Multiple Regression 10

*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: Tue, 14 Dec 2010 20:36:58 +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/14/t1292358910278970gys2bq8x4.htm/, Retrieved Tue, 14 Dec 2010 21:35:13 +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/14/t1292358910278970gys2bq8x4.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 «

2 1 22 15 16 17 10 1 2 22 23 24 42 9 1 2 22 26 22 39 30 1 2 23 19 21 22 18 1 2 21 19 23 20 16 1 2 21 16 23 31 20 1 1 24 23 21 42 20 2 1 22 22 20 30 18 1 2 21 19 22 33 21 1 2 23 24 20 29 20 1 1 20 19 12 31 20 2 1 23 25 23 39 20 1 1 20 23 23 44 29 1 2 21 31 30 40 14 2 1 22 29 22 42 25 2 2 22 18 21 28 19 2 2 21 17 21 29 19 1 1 20 22 15 35 25 1 1 21 21 22 26 25 1 2 21 24 24 42 19 1 1 20 22 23 26 19 1 1 21 16 15 30 18 1 2 23 22 24 28 24 1 1 23 21 24 24 18 2 1 21 25 21 26 26 1 1 22 22 21 39 26 2 1 20 24 18 33 24 2 1 23 21 20 50 29 2 1 21 25 19 40 26 1 1 21 29 29 49 28 2 1 23 19 20 31 18 2 1 23 29 23 37 19 2 2 22 25 24 29 21 1 1 21 19 27 37 13 1 1 0 27 28 16 19 1 2 21 25 24 28 26 1 2 21 23 29 29 17 1 1 22 24 24 31 19 2 2 22 23 22 34 28 1 2 22 25 25 30 15 1 1 22 26 24 31 16 1 1 23 23 14 44 18 2 1 0 22 22 35 25 1 2 22 32 24 47 15 1 2 21 22 24 39 24 1 1 23 18 24 34 24 2 1 21 19 24 15 14 2 2 32 23 22 26 19 2 2 32 24 22 25 20 2 1 21 19 21 30 27 1 1 20 16 21 25 20 1 1 21 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 7 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation PS[t] = + 6.5867952337856 -0.878020762828454Roken[t] -1.3024665063434Geslacht[t] + 0.0879722811529304Leeftijd[t] + 0.401296015151827O[t] + 0.130024469727997CMD[t] + 0.169296265598382PEC[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) 6.5867952337856 3.140785 2.0972 0.037713 0.018857 Roken -0.878020762828454 0.58383 -1.5039 0.134783 0.067391 Geslacht -1.3024665063434 0.609028 -2.1386 0.034144 0.017072 Leeftijd 0.0879722811529304 0.085701 1.0265 0.306362 0.153181 O 0.401296015151827 0.079976 5.0177 2e-06 1e-06 CMD 0.130024469727997 0.042259 3.0769 0.002502 0.001251 PEC 0.169296265598382 0.058105 2.9136 0.004139 0.00207 Multiple Linear Regression - Regression Statistics Multiple R 0.534702007831309 R-squared 0.285906237178833 Adjusted R-squared 0.256357529751751 F-TEST (value) 9.6757612116998 F-TEST (DF numerator) 6 F-TEST (DF denominator) 145 p-value 5.97857463535689e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.5800265148466 Sum Squared Residuals 1858.40552781568 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 15.7877922709388 -0.787792270938764 2 23 21.65503012624 1.34496987376001 3 26 24.0175862643184 1.98241373568164 4 19 19.4622913577629 -0.462291357762933 5 19 19.490297355108 -0.490297355107969 6 16 21.5977515845095 -5.59775158450947 7 23 23.791812071016 -0.791812071015971 8 22 20.4376645627971 1.5623354372029 9 19 21.625800774412 -2.62580077441201 10 24 20.3097591619039 3.69024083809615 11 19 18.3979896430298 0.602010356970163 12 25 23.2383376481542 1.76166235184575 13 23 26.0262303065493 -3.02623030654934 14 31 24.5612663245339 6.43873367546606 15 29 23.9856240890254 5.01437591097461 16 18 19.4457413977479 -1.44574139774791 17 17 19.487793586323 -2.48779358632298 18 22 20.9684568953892 1.03154310461078 19 21 22.695281055053 -1.69528105505296 20 24 23.2600205010709 0.73997949892912 21 22 21.9928271954616 0.00717280453843304 22 16 19.2212329687135 -3.22123296871349 23 22 22.4621038151767 -0.462103815176689 24 21 22.2286948490178 -1.22869484901781 25 25 21.5852605426711 3.41473945732894 26 22 24.2415716931164 -2.24157169311641 27 24 20.8649789729619 3.13502102703813 28 21 24.9883851600922 -3.98838516009217 29 25 22.6030110885594 2.39698891144063 30 29 29.0028047616548 -0.00280476165483319 31 19 20.655661313678 -1.65566131367803 32 29 22.8089924430999 6.19100755690013 33 25 21.1182464441282 3.88175355587184 34 19 24.1004751106395 -5.10047511063948 35 27 20.9396169508821 6.06038304911788 36 25 22.6247517840676 2.37524821593241 37 23 23.2375899391693 -0.237589939169288 38 24 23.2201901215592 0.779809878440759 39 23 22.1508506216532 0.849149378346839 40 25 21.5118100982461 3.48818990175386 41 26 22.7123013247641 3.2876986752359 42 23 20.8162240920595 2.18377590794052 43 22 21.1400626155649 0.859937384435056 44 32 23.3209300684703 8.67906993152973 45 22 23.7164284198788 -1.7164284198788 46 18 24.5447171398881 -6.54471713988807 47 19 19.327324233938 -0.327324233937992 48 23 20.4667112849731 2.53328871502695 49 24 20.5059830808434 3.49401691915657 50 19 22.2746546871814 -3.27465468718143 51 16 21.2295069610283 -5.2295069610283 52 23 23.2041563279971 -0.204156327997115 53 17 20.1408329462216 -3.14083294622163 54 17 23.024638582614 -6.02463858261398 55 28 22.0402923478297 5.95970765217031 56 24 21.4911588028661 2.50884119713385 57 21 19.1837982819563 1.81620171804371 58 14 19.8254930673672 -5.8254930673672 59 21 22.1305199181195 -1.13051991811953 60 20 23.3928832060952 -3.39288320609515 61 25 23.5335138555581 1.46648614444186 62 20 21.758940103356 -1.75894010335598 63 17 22.6317269381337 -5.63172693813372 64 26 27.3214874520953 -1.32148745209528 65 17 20.5164901142594 -3.51649011425943 66 17 20.8737980699247 -3.87379806992467 67 24 22.6201774748072 1.37982252519276 68 30 25.3710131055139 4.62898689448607 69 25 22.4038285239453 2.59617147605475 70 15 21.790197578471 -6.79019757847097 71 25 22.9675822691833 2.03241773081669 72 18 25.5699234228905 -7.56992342289053 73 20 23.0677204398956 -3.06772043989557 74 32 27.6931745675202 4.30682543247979 75 14 15.0959826315886 -1.09598263158855 76 20 20.3422511945641 -0.342251194564103 77 25 23.5491197566125 1.45088024338749 78 25 24.7105733939914 0.289426606008589 79 25 22.5073642889642 2.49263571103581 80 35 22.1461328600553 12.8538671399447 81 29 24.165574287349 4.83442571265101 82 25 25.8814100477762 -0.881410047776233 83 21 22.6201774748072 -1.62017747480724 84 21 21.2736331370505 -0.273633137050487 85 24 25.6690172748622 -1.66901727486218 86 26 22.066796477942 3.93320352205802 87 24 24.1987267141688 -0.198726714168755 88 20 24.9549707593868 -4.95497075938679 89 24 24.2490706227881 -0.249070622788071 90 18 19.1104003443211 -1.1104003443211 91 17 19.1417029008237 -2.14170290082371 92 22 22.8699470918869 -0.869947091886888 93 22 24.1574241234088 -2.15742412340876 94 22 20.9021802283569 1.09781977164312 95 24 25.4701691767594 -1.47016917675935 96 32 24.0574796384729 7.94252036152708 97 19 20.5529383248676 -1.55293832486762 98 21 21.4789497207493 -0.478949720749304 99 23 23.7549074253766 -0.754907425376594 100 26 21.3554274311921 4.64457256880795 101 18 23.0795016295047 -5.07950162950466 102 19 19.5797669430609 -0.579766943060935 103 22 24.5765478486784 -2.57654784867839 104 27 20.5743824106202 6.4256175893798 105 21 20.9549388564469 0.0450611435531078 106 20 21.4534421563874 -1.45344215638739 107 21 24.1106031644278 -3.11060316442777 108 20 24.776673696884 -4.776673696884 109 29 22.1817736302569 6.81822636974314 110 30 23.6850402536303 6.31495974636969 111 23 23.1565001614552 -0.15650016145517 112 29 19.7725095467781 9.22749045322193 113 19 22.6820303257981 -3.68203032579812 114 26 24.7233989023411 1.2766010976589 115 22 21.3335130357434 0.666486964256646 116 26 26.2698303211394 -0.269830321139417 117 27 25.2073830371562 1.79261696284381 118 19 22.5497362940165 -3.54973629401647 119 24 23.3416789520276 0.658321047972382 120 26 21.1291345835847 4.8708654164153 121 22 19.7302231514717 2.26977684852833 122 23 24.7830704652235 -1.78307046522347 123 25 22.8798036738068 2.1201963261932 124 19 23.6649475418916 -4.66494754189157 125 20 22.4456472811581 -2.44564728115814 126 25 23.6901280651443 1.3098719348557 127 14 19.122372548104 -5.12237254810401 128 20 18.7560127867263 1.24398721327374 129 27 25.5380495215427 1.46195047845731 130 21 22.9821585015312 -1.98215850153116 131 21 21.2947998235142 -0.294799823514223 132 14 19.3077908812097 -5.30779088120966 133 21 24.5187816830184 -3.51878168301841 134 23 21.916120712834 1.08387928716601 135 18 20.8043062838964 -2.80430628389641 136 20 21.7989217514557 -1.79892175145568 137 19 22.2076156611301 -3.20761566113006 138 15 20.456567023009 -5.45656702300905 139 23 21.7382490623902 1.26175093760978 140 26 25.6139053712061 0.386094628793907 141 21 23.3127367119725 -2.31273671197253 142 13 16.1424490270512 -3.14244902705121 143 24 21.0414967689431 2.95850323105694 144 17 18.2144582077956 -1.21445820779565 145 21 24.4858383673783 -3.48583836737829 146 28 25.9701751193018 2.02982488069825 147 22 22.0836230618767 -0.0836230618766936 148 25 19.4428607452633 5.55713925473672 149 18 20.8929452247211 -2.89294522472114 150 27 24.7899124477074 2.21008755229263 151 25 23.6429302224637 1.35706977753635 152 21 21.9006150715596 -0.900615071559567 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.432356550720764 0.864713101441527 0.567643449279236 11 0.40025026463314 0.80050052926628 0.59974973536686 12 0.27265282388051 0.54530564776102 0.72734717611949 13 0.186051669671825 0.37210333934365 0.813948330328175 14 0.542168424752701 0.915663150494598 0.457831575247299 15 0.50533126121678 0.98933747756644 0.49466873878322 16 0.495370815000722 0.990741630001444 0.504629184999278 17 0.445440151396905 0.89088030279381 0.554559848603095 18 0.388733663585913 0.777467327171825 0.611266336414087 19 0.306882365923537 0.613764731847075 0.693117634076463 20 0.23386823460055 0.467736469201099 0.76613176539945 21 0.176081090253413 0.352162180506826 0.823918909746587 22 0.156692866161707 0.313385732323414 0.843307133838293 23 0.112447546274893 0.224895092549785 0.887552453725107 24 0.0828561644736478 0.165712328947296 0.917143835526352 25 0.0892839624721971 0.178567924944394 0.910716037527803 26 0.0773165705974768 0.154633141194954 0.922683429402523 27 0.066056318703121 0.132112637406242 0.933943681296879 28 0.111914519376095 0.223829038752191 0.888085480623905 29 0.0896828436951455 0.179365687390291 0.910317156304854 30 0.0668473718766257 0.133694743753251 0.933152628123374 31 0.0550948608540267 0.110189721708053 0.944905139145973 32 0.0839051837389558 0.167810367477912 0.916094816261044 33 0.0749804827154979 0.149960965430996 0.925019517284502 34 0.124122204730737 0.248244409461475 0.875877795269263 35 0.117783398901176 0.235566797802352 0.882216601098824 36 0.101334670187886 0.202669340375771 0.898665329812114 37 0.0784069829338158 0.156813965867632 0.921593017066184 38 0.0617346298717905 0.123469259743581 0.93826537012821 39 0.0470602024237269 0.0941204048474538 0.952939797576273 40 0.0474262489454695 0.094852497890939 0.95257375105453 41 0.0491130073079332 0.0982260146158665 0.950886992692067 42 0.0481278502174837 0.0962557004349675 0.951872149782516 43 0.0541456792460446 0.108291358492089 0.945854320753955 44 0.148082754862538 0.296165509725077 0.851917245137461 45 0.13122573246677 0.26245146493354 0.86877426753323 46 0.20194823812014 0.403896476240279 0.79805176187986 47 0.168262767368326 0.336525534736652 0.831737232631674 48 0.149178113032168 0.298356226064337 0.850821886967831 49 0.14131300241136 0.28262600482272 0.85868699758864 50 0.137347983331985 0.27469596666397 0.862652016668015 51 0.157829625882356 0.315659251764712 0.842170374117644 52 0.130817353170346 0.261634706340692 0.869182646829654 53 0.123172217673059 0.246344435346118 0.876827782326941 54 0.162758152874464 0.325516305748928 0.837241847125536 55 0.19288708377865 0.385774167557299 0.80711291622135 56 0.170863481201804 0.341726962403608 0.829136518798196 57 0.165768255604088 0.331536511208175 0.834231744395912 58 0.200783697501669 0.401567395003339 0.799216302498331 59 0.174315153008965 0.34863030601793 0.825684846991035 60 0.178811801185642 0.357623602371284 0.821188198814358 61 0.160868835217006 0.321737670434012 0.839131164782994 62 0.157826746926803 0.315653493853605 0.842173253073197 63 0.202423279404688 0.404846558809377 0.797576720595312 64 0.174864983397951 0.349729966795902 0.825135016602049 65 0.18045281933459 0.36090563866918 0.81954718066541 66 0.276142697274443 0.552285394548886 0.723857302725557 67 0.243922112131126 0.487844224262251 0.756077887868874 68 0.287802315419413 0.575604630838826 0.712197684580587 69 0.270287842701227 0.540575685402453 0.729712157298773 70 0.370989449034487 0.741978898068974 0.629010550965513 71 0.345029399920885 0.69005879984177 0.654970600079115 72 0.483391881514233 0.966783763028466 0.516608118485767 73 0.46780796587608 0.93561593175216 0.53219203412392 74 0.512918501491588 0.974162997016824 0.487081498508412 75 0.4736857521619 0.9473715043238 0.5263142478381 76 0.429264121107502 0.858528242215003 0.570735878892498 77 0.393514671342652 0.787029342685303 0.606485328657348 78 0.367181406171089 0.734362812342178 0.632818593828911 79 0.349867922590938 0.699735845181876 0.650132077409062 80 0.862771485983476 0.274457028033049 0.137228514016524 81 0.900051160313747 0.199897679372507 0.0999488396862534 82 0.877891057707669 0.244217884584662 0.122108942292331 83 0.856035954344368 0.287928091311264 0.143964045655632 84 0.82832969534546 0.343340609309079 0.171670304654539 85 0.800990549361206 0.398018901277588 0.199009450638794 86 0.80586501948417 0.388269961031662 0.194134980515831 87 0.772365994015475 0.45526801196905 0.227634005984525 88 0.79408443054432 0.411831138911361 0.20591556945568 89 0.757509246799424 0.484981506401152 0.242490753200576 90 0.725003413302563 0.549993173394874 0.274996586697437 91 0.707011668740476 0.585976662519049 0.292988331259524 92 0.669285129641017 0.661429740717966 0.330714870358983 93 0.641951138631042 0.716097722737916 0.358048861368958 94 0.59766386780529 0.80467226438942 0.40233613219471 95 0.555233330904036 0.889533338191928 0.444766669095964 96 0.73035085125937 0.53929829748126 0.26964914874063 97 0.695045214392768 0.609909571214465 0.304954785607232 98 0.649406329588502 0.701187340822995 0.350593670411498 99 0.601557119986164 0.796885760027672 0.398442880013836 100 0.648782922314135 0.70243415537173 0.351217077685865 101 0.664912428839276 0.670175142321448 0.335087571160724 102 0.617087891562988 0.765824216874023 0.382912108437012 103 0.610094581644188 0.779810836711623 0.389905418355812 104 0.738421364790522 0.523157270418956 0.261578635209478 105 0.694305138628639 0.611389722742722 0.305694861371361 106 0.657393110025726 0.685213779948547 0.342606889974274 107 0.623805969738312 0.752388060523376 0.376194030261688 108 0.703702135655018 0.592595728689963 0.296297864344982 109 0.848891904298643 0.302216191402713 0.151108095701357 110 0.88929959545351 0.221400809092979 0.11070040454649 111 0.863170307744806 0.273659384510389 0.136829692255194 112 0.966044069189913 0.0679118616201731 0.0339559308100866 113 0.96663864861835 0.0667227027632984 0.0333613513816492 114 0.954376575717685 0.0912468485646305 0.0456234242823153 115 0.937782239302536 0.124435521394927 0.0622177606974636 116 0.917060896492614 0.165878207014771 0.0829391035073855 117 0.898749047289424 0.202501905421151 0.101250952710576 118 0.884356447722752 0.231287104554495 0.115643552277248 119 0.85752686349467 0.284946273010661 0.142473136505331 120 0.918129342164077 0.163741315671846 0.0818706578359229 121 0.917370628117356 0.165258743765288 0.082629371882644 122 0.895151673206679 0.209696653586642 0.104848326793321 123 0.873723756895788 0.252552486208423 0.126276243104212 124 0.882429460546323 0.235141078907354 0.117570539453677 125 0.860757239595526 0.278485520808949 0.139242760404475 126 0.839248574305046 0.321502851389908 0.160751425694954 127 0.85284910418387 0.294301791632259 0.147150895816129 128 0.841327584367174 0.317344831265651 0.158672415632826 129 0.794939328051083 0.410121343897834 0.205060671948917 130 0.736095660511103 0.527808678977793 0.263904339488897 131 0.683011516413236 0.633976967173528 0.316988483586764 132 0.725630614850558 0.548738770298884 0.274369385149442 133 0.785274823897846 0.429450352204308 0.214725176102154 134 0.719805899989074 0.560388200021853 0.280194100010926 135 0.76393604723597 0.472127905528061 0.236063952764031 136 0.681687268779393 0.636625462441214 0.318312731220607 137 0.626277774224825 0.74744445155035 0.373722225775175 138 0.778740438034608 0.442519123930784 0.221259561965392 139 0.793958362932702 0.412083274134595 0.206041637067298 140 0.680255016095074 0.639489967809853 0.319744983904926 141 0.539045594429851 0.921908811140297 0.460954405570149 142 0.954125271943062 0.0917494561138752 0.0458747280569376 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 8 0.0601503759398496 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/10j17f1292359006.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/10j17f1292359006.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/1c0sl1292359006.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/1c0sl1292359006.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/2c0sl1292359006.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/2c0sl1292359006.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/3n9r61292359006.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/3n9r61292359006.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/4n9r61292359006.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/4n9r61292359006.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/5n9r61292359006.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/5n9r61292359006.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/6g08r1292359006.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/6g08r1292359006.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/7g08r1292359006.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/7g08r1292359006.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/8qapu1292359006.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/8qapu1292359006.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/9qapu1292359006.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292358910278970gys2bq8x4/9qapu1292359006.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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Software written by Ed van Stee & Patrick Wessa

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