WS7

*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: Mon, 22 Nov 2010 19:33:23 +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/22/t1290454742cv9f4o6pnkdkfb0.htm/, Retrieved Mon, 22 Nov 2010 20:39:14 +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/22/t1290454742cv9f4o6pnkdkfb0.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 «

14 1 12 53 32 3 3 18 4 11 86 51 3 3 11 1 14 66 42 4 4 12 2 12 67 41 3 3 16 3 21 76 46 3 2 18 2 12 78 47 3 3 14 2 22 53 37 3 4 14 1 11 80 49 2 2 15 2 10 74 45 3 3 15 1 13 76 47 3 4 17 2 10 79 49 3 3 19 2 8 54 33 3 3 10 2 15 67 42 3 4 16 2 14 54 33 2 2 18 1 10 87 53 3 2 14 2 14 58 36 3 3 14 4 14 75 45 2 2 17 2 11 88 54 3 4 14 2 10 64 41 2 2 16 2 13 57 36 1 1 18 1 7 66 41 2 3 11 1 14 68 44 3 4 14 2 12 54 33 3 2 12 2 14 56 37 3 3 17 2 11 86 52 3 3 9 2 9 80 47 3 4 16 1 11 76 43 2 3 14 3 15 69 44 3 3 15 2 14 78 45 3 4 11 2 13 67 44 4 4 16 4 9 80 49 3 4 13 3 15 54 33 3 3 17 1 10 71 43 3 4 15 1 11 84 54 3 3 14 2 13 74 42 2 2 16 2 8 71 44 3 4 9 1 20 63 37 3 3 15 1 12 71 43 3 2 17 3 10 76 46 3 4 13 2 10 69 42 4 4 15 2 9 74 45 3 4 16 3 14 75 44 3 4 16 1 8 54 33 1 2 12 1 14 52 31 2 2 12 1 11 69 42 3 3 11 3 13 68 40 4 4 15 3 9 65 43 4 5 15 2 11 75 46 2 2 17 2 15 74 42 1 3 13 1 11 75 45 3 3 16 2 10 72 44 3 2 14 2 14 67 40 1 2 11 1 18 63 37 3 3 12 2 14 62 46 2 2 12 1 11 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 15 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation happiness[t] = + 16.8047526382411 + 0.312091001977892luck[t] -0.357308069520522depression[t] + 0.0686057180561021belonging[t] -0.0592332381375093belonging_final[t] -0.352905082725952popularity[t] -0.0280289123784063friends[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) 16.8047526382411 1.616899 10.3932 0 0 luck 0.312091001977892 0.182079 1.714 0.088688 0.044344 depression -0.357308069520522 0.053825 -6.6383 0 0 belonging 0.0686057180561021 0.047696 1.4384 0.152509 0.076255 belonging_final -0.0592332381375093 0.068828 -0.8606 0.390903 0.195452 popularity -0.352905082725952 0.263224 -1.3407 0.182143 0.091072 friends -0.0280289123784063 0.232349 -0.1206 0.904151 0.452076 Multiple Linear Regression - Regression Statistics Multiple R 0.581195686546521 R-squared 0.337788426060282 Adjusted R-squared 0.310003325055818 F-TEST (value) 12.1571782663671 F-TEST (DF numerator) 6 F-TEST (DF denominator) 143 p-value 5.10060882419339e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.93458580398152 Sum Squared Residuals 535.194979314254 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 13.4269842572330 0.573015742767027 2 18 15.8591225039257 2.14087749607433 3 11 12.6309760764416 -1.63097607644163 4 12 14.1664561687585 -2.16645616875852 5 16 11.6120887292475 4.3879112707525 6 18 14.5657196385506 3.43428036144941 7 14 9.84179946093952 4.15820053906048 8 14 15.0106156610348 -1.01061566103476 9 15 15.1243793816422 -0.124379381642241 10 15 13.7310802185616 1.26891978143843 11 17 15.2304750193727 1.76952498062729 12 19 15.1776800172114 3.82231998278865 13 10 13.0072698096810 -3.00726980968104 14 16 13.4147655951926 2.58523440480742 15 18 15.258325721672 2.74167427832799 16 14 13.1305547579001 0.869445242099893 17 14 14.7688688206764 -0.768868820676399 18 17 15.1664233092912 1.83357669070884 19 14 15.0561891487356 -1.05618914873562 20 16 14.1811250995732 1.81887490042676 21 18 15.9252048790531 2.07479512094691 22 11 13.0026261190048 -2.00262611900476 23 14 13.7764766515077 0.223523348492326 24 12 12.9341100836504 -0.934110083650394 25 17 15.1757072618324 1.82429273816762 26 9 15.7468263708459 -6.74682637084595 27 16 15.063563305257 0.936436694742997 28 14 13.3661346838745 0.633865316125474 29 15 13.9415410634062 1.05845893659384 30 11 13.2505143897211 -2.25051438972111 31 16 16.2525418985267 -0.252541898526714 32 13 12.9886145325456 0.0113854674544035 33 17 14.6969087893927 2.30309121060734 34 15 14.6079383474673 0.392061652532734 35 14 14.6110888825976 -0.611088882597563 36 16 15.6643826922741 0.335617307725919 37 9 10.9584106909421 -1.95841069094209 38 15 14.0383504751084 0.961649524891574 39 17 15.4864196692164 1.51358033078358 40 13 14.5781165106699 -1.5781165106699 41 15 15.4536585387844 -0.453658538784356 42 16 14.1070481493533 1.89295185064675 43 16 15.5994280930638 0.400571906936228 44 12 13.0839296333775 -1.08392963337751 45 12 14.2896514342758 -2.28965143427585 46 11 13.8681440623051 -2.86814406230514 47 15 14.885830559428 0.114169440572010 48 15 15.1573777871447 -0.157377787144671 49 17 14.2213489139041 2.77865108609593 50 13 14.5235860281999 -1.52358602819993 51 16 15.0744300960460 0.925569903954048 52 14 14.2449123456853 -0.244912345685298 53 11 11.6730268299831 -0.673026829983132 54 12 13.1935792438538 -1.19357924385378 55 12 14.2053876423859 -2.20538764238588 56 15 14.7405992044163 0.259400795583724 57 16 14.4053602558066 1.59463974419337 58 15 14.7982131440782 0.201786855921782 59 12 15.6240171280920 -3.62401712809198 60 12 13.1538537257118 -1.15385372571184 61 8 10.9494536961730 -2.94945369617297 62 13 14.2346464016651 -1.23464640166515 63 11 14.2754604824132 -3.27546048241321 64 14 12.3220616431688 1.67793835683121 65 15 13.4191685819872 1.58083141801285 66 10 15.5379257594857 -5.53792575948567 67 11 11.9680147753628 -0.96801477536282 68 12 14.5500615647167 -2.55006156471673 69 15 13.9964870310256 1.00351296897439 70 15 14.2916862179009 0.70831378209911 71 14 14.2276014764028 -0.227601476402849 72 16 12.9605856201672 3.03941437983281 73 15 14.0429044830830 0.957095516917027 74 15 15.1183310627973 -0.118331062797338 75 13 15.7811443059510 -2.78114430595098 76 12 12.0833081117441 -0.0833081117441266 77 17 13.8964987771313 3.10350122286871 78 13 12.3802416236037 0.619758376396347 79 15 14.1117769385956 0.88822306140444 80 13 15.2293348551736 -2.22933485517360 81 15 15.4037717469907 -0.403771746990673 82 16 15.0552855929611 0.94471440703885 83 15 15.9000523009502 -0.900052300950239 84 16 14.8125290835461 1.18747091645393 85 15 14.6566612149741 0.34333878502595 86 14 14.1398058509740 -0.139805850973965 87 15 14.8140858882190 0.185914111780971 88 14 13.9323433647553 0.067656635244675 89 13 12.2955895354633 0.704410464536653 90 7 10.7215402321947 -3.72154023219466 91 17 14.5207693084644 2.47923069153556 92 13 13.3415196152715 -0.341519615271548 93 15 13.8181050940071 1.18189490599288 94 14 13.6809561516975 0.319043848302482 95 13 15.7296382156817 -2.72963821568173 96 16 15.0882680565617 0.91173194343828 97 12 12.8120266752704 -0.812026675270434 98 14 15.6752859432909 -1.67528594329087 99 17 15.0976405364803 1.90235946351969 100 15 14.5373614949131 0.462638505086907 101 17 14.8806568226501 2.11934317734991 102 12 12.2189002493808 -0.218900249380763 103 16 14.7497934742558 1.25020652574424 104 11 14.0838342801075 -3.08383428010754 105 15 13.9669610687333 1.03303893126668 106 9 11.3810003174450 -2.38100031744502 107 16 16.4278994433445 -0.427899443344484 108 15 12.5530603722695 2.44693962773047 109 10 13.3695485276500 -3.36954852764995 110 10 9.47053886995108 0.529461130048915 111 15 14.3191508974368 0.680849102563173 112 11 13.3970722721771 -2.39707227217714 113 13 15.488124066258 -2.48812406625801 114 14 12.5418433663390 1.45815663366102 115 18 14.4004792900600 3.59952070994002 116 16 15.4049391000889 0.595060899911075 117 14 12.9649886069618 1.03501139303824 118 14 14.1773854533501 -0.177385453350076 119 14 15.6284495772727 -1.62844957727267 120 14 13.8151692291838 0.18483077081623 121 12 12.9886145325456 -0.988614532545597 122 14 14.0571873911343 -0.0571873911343368 123 15 15.9968970175560 -0.996897017555977 124 15 16.1826166508680 -1.18261665086802 125 15 14.0054405969834 0.99455940301663 126 13 14.9916334261272 -1.99163342612721 127 17 15.6513296311236 1.34867036887643 128 17 15.4957036217576 1.50429637824236 129 19 15.1263505161403 3.87364948385969 130 15 14.7363449653147 0.263655034685301 131 13 14.0459288752837 -1.04592887528369 132 9 11.2705902202974 -2.27059022029735 133 15 14.9869012080736 0.0130987919264474 134 15 12.7044627602444 2.29553723975563 135 15 13.9695960093593 1.03040399064067 136 16 13.7701269429089 2.2298730570911 137 11 9.79003006202513 1.20996993797487 138 14 13.8520229971859 0.147977002814128 139 11 11.4796950753115 -0.479695075311511 140 15 14.4179944029963 0.582005597003694 141 13 14.3164527732404 -1.31645277324038 142 15 14.1509728761924 0.84902712380758 143 16 14.6219579468735 1.37804205312650 144 14 15.1400999492787 -1.14009994927871 145 15 14.2442561566541 0.755743843345896 146 16 15.2038247015882 0.796175298411842 147 16 14.8094421975427 1.19055780245726 148 11 13.4657937065098 -2.46579370650975 149 12 14.4363238776840 -2.43632387768402 150 9 11.7119248066375 -2.71192480663747 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.707926570703774 0.584146858592453 0.292073429296226 11 0.791422092954732 0.417155814090535 0.208577907045268 12 0.90455181212991 0.190896375740180 0.0954481878700898 13 0.978821901791424 0.0423561964171521 0.0211780982085761 14 0.965265702576131 0.0694685948477373 0.0347342974238686 15 0.958689006328004 0.082621987343991 0.0413109936719955 16 0.939039095681376 0.121921808637248 0.0609609043186238 17 0.962455515683758 0.0750889686324836 0.0375444843162418 18 0.964697711349097 0.0706045773018065 0.0353022886509033 19 0.961033026520748 0.0779339469585035 0.0389669734792517 20 0.949069735365128 0.101860529269744 0.050930264634872 21 0.954475954793758 0.091048090412483 0.0455240452062415 22 0.957277106564397 0.0854457868712065 0.0427228934356032 23 0.946415550501073 0.107168898997854 0.053584449498927 24 0.934349743397846 0.131300513204308 0.065650256602154 25 0.916740240824711 0.166519518350578 0.083259759175289 26 0.99662577471859 0.00674845056281847 0.00337422528140924 27 0.99570744551143 0.00858510897714174 0.00429255448857087 28 0.993531321932617 0.0129373561347662 0.0064686780673831 29 0.991264775624384 0.0174704487512315 0.00873522437561573 30 0.991033985017616 0.0179320299647673 0.00896601498238367 31 0.98762299726732 0.0247540054653618 0.0123770027326809 32 0.98253753706772 0.0349249258645602 0.0174624629322801 33 0.986490251472523 0.0270194970549536 0.0135097485274768 34 0.980692688264238 0.0386146234715248 0.0193073117357624 35 0.979772948333338 0.0404541033333245 0.0202270516666623 36 0.97373485505819 0.052530289883622 0.026265144941811 37 0.9789695084954 0.0420609830092019 0.0210304915046010 38 0.972087070234764 0.0558258595304728 0.0279129297652364 39 0.968619034263154 0.0627619314736917 0.0313809657368459 40 0.962242363033813 0.0755152739323749 0.0377576369661874 41 0.94994324819125 0.100113503617499 0.0500567518087494 42 0.947948309074729 0.104103381850543 0.0520516909252713 43 0.932449273508244 0.135101452983512 0.067550726491756 44 0.92320828762842 0.153583424743162 0.0767917123715808 45 0.928316009311869 0.143367981376263 0.0716839906881313 46 0.93833689985329 0.123326200293422 0.061663100146711 47 0.92241858281194 0.155162834376120 0.0775814171880598 48 0.90832431126385 0.183351377472301 0.0916756887361503 49 0.915555143634696 0.168889712730608 0.084444856365304 50 0.905437322286731 0.189125355426537 0.0945626777132687 51 0.88662207703862 0.22675584592276 0.11337792296138 52 0.875326433960514 0.249347132078973 0.124673566039486 53 0.849432565123134 0.301134869753732 0.150567434876866 54 0.856827237269673 0.286345525460654 0.143172762730327 55 0.856199176961389 0.287601646077222 0.143800823038611 56 0.827251506998528 0.345496986002944 0.172748493001472 57 0.81006731019831 0.379865379603381 0.189932689801691 58 0.78025115164022 0.439497696719561 0.219748848359781 59 0.87421655738853 0.251566885222941 0.125783442611470 60 0.858354028511547 0.283291942976906 0.141645971488453 61 0.88997624375896 0.220047512482079 0.110023756241040 62 0.873265615422121 0.253468769155758 0.126734384577879 63 0.90961718873141 0.180765622537181 0.0903828112685906 64 0.914011545004525 0.171976909990949 0.0859884549954746 65 0.906661935350621 0.186676129298758 0.093338064649379 66 0.987495284637022 0.0250094307259561 0.0125047153629781 67 0.984364868365097 0.0312702632698052 0.0156351316349026 68 0.987657063427906 0.0246858731441869 0.0123429365720935 69 0.984464406543615 0.0310711869127709 0.0155355934563854 70 0.98068847270715 0.0386230545856990 0.0193115272928495 71 0.974496179462599 0.0510076410748029 0.0255038205374014 72 0.983638976387831 0.0327220472243376 0.0163610236121688 73 0.979609328797364 0.0407813424052731 0.0203906712026366 74 0.973135130417712 0.0537297391645763 0.0268648695822882 75 0.981015488508856 0.0379690229822874 0.0189845114911437 76 0.974605266915566 0.0507894661688684 0.0253947330844342 77 0.984646770495668 0.0307064590086644 0.0153532295043322 78 0.980095570633206 0.0398088587335882 0.0199044293667941 79 0.974755080704555 0.05048983859089 0.025244919295445 80 0.975672785795474 0.048654428409052 0.024327214204526 81 0.968381156164995 0.0632376876700096 0.0316188438350048 82 0.96101432451771 0.0779713509645795 0.0389856754822897 83 0.952321206659246 0.0953575866815087 0.0476787933407543 84 0.943852062603842 0.112295874792317 0.0561479373961585 85 0.928574284650577 0.142851430698846 0.0714257153494229 86 0.910039314380572 0.179921371238855 0.0899606856194277 87 0.889110581373619 0.221778837252762 0.110889418626381 88 0.863687502423536 0.272624995152927 0.136312497576464 89 0.838624788246227 0.322750423507545 0.161375211753773 90 0.907505616393845 0.18498876721231 0.092494383606155 91 0.92503894558785 0.149922108824301 0.0749610544121505 92 0.9068682633522 0.186263473295600 0.0931317366477998 93 0.892164657894782 0.215670684210435 0.107835342105218 94 0.866949354416358 0.266101291167284 0.133050645583642 95 0.891515082811512 0.216969834376976 0.108484917188488 96 0.871265170728441 0.257469658543118 0.128734829271559 97 0.845260680476915 0.309478639046170 0.154739319523085 98 0.83590745026863 0.328185099462739 0.164092549731370 99 0.834777760668084 0.330444478663832 0.165222239331916 100 0.801623654034906 0.396752691930188 0.198376345965094 101 0.807873847893213 0.384252304213573 0.192126152106786 102 0.770392957998626 0.459214084002748 0.229607042001374 103 0.744484260590067 0.511031478819865 0.255515739409933 104 0.812278487581478 0.375443024837045 0.187721512418522 105 0.789812323837931 0.420375352324137 0.210187676162069 106 0.802929279747815 0.39414144050437 0.197070720252185 107 0.766208203508212 0.467583592983576 0.233791796491788 108 0.777499256891151 0.445001486217697 0.222500743108849 109 0.842649469349747 0.314701061300506 0.157350530650253 110 0.81002861492374 0.37994277015252 0.18997138507626 111 0.777335455149941 0.445329089700118 0.222664544850059 112 0.79848549850053 0.403029002998941 0.201514501499470 113 0.83648910608806 0.327021787823880 0.163510893911940 114 0.892727067302901 0.214545865394197 0.107272932697099 115 0.949829384960295 0.100341230079411 0.0501706150397054 116 0.932021434320604 0.135957131358792 0.0679785656793958 117 0.933245094372629 0.133509811254742 0.0667549056273708 118 0.910035295377994 0.179929409244011 0.0899647046220055 119 0.894217329139994 0.211565341720013 0.105782670860007 120 0.859952906302509 0.280094187394982 0.140047093697491 121 0.8205816344487 0.358836731102601 0.179418365551300 122 0.776779372858175 0.446441254283649 0.223220627141825 123 0.748370972136259 0.503258055727482 0.251629027863741 124 0.730476772605416 0.539046454789168 0.269523227394584 125 0.680087831626453 0.639824336747093 0.319912168373547 126 0.67916202737823 0.64167594524354 0.32083797262177 127 0.621888200621245 0.75622359875751 0.378111799378755 128 0.623101623770175 0.75379675245965 0.376898376229825 129 0.703265672736142 0.593468654527717 0.296734327263858 130 0.63020481443214 0.739590371135721 0.369795185567861 131 0.554107485110172 0.891785029779656 0.445892514889828 132 0.581236153274366 0.837527693451268 0.418763846725634 133 0.497423495760365 0.994846991520731 0.502576504239635 134 0.492121878937946 0.984243757875893 0.507878121062054 135 0.459099676346835 0.91819935269367 0.540900323653165 136 0.57210884473893 0.85578231052214 0.42789115526107 137 0.522119901169434 0.955760197661133 0.477880098830566 138 0.393374354718099 0.786748709436198 0.606625645281901 139 0.450020431273969 0.900040862547938 0.549979568726031 140 0.437007520043181 0.874015040086362 0.562992479956819 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0152671755725191 NOK 5% type I error level 23 0.175572519083969 NOK 10% type I error level 41 0.312977099236641 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/105e0o1290454385.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/105e0o1290454385.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/1yv3u1290454385.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/1yv3u1290454385.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/2yv3u1290454385.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/2yv3u1290454385.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/39mlx1290454385.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/39mlx1290454385.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/49mlx1290454385.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/49mlx1290454385.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/59mlx1290454385.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/59mlx1290454385.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/61v201290454385.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/61v201290454385.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/7u5j31290454385.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/7u5j31290454385.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/8u5j31290454385.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/8u5j31290454385.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/9u5j31290454385.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290454742cv9f4o6pnkdkfb0/9u5j31290454385.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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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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