WS 10 - 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, 10 Dec 2010 20:15:37 +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/10/t1292012078ujcdbvbase33sf3.htm/, Retrieved Fri, 10 Dec 2010 21:14:48 +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/10/t1292012078ujcdbvbase33sf3.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 «

2 24 14 11 12 24 26 2 25 11 7 8 25 23 2 17 6 17 8 30 25 1 18 12 10 8 19 23 2 18 8 12 9 22 19 2 16 10 12 7 22 29 2 20 10 11 4 25 25 2 16 11 11 11 23 21 2 18 16 12 7 17 22 2 17 11 13 7 21 25 1 23 13 14 12 19 24 2 30 12 16 10 19 18 1 23 8 11 10 15 22 2 18 12 10 8 16 15 2 15 11 11 8 23 22 1 12 4 15 4 27 28 1 21 9 9 9 22 20 2 15 8 11 8 14 12 1 20 8 17 7 22 24 2 31 14 17 11 23 20 1 27 15 11 9 23 21 2 34 16 18 11 21 20 2 21 9 14 13 19 21 2 31 14 10 8 18 23 1 19 11 11 8 20 28 2 16 8 15 9 23 24 1 20 9 15 6 25 24 2 21 9 13 9 19 24 2 22 9 16 9 24 23 1 17 9 13 6 22 23 2 24 10 9 6 25 29 1 25 16 18 16 26 24 2 26 11 18 5 29 18 2 25 8 12 7 32 25 1 17 9 17 9 25 21 1 32 16 9 6 29 26 1 33 11 9 6 28 22 1 13 16 12 5 17 22 2 32 12 18 12 28 22 1 25 12 12 7 29 23 1 29 14 18 10 26 30 2 22 9 14 9 25 23 1 18 10 15 8 14 17 1 17 9 16 5 25 23 2 20 10 10 8 26 23 2 15 12 11 8 20 25 2 20 14 14 10 18 24 2 33 14 9 6 32 24 2 29 10 12 8 25 23 1 23 14 17 7 25 21 2 26 16 5 4 23 24 1 18 9 12 8 21 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation PE[t] = + 7.07697462326621 -0.630456701488424gendeR[t] + 0.0888573959968063COM[t] -0.109453550630909DA[t] + 0.665543146599335PC[t] + 0.114839167100403PS[t] -0.0871517232603647`O `[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) 7.07697462326621 1.876844 3.7707 0.000233 0.000116 gendeR -0.630456701488424 0.44232 -1.4253 0.156109 0.078054 COM 0.0888573959968063 0.047968 1.8524 0.065905 0.032953 DA -0.109453550630909 0.087608 -1.2494 0.213454 0.106727 PC 0.665543146599335 0.086015 7.7375 0 0 PS 0.114839167100403 0.063017 1.8223 0.070369 0.035184 `O ` -0.0871517232603647 0.061658 -1.4135 0.159563 0.079781 Multiple Linear Regression - Regression Statistics Multiple R 0.644361482982939 R-squared 0.415201720751972 Adjusted R-squared 0.392117578150076 F-TEST (value) 17.9864475762627 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 1.11022302462516e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.68633275396784 Sum Squared Residuals 1096.89031708615 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 14.8930019802121 -3.89300198021215 2 7 13.0243417785859 -6.0243417785859 3 17 13.2606427527473 3.73935724725274 4 10 12.2343081548633 -2.23430815486332 5 12 13.4003331968406 -1.40033319684055 6 12 10.8011077777828 1.1988922222172 7 11 9.8530323163147 1.14696768368531 8 11 14.1658797667326 -3.16587976673255 9 12 10.3579674933115 1.64203250668851 10 13 11.0142793490898 1.98572065091025 11 14 15.1441624473534 -1.14416244735343 12 16 14.4369851148371 1.56301488516292 13 11 14.0752906854284 -3.07529068542842 14 10 11.9565477381566 -1.95654773815662 15 11 11.9932412076774 -0.993241207677377 16 15 10.3975743180338 4.60242568196617 17 9 14.1007568124281 -5.10075681242811 18 11 12.1595665882701 -1.15956658827012 19 17 12.4416597808221 4.55834021917791 20 17 15.2575317780523 1.74246822194772 21 11 14.0048673284635 -3.00486732846353 22 18 15.0755185305801 2.92448146941993 23 14 15.7008034727755 -1.70080347277546 24 10 12.4252513329712 -2.42525133297117 25 11 12.1116996522896 -1.11169965228962 26 15 12.9016989556455 2.09830104435448 27 15 12.0111805848931 2.98881941510695 28 13 12.7771757165970 0.222824283402974 29 16 13.5273806713562 2.47261932864379 30 13 11.4872426188618 1.51275738113821 31 9 11.1909413004591 -2.19094130045913 32 18 18.4595633435545 -0.459563343554469 33 18 12.0116850194881 5.98831498051188 34 12 13.3167300070614 -1.31673000706137 35 17 14.0026930064817 2.99730699351827 36 9 12.5963477043192 -3.59634770431925 37 9 13.4662405794117 -4.46624057941166 38 12 9.21305092161721 2.78694907838279 39 18 16.6307318108915 1.36926818910847 40 12 13.3391584512457 -1.33915845124567 41 18 14.5177308096453 3.48226919035468 42 14 13.6422198384566 0.357780161543384 43 15 12.4019297601853 2.59807023981468 44 16 11.1662169735637 4.83378302643633 45 10 12.8043475163332 -2.80434751633316 46 11 11.2778149859642 -0.277814985964163 47 14 12.6917545469446 1.30824545305540 48 9 12.7924764479114 -3.79247644791139 49 12 13.4892249132040 -1.48922491320402 50 17 12.6574833361094 4.34251666389064 51 5 9.58692877756963 -4.58692877756963 52 12 12.7051954176965 -0.705195417696499 53 12 12.3100105989173 -0.310010598917340 54 6 9.12710379320632 -3.12710379320632 55 24 23.0719000844326 0.928099915567425 56 12 12.2565425666583 -0.256542566658277 57 12 12.6334554152853 -0.633455415285316 58 14 11.2830695254655 2.71693047453455 59 7 9.49501783063909 -2.49501783063909 60 13 10.9559274448155 2.04407255518451 61 12 13.5392469463399 -1.53924694633987 62 13 11.8757452631585 1.12425473684145 63 14 11.1656029219726 2.83439707802743 64 8 12.6469851615850 -4.64698516158498 65 11 9.11526994686427 1.88473005313573 66 9 12.0925715640434 -3.09257156404339 67 11 13.4541775818979 -2.45417758189787 68 13 13.7445429860768 -0.744542986076818 69 10 9.18929159905334 0.810708400946656 70 11 13.0362080535695 -2.03620805356954 71 12 13.0971440611165 -1.09714406111646 72 9 11.5852046888659 -2.58520468886591 73 15 14.3213021708508 0.678697829149221 74 18 15.3393649671351 2.66063503286491 75 15 12.4571732376135 2.54282676238647 76 12 12.5561881482419 -0.556188148241892 77 13 9.66494596661046 3.33505403338954 78 14 12.7933325660055 1.20666743399449 79 10 12.2596118796996 -2.25961187969956 80 13 12.6774360981264 0.322563901873584 81 13 14.1312024363452 -1.13120243634517 82 11 12.3998959546669 -1.39989595466689 83 13 11.9575753646257 1.04242463537431 84 16 14.7828067219213 1.21719327807870 85 8 9.48399499925766 -1.48399499925766 86 16 11.3420214892369 4.65797851076306 87 11 11.4398804507600 -0.439880450760020 88 9 11.0548184929621 -2.05481849296209 89 16 17.4915493530026 -1.49154935300257 90 12 11.1906979163541 0.809302083645878 91 14 11.7789734626264 2.22102653737363 92 8 10.2409291233578 -2.24092912335779 93 9 9.3092824380134 -0.309282438013395 94 15 11.4530745165076 3.54692548349241 95 11 13.2332272356225 -2.23322723562246 96 21 16.8715312915167 4.12846870848331 97 14 13.0421014330892 0.957898566910836 98 18 15.5379836258277 2.46201637417226 99 12 12.0454473355739 -0.0454473355738553 100 13 13.0424125660534 -0.042412566053429 101 15 14.2317919427418 0.76820805725823 102 12 11.3582208733495 0.641779126650482 103 19 14.1659144203829 4.83408557961712 104 15 14.3200387080468 0.679961291953193 105 11 12.752246452834 -1.75224645283401 106 11 11.1083088376633 -0.108308837663261 107 10 12.0507658697514 -2.05076586975142 108 13 15.1241132620185 -2.12411326201848 109 15 15.1528532131991 -0.152853213199097 110 12 9.67994744103673 2.32005255896327 111 12 10.7062465868546 1.29375341314538 112 16 15.3904213119032 0.60957868809682 113 9 15.1405182889701 -6.14051828897008 114 18 17.7605441329622 0.239455867037837 115 8 14.6058773039911 -6.60587730399114 116 13 10.6403047365358 2.35969526346421 117 17 13.8228306651029 3.17716933489713 118 9 10.7568073749522 -1.75680737495220 119 15 12.9298550487309 2.07014495126909 120 8 9.41132943960332 -1.41132943960332 121 7 10.9195896665365 -3.91958966653653 122 12 11.072716002041 0.927283997958995 123 14 14.7746452715422 -0.774645271542197 124 6 10.3845428952891 -4.38454289528913 125 8 9.97723385120437 -1.97723385120437 126 17 12.1206981302002 4.87930186979976 127 10 10.0007433610401 -0.000743361040053847 128 11 12.2037604617204 -1.20376046172035 129 14 12.4565248656558 1.54347513434423 130 11 13.3473760152473 -2.34737601524728 131 13 15.7057751810833 -2.70577518108331 132 12 12.2147399599820 -0.214739959981965 133 11 10.0446267680933 0.955373231906655 134 9 9.71739581189561 -0.717395811895613 135 12 12.3752699428144 -0.375269942814357 136 20 14.4273692568803 5.57263074311969 137 12 11.0552234808148 0.944776519185156 138 13 14.0010468682671 -1.00104686826712 139 12 12.7608780174415 -0.760878017441517 140 12 16.2192745071120 -4.21927450711202 141 9 14.9909551299074 -5.99095512990742 142 15 15.2367698927996 -0.23676989279965 143 24 21.8977139253599 2.10228607464009 144 7 9.68796016061504 -2.68796016061504 145 17 14.9345646236828 2.06543537631718 146 11 11.6439439271603 -0.643943927160331 147 17 14.7905432954693 2.20945670453067 148 11 12.5659739561322 -1.56597395613224 149 12 12.8884618900618 -0.888461890061799 150 14 14.7349325714544 -0.734932571454359 151 11 13.8854030380856 -2.88540303808559 152 16 12.541655323061 3.45834467693902 153 21 14.0808478102729 6.91915218972713 154 14 11.9152243519202 2.08477564807980 155 20 16.0543865342792 3.94561346572078 156 13 10.6865718625929 2.31342813740711 157 11 12.7605624243228 -1.76056242432280 158 15 13.6125830044915 1.38741699550853 159 19 17.6773054071847 1.32269459281528 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.57871416169236 0.84257167661528 0.42128583830764 11 0.722915148423355 0.554169703153291 0.277084851576645 12 0.857343223601124 0.285313552797753 0.142656776398876 13 0.862713268066574 0.274573463866852 0.137286731933426 14 0.812345370813599 0.375309258372803 0.187654629186401 15 0.737201787413565 0.52559642517287 0.262798212586435 16 0.709434363686009 0.581131272627983 0.290565636313992 17 0.720509697021015 0.55898060595797 0.279490302978985 18 0.642900082847337 0.714199834305325 0.357099917152663 19 0.762073378459886 0.475853243080228 0.237926621540114 20 0.834052762182055 0.33189447563589 0.165947237817945 21 0.793534781757314 0.412930436485373 0.206465218242686 22 0.837654325359266 0.324691349281469 0.162345674640734 23 0.792675346073549 0.414649307852903 0.207324653926451 24 0.826528700291544 0.346942599416912 0.173471299708456 25 0.782054947908725 0.43589010418255 0.217945052091275 26 0.756328928175192 0.487342143649617 0.243671071824808 27 0.742329255080695 0.515341489838609 0.257670744919305 28 0.68544187378278 0.62911625243444 0.31455812621722 29 0.657203815740659 0.685592368518683 0.342796184259341 30 0.607411563017672 0.785176873964655 0.392588436982328 31 0.683698438240233 0.632603123519533 0.316301561759767 32 0.663444112859288 0.673111774281424 0.336555887140712 33 0.73091341420865 0.5381731715827 0.26908658579135 34 0.76640501884182 0.467189962316361 0.233594981158180 35 0.762480644393395 0.47503871121321 0.237519355606605 36 0.818085967621205 0.36382806475759 0.181914032378795 37 0.872176262163292 0.255647475673415 0.127823737836708 38 0.864155926371609 0.271688147256782 0.135844073628391 39 0.854698175680003 0.290603648639994 0.145301824319997 40 0.830914171513378 0.338171656973244 0.169085828486622 41 0.873432331815563 0.253135336368875 0.126567668184437 42 0.843464903794054 0.313070192411891 0.156535096205946 43 0.847222438189901 0.305555123620198 0.152777561810099 44 0.8844908323134 0.231018335373199 0.115509167686599 45 0.89216680723307 0.215666385533859 0.107833192766929 46 0.867188199427109 0.265623601145782 0.132811800572891 47 0.84791917121079 0.304161657578419 0.152080828789209 48 0.866616396065724 0.266767207868552 0.133383603934276 49 0.84322554803318 0.313548903933640 0.156774451966820 50 0.880052478724679 0.239895042550642 0.119947521275321 51 0.916350202442147 0.167299595115705 0.0836497975578525 52 0.899763591678631 0.200472816642739 0.100236408321369 53 0.876397971713067 0.247204056573866 0.123602028286933 54 0.893373362801284 0.213253274397432 0.106626637198716 55 0.870815822863114 0.258368354273771 0.129184177136886 56 0.844700201814819 0.310599596370363 0.155299798185181 57 0.814997907880895 0.37000418423821 0.185002092119105 58 0.812205863662938 0.375588272674124 0.187794136337062 59 0.821435135238503 0.357129729522993 0.178564864761497 60 0.80489657830825 0.390206843383499 0.195103421691749 61 0.787380061653041 0.425239876693918 0.212619938346959 62 0.757462584111723 0.485074831776555 0.242537415888277 63 0.762069987548672 0.475860024902655 0.237930012451328 64 0.83269344258771 0.33461311482458 0.16730655741229 65 0.817159226142617 0.365681547714767 0.182840773857383 66 0.821731125922336 0.356537748155328 0.178268874077664 67 0.816438360243253 0.367123279513493 0.183561639756746 68 0.790393989794633 0.419212020410733 0.209606010205367 69 0.76323396848689 0.473532063026221 0.236766031513111 70 0.747294899888791 0.505410200222418 0.252705100111209 71 0.719320469517136 0.561359060965729 0.280679530482864 72 0.713998319110725 0.57200336177855 0.286001680889275 73 0.683906017892588 0.632187964214823 0.316093982107412 74 0.687785134232255 0.62442973153549 0.312214865767745 75 0.683896054468047 0.632207891063905 0.316103945531953 76 0.644402002428524 0.711195995142952 0.355597997571476 77 0.684496272584352 0.631007454831296 0.315503727415648 78 0.652057103663215 0.695885792673571 0.347942896336785 79 0.634894207563771 0.730211584872458 0.365105792436229 80 0.591306539520357 0.817386920959286 0.408693460479643 81 0.55159773036999 0.896804539260019 0.448402269630010 82 0.520712941103795 0.95857411779241 0.479287058896206 83 0.482352000082721 0.964704000165443 0.517647999917279 84 0.444147296432954 0.888294592865908 0.555852703567046 85 0.412798778956185 0.82559755791237 0.587201221043815 86 0.510705845152269 0.978588309695462 0.489294154847731 87 0.465285754146782 0.930571508293564 0.534714245853218 88 0.438478898014096 0.876957796028192 0.561521101985904 89 0.411583080076509 0.823166160153018 0.588416919923491 90 0.370051081536385 0.74010216307277 0.629948918463615 91 0.357524823527274 0.715049647054548 0.642475176472726 92 0.341072770033335 0.68214554006667 0.658927229966665 93 0.29872658295875 0.5974531659175 0.70127341704125 94 0.328625244959595 0.65725048991919 0.671374755040405 95 0.318346801642028 0.636693603284056 0.681653198357972 96 0.364720692897503 0.729441385795007 0.635279307102497 97 0.328378266467712 0.656756532935424 0.671621733532288 98 0.311906261737651 0.623812523475301 0.688093738262349 99 0.27028239091408 0.54056478182816 0.72971760908592 100 0.231847530833082 0.463695061666165 0.768152469166918 101 0.198081763799446 0.396163527598892 0.801918236200554 102 0.168391013506115 0.336782027012231 0.831608986493885 103 0.242238207966585 0.48447641593317 0.757761792033415 104 0.207144739002737 0.414289478005474 0.792855260997263 105 0.195789084926516 0.391578169853032 0.804210915073484 106 0.163525277018512 0.327050554037025 0.836474722981488 107 0.150310015379068 0.300620030758135 0.849689984620932 108 0.142916960258222 0.285833920516444 0.857083039741778 109 0.117129431526761 0.234258863053521 0.882870568473239 110 0.112275305524993 0.224550611049986 0.887724694475007 111 0.0975032007972832 0.195006401594566 0.902496799202717 112 0.08271509579111 0.16543019158222 0.91728490420889 113 0.203422233492149 0.406844466984297 0.796577766507851 114 0.17161472605435 0.3432294521087 0.82838527394565 115 0.360072781360144 0.720145562720288 0.639927218639856 116 0.349256250529364 0.698512501058729 0.650743749470636 117 0.383888654471053 0.767777308942106 0.616111345528947 118 0.342886778484914 0.685773556969828 0.657113221515086 119 0.310954129075742 0.621908258151484 0.689045870924258 120 0.271868881511098 0.543737763022196 0.728131118488902 121 0.309663660304777 0.619327320609555 0.690336339695223 122 0.292682942375199 0.585365884750398 0.707317057624801 123 0.24672286766917 0.49344573533834 0.75327713233083 124 0.341897173563019 0.683794347126039 0.65810282643698 125 0.300967763752404 0.601935527504807 0.699032236247596 126 0.394937696821314 0.789875393642629 0.605062303178686 127 0.338385686656943 0.676771373313886 0.661614313343057 128 0.309573798164752 0.619147596329505 0.690426201835248 129 0.260212000931671 0.520424001863342 0.739787999068329 130 0.300748453208418 0.601496906416836 0.699251546791582 131 0.298501597092249 0.597003194184498 0.701498402907751 132 0.243683606666525 0.48736721333305 0.756316393333475 133 0.195869120993557 0.391738241987114 0.804130879006443 134 0.153205646842774 0.306411293685547 0.846794353157226 135 0.124083794280359 0.248167588560719 0.87591620571964 136 0.217986715185485 0.435973430370970 0.782013284814515 137 0.189201414949376 0.378402829898752 0.810798585050624 138 0.15854253604513 0.31708507209026 0.84145746395487 139 0.138129514391643 0.276259028783285 0.861870485608357 140 0.168751261970159 0.337502523940318 0.831248738029841 141 0.390353881646148 0.780707763292296 0.609646118353852 142 0.364929767156905 0.729859534313809 0.635070232843095 143 0.290607649341727 0.581215298683454 0.709392350658273 144 0.251236051413389 0.502472102826777 0.748763948586611 145 0.198572652014869 0.397145304029738 0.80142734798513 146 0.191470921438581 0.382941842877162 0.808529078561419 147 0.125110760044787 0.250221520089573 0.874889239955214 148 0.101642776175206 0.203285552350412 0.898357223824794 149 0.0544785350585731 0.108957070117146 0.945521464941427 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/10/t1292012078ujcdbvbase33sf3/10vj8x1292012125.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/10vj8x1292012125.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/1o0cm1292012125.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/1o0cm1292012125.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/2grs61292012125.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/2grs61292012125.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/3grs61292012125.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/3grs61292012125.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/4grs61292012125.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/4grs61292012125.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/591aa1292012125.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/591aa1292012125.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/691aa1292012125.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/691aa1292012125.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/7karv1292012125.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/7karv1292012125.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/8karv1292012125.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/8karv1292012125.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/9vj8x1292012125.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292012078ujcdbvbase33sf3/9vj8x1292012125.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') }

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Software written by Ed van Stee & Patrick Wessa

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