workshop 7.3

*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: Tue, 23 Nov 2010 16:16:23 +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/23/t1290529236g94n5vc7q2j8dh7.htm/, Retrieved Tue, 23 Nov 2010 17:20:49 +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/23/t1290529236g94n5vc7q2j8dh7.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 «

9 4 2 5 4 3 9 4 2 4 3 2 9 5 4 4 2 2 9 3 2 4 2 2 9 4 3 2 2 2 9 3 4 5 2 2 10 4 3 5 3 2 10 3 3 4 2 1 10 2 3 3 1 2 10 4 2 4 2 2 10 2 4 4 2 2 10 2 3 3 2 2 10 1 3 3 2 2 10 4 4 4 2 2 10 4 4 5 1 1 10 2 3 4 2 2 10 2 3 2 2 1 10 3 3 4 3 2 10 3 4 4 4 2 10 3 2 4 4 2 10 4 5 4 4 4 10 3 4 4 4 2 10 2 2 4 4 4 10 2 3 5 2 2 10 4 4 4 2 2 10 4 4 4 4 2 10 3 3 4 2 2 10 4 4 4 3 2 10 2 4 4 2 2 10 4 1 4 4 2 10 4 4 4 3 3 10 5 5 2 4 2 10 5 2 4 2 2 10 4 4 4 2 2 10 4 3 5 4 3 10 4 2 5 5 4 10 2 4 4 2 1 10 4 5 3 4 2 10 4 4 4 4 3 10 4 4 5 5 3 10 3 4 4 3 2 10 2 3 4 2 2 10 3 4 5 3 2 10 4 2 4 2 2 10 3 2 5 1 2 10 2 4 4 2 2 10 4 2 4 4 4 10 4 4 4 4 4 10 3 4 3 4 2 10 4 1 4 4 3 10 3 4 4 2 2 10 4 2 4 2 2 10 2 1 2 1 1 10 4 4 3 4 3 10 4 3 5 2 4 10 4 2 4 4 2 10 4 4 4 2 2 10 3 3 5 2 1 10 1 2 3 1 2 10 3 2 5 2 2 10 3 3 4 2 2 10 4 2 5 2 2 10 2 1 4 2 2 10 3 3 4 1 1 10 5 2 5 5 2 10 4 3 4 3 3 10 4 3 4 2 2 10 3 3 5 1 1 10 4 2 4 2 2 10 2 3 3 4 4 10 3 2 4 2 2 10 4 4 5 5 3 10 3 4 5 4 4 10 4 4 5 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 16 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation YT[t] = + 8.56713904540317 -0.735371589104438T1[t] + 0.0759378528567064X1[t] + 0.251758435553541X2[t] + 0.366360559218664X3[t] -0.117608217425018X4[t] + 0.000361144076985856t + 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) 8.56713904540317 3.75563 2.2811 0.023948 0.011974 T1 -0.735371589104438 0.380985 -1.9302 0.055471 0.027735 X1 0.0759378528567064 0.073314 1.0358 0.301965 0.150982 X2 0.251758435553541 0.08442 2.9822 0.003341 0.001671 X3 0.366360559218664 0.072063 5.0839 1e-06 1e-06 X4 -0.117608217425018 0.089717 -1.3109 0.191902 0.095951 t 0.000361144076985856 0.001663 0.2172 0.828335 0.414167 Multiple Linear Regression - Regression Statistics Multiple R 0.478480661179188 R-squared 0.228943743122473 Adjusted R-squared 0.198101492847372 F-TEST (value) 7.42305574594532 F-TEST (DF numerator) 6 F-TEST (DF denominator) 150 p-value 5.69652836457379e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.861155699499398 Sum Squared Residuals 111.238370817045 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 4.47244135562101 -0.472441355621013 2 4 3.97229172235076 0.0277082776492371 3 5 3.75816801292248 1.24183198707752 4 3 3.60665345128606 -0.606653451286056 5 4 3.17943557711267 0.820564422887334 6 3 4.01100988070698 -1.01100988070698 7 4 3.56642214204148 0.433577857958518 8 3 3.06627250877128 -0.0662725087712795 9 2 2.33090644065104 -0.330906440651041 10 4 2.87344872664353 1.12655127335647 11 2 3.02568557643392 -1.02568557643392 12 2 2.69835043210066 -0.698350432100663 13 1 2.69871157617765 -1.69871157617765 14 4 3.02676900866488 0.973230991335118 15 4 3.03013624650176 0.969863753498236 16 2 2.95155344396215 -0.951553443962148 17 2 2.56600593435707 -0.566005934357069 18 3 3.31863629133478 -0.318636291334784 19 3 3.76129584748714 -0.76129584748714 20 3 3.60978128585071 -0.609781285850714 21 4 3.60273955364778 0.397260446352219 22 3 3.7623792797181 -0.762379279718098 23 2 3.37564828323163 -1.37564828323163 24 2 3.20620103213158 -1.20620103213158 25 4 3.03074159351173 0.969258406488273 26 4 3.76382385602604 0.236176143973959 27 3 2.95552602880899 0.0444739711910075 28 4 3.39818558496135 0.601814415038651 29 2 3.03218616981967 -1.03218616981967 30 4 3.53745487376387 0.462545126236133 31 4 3.28166079976729 0.718339200232712 32 5 3.33841170223758 1.66158829776242 33 5 2.8817550404142 2.1182449595858 34 4 3.0339918902046 0.9660081097954 35 4 3.82528651799073 0.174713482009269 36 4 3.99846215100466 0.00153784899534324 37 2 3.15268353986058 -1.15268353986058 38 4 3.59233700225304 0.407662997746964 39 4 3.65091051160184 0.349089488398161 40 4 4.26939065045103 -0.269390650451030 41 3 3.40288045796216 -0.402880457962165 42 2 2.96094318996378 -0.96094318996378 43 3 3.65536118166968 -0.655361181669678 44 4 2.88572762526105 1.11427237473895 45 3 2.77148664567291 0.228513354327091 46 2 3.03832561912843 -1.03832561912843 47 4 3.38431574107930 0.615684258920705 48 4 3.53655259086969 0.463447409130307 49 3 3.52037173424317 -0.520371734243174 50 4 3.42706953787857 0.572930462121435 51 3 3.04013133951336 -0.040131339513359 52 4 2.88861677787693 1.11138322212307 53 2 2.06077085619648 -0.0607708561964836 54 4 3.40456923720309 0.595430762796915 55 4 2.9821800636681 1.01781993633190 56 4 3.62278247262220 0.377217527377796 57 4 3.04229820397527 0.957701796024726 58 3 3.33608814817411 -0.336088148174114 59 1 2.27302579164363 -1.27302579164363 60 3 3.14326436604636 -0.143264366046361 61 3 2.96780492742651 0.0321950725734884 62 4 3.14398665420033 0.856013345799667 63 2 2.81665150986707 -0.816651509867071 64 3 2.72013601786382 0.279863982136177 65 5 4.24415176408728 0.755848235912717 66 4 3.21836298960509 0.781637010394913 67 4 2.96997179188843 1.03002820811157 68 3 2.97333902972531 0.0266609702746920 69 4 2.89475622718569 1.10524377281431 70 2 3.21680147215313 -1.21680147215313 71 3 2.89547851533966 0.104521484660336 72 4 4.28094726091458 -0.280947260914578 73 3 3.79733962834788 -0.797339628347881 74 4 3.66655664805624 0.333443351943761 75 4 2.66170665679757 1.33829334320243 76 3 3.09083030600632 -0.0908303060063177 77 3 3.30127952106853 -0.301279521068533 78 2 3.22570281228881 -1.22570281228881 79 4 3.54774805725625 0.452251942743745 80 3 3.03287903016106 -0.0328790301610601 81 2 2.72326937341269 -0.723269373412687 82 2 3.70811007148054 -1.70811007148054 83 3 3.78440906841423 -0.784409068414235 84 2 2.78256517091546 -0.782565170915462 85 2 3.05241023813088 -1.05241023813088 86 4 3.26725623571312 0.732743764286884 87 4 3.27062347355 0.729376526450002 88 4 3.78621478879916 0.213785211200836 89 2 2.97791696158212 -0.977916961582115 90 2 3.5517206421031 -1.5517206421031 91 4 2.90570749063928 1.09429250936072 92 2 2.65130410540283 -0.651304105402826 93 3 3.09396366155518 -0.0939636615551816 94 3 3.23148111752059 -0.231481117520586 95 5 3.88122265089828 1.11877734910172 96 3 2.66929068241427 0.330709317585726 97 4 3.22955845599165 0.770441544008352 98 3 3.05710511113169 -0.0571051111316942 99 2 2.86392018492696 -0.863920184926956 100 4 3.05782739928567 0.942172600714334 101 3 3.09985890793096 -0.099858907930964 102 3 2.98261183458293 0.0173881654170684 103 3 2.90703512580321 0.0929648741967886 104 4 3.60145311750911 0.398546882490891 105 1 2.16902410800006 -1.16902410800006 106 3 2.98405641089087 0.0159435891091249 107 2 3.02007573201638 -1.02007573201638 108 3 3.3094688936952 -0.309468893695199 109 2 3.16096042581867 -1.16096042581867 110 2 2.56092806270834 -0.560928062708337 111 2 2.82658354928247 -0.826583549282474 112 4 2.58258913408584 1.41741086591416 113 5 4.23754180279918 0.76245819720082 114 5 2.66225536885641 2.33774463114359 115 3 2.98730670758375 0.0126932924162523 116 4 2.56008883341036 1.43991116658964 117 4 2.08087798336368 1.91912201663632 118 3 3.0226576281031 -0.0226576281030992 119 2 2.85460106576317 -0.854601065763168 120 4 3.97058588819965 0.0294141118003487 121 2 2.73771513649212 -0.737715136492121 122 3 2.62046806314409 0.379531936855911 123 2 3.28362466032149 -1.28362466032149 124 2 2.91461915141991 -0.914619151419914 125 2 2.69748934823175 -0.697489348231753 126 4 3.18482536271232 0.815174637287684 127 4 3.35800099572624 0.641999004273758 128 4 2.99200158058456 1.00799841941544 129 4 3.60747562567386 0.39252437432614 130 3 3.54962440447903 -0.549624404479028 131 2 2.99308501281552 -0.993085012815521 132 4 3.80210512818654 0.197894871813458 133 3 3.80246627226353 -0.802466272263528 134 2 2.91823059218977 -0.918230592189773 135 4 3.8031885604175 0.196811439582501 136 3 2.91594678658385 0.0840532134161509 137 3 3.07118973013414 -0.0711897301341425 138 3 2.99561302135442 0.0043869786455776 139 3 2.74120963611797 0.258790363882029 140 3 3.14960170398193 -0.149601703981933 141 4 3.653479719166 0.346520280833998 142 5 3.86210632734971 1.13789367265029 143 2 3.03908910630766 -1.03908910630766 144 4 3.12892401018497 0.871075989815035 145 3 3.72785605457076 -0.727856054570756 146 3 2.37737708543821 0.622622914561792 147 1 2.49534644694021 -1.49534644694021 148 2 3.07516231498099 -1.07516231498099 149 4 2.82376502350443 1.17623497649557 150 4 2.84066816828492 1.15933183171508 151 5 4.05771920744292 0.942280792557081 152 2 2.82184236197549 -0.821842361975493 153 4 3.40466432377616 0.595335676223836 154 3 3.00139132658620 -0.00139132658619608 155 2 3.36811302988185 -1.36811302988185 156 4 3.32680380939052 0.67319619060948 157 2 2.47382952384526 -0.473829523845264 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.814900628656109 0.370198742687782 0.185099371343891 11 0.832742451356617 0.334515097286766 0.167257548643383 12 0.753553513237782 0.492892973524437 0.246446486762218 13 0.731787354144662 0.536425291710675 0.268212645855338 14 0.921384959384112 0.157230081231776 0.0786150406158878 15 0.918143259084963 0.163713481830074 0.0818567409150371 16 0.886271201335923 0.227457597328153 0.113728798664077 17 0.839610862753665 0.320778274492669 0.160389137246335 18 0.799566878492577 0.400866243014847 0.200433121507423 19 0.740015147632863 0.519969704734274 0.259984852367137 20 0.6816190039514 0.636761992097199 0.318380996048600 21 0.699069517404997 0.601860965190005 0.300930482595003 22 0.641802759355697 0.716394481288606 0.358197240644303 23 0.60242926640345 0.7951414671931 0.39757073359655 24 0.560393627690797 0.879212744618406 0.439606372309203 25 0.666259128042566 0.667481743914868 0.333740871957434 26 0.631404493970282 0.737191012059436 0.368595506029718 27 0.584168585916401 0.831662828167197 0.415831414083599 28 0.558615220264388 0.882769559471224 0.441384779735612 29 0.576751849851059 0.846496300297882 0.423248150148941 30 0.62391965893079 0.75216068213842 0.37608034106921 31 0.61996959935479 0.76006080129042 0.38003040064521 32 0.677085744253664 0.645828511492672 0.322914255746336 33 0.85505346900773 0.289893061984539 0.144946530992269 34 0.831333767231654 0.337332465536693 0.168666232768346 35 0.79176167375563 0.416476652488739 0.208238326244370 36 0.74828187648857 0.50343624702286 0.25171812351143 37 0.860312112734253 0.279375774531494 0.139687887265747 38 0.829750113999746 0.340499772000509 0.170249886000254 39 0.793452361269935 0.413095277460131 0.206547638730065 40 0.760699959156569 0.478600081686863 0.239300040843432 41 0.745107246560874 0.509785506878253 0.254892753439126 42 0.772255768068697 0.455488463862606 0.227744231931303 43 0.755948480310672 0.488103039378657 0.244051519689328 44 0.768504355005526 0.462991289988948 0.231495644994474 45 0.726401866632919 0.547196266734162 0.273598133367081 46 0.764600550724695 0.47079889855061 0.235399449275305 47 0.73366409938386 0.532671801232281 0.266335900616140 48 0.693200899184437 0.613598201631127 0.306799100815563 49 0.67740691295642 0.645186174087161 0.322593087043580 50 0.641442802938396 0.717114394123208 0.358557197061604 51 0.594958167923672 0.810083664152656 0.405041832076328 52 0.598786386037036 0.802427227925929 0.401213613962964 53 0.563279566782059 0.873440866435882 0.436720433217941 54 0.522883942336094 0.954232115327811 0.477116057663906 55 0.509730233095537 0.980539533808926 0.490269766904463 56 0.465225306538893 0.930450613077787 0.534774693461107 57 0.452115247684887 0.904230495369775 0.547884752315113 58 0.414411920865886 0.828823841731772 0.585588079134114 59 0.52149514598771 0.95700970802458 0.47850485401229 60 0.475400568939524 0.950801137879048 0.524599431060476 61 0.427909184554166 0.855818369108332 0.572090815445834 62 0.417684313987474 0.835368627974948 0.582315686012526 63 0.422143213933684 0.844286427867369 0.577856786066316 64 0.3775280752033 0.7550561504066 0.6224719247967 65 0.362932474531370 0.725864949062739 0.63706752546863 66 0.342147391618936 0.684294783237873 0.657852608381064 67 0.344306272112153 0.688612544224307 0.655693727887847 68 0.302059315114574 0.604118630229148 0.697940684885426 69 0.315523637189989 0.631047274379978 0.684476362810011 70 0.400164310430221 0.800328620860441 0.59983568956978 71 0.357493939045512 0.714987878091024 0.642506060954488 72 0.326958603441712 0.653917206883423 0.673041396558288 73 0.331325288406838 0.662650576813676 0.668674711593162 74 0.294533441551453 0.589066883102906 0.705466558448547 75 0.344599280604297 0.689198561208593 0.655400719395703 76 0.305235845811362 0.610471691622725 0.694764154188638 77 0.273866907082256 0.547733814164512 0.726133092917744 78 0.318243755162415 0.636487510324831 0.681756244837584 79 0.290438117301476 0.580876234602952 0.709561882698524 80 0.254522822402585 0.50904564480517 0.745477177597415 81 0.24711436623242 0.49422873246484 0.75288563376758 82 0.352291216391647 0.704582432783293 0.647708783608353 83 0.340236436660959 0.680472873321918 0.659763563339041 84 0.332616475110168 0.665232950220336 0.667383524889832 85 0.352752788214958 0.705505576429916 0.647247211785042 86 0.342613323767172 0.685226647534345 0.657386676232828 87 0.332812688798489 0.665625377596978 0.66718731120151 88 0.293970487367053 0.587940974734106 0.706029512632947 89 0.303840583222297 0.607681166444593 0.696159416777703 90 0.403484817307944 0.806969634615889 0.596515182692056 91 0.434422112669342 0.868844225338684 0.565577887330658 92 0.412318545315396 0.824637090630791 0.587681454684604 93 0.369736985285203 0.739473970570406 0.630263014714797 94 0.32830919541267 0.65661839082534 0.67169080458733 95 0.345531679402732 0.691063358805464 0.654468320597268 96 0.311205698474319 0.622411396948637 0.688794301525681 97 0.303595100013991 0.607190200027982 0.696404899986009 98 0.262792153922191 0.525584307844381 0.73720784607781 99 0.258093273491288 0.516186546982577 0.741906726508712 100 0.259745593382293 0.519491186764585 0.740254406617707 101 0.221931927710361 0.443863855420723 0.778068072289639 102 0.186724530726387 0.373449061452775 0.813275469273613 103 0.156157534318704 0.312315068637409 0.843842465681296 104 0.135850666687528 0.271701333375057 0.864149333312472 105 0.154521807826980 0.309043615653959 0.84547819217302 106 0.126389578056595 0.25277915611319 0.873610421943405 107 0.147116171318016 0.294232342636032 0.852883828681984 108 0.125466006542988 0.250932013085976 0.874533993457012 109 0.142388097480975 0.284776194961950 0.857611902519025 110 0.134249274770545 0.268498549541089 0.865750725229455 111 0.156567620039172 0.313135240078343 0.843432379960828 112 0.196927678406044 0.393855356812088 0.803072321593956 113 0.174779015909973 0.349558031819947 0.825220984090027 114 0.494603095411647 0.989206190823294 0.505396904588353 115 0.439937068265967 0.879874136531933 0.560062931734034 116 0.489532870961681 0.979065741923362 0.510467129038319 117 0.812484260504027 0.375031478991945 0.187515739495973 118 0.78330397396203 0.433392052075939 0.216696026037970 119 0.758389021497587 0.483221957004826 0.241610978502413 120 0.714836369087296 0.570327261825408 0.285163630912704 121 0.685925220541633 0.628149558916734 0.314074779458367 122 0.645633969832881 0.708732060334238 0.354366030167119 123 0.653255383837443 0.693489232325114 0.346744616162557 124 0.628217451867937 0.743565096264126 0.371782548132063 125 0.653823162852743 0.692353674294513 0.346176837147257 126 0.635566767138124 0.728866465723752 0.364433232861876 127 0.606239950423034 0.787520099153931 0.393760049576966 128 0.673062408081664 0.653875183836671 0.326937591918336 129 0.617273765919448 0.765452468161104 0.382726234080552 130 0.592981099961349 0.814037800077303 0.407018900038651 131 0.579906861267479 0.840186277465042 0.420093138732521 132 0.511701066609348 0.976597866781303 0.488298933390652 133 0.614894134511224 0.770211730977553 0.385105865488776 134 0.586084325050544 0.827831349898912 0.413915674949456 135 0.562946829378229 0.874106341243542 0.437053170621771 136 0.483144039632516 0.966288079265032 0.516855960367484 137 0.487487325135399 0.974974650270798 0.512512674864601 138 0.436938933493837 0.873877866987675 0.563061066506163 139 0.355541990837327 0.711083981674653 0.644458009162673 140 0.288796039099582 0.577592078199164 0.711203960900418 141 0.240407881704033 0.480815763408066 0.759592118295967 142 0.195794658850956 0.391589317701912 0.804205341149044 143 0.144131629985642 0.288263259971283 0.855868370014358 144 0.0947164893389675 0.189432978677935 0.905283510661033 145 0.084726664148586 0.169453328297172 0.915273335851414 146 0.0857080830678513 0.171416166135703 0.914291916932149 147 0.0528165441478915 0.105633088295783 0.947183455852109 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/Nov/23/t1290529236g94n5vc7q2j8dh7/10w6hn1290528966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/10w6hn1290528966.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/1pn2t1290528966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/1pn2t1290528966.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/20wje1290528966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/20wje1290528966.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/30wje1290528966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/30wje1290528966.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/40wje1290528966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/40wje1290528966.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/50wje1290528966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/50wje1290528966.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/6t6ih1290528966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/6t6ih1290528966.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/780781290528966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/780781290528966.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/880781290528966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/880781290528966.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/980781290528966.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290529236g94n5vc7q2j8dh7/980781290528966.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = 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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