*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, 12 Dec 2010 12:53:05 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa.htm/, Retrieved Sun, 12 Dec 2010 13:51:11 +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/12/t1292158268w6jav2wn2yvf8pa.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 «

24 14 11 24 5 3 25 11 7 25 4 2 17 6 17 30 4 4 18 12 10 19 4 2 18 8 12 22 2 4 16 10 12 22 5 2 20 10 11 25 5 3 16 11 11 23 4 4 18 16 12 17 3 1 17 11 13 21 4 2 23 13 14 19 4 2 30 12 16 19 NA 2 23 8 11 15 3 2 18 12 10 16 3 1 15 11 11 23 4 2 12 4 15 27 5 4 21 9 9 22 4 2 15 8 11 14 2 2 20 8 17 22 4 3 31 14 17 23 4 2 27 15 11 23 4 3 34 16 18 21 4 2 21 9 14 19 4 3 31 14 10 18 4 2 19 11 11 20 5 3 16 8 15 23 4 3 20 9 15 25 4 4 21 9 13 19 4 2 22 9 16 24 4 4 17 9 13 22 4 3 24 10 9 25 4 4 25 16 18 26 4 3 26 11 18 29 2 4 25 8 12 32 4 4 17 9 17 25 4 3 32 16 9 29 5 5 33 11 9 28 5 4 13 16 12 17 4 2 32 12 18 28 3 4 25 12 12 29 4 4 29 14 18 26 5 5 22 9 14 25 4 4 18 10 15 14 4 2 17 9 16 25 5 4 20 10 10 26 4 4 15 12 11 20 5 1 20 14 14 18 4 2 33 14 9 32 4 5 29 10 12 25 4 4 23 14 17 25 3 2 26 16 5 23 4 3 18 9 12 21 4 4 20 10 12 20 4 2 11 6 6 15 2 1 28 8 24 30 3 4 26 13 12 24 5 2 22 10 12 26 4 4 17 8 14 24 4 2 12 7 7 22 5 3 14 15 13 14 3 2 17 9 12 24 5 3 21 10 13 24 4 2 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 7 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation PS[t] = + 9.56730396906726 + 0.137042226462313CM[t] -0.132584963543833D[t] + 0.0273702108583212PE[t] + 0.93014119644806Organization[t] + 2.54347193311708Goals[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) 9.56730396906726 1.534874 6.2333 0 0 CM 0.137042226462313 0.048349 2.8344 0.005215 0.002608 D -0.132584963543833 0.086392 -1.5347 0.126939 0.06347 PE 0.0273702108583212 0.066747 0.4101 0.68234 0.34117 Organization 0.93014119644806 0.25964 3.5824 0.000458 0.000229 Goals 2.54347193311708 0.241493 10.5323 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.783062592768742 R-squared 0.613187024193705 Adjusted R-squared 0.600462913147445 F-TEST (value) 48.190951962334 F-TEST (DF numerator) 5 F-TEST (DF denominator) 152 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.66923088196573 Sum Squared Residuals 1082.96861218841 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.5823220155822 0.417677984417778 2 25 20.5340251596776 4.46597484032243 3 30 25.4612581405156 4.53874185948438 4 19 19.5242552434725 -0.524255243472516 5 22 23.3359969927025 -1.33599699270254 6 22 20.5002223358003 1.49977766419974 7 25 23.5644929639083 1.43550703609173 8 23 24.4970698311842 -1.49706983118421 9 17 15.5750426814487 1.42495731855131 10 21 19.601908613129 1.398091386871 11 19 20.1863622556735 -1.18636225567353 12 19 23.8370352443697 -4.83703524436967 13 15 15.0506421139074 -0.0506421139073731 14 16 12.2730837384877 3.72691626151227 15 23 21.9166177100231 1.08338228997686 16 27 25.3057666026326 1.69423339736737 17 22 25.8105562362231 -3.81055623622311 18 14 15.0637429596978 -1.0637429596978 19 22 20.2322257364032 1.76777426359684 20 23 22.9307225349772 0.069277465022762 21 23 23.4055526995608 -0.405552699560756 22 21 24.9860895900413 -3.98608959004132 23 19 22.0406342603949 -3.04063426039491 24 18 21.2948657739021 -3.29486577390213 25 20 19.4608336321319 0.539166367868087 26 23 23.4198895075544 -0.419889507554415 27 25 26.4152474460659 -1.41524744606592 28 19 20.7213441713374 -1.72134417133736 29 24 24.4105504733337 -0.41055047333375 30 22 22.6712521847099 -0.671252184709905 31 25 21.715644594517 3.28435540548297 32 26 21.1988011789195 4.80119882108053 33 29 23.1555749708348 5.84442502916515 34 32 29.520031316767 2.47996868323297 35 25 25.4456933447106 -0.445693344710555 36 29 28.7021884557749 0.297811544225055 37 28 29.3634446787023 -1.36344467870227 38 17 14.8186107705976 2.18138922940243 39 28 24.6252351166595 3.37476488334048 40 29 32.5460684901362 -3.54606849013617 41 26 26.6666037496207 -0.666603749620719 42 25 30.9262762248518 -5.92627622485179 43 14 14.9662742354739 -0.966274235473857 44 25 24.150453489719 0.849546510281025 45 26 23.5271680382749 2.47283196172513 46 20 21.6426506127428 -1.64265061274276 47 18 14.9177643018125 3.08223569818753 48 32 33.4385739495964 -1.43857394959643 49 25 19.2057467282566 5.7942532717434 50 25 24.4968740798212 0.503125920178834 51 23 27.0636944220548 -4.06369442205483 52 21 21.1182500452014 -0.118250045201449 53 20 19.8472342700528 0.152765729947164 54 15 10.9650029840736 4.03499701592642 55 30 27.4728897097919 2.52711029020812 56 24 23.4792783643602 0.520721635639757 57 26 22.0270337146188 3.97296628538118 58 24 24.756429199408 -0.756429199407985 59 22 25.7303008831187 -3.73030088311867 60 14 13.3133214589235 0.686678541076512 61 24 20.2826624825221 3.71733751747792 62 24 20.7009195098162 3.29908049018383 63 24 21.8804017913291 2.11959820867087 64 24 21.1769856366029 2.82301436339708 65 19 17.6974914830428 1.30250851695722 66 31 35.9504581187504 -4.9504581187504 67 22 20.2281068593755 1.77189314062454 68 27 24.5449595050988 2.45504049490115 69 19 13.9582948707993 5.0417051292007 70 25 25.5496165875396 -0.549616587539556 71 20 19.031682149708 0.968317850291995 72 21 21.7204529686256 -0.7204529686256 73 27 25.7830677272411 1.21693227275892 74 23 22.6288121296593 0.371187870340736 75 25 25.5293767245884 -0.529376724588386 76 20 17.6559848166483 2.34401518335175 77 21 19.9750039627408 1.0249960372592 78 22 24.6783825326171 -2.67838253261706 79 23 21.6528450373315 1.34715496266848 80 25 23.5000202108365 1.49997978916348 81 25 27.4169940391458 -2.41699403914577 82 17 18.0174925554344 -1.01749255543442 83 19 17.0363727488395 1.96362725116052 84 25 25.8895560269798 -0.889556026979772 85 19 19.2321881515532 -0.232188151553213 86 20 16.7713939939225 3.22860600607748 87 26 27.8376734888218 -1.83767348882182 88 23 22.1458426394797 0.854157360520261 89 27 29.9812078187391 -2.98120781873914 90 17 20.4649039715166 -3.46490397151663 91 17 18.2314129513123 -1.23141295131226 92 19 20.4252443467853 -1.42524434678534 93 17 17.0877758673701 -0.0877758673700634 94 22 22.0165637678727 -0.0165637678727072 95 21 19.4326034298111 1.56739657018891 96 32 31.8849451767405 0.115054823259466 97 21 26.2050403241149 -5.20504032411486 98 21 25.6572647154001 -4.65726471540005 99 18 22.9631766421015 -4.96317664210148 100 18 18.1549592902804 -0.154959290280435 101 23 23.8307938035214 -0.830793803521384 102 19 21.9858984178706 -2.98589841787061 103 20 19.1914461519395 0.808553848060547 104 21 21.9018078560028 -0.901807856002795 105 20 18.8419967864662 1.15800321353384 106 17 19.4657217770348 -2.46572177703478 107 18 17.9660917325567 0.0339082674432657 108 19 19.8987038890297 -0.89870388902973 109 22 27.1069247080872 -5.10692470808724 110 15 19.4939831906049 -4.49398319060487 111 14 17.5892386274209 -3.5892386274209 112 18 13.5082103697284 4.4917896302716 113 24 17.9958531326457 6.00414686735431 114 35 30.1185884310922 4.88141156890777 115 29 30.4060932104153 -1.40609321041527 116 21 19.8750602005441 1.12493979945588 117 25 21.7020041803515 3.29799581964846 118 20 18.3552319559126 1.64476804408736 119 22 25.4025711086592 -3.40257110865919 120 13 13.169137931761 -0.169137931760993 121 26 27.2332705264357 -1.23327052643568 122 17 16.0735377354535 0.926462264546504 123 25 22.9206568381586 2.0793431618414 124 20 19.5458773398675 0.454122660132474 125 19 19.7358468726182 -0.735846872618248 126 21 18.6434684182609 2.35653158173909 127 22 20.5017668039164 1.49823319608362 128 24 22.8989060139935 1.10109398600653 129 21 21.429032790412 -0.429032790412031 130 26 23.9004504821096 2.09954951789041 131 24 27.702666102896 -3.70266610289603 132 16 17.8992819847342 -1.89928198473419 133 23 27.296612366982 -4.29661236698198 134 18 22.2552922716638 -4.25529227166376 135 16 15.8486540664446 0.151345933555434 136 26 22.9727975720802 3.02720242791982 137 19 17.6063658760475 1.39363412395252 138 21 17.4288213597851 3.57117864021491 139 21 17.1342972145985 3.86570278540154 140 22 20.5594113632952 1.44058863670475 141 23 20.392556881546 2.60744311845396 142 29 31.6911831005133 -2.69118310051328 143 21 24.5424602658872 -3.54246026588716 144 21 19.6077191719929 1.3922808280071 145 23 21.6156939574751 1.38430604252489 146 27 28.0519532239084 -1.05195322390844 147 25 24.9066543381079 0.0933456618920731 148 21 26.2989117768828 -5.29891177688283 149 10 10.7122448469304 -0.712244846930381 150 20 18.6454373947607 1.35456260523926 151 26 25.0720308521873 0.927969147812676 152 24 25.3291728550554 -1.32917285505539 153 29 31.2628494236075 -2.26284942360752 154 19 21.2217118312064 -2.22171183120641 155 24 24.8670785402167 -0.867078540216665 156 19 20.7438216581005 -1.74382165810047 157 24 24.6201621731866 -0.620162173186625 158 22 27.6351269677012 -5.63512696770117 159 17 NA NA Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.257266786736688 0.514533573473376 0.742733213263312 10 0.140509943586665 0.281019887173329 0.859490056413335 11 0.351478396431982 0.702956792863964 0.648521603568018 12 0.802039645202383 0.395920709595235 0.197960354797617 13 0.715370321936827 0.569259356126347 0.284629678063173 14 0.69000261323477 0.619994773530459 0.30999738676523 15 0.63037266575519 0.73925466848962 0.36962733424481 16 0.549054059257429 0.901891881485143 0.450945940742571 17 0.544940857624598 0.910118284750804 0.455059142375402 18 0.473953909664688 0.947907819329377 0.526046090335312 19 0.420258877103396 0.840517754206792 0.579741122896604 20 0.342873709335568 0.685747418671137 0.657126290664432 21 0.276729989376957 0.553459978753913 0.723270010623043 22 0.390109622293539 0.780219244587078 0.609890377706461 23 0.397757258824783 0.795514517649566 0.602242741175217 24 0.528698902988643 0.942602194022715 0.471301097011357 25 0.457946704560399 0.915893409120799 0.542053295439601 26 0.38902535575288 0.778050711505761 0.61097464424712 27 0.343020363712708 0.686040727425416 0.656979636287292 28 0.294047683271015 0.58809536654203 0.705952316728985 29 0.240402125835273 0.480804251670546 0.759597874164727 30 0.194514267537045 0.389028535074091 0.805485732462955 31 0.200087916054444 0.400175832108888 0.799912083945556 32 0.383838926778712 0.767677853557425 0.616161073221288 33 0.630033226359596 0.739933547280808 0.369966773640404 34 0.59984140384349 0.80031719231302 0.40015859615651 35 0.552895631282165 0.89420873743567 0.447104368717835 36 0.495996653481539 0.991993306963078 0.504003346518461 37 0.460343425210802 0.920686850421604 0.539656574789198 38 0.418092279728321 0.836184559456642 0.581907720271679 39 0.430290652780377 0.860581305560754 0.569709347219623 40 0.549456280867923 0.901087438264153 0.450543719132077 41 0.502244602275149 0.995510795449702 0.497755397724851 42 0.699388891846684 0.601222216306632 0.300611108153316 43 0.659150599854239 0.681698800291522 0.340849400145761 44 0.61261657866631 0.774766842667381 0.38738342133369 45 0.614360640718943 0.771278718562114 0.385639359281057 46 0.581712359331663 0.836575281336673 0.418287640668337 47 0.579888938573267 0.840222122853465 0.420111061426733 48 0.549916381788182 0.900167236423635 0.450083618211818 49 0.699927355996021 0.600145288007958 0.300072644003979 50 0.655451334791276 0.689097330417449 0.344548665208724 51 0.710642646097036 0.578714707805928 0.289357353902964 52 0.666038130118869 0.667923739762263 0.333961869881131 53 0.62134864200092 0.75730271599816 0.37865135799908 54 0.647351119487362 0.705297761025275 0.352648880512638 55 0.639162231153473 0.721675537693054 0.360837768846527 56 0.593301590733549 0.813396818532902 0.406698409266451 57 0.643216060954489 0.713567878091023 0.356783939045511 58 0.599738579870529 0.800522840258942 0.400261420129471 59 0.636369378904517 0.727261242190966 0.363630621095483 60 0.593141079393605 0.81371784121279 0.406858920606395 61 0.624782492761479 0.750435014477043 0.375217507238521 62 0.642153456830941 0.715693086338118 0.357846543169059 63 0.633267375605332 0.733465248789335 0.366732624394668 64 0.639289059829317 0.721421880341366 0.360710940170683 65 0.603829916389799 0.792340167220403 0.396170083610201 66 0.721366482421632 0.557267035156736 0.278633517578368 67 0.697736595572646 0.604526808854708 0.302263404427354 68 0.693409802029825 0.61318039594035 0.306590197970175 69 0.7869095132308 0.426180973538401 0.213090486769201 70 0.754329988627615 0.49134002274477 0.245670011372385 71 0.721079458132792 0.557841083734417 0.278920541867208 72 0.686423791946748 0.627152416106504 0.313576208053252 73 0.662650841926502 0.674698316146996 0.337349158073498 74 0.622815318603046 0.754369362793908 0.377184681396954 75 0.581222342038926 0.837555315922148 0.418777657961074 76 0.5805560352585 0.838887929483 0.4194439647415 77 0.552353456381906 0.895293087236187 0.447646543618094 78 0.55080410858602 0.89839178282796 0.44919589141398 79 0.515722357473093 0.968555285053814 0.484277642526907 80 0.49313437979647 0.98626875959294 0.50686562020353 81 0.488263343754896 0.976526687509793 0.511736656245104 82 0.451492400247172 0.902984800494344 0.548507599752828 83 0.435106682462737 0.870213364925474 0.564893317537263 84 0.393655250768624 0.787310501537248 0.606344749231376 85 0.357910304302251 0.715820608604501 0.642089695697749 86 0.383084737360308 0.766169474720616 0.616915262639692 87 0.354966254595792 0.709932509191583 0.645033745404208 88 0.318646499465067 0.637292998930134 0.681353500534933 89 0.324783834852699 0.649567669705398 0.675216165147301 90 0.349579019218022 0.699158038436043 0.650420980781978 91 0.311797471076438 0.623594942152876 0.688202528923562 92 0.281313689032769 0.562627378065537 0.718686310967231 93 0.24323645237137 0.486472904742739 0.75676354762863 94 0.209638953893932 0.419277907787863 0.790361046106068 95 0.199793845807043 0.399587691614086 0.800206154192957 96 0.173700290973347 0.347400581946694 0.826299709026653 97 0.259765925394397 0.519531850788795 0.740234074605603 98 0.336854179198392 0.673708358396784 0.663145820801608 99 0.439489325106515 0.87897865021303 0.560510674893485 100 0.393037116086645 0.78607423217329 0.606962883913355 101 0.349509572899813 0.699019145799626 0.650490427100187 102 0.347933193637521 0.695866387275043 0.652066806362479 103 0.313618330954673 0.627236661909346 0.686381669045327 104 0.274576028315041 0.549152056630081 0.72542397168496 105 0.245456110201953 0.490912220403906 0.754543889798047 106 0.235442917623559 0.470885835247118 0.76455708237644 107 0.198581126814363 0.397162253628725 0.801418873185637 108 0.167826159106107 0.335652318212215 0.832173840893893 109 0.234518400922786 0.469036801845571 0.765481599077214 110 0.311952078002179 0.623904156004357 0.688047921997821 111 0.332608006742247 0.665216013484494 0.667391993257753 112 0.402407033349336 0.804814066698672 0.597592966650664 113 0.615512087933351 0.768975824133299 0.384487912066649 114 0.7286646089335 0.542670782133001 0.271335391066501 115 0.688192549253661 0.623614901492679 0.311807450746339 116 0.66565534170841 0.66868931658318 0.33434465829159 117 0.693575009367302 0.612849981265396 0.306424990632698 118 0.659106283047756 0.681787433904489 0.340893716952244 119 0.718309833669582 0.563380332660836 0.281690166330418 120 0.66895798340588 0.662084033188241 0.33104201659412 121 0.622615256040371 0.754769487919257 0.377384743959629 122 0.591885543396111 0.816228913207778 0.408114456603889 123 0.552517143978612 0.894965712042775 0.447482856021388 124 0.493624181032176 0.987248362064353 0.506375818967824 125 0.436458186010149 0.872916372020298 0.563541813989851 126 0.434615506270784 0.869231012541568 0.565384493729216 127 0.407273071291543 0.814546142583085 0.592726928708457 128 0.369563949593786 0.739127899187572 0.630436050406214 129 0.314614927221758 0.629229854443517 0.685385072778242 130 0.311278176332614 0.622556352665229 0.688721823667386 131 0.32447536681193 0.64895073362386 0.67552463318807 132 0.272063240823279 0.544126481646558 0.727936759176721 133 0.323717757216435 0.64743551443287 0.676282242783565 134 0.455748079514834 0.911496159029669 0.544251920485166 135 0.40603730863505 0.8120746172701 0.59396269136495 136 0.402438881501297 0.804877763002593 0.597561118498703 137 0.353344261991411 0.706688523982822 0.646655738008589 138 0.416265763762443 0.832531527524886 0.583734236237557 139 0.633098965000126 0.733802069999748 0.366901034999874 140 0.624698203331407 0.750603593337186 0.375301796668593 141 0.660069881459465 0.67986023708107 0.339930118540535 142 0.580650706331305 0.83869858733739 0.419349293668695 143 0.76294675141347 0.474106497173061 0.23705324858653 144 0.88211235880454 0.235775282390919 0.11788764119546 145 0.817838571683145 0.364322856633709 0.182161428316855 146 0.724453248053103 0.551093503893794 0.275546751946897 147 0.668327747006115 0.66334450598777 0.331672252993885 148 0.631574942547554 0.736850114904892 0.368425057452446 149 0.469541957141955 0.93908391428391 0.530458042858045 150 0.343330148750339 0.686660297500678 0.65666985124966 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 0 0 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/10bp2g1292158374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/10bp2g1292158374.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/14n541292158374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/14n541292158374.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/24n541292158374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/24n541292158374.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/3fxmp1292158374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/3fxmp1292158374.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/4fxmp1292158374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/4fxmp1292158374.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/5fxmp1292158374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/5fxmp1292158374.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/6pola1292158374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/6pola1292158374.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/70f3v1292158374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/70f3v1292158374.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/80f3v1292158374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/80f3v1292158374.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/90f3v1292158374.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292158268w6jav2wn2yvf8pa/90f3v1292158374.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• 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.

FreeStatistics.org is powered by