*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: Sun, 26 Dec 2010 20:18:12 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu.htm/, Retrieved Sun, 26 Dec 2010 21:16:42 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu.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 «

27 5 26 49 35 18 36 4 25 45 34 10 25 4 17 54 13 23 27 3 37 36 35 14 25 3 35 36 28 20 44 3 15 53 32 15 50 4 27 46 35 18 41 4 36 42 36 19 48 5 25 41 27 19 43 4 30 45 29 14 47 2 27 47 27 15 41 3 33 42 28 14 44 2 29 45 29 16 47 5 30 40 28 13 40 3 25 45 30 13 46 3 23 40 25 14 28 3 26 42 15 23 56 3 24 45 33 17 49 4 35 47 31 14 25 4 39 31 37 21 41 4 23 46 37 15 26 3 32 34 34 19 50 5 29 43 32 20 47 4 26 45 21 18 52 2 21 42 25 13 37 5 35 51 32 20 41 3 23 44 28 12 45 4 21 47 22 17 26 4 28 47 25 13 3 30 41 26 17 52 4 21 44 34 16 46 2 29 51 34 20 58 3 28 46 36 18 54 5 19 47 36 9 29 3 26 46 26 14 50 3 33 38 26 12 43 2 34 50 34 21 30 3 33 48 33 16 47 2 40 36 31 12 45 3 24 51 33 20 48 1 35 35 22 18 48 3 35 49 29 22 26 4 32 38 24 17 46 5 20 47 37 16 3 35 36 32 14 50 3 35 47 23 19 25 4 21 46 29 21 47 2 33 43 35 18 47 2 40 53 20 23 41 3 22 55 28 20 45 2 35 39 26 10 41 4 20 55 36 16 45 5 28 41 26 18 40 3 46 33 33 12 29 4 18 52 25 15 34 5 22 42 29 19 45 5 20 56 32 11 52 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation leeftijd[t] = + 77.3754429800317 -0.381240306445034opleiding[t] -0.524053055241366Neuroticisme[t] -0.0822231173384081Extraversie[t] -0.293690031586825Openheid[t] -0.513130921270904Extrinsieke_waarden[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) 77.3754429800317 6.523045 11.8619 0 0 opleiding -0.381240306445034 0.06365 -5.9897 0 0 Neuroticisme -0.524053055241366 0.084094 -6.2318 0 0 Extraversie -0.0822231173384081 0.09282 -0.8858 0.376835 0.188418 Openheid -0.293690031586825 0.074976 -3.9171 0.000125 6.3e-05 Extrinsieke_waarden -0.513130921270904 0.073941 -6.9397 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.676772943083343 R-squared 0.458021616489690 Adjusted R-squared 0.443683564015872 F-TEST (value) 31.9444790236379 F-TEST (DF numerator) 5 F-TEST (DF denominator) 189 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.81271872174484 Sum Squared Residuals 18198.7058065834 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 27 38.2994215735336 -11.2994215735336 2 36 43.9323448063280 -7.93234480632796 3 25 46.8815498790148 -21.8815498790148 4 27 36.4187427892518 -9.4187427892518 5 25 36.4438935932169 -11.4438935932169 6 44 46.9180561832985 -2.91805618329848 7 50 38.4032781767527 11.5967218232473 8 41 33.2088721960763 7.79112780392365 9 48 41.3176488989062 6.68235110109383 10 43 40.7280060029716 2.27199399702839 11 47 42.9724486888117 4.02755131118829 12 41 40.0774465272946 0.922553472705404 13 44 40.9882778285612 3.01172217143876 14 47 41.5647022360763 5.43529776392365 15 40 43.9489524753076 -3.94895247530756 16 46 46.3634934091455 -0.363493409145547 17 28 42.9456100331747 -14.9456100331747 18 56 41.5394117507048 14.4605882492952 19 49 37.3559144289143 11.6440855710857 20 25 31.2212154469461 -6.2212154469461 21 41 41.4515030983573 -0.451503098357265 22 26 36.9314897253678 -10.9314897253678 23 50 37.0754093640589 12.9245906359411 24 47 43.1212147915481 3.87878520845194 25 52 48.1415245126674 3.85847548733260 26 37 33.2733060939034 3.7266939060966 27 41 46.1797926875732 -5.17979268757325 28 45 45.7964747227621 -0.796474722762152 29 26 43.2995569263957 -17.2995569263957 30 3 10.638719027923 -7.638719027923 31 4 15.2124132407092 -11.2124132407092 32 2 1.16178822086120 0.838211779138798 33 3 6.63875131709352 -3.63875131709352 34 5 25.0173443359115 -20.0173443359115 35 3 11.4507469147986 -8.45074691479858 36 3 17.1537857236842 -14.1537857236842 37 2 13.8536155078759 -11.8536155078759 38 3 8.11040953847082 -5.11040953847081 39 2 14.0958322598179 -12.0958322598179 40 3 8.28152208313382 -5.28152208313382 41 1 13.9645619499964 -12.9645619499964 42 3 16.1663774968611 -13.1663774968611 43 4 14.6916293430593 -10.6916293430593 44 5 35.8394546440638 -30.8394546440638 45 35 29.5060761943951 5.49392380560494 46 35 36.4469146023797 -1.44691460237965 47 21 28.0844714903313 -7.08447149033134 48 33 26.3305434302335 6.66945656976653 49 40 31.2168298759616 8.78317012403837 50 22 25.8469649680795 -3.84696496807946 51 35 33.9656454388723 1.03435456112769 52 20 20.4440402316894 -0.444040231689448 53 28 33.3522008401327 -5.3522008401327 54 46 35.9445500352180 10.0554499647820 55 18 30.6651582234731 -12.6651582234731 56 22 28.8218662501492 -6.82186625014923 57 20 21.5405593543360 -1.54055935433596 58 25 26.0871470925543 -1.08714709255433 59 31 35.5940478535116 -4.59404785351156 60 21 25.4510823415414 -4.45108234154141 61 23 26.6042030905924 -3.60420309059243 62 26 35.1628504917917 -9.16285049179172 63 34 32.1940777893632 1.80592221063683 64 31 32.9672127172928 -1.96721271729283 65 23 25.4012672486250 -2.40126724862503 66 31 23.9573355484747 7.04266445152533 67 26 25.9980174765711 0.00198252342885122 68 36 28.3043554246475 7.69564457535252 69 28 31.3139884695797 -3.31398846957972 70 34 27.1440603580208 6.85593964197917 71 25 36.5155925413594 -11.5155925413594 72 33 39.2863509146685 -6.28635091466854 73 46 36.6512051643813 9.34879483561872 74 24 30.1353899682791 -6.13538996827909 75 32 34.8180947387095 -2.81809473870947 76 33 26.447856946269 6.55214305373099 77 42 39.7936169480747 2.20638305192533 78 17 21.5658598462132 -4.56585984621321 79 36 25.1617090275539 10.8382909724461 80 40 29.6342248842419 10.3657751157581 81 30 34.7644983077102 -4.76449830771017 82 19 40.1436131568629 -21.1436131568629 83 33 27.1420121062529 5.85798789374709 84 35 27.4302785303456 7.56972146965436 85 23 28.4122905914783 -5.41229059147828 86 15 21.6047824701026 -6.60478247010257 87 38 39.4387169800255 -1.43871698002551 88 37 30.2337994488215 6.76620055117846 89 23 25.8880281665566 -2.88802816655662 90 41 30.7337827239817 10.2662172760183 91 34 33.1514511692101 0.848548830789893 92 38 30.5202008307466 7.4797991692534 93 45 28.4914218115976 16.5085781884024 94 27 24.6458348383929 2.35416516160715 95 46 37.5496273254368 8.45037267456315 96 26 36.9388788559298 -10.9388788559298 97 44 35.8220316198358 8.1779683801642 98 36 30.1216104926776 5.87838950732237 99 20 30.2353511596742 -10.2353511596742 100 44 29.0980857682649 14.9019142317351 101 27 36.3254104836625 -9.32541048366253 102 27 31.7583176299696 -4.75831762996962 103 41 37.8150157848311 3.18498421516886 104 30 26.5249555037158 3.47504449628421 105 33 36.2109566022745 -3.21095660227445 106 37 29.9112169466359 7.08878305336409 107 30 33.6919584065864 -3.69195840658638 108 20 24.6267340966874 -4.62673409668739 109 44 34.3869464877731 9.61305351222692 110 20 25.5991316892990 -5.59913168929905 111 33 29.9182081124234 3.08179188757662 112 31 37.7010402460891 -6.70104024608906 113 23 37.0327999915710 -14.0327999915710 114 33 29.4425778175062 3.55742218249378 115 33 24.8113879629644 8.18861203703556 116 32 26.4819563508857 5.51804364911432 117 25 24.0568339669235 0.943166033076527 118 37 41.2419483071221 -4.24194830712205 119 48 39.896119094429 8.103880905571 120 45 35.6630744986530 9.33692550134704 121 32 43.2926306536891 -11.2926306536891 122 46 38.4618530203187 7.53814697968128 123 20 43.1543495196424 -23.1543495196424 124 42 34.2961589818231 7.70384101817685 125 45 23.5410309168328 21.4589690831672 126 29 35.2570988026026 -6.25709880260262 127 51 45.5953095796677 5.40469042033231 128 55 38.5839774440403 16.4160225559597 129 50 42.5554801976197 7.44451980238029 130 44 42.6700381462429 1.32996185375712 131 41 28.2817511388355 12.7182488611645 132 40 35.0819076943277 4.91809230567229 133 47 35.2708785365494 11.7291214634506 134 42 28.2778813346773 13.7221186653227 135 40 39.0628846100381 0.937115389961859 136 51 37.0377725968859 13.9622274031141 137 43 39.2157904982233 3.78420950177667 138 45 41.1071471127273 3.89285288727269 139 41 29.4803405404480 11.5196594595520 140 41 36.7808134570815 4.21918654291845 141 37 39.6018243589976 -2.60182435899761 142 46 33.7762476768252 12.2237523231748 143 38 36.6709444404455 1.32905555955446 144 39 33.338301051757 5.66169894824299 145 45 27.4489008280683 17.5510991719317 146 28 14.9553629751749 13.0446370248251 147 45 27.912586377261 17.087413622739 148 21 20.1542256132023 0.845774386797683 149 33 41.9980838553634 -8.9980838553634 150 14 26.8269451221798 -12.8269451221798 151 16 26.1041038881578 -10.1041038881578 152 14 46.3388547278599 -32.3388547278599 153 40 41.6414841221541 -1.64148412215411 154 49 36.9853854743793 12.0146145256207 155 38 43.98721714535 -5.98721714535 156 32 37.1689129928571 -5.16891299285709 157 46 38.1488394816012 7.85116051839881 158 32 32.6338163476258 -0.633816347625763 159 41 48.3893007545774 -7.3893007545774 160 43 39.2189630631194 3.78103693688065 161 44 37.5127450656448 6.48725493435517 162 47 41.6961774365424 5.30382256345756 163 28 41.3968606710783 -13.3968606710783 164 52 41.9258254694796 10.0741745305204 165 27 34.5157610912369 -7.51576109123693 166 45 43.5914056893425 1.40859431065747 167 27 29.2581168969254 -2.25811689692537 168 25 43.5145649322564 -18.5145649322564 169 28 34.2091344539451 -6.2091344539451 170 25 38.6933444721913 -13.6933444721913 171 52 41.0377977306198 10.9622022693802 172 44 43.377699387639 0.622300612361028 173 43 33.7906572827993 9.20934271720067 174 47 41.7961089629941 5.20389103700586 175 52 41.9401999706418 10.0598000293582 176 40 37.4184358875708 2.58156411242923 177 42 34.4876426708326 7.51235732916744 178 45 41.1310000187991 3.86899998120093 179 45 42.5389511038338 2.46104889616623 180 50 41.8769299995799 8.12307000042006 181 49 42.3736149110837 6.62638508891627 182 52 31.6019851362989 20.3980148637011 183 48 37.4241846092114 10.5758153907886 184 51 31.3353759716143 19.6646240283857 185 49 40.8283276643394 8.17167233566064 186 31 34.6404262430326 -3.64042624303255 187 43 38.1971384200241 4.80286157997588 188 31 39.5113986093825 -8.51139860938249 189 28 44.7802645140221 -16.7802645140221 190 43 41.5514916616794 1.44850833832062 191 31 43.0297061765799 -12.0297061765799 192 51 50.3968558107899 0.603144189210117 193 58 34.9428878154318 23.0571121845682 194 25 34.1774020071365 -9.17740200713653 195 27 38.2994215735338 -11.2994215735338 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.753596748058598 0.492806503882805 0.246403251941402 10 0.829275545347668 0.341448909304664 0.170724454652332 11 0.86190093360644 0.276198132787121 0.138099066393560 12 0.804939294512478 0.390121410975043 0.195060705487522 13 0.733697719349466 0.532604561301069 0.266302280650534 14 0.704254270284072 0.591491459431855 0.295745729715928 15 0.617948374526635 0.76410325094673 0.382051625473365 16 0.533730108069584 0.932539783860832 0.466269891930416 17 0.464408487216111 0.928816974432221 0.535591512783889 18 0.53376398965997 0.932472020680061 0.466236010340030 19 0.561222758595129 0.877554482809742 0.438777241404871 20 0.523438099617184 0.953123800765631 0.476561900382816 21 0.453030431710113 0.906060863420226 0.546969568289887 22 0.423529876267264 0.847059752534528 0.576470123732736 23 0.496125612590408 0.992251225180815 0.503874387409592 24 0.473789107653785 0.94757821530757 0.526210892346215 25 0.457624467841878 0.915248935683756 0.542375532158122 26 0.390949019844152 0.781898039688305 0.609050980155848 27 0.345367931369276 0.690735862738553 0.654632068630724 28 0.289847047213653 0.579694094427307 0.710152952786347 29 0.429052637919354 0.858105275838708 0.570947362080646 30 0.371752470553792 0.743504941107584 0.628247529446208 31 0.327246720860111 0.654493441720221 0.67275327913989 32 0.285664160055701 0.571328320111403 0.714335839944299 33 0.237085476584328 0.474170953168656 0.762914523415672 34 0.249042539558333 0.498085079116667 0.750957460441667 35 0.214643918646213 0.429287837292427 0.785356081353787 36 0.193495731063746 0.386991462127492 0.806504268936254 37 0.175075611406021 0.350151222812043 0.824924388593979 38 0.152190276322623 0.304380552645247 0.847809723677377 39 0.138980411317783 0.277960822635565 0.861019588682217 40 0.123260504088513 0.246521008177027 0.876739495911486 41 0.127639895857206 0.255279791714413 0.872360104142794 42 0.135264600064048 0.270529200128095 0.864735399935952 43 0.153870919441387 0.307741838882773 0.846129080558613 44 0.283115972978787 0.566231945957574 0.716884027021213 45 0.264137311369097 0.528274622738194 0.735862688630903 46 0.293773769646929 0.587547539293858 0.706226230353071 47 0.319214266534285 0.638428533068569 0.680785733465715 48 0.295235476932863 0.590470953865726 0.704764523067137 49 0.291631164067751 0.583262328135501 0.70836883593225 50 0.273863041454899 0.547726082909798 0.726136958545101 51 0.238004727457216 0.476009454914431 0.761995272542784 52 0.205559226651333 0.411118453302666 0.794440773348667 53 0.179887115413363 0.359774230826727 0.820112884586637 54 0.319197266369079 0.638394532738159 0.68080273363092 55 0.330938742824955 0.66187748564991 0.669061257175045 56 0.335190836289038 0.670381672578076 0.664809163710962 57 0.307370662480757 0.614741324961514 0.692629337519243 58 0.272065223136113 0.544130446272226 0.727934776863887 59 0.268933230431782 0.537866460863563 0.731066769568218 60 0.243110541726417 0.486221083452835 0.756889458273583 61 0.233899358316057 0.467798716632114 0.766100641683943 62 0.212826255023557 0.425652510047115 0.787173744976443 63 0.23644689901478 0.47289379802956 0.76355310098522 64 0.218001981875874 0.436003963751748 0.781998018124126 65 0.194319193655867 0.388638387311735 0.805680806344133 66 0.179551889397494 0.359103778794988 0.820448110602506 67 0.153468057186962 0.306936114373924 0.846531942813038 68 0.136799008073257 0.273598016146514 0.863200991926743 69 0.115548427799954 0.231096855599908 0.884451572200046 70 0.0989384884424324 0.197876976884865 0.901061511557568 71 0.113431430555410 0.226862861110820 0.88656856944459 72 0.0953083299314296 0.190616659862859 0.90469167006857 73 0.105128212591925 0.210256425183850 0.894871787408075 74 0.092882294254028 0.185764588508056 0.907117705745972 75 0.0778859701870721 0.155771940374144 0.922114029812928 76 0.071296054385119 0.142592108770238 0.928703945614881 77 0.0661338593780722 0.132267718756144 0.933866140621928 78 0.0619935774489244 0.123987154897849 0.938006422551076 79 0.0949651350184253 0.189930270036851 0.905034864981575 80 0.143430062605732 0.286860125211463 0.856569937394268 81 0.123872289992547 0.247744579985094 0.876127710007453 82 0.191584535097964 0.383169070195927 0.808415464902036 83 0.182464746523293 0.364929493046586 0.817535253476707 84 0.167741744235489 0.335483488470978 0.832258255764511 85 0.159082969903820 0.318165939807640 0.84091703009618 86 0.167037318709274 0.334074637418549 0.832962681290726 87 0.14711170309955 0.2942234061991 0.85288829690045 88 0.134150072167395 0.268300144334790 0.865849927832605 89 0.120428969235971 0.240857938471942 0.879571030764029 90 0.152849871057663 0.305699742115325 0.847150128942337 91 0.135574409675714 0.271148819351429 0.864425590324285 92 0.126540718661077 0.253081437322154 0.873459281338923 93 0.168364441448698 0.336728882897396 0.831635558551302 94 0.143261385348684 0.286522770697369 0.856738614651316 95 0.165523432520030 0.331046865040059 0.83447656747997 96 0.175807629743491 0.351615259486982 0.82419237025651 97 0.191599033168849 0.383198066337699 0.80840096683115 98 0.177086676518139 0.354173353036277 0.822913323481861 99 0.187300037949185 0.374600075898369 0.812699962050815 100 0.242221863006252 0.484443726012504 0.757778136993748 101 0.229573057193280 0.459146114386559 0.77042694280672 102 0.206660297800105 0.41332059560021 0.793339702199895 103 0.197024419280933 0.394048838561866 0.802975580719067 104 0.169726856517068 0.339453713034136 0.830273143482932 105 0.145733498674195 0.29146699734839 0.854266501325805 106 0.142433431084286 0.284866862168572 0.857566568915714 107 0.122246849104353 0.244493698208707 0.877753150895647 108 0.111886982860221 0.223773965720442 0.888113017139779 109 0.116006009220364 0.232012018440727 0.883993990779636 110 0.105967994703826 0.211935989407652 0.894032005296174 111 0.0917049383259773 0.183409876651955 0.908295061674023 112 0.0789823061240814 0.157964612248163 0.921017693875919 113 0.0910766564537505 0.182153312907501 0.90892334354625 114 0.0758501495059605 0.151700299011921 0.92414985049404 115 0.068678395722384 0.137356791444768 0.931321604277616 116 0.0584965918011765 0.116993183602353 0.941503408198823 117 0.0519874059353421 0.103974811870684 0.948012594064658 118 0.0473503038061032 0.0947006076122065 0.952649696193897 119 0.0644588404342743 0.128917680868549 0.935541159565726 120 0.0721938163761281 0.144387632752256 0.927806183623872 121 0.0736145514704537 0.147229102940907 0.926385448529546 122 0.0742006610039317 0.148401322007863 0.925799338996068 123 0.181227945354675 0.36245589070935 0.818772054645325 124 0.181005746417144 0.362011492834288 0.818994253582856 125 0.262049001961719 0.524098003923438 0.737950998038281 126 0.279752922284875 0.55950584456975 0.720247077715125 127 0.258656015105330 0.517312030210659 0.74134398489467 128 0.330999061073412 0.661998122146824 0.669000938926588 129 0.312384859570869 0.624769719141738 0.687615140429131 130 0.276550720893577 0.553101441787153 0.723449279106423 131 0.269058957758698 0.538117915517395 0.730941042241302 132 0.236283914358532 0.472567828717064 0.763716085641468 133 0.226352771353439 0.452705542706879 0.77364722864656 134 0.216133445478983 0.432266890957967 0.783866554521017 135 0.187859709859724 0.375719419719449 0.812140290140276 136 0.203558907755336 0.407117815510672 0.796441092244664 137 0.174019631733200 0.348039263466399 0.8259803682668 138 0.149741471562328 0.299482943124655 0.850258528437672 139 0.139864850677877 0.279729701355754 0.860135149322123 140 0.116463445480560 0.232926890961119 0.88353655451944 141 0.0990164611488512 0.198032922297702 0.900983538851149 142 0.102450276546640 0.204900553093280 0.89754972345336 143 0.0852178589327163 0.170435717865433 0.914782141067284 144 0.0853451212182001 0.170690242436400 0.9146548787818 145 0.199209001318809 0.398418002637618 0.800790998681191 146 0.212797924397802 0.425595848795605 0.787202075602198 147 0.276658811211827 0.553317622423655 0.723341188788173 148 0.236911783553755 0.47382356710751 0.763088216446245 149 0.23772871655751 0.47545743311502 0.76227128344249 150 0.240806817221542 0.481613634443083 0.759193182778458 151 0.234403944081352 0.468807888162704 0.765596055918648 152 0.691383996310733 0.617232007378534 0.308616003689267 153 0.645797581798041 0.708404836403917 0.354202418201959 154 0.636519598782352 0.726960802435297 0.363480401217648 155 0.587151457081716 0.825697085836567 0.412848542918284 156 0.538591054857326 0.922817890285348 0.461408945142674 157 0.544367630516364 0.911264738967271 0.455632369483636 158 0.491029901418198 0.982059802836395 0.508970098581802 159 0.452782756283125 0.90556551256625 0.547217243716875 160 0.402067665505432 0.804135331010865 0.597932334494568 161 0.383801622278524 0.767603244557047 0.616198377721476 162 0.336635269357101 0.673270538714201 0.6633647306429 163 0.354498341011755 0.70899668202351 0.645501658988245 164 0.311463206013254 0.622926412026507 0.688536793986746 165 0.330594529454400 0.661189058908801 0.6694054705456 166 0.28330924163084 0.56661848326168 0.71669075836916 167 0.356284165483809 0.712568330967618 0.643715834516191 168 0.451175249781140 0.902350499562281 0.54882475021886 169 0.388907215202411 0.777814430404823 0.611092784797589 170 0.417572500064654 0.835145000129309 0.582427499935346 171 0.415509425954727 0.831018851909455 0.584490574045273 172 0.350619785509424 0.701239571018848 0.649380214490576 173 0.293972332124905 0.58794466424981 0.706027667875095 174 0.244875723813208 0.489751447626416 0.755124276186792 175 0.234667492878510 0.469334985757020 0.76533250712149 176 0.203567858505621 0.407135717011241 0.79643214149438 177 0.154321570401304 0.308643140802608 0.845678429598696 178 0.136664767572460 0.273329535144920 0.86333523242754 179 0.0998084511099069 0.199616902219814 0.900191548890093 180 0.184349285785555 0.36869857157111 0.815650714214445 181 0.151197241043879 0.302394482087759 0.84880275895612 182 0.113111585179523 0.226223170359047 0.886888414820477 183 0.0726699951520893 0.145339990304179 0.92733000484791 184 0.0654612541055095 0.130922508211019 0.93453874589449 185 0.230198659572979 0.460397319145958 0.769801340427021 186 0.135809291066651 0.271618582133302 0.864190708933349 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 1 0.00561797752808989 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/10zbea1293394680.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/10zbea1293394680.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/1ashz1293394680.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/1ashz1293394680.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/2ashz1293394680.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/2ashz1293394680.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/3ljg21293394680.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/3ljg21293394680.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/4ljg21293394680.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/4ljg21293394680.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/5ljg21293394680.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/5ljg21293394680.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/6wty51293394680.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/6wty51293394680.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/7okf81293394680.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/7okf81293394680.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/8okf81293394680.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/8okf81293394680.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/9okf81293394680.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293394602qeiw48dzdjmirdu/9okf81293394680.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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Software written by Ed van Stee & Patrick Wessa

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