Multiple Regression_1

*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, 23 Nov 2010 09:48:38 +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/Nov/23/t1290505809huz9ba60pjk8a2f.htm/, Retrieved Tue, 23 Nov 2010 10:50:21 +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/Nov/23/t1290505809huz9ba60pjk8a2f.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 «

1 3 4 4 2 1 3 2 2 2 1 3 5 5 4 1 5 4 5 3 2 3 1 1 2 1 2 2 4 1 4 3 5 6 4 1 2 1 5 3 1 2 3 4 1 2 3 5 5 4 1 7 2 7 4 1 4 2 2 4 2 6 2 7 3 1 2 2 5 4 1 4 1 5 1 1 4 4 7 4 1 2 3 3 1 1 6 6 6 4 1 1 1 2 4 2 3 3 6 3 1 2 2 1 2 2 5 5 5 6 1 3 5 4 5 2 5 3 4 4 1 1 3 7 6 1 7 5 7 1 1 2 5 5 2 2 5 4 6 4 1 5 2 5 4 1 1 1 1 1 2 4 4 6 2 1 5 6 4 1 1 2 2 2 2 1 1 3 2 2 1 5 2 6 2 2 7 4 6 6 1 4 2 6 2 1 1 1 1 1 1 5 5 6 4 1 5 5 6 3 1 1 1 1 3 1 6 1 1 1 1 5 2 7 4 1 5 4 2 3 1 3 5 3 4 1 4 3 5 3 1 4 3 3 2 1 4 1 4 1 1 5 2 2 5 1 3 3 3 4 2 2 2 7 1 2 6 5 7 2 1 1 4 5 4 1 4 4 1 3 1 3 2 2 2 2 3 3 5 3 1 6 6 2 3 1 3 2 4 2 2 5 3 7 2 1 2 2 2 4 1 4 5 5 4 1 3 5 6 2 1 2 5 3 2 1 6 6 7 5 2 5 4 4 4 1 5 2 3 5 1 4 5 5 5 2 1 2 3 2 1 3 1 2 3 1 4 6 6 4 1 2 6 6 2 1 5 3 5 2 1 2 4 2 2 3 4 5 3 5 2 2 2 4 2 2 5 4 6 3 1 3 3 5 2 1 1 2 2 2 1 5 2 5 2 1 2 3 2 2 1 2 3 1 2 1 2 7 2 1 1 5 2 4 3 1 5 2 5 3 1 2 2 5 3 1 4 5 3 3 1 2 1 2 1 3 6 5 7 4 1 1 2 1 1 1 1 1 5 1 1 4 2 5 1 1 2 2 2 3 1 4 0 6 2 1 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 14 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Depressed[t] = + 0.740696636831173 + 0.00475423720840306`high-strung`[t] + 0.0425359188269914cannotdo[t] + 0.0431590863474944worrytoomuch[t] + 0.0696672775570097limitactivity[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) 0.740696636831173 0.144748 5.1171 1e-06 0 `high-strung` 0.00475423720840306 0.032556 0.146 0.884089 0.442044 cannotdo 0.0425359188269914 0.029214 1.456 0.147458 0.073729 worrytoomuch 0.0431590863474944 0.028942 1.4912 0.137977 0.068989 limitactivity 0.0696672775570097 0.036266 1.921 0.0566 0.0283 Multiple Linear Regression - Regression Statistics Multiple R 0.30396767880756 R-squared 0.092396349759656 Adjusted R-squared 0.0685120431743836 F-TEST (value) 3.86849622072053 F-TEST (DF numerator) 4 F-TEST (DF denominator) 152 p-value 0.00506294335989188 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.553042530641777 Sum Squared Residuals 46.4901181861965 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1 1.23707392426831 -0.237073924268314 2 1 1.06568391391937 -0.0656839139193697 3 1 1.46210348455685 -0.462103484556846 4 1 1.35940876258965 -0.359408762589649 5 2 0.979988908744885 1.02001109125511 6 1 1.07758057184895 -0.0775805718489468 7 4 1.50526257090434 2.49473742909566 8 1 1.21753829448347 -0.217538294483469 9 1 1.12011649067594 -0.120116490675938 10 2 1.46210348455685 0.537896515443153 11 1 1.43983084960447 -0.439830849604475 12 1 1.20977270624179 -0.209772706241793 13 2 1.36540933483906 0.634590665160938 14 1 1.32974149086747 -0.32974149086747 15 1 1.08771221378626 -0.0877122137862561 16 1 1.51063997563325 -0.510639975633248 17 1 1.07695740432844 -0.0769574043284435 18 1 1.56206120135654 -0.562061201356542 19 1 1.15297407578959 -0.152974075789592 20 2 1.35052345569335 0.64947654430665 21 1 1.01777059036347 -0.0177705903634728 22 2 1.61094651408767 0.389053485912327 23 1 1.48861167576636 -0.488611675766362 24 2 1.34338103497218 0.656618965027824 25 1 1.59317590029507 -0.593175900295067 26 1 1.35843677341442 -0.358436773414419 27 1 1.31801469223442 -0.318014692234425 28 2 1.47223512649416 0.527764873505843 29 1 1.34400420249268 -0.344004202492679 30 1 0.900813156771069 0.0991868432289313 31 2 1.32814633417173 0.671853665828266 32 1 1.26198695878212 -0.261986958782121 33 1 1.06092967671097 -0.0609296767109673 34 1 1.09871135832956 -0.0987113583295556 35 1 1.24782873372615 -0.247828733726155 36 2 1.62107815602498 0.378921843975018 37 1 1.24307449651775 -0.243074496517752 38 1 0.900813156771069 0.0991868432289313 39 1 1.51477104532115 -0.514771045321148 40 1 1.44510376776414 -0.445103767764138 41 1 1.04014771188509 -0.0401477118850881 42 1 0.924584342813084 0.0754156571869161 43 1 1.43032237518767 -0.430322375187669 44 1 1.22993150354717 -0.229931503547169 45 1 1.37578531186186 -0.375785311861858 46 1 1.31211860655426 -0.312118606554258 47 1 1.15613315630226 -0.156133156302259 48 1 1.04455312743876 -0.0445531274387615 49 1 1.28419422100721 -0.284194221007205 50 1 1.29071347420788 -0.290713474207875 51 2 1.20705783089143 0.79294216910857 52 2 1.42334981376303 0.576650186236974 53 1 1.41005909131305 -0.41005909131305 54 1 1.18201817999127 -0.182018179991271 55 1 1.06568391391937 -0.0656839139193703 56 2 1.30736436934586 0.692635630654145 57 1 1.31975757840955 -0.319757578409554 58 1 1.15200208661436 -0.152002086614359 59 2 1.33352373890064 0.66647626109936 60 1 1.20026423182499 -0.200264231824987 61 1 1.46685772176525 -0.46685772176525 62 1 1.36592801579032 -0.365928015790322 63 1 1.23169651953944 -0.231696519539436 64 1 1.67488756526105 -0.674887565261047 65 2 1.38591695379917 0.614083046200832 66 1 1.3273533073547 -0.3273533073547 67 1 1.53652499932226 -0.53652499932226 68 2 1.09933452585006 0.90066547414994 69 1 1.09281527264939 -0.0928152726493887 70 1 1.55255272693974 -0.552552726939736 71 1 1.40370969740891 -0.403709697408911 72 1 1.24720556620565 -0.247205566205651 73 1 1.14600151436495 -0.14600151436495 74 3 1.45020682662727 1.54979317337273 75 2 1.14724784940596 0.852752150594044 76 2 1.40256784893715 0.597432151062853 77 1 1.23769709178885 -0.237697091788845 78 1 1.05617543950256 -0.0561754395025643 79 1 1.20466964737866 -0.20466964737866 80 1 1.10346559553796 -0.103465595537959 81 1 1.06030650919046 -0.0603065091904641 82 1 1.20394199328891 -0.203941993288914 83 1 1.23117783858818 -0.231177838588175 84 1 1.27433692493567 -0.27433692493567 85 1 1.26007421331046 -0.260074213310461 86 1 1.31087227151325 -0.310872271513251 87 1 0.948726480326966 0.0512735196730337 88 3 1.56268436887705 1.43731563112295 89 1 0.94334907559806 0.05665092440194 90 1 1.07344950216105 -0.073449502161047 91 1 1.13024813261325 -0.130248132613247 92 1 1.13059695426798 -0.130596954267977 93 1 1.15800265886377 -0.158002658863769 94 1 1.26295894795735 -0.262958947957354 95 1 1.45620739887668 -0.456207398876680 96 1 1.17375604061547 -0.173756040615472 97 1 1.18916060071244 -0.189160600712445 98 1 1.20466964737866 -0.20466964737866 99 1 1.27909116214407 -0.279091162144073 100 2 1.42432180293826 0.575678197061741 101 1 1.33036465838797 -0.330364658387973 102 1 1.40194468141664 -0.401944681416644 103 1 1.28498724782424 -0.284987247824240 104 2 1.48763968659113 0.512360313408871 105 1 1.13059695426798 -0.130596954267977 106 2 1.47161195897365 0.528388041026347 107 2 1.16213372855167 0.837866271448331 108 3 1.43945201716946 1.56054798283054 109 2 1.33227740385963 0.667722596140366 110 2 1.28085617813634 0.71914382186366 111 1 1.47223512649416 -0.472235126494157 112 1 1.40291667059188 -0.402916670591876 113 1 0.964754207944443 0.0352457920555574 114 1 0.987131329466058 0.0128686705339421 115 1 1.65348243291466 -0.653482432914664 116 1 1.20581149585042 -0.205811495850424 117 1 1.06092967671097 -0.0609296767109673 118 2 1.24234684242801 0.757653157571994 119 1 1.33800363024327 -0.33800363024327 120 1 1.33290057138014 -0.332900571380137 121 1 1.42432180293826 -0.424321802938259 122 1 0.986508161945555 0.0134918380544454 123 1 1.42369863541776 -0.423698635417756 124 1 1.17313287309497 -0.173132873094968 125 1 0.991262399153958 0.00873760084604235 126 1 1.23294285458044 -0.232942854580442 127 1 1.49874331770367 -0.498743317703672 128 2 1.35878559506915 0.641214404930851 129 2 1.37956755989503 0.620432440104972 130 1 1.01777059036347 -0.0177705903634728 131 1 1.33924996528428 -0.339249965284276 132 1 1.33924996528428 -0.339249965284276 133 1 1.32498725365907 -0.324987253659067 134 4 1.38716328884017 2.61283671115983 135 1 1.47161195897365 -0.471611958973653 136 2 1.34400420249268 0.65599579750732 137 1 1.28085617813634 -0.28085617813634 138 1 1.50939364059224 -0.509393640592242 139 1 1.28974148503264 -0.289741485032643 140 1 1.42334981376303 -0.423349813763026 141 1 0.900813156771069 0.0991868432289313 142 1 1.17375604061547 -0.173756040615472 143 1 1.19991541017026 -0.199915410170257 144 1 1.11598542098804 -0.115985420988038 145 1 1.49239392379953 -0.492393923799533 146 1 1.21691512696297 -0.216915126962966 147 1 1.06092967671097 -0.0609296767109673 148 2 1.30895952604159 0.691040473958409 149 1 1.31801469223442 -0.318014692234425 150 1 1.45145316166828 -0.451453161668277 151 3 1.50463940338384 1.49536059661616 152 1 1.07344950216105 -0.073449502161047 153 1 1.07043815112777 -0.0704381511277733 154 1 1.23294285458044 -0.232942854580442 155 1 1.08743786792048 -0.0874378679204824 156 2 1.28595923699947 0.714040763000528 157 1 1.48465046537499 -0.484650465374994 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.999893996376565 0.000212007246869141 0.000106003623434570 9 0.999671363710792 0.00065727257841556 0.00032863628920778 10 0.999284961983639 0.00143007603272178 0.000715038016360892 11 0.998430798159636 0.00313840368072732 0.00156920184036366 12 0.998133438071783 0.00373312385643496 0.00186656192821748 13 0.998710624397887 0.00257875120422554 0.00128937560211277 14 0.998523643415673 0.00295271316865352 0.00147635658432676 15 0.997191003539627 0.0056179929207465 0.00280899646037325 16 0.997370678002703 0.00525864399459345 0.00262932199729672 17 0.995523138765742 0.0089537224685164 0.0044768612342582 18 0.995631284395103 0.00873743120979502 0.00436871560489751 19 0.993522952093984 0.0129540958120324 0.00647704790601622 20 0.992674872640092 0.0146502547198166 0.0073251273599083 21 0.988307565294534 0.0233848694109328 0.0116924347054664 22 0.983488795625204 0.0330224087495926 0.0165112043747963 23 0.983879482932365 0.0322410341352692 0.0161205170676346 24 0.984714005946743 0.0305719881065150 0.0152859940532575 25 0.98456568949869 0.0308686210026217 0.0154343105013109 26 0.98124160928671 0.037516781426581 0.0187583907132905 27 0.975687314989355 0.0486253700212908 0.0243126850106454 28 0.972605058208618 0.0547898835827631 0.0273949417913816 29 0.966053027371309 0.0678939452573824 0.0339469726286912 30 0.953292124321644 0.0934157513567124 0.0467078756783562 31 0.95564449755485 0.0887110048902995 0.0443555024451498 32 0.945796690515178 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0.378249601369719 0.81087519931514 68 0.244152487391067 0.488304974782133 0.755847512608933 69 0.209789257778841 0.419578515557682 0.790210742221159 70 0.205908355900521 0.411816711801042 0.794091644099479 71 0.188440617252211 0.376881234504422 0.811559382747789 72 0.164641404154797 0.329282808309594 0.835358595845203 73 0.138525811828563 0.277051623657127 0.861474188171437 74 0.408517850743635 0.81703570148727 0.591482149256365 75 0.466156734515323 0.932313469030646 0.533843265484677 76 0.47214530366729 0.94429060733458 0.52785469633271 77 0.434795207353973 0.869590414707946 0.565204792646027 78 0.389911043461747 0.779822086923495 0.610088956538253 79 0.352466081749038 0.704932163498077 0.647533918250962 80 0.31128969590394 0.62257939180788 0.68871030409606 81 0.271541436308586 0.543082872617172 0.728458563691414 82 0.239503677467038 0.479007354934075 0.760496322532962 83 0.210786103538301 0.421572207076603 0.789213896461699 84 0.186511843050735 0.373023686101471 0.813488156949265 85 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0.0819660756002804 0.95901696219986 103 0.0337362442111457 0.0674724884222914 0.966263755788854 104 0.0316884718443685 0.063376943688737 0.968311528155631 105 0.024733550603873 0.049467101207746 0.975266449396127 106 0.0232206801758825 0.046441360351765 0.976779319824117 107 0.0328666576860999 0.0657333153721999 0.9671333423139 108 0.134472666647289 0.268945333294579 0.86552733335271 109 0.146042754882949 0.292085509765897 0.853957245117051 110 0.164958725245015 0.329917450490029 0.835041274754985 111 0.152340955808465 0.304681911616929 0.847659044191535 112 0.136990925199356 0.273981850398712 0.863009074800644 113 0.110694791387565 0.22138958277513 0.889305208612435 114 0.087978367259131 0.175956734518262 0.912021632740869 115 0.095646478956813 0.191292957913626 0.904353521043187 116 0.076519128135255 0.15303825627051 0.923480871864745 117 0.0593901946542626 0.118780389308525 0.940609805345737 118 0.09035375521605 0.1807075104321 0.90964624478395 119 0.0779853906054513 0.155970781210903 0.922014609394549 120 0.064414170042372 0.128828340084744 0.935585829957628 121 0.0585143281033888 0.117028656206778 0.941485671896611 122 0.0447239638528673 0.0894479277057346 0.955276036147133 123 0.0396194123967807 0.0792388247935613 0.96038058760322 124 0.0298943191337734 0.0597886382675468 0.970105680866227 125 0.0216282276687471 0.0432564553374941 0.978371772331253 126 0.0156147516804245 0.031229503360849 0.984385248319575 127 0.0190666879381920 0.0381333758763841 0.980933312061808 128 0.0190202281383123 0.0380404562766245 0.980979771861688 129 0.0254049543855697 0.0508099087711394 0.97459504561443 130 0.0177364979239442 0.0354729958478883 0.982263502076056 131 0.0181214589840572 0.0362429179681144 0.981878541015943 132 0.0208388736365747 0.0416777472731494 0.979161126363425 133 0.0258824507750476 0.0517649015500951 0.974117549224952 134 0.796916118220852 0.406167763558295 0.203083881779148 135 0.783655170586731 0.432689658826538 0.216344829413269 136 0.823405330047904 0.353189339904192 0.176594669952096 137 0.7677838207467 0.464432358506600 0.232216179253300 138 0.794557633492814 0.410884733014372 0.205442366507186 139 0.7319776056631 0.536044788673801 0.268022394336900 140 0.671620201218592 0.656759597562816 0.328379798781408 141 0.59092100892742 0.81815798214516 0.40907899107258 142 0.527442559748788 0.945114880502425 0.472557440251212 143 0.460449666336107 0.920899332672215 0.539550333663893 144 0.383805839969128 0.767611679938256 0.616194160030872 145 0.291844863302763 0.583689726605527 0.708155136697237 146 0.215924242791552 0.431848485583103 0.784075757208448 147 0.139787508036857 0.279575016073714 0.860212491963143 148 0.087461317016423 0.174922634032846 0.912538682983577 149 0.0524718109818999 0.104943621963800 0.9475281890181 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 11 0.0774647887323944 NOK 5% type I error level 29 0.204225352112676 NOK 10% type I error level 43 0.302816901408451 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/10dwut1290505703.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/10dwut1290505703.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/1odx01290505703.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/1odx01290505703.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/2hmxl1290505703.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/2hmxl1290505703.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/3hmxl1290505703.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/3hmxl1290505703.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/4hmxl1290505703.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/4hmxl1290505703.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/5aewn1290505703.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/5aewn1290505703.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/6aewn1290505703.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/6aewn1290505703.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/7kndq1290505703.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/7kndq1290505703.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/8dwut1290505703.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/8dwut1290505703.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/9dwut1290505703.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290505809huz9ba60pjk8a2f/9dwut1290505703.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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Software written by Ed van Stee & Patrick Wessa

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