891640 -2232.05468916404 42 33026 33507.167754301 -481.167754300992 43 34646 31902.0309330968 2743.96906690325 44 37135 34593.9027223519 2541.09727764810 45 37985 37711.8920604461 273.107939553917 46 43121 38172.5253388683 4948.47466113173 47 43722 43718.9495904342 3.05040956584889 48 43630 43978.0808706104 -348.080870610374 49 42234 42854.1432762828 -620.143276282826 50 39351 41238.9173948937 -1887.91739489366 51 39327 37975.2563556683 1351.74364433171 52 35704 38412.1379078617 -2708.1379078617 53 30466 34672.5305321115 -4206.53053211148 54 28155 28682.28622801 -527.286228010027 55 29257 27022.6003043598 2234.39969564017 56 29998 29396.9133890560 601.086610943969 57 32529 30501.8814441474 2027.11855585256 58 34787 33153.7763147518 1633.22368524821 59 33855 35524.3097337486 -1669.30973374856 60 34556 33801.9606482374 754.039351762602 61 31348 34319.9117333659 -2971.91173336589 62 30805 30738.5945020235 66.4054979765514 63 28353 30156.9555241702 -1803.95552417021 64 24514 27950.2985257567 -3436.29852575665 65 21106 23618.7199715496 -2512.71997154965 66 21346 20331.3155052492 1014.68449475084 67 23335 21525.7053665146 1809.29463348538 68 24379 24408.7908763301 -29.7908763300542 69 26290 25363.6209970909 926.379002909145 70 30084 27161.5409606031 2922.45903939692 71 29429 31346.9395869113 -1917.93958691132 72 30632 29974.4786550086 657.52134499142 73 27349 30749.3158919639 -3400.31589196388 74 27264 27033.0277893280 230.972210671969 75 27474 26905.4341817486 568.56581825137 76 24482 27828.369373736 -3346.36937373598 77 21453 24221.2024499269 -2768.20244992687 78 18788 20817.3743285179 -2029.37432851788 79 19282 18474.2956247857 807.704375214252 80 19713 19745.1252665202 -32.1252665201696 81 21917 20654.8593998979 1262.14060010210 82 23812 23051.626985707 760.373014293006 83 23785 25061.1148755342 -1276.11487553423 84 24696 24483.7153302016 212.284669798376 85 24562 25248.8468245047 -686.8468245047 86 23580 25085.2719565171 -1505.27195651714 87 24939 23761.080127354 1177.91987264599 88 23899 25477.8371173302 -1578.83711733024 89 21454 24348.4555301356 -2894.45553013558 90 19761 21251.5958531549 -1490.59585315488 91 19815 19664.3622745450 150.637725454974 92 20780 20290.2062399951 489.793760004865 93 23462 21685.2631823490 1776.73681765102 94 25005 24719.7678004720 285.232199528046 95 24725 26166.8874688397 -1441.88746883968 96 26198 25237.2505648432 960.7494351568 97 27543 26762.2255128213 780.774487178695 98 26471 28340.5701028946 -1869.57010289458 99 26558 26693.7206977357 -135.720697735664 100 25317 26647.5195245456 -1330.51952454560 101 22896 25425.5194883153 -2529.51948831533 102 22248 22615.2423270939 -367.242327093904 103 23406 22261.0043697653 1144.99563023470 104 25073 24104.8002322821 968.19976771795 105 27691 26048.4408994399 1642.55910056005 106 30599 28773.460039619 1825.53996038097 107 31948 31724.6558727244 223.344127275565 108 32946 32650.3768394595 295.623160540539 109 34012 33238.5057245544 773.494275445636 110 32936 34241.1811577211 -1305.18115772115 111 32974 32744.6973463677 229.302653632283 112 30951 32682.522174245 -1731.52217424498 113 29812 30536.8508355706 -724.85083557057 114 29010 29297.9732294814 -287.973229481402 115 31068 28825.7160358559 2242.28396414414 116 32447 31469.1263613346 977.873638665416 117 34844 33076.8936831658 1767.10631683425 118 35676 35382.5082104248 293.491789575225 119 35387 35985.7915369092 -598.791536909233 120 36488 35160.4996825794 1327.50031742058 121 35652 36378.7401984922 -726.740198492183 122 33488 35398.3858905371 -1910.38589053708 123 32914 32687.0614783487 226.938521651301 124 29781 32350.9983977829 -2569.9983977829 125 27951 29100.9238101073 -1149.92381010733 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.70338973942515 0.5932205211497 0.296610260574850 9 0.56377489901037 0.87245020197926 0.43622510098963 10 0.596130282228933 0.807739435542134 0.403869717771067 11 0.469455430757428 0.938910861514856 0.530544569242572 12 0.658353611077724 0.683292777844552 0.341646388922276 13 0.649353949751143 0.701292100497714 0.350646050248857 14 0.550936567175016 0.898126865649967 0.449063432824984 15 0.457518776051861 0.915037552103722 0.542481223948139 16 0.378734737106478 0.757469474212955 0.621265262893522 17 0.324270936824135 0.64854187364827 0.675729063175865 18 0.328078585464196 0.656157170928393 0.671921414535804 19 0.411830396376097 0.823660792752195 0.588169603623903 20 0.80701140350575 0.385977192988501 0.192988596494251 21 0.897010335707207 0.205979328585586 0.102989664292793 22 0.86289109903974 0.27421780192052 0.13710890096026 23 0.830496536275298 0.339006927449404 0.169503463724702 24 0.885543248294458 0.228913503411084 0.114456751705542 25 0.929356705651338 0.141286588697324 0.0706432943486618 26 0.916452534629813 0.167094930740374 0.0835474653701872 27 0.902943921866784 0.194112156266432 0.097056078133216 28 0.899883636282904 0.200232727434191 0.100116363717096 29 0.886003484874173 0.227993030251655 0.113996515125827 30 0.945228917722532 0.109542164554935 0.0547710822774676 31 0.999721105844668 0.000557788310663017 0.000278894155331509 32 0.999626948621493 0.000746102757014502 0.000373051378507251 33 0.999693948871695 0.000612102256609890 0.000306051128304945 34 0.9994986762997 0.00100264740060091 0.000501323700300457 35 0.999298043982954 0.00140391203409219 0.000701956017046096 36 0.999023989989 0.00195202002200030 0.000976010011000151 37 0.99853129818746 0.00293740362508081 0.00146870181254040 38 0.998657637015926 0.00268472596814755 0.00134236298407378 39 0.99808854169432 0.00382291661135918 0.00191145830567959 40 0.998276449111683 0.00344710177663374 0.00172355088831687 41 0.998753220881945 0.00249355823610992 0.00124677911805496 42 0.998334827071928 0.00333034585614322 0.00166517292807161 43 0.998722900500492 0.00255419899901578 0.00127709949950789 44 0.998878258270273 0.0022434834594542 0.0011217417297271 45 0.998254828555675 0.00349034288864994 0.00174517144432497 46 0.999829184488151 0.000341631023697889 0.000170815511848944 47 0.999716495755975 0.000567008488049238 0.000283504244024619 48 0.999567738070495 0.000864523859010315 0.000432261929505157 49 0.999391172794891 0.00121765441021719 0.000608827205108595 50 0.999258141162963 0.00148371767407379 0.000741858837036896 51 0.999402185745545 0.00119562850891058 0.000597814254455291 52 0.999495020287436 0.00100995942512901 0.000504979712564503 53 0.999885327498467 0.000229345003066579 0.000114672501533290 54 0.999859894825038 0.000280210349924024 0.000140105174962012 55 0.99989751422582 0.000204971548361186 0.000102485774180593 56 0.9998342300101 0.000331539979802074 0.000165769989901037 57 0.999827265241431 0.000345469517137336 0.000172734758568668 58 0.999791152112245 0.000417695775509557 0.000208847887754779 59 0.999800735398592 0.00039852920281608 0.00019926460140804 60 0.999752920015538 0.000494159968925068 0.000247079984462534 61 0.999874733500774 0.000250532998451961 0.000125266499225981 62 0.99983725401301 0.000325491973980184 0.000162745986990092 63 0.999828897271305 0.000342205457390348 0.000171102728695174 64 0.999931907422903 0.000136185154194786 6.80925770973931e-05 65 0.999946678319772 0.000106643360455195 5.33216802275974e-05 66 0.99992915119899 0.000141697602020721 7.08488010103607e-05 67 0.999919212594256 0.000161574811487506 8.07874057437528e-05 68 0.999864649226317 0.000270701547365096 0.000135350773682548 69 0.999786024045033 0.000427951909934782 0.000213975954967391 70 0.999878767430168 0.000242465139663161 0.000121232569831581 71 0.999911332826847 0.000177334346306803 8.86671731534016e-05 72 0.999872553594583 0.000254892810834602 0.000127446405417301 73 0.999972911045603 5.41779087938425e-05 2.70889543969213e-05 74 0.999968442236395 6.31155272103652e-05 3.15577636051826e-05 75 0.999943549449114 0.000112901101772683 5.64505508863413e-05 76 0.999986612707745 2.67745845103121e-05 1.33872922551560e-05 77 0.99998930707681 2.13858463785590e-05 1.06929231892795e-05 78 0.999987918381178 2.41632376447028e-05 1.20816188223514e-05 79 0.999981997040796 3.60059184081912e-05 1.80029592040956e-05 80 0.999966897214427 6.62055711451267e-05 3.31027855725633e-05 81 0.99995325233123 9.34953375419370e-05 4.67476687709685e-05 82 0.99991474895246 0.000170502095078412 8.5251047539206e-05 83 0.99990104838663 0.000197903226739557 9.89516133697787e-05 84 0.999823755977887 0.000352488044225166 0.000176244022112583 85 0.999727242840323 0.000545514319353707 0.000272757159676854 86 0.999660189870596 0.000679620258808833 0.000339810129404417 87 0.999587414330024 0.000825171339952945 0.000412585669976473 88 0.99966707234961 0.000665855300777662 0.000332927650388831 89 0.99985532807387 0.000289343852260695 0.000144671926130347 90 0.999798734035571 0.000402531928858096 0.000201265964429048 91 0.999622548149846 0.00075490370030839 0.000377451850154195 92 0.999311769705834 0.00137646058833207 0.000688230294166036 93 0.999097507000582 0.00180498599883602 0.00090249299941801 94 0.998475823556986 0.00304835288602881 0.00152417644301441 95 0.998880201533106 0.00223959693378724 0.00111979846689362 96 0.998149603634675 0.00370079273064949 0.00185039636532474 97 0.99679754097771 0.0064049180445806 0.0032024590222903 98 0.998423785578812 0.00315242884237638 0.00157621442118819 99 0.997116822309023 0.00576635538195323 0.00288317769097661 100 0.996758321877377 0.00648335624524657 0.00324167812262329 101 0.999317434433534 0.00136513113293249 0.000682565566466246 102 0.99906102632505 0.0018779473498987 0.00093897367494935 103 0.998116984095003 0.00376603180999341 0.00188301590499671 104 0.996690044715 0.00661991057000068 0.00330995528500034 105 0.994003999039012 0.011992001921975 0.0059960009609875 106 0.989080029983223 0.0218399400335539 0.0109199700167769 107 0.987444594644892 0.0251108107102153 0.0125554053551076 108 0.986142679959347 0.0277146400813068 0.0138573200406534 109 0.975576430505102 0.0488471389897953 0.0244235694948977 110 0.978203069570552 0.0435938608588951 0.0217969304294476 111 0.95878324287811 0.0824335142437807 0.0412167571218904 112 0.960892398041997 0.0782152039160065 0.0391076019580032 113 0.934343546779095 0.131312906441810 0.0656564532209049 114 0.926003965974093 0.147992068051813 0.0739960340259067 115 0.923316012342436 0.153367975315128 0.0766839876575639 116 0.861830438141017 0.276339123717965 0.138169561858983 117 0.95686846275074 0.0862630744985195 0.0431315372492597 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 74 0.672727272727273 NOK 5% type I error level 80 0.727272727272727 NOK 10% type I error level 83 0.754545454545455 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/10fn5p1292588728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/10fn5p1292588728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/1848w1292588728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/1848w1292588728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/2848w1292588728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/2848w1292588728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/31vpy1292588728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/31vpy1292588728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/41vpy1292588728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/41vpy1292588728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/51vpy1292588728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/51vpy1292588728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/6tm611292588728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/6tm611292588728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/74v641292588728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/74v641292588728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/84v641292588728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/84v641292588728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/94v641292588728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/17/t12925886525esubilo0lalgu9/94v641292588728.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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