workshop 7.2

*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 16:02:49 +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/t1290528123w1mznyykyjyy1ou.htm/, Retrieved Tue, 23 Nov 2010 17:02:03 +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/t1290528123w1mznyykyjyy1ou.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 18 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation YT[t] = + 8.33389075361305 -0.707921514339938T1[t] + 0.0765528746818012X1[t] + 0.247513466468539X2[t] + 0.36568320992491X3[t] -0.115580997002372X4[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) 8.33389075361305 3.587474 2.3231 0.021511 0.010756 T1 -0.707921514339938 0.35828 -1.9759 0.04999 0.024995 X1 0.0765528746818012 0.073027 1.0483 0.296186 0.148093 X2 0.247513466468539 0.081868 3.0233 0.002938 0.001469 X3 0.36568320992491 0.071768 5.0953 1e-06 1e-06 X4 -0.115580997002372 0.088948 -1.2994 0.195782 0.097891 Multiple Linear Regression - Regression Statistics Multiple R 0.478227147881944 R-squared 0.228701204971298 Adjusted R-squared 0.203161509771673 F-TEST (value) 8.9547350970206 F-TEST (DF numerator) 5 F-TEST (DF denominator) 151 p-value 1.80539287630843e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.858434433593512 Sum Squared Residuals 111.273361193631 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 4.46926005495242 -0.469260054952424 2 4 3.97164437556135 0.0283556244386497 3 5 3.75906691500004 1.24093308499996 4 3 3.60596116563644 -0.605961165636439 5 4 3.18748710738116 0.812512892618836 6 3 4.00658038146858 -1.00658038146858 7 4 3.58778920237175 0.412210797628248 8 3 3.09017352298067 -0.0901735229806749 9 2 2.36139584958485 -0.361395849584854 10 4 2.8980396512965 1.10196034870350 11 2 3.05114540066010 -1.05114540066010 12 2 2.72707905950976 -0.727079059509764 13 1 2.72707905950976 -1.72707905950976 14 4 3.05114540066010 0.948854599339896 15 4 3.04855665420610 0.951443345793895 16 2 2.9745925259783 -0.974592525978303 17 2 2.5951465900436 -0.595146590043597 18 3 3.34027573590321 -0.340275735903213 19 3 3.78251182050992 -0.782511820509925 20 3 3.62940607114632 -0.629406071146322 21 4 3.62790270118698 0.372097298813019 22 3 3.78251182050992 -0.782511820509925 23 2 3.39824407714158 -1.39824407714158 24 2 3.22210599244684 -1.22210599244684 25 4 3.05114540066010 0.948854599339896 26 4 3.78251182050992 0.217488179490076 27 3 2.9745925259783 0.0254074740216973 28 4 3.41682861058501 0.583171389414986 29 2 3.05114540066010 -1.05114540066010 30 4 3.55285319646452 0.447146803535479 31 4 3.30124761358264 0.698752386417358 32 5 3.36403776225465 1.63596223774535 33 5 2.8980396512965 2.1019603487035 34 4 3.05114540066010 0.948854599339896 35 4 3.83789141529429 0.162108584705710 36 4 4.01144075353503 -0.0114407535350267 37 2 3.16672639766248 -1.16672639766248 38 4 3.61155122872319 0.388448771276813 39 4 3.66693082350755 0.333069176492448 40 4 4.280127499901 -0.280127499901001 41 3 3.41682861058501 -0.416828610585014 42 2 2.9745925259783 -0.974592525978303 43 3 3.66434207705355 -0.664342077053553 44 4 2.8980396512965 1.10196034870350 45 3 2.77986990784013 0.22013009215987 46 2 3.05114540066010 -1.05114540066010 47 4 3.39824407714158 0.601755922858422 48 4 3.55134982650518 0.44865017349482 49 3 3.53499835404139 -0.534998354041386 50 4 3.43727219946215 0.562727800537851 51 3 3.05114540066010 -0.0511454006601039 52 4 2.8980396512965 1.10196034870350 53 2 2.07635763075508 -0.0763576307550847 54 4 3.41941735703901 0.580582642960986 55 4 2.99094399844210 1.00905600155790 56 4 3.62940607114632 0.370593928853678 57 4 3.05114540066010 0.948854599339896 58 3 3.33768698944921 -0.337686989449214 59 1 2.28484297490305 -1.28484297490305 60 3 3.14555311776504 -0.14555311776504 61 3 2.9745925259783 0.0254074740216973 62 4 3.14555311776504 0.85444688223496 63 2 2.8214867766147 -0.8214867766147 64 3 2.72449031305576 0.275509686944235 65 5 4.24260274753977 0.757397252460229 66 4 3.22469473890084 0.77530526109916 67 4 2.97459252597830 1.02540747402170 68 3 2.97200377952430 0.0279962204756967 69 4 2.8980396512965 1.10196034870350 70 2 3.22728348535484 -1.22728348535484 71 3 2.8980396512965 0.101960348703499 72 4 4.280127499901 -0.280127499901001 73 3 3.79886329297372 -0.798863292973719 74 4 3.66434207705355 0.335657922946447 75 4 2.66687765729176 1.33312234270824 76 3 3.09017352298067 -0.0901735229806749 77 3 3.29865886712864 -0.298658867128643 78 2 3.22210599244684 -1.22210599244684 79 4 3.55134982650518 0.44865017349482 80 3 3.02997212076267 -0.0299721207626679 81 2 2.72707905950976 -0.727079059509764 82 2 3.70595894582812 -1.70595894582812 83 3 3.78251182050992 -0.782511820509925 84 2 2.78245865429413 -0.78245865429413 85 2 3.05114540066010 -1.05114540066010 86 4 3.26372286122141 0.736277138778588 87 4 3.26113411476741 0.738865885232587 88 4 3.78251182050992 0.217488179490076 89 2 2.9745925259783 -0.974592525978303 90 2 3.55134982650518 -1.55134982650518 91 4 2.8954509048425 1.10454909515750 92 2 2.65052618482796 -0.650526184827963 93 3 3.09276226943467 -0.0927622694346742 94 3 3.22210599244684 -0.222105992446841 95 5 3.87541616765552 1.12458383234448 96 3 2.66687765729176 0.333122342708243 97 4 3.22469473890084 0.77530526109916 98 3 3.05114540066010 -0.0511454006601039 99 2 2.85901152897593 -0.85901152897593 100 4 3.05114540066010 0.948854599339896 101 3 3.09017352298067 -0.0901735229806749 102 3 2.9745925259783 0.0254074740216973 103 3 2.8980396512965 0.101960348703499 104 4 3.58778920237175 0.412210797628248 105 1 2.17185072435468 -1.17185072435468 106 3 2.9745925259783 0.0254074740216973 107 2 3.01879814120687 -1.01879814120687 108 3 3.30124761358264 -0.301247613582642 109 2 3.14555311776504 -1.14555311776504 110 2 2.55352972126903 -0.553529721269027 111 2 2.81998340665536 -0.81998340665536 112 4 2.57397331014616 1.42602668985384 113 5 4.22474790511664 0.775252094883364 114 5 2.64793743837396 2.35206256162604 115 3 2.9745925259783 0.0254074740216973 116 4 2.55611846772303 1.44388153227697 117 4 2.07894637720908 1.92105362279092 118 3 3.01211727833953 -0.0121172783395329 119 2 2.84266005651214 -0.842660056512136 120 4 3.95606115875066 0.0439388412493387 121 2 2.72707905950976 -0.727079059509764 122 3 2.61149806250739 0.388501937492608 123 2 3.26113411476741 -1.26113411476741 124 2 2.8980396512965 -0.898039651296502 125 2 2.68805093718919 -0.688050937189193 126 4 3.16672639766248 0.833273602337524 127 4 3.34027573590321 0.659724264096787 128 4 2.97459252597830 1.02540747402170 129 4 3.59037794882575 0.409622051174249 130 3 3.53499835404139 -0.534998354041386 131 2 2.9745925259783 -0.974592525978303 132 4 3.78251182050992 0.217488179490076 133 3 3.78251182050992 -0.782511820509925 134 2 2.8980396512965 -0.898039651296502 135 4 3.78251182050992 0.217488179490076 136 3 2.9006283977505 0.0993716022494993 137 3 3.05114540066010 -0.0511454006601039 138 3 2.9745925259783 0.0254074740216973 139 3 2.72966780596376 0.270332194036237 140 3 3.13437913820924 -0.134379138209244 141 4 3.62940607114632 0.370593928853678 142 5 3.84530196918193 1.15469803081807 143 2 3.01362064829887 -1.01362064829887 144 4 3.10911374189847 0.890886258101531 145 3 3.70854769228212 -0.708547692282123 146 3 2.36398459603885 0.636015403961147 147 1 2.47956559304123 -1.47956559304123 148 2 3.05114540066010 -1.05114540066010 149 4 2.80363193419157 1.19636806580843 150 4 2.81998340665536 1.18001659334464 151 5 4.03261403343246 0.967385966567537 152 2 2.80622068064556 -0.806220680645565 153 4 3.37521174181044 0.624788258189556 154 3 2.9745925259783 0.0254074740216973 155 2 3.34027573590321 -1.34027573590321 156 4 3.30124761358264 0.698752386417358 157 2 2.45688894318445 -0.456888943184449 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.478516808529534 0.957033617059067 0.521483191470466 10 0.699572051804781 0.600855896390437 0.300427948195219 11 0.780560893564702 0.438878212870595 0.219439106435298 12 0.768244334651571 0.463511330696857 0.231755665348429 13 0.875271962661018 0.249456074677964 0.124728037338982 14 0.90977637174767 0.18044725650466 0.09022362825233 15 0.88834616526325 0.223307669473501 0.111653834736751 16 0.870492803375496 0.259014393249007 0.129507196624504 17 0.839516689581751 0.320966620836498 0.160483310418249 18 0.783254306418867 0.433491387162267 0.216745693581134 19 0.726656408485754 0.546687183028493 0.273343591514246 20 0.660211848210979 0.679576303578042 0.339788151789021 21 0.660847588270224 0.678304823459552 0.339152411729776 22 0.606481242314824 0.787037515370353 0.393518757685176 23 0.590115278290767 0.819769443418466 0.409884721709233 24 0.619949318179881 0.760101363640239 0.380050681820119 25 0.642192163329236 0.715615673341527 0.357807836670764 26 0.594939606764986 0.810120786470027 0.405060393235014 27 0.535235464913179 0.929529070173642 0.464764535086821 28 0.506216372845769 0.987567254308462 0.493783627154231 29 0.537069153889378 0.925861692221244 0.462930846110622 30 0.573510510680005 0.85297897863999 0.426489489319995 31 0.580690575485696 0.838618849028608 0.419309424514304 32 0.657980565695803 0.684038868608393 0.342019434304197 33 0.908650861958864 0.182698276082271 0.0913491380411355 34 0.908266076530464 0.183467846939073 0.0917339234695364 35 0.886780727916799 0.226438544166402 0.113219272083201 36 0.862641423852392 0.274717152295215 0.137358576147608 37 0.886842904853328 0.226314190293343 0.113157095146672 38 0.860436524869458 0.279126950261084 0.139563475130542 39 0.830740036478442 0.338519927043115 0.169259963521558 40 0.79771761415709 0.404564771685819 0.202282385842909 41 0.767001447984225 0.465997104031551 0.232998552015775 42 0.766880912704316 0.466238174591367 0.233119087295684 43 0.74326116351356 0.513477672972881 0.256738836486440 44 0.781164077443932 0.437671845112136 0.218835922556068 45 0.747904851060334 0.504190297879333 0.252095148939666 46 0.762661150139035 0.47467769972193 0.237338849860965 47 0.73908513907384 0.52182972185232 0.26091486092616 48 0.702632362957381 0.594735274085238 0.297367637042619 49 0.674812173905653 0.650375652188694 0.325187826094347 50 0.646777248494002 0.706445503011995 0.353222751505998 51 0.598483745067876 0.803032509864247 0.401516254932124 52 0.625391459057925 0.74921708188415 0.374608540942075 53 0.579830328944867 0.840339342110265 0.420169671055133 54 0.545669462891495 0.90866107421701 0.454330537108505 55 0.542212335675389 0.915575328649223 0.457787664324611 56 0.50598768754051 0.98802462491898 0.49401231245949 57 0.51225637394826 0.97548725210348 0.48774362605174 58 0.466837074967294 0.933674149934589 0.533162925032705 59 0.541974097130315 0.91605180573937 0.458025902869685 60 0.493972016016417 0.987944032032835 0.506027983983583 61 0.445477687859766 0.890955375719532 0.554522312140234 62 0.447618843646286 0.895237687292571 0.552381156353714 63 0.440831037734451 0.881662075468902 0.559168962265549 64 0.400882215253698 0.801764430507397 0.599117784746302 65 0.397559041866031 0.795118083732062 0.602440958133969 66 0.383459154389234 0.766918308778468 0.616540845610766 67 0.399251196884878 0.798502393769756 0.600748803115122 68 0.354464382014967 0.708928764029934 0.645535617985033 69 0.37985019466884 0.75970038933768 0.62014980533116 70 0.437905199823253 0.875810399646507 0.562094800176747 71 0.392299320940243 0.784598641880486 0.607700679059757 72 0.352293967569652 0.704587935139303 0.647706032430349 73 0.34712513870828 0.69425027741656 0.65287486129172 74 0.310781580130204 0.621563160260407 0.689218419869796 75 0.362378445684524 0.724756891369049 0.637621554315476 76 0.319356808447107 0.638713616894214 0.680643191552893 77 0.283300405288826 0.566600810577651 0.716699594711174 78 0.321851423751779 0.643702847503558 0.678148576248221 79 0.291059779450706 0.582119558901411 0.708940220549295 80 0.253275024400289 0.506550048800579 0.74672497559971 81 0.244351734330951 0.488703468661902 0.755648265669049 82 0.351224131811136 0.702448263622273 0.648775868188864 83 0.341637645416435 0.683275290832869 0.658362354583565 84 0.335701150201324 0.671402300402648 0.664298849798676 85 0.358114743350772 0.716229486701544 0.641885256649228 86 0.347211491902511 0.694422983805023 0.652788508097489 87 0.337073240768094 0.674146481536188 0.662926759231906 88 0.298166686522728 0.596333373045457 0.701833313477272 89 0.30852526903345 0.6170505380669 0.69147473096655 90 0.403136734160616 0.806273468321232 0.596863265839384 91 0.436304403286227 0.872608806572455 0.563695596713773 92 0.412238897217148 0.824477794434295 0.587761102782853 93 0.367113806244687 0.734227612489374 0.632886193755313 94 0.325254368996299 0.650508737992598 0.674745631003701 95 0.349558824738267 0.699117649476534 0.650441175261733 96 0.317927959281961 0.635855918563922 0.682072040718039 97 0.313106220215192 0.626212440430383 0.686893779784808 98 0.271719176708363 0.543438353416726 0.728280823291637 99 0.265633691472607 0.531267382945215 0.734366308527393 100 0.270002741131279 0.540005482262559 0.72999725886872 101 0.231443931650196 0.462887863300392 0.768556068349804 102 0.195678467407945 0.391356934815890 0.804321532592055 103 0.164652391764419 0.329304783528838 0.835347608235581 104 0.144129921653128 0.288259843306255 0.855870078346872 105 0.162573636733919 0.325147273467838 0.837426363266081 106 0.133791883418128 0.267583766836256 0.866208116581872 107 0.148599568030554 0.297199136061108 0.851400431969446 108 0.123657803260759 0.247315606521517 0.876342196739241 109 0.134110664532346 0.268221329064693 0.865889335467654 110 0.119995857836527 0.239991715673054 0.880004142163473 111 0.116161724073133 0.232323448146267 0.883838275926867 112 0.164494776612278 0.328989553224556 0.835505223387722 113 0.153006333726771 0.306012667453541 0.84699366627323 114 0.490404398897513 0.980808797795025 0.509595601102487 115 0.439381482237435 0.87876296447487 0.560618517762565 116 0.513323613650873 0.973352772698253 0.486676386349127 117 0.83886388646353 0.32227222707294 0.16113611353647 118 0.8128053020516 0.374389395896801 0.187194697948401 119 0.786819161717192 0.426361676565616 0.213180838282808 120 0.744550375205665 0.51089924958867 0.255449624794335 121 0.711509073442543 0.576981853114914 0.288490926557457 122 0.681053678082917 0.637892643834167 0.318946321917083 123 0.68436680340694 0.631266393186121 0.315633196593061 124 0.65495541313343 0.690089173733139 0.345044586866569 125 0.644310836396074 0.711378327207853 0.355689163603926 126 0.651380011786689 0.697239976426623 0.348619988213311 127 0.638289798638437 0.723420402723125 0.361710201361563 128 0.716684175536015 0.56663164892797 0.283315824463985 129 0.664317821510782 0.671364356978435 0.335682178489218 130 0.64226638926656 0.715467221466879 0.357733610733440 131 0.621088869934563 0.757822260130875 0.378911130065437 132 0.553176344118875 0.89364731176225 0.446823655881125 133 0.597149550747423 0.805700898505155 0.402850449252577 134 0.5445755807565 0.910848838487 0.4554244192435 135 0.474316721188373 0.948633442376747 0.525683278811627 136 0.415346516010257 0.830693032020514 0.584653483989743 137 0.342274581821334 0.684549163642667 0.657725418178666 138 0.277347193606545 0.554694387213089 0.722652806393455 139 0.228488327468749 0.456976654937499 0.77151167253125 140 0.184861908683887 0.369723817367774 0.815138091316113 141 0.176974519404651 0.353949038809302 0.82302548059535 142 0.182597227441929 0.365194454883857 0.817402772558071 143 0.131544370816265 0.263088741632530 0.868455629183735 144 0.109943167222918 0.219886334445836 0.890056832777082 145 0.0741942899200113 0.148388579840023 0.925805710079989 146 0.123552961809527 0.247105923619054 0.876447038190473 147 0.0776491481155255 0.155298296231051 0.922350851884474 148 0.0988286351840017 0.197657270368003 0.901171364815998 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:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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