mini tutorial

*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, 12 Nov 2010 10:00:34 +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/12/t1289556026fxdpe2hqveigs2p.htm/, Retrieved Fri, 12 Nov 2010 11:00:29 +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/12/t1289556026fxdpe2hqveigs2p.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 «

11 24 7 25 17 30 10 19 12 22 12 22 11 25 11 23 12 17 13 21 14 19 16 19 11 15 10 16 11 23 15 27 9 22 11 14 17 22 17 23 11 23 18 21 14 19 10 18 11 20 15 23 15 25 13 19 16 24 13 22 9 25 18 26 18 29 12 32 17 25 9 29 9 28 12 17 18 28 12 29 18 26 14 25 15 14 16 25 10 26 11 20 14 18 9 32 12 25 17 25 5 23 12 21 12 20 6 15 24 30 12 24 12 26 14 24 7 22 13 14 12 24 13 24 14 24 8 24 11 19 9 31 11 22 13 27 10 19 11 25 12 20 9 21 15 27 18 23 15 25 12 20 13 21 14 22 10 23 13 25 13 25 11 17 13 19 16 25 8 19 16 20 11 26 9 23 16 27 12 17 14 17 8 19 9 17 15 22 11 21 21 32 14 21 18 21 12 18 13 18 15 23 12 19 19 20 15 21 11 20 11 17 10 18 13 19 15 22 12 15 12 14 16 18 9 24 18 35 8 29 13 21 17 25 9 20 15 22 8 13 7 26 12 17 14 25 6 20 8 19 17 21 10 22 11 24 14 21 11 26 13 24 12 16 11 23 9 18 12 16 20 26 12 19 13 21 12 21 12 22 9 23 15 29 24 21 7 21 17 23 11 27 17 25 11 21 12 10 14 20 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 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation ParentalExpectations[t] = + 7.64931751839037 + 0.207693455751869`PersonalStandards `[t] + 0.00758410824477988t + 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) 7.64931751839037 1.548061 4.9412 2e-06 1e-06 `PersonalStandards ` 0.207693455751869 0.063447 3.2735 0.001308 0.000654 t 0.00758410824477988 0.005811 1.3052 0.193758 0.096879 Multiple Linear Regression - Regression Statistics Multiple R 0.263673688616257 R-squared 0.0695238140685031 Adjusted R-squared 0.0575946321975864 F-TEST (value) 5.82804544526245 F-TEST (DF numerator) 2 F-TEST (DF denominator) 156 p-value 0.00362251737467945 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.34479026414091 Sum Squared Residuals 1745.26901813033 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 12.64154456468 -1.64154456468001 2 7 12.8568221286767 -5.85682212867666 3 17 13.9028735156808 3.09712648431922 4 10 11.625829610655 -1.625829610655 5 12 12.2564940861554 -0.256494086155389 6 12 12.2640781944002 -0.264078194400169 7 11 12.8947426699006 -1.89474266990056 8 11 12.4869398666416 -1.4869398666416 9 12 11.2483632403752 0.751636759624836 10 13 12.0867211716274 0.91327882837258 11 14 11.6789183683685 2.32108163163154 12 16 11.6865024766132 4.31349752338676 13 11 10.8633127618505 0.136687238149455 14 10 11.0785903258472 -1.07859032584719 15 11 12.5400286243551 -1.54002862435506 16 15 13.3783865556073 1.62161344439269 17 9 12.3475033850927 -3.34750338509275 18 11 10.6935398473226 0.306460152677425 19 17 12.3626716015823 4.63732839841769 20 17 12.577949165579 4.42205083442104 21 11 12.5855332738237 -1.58553327382374 22 18 12.1777304705648 5.82226952943522 23 14 11.7699276673058 2.23007233269418 24 10 11.5698183197987 -1.56981831979873 25 11 11.9927893395472 -0.992789339547249 26 15 12.6234538150476 2.37654618495236 27 15 13.0464248347962 1.95357516520385 28 13 11.8078482085297 1.19215179147028 29 16 12.8538995955338 3.14610040446616 30 13 12.4460967922749 0.553903207725114 31 9 13.0767612677753 -4.07676126777527 32 18 13.2920388317719 4.70796116822808 33 18 13.9227033072723 4.07729669272769 34 12 14.5533677827727 -2.5533677827727 35 17 13.1070977007544 3.89290229924561 36 9 13.9454556320066 -4.94545563200665 37 9 13.7453462844996 -4.74534628449956 38 12 11.4683023794738 0.53169762052622 39 18 13.7605145009891 4.23948549901088 40 12 13.9757920649858 -1.97579206498577 41 18 13.3602958059749 4.63970419402506 42 14 13.1601864584679 0.839813541532148 43 15 10.8831425534421 4.11685744655793 44 16 13.1753546749574 2.82464532504259 45 10 13.3906322389541 -3.39063223895406 46 11 12.1520556126876 -1.15205561268763 47 14 11.7442528094287 2.25574719057133 48 9 14.6595452981996 -5.65954529819961 49 12 13.2132752161813 -1.21327521618131 50 17 13.2208593244261 3.77914067557391 51 5 12.8130565211671 -7.81305652116713 52 12 12.4052537179082 -0.405253717908175 53 12 12.2051443704011 -0.205144370401085 54 6 11.1742611998865 -5.17426119988652 55 24 14.2972471444093 9.70275285559067 56 12 13.0586705181429 -1.0586705181429 57 12 13.4816415378914 -1.48164153789142 58 14 13.0738387346325 0.926161265367539 59 7 12.6660359313735 -5.6660359313735 60 13 11.0120723936033 1.98792760639667 61 12 13.0965910593668 -1.0965910593668 62 13 13.1041751676116 -0.104175167611581 63 14 13.1117592758564 0.88824072414364 64 8 13.1193433841011 -5.11934338410114 65 11 12.0884602135866 -1.08846021358658 66 9 14.5883657908538 -5.58836579085378 67 11 12.7267087973317 -1.72670879733174 68 13 13.7727601843359 -0.772760184335867 69 10 12.1187966465657 -2.11879664656569 70 11 13.3725414893217 -2.37254148932169 71 12 12.3416583188071 -0.341658318807123 72 9 12.5569358828038 -3.55693588280377 73 15 13.8106807255598 1.18931927444023 74 18 12.9874910107971 5.01250898920293 75 15 13.4104620305456 1.58953796945441 76 12 12.379578860031 -0.379578860031023 77 13 12.5948564240277 0.405143575972328 78 14 12.8101339880243 1.18986601197568 79 10 13.025411552021 -3.02541155202097 80 13 13.4483825717695 -0.448382571769488 81 13 13.4559666800143 -0.455966680014267 82 11 11.8020031422441 -0.802003142244095 83 13 12.2249741619926 0.775025838007387 84 16 13.4787190047486 2.52128099525139 85 8 12.2401423784822 -4.24014237848217 86 16 12.4554199424788 3.54458005752118 87 11 13.7091647852348 -2.70916478523482 88 9 13.093668526224 -4.09366852622399 89 16 13.9320264574762 2.06797354252376 90 12 11.8626760082023 0.137323991797666 91 14 11.8702601164471 2.12973988355289 92 8 12.2932311361956 -4.29323113619563 93 9 11.8854283329367 -2.88542833293667 94 15 12.9314797199408 2.0685202800592 95 11 12.7313703724337 -1.73137037243371 96 21 15.023582493949 5.97641750605095 97 14 12.7465385889233 1.25346141107673 98 18 12.7541226971681 5.24587730283195 99 12 12.1386264381572 -0.138626438157222 100 13 12.146210546402 0.853789453597998 101 15 13.1922619334061 1.80773806659387 102 12 12.3690722186434 -0.369072218643431 103 19 12.5843497826401 6.41565021735992 104 15 12.7996273466367 2.20037265336327 105 11 12.5995179991296 -1.59951799912964 106 11 11.9840217401188 -0.984021740118812 107 10 12.1992993041155 -2.19929930411546 108 13 12.4145768681121 0.58542313188789 109 15 13.0452413436125 1.9547586563875 110 12 11.5989712615942 0.401028738405806 111 12 11.3988619140871 0.601138085912896 112 16 12.2372198453394 3.76278015466064 113 9 13.4909646880954 -4.49096468809536 114 18 15.7831768096107 2.2168231903893 115 8 14.5446001833443 -6.54460018334426 116 13 12.8906366455741 0.109363354425913 117 17 13.7289945768263 3.27100542317366 118 9 12.6981114063118 -3.69811140631178 119 15 13.1210824260603 1.8789175739397 120 8 11.2594254325383 -3.25942543253825 121 7 13.9670244655573 -6.96702446555733 122 12 12.1053674720353 -0.10536747203529 123 14 13.774499226295 0.225500773704977 124 6 12.7436160557805 -6.74361605578046 125 8 12.5435067082734 -4.54350670827337 126 17 12.9664777280219 4.03352227197811 127 10 13.1817552920185 -3.18175529201854 128 11 13.6047263117671 -2.60472631176705 129 14 12.9892300527562 1.01076994724377 130 11 14.0352814397604 -3.03528143976035 131 13 13.6274786365014 -0.627478636501393 132 12 11.9735150987312 0.0264849012687799 133 11 13.4349533972391 -2.43495339723908 134 9 12.4040702267245 -3.40407022672452 135 12 11.9962674234656 0.00373257653444032 136 20 14.080786089229 5.91921391077097 137 12 12.6345160072107 -0.634516007210727 138 13 13.0574870269592 -0.0574870269592447 139 12 13.065071135204 -1.06507113520402 140 12 13.2803486992007 -1.28034869920067 141 9 13.4956262631973 -4.49562626319732 142 15 14.7493711059533 0.250628894046683 143 24 13.0954075681831 10.9045924318169 144 7 13.1029916764279 -6.10299167642792 145 17 13.5259626961764 3.47403730382356 146 11 14.3643206274287 -3.3643206274287 147 17 13.9565178241697 3.04348217583026 148 11 13.133328109407 -2.13332810940704 149 12 10.8562842043813 1.14371579561874 150 14 12.9408028701447 1.05919712985527 151 11 14.1945477129007 -3.19454771290073 152 16 13.7867449096418 2.21325509035823 153 21 14.8327962966459 6.16720370335411 154 14 12.763445847372 1.23655415262802 155 20 13.8094972343761 6.19050276562389 156 13 12.7786140638615 0.221385936138456 157 11 13.8246654508657 -2.82466545086567 158 15 13.4168626476067 1.58313735239329 159 19 12.3859794770921 6.61402052290785 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.440022843964063 0.880045687928127 0.559977156035937 7 0.439964554193698 0.879929108387396 0.560035445806302 8 0.315271667255817 0.630543334511634 0.684728332744183 9 0.252320877442337 0.504641754884673 0.747679122557663 10 0.162028730375548 0.324057460751096 0.837971269624452 11 0.112369106825472 0.224738213650945 0.887630893174528 12 0.0961056182003342 0.192211236400668 0.903894381799666 13 0.0691651083182516 0.138330216636503 0.930834891681748 14 0.0713098638987702 0.14261972779754 0.92869013610123 15 0.100285734063127 0.200571468126255 0.899714265936873 16 0.0652595285058838 0.130519057011768 0.934740471494116 17 0.104838022955825 0.20967604591165 0.895161977044175 18 0.0708450071953487 0.141690014390697 0.929154992804651 19 0.085959007409607 0.171918014819214 0.914040992590393 20 0.0771462217495038 0.154292443499008 0.922853778250496 21 0.090893055925312 0.181786111850624 0.909106944074688 22 0.112464977795347 0.224929955590695 0.887535022204653 23 0.0828104252580064 0.165620850516013 0.917189574741994 24 0.0981078722699962 0.196215744539992 0.901892127730004 25 0.0948908872883478 0.189781774576696 0.905109112711652 26 0.0705419127372571 0.141083825474514 0.929458087262743 27 0.051446307128726 0.102892614257452 0.948553692871274 28 0.037299158348356 0.0745983166967119 0.962700841651644 29 0.027525660449084 0.055051320898168 0.972474339550916 30 0.0215305378521566 0.0430610757043133 0.978469462147843 31 0.057562766912112 0.115125533824224 0.942437233087888 32 0.0599589583173707 0.119917916634741 0.94004104168263 33 0.0520520779820221 0.104104155964044 0.947947922017978 34 0.0720727844338094 0.144145568867619 0.92792721556619 35 0.0649914646323516 0.129982929264703 0.935008535367648 36 0.137668328122576 0.275336656245153 0.862331671877424 37 0.2016556992784 0.4033113985568 0.7983443007216 38 0.169067645943337 0.338135291886674 0.830932354056663 39 0.18245847327199 0.36491694654398 0.81754152672801 40 0.167867610275879 0.335735220551757 0.832132389724121 41 0.185803127484676 0.371606254969352 0.814196872515324 42 0.153943488036231 0.307886976072462 0.846056511963769 43 0.144802196941911 0.289604393883821 0.85519780305809 44 0.127452235976313 0.254904471952627 0.872547764023687 45 0.15409456557495 0.3081891311499 0.84590543442505 46 0.144077556590222 0.288155113180443 0.855922443409779 47 0.12371670254401 0.24743340508802 0.87628329745599 48 0.183559208123538 0.367118416247076 0.816440791876462 49 0.159409247507888 0.318818495015775 0.840590752492112 50 0.164635463451348 0.329270926902697 0.835364536548652 51 0.378931300933312 0.757862601866623 0.621068699066688 52 0.336593927011703 0.673187854023406 0.663406072988297 53 0.295879069421792 0.591758138843584 0.704120930578208 54 0.374643363200204 0.749286726400408 0.625356636799796 55 0.736788915539758 0.526422168920484 0.263211084460242 56 0.70089149733058 0.59821700533884 0.29910850266942 57 0.66553041262521 0.668939174749579 0.33446958737479 58 0.627340757481834 0.745318485036332 0.372659242518166 59 0.694564037533467 0.610871924933065 0.305435962466533 60 0.672853694704598 0.654292610590803 0.327146305295402 61 0.631755870115253 0.736488259769493 0.368244129884747 62 0.587316491847403 0.825367016305193 0.412683508152597 63 0.548323976169483 0.903352047661033 0.451676023830517 64 0.590886937903324 0.818226124193352 0.409113062096676 65 0.546570584351633 0.906858831296734 0.453429415648367 66 0.601245601614439 0.797508796771122 0.398754398385561 67 0.561026927186381 0.877946145627238 0.438973072813619 68 0.515725780226923 0.968548439546154 0.484274219773077 69 0.47889203463159 0.95778406926318 0.52110796536841 70 0.446280755444125 0.89256151088825 0.553719244555875 71 0.401566419231064 0.803132838462128 0.598433580768936 72 0.391527653935173 0.783055307870345 0.608472346064827 73 0.362493349191718 0.724986698383435 0.637506650808282 74 0.441336489671955 0.88267297934391 0.558663510328045 75 0.41416765225503 0.82833530451006 0.58583234774497 76 0.370009989376821 0.740019978753642 0.629990010623179 77 0.330532974990406 0.661065949980813 0.669467025009594 78 0.299950740265959 0.599901480531918 0.700049259734041 79 0.282834063383631 0.565668126767263 0.717165936616369 80 0.245575401301213 0.491150802602427 0.754424598698787 81 0.211153426041608 0.422306852083216 0.788846573958392 82 0.179721256630814 0.359442513261628 0.820278743369186 83 0.154991056345343 0.309982112690686 0.845008943654657 84 0.149445522995386 0.298891045990772 0.850554477004614 85 0.1560501753174 0.3121003506348 0.8439498246826 86 0.167994158440383 0.335988316880765 0.832005841559617 87 0.152670094856436 0.305340189712872 0.847329905143564 88 0.157996741892735 0.31599348378547 0.842003258107265 89 0.145638988274717 0.291277976549434 0.854361011725283 90 0.121539417095583 0.243078834191167 0.878460582904417 91 0.112013522094115 0.22402704418823 0.887986477905885 92 0.118851153413732 0.237702306827463 0.881148846586268 93 0.108460380257735 0.216920760515469 0.891539619742265 94 0.0986070901989002 0.1972141803978 0.9013929098011 95 0.082953715298245 0.16590743059649 0.917046284701755 96 0.136256677919764 0.272513355839528 0.863743322080236 97 0.118039732877469 0.236079465754938 0.881960267122531 98 0.166609172755364 0.333218345510728 0.833390827244636 99 0.139348204020039 0.278696408040079 0.86065179597996 100 0.11890228721773 0.237804574435461 0.88109771278227 101 0.108373191458501 0.216746382917001 0.8916268085415 102 0.0883078051065237 0.176615610213047 0.911692194893476 103 0.174132482384288 0.348264964768576 0.825867517615712 104 0.172202313244704 0.344404626489407 0.827797686755296 105 0.14613076254298 0.292261525085961 0.85386923745702 106 0.121749593294331 0.243499186588662 0.878250406705669 107 0.102882731333254 0.205765462666508 0.897117268666746 108 0.0879143587917579 0.175828717583516 0.912085641208242 109 0.0859269143323084 0.171853828664617 0.914073085667692 110 0.073256095359143 0.146512190718286 0.926743904640857 111 0.0641789653407298 0.12835793068146 0.93582103465927 112 0.0944696801241092 0.188939360248218 0.90553031987589 113 0.0918440966221911 0.183688193244382 0.908155903377809 114 0.0980113763821957 0.196022752764391 0.901988623617804 115 0.126327009864483 0.252654019728965 0.873672990135517 116 0.109910821947581 0.219821643895163 0.890089178052419 117 0.145361748679571 0.290723497359142 0.85463825132043 118 0.128744942715153 0.257489885430306 0.871255057284847 119 0.140864708131266 0.281729416262532 0.859135291868734 120 0.120757033602113 0.241514067204226 0.879242966397887 121 0.159128448813664 0.318256897627328 0.840871551186336 122 0.137575523903049 0.275151047806098 0.862424476096951 123 0.120300976955969 0.240601953911939 0.87969902304403 124 0.156585613588592 0.313171227177183 0.843414386411408 125 0.15288442134802 0.305768842696039 0.84711557865198 126 0.206678198969149 0.413356397938298 0.793321801030851 127 0.177987046302195 0.355974092604389 0.822012953697805 128 0.148014953832912 0.296029907665825 0.851985046167088 129 0.129479270204586 0.258958540409171 0.870520729795414 130 0.108807030423736 0.217614060847471 0.891192969576264 131 0.083752813173881 0.167505626347762 0.91624718682612 132 0.0649037856883659 0.129807571376732 0.935096214311634 133 0.0507280911406624 0.101456182281325 0.949271908859338 134 0.044552722239486 0.089105444478972 0.955447277760514 135 0.0318425790597831 0.0636851581195662 0.968157420940217 136 0.0689256300043028 0.137851260008606 0.931074369995697 137 0.0497823918181039 0.0995647836362079 0.950217608181896 138 0.035561673155573 0.071123346311146 0.964438326844427 139 0.0242587462760752 0.0485174925521505 0.975741253723925 140 0.0162174947550079 0.0324349895100158 0.983782505244992 141 0.0193065872882041 0.0386131745764082 0.980693412711796 142 0.012373538937936 0.024747077875872 0.987626461062064 143 0.268860691465393 0.537721382930786 0.731139308534607 144 0.362772397723172 0.725544795446345 0.637227602276828 145 0.391601888705476 0.783203777410952 0.608398111294524 146 0.37187803446089 0.743756068921779 0.62812196553911 147 0.357579431329028 0.715158862658055 0.642420568670972 148 0.29896173076928 0.597923461538559 0.70103826923072 149 0.218701962858799 0.437403925717599 0.7812980371412 150 0.149966352644756 0.299932705289512 0.850033647355244 151 0.207436885955155 0.41487377191031 0.792563114044845 152 0.131705781341564 0.263411562683128 0.868294218658436 153 0.147138339608836 0.294276679217671 0.852861660391164 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 5 0.0337837837837838 OK 10% type I error level 11 0.0743243243243243 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/10wtou1289556022.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/10wtou1289556022.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/1pari1289556022.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/1pari1289556022.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/2pari1289556022.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/2pari1289556022.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/3i18l1289556022.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/3i18l1289556022.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/4i18l1289556022.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/4i18l1289556022.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/5i18l1289556022.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/5i18l1289556022.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/6ssqo1289556022.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/6ssqo1289556022.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/73k791289556022.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/73k791289556022.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/83k791289556022.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/83k791289556022.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/9wtou1289556022.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/12/t1289556026fxdpe2hqveigs2p/9wtou1289556022.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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