WS7 Multiple

*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, 24 Nov 2010 00:25:48 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4.htm/, Retrieved Wed, 24 Nov 2010 01:24:50 +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/Nov/24/t1290558279rs5z7410wllese4.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 «

1 3 1 3 4 2 1 1 1 3 3 3 1 2 2 3 3 4 2 4 1 3 5 3 2 1 1 3 4 2 2 4 1 3 1 2 3 1 3 5 3 1 1 1 1 5 2 1 1 1 3 2 3 1 2 4 2 2 5 2 3 5 3 1 3 1 3 3 2 1 1 1 2 4 4 1 2 1 3 4 1 1 2 1 3 4 2 2 5 2 3 4 4 2 2 1 3 5 2 1 2 1 3 3 3 2 2 1 3 5 3 1 2 1 3 3 3 2 3 1 3 4 1 1 3 1 3 4 3 2 3 2 3 4 3 2 1 1 3 3 2 1 1 2 3 5 2 2 4 1 2 4 2 1 1 4 3 5 2 1 3 1 3 2 4 1 2 1 2 5 3 2 1 1 3 4 1 2 2 1 3 5 2 2 1 1 3 4 1 1 2 1 3 5 3 2 1 1 2 3 2 1 1 1 3 3 1 1 1 1 3 4 3 2 1 1 3 4 2 1 3 1 3 5 3 2 3 1 1 5 1 1 1 1 3 3 3 2 3 1 2 5 3 1 1 1 3 5 2 2 2 1 3 4 3 1 3 1 3 5 3 1 2 1 2 3 3 2 1 3 2 4 3 1 1 2 3 5 3 1 1 1 3 3 3 1 1 1 3 5 2 2 1 1 3 4 2 1 3 2 2 3 3 2 2 1 2 5 1 2 2 1 3 4 3 1 2 1 2 5 3 1 4 1 3 3 1 1 3 1 3 5 1 2 3 1 3 4 1 1 3 1 2 5 4 2 1 1 3 4 3 2 3 1 3 5 1 1 1 1 3 5 2 1 1 2 3 5 4 2 1 1 3 4 3 1 1 1 2 5 3 2 3 1 3 4 2 2 3 1 3 5 3 1 1 1 2 4 3 1 1 1 3 3 3 1 2 1 3 4 2 1 2 2 3 3 3 2 1 1 2 5 2 1 4 1 2 4 3 2 3 1 3 4 1 1 2 1 2 4 3 1 1 1 3 4 2 1 1 1 3 4 2 2 3 1 3 3 4 2 2 1 3 4 2 1 1 1 3 3 3 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 12 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 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 Gender[t] = + 3.78655833907257 -0.102045310896942Weight[t] -0.174659926437502Drugs[t] -0.0207654197460563Sports[t] -0.207471195750587Vegetables[t] + 0.27079311874039`Alcohol `[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) 3.78655833907257 0.441588 8.5749 0 0 Weight -0.102045310896942 0.069263 -1.4733 0.14271 0.071355 Drugs -0.174659926437502 0.085561 -2.0413 0.042924 0.021462 Sports -0.0207654197460563 0.081789 -0.2539 0.799918 0.399959 Vegetables -0.207471195750587 0.06821 -3.0417 0.002766 0.001383 `Alcohol ` 0.27079311874039 0.098704 2.7435 0.006801 0.0034 Multiple Linear Regression - Regression Statistics Multiple R 0.513150770489091 R-squared 0.263323713253547 Adjusted R-squared 0.239405651995546 F-TEST (value) 11.0094087649121 F-TEST (DF numerator) 5 F-TEST (DF denominator) 154 p-value 4.47475256848406e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.861618664997342 Sum Squared Residuals 114.327555476257 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1 2.95516767518455 -1.95516767518455 2 1 3.63752261146938 -2.63752261146938 3 1 3.6316104928753 -2.6316104928753 4 2 2.91644428727736 -0.916444287277362 5 2 3.15925829697839 -1.15925829697839 6 2 3.47553595153933 -1.47553595153933 7 3 2.70508568162147 0.294914318378529 8 1 3.26187673024706 -2.26187673024706 9 1 2.76738194085964 -1.76738194085964 10 2 2.49175666184553 -0.491756661845531 11 3 2.37996611701793 0.620033882982073 12 3 3.17365905675049 -0.17365905675049 13 2 2.51482269722795 -0.514822697227954 14 3 3.03880247654046 -0.0388024765404633 15 3 2.49175666184553 0.508243338154469 16 3 2.49405727748190 0.505942722518103 17 3 2.76209723920602 0.237902760793982 18 3 2.77076251481634 0.229237485183657 19 3 2.58743731276851 0.412562687231485 20 3 2.56329131906576 0.436708680934245 21 3 2.83133128078988 0.168668719210124 22 3 2.73203912690920 0.267960873090797 23 3 2.87618839966999 0.123811600330012 24 3 3.44445217549088 -0.44445217549088 25 3 2.32638942795879 0.673610572041214 26 2 3.88399310207472 -1.88399310207472 27 3 2.55462604345543 0.44537395654457 28 3 2.71891331902184 0.281086680978161 29 2 2.77414308877305 -0.774143088773045 30 3 3.01803705679441 -0.0180370567944066 31 3 2.94880301521055 0.0511969847894516 32 3 3.03880247654046 -0.0388024765404633 33 3 2.77414308877305 0.225856911226955 34 2 3.17365905675049 -1.17365905675049 35 3 3.34831898318799 -0.348318983187993 36 3 2.87618839966999 0.123811600330012 37 3 2.65667135435237 0.343328645647627 38 3 2.35920069727187 0.64079930272813 39 1 3.14422836139411 -2.14422836139411 40 3 2.56329131906576 0.436708680934245 41 2 2.7949085085191 -0.794908508519102 42 3 2.74133181945996 0.258668180540039 43 3 2.48201142791487 0.517988572085131 44 3 2.58743731276851 0.412562687231485 45 2 3.51981994804771 -1.51981994804771 46 2 3.16774693815643 -1.16774693815643 47 3 2.7949085085191 0.205091491480898 48 3 2.99899913031299 0.00100086968701296 49 3 2.94880301521055 0.0511969847894516 50 3 2.92746447309276 0.0725355269072376 51 2 2.77076251481634 -0.770762514816343 52 2 2.91599174589746 -0.915991745897464 53 3 2.68948262366546 0.310517376334543 54 2 2.17249492126734 -0.172494921267340 55 3 2.93337659168682 0.0666234083131816 56 3 2.70852055014688 0.291479449853123 57 3 2.83133128078988 0.168668719210124 58 2 2.59948316233554 -0.599483162335542 59 3 2.46124600816881 0.538753991831187 60 3 3.14422836139411 -0.144228361394108 61 3 3.24036155369699 -0.240361553696995 62 3 2.59948316233554 0.400516837664458 63 3 2.89695381941604 0.103046180583956 64 2 2.35920069727187 -0.359200697271870 65 3 2.63590593460632 0.364094065393684 66 3 2.7949085085191 0.205091491480898 67 2 2.89695381941604 -0.896953819416044 68 3 2.7915279345624 0.208472065437600 69 3 3.13493566884335 -0.134935668843350 70 3 2.97823371056693 0.0217662894330696 71 2 2.34715484770484 -0.347154847704843 72 2 2.46124600816881 -0.461246008168813 73 3 3.03880247654046 -0.0388024765404633 74 2 2.89695381941604 -0.896953819416044 75 3 3.07161374585355 -0.0716137458535476 76 3 2.63590593460632 0.364094065393684 77 3 2.59610258837884 0.40389741162116 78 3 3.07161374585355 -0.0716137458535476 79 3 2.58405673881181 0.415943261188188 80 3 2.65667135435237 0.343328645647627 81 3 2.6202485820816 0.379751417918401 82 3 2.86414255010296 0.135857449897040 83 3 3.26979224905338 -0.269792249053377 84 2 2.6687172039194 -0.6687172039194 85 3 3.03880247654046 -0.0388024765404633 86 3 2.86414255010296 0.135857449897040 87 3 2.96956843495661 0.0304315650433949 88 3 2.6687172039194 0.3312827960806 89 3 3.68581459887489 -0.685814598874887 90 2 3.07161374585355 -1.07161374585355 91 3 2.6653366299627 0.334663370037302 92 3 2.56667189302246 0.433328106977542 93 3 2.62999381601226 0.37000618398774 94 3 2.55462604345543 0.44537395654457 95 3 2.27454023216428 0.725459767835718 96 1 2.59948316233554 -1.59948316233554 97 3 2.17249492126734 0.82750507873266 98 1 2.89695381941604 -1.89695381941604 99 3 2.89695381941604 0.103046180583956 100 3 2.53386062370937 0.466139376290626 101 3 2.48201142791487 0.517988572085131 102 3 2.65075923575832 0.349240764241683 103 2 2.71408115874812 -0.714081158748119 104 3 2.6687172039194 0.3312827960806 105 3 2.87618839966999 0.123811600330012 106 2 2.76209723920602 -0.762097239206017 107 3 3.07161374585355 -0.0716137458535476 108 3 2.51482269722795 0.485177302772046 109 3 2.86076197614626 0.139238023853742 110 2 3.63218361524704 -1.63218361524704 111 4 3.80243730397621 0.197562696023788 112 4 3.44445217549088 0.55554782450912 113 2 3.88990522066877 -1.88990522066877 114 5 3.79652518538216 1.20347481461784 115 4 4.05246500297054 -0.0524650029705445 116 4 3.88990522066877 0.110094779331227 117 4 3.26468418183204 0.735315818167963 118 4 3.99195053156572 0.00804946843428492 119 5 3.61911210192838 1.38088789807162 120 3 3.88990522066877 -0.889905220668773 121 1 4.09399584246266 -3.09399584246266 122 5 3.53547730057243 1.46452269942757 123 3 3.64090318542607 -0.640903185426072 124 5 4.09399584246266 0.906004157537342 125 3 3.67371445473916 -0.673714454739156 126 4 3.42959887433888 0.570401125661121 127 4 3.57166914384221 0.428330856157786 128 4 3.42368675574482 0.576313244255177 129 4 3.48700867873463 0.512991321265375 130 4 3.31928653464281 0.68071346535719 131 5 3.75499434589004 1.24500565410996 132 4 3.61911210192838 0.380887898071617 133 5 3.99195053156571 1.00804946843429 134 3 3.26468418183204 -0.264684181832037 135 4 3.57166914384221 0.428330856157786 136 4 3.49292079732868 0.507079202671318 137 4 3.78785990977183 0.21214009022817 138 4 3.61911210192838 0.380887898071617 139 4 3.75499434589004 0.245005654109958 140 5 3.74632907027972 1.25367092972028 141 5 4.05246500297054 0.947534997029456 142 5 3.67371445473916 1.32628554526084 143 5 3.87780507653304 1.12219492346696 144 5 3.9504196920736 1.04958030792640 145 4 3.3521520985246 0.647847901475401 146 4 3.68243402491819 0.317565975081815 147 4 3.79652518538216 0.203474814617845 148 4 3.91933591602515 0.0806640839748456 149 5 3.79652518538216 1.20347481461784 150 4 3.61911210192838 0.380887898071617 151 5 3.92965427232754 1.07034572767246 152 4 3.41164090617780 0.588359093822205 153 5 3.61911210192838 1.38088789807162 154 5 3.88990522066877 1.11009477933123 155 5 3.67371445473916 1.32628554526084 156 4 3.69447987448521 0.305520125514787 157 4 3.88990522066877 0.110094779331227 158 4 3.88652464671207 0.113475353287930 159 5 3.57758126243627 1.42241873756373 160 4 3.74632907027972 0.253670929720283 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.816872916318945 0.366254167362109 0.183127083681055 10 0.704071884664934 0.591856230670132 0.295928115335066 11 0.652130068762934 0.695739862474133 0.347869931237066 12 0.751585833311695 0.49682833337661 0.248414166688305 13 0.751895899080638 0.496208201838723 0.248104100919362 14 0.717798189664107 0.564403620671787 0.282201810335893 15 0.710981438596869 0.578037122806262 0.289018561403131 16 0.639388961037289 0.721222077925423 0.360611038962711 17 0.55306530930658 0.893869381386841 0.446934690693421 18 0.511530210503718 0.976939578992563 0.488469789496282 19 0.430661879831073 0.861323759662147 0.569338120168927 20 0.382322136773715 0.76464427354743 0.617677863226285 21 0.321881591715441 0.643763183430883 0.678118408284559 22 0.29298493902991 0.58596987805982 0.70701506097009 23 0.233748331836591 0.467496663673181 0.766251668163409 24 0.255316598507098 0.510633197014195 0.744683401492902 25 0.200329917285456 0.400659834570913 0.799670082714544 26 0.181414475343145 0.36282895068629 0.818585524656855 27 0.140015381709878 0.280030763419755 0.859984618290123 28 0.115885451188042 0.231770902376083 0.884114548811958 29 0.161656710262249 0.323313420524499 0.83834328973775 30 0.135302974937279 0.270605949874559 0.86469702506272 31 0.103651074239862 0.207302148479724 0.896348925760138 32 0.0787601977901032 0.157520395580206 0.921239802209897 33 0.0585602782076591 0.117120556415318 0.94143972179234 34 0.0635650605422357 0.127130121084471 0.936434939457764 35 0.0525882564196471 0.105176512839294 0.947411743580353 36 0.0393567022329153 0.0787134044658305 0.960643297767085 37 0.028301969995425 0.05660393999085 0.971698030004575 38 0.0204134861515632 0.0408269723031265 0.979586513848437 39 0.162156917980994 0.324313835961987 0.837843082019006 40 0.134877303535578 0.269754607071155 0.865122696464422 41 0.160775631415202 0.321551262830404 0.839224368584798 42 0.132493577627898 0.264987155255797 0.867506422372102 43 0.107143727912727 0.214287455825454 0.892856272087273 44 0.0867265084030721 0.173453016806144 0.913273491596928 45 0.0883527799847347 0.176705559969469 0.911647220015265 46 0.0860409396150161 0.172081879230032 0.913959060384984 47 0.0685472965027109 0.137094593005422 0.931452703497289 48 0.0555103807180099 0.111020761436020 0.94448961928199 49 0.044312856406385 0.08862571281277 0.955687143593615 50 0.0381215543805202 0.0762431087610403 0.96187844561948 51 0.0397260534227662 0.0794521068455324 0.960273946577234 52 0.0429153762399809 0.0858307524799617 0.95708462376002 53 0.0331445724948957 0.0662891449897914 0.966855427505104 54 0.0467294234437122 0.0934588468874244 0.953270576556288 55 0.0395112428833086 0.0790224857666172 0.96048875711669 56 0.0316100848265066 0.0632201696530131 0.968389915173493 57 0.0245848942092155 0.0491697884184309 0.975415105790784 58 0.0258538698428458 0.0517077396856916 0.974146130157154 59 0.0202886073972866 0.0405772147945731 0.979711392602713 60 0.0154258140432888 0.0308516280865776 0.984574185956711 61 0.0128634218505714 0.0257268437011428 0.987136578149429 62 0.0102307479937874 0.0204614959875749 0.989769252006213 63 0.00758935160902525 0.0151787032180505 0.992410648390975 64 0.00827939230976398 0.0165587846195280 0.991720607690236 65 0.00632325764215776 0.0126465152843155 0.993676742357842 66 0.00470042536157679 0.00940085072315358 0.995299574638423 67 0.00537937452681707 0.0107587490536341 0.994620625473183 68 0.0039476274055678 0.0078952548111356 0.996052372594432 69 0.00324239397867385 0.0064847879573477 0.996757606021326 70 0.00257484872648366 0.00514969745296732 0.997425151273516 71 0.00328562737744985 0.0065712547548997 0.99671437262255 72 0.00333776848213643 0.00667553696427286 0.996662231517864 73 0.00243859238157683 0.00487718476315365 0.997561407618423 74 0.00281222940677439 0.00562445881354879 0.997187770593226 75 0.00200490465111266 0.00400980930222532 0.997995095348887 76 0.00149122407410552 0.00298244814821104 0.998508775925894 77 0.00113725093062312 0.00227450186124623 0.998862749069377 78 0.000786571193664492 0.00157314238732898 0.999213428806335 79 0.000542251525888619 0.00108450305177724 0.999457748474111 80 0.000362549724738328 0.000725099449476656 0.999637450275262 81 0.000280274436765880 0.000560548873531761 0.999719725563234 82 0.000184415893823889 0.000368831787647779 0.999815584106176 83 0.000143376728131069 0.000286753456262139 0.999856623271869 84 0.000148744014506164 0.000297488029012328 0.999851255985494 85 0.000100573697712087 0.000201147395424173 0.999899426302288 86 6.41277486835746e-05 0.000128255497367149 0.999935872251316 87 4.01455411493225e-05 8.0291082298645e-05 0.99995985445885 88 2.72119670741097e-05 5.44239341482193e-05 0.999972788032926 89 2.86178763386354e-05 5.72357526772708e-05 0.999971382123661 90 4.51070512741976e-05 9.02141025483953e-05 0.999954892948726 91 3.24612636327273e-05 6.49225272654547e-05 0.999967538736367 92 2.16543319603123e-05 4.33086639206246e-05 0.99997834566804 93 1.60008118215821e-05 3.20016236431642e-05 0.999983999188178 94 9.65954933074491e-06 1.93190986614898e-05 0.99999034045067 95 6.38451249530044e-06 1.27690249906009e-05 0.999993615487505 96 6.6522130918953e-05 0.000133044261837906 0.999933477869081 97 5.03957840616786e-05 0.000100791568123357 0.999949604215938 98 0.000899436675551746 0.00179887335110349 0.999100563324448 99 0.000625994247973539 0.00125198849594708 0.999374005752026 100 0.000430289293424228 0.000860578586848457 0.999569710706576 101 0.000293487062150801 0.000586974124301602 0.99970651293785 102 0.000209581149155031 0.000419162298310061 0.999790418850845 103 0.000169585327409537 0.000339170654819074 0.99983041467259 104 0.000116246473739042 0.000232492947478084 0.99988375352626 105 8.42685219615734e-05 0.000168537043923147 0.999915731478038 106 0.000148498417692587 0.000296996835385174 0.999851501582307 107 0.000120910586202183 0.000241821172404367 0.999879089413798 108 8.00686891492178e-05 0.000160137378298436 0.99991993131085 109 6.32944479054834e-05 0.000126588895810967 0.999936705552094 110 0.00106413961411846 0.00212827922823691 0.998935860385882 111 0.00237488832984502 0.00474977665969004 0.997625111670155 112 0.00314709375565283 0.00629418751130567 0.996852906244347 113 0.0135442978179411 0.0270885956358822 0.98645570218206 114 0.062193973255585 0.12438794651117 0.937806026744415 115 0.0816420880103143 0.163284176020629 0.918357911989686 116 0.0797500964654817 0.159500192930963 0.920249903534518 117 0.0865186046985411 0.173037209397082 0.913481395301459 118 0.0779191751506557 0.155838350301311 0.922080824849344 119 0.121715196398044 0.243430392796088 0.878284803601956 120 0.140260739032399 0.280521478064798 0.859739260967601 121 0.96689327992306 0.0662134401538783 0.0331067200769391 122 0.990608119659004 0.0187837606819921 0.00939188034099605 123 0.99695413257357 0.00609173485285957 0.00304586742642978 124 0.996850593867904 0.00629881226419272 0.00314940613209636 125 0.999677805264337 0.000644389471325197 0.000322194735662599 126 0.999507738960999 0.000984522078003075 0.000492261039001537 127 0.99945150594936 0.00109698810128255 0.000548494050641273 128 0.999148582993493 0.00170283401301336 0.000851417006506679 129 0.998718969654396 0.00256206069120847 0.00128103034560423 130 0.998263789899853 0.00347242020029508 0.00173621010014754 131 0.99820240133793 0.00359519732414099 0.00179759866207050 132 0.997374811362138 0.00525037727572432 0.00262518863786216 133 0.996993756116884 0.00601248776623282 0.00300624388311641 134 0.998099153310492 0.00380169337901673 0.00190084668950836 135 0.99759859118675 0.00480281762649918 0.00240140881324959 136 0.99634195181403 0.00731609637194035 0.00365804818597018 137 0.994183318841572 0.0116333623168556 0.00581668115842779 138 0.992266336329773 0.0154673273404536 0.0077336636702268 139 0.996660232163834 0.00667953567233236 0.00333976783616618 140 0.995219673273027 0.00956065345394586 0.00478032672697293 141 0.991582559586298 0.0168348808274035 0.00841744041370176 142 0.988394164600395 0.0232116707992108 0.0116058353996054 143 0.98109564373034 0.03780871253932 0.01890435626966 144 0.96914859811521 0.0617028037695795 0.0308514018847898 145 0.949198999803472 0.101602000393057 0.0508010001965284 146 0.914651036112048 0.170697927775903 0.0853489638879517 147 0.886260050270673 0.227479899458655 0.113739949729327 148 0.890385922567495 0.219228154865010 0.109614077432505 149 0.819679414757416 0.360641170485167 0.180320585242584 150 0.845536523799775 0.308926952400451 0.154463476200225 151 0.711509524585484 0.576980950829032 0.288490475414516 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 62 0.433566433566434 NOK 5% type I error level 79 0.552447552447552 NOK 10% type I error level 92 0.643356643356643 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/10n9r31290558335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/10n9r31290558335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/1z78h1290558334.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/1z78h1290558334.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/2z78h1290558334.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/2z78h1290558334.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/3z78h1290558334.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/3z78h1290558334.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/4k9sx1290558335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/4k9sx1290558335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/5k9sx1290558335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/5k9sx1290558335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/6k9sx1290558335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/6k9sx1290558335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/7visi1290558335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/7visi1290558335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/8n9r31290558335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/8n9r31290558335.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/9n9r31290558335.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290558279rs5z7410wllese4/9n9r31290558335.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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

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

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Software written by Ed van Stee & Patrick Wessa

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