Multiple Linear Regression - Celebrity 1

*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, 14 Dec 2010 13:02:24 +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/14/t1292331660w0w02thaiwqhhpa.htm/, Retrieved Tue, 14 Dec 2010 14:01:04 +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/14/t1292331660w0w02thaiwqhhpa.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 «

6 2 1 1 3 73 62 66 4 1 1 1 1 58 54 54 5 1 1 1 3 68 41 82 4 1 1 1 3 62 49 61 4 1 1 2 3 65 49 65 6 1 1 1 3 81 72 77 6 1 1 1 1 73 78 66 4 2 1 4 3 64 58 66 4 1 1 1 3 68 58 66 6 1 1 1 1 51 23 48 4 1 1 1 1 68 39 57 6 1 1 1 3 61 63 80 5 1 1 1 1 69 46 60 4 1 1 3 3 73 58 70 6 2 1 1 3 61 39 85 3 2 1 1 1 62 44 59 5 1 1 1 1 63 49 72 6 1 1 6 1 69 57 70 4 2 1 1 3 47 76 74 6 2 1 1 1 66 63 70 2 1 1 1 3 58 18 51 7 2 1 1 3 63 40 70 5 1 1 1 1 69 59 71 2 2 1 1 3 59 62 72 4 1 1 1 1 59 70 50 4 2 1 1 4 63 65 69 6 2 1 1 3 65 56 73 6 1 1 1 3 65 45 66 5 2 1 1 3 71 57 73 6 1 1 4 3 60 50 58 6 2 1 1 1 81 40 78 4 1 1 1 3 67 58 83 6 2 1 1 3 66 49 76 6 1 1 1 3 62 49 77 6 1 1 1 3 63 27 79 2 2 1 1 1 73 51 71 4 2 1 1 3 55 75 79 5 1 1 1 1 59 65 60 3 1 1 1 2 64 47 73 7 2 1 1 3 63 49 70 5 1 1 1 1 64 65 42 3 1 1 1 1 73 61 74 8 1 1 1 3 54 46 68 8 1 1 1 3 76 69 83 5 2 1 2 1 74 55 62 6 2 1 1 3 63 78 79 3 2 1 1 3 73 58 61 5 2 1 1 3 67 34 86 4 2 1 2 3 68 67 64 5 1 1 4 3 66 45 75 5 2 1 1 1 62 68 59 6 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 7 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Celebrity[t] = + 1.43920785893858 -0.478161596531039Gender[t] + 1.68226050071978Age[t] + 0.00423606441239899Raised[t] + 0.132214711993717Marital[t] + 0.00306708618950928NV[t] + 0.00539714070616665ANX[t] + 0.0275617336070562GR[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) 1.43920785893858 1.626275 0.885 0.377711 0.188855 Gender -0.478161596531039 0.238367 -2.006 0.046812 0.023406 Age 1.68226050071978 1.006219 1.6719 0.096817 0.048409 Raised 0.00423606441239899 0.133859 0.0316 0.9748 0.4874 Marital 0.132214711993717 0.124442 1.0625 0.289884 0.144942 NV 0.00306708618950928 0.016603 0.1847 0.85371 0.426855 ANX 0.00539714070616665 0.009252 0.5834 0.560606 0.280303 GR 0.0275617336070562 0.013187 2.09 0.038449 0.019224 Multiple Linear Regression - Regression Statistics Multiple R 0.300778597585664 R-squared 0.0904677647655988 Adjusted R-squared 0.0443320716739987 F-TEST (value) 1.96090615970545 F-TEST (DF numerator) 7 F-TEST (DF denominator) 138 p-value 0.0646904918120191 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.36325856776735 Sum Squared Residuals 256.469401317569 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6 4.94361980067204 1.05638019932796 2 4 4.737427751439 -0.737427751439003 3 5 5.73409374913894 -0.734093749138936 4 4 5.18007195190303 -1.18007195190303 5 4 5.30375620931218 -1.30375620931218 6 6 5.80346856345844 0.196531436541558 7 6 5.24370622451432 0.756293775485685 8 4 4.90713565537899 -0.90713565537899 9 4 5.38485740343087 -1.38485740343087 10 6 4.38327638457893 1.61672361542107 11 4 4.76982670356276 -0.769826703562764 12 6 5.77623777413393 0.223762225866075 13 5 4.89335897551661 0.106641024483392 14 4 5.51891189763144 -1.51891189763144 15 6 5.30635346869017 0.693646531309833 16 3 4.35537176063961 -1.35537176063961 17 5 5.22188868378273 -0.221888683782726 18 6 5.249525181417 0.750474818583002 19 4 5.15992939848759 -1.15992939848759 20 6 4.77336484849244 1.22663515150756 21 2 4.72487490918327 -2.72487490918327 22 7 4.90445877766951 2.09554122233049 23 5 5.26670087437439 -0.266700874374392 24 2 5.06605099566125 -3.06605099566125 25 4 4.71660215449895 -0.716602154498953 26 4 5.14404027371034 -1.14404027371034 27 6 5.07963240216836 0.920367597831637 28 6 5.30549331568218 0.694506684317824 29 5 5.10343206001159 -0.103432060011586 30 6 5.10935791264621 0.89064208735379 31 6 4.91573077394969 1.08426922605031 32 4 5.85033978856132 -1.85033978856132 33 6 5.12760470423587 0.872395295764125 34 6 5.62105968961593 0.378940310384068 35 6 5.56051314748389 0.439486852516112 36 2 4.75763049695206 -2.75763049695206 37 4 5.31687761533277 -1.31687761533277 38 5 4.96523378703868 0.0347662129613183 39 3 5.37393793416068 -2.37393793416068 40 7 4.95303304402501 2.04696695597499 41 5 4.48445801305922 0.515541986940783 42 3 5.37244870136593 -2.37244870136593 43 8 5.33227597551785 2.66772402448215 44 8 5.93731211203473 2.06268788796527 45 5 4.53846660791513 0.461533392084873 46 6 5.35760572696735 0.642394273032652 47 3 4.7842225698121 -1.7842225698121 48 5 5.32533201590345 -0.325332015903446 49 4 4.90438267045362 -0.904382670453618 50 5 5.56932419757239 -0.569324197572388 51 5 4.48490313758761 0.515096862412386 52 6 5.32101873006295 0.678981269937045 53 5 4.88901010491383 0.110989895086174 54 6 5.3001427534775 0.699857246522498 55 6 5.12450927061897 0.875490729381035 56 4 4.63906759486418 -0.63906759486418 57 8 5.80589164326143 2.19410835673857 58 6 4.54571079834806 1.45428920165194 59 4 4.67753466745255 -0.67753466745255 60 6 4.50093355810949 1.49906644189051 61 5 4.37818564984906 0.621814350150941 62 5 5.55894605885185 -0.558946058851848 63 6 5.40929806270017 0.590701937299834 64 6 5.55862405565859 0.44137594434141 65 6 4.82384960448203 1.17615039551797 66 6 4.49892097038312 1.50107902961688 67 6 4.73366983751221 1.26633016248779 68 6 4.97160134201094 1.02839865798906 69 7 4.86568773417053 2.13431226582947 70 4 5.1818882881658 -1.1818882881658 71 4 5.3526141629817 -1.3526141629817 72 3 4.59586116947693 -1.59586116947693 73 6 5.14983727344706 0.850162726552943 74 5 5.35898171795395 -0.358981717953955 75 5 5.21272946731273 -0.212729467312726 76 3 5.08089440567759 -2.08089440567759 77 5 5.08472402213396 -0.0847240221339615 78 4 4.45029572083981 -0.450295720839812 79 3 5.08401255010695 -2.08401255010695 80 7 5.56798631582375 1.43201368417625 81 4 4.79056872697555 -0.790568726975553 82 4 5.31718563036399 -1.31718563036399 83 5 5.49094906704222 -0.490949067042221 84 6 5.13189131621833 0.868108683781672 85 2 5.32136273460742 -3.32136273460742 86 2 4.12673566808075 -2.12673566808075 87 6 5.87524946445846 0.124750535541543 88 4 4.42023047439995 -0.420230474399951 89 5 5.16767270159717 -0.167672701597171 90 6 4.78653146936923 1.21346853063077 91 7 5.29398264688672 1.70601735311328 92 8 4.98683845775011 3.01316154224989 93 6 5.037627994834 0.962372005165996 94 6 5.03553791196347 0.96446208803653 95 3 4.85297880128706 -1.85297880128706 96 7 4.78696714213855 2.21303285786145 97 3 5.29676883354378 -2.29676883354378 98 6 4.77808216907332 1.22191783092668 99 4 4.60287726723866 -0.602877267238663 100 4 5.56751407579659 -1.56751407579658 101 6 5.36903896769344 0.630961032306563 102 6 5.40459884147673 0.595401158523274 103 6 6.22937236088053 -0.229372360880531 104 4 4.9895888306684 -0.989588830668399 105 7 6.77062763911947 0.229372360880531 106 5 5.43352469507271 -0.433524695072706 107 7 5.57143715315705 1.42856284684295 108 4 5.49346927291676 -1.49346927291676 109 6 4.9304892363833 1.06951076361671 110 6 5.90144715312863 0.0985528468713707 111 6 4.51617091669793 1.48382908330207 112 5 4.32266275137232 0.677337248627681 113 5 5.40656492575364 -0.406564925753638 114 6 5.51152385264879 0.488476147351206 115 7 5.28626074158593 1.71373925841407 116 4 4.67391219547654 -0.673912195476545 117 4 5.49452830778287 -1.49452830778287 118 8 5.51392188347574 2.48607811652426 119 6 5.06163546175183 0.938364538248175 120 3 4.86211208354529 -1.86211208354529 121 4 5.31758343674462 -1.31758343674462 122 5 5.18953177375749 -0.189531773757492 123 5 5.13830596036187 -0.138305960361872 124 6 5.14280506779856 0.857194932201442 125 8 5.4698726587687 2.5301273412313 126 2 4.69334357637887 -2.69334357637887 127 4 4.36374296224895 -0.363742962248955 128 7 5.50061142192204 1.49938857807796 129 5 5.27057737323336 -0.270577373233362 130 6 5.42370058507718 0.576299414922816 131 6 5.51150774476203 0.488492255237968 132 4 5.4649674639417 -1.4649674639417 133 5 4.76121092682954 0.238789073170465 134 6 5.2031345780734 0.796865421926596 135 6 5.96222178793187 0.0377782120681267 136 6 5.23733735653841 0.76266264346159 137 6 5.15908840099119 0.840911599008806 138 5 5.61238347793582 -0.612383477935819 139 5 4.64644581352182 0.353554186478179 140 6 4.9443563216751 1.0556436783249 141 4 5.34270715007612 -1.34270715007612 142 6 5.30284125797226 0.69715874202774 143 3 5.63089966464894 -2.63089966464894 144 6 5.1777625416761 0.822237458323896 145 8 5.43641467177882 2.56358532822118 146 4 5.36425989916202 -1.36425989916202 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.579406030294893 0.841187939410214 0.420593969705107 12 0.423506637212798 0.847013274425597 0.576493362787202 13 0.281324238318835 0.56264847663767 0.718675761681165 14 0.194714125243897 0.389428250487795 0.805285874756103 15 0.133369214391858 0.266738428783716 0.866630785608142 16 0.325540467694169 0.651080935388337 0.674459532305831 17 0.239014274733932 0.478028549467864 0.760985725266068 18 0.24887799622028 0.49775599244056 0.75112200377972 19 0.203170982755861 0.406341965511721 0.79682901724414 20 0.159448900712008 0.318897801424016 0.840551099287992 21 0.163552537222012 0.327105074444025 0.836447462777988 22 0.306931394977099 0.613862789954199 0.6930686050229 23 0.254600794848086 0.509201589696173 0.745399205151914 24 0.489582365727334 0.979164731454667 0.510417634272666 25 0.42022941192008 0.840458823840159 0.57977058807992 26 0.357086877032824 0.714173754065649 0.642913122967176 27 0.333474565506121 0.666949131012241 0.666525434493879 28 0.348239282020011 0.696478564040022 0.651760717979989 29 0.286988507076911 0.573977014153823 0.713011492923089 30 0.352041984479122 0.704083968958245 0.647958015520878 31 0.303044359349893 0.606088718699787 0.696955640650107 32 0.320386014855599 0.640772029711199 0.6796139851444 33 0.288293211232051 0.576586422464102 0.711706788767949 34 0.259164270498607 0.518328540997213 0.740835729501393 35 0.217065102702245 0.434130205404489 0.782934897297755 36 0.470378980171835 0.94075796034367 0.529621019828165 37 0.43886177669713 0.87772355339426 0.56113822330287 38 0.388227563172261 0.776455126344523 0.611772436827739 39 0.483571059254362 0.967142118508723 0.516428940745638 40 0.575872929874972 0.848254140250055 0.424127070125028 41 0.546201820198553 0.907596359602894 0.453798179801447 42 0.630239682411218 0.739520635177564 0.369760317588782 43 0.793380632638283 0.413238734723433 0.206619367361717 44 0.85210644825024 0.295787103499518 0.147893551749759 45 0.821657274692773 0.356685450614454 0.178342725307227 46 0.795765653183664 0.408468693632673 0.204234346816336 47 0.810051896923672 0.379896206152656 0.189948103076328 48 0.775093789192418 0.449812421615164 0.224906210807582 49 0.746560899588465 0.506878200823069 0.253439100411535 50 0.709947702284338 0.580104595431324 0.290052297715662 51 0.672719044416778 0.654561911166444 0.327280955583222 52 0.632990018063212 0.734019963873576 0.367009981936788 53 0.583656511719199 0.832686976561602 0.416343488280801 54 0.548949381022314 0.902101237955372 0.451050618977686 55 0.523006348312241 0.953987303375519 0.476993651687759 56 0.479349409855191 0.958698819710381 0.520650590144809 57 0.553718885292168 0.892562229415664 0.446281114707832 58 0.55484235694602 0.89031528610796 0.44515764305398 59 0.513015551537808 0.973968896924385 0.486984448462193 60 0.523124757155617 0.953750485688767 0.476875242844383 61 0.494204394379852 0.988408788759704 0.505795605620148 62 0.450009726528115 0.90001945305623 0.549990273471885 63 0.410375608653491 0.820751217306982 0.589624391346509 64 0.368508185257597 0.737016370515194 0.631491814742403 65 0.356872095379167 0.713744190758334 0.643127904620833 66 0.366144454474286 0.732288908948572 0.633855545525714 67 0.355634679228313 0.711269358456627 0.644365320771687 68 0.340818187001408 0.681636374002817 0.659181812998592 69 0.405801062290079 0.811602124580158 0.594198937709921 70 0.393813251794603 0.787626503589206 0.606186748205397 71 0.390636586197268 0.781273172394537 0.609363413802732 72 0.404641919245441 0.809283838490883 0.595358080754559 73 0.376238080406318 0.752476160812635 0.623761919593682 74 0.332623656339248 0.665247312678497 0.667376343660752 75 0.289705936231644 0.579411872463287 0.710294063768356 76 0.339097243172347 0.678194486344695 0.660902756827653 77 0.294811810548675 0.589623621097351 0.705188189451325 78 0.257520213396646 0.515040426793292 0.742479786603354 79 0.307150428584283 0.614300857168566 0.692849571415717 80 0.30826999596925 0.6165399919385 0.69173000403075 81 0.279348379338456 0.558696758676912 0.720651620661544 82 0.275492618021311 0.550985236042623 0.724507381978689 83 0.246334013238421 0.492668026476841 0.75366598676158 84 0.224248121023797 0.448496242047594 0.775751878976203 85 0.450162251277201 0.900324502554402 0.549837748722799 86 0.537983486566725 0.92403302686655 0.462016513433275 87 0.487766806303713 0.975533612607425 0.512233193696287 88 0.445274640177503 0.890549280355007 0.554725359822497 89 0.398305324493831 0.796610648987662 0.601694675506169 90 0.376328395071261 0.752656790142522 0.623671604928739 91 0.408335880092589 0.816671760185178 0.591664119907411 92 0.614710663384264 0.770578673231473 0.385289336615736 93 0.595754055184343 0.808491889631315 0.404245944815657 94 0.572151086189437 0.855697827621127 0.427848913810563 95 0.58562263126071 0.82875473747858 0.41437736873929 96 0.682566327072551 0.634867345854898 0.317433672927449 97 0.752265807479875 0.495468385040249 0.247734192520124 98 0.731748646729818 0.536502706540365 0.268251353270182 99 0.69534824245669 0.60930351508662 0.30465175754331 100 0.703157337224089 0.593685325551822 0.296842662775911 101 0.660348261876703 0.679303476246594 0.339651738123297 102 0.618390286186248 0.763219427627504 0.381609713813752 103 0.578373829002141 0.843252341995718 0.421626170997859 104 0.58629686409344 0.82740627181312 0.41370313590656 105 0.529852642930383 0.940294714139234 0.470147357069617 106 0.486178858318113 0.972357716636226 0.513821141681887 107 0.504016311766944 0.991967376466112 0.495983688233056 108 0.540934983410975 0.91813003317805 0.459065016589025 109 0.510431735206007 0.979136529587985 0.489568264793993 110 0.451358655756301 0.902717311512602 0.548641344243699 111 0.475036395237248 0.950072790474496 0.524963604762752 112 0.438659969789092 0.877319939578185 0.561340030210908 113 0.410093786617131 0.820187573234263 0.589906213382869 114 0.360872161247105 0.721744322494211 0.639127838752894 115 0.342220914540049 0.684441829080099 0.657779085459951 116 0.292976362435016 0.585952724870033 0.707023637564984 117 0.371974453916266 0.743948907832532 0.628025546083734 118 0.470171855533086 0.940343711066171 0.529828144466914 119 0.529816358820859 0.940367282358282 0.470183641179141 120 0.539409209724829 0.921181580550343 0.460590790275171 121 0.640789280515944 0.718421438968111 0.359210719484056 122 0.573124180797075 0.85375163840585 0.426875819202925 123 0.547541776714514 0.904916446570972 0.452458223285486 124 0.474765129579865 0.949530259159731 0.525234870420135 125 0.539293097219562 0.921413805560877 0.460706902780438 126 0.742975627683427 0.514048744633147 0.257024372316573 127 0.785989084395947 0.428021831208107 0.214010915604053 128 0.758960438424313 0.482079123151375 0.241039561575687 129 0.672078158259681 0.655843683480638 0.327921841740319 130 0.61932885011038 0.76134229977924 0.38067114988962 131 0.519596002760921 0.960807994478158 0.480403997239079 132 0.916802484029358 0.166395031941285 0.0831975159706423 133 0.843835578960107 0.312328842079786 0.156164421039893 134 0.728798552689814 0.542402894620372 0.271201447310186 135 0.782287233424678 0.435425533150645 0.217712766575322 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 = 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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