W7

*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 10:43:05 +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/t1290508895t8aabehvlvn6h64.htm/, Retrieved Tue, 23 Nov 2010 11:41:47 +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/t1290508895t8aabehvlvn6h64.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 «

26 24 14 11 12 24 23 25 11 7 8 25 25 17 6 17 8 30 23 18 12 10 8 19 19 18 8 12 9 22 29 16 10 12 7 22 25 20 10 11 4 25 21 16 11 11 11 23 22 18 16 12 7 17 25 17 11 13 7 21 24 23 13 14 12 19 18 30 12 16 10 19 22 23 8 11 10 15 15 18 12 10 8 16 22 15 11 11 8 23 28 12 4 15 4 27 20 21 9 9 9 22 12 15 8 11 8 14 24 20 8 17 7 22 20 31 14 17 11 23 21 27 15 11 9 23 20 34 16 18 11 21 21 21 9 14 13 19 23 31 14 10 8 18 28 19 11 11 8 20 24 16 8 15 9 23 24 20 9 15 6 25 24 21 9 13 9 19 23 22 9 16 9 24 23 17 9 13 6 22 29 24 10 9 6 25 24 25 16 18 16 26 18 26 11 18 5 29 25 25 8 12 7 32 21 17 9 17 9 25 26 32 16 9 6 29 22 33 11 9 6 28 22 13 16 12 5 17 22 32 12 18 12 28 23 25 12 12 7 29 30 29 14 18 10 26 23 22 9 14 9 25 17 18 10 15 8 14 23 17 9 16 5 25 23 20 10 10 8 26 25 15 12 11 8 20 24 20 14 14 10 18 24 33 14 9 6 32 23 29 10 12 8 25 21 23 14 17 7 25 24 26 16 5 4 23 24 18 9 12 8 21 28 20 10 12 8 20 16 11 6 6 4 15 20 28 8 24 20 30 29 26 13 12 8 24 27 22 10 12 8 26 22 17 8 14 6 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation ParentalCriticism[t] = + 2.77548963490739 -0.0986398562189426Organization[t] + 0.0438195865695189ConcernOverMistakes[t] + 0.110456538155872DoubtsAboutActions[t] + 0.421047435532671ParentalExpectations[t] + 0.00840042269626758PersonalStandards[t] -0.00117382973676924t + 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) 2.77548963490739 1.535193 1.8079 0.072598 0.036299 Organization -0.0986398562189426 0.049996 -1.973 0.050313 0.025157 ConcernOverMistakes 0.0438195865695189 0.038702 1.1322 0.25932 0.12966 DoubtsAboutActions 0.110456538155872 0.069456 1.5903 0.11384 0.05692 ParentalExpectations 0.421047435532671 0.05473 7.6931 0 0 PersonalStandards 0.00840042269626758 0.051029 0.1646 0.869462 0.434731 t -0.00117382973676924 0.00384 -0.3057 0.760265 0.380132 Multiple Linear Regression - Regression Statistics Multiple R 0.627452204404761 R-squared 0.393696268812394 Adjusted R-squared 0.369763226791831 F-TEST (value) 16.4499050506880 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 1.47659662275146e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.14906375448968 Sum Squared Residuals 702.008203170918 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 7.64087309089847 4.35912690910153 2 8 5.97227948248611 2.02772051751389 3 8 9.12346302578399 -1.12346302578399 4 8 6.98639102560222 1.01360897439778 5 9 7.80524660727188 1.19475339272812 6 7 6.95094811851839 0.0490518814816109 7 4 7.1237658924916 -3.12376589249160 8 11 7.43552883411586 3.56447116588414 9 7 8.3462819114336 -1.34628191143361 10 7 7.90773536200888 -0.907735362008876 11 12 8.89327857436004 3.10672142563996 12 10 10.5223193208330 -0.522319320833031 13 10 7.23918393916195 2.76081606083805 14 8 7.73857030989726 0.261429690102736 15 8 7.28485258317001 0.715147416829988 16 4 7.50497652223568 -3.50497652223568 17 9 6.67129378547812 2.32870621452188 18 8 7.86075623741511 0.139243762584893 19 7 9.48849006066479 -2.48849006066479 20 11 11.0350307597 -0.035030759699995 21 9 8.34411065242605 0.655889347573946 22 11 11.7893015263869 -0.789301526386893 23 13 8.64564686041312 4.35435313958688 24 8 7.74508170988606 0.254918290113943 25 8 6.83135222667794 1.16864777332206 26 9 8.47130045786025 0.528699542139747 27 6 8.77266235794997 -2.77266235794997 28 9 7.92281070753977 1.07718929246023 29 9 9.36924074067081 -0.369240740670812 30 6 7.8690258260959 -1.8690258260959 31 6 6.0342180291461 -0.0342180291461004 32 16 11.0306296384991 4.9693703615009 33 5 11.1380331099549 -6.13803310995495 34 7 7.57010774054122 -0.570107740541224 35 9 9.76982740006942 -0.769827400069425 36 6 7.37116606139553 -1.37116606139553 37 6 7.24768812962843 -1.24768812962843 38 5 8.0931429162197 -3.09314291621970 39 12 11.1014043415353 0.898595658464721 40 7 8.17696935909318 -1.17696935909318 41 10 10.3825913035209 -0.382591303520850 42 9 8.52028650572374 0.479713494276262 43 8 9.37477279105215 -1.37477279105215 44 5 9.14093578446795 -4.14093578446795 45 8 6.86379306209585 1.13620693790415 46 8 7.0377995627404 0.962200437259593 47 10 8.8216180595874 1.17838194041260 48 6 7.40246759533877 -1.40246759533877 49 8 8.08716847064352 -0.0871684706435167 50 7 10.5674201642144 -3.56742016421436 51 4 5.55332853005648 -1.55332853005648 52 8 7.35893344400862 0.641066555991385 53 8 7.15289547799472 0.847104522005282 54 4 4.93091076445874 -0.93091076445874 55 20 13.2058837378719 6.79411626212815 56 8 7.67862295723527 0.321377042764734 57 8 7.38488172458323 0.615118275416773 58 6 8.26219019245464 -2.26219019245464 59 4 4.37548986027952 -0.375489860279517 60 8 8.98836701518195 -0.988367015181952 61 9 7.23111080167803 1.76888919832197 62 6 8.03535914812683 -2.03535914812683 63 7 8.19394723221966 -1.19394723221966 64 9 6.12768516574899 2.87231483425101 65 5 6.76436507832407 -1.76436507832407 66 5 6.27445113932131 -1.27445113932131 67 8 7.38787707236855 0.61212292763145 68 8 8.15134129515693 -0.151341295156930 69 6 6.42889263930453 -0.428892639304534 70 8 7.160271157231 0.839728842768993 71 7 7.85324929629094 -0.853249296290936 72 7 6.21477398546368 0.78522601453632 73 9 8.97638318870842 0.0236168112915778 74 11 11.1195891858071 -0.119589185807133 75 6 8.88059619378321 -2.88059619378321 76 8 7.94783514729018 0.0521648527098195 77 6 7.98518003783487 -1.98518003783487 78 9 8.6417375387904 0.358262461209604 79 8 6.38393593538546 1.61606406461454 80 6 8.63710399214164 -2.63710399214164 81 10 8.25500256293017 1.74499743706983 82 8 6.3404200986823 1.65957990131770 83 8 8.38689939892296 -0.386899398922961 84 10 9.01634496033092 0.98365503966908 85 5 6.09466753014214 -1.09466753014214 86 7 9.34718438841318 -2.34718438841318 87 5 7.18071937903479 -2.18071937903479 88 8 5.99795876225553 2.00204123774447 89 14 10.0169392146571 3.98306078534287 90 7 7.73092191660853 -0.730921916608532 91 8 9.0244866478904 -1.02448664789040 92 6 4.81860682183499 1.18139317816501 93 5 6.24597618680964 -1.24597618680964 94 6 9.2614696336683 -3.26146963366831 95 10 6.63531134770756 3.36468865229244 96 12 11.6719479561655 0.328052043834517 97 9 9.39241651319525 -0.392416513195247 98 12 11.0509830628583 0.949016937141722 99 7 7.618301333518 -0.618301333518005 100 8 8.47736994961622 -0.477369949616221 101 10 9.20683297855776 0.793167021442236 102 6 7.22698884441415 -1.22698884441415 103 10 11.1147577763564 -1.11475777635639 104 10 8.64785977857664 1.35214022142336 105 10 7.14545395226315 2.85454604773685 106 5 8.58767601464181 -3.58767601464181 107 7 7.13855788441745 -0.138557884417447 108 10 8.84812179427727 1.15187820572273 109 11 9.71850724372987 1.28149275627013 110 6 8.04483145596506 -2.04483145596506 111 7 7.3945193407566 -0.394519340756603 112 12 9.27523146138366 2.72476853861634 113 11 6.46495043798494 4.53504956201506 114 11 10.7063495544802 0.293650445519819 115 11 5.04088977265727 5.95911022734273 116 5 7.50676006509314 -2.50676006509314 117 8 10.1203219138584 -2.12032191385837 118 6 6.6802107229245 -0.680210722924503 119 9 9.41084937770535 -0.410849377705347 120 4 6.92131056606663 -2.92131056606663 121 4 6.11491236900386 -2.11491236900386 122 7 8.0779172514349 -1.07791725143491 123 11 9.37204841270056 1.62795158729944 124 6 4.39917751298557 1.60082248701443 125 7 6.73245493576641 0.267545064233594 126 8 9.78449932682077 -1.78449932682077 127 4 6.19528646751742 -2.19528646751742 128 8 6.98514875358318 1.01485124641682 129 9 8.02382025106071 0.976179748939288 130 8 7.99926603559248 0.000733964407517163 131 11 8.7004801583288 2.29951984167121 132 8 7.43130534710353 0.568694652896472 133 5 6.61850734618277 -1.61850734618277 134 4 5.87487997583076 -1.87487997583076 135 8 7.5600586164588 0.439941383541198 136 10 11.6603759014802 -1.66037590148023 137 6 8.07874264848995 -2.07874264848995 138 9 9.09543955505511 -0.0954395550551145 139 9 7.1025341321843 1.8974658678157 140 13 8.76890005474123 4.23109994525876 141 9 8.07263742803369 0.92736257196631 142 10 9.63811882160726 0.361881178392735 143 20 14.5008423616163 5.49915763838367 144 5 5.93990191920628 -0.939901919206278 145 11 10.1423699263149 0.857630073685106 146 6 8.13315976875305 -2.13315976875305 147 9 10.4491123939624 -1.44911239396242 148 7 7.30739695176091 -0.307396951760907 149 9 8.15006655515239 0.849933444847613 150 10 8.53697381117228 1.46302618882772 151 9 6.9276847872823 2.07231521271769 152 8 10.1623331133375 -2.16233311333747 153 7 11.7011124685665 -4.70111246856651 154 6 9.42345345743635 -3.42345345743635 155 13 11.3347214077981 1.66527859220190 156 6 7.89320172361206 -1.89320172361206 157 8 7.83031371067853 0.169686289321474 158 10 9.3204344325448 0.679565567455197 159 16 11.8844738374886 4.11552616251145 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.799046418829632 0.401907162340736 0.200953581170368 11 0.919877222362598 0.160245555274804 0.0801227776374018 12 0.896852792641402 0.206294414717196 0.103147207358598 13 0.881660669141653 0.236678661716695 0.118339330858347 14 0.819070294570914 0.361859410858173 0.180929705429086 15 0.780115807489214 0.439768385021572 0.219884192510786 16 0.731241190810519 0.537517618378963 0.268758809189481 17 0.69489587226882 0.61020825546236 0.30510412773118 18 0.612483667722277 0.775032664555446 0.387516332277723 19 0.540840707025574 0.918318585948853 0.459159292974426 20 0.45648054726204 0.91296109452408 0.54351945273796 21 0.379706163882132 0.759412327764264 0.620293836117868 22 0.307573220896102 0.615146441792205 0.692426779103898 23 0.613965569324333 0.772068861351335 0.386034430675667 24 0.601322964862971 0.797354070274058 0.398677035137029 25 0.548560110465915 0.90287977906817 0.451439889534085 26 0.514596687503098 0.970806624993803 0.485403312496902 27 0.499934999917408 0.999869999834816 0.500065000082592 28 0.447452793676121 0.894905587352242 0.552547206323879 29 0.388062540913924 0.776125081827847 0.611937459086076 30 0.351038079892999 0.702076159785997 0.648961920107001 31 0.297166859348969 0.594333718697937 0.702833140651032 32 0.66563455477352 0.668730890452961 0.334365445226481 33 0.852052090768774 0.295895818462453 0.147947909231226 34 0.822986983178255 0.35402603364349 0.177013016821745 35 0.79046836953877 0.419063260922459 0.209531630461230 36 0.776954097486149 0.446091805027702 0.223045902513851 37 0.734528901053437 0.530942197893125 0.265471098946562 38 0.781812123085101 0.436375753829798 0.218187876914899 39 0.778448840932134 0.443102318135731 0.221551159067866 40 0.73839161922267 0.523216761554659 0.261608380777330 41 0.691799820155711 0.616400359688578 0.308200179844289 42 0.669322962437202 0.661354075125595 0.330677037562798 43 0.624041871709607 0.751916256580786 0.375958128290393 44 0.667777521487947 0.664444957024106 0.332222478512053 45 0.671376794003063 0.657246411993873 0.328623205996937 46 0.646380637151757 0.707238725696486 0.353619362848243 47 0.619459855908142 0.761080288183716 0.380540144091858 48 0.57838481209354 0.84323037581292 0.42161518790646 49 0.528536130391407 0.942927739217186 0.471463869608593 50 0.553746987057794 0.892506025884413 0.446253012942206 51 0.534782435701251 0.930435128597499 0.465217564298749 52 0.504297812784558 0.991404374430885 0.495702187215442 53 0.463419065550335 0.92683813110067 0.536580934449665 54 0.415238562380096 0.830477124760191 0.584761437619904 55 0.909613633698536 0.180772732602928 0.090386366301464 56 0.889156473844252 0.221687052311496 0.110843526155748 57 0.869896489141992 0.260207021716016 0.130103510858008 58 0.861037642401887 0.277924715196225 0.138962357598113 59 0.834049451135169 0.331901097729661 0.165950548864831 60 0.803697376894625 0.39260524621075 0.196302623105375 61 0.806536737440184 0.386926525119631 0.193463262559816 62 0.794081579611922 0.411836840776156 0.205918420388078 63 0.765472449955225 0.46905510008955 0.234527550044775 64 0.819818482066105 0.36036303586779 0.180181517933895 65 0.8029801301122 0.394039739775601 0.197019869887800 66 0.77787286311102 0.44425427377796 0.22212713688898 67 0.748713664215291 0.502572671569418 0.251286335784709 68 0.717360803776262 0.565278392447476 0.282639196223738 69 0.682842184013772 0.634315631972456 0.317157815986228 70 0.652548694307852 0.694902611384296 0.347451305692148 71 0.616860952826937 0.766278094346125 0.383139047173063 72 0.581443347681924 0.837113304636152 0.418556652318076 73 0.535456180764197 0.929087638471607 0.464543819235803 74 0.488419971134341 0.976839942268682 0.511580028865659 75 0.513230349893092 0.973539300213815 0.486769650106908 76 0.467316149780344 0.934632299560689 0.532683850219656 77 0.46550438359834 0.93100876719668 0.53449561640166 78 0.423845702525223 0.847691405050446 0.576154297474777 79 0.406151191336014 0.812302382672027 0.593848808663986 80 0.414233232347135 0.82846646469427 0.585766767652865 81 0.402762265769488 0.805524531538977 0.597237734230512 82 0.389323756756477 0.778647513512953 0.610676243243523 83 0.345326138213460 0.690652276426919 0.65467386178654 84 0.317421056028862 0.634842112057723 0.682578943971138 85 0.286282287523607 0.572564575047215 0.713717712476392 86 0.290903228430511 0.581806456861022 0.709096771569489 87 0.293142548603782 0.586285097207565 0.706857451396218 88 0.285841510096717 0.571683020193435 0.714158489903283 89 0.403600936022627 0.807201872045254 0.596399063977373 90 0.361035547828396 0.722071095656793 0.638964452171604 91 0.325354888682770 0.650709777365539 0.67464511131723 92 0.297825982846674 0.595651965693347 0.702174017153326 93 0.268758521561486 0.537517043122973 0.731241478438514 94 0.315104701239063 0.630209402478126 0.684895298760937 95 0.378439578217825 0.756879156435649 0.621560421782176 96 0.337062346879123 0.674124693758246 0.662937653120877 97 0.295075190159046 0.590150380318093 0.704924809840954 98 0.266651146240089 0.533302292480178 0.733348853759911 99 0.229387588051166 0.458775176102331 0.770612411948834 100 0.194326912148498 0.388653824296995 0.805673087851502 101 0.168987983326642 0.337975966653283 0.831012016673358 102 0.148148635985262 0.296297271970525 0.851851364014738 103 0.131577887719309 0.263155775438617 0.868422112280691 104 0.115915653448884 0.231831306897767 0.884084346551116 105 0.144461059238831 0.288922118477662 0.855538940761169 106 0.180441430477057 0.360882860954114 0.819558569522943 107 0.150102766804474 0.300205533608947 0.849897233195526 108 0.133774495762352 0.267548991524704 0.866225504237648 109 0.119146429991442 0.238292859982884 0.880853570008558 110 0.114427974969377 0.228855949938755 0.885572025030623 111 0.093011932640009 0.186023865280018 0.906988067359991 112 0.152086431077202 0.304172862154405 0.847913568922798 113 0.339935945592861 0.679871891185722 0.660064054407139 114 0.299617167011199 0.599234334022399 0.700382832988801 115 0.601927317675846 0.796145364648309 0.398072682324154 116 0.587555427146818 0.824889145706365 0.412444572853182 117 0.583867999960535 0.83226400007893 0.416132000039465 118 0.532866341222445 0.93426731755511 0.467133658777555 119 0.477007536853317 0.954015073706635 0.522992463146683 120 0.53617486138787 0.92765027722426 0.46382513861213 121 0.506516195834158 0.986967608331685 0.493483804165842 122 0.521113829438166 0.957772341123668 0.478886170561834 123 0.478560920557643 0.957121841115286 0.521439079442357 124 0.488737086402449 0.977474172804898 0.511262913597551 125 0.432236053870439 0.864472107740877 0.567763946129561 126 0.435921680986355 0.87184336197271 0.564078319013645 127 0.42756533731677 0.85513067463354 0.57243466268323 128 0.38959166500254 0.77918333000508 0.61040833499746 129 0.347450854448223 0.694901708896446 0.652549145551777 130 0.307932440429895 0.615864880859789 0.692067559570105 131 0.302334239564992 0.604668479129985 0.697665760435008 132 0.250925951423822 0.501851902847645 0.749074048576178 133 0.206446731951734 0.412893463903468 0.793553268048266 134 0.17452530938833 0.34905061877666 0.82547469061167 135 0.141640685543075 0.283281371086150 0.858359314456925 136 0.134944014570505 0.269888029141011 0.865055985429495 137 0.187690242936650 0.375380485873301 0.81230975706335 138 0.224152900029298 0.448305800058597 0.775847099970702 139 0.193983532838732 0.387967065677464 0.806016467161268 140 0.222485955428666 0.444971910857333 0.777514044571334 141 0.178412836810778 0.356825673621557 0.821587163189222 142 0.146371284397167 0.292742568794335 0.853628715602833 143 0.208984844371777 0.417969688743555 0.791015155628223 144 0.152261263975150 0.304522527950301 0.84773873602485 145 0.103453992665241 0.206907985330481 0.89654600733476 146 0.067412308706125 0.13482461741225 0.932587691293875 147 0.0443977865956503 0.0887955731913007 0.95560221340435 148 0.022390426111425 0.04478085222285 0.977609573888575 149 0.0101777878334201 0.0203555756668402 0.98982221216658 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 2 0.0142857142857143 OK 10% type I error level 3 0.0214285714285714 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/10vfro1290508974.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/10vfro1290508974.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/1zntf1290508974.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/1zntf1290508974.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/2zntf1290508974.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/2zntf1290508974.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/3zntf1290508974.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/3zntf1290508974.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/4sea01290508974.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/4sea01290508974.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/5sea01290508974.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/5sea01290508974.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/6sea01290508974.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/6sea01290508974.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/73oal1290508974.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/73oal1290508974.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/8vfro1290508974.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/8vfro1290508974.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/9vfro1290508974.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290508895t8aabehvlvn6h64/9vfro1290508974.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 5 ; 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') }

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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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