multiple regression

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 24 Dec 2010 11:02:48 +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/24/t1293188433eo02pkewoj75zsn.htm/, Retrieved Fri, 24 Dec 2010 12:00:45 +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/24/t1293188433eo02pkewoj75zsn.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 «

4 1 27 5 26 49 35 4 1 36 4 25 45 34 5 1 25 4 17 54 13 2 1 27 3 37 36 35 3 2 25 3 35 36 28 5 2 44 3 15 53 32 4 1 50 4 27 46 35 4 1 41 4 36 42 36 4 1 48 5 25 41 27 4 2 43 4 30 45 29 5 2 47 2 27 47 27 4 2 41 3 33 42 28 3 1 44 2 29 45 29 4 2 47 5 30 40 28 3 2 40 3 25 45 30 3 2 46 3 23 40 25 4 1 28 3 26 42 15 3 1 56 3 24 45 33 4 2 49 4 35 47 31 2 2 25 4 39 31 37 4 2 41 4 23 46 37 3 2 26 3 32 34 34 4 1 50 5 29 43 32 4 1 47 4 26 45 21 3 1 52 2 21 42 25 3 2 37 5 35 51 32 2 2 41 3 23 44 28 4 1 45 4 21 47 22 5 2 26 4 28 47 25 4 1 3 30 41 26 2 1 52 4 21 44 34 5 1 46 2 29 51 34 4 1 58 3 28 46 36 3 1 54 5 19 47 36 4 1 29 3 26 46 26 2 2 50 3 33 38 26 3 1 43 2 34 50 34 3 2 30 3 33 48 33 3 2 47 2 40 36 31 5 1 45 3 24 51 33 2 48 1 35 35 22 4 2 48 3 35 49 29 4 2 26 4 32 38 24 4 1 46 5 20 47 37 2 2 3 35 36 32 4 2 50 3 35 47 23 3 1 25 4 21 46 29 4 1 47 2 33 43 35 1 2 47 2 40 53 20 2 1 41 3 22 55 28 2 2 45 2 35 39 26 4 2 41 4 20 55 36 3 2 45 5 28 41 26 4 2 40 3 46 33 33 3 1 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 13 seconds R Server 'George Udny Yule' @ 72.249.76.132 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 Teamwork33[t] = + 55.6998054685839 -0.189599030063311geslacht[t] -0.36257731331915leeftijd[t] -0.312586350508122opleiding[t] -0.437634633702588Neuroticisme[t] -0.193414361348253Extraversie[t] -0.451755541671208`Openheid `[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) 55.6998054685839 5.404109 10.3069 0 0 geslacht -0.189599030063311 0.056822 -3.3367 0.001022 0.000511 leeftijd -0.36257731331915 0.059629 -6.0805 0 0 opleiding -0.312586350508122 0.076485 -4.0869 6.5e-05 3.2e-05 Neuroticisme -0.437634633702588 0.057654 -7.5907 0 0 Extraversie -0.193414361348253 0.065404 -2.9572 0.003503 0.001751 `Openheid ` -0.451755541671208 0.057789 -7.8174 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.726089862984427 R-squared 0.527206489128744 Adjusted R-squared 0.51211733452647 F-TEST (value) 34.9394318651416 F-TEST (DF numerator) 6 F-TEST (DF denominator) 188 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.51089716761969 Sum Squared Residuals 13617.8496723858 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 7.49043908553882 -3.49043908553882 2 4 6.2028772369415 -2.20287723694151 3 5 21.438441876034 -16.438441876034 4 2 5.81601751335397 -3.81601751335397 5 3 10.3891311690326 -7.38913116903258 6 5 7.1577885804154 -2.15778858041540 7 4 -0.393644319951218 4.39364431995122 8 4 -0.747258299680351 4.74725829968035 9 4 5.47530936369507 -1.47530936369507 10 4 3.54584155348726 0.454158446512739 11 5 4.55029126298058 0.449708737019420 12 4 4.30267725524188 -0.302677255241885 13 3 4.43567060495026 -1.43567060495026 14 4 3.20177329811501 0.79822670188499 15 3 6.68257747079457 -3.68257747079457 16 3 8.60823237338215 -5.60823237338215 17 4 18.1420458360980 -14.1420458360980 18 3 0.153307496440445 2.84669250355956 19 4 -2.10813530097951 6.10813530097951 20 2 5.22727821541455 -3.22727821541455 21 4 3.52697992132577 0.473020078674229 22 3 9.0157532294905 -6.0157532294905 23 4 0.354009771193873 3.64599022880613 24 4 7.64971419845399 -3.64971419845399 25 3 7.42339441874735 -4.42339441874735 26 3 0.704793121277957 2.29520687872204 27 2 8.29219486957127 -6.29219486957127 28 4 9.72445772923752 -5.72445772923752 29 5 12.0051185913063 -7.00511859130632 30 4 21.1695795231163 -17.1695795231163 31 1 9.73524341423399 -8.73524341423399 32 1 6.48561452294026 -5.48561452294026 33 1 6.41353518685714 -5.41353518685714 34 1 8.3706636596714 -7.37066365967139 35 1 14.9229789148632 -13.9229789148632 36 2 11.8026163579263 -9.80261635792626 37 1 6.38087003596339 -5.38087003596339 38 2 9.86435009272884 -7.86435009272884 39 2 9.5505726852 -7.5505726852 40 1 8.9724934369157 -7.9724934369157 41 48 20.5743477343737 27.4256522656263 42 48 12.7554983312152 35.2445016687848 43 26 19.7320098068829 6.26799019311715 44 46 15.3258843249679 30.6741156750321 45 3 1.28314857955144 1.71685142044856 46 3 12.0330128244449 -9.03301282444492 47 4 2.79820190513254 1.20179809486746 48 2 0.854716921041033 1.14528307895897 49 2 3.05685881270109 -1.05685881270109 50 3 1.24335939510434 1.75664060489566 51 2 6.13673461768359 -4.13673461768359 52 4 -1.31576798253660 5.3157679825366 53 5 7.19052874315968 -2.19052874315968 54 3 10.0906202084505 -7.09062020845054 55 4 8.5589228315201 -4.55892283152010 56 5 4.52478857798566 0.475211422014343 57 5 -3.59028868552172 8.59028868552172 58 3 3.55667583791473 -0.55667583791473 59 4 7.8463824282773 -3.8463824282773 60 3 1.94550862691988 1.05449137308012 61 3 -1.18091958039512 4.18091958039512 62 2 12.2205870112505 -10.2205870112505 63 3 8.17655727478 -5.17655727477999 64 4 9.92320152995496 -5.92320152995495 65 4 -0.317391006935464 4.31739100693546 66 4 -2.03104467769895 6.03104467769895 67 4 0.512435069302013 3.48756493069799 68 3 -0.236650717953086 3.23665071795309 69 3 6.81370066366179 -3.81370066366179 70 3 -1.38188223481098 4.38188223481098 71 2 9.14829708889404 -7.14829708889404 72 3 13.0848406879182 -10.0848406879182 73 3 7.10599088934759 -4.10599088934759 74 3 7.58704453420239 -4.58704453420239 75 3 10.5228571031859 -7.52285710318591 76 5 0.274822569311912 4.72517743068809 77 3 13.0671145430685 -10.0671145430685 78 5 -0.200172722412482 5.20017272241248 79 4 0.921599395738023 3.07840060426198 80 4 7.45902975122535 -3.45902975122536 81 4 12.4558171993673 -8.45581719936729 82 5 19.8807693942138 -14.8807693942138 83 4 3.27341914992601 0.726580850073986 84 5 -0.529596234710519 5.52959623471052 85 3 2.59897049424681 0.401029505753186 86 3 -1.46044406953657 4.46044406953657 87 2 14.5647980920523 -12.5647980920523 88 3 2.23854674657396 0.76145325342604 89 4 1.98474324283436 2.01525675716564 90 5 7.22862136896056 -2.22862136896056 91 5 9.7920390734676 -4.79203907346761 92 3 2.78890834110251 0.211091658897495 93 2 -0.284512375944478 2.28451237594448 94 3 -0.084792939532401 3.0847929395324 95 4 11.3852339257169 -7.38523392571692 96 1 6.91731042626236 -5.91731042626236 97 4 9.52457273048141 -5.52457273048141 98 3 0.897839905618154 2.10216009438185 99 3 9.6197855591749 -6.6197855591749 100 4 4.55595875620675 -0.555958756206747 101 3 13.2430831143542 -10.2430831143542 102 4 6.44344747070793 -2.44344747070793 103 2 6.66629642871685 -4.66629642871685 104 3 1.83433034249057 1.16566965750943 105 3 12.1496154968744 -9.14961549687444 106 3 0.758373590699663 2.24162640930034 107 2 7.40157032588241 -5.40157032588241 108 5 -0.328714952309823 5.32871495230982 109 5 11.0764859960405 -6.07648599604053 110 4 -0.334579352220744 4.33457935222074 111 2 1.56661892143015 0.433381078569853 112 3 15.0818025005225 -12.0818025005225 113 3 10.1449546796304 -7.14495467963036 114 3 5.85813409527247 -2.85813409527247 115 4 -0.300500921227096 4.3005009212271 116 5 1.21504416890329 3.78495583109671 117 4 10.5089164907078 -6.50891649070777 118 22 25.2902108490328 -3.29021084903285 119 16 25.703353397549 -9.70335339754897 120 36 24.6584206339219 11.3415793660781 121 35 30.1252203187858 4.87477968121417 122 25 26.9689653449368 -1.96896534493676 123 27 33.8978088897112 -6.89780888971123 124 32 25.5933682392142 6.40663176078581 125 36 22.2688641850646 13.7311358149354 126 51 27.6213359445297 23.3786640554703 127 30 24.2854243368059 5.71457566319407 128 20 25.7606513910220 -5.76065139102197 129 29 23.6697500740080 5.33024992599203 130 26 26.3567442029008 -0.35674420290077 131 20 24.7596110009139 -4.75961100091395 132 40 24.1396825307418 15.8603174692582 133 29 23.6568159360968 5.34318406390317 134 32 22.2418091391848 9.75819086081517 135 33 30.2776732118134 2.7223267881866 136 32 29.2777307633475 2.72226923665249 137 34 26.3324686985462 7.66753130145384 138 24 22.4530850416796 1.54691495832038 139 25 26.5822879859135 -1.58228798591351 140 41 28.0326735213808 12.9673264786192 141 39 23.7356654627601 15.2643345372399 142 21 21.4490311081455 -0.449031108145488 143 38 23.3457616588666 14.6542383411334 144 28 26.6474115514757 1.35258844852431 145 37 24.0895490795249 12.9104509204751 146 46 12.4633813629491 33.5366186370509 147 39 12.3058787494803 26.6941212505197 148 21 11.5711827037435 9.42881729625647 149 31 24.4848914909306 6.51510850906942 150 25 10.8946973340974 14.1053026659026 151 29 13.7356492310377 15.2643507689623 152 31 22.8357877366597 8.16421226334031 153 3 5.2871865835644 -2.2871865835644 154 4 -2.59657584568818 6.59657584568818 155 1 10.045590208559 -9.045590208559 156 1 9.52600784199112 -8.52600784199112 157 5 2.88730106013217 2.11269893986783 158 4 4.38806400479118 -0.388064004791184 159 3 11.5278536673446 -8.52785366734465 160 3 2.08532527411618 0.914674725883816 161 4 3.00583317637193 0.99416682362807 162 3 0.574915630846371 2.42508436915363 163 2 12.3705193858617 -10.3705193858617 164 1 1.45944363063282 -0.459443630632818 165 1 8.13608420833946 -7.13608420833946 166 5 4.14563857232211 0.854361427677887 167 4 -1.77549668997964 5.77549668997964 168 3 12.9822080310787 -9.98220803107873 169 4 9.10209637283875 -5.10209637283875 170 5 13.507974096692 -8.50797409669199 171 4 -0.372017221557885 4.37201722155788 172 4 10.0298591080536 -6.02985910805359 173 2 -1.52871905925348 3.52871905925348 174 3 3.70069691844701 -0.700696918447011 175 4 -0.469813712285109 4.46981371228511 176 3 3.42071674560706 -0.420716745607056 177 4 1.27655727161663 2.72344272838337 178 3 3.28638587754914 -0.286385877549136 179 4 6.5252853613354 -2.5252853613354 180 1 0.468376405598805 0.531623594401195 181 2 4.29927877414268 -2.29927877414268 182 3 -8.4854162866248 11.4854162866248 183 3 1.41449234234879 1.58550765765121 184 5 -9.13326352742276 14.1332635274228 185 4 0.382107867338101 3.6178921326619 186 3 4.60459360858908 -1.60459360858908 187 3 1.36387311038524 1.63612688961476 188 3 5.76147521941344 -2.76147521941344 189 3 11.9830168702179 -8.98301687021793 190 4 6.60651852317355 -2.60651852317355 191 3 12.1621882751171 -9.1621882751171 192 2 10.0663235120214 -8.0663235120214 193 4 -4.53411295206 8.53411295206 194 2 5.16872141993684 -3.16872141993684 195 4 7.49043908553895 -3.49043908553895 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0002159835566622 0.0004319671133244 0.999784016443338 11 1.46898784608529e-05 2.93797569217058e-05 0.99998531012154 12 6.47391040054466e-07 1.29478208010893e-06 0.99999935260896 13 1.42939907504496e-07 2.85879815008991e-07 0.999999857060093 14 8.76737946807497e-09 1.75347589361499e-08 0.99999999123262 15 3.48740631134593e-09 6.97481262269186e-09 0.999999996512594 16 2.58045211477036e-10 5.16090422954072e-10 0.999999999741955 17 2.70998481543949e-11 5.41996963087897e-11 0.9999999999729 18 3.04604061880162e-12 6.09208123760324e-12 0.999999999996954 19 4.59578877009915e-13 9.19157754019831e-13 0.99999999999954 20 2.94392286527705e-14 5.8878457305541e-14 0.99999999999997 21 1.81292991311512e-15 3.62585982623024e-15 0.999999999999998 22 2.12178326141188e-16 4.24356652282376e-16 1 23 1.31978406470402e-17 2.63956812940804e-17 1 24 7.89269626156615e-19 1.57853925231323e-18 1 25 4.63504125564217e-20 9.27008251128435e-20 1 26 2.03002650192292e-19 4.06005300384585e-19 1 27 4.84475265354455e-19 9.6895053070891e-19 1 28 4.0623244326456e-20 8.1246488652912e-20 1 29 7.97349869816906e-21 1.59469973963381e-20 1 30 1.35975919985693e-21 2.71951839971386e-21 1 31 1.30837291067363e-22 2.61674582134725e-22 1 32 1.54593735070913e-23 3.09187470141826e-23 1 33 1.25881621932171e-24 2.51763243864341e-24 1 34 1.10894328696068e-25 2.21788657392136e-25 1 35 2.36739003898186e-26 4.73478007796373e-26 1 36 7.62434716354625e-27 1.52486943270925e-26 1 37 1.84682593789920e-27 3.69365187579841e-27 1 38 2.86479148741725e-28 5.72958297483451e-28 1 39 5.55277178399254e-29 1.11055435679851e-28 1 40 2.71954942962187e-29 5.43909885924374e-29 1 41 6.36432108100397e-05 0.000127286421620079 0.99993635678919 42 0.000410590723242719 0.000821181446485437 0.999589409276757 43 0.00156763302797446 0.00313526605594891 0.998432366972026 44 0.0156305882567479 0.0312611765134958 0.984369411743252 45 0.05484949672653 0.10969899345306 0.94515050327347 46 0.0783954752631923 0.156790950526385 0.921604524736808 47 0.0820650017613152 0.164130003522630 0.917934998238685 48 0.0703383521846401 0.140676704369280 0.92966164781536 49 0.0551101602250972 0.110220320450194 0.944889839774903 50 0.0581567043290416 0.116313408658083 0.941843295670958 51 0.0465536024097328 0.0931072048194656 0.953446397590267 52 0.0622902515198886 0.124580503039777 0.937709748480111 53 0.0484282816994033 0.0968565633988065 0.951571718300597 54 0.0425744158905514 0.0851488317811027 0.957425584109449 55 0.0486283000603709 0.0972566001207419 0.951371699939629 56 0.0380117271553801 0.0760234543107603 0.96198827284462 57 0.03600425419908 0.07200850839816 0.96399574580092 58 0.0324435471824244 0.0648870943648489 0.967556452817576 59 0.0350615322481179 0.0701230644962357 0.964938467751882 60 0.0319797215805089 0.0639594431610177 0.96802027841949 61 0.0251836799733799 0.0503673599467598 0.97481632002662 62 0.030766720909255 0.06153344181851 0.969233279090745 63 0.0269501981784272 0.0539003963568544 0.973049801821573 64 0.0220009727301157 0.0440019454602314 0.977999027269884 65 0.0179133563819911 0.0358267127639821 0.98208664361801 66 0.0139884670709253 0.0279769341418506 0.986011532929075 67 0.0107771276389325 0.0215542552778650 0.989222872361068 68 0.0100377003260115 0.0200754006520230 0.989962299673989 69 0.00789519489350391 0.0157903897870078 0.992104805106496 70 0.00692185036073832 0.0138437007214766 0.993078149639262 71 0.00515173846531496 0.0103034769306299 0.994848261534685 72 0.0044315861636955 0.008863172327391 0.995568413836305 73 0.00651286342590215 0.0130257268518043 0.993487136574098 74 0.00678668635632743 0.0135733727126549 0.993213313643672 75 0.0054218151949573 0.0108436303899146 0.994578184805043 76 0.00472494119199224 0.00944988238398448 0.995275058808008 77 0.00512503301623954 0.0102500660324791 0.99487496698376 78 0.00572781315196961 0.0114556263039392 0.99427218684803 79 0.00455345775944239 0.00910691551888478 0.995446542240558 80 0.00348557137149964 0.00697114274299928 0.9965144286285 81 0.00278478403054483 0.00556956806108965 0.997215215969455 82 0.00305891723915958 0.00611783447831916 0.99694108276084 83 0.00222068641514825 0.0044413728302965 0.997779313584852 84 0.00201872320369627 0.00403744640739254 0.997981276796304 85 0.00148611459649725 0.0029722291929945 0.998513885403503 86 0.00216788035171953 0.00433576070343906 0.99783211964828 87 0.00221386966446029 0.00442773932892059 0.99778613033554 88 0.00183208216951977 0.00366416433903953 0.99816791783048 89 0.00138207000098408 0.00276414000196817 0.998617929999016 90 0.000979241750769283 0.00195848350153857 0.99902075824923 91 0.000681399281698594 0.00136279856339719 0.999318600718301 92 0.000508099497725068 0.00101619899545014 0.999491900502275 93 0.000478280585309209 0.000956561170618418 0.99952171941469 94 0.000350963147002301 0.000701926294004602 0.999649036852998 95 0.000331634005213078 0.000663268010426157 0.999668365994787 96 0.000245127358696171 0.000490254717392342 0.999754872641304 97 0.000218854838333249 0.000437709676666499 0.999781145161667 98 0.000178124849747466 0.000356249699494932 0.999821875150253 99 0.000259757816932522 0.000519515633865045 0.999740242183067 100 0.000191555253406719 0.000383110506813437 0.999808444746593 101 0.000151596038458539 0.000303192076917079 0.999848403961541 102 0.000100350930789227 0.000200701861578453 0.99989964906921 103 0.000161110656663441 0.000322221313326882 0.999838889343337 104 0.000112243467367735 0.000224486934735470 0.999887756532632 105 9.06556921776654e-05 0.000181311384355331 0.999909344307822 106 7.70631204286503e-05 0.000154126240857301 0.999922936879571 107 6.16398339991299e-05 0.000123279667998260 0.999938360166 108 4.54095164131261e-05 9.08190328262521e-05 0.999954590483587 109 7.25040277361824e-05 0.000145008055472365 0.999927495972264 110 5.80819581568907e-05 0.000116163916313781 0.999941918041843 111 4.60505596644957e-05 9.21011193289914e-05 0.999953949440336 112 5.33111158856538e-05 0.000106622231771308 0.999946688884114 113 4.39428816598311e-05 8.78857633196622e-05 0.99995605711834 114 5.76035197264051e-05 0.000115207039452810 0.999942396480274 115 4.66613068630819e-05 9.33226137261638e-05 0.999953338693137 116 5.09551491611034e-05 0.000101910298322207 0.999949044850839 117 0.000163223093655003 0.000326446187310006 0.999836776906345 118 0.00712952039651895 0.0142590407930379 0.992870479603481 119 0.0493799160275222 0.0987598320550443 0.950620083972478 120 0.260540604392089 0.521081208784177 0.739459395607911 121 0.394985030496392 0.789970060992784 0.605014969503608 122 0.436547895307922 0.873095790615844 0.563452104692078 123 0.399466873494569 0.798933746989137 0.600533126505431 124 0.442591031242514 0.885182062485029 0.557408968757486 125 0.538154547075117 0.923690905849766 0.461845452924883 126 0.967896935524085 0.0642061289518305 0.0321030644759153 127 0.968762853539504 0.062474292920992 0.031237146460496 128 0.991663559439295 0.01667288112141 0.008336440560705 129 0.99219079207434 0.0156184158513213 0.00780920792566063 130 0.992017737183872 0.0159645256322559 0.00798226281612796 131 0.994670170329043 0.0106596593419134 0.00532982967095671 132 0.998154092168348 0.00369181566330454 0.00184590783165227 133 0.997859733518589 0.00428053296282251 0.00214026648141126 134 0.997334339576526 0.00533132084694811 0.00266566042347406 135 0.996776498879108 0.00644700224178445 0.00322350112089222 136 0.997719057346688 0.004561885306624 0.002280942653312 137 0.997008448477282 0.00598310304543567 0.00299155152271783 138 0.998427136052092 0.00314572789581579 0.00157286394790789 139 0.9984180041155 0.00316399176900193 0.00158199588450096 140 0.998585233053872 0.00282953389225617 0.00141476694612809 141 0.999518558426016 0.000962883147966958 0.000481441573983479 142 0.999949450618505 0.000101098762989565 5.05493814947824e-05 143 0.99995073020335 9.85395932984664e-05 4.92697966492332e-05 144 0.999919666861899 0.000160666276202203 8.03331381011017e-05 145 0.999955056769719 8.98864605624566e-05 4.49432302812283e-05 146 0.999999996656768 6.68646338306663e-09 3.34323169153332e-09 147 0.999999997453273 5.09345350101669e-09 2.54672675050835e-09 148 0.9999999951192 9.76159905468904e-09 4.88079952734452e-09 149 0.999999997909585 4.18082969165697e-09 2.09041484582849e-09 150 0.999999997690024 4.61995127703249e-09 2.30997563851624e-09 151 0.999999998095126 3.80974830521087e-09 1.90487415260543e-09 152 1 3.30634857095627e-27 1.65317428547813e-27 153 1 2.79630346664577e-26 1.39815173332289e-26 154 1 2.15871539322375e-25 1.07935769661187e-25 155 1 8.30831465454634e-25 4.15415732727317e-25 156 1 7.19969358263877e-25 3.59984679131939e-25 157 1 2.05820906109168e-24 1.02910453054584e-24 158 1 1.66759614120743e-23 8.33798070603714e-24 159 1 1.33597651320567e-22 6.67988256602833e-23 160 1 1.20825050737338e-21 6.04125253686689e-22 161 1 1.04677953003320e-20 5.23389765016598e-21 162 1 8.64889831781923e-20 4.32444915890962e-20 163 1 6.25197171023116e-19 3.12598585511558e-19 164 1 2.25171591530662e-18 1.12585795765331e-18 165 1 1.19402217062670e-18 5.97011085313349e-19 166 1 5.80672969566772e-18 2.90336484783386e-18 167 1 5.04938992744853e-17 2.52469496372426e-17 168 1 4.15616664309051e-16 2.07808332154526e-16 169 0.999999999999998 3.7896173548211e-15 1.89480867741055e-15 170 0.99999999999999 2.05355241677018e-14 1.02677620838509e-14 171 0.999999999999933 1.32990798283547e-13 6.64953991417735e-14 172 0.999999999999766 4.69081929565034e-13 2.34540964782517e-13 173 0.9999999999992 1.60057042611828e-12 8.00285213059138e-13 174 0.999999999992874 1.42513972608697e-11 7.12569863043483e-12 175 0.999999999956387 8.72253583271511e-11 4.36126791635756e-11 176 0.999999999645077 7.09844999959725e-10 3.54922499979862e-10 177 0.999999997973853 4.05229422485849e-09 2.02614711242925e-09 178 0.999999984566573 3.08668546203582e-08 1.54334273101791e-08 179 0.999999945239067 1.09521866451742e-07 5.4760933225871e-08 180 0.999999871349217 2.57301566426044e-07 1.28650783213022e-07 181 0.99999915767119 1.68465762039943e-06 8.42328810199713e-07 182 0.999998174012157 3.65197568562205e-06 1.82598784281103e-06 183 0.99998540765764 2.91846847209865e-05 1.45923423604932e-05 184 0.999870179954466 0.000259640091067465 0.000129820045533732 185 0.998503770993002 0.00299245801399561 0.00149622900699781 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 129 0.732954545454545 NOK 5% type I error level 148 0.840909090909091 NOK 10% type I error level 163 0.926136363636364 NOK

Charts produced by software:

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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') }

Copyright

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

Software written by Ed van Stee & Patrick Wessa

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• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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