*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: Wed, 01 Dec 2010 10:11:37 +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/01/t1291198402q3oewaxujnsd3ma.htm/, Retrieved Wed, 01 Dec 2010 11:13:35 +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/01/t1291198402q3oewaxujnsd3ma.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 27 1 5 26 49 35 4 36 1 4 25 45 34 5 25 1 4 17 54 13 2 27 1 3 37 36 35 3 25 2 3 35 36 28 5 44 2 3 15 53 32 4 50 1 4 27 46 35 4 41 1 4 36 42 36 4 48 1 5 25 41 27 4 43 2 4 30 45 29 5 47 2 2 27 47 27 4 41 2 3 33 42 28 3 44 1 2 29 45 29 4 47 2 5 30 40 28 3 40 2 3 25 45 30 3 46 2 3 23 40 25 4 28 1 3 26 42 15 3 56 1 3 24 45 33 4 49 2 4 35 47 31 2 25 2 4 39 31 37 4 41 2 4 23 46 37 3 26 2 3 32 34 34 4 50 1 5 29 43 32 4 47 1 4 26 45 21 3 52 1 2 21 42 25 3 37 2 5 35 51 32 2 41 2 3 23 44 28 4 45 1 4 21 47 22 5 26 2 4 28 47 25 4 1 3 30 41 26 2 52 1 4 21 44 34 5 46 1 2 29 51 34 4 58 1 3 28 46 36 3 54 1 5 19 47 36 4 29 1 3 26 46 26 2 50 2 3 33 38 26 3 43 1 2 34 50 34 3 30 2 3 33 48 33 3 47 2 2 40 36 31 5 45 1 3 24 51 33 48 2 1 35 35 22 4 48 2 3 35 49 29 4 26 2 4 32 38 24 4 46 1 5 20 47 37 2 2 3 35 36 32 4 50 2 3 35 47 23 3 25 1 4 21 46 29 4 47 1 2 33 43 35 1 47 2 2 40 53 20 2 41 1 3 22 55 28 2 45 2 2 35 39 26 4 41 2 4 20 55 36 3 45 2 5 28 41 26 4 40 2 3 46 33 33 3 2 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 79 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 Teamwork[t] = + 45.5524104419848 -0.337389511564904leeftijd[t] -0.230173178231959geslacht[t] -0.101544702076264opleiding[t] + 0.128159964550332Neuroticisme[t] -0.445772756009979Extraversie[t] -0.327842515186265`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) 45.5524104419848 6.243397 7.2961 0 0 leeftijd -0.337389511564904 0.060011 -5.6221 0 0 geslacht -0.230173178231959 0.067431 -3.4134 0.000786 0.000393 opleiding -0.101544702076264 0.080315 -1.2643 0.207677 0.103838 Neuroticisme 0.128159964550332 0.075332 1.7013 0.090546 0.045273 Extraversie -0.445772756009979 0.049427 -9.0188 0 0 `Openheid ` -0.327842515186265 0.073437 -4.4642 1.4e-05 7e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.761884570669444 R-squared 0.580468099024164 Adjusted R-squared 0.567078783035573 F-TEST (value) 43.3530808832056 F-TEST (DF numerator) 6 F-TEST (DF denominator) 188 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.13201861246577 Sum Squared Residuals 15678.0276204232 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 5.71980294341926 -1.71980294341926 2 4 4.76761561608748 -0.767615616087484 3 5 10.3263585417205 -5.32635854172049 4 2 13.1276977857554 -11.1276977857554 5 3 15.6108813078564 -12.6108813078564 6 5 -2.25222561579813 7.25222561579813 7 4 -0.47313288791683 4.47313288791683 8 4 5.17206090597398 -1.17206090597398 9 4 4.6953854055761 -0.695385405576099 10 4 4.45572825558414 -0.455728255584136 11 5 2.68891923817863 2.31108076182137 12 4 7.28169265765741 -3.28169265765741 13 3 4.42344136185339 -1.42344136185339 14 4 5.56133180248442 -1.56133180248442 15 3 4.60079915441719 -1.60079915441719 16 3 6.18821851190832 -3.18821851190832 17 4 15.2627624318022 -11.2627624318022 18 3 -1.67894736249845 4.67894736249845 19 4 1.52496046655388 2.47503953344612 20 2 15.3002576073550 -13.3002576073550 21 4 1.16487464936152 2.83512535063848 22 3 13.8135023235429 -10.8135023235429 23 4 2.00248815269633 1.99751184730367 24 4 5.44644365084527 -1.44644365084527 25 3 3.3477338817065 -0.347733881706499 26 3 3.36115636403028 -0.361156364030282 27 2 5.10854750013413 -3.10854750013413 28 4 4.2610348240172 -0.261034824017198 29 5 10.3548545718119 -5.35485457181194 30 4 34.4869421933677 -30.4869421933677 31 52 31.0054416338345 20.9945583661655 32 46 31.8783926407269 14.1216073592731 33 58 30.5452613449858 27.4547386550142 34 54 30.7991347565724 23.2008652434276 35 29 35.5339208244244 -6.53392082442441 36 50 33.1325961667367 16.8674038332633 37 43 31.5703516809815 11.4296483190185 38 30 31.2937865201702 -1.29378652017020 39 47 29.5110876909117 17.4889123090883 40 45 18.1766450606905 26.8233549393095 41 2 18.9048825867587 -16.9048825867587 42 2 24.9181328205113 -22.9181328205113 43 2 19.1906044400042 -17.1906044400042 44 1 37.6840864679064 -36.6840864679064 45 3 -0.223570318248028 3.22357031824803 46 3 9.5024284907722 -6.50242849077221 47 4 4.16794595078603 -0.167945950786026 48 2 -0.511799274591794 2.51179927459179 49 2 -0.521448090925276 2.52144809092528 50 3 2.16792560494278 0.832074395057219 51 2 3.70713316360349 -1.70713316360349 52 4 2.15850697601280 1.84149302398720 53 5 6.05428614410388 -1.05428614410388 54 3 6.21503031400314 -3.21503031400314 55 4 9.54429757278717 -5.54429757278717 56 5 5.77095462871925 -0.770954628719251 57 5 -0.785896685983955 5.78589668598396 58 3 4.29959378384177 -1.29959378384177 59 4 3.13593049768654 0.864069502313457 60 3 3.12137372320673 -0.121373723206727 61 3 0.500917600136695 2.49908239986331 62 2 12.1632459141473 -10.1632459141473 63 3 7.89457494853773 -4.89457494853773 64 4 9.13557323477626 -5.13557323477626 65 4 0.880229657432748 3.11977034256725 66 4 -0.9476343029045 4.9476343029045 67 4 0.269457174869784 3.73054282513022 68 3 -2.38523971678086 5.38523971678086 69 3 6.9815502387068 -3.9815502387068 70 3 -2.95010962472668 5.95010962472668 71 2 5.89541330468906 -3.89541330468906 72 3 9.77309412192136 -6.77309412192136 73 3 2.07810537580917 0.921894624190834 74 3 8.62138581381169 -5.62138581381169 75 3 9.33227299702776 -6.33227299702776 76 5 -1.48481512141642 6.48481512141642 77 3 7.83350388390858 -4.83350388390858 78 5 3.19982271161539 1.80017728838461 79 4 2.82621414865867 1.17378585134133 80 4 6.36723984140592 -2.36723984140592 81 4 11.2435435967556 -7.24354359675559 82 5 18.9690654674542 -13.9690654674542 83 4 3.69977597200601 0.300224027993989 84 5 -2.4769879234395 7.4769879234395 85 3 3.43715496523528 -0.437154965235284 86 3 2.48105249172795 0.518947508272047 87 2 10.8461592865560 -8.84615928655595 88 3 -0.321635183344728 3.32163518334473 89 4 2.17317122158446 1.82682877841554 90 5 5.80127206683214 -0.80127206683214 91 5 7.99524473553121 -2.99524473553121 92 3 1.19415090443123 1.80584909556877 93 2 -2.78038084987394 4.78038084987394 94 3 0.247148516330718 2.75285148366928 95 4 6.27951101731234 -2.27951101731234 96 1 4.32106370492077 -3.32106370492077 97 4 7.07579320239772 -3.07579320239772 98 3 -1.22048774933886 4.22048774933886 99 3 12.2988204037637 -9.29882040376366 100 4 3.62000768796811 0.379992312031893 101 3 11.4677747483351 -8.46777474833506 102 4 4.30720047447823 -0.307200474478235 103 2 1.67394426264011 0.326055737359886 104 3 2.44893374649922 0.551066253500782 105 3 10.2042912879814 -7.20429128798145 106 3 -2.53180049877974 5.53180049877974 107 2 5.35061140860113 -3.35061140860113 108 5 1.14405475671713 3.85594524328287 109 5 8.3953500290235 -3.3953500290235 110 4 1.77627988959725 2.22372011040275 111 2 0.0489377376672431 1.95106226233276 112 3 12.7805600875802 -9.78056008758025 113 3 7.48857211487927 -4.48857211487927 114 3 4.90734134975848 -1.90734134975848 115 4 -0.456724335381582 4.45672433538158 116 5 1.84995907805439 3.15004092194561 117 4 11.5594323098760 -7.55943230987598 118 22 29.551611857446 -7.55161185744601 119 16 28.2615312236473 -12.2615312236473 120 36 28.6132023396369 7.38679766036315 121 35 31.9075876829920 3.09241231700804 122 25 27.5066961363315 -2.50669613633152 123 27 39.0942890051891 -12.0942890051891 124 32 28.2949885400947 3.70501145990525 125 36 26.2862608296593 9.71373917034072 126 51 32.8087436433835 18.1912563566165 127 30 25.735214831222 4.26478516877802 128 20 21.3709353264023 -1.37093532640233 129 29 25.8555992301928 3.14440076980722 130 26 24.1924863798898 1.80751362011017 131 20 27.2188378727945 -7.21883787279453 132 40 27.8223085255813 12.1776914744186 133 29 26.1506329677175 2.84936703228246 134 32 26.6992248080078 5.30077519199224 135 33 26.2788768192729 6.72112318072706 136 32 25.9202819300446 6.0797180699554 137 34 27.9212225539345 6.07877744606548 138 24 26.3210953339826 -2.32109533398262 139 25 24.44292440097 0.557075599030015 140 41 29.6555524898745 11.3444475101255 141 39 28.8567484460228 10.1432515539772 142 21 26.2047227355897 -5.20472273558967 143 38 30.4855922676578 7.51440773234219 144 28 23.9145440312026 4.08545596879741 145 37 14.4763104591375 22.5236895408625 146 46 19.3203994946702 26.6796005053298 147 39 15.2110116887673 23.7889883112327 148 21 18.8906950186685 2.10930498133154 149 31 8.8456887139435 22.1543112860565 150 25 4.480600695914 20.519399304086 151 29 7.94045162057148 21.0595483794285 152 31 17.1295869175355 13.8704130824645 153 3 3.85379914569501 -0.85379914569501 154 4 2.67282590767451 1.32717409232549 155 1 12.2298547373185 -11.2298547373185 156 1 10.6062574488159 -9.60625744881589 157 5 5.70311267211918 -0.703112672119176 158 4 10.6618447404868 -6.66184474048679 159 3 4.45202919382421 -1.45202919382421 160 3 7.00162325190522 -4.00162325190522 161 4 6.75668428548451 -2.75668428548451 162 3 0.883263700711627 2.11673629928837 163 2 16.5453084168261 -14.5453084168261 164 1 3.07120620590152 -2.07120620590152 165 1 15.6932189535923 -14.6932189535923 166 5 0.476409652558602 4.5235903474414 167 4 9.7580431355438 -5.75804313554379 168 3 7.24370825253617 -4.24370825253617 169 4 10.5612782733924 -6.56127827339237 170 5 12.0484084041503 -7.04840840415034 171 4 -2.41370759299094 6.41370759299094 172 4 11.3819048939138 -7.3819048939138 173 2 4.37888313041509 -2.37888313041509 174 3 6.35948042983969 -3.35948042983969 175 4 -0.158697062072344 4.15869706207234 176 3 8.67903948550988 -5.67903948550988 177 4 3.7419430006266 0.258056999373399 178 3 2.85918306085988 0.140816939140122 179 4 6.17103718222979 -2.17103718222979 180 1 2.55596142580341 -1.55596142580341 181 2 -1.29533887232572 3.29533887232572 182 3 0.808583581904823 2.19141641809518 183 3 2.55271260837623 0.447287391623767 184 5 -1.33759722097115 6.33759722097115 185 4 -0.00264390432275619 4.00264390432276 186 3 8.29457560000116 -5.29457560000116 187 3 1.10428018650930 1.89571981349070 188 3 11.5015589065257 -8.50155890652568 189 3 9.18315417403906 -6.18315417403906 190 4 8.79003681502858 -4.79003681502858 191 3 7.90850989522285 -4.90850989522285 192 2 4.50592643797805 -2.50592643797805 193 4 1.84472463618703 2.15527536381297 194 2 10.1001855224273 -8.10018552242727 195 4 5.71980294341946 -1.71980294341946 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.000173300316017149 0.000346600632034297 0.999826699683983 11 1.09596655118670e-05 2.19193310237339e-05 0.999989040334488 12 4.4972658468272e-07 8.9945316936544e-07 0.999999550273415 13 9.23387117627485e-08 1.84677423525497e-07 0.999999907661288 14 5.26853697282594e-09 1.05370739456519e-08 0.999999994731463 15 1.94165482223767e-09 3.88330964447534e-09 0.999999998058345 16 1.32325023848456e-10 2.64650047696912e-10 0.999999999867675 17 1.23875477757535e-11 2.47750955515070e-11 0.999999999987612 18 1.29386150494948e-12 2.58772300989896e-12 0.999999999998706 19 1.78041354711013e-13 3.56082709422026e-13 0.999999999999822 20 1.13842776791048e-14 2.27685553582096e-14 0.999999999999989 21 6.53066267983013e-16 1.30613253596603e-15 1 22 7.41432159546549e-17 1.4828643190931e-16 1 23 4.27471698570774e-18 8.54943397141549e-18 1 24 2.35921643593315e-19 4.7184328718663e-19 1 25 1.26725445490410e-20 2.53450890980819e-20 1 26 5.16731020361028e-20 1.03346204072206e-19 1 27 1.11516895865872e-19 2.23033791731743e-19 1 28 8.35863912376145e-21 1.67172782475229e-20 1 29 1.47617221958398e-21 2.95234443916797e-21 1 30 3.95025166909836e-22 7.90050333819672e-22 1 31 0.0534289366527291 0.106857873305458 0.946571063347271 32 0.133643443578023 0.267286887156046 0.866356556421977 33 0.352909059516613 0.705818119033225 0.647090940483387 34 0.411961354782042 0.823922709564083 0.588038645217958 35 0.372919571652933 0.745839143305866 0.627080428347067 36 0.524796892734676 0.950406214530649 0.475203107265324 37 0.524942121997852 0.950115756004296 0.475057878002148 38 0.6353882830628 0.729223433874401 0.364611716937201 39 0.75936492622368 0.48127014755264 0.24063507377632 40 0.916498725001147 0.167002549997706 0.0835012749988528 41 0.976301705185563 0.0473965896288748 0.0236982948144374 42 0.98783566572488 0.0243286685502415 0.0121643342751208 43 0.993206907047358 0.0135861859052839 0.00679309295264195 44 0.999184307988688 0.00163138402262499 0.000815692011312493 45 0.998902088388313 0.00219582322337428 0.00109791161168714 46 0.999749168918518 0.000501662162964396 0.000250831081482198 47 0.99972254512714 0.000554909745719982 0.000277454872859991 48 0.999609269710112 0.000781460579776555 0.000390730289888278 49 0.99953736323249 0.000925273535020574 0.000462636767510287 50 0.999345165022678 0.00130966995464441 0.000654834977322207 51 0.999030404053492 0.00193919189301654 0.000969595946508271 52 0.998772450559388 0.00245509888122302 0.00122754944061151 53 0.998267383715214 0.00346523256957302 0.00173261628478651 54 0.998301802126105 0.00339639574779006 0.00169819787389503 55 0.99787251670059 0.00425496659882189 0.00212748329941094 56 0.99719697812355 0.00560604375290082 0.00280302187645041 57 0.996756654066645 0.00648669186670973 0.00324334593335487 58 0.995540724679569 0.00891855064086213 0.00445927532043107 59 0.994130886938023 0.0117382261239535 0.00586911306197673 60 0.992193372627715 0.0156132547445697 0.00780662737228484 61 0.991913936386719 0.0161721272265619 0.00808606361328093 62 0.992835397787447 0.0143292044251067 0.00716460221255335 63 0.993412220651931 0.0131755586961380 0.00658777934806898 64 0.993025378586823 0.0139492428263531 0.00697462141317653 65 0.99108701097434 0.0178259780513185 0.00891298902565924 66 0.988770051518383 0.0224598969632345 0.0112299484816173 67 0.98653272332379 0.0269345533524188 0.0134672766762094 68 0.984920026538901 0.0301599469221981 0.0150799734610990 69 0.98056815080556 0.0388636983888805 0.0194318491944402 70 0.98036920514492 0.0392615897101622 0.0196307948550811 71 0.974839474247187 0.0503210515056254 0.0251605257528127 72 0.969110355146627 0.0617792897067458 0.0308896448533729 73 0.96264233092055 0.074715338158898 0.037357669079449 74 0.957052628909065 0.0858947421818701 0.0429473710909351 75 0.950503007470658 0.098993985058684 0.049496992529342 76 0.944219180026694 0.111561639946612 0.0557808199733058 77 0.93938082141769 0.121238357164618 0.0606191785823088 78 0.928680093293422 0.142639813413156 0.071319906706578 79 0.916074393750457 0.167851212499086 0.083925606249543 80 0.91386206487362 0.172275870252758 0.086137935126379 81 0.9149222340632 0.170155531873599 0.0850777659367993 82 0.92545141526038 0.14909716947924 0.07454858473962 83 0.9109431282721 0.1781137434558 0.0890568717279 84 0.903739357506467 0.192521284987067 0.0962606424935336 85 0.8898319111635 0.220336177673000 0.110168088836500 86 0.873874167556535 0.252251664886929 0.126125832443465 87 0.876263324183363 0.247473351633274 0.123736675816637 88 0.859460293621132 0.281079412757737 0.140539706378868 89 0.840511097613778 0.318977804772444 0.159488902386222 90 0.830379029500756 0.339241940998488 0.169620970499244 91 0.821901641975654 0.356196716048691 0.178098358024346 92 0.7947044007334 0.410591198533201 0.205295599266601 93 0.777852579871605 0.444294840256790 0.222147420128395 94 0.751450873340461 0.497098253319079 0.248549126659539 95 0.753101106961662 0.493797786076676 0.246898893038338 96 0.722326587161721 0.555346825676557 0.277673412838279 97 0.705685081612402 0.588629836775197 0.294314918387598 98 0.688225706948976 0.623548586102048 0.311774293051024 99 0.715595548697011 0.568808902605978 0.284404451302989 100 0.689922087268952 0.620155825462097 0.310077912731049 101 0.69497132170039 0.610057356599219 0.305028678299610 102 0.657600983078823 0.684798033842354 0.342399016921177 103 0.620588026175963 0.758823947648074 0.379411973824037 104 0.583779214858291 0.832441570283417 0.416220785141709 105 0.611766254393733 0.776467491212535 0.388233745606267 106 0.587299113499716 0.825401773000569 0.412700886500284 107 0.54904691544456 0.90190616911088 0.45095308455544 108 0.527453893282744 0.945092213434512 0.472546106717256 109 0.511622461343456 0.976755077313088 0.488377538656544 110 0.47422787078563 0.94845574157126 0.52577212921437 111 0.451519676395938 0.903039352791875 0.548480323604062 112 0.543842175710127 0.912315648579745 0.456157824289873 113 0.504842847461544 0.990314305076913 0.495157152538456 114 0.473412641448082 0.946825282896164 0.526587358551918 115 0.432069157796274 0.864138315592548 0.567930842203726 116 0.390345526688167 0.780691053376334 0.609654473311833 117 0.516289602089651 0.967420795820697 0.483710397910349 118 0.520642339531870 0.958715320936259 0.479357660468129 119 0.568743276085664 0.862513447828672 0.431256723914336 120 0.615328071844422 0.769343856311156 0.384671928155578 121 0.652650489645383 0.694699020709234 0.347349510354617 122 0.631643157429954 0.736713685140092 0.368356842570046 123 0.613763812302218 0.772472375395563 0.386236187697782 124 0.590569422698619 0.818861154602762 0.409430577301381 125 0.589756896976108 0.820486206047785 0.410243103023892 126 0.84015919623486 0.319681607530280 0.159840803765140 127 0.815930993162076 0.368138013675849 0.184069006837924 128 0.829992209716144 0.340015580567711 0.170007790283856 129 0.800975707526272 0.398048584947456 0.199024292473728 130 0.805811194181879 0.388377611636242 0.194188805818121 131 0.842633509561012 0.314732980877976 0.157366490438988 132 0.86791944359347 0.264161112813059 0.132080556406529 133 0.841548519134557 0.316902961730886 0.158451480865443 134 0.812315439523683 0.375369120952634 0.187684560476317 135 0.84276556934146 0.314468861317080 0.157234430658540 136 0.838116522146566 0.323766955706868 0.161883477853434 137 0.823241926028893 0.353516147942214 0.176758073971107 138 0.809258700459195 0.381482599081609 0.190741299540805 139 0.837561487562319 0.324877024875362 0.162438512437681 140 0.888128901029746 0.223742197940508 0.111871098970254 141 0.906508421702725 0.186983156594551 0.0934915782972754 142 0.912967351924274 0.174065296151452 0.0870326480757262 143 0.962420768276333 0.0751584634473333 0.0375792317236666 144 0.957835800505234 0.084328398989532 0.042164199494766 145 0.996081812021198 0.007836375957603 0.0039181879788015 146 0.999680268959467 0.000639462081065248 0.000319731040532624 147 0.99998938485569 2.12302886198245e-05 1.06151443099122e-05 148 0.999997049938924 5.9001221519506e-06 2.9500610759753e-06 149 0.999999995716392 8.56721525843379e-09 4.28360762921689e-09 150 0.999999996305827 7.38834608377859e-09 3.69417304188929e-09 151 0.99999999501365 9.97269972848212e-09 4.98634986424106e-09 152 1 1.97211809558101e-28 9.86059047790503e-29 153 1 1.79342634232052e-27 8.96713171160262e-28 154 1 1.63849121687569e-26 8.19245608437843e-27 155 1 6.31488591141798e-26 3.15744295570899e-26 156 1 5.65211273469902e-26 2.82605636734951e-26 157 1 1.75488531999251e-25 8.77442659996257e-26 158 1 1.42145609548231e-24 7.10728047741154e-25 159 1 1.34856560813031e-23 6.74282804065154e-24 160 1 1.28973693201584e-22 6.44868466007922e-23 161 1 1.19822851170118e-21 5.99114255850592e-22 162 1 1.08336948582014e-20 5.41684742910069e-21 163 1 7.72228051228693e-20 3.86114025614347e-20 164 1 3.00243264016310e-19 1.50121632008155e-19 165 1 1.48322475497325e-19 7.41612377486624e-20 166 1 7.83125610163132e-19 3.91562805081566e-19 167 1 7.49157140913349e-18 3.74578570456674e-18 168 1 7.35901551977213e-17 3.67950775988606e-17 169 1 7.21733212541535e-16 3.60866606270767e-16 170 0.999999999999998 4.34233208701896e-15 2.17116604350948e-15 171 0.999999999999985 3.06461143034374e-14 1.53230571517187e-14 172 0.999999999999942 1.16353383088316e-13 5.81766915441578e-14 173 0.999999999999782 4.36928453228393e-13 2.18464226614196e-13 174 0.999999999997889 4.2218706624973e-12 2.11093533124865e-12 175 0.999999999985792 2.84151886905057e-11 1.42075943452529e-11 176 0.9999999998756 2.48799165963366e-10 1.24399582981683e-10 177 0.999999999221516 1.55696890534207e-09 7.78484452671035e-10 178 0.99999999352842 1.29431613466353e-08 6.47158067331767e-09 179 0.999999974981018 5.00379630783757e-08 2.50189815391879e-08 180 0.999999935984714 1.28030571956975e-07 6.40152859784877e-08 181 0.999999543192126 9.13615748349212e-07 4.56807874174606e-07 182 0.999998879256905 2.24148618897964e-06 1.12074309448982e-06 183 0.99999027810708 1.94437858419535e-05 9.72189292097676e-06 184 0.999903575242423 0.000192849515154594 9.6424757577297e-05 185 0.998802497832625 0.00239500433474925 0.00119750216737462 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 77 0.4375 NOK 5% type I error level 92 0.522727272727273 NOK 10% type I error level 99 0.5625 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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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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