WS 10 - Multiple regression

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 11 Dec 2010 15:55:17 +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/11/t12920828190l47edivypr80ly.htm/, Retrieved Sat, 11 Dec 2010 16:53:42 +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/11/t12920828190l47edivypr80ly.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2 24 14 11 12 24 26 2 25 11 7 8 25 23 2 17 6 17 8 30 25 1 18 12 10 8 19 23 2 18 8 12 9 22 19 2 16 10 12 7 22 29 2 20 10 11 4 25 25 2 16 11 11 11 23 21 2 18 16 12 7 17 22 2 17 11 13 7 21 25 1 23 13 14 12 19 24 2 30 12 16 10 19 18 1 23 8 11 10 15 22 2 18 12 10 8 16 15 2 15 11 11 8 23 22 1 12 4 15 4 27 28 1 21 9 9 9 22 20 2 15 8 11 8 14 12 1 20 8 17 7 22 24 2 31 14 17 11 23 20 1 27 15 11 9 23 21 2 34 16 18 11 21 20 2 21 9 14 13 19 21 2 31 14 10 8 18 23 1 19 11 11 8 20 28 2 16 8 15 9 23 24 1 20 9 15 6 25 24 2 21 9 13 9 19 24 2 22 9 16 9 24 23 1 17 9 13 6 22 23 2 24 10 9 6 25 29 1 25 16 18 16 26 24 2 26 11 18 5 29 18 2 25 8 12 7 32 25 1 17 9 17 9 25 21 1 32 16 9 6 29 26 1 33 11 9 6 28 22 1 13 16 12 5 17 22 2 32 12 18 12 28 22 1 25 12 12 7 29 23 1 29 14 18 10 26 30 2 22 9 14 9 25 23 1 18 10 15 8 14 17 1 17 9 16 5 25 23 2 20 10 10 8 26 23 2 15 12 11 8 20 25 2 20 14 14 10 18 24 2 33 14 9 6 32 24 2 29 10 12 8 25 23 1 23 14 17 7 25 21 2 26 16 5 4 23 24 1 18 9 12 8 21 2 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 7 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation COM[t] = -1.76493979259821 -0.131393212690802G[t] + 0.812849739916337DA[t] + 0.24845330662011PE[t] + 0.190333948740538PC[t] + 0.56590043905433PS[t] -0.115683772583743`O `[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) -1.76493979259821 3.278744 -0.5383 0.591159 0.29558 G -0.131393212690802 0.744476 -0.1765 0.860143 0.430072 DA 0.812849739916337 0.131658 6.1739 0 0 PE 0.24845330662011 0.134124 1.8524 0.065905 0.032953 PC 0.190333948740538 0.169107 1.1255 0.262141 0.13107 PS 0.56590043905433 0.096123 5.8873 0 0 `O ` -0.115683772583743 0.103352 -1.1193 0.26477 0.132385 Multiple Linear Regression - Regression Statistics Multiple R 0.638198057370523 R-squared 0.407296760431509 Adjusted R-squared 0.383900579922227 F-TEST (value) 17.4086860147926 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 2.77555756156289e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.49195510423555 Sum Squared Residuals 3067.00442008711 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 24.9429963486832 -0.942996348683151 2 25 21.6622498642971 3.33775013570285 3 17 22.6806688810207 -5.68066888102073 4 18 19.9564501024386 -1.95645010243863 5 18 19.4213348995612 -1.42133489956121 6 16 19.5095287560754 -3.50952875607538 7 20 20.8505100107316 -0.850510010731612 8 16 22.326631604058 -6.32663160405803 9 18 22.3669114083879 -4.36691140838794 10 17 20.4676664538925 -3.46766645389246 11 23 22.4087650912138 0.591234908786182 12 30 22.2748634898683 7.72513651013172 13 23 15.1862543632409 7.8137456367591 14 18 19.0528257532548 -1.05282575325478 15 15 21.6399459852527 -6.63994598525267 16 12 17.8833675707623 -5.88336757076227 17 21 19.5045341597243 1.49546584027573 18 15 15.2651305398521 -0.265130539852111 19 20 19.8359078849528 0.164092115047235 20 31 26.3715844361114 4.62841556388856 21 27 25.3287558789331 1.6712441210669 22 34 27.1139363444556 6.88606365554444 23 21 19.5633581853494 1.43664181465056 24 31 20.8848559305262 10.1151440694738 25 19 19.379535245278 -0.379535245278024 26 16 20.1541763955572 -4.15417639555715 27 20 21.6592183800513 -1.65921838005134 28 21 18.2065177660159 2.79348223398405 29 22 21.8970636537317 0.10293634626833 30 17 19.5802942222319 -2.58029422223187 31 24 20.2715362046375 3.7284637953625 32 25 30.5637664057857 -5.56376640578574 33 26 26.6662550100328 -0.666255010032776 34 25 24.005568757121 0.994431242879022 35 17 23.0741781572644 -6.0741781572644 36 32 27.8906809307949 4.10931906920513 37 33 23.7232668824938 9.27673311750617 38 13 22.1176367235977 -9.11763672359766 39 32 27.7828068617436 4.21719313825642 40 25 25.9220271574816 -0.922027157481621 41 29 27.1019605980074 1.89803940199262 42 22 21.9660574795458 0.0339425204542188 43 18 17.4376175959373 0.562382404062688 44 17 21.8330215105146 -4.83302151051465 45 20 22.1606604832955 -2.16066048329547 46 15 20.4080430902548 -5.40804309025479 47 20 22.1436532819039 -2.14365328190395 48 33 28.0626571006019 4.93734289939812 49 29 22.0916666574814 6.90833334251864 50 23 26.757758959365 -3.757758959365 51 26 23.2207715049841 2.77922849501594 52 18 19.0309246014548 -1.03092460145476 53 20 18.8151388119818 1.1848611880182 54 11 11.7389940806761 -0.738994080676097 55 28 29.0393609676901 -1.03936096769014 56 26 23.2702128026736 2.72978719732642 57 22 22.1948320062007 -0.19483200620072 58 17 20.1319892269372 -3.13198922693724 59 12 15.5047881422787 -3.50478814227875 60 14 20.9892502421717 -6.98925024217172 61 17 20.8032760947745 -3.80327609477455 62 21 21.4092610676731 -0.409261067673123 63 19 22.8796194998407 -3.87961949984067 64 18 23.0451523878524 -5.0451523878524 65 10 17.8768088703137 -7.87680887031365 66 29 24.3051640702463 4.69483592975366 67 31 18.4041287812818 12.5958712187182 68 19 23.0218318601521 -4.02183186015208 69 9 20.0258711870156 -11.0258711870156 70 20 22.5560887583009 -2.55608875830091 71 28 17.693208018911 10.306791981089 72 19 18.0795212927468 0.920478707253165 73 30 22.9992603465233 7.00073965347668 74 29 27.2172293775875 1.78277062241254 75 26 21.5435346074676 4.45646539253241 76 23 19.4935320073772 3.50646799262281 77 13 22.7158817249009 -9.71588172490094 78 21 22.5912216095481 -1.59122160954806 79 19 21.5259492231535 -2.5259492231535 80 28 23.0193787918113 4.98062120818873 81 23 25.6408449436037 -2.64084494360373 82 18 13.8489527737008 4.15104722629917 83 21 20.6861005821919 0.313899417808097 84 20 21.8561577417173 -1.85615774171726 85 23 19.9201128197837 3.0798871802163 86 21 20.7628097072822 0.237190292717798 87 21 21.853821383801 -0.853821383801027 88 15 22.7718021836753 -7.77180218367526 89 28 27.1006677069301 0.899332293069894 90 19 17.6054967414737 1.39450325852634 91 26 21.1970849453685 4.80291505463146 92 10 13.1418504270284 -3.14185042702844 93 16 17.0609511188811 -1.06095111888111 94 22 21.1057086804488 0.89429131955115 95 19 18.6846946618737 0.315305338126302 96 31 28.7033339676536 2.29666603234641 97 31 25.1610363575753 5.83896364242467 98 29 24.7500373008633 4.24996269913666 99 19 17.4899406533025 1.51005934669754 100 22 18.9729451937469 3.02705480625307 101 23 22.3172611418816 0.68273885811841 102 15 16.2398076637836 -1.23980766378358 103 20 21.3789421742014 -1.37894217420141 104 18 19.5754702240473 -1.57547022404732 105 23 21.9516753772336 1.04832462276643 106 25 21.0532703452311 3.94672965476892 107 21 16.5115261777901 4.48847382220993 108 24 19.569398880701 4.43060111929903 109 25 25.3244868239239 -0.324486823923948 110 17 19.5347608742898 -2.53476087428981 111 13 14.5134634896455 -1.51346348964548 112 28 18.1441293531272 9.85587064687278 113 21 20.0727599827069 0.92724001729313 114 25 28.1993393624112 -3.19933936241119 115 9 20.6810580737745 -11.6810580737745 116 16 17.8955263219369 -1.89552632193692 117 19 21.1236881841702 -2.12368818417025 118 17 19.4117214751196 -2.41172147511961 119 25 24.4653743960008 0.53462560399916 120 20 15.5153998331406 4.48460016685943 121 29 21.5824982809731 7.41750171902693 122 14 18.9967653443087 -4.99676534430871 123 22 26.8737091669435 -4.87370916694351 124 15 15.5337097000078 -0.533709700007815 125 19 25.4092467019303 -6.40924670193028 126 20 21.8831811742809 -1.88318117428092 127 15 17.5257328923904 -2.52573289239038 128 20 21.743111333972 -1.74311133397203 129 18 20.1682541454936 -2.16825414549357 130 33 25.4291452044134 7.57085479558655 131 22 23.8678831867946 -1.86788318679461 132 16 16.5484737239343 -0.548473723934336 133 17 18.9805095688634 -1.98050956886341 134 16 15.1293616021367 0.870638397863306 135 21 17.1299559186832 3.87004408131681 136 26 27.5800944393104 -1.5800944393104 137 18 21.2325898758653 -3.23258987586534 138 18 23.1807825749856 -5.18078257498559 139 17 18.2770155975882 -1.27701559758816 140 22 24.70965448444 -2.70965448444001 141 30 24.8287859338627 5.17121406613726 142 30 27.2226794834565 2.7773205165435 143 24 29.9801931815366 -5.98019318153662 144 21 21.9633614489398 -0.963361448939817 145 21 25.4587603637184 -4.45876036371842 146 29 27.3557609984031 1.64423900159689 147 31 23.1741524897411 7.82584751025892 148 20 19.0548724364291 0.945127563570916 149 16 14.2688752190188 1.73112478098117 150 22 18.9924840235404 3.00751597645964 151 20 20.2765822914909 -0.276582291490852 152 28 27.2809941118217 0.719005888178254 153 38 26.6511545416438 11.3488454583562 154 22 19.2721744974194 2.72782550258065 155 20 25.6249634727582 -5.62496347275816 156 17 17.9825672375456 -0.98256723754556 157 28 24.4130280988885 3.58697190111148 158 22 24.0742261499925 -2.07422614999253 159 31 26.050457638561 4.94954236143896 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.21446582796536 0.428931655930719 0.78553417203464 11 0.266390871111418 0.532781742222835 0.733609128888583 12 0.747268877478755 0.505462245042491 0.252731122521245 13 0.753242879881103 0.493514240237795 0.246757120118897 14 0.718039245412714 0.563921509174571 0.281960754587286 15 0.717582802361752 0.564834395276496 0.282417197638248 16 0.661407828618651 0.677184342762698 0.338592171381349 17 0.573685042004039 0.852629915991921 0.426314957995961 18 0.526167610431409 0.947664779137182 0.473832389568591 19 0.445270221087069 0.890540442174139 0.554729778912931 20 0.463058273035713 0.926116546071425 0.536941726964287 21 0.38395578347535 0.7679115669507 0.61604421652465 22 0.389846251555143 0.779692503110286 0.610153748444857 23 0.317797521517856 0.635595043035711 0.682202478482144 24 0.628274983438163 0.743450033123674 0.371725016561837 25 0.558828847803692 0.882342304392616 0.441171152196308 26 0.516250296771878 0.967499406456244 0.483749703228122 27 0.449047674408909 0.898095348817819 0.550952325591091 28 0.414043670443754 0.828087340887508 0.585956329556246 29 0.354055764264676 0.708111528529352 0.645944235735324 30 0.303898219837532 0.607796439675063 0.696101780162468 31 0.3801686489443 0.7603372978886 0.6198313510557 32 0.443296386353287 0.886592772706574 0.556703613646713 33 0.397171351907131 0.794342703814262 0.602828648092869 34 0.404285471690861 0.808570943381722 0.595714528309139 35 0.408626478917404 0.817252957834808 0.591373521082596 36 0.407978657215921 0.815957314431843 0.592021342784078 37 0.58557196078044 0.82885607843912 0.41442803921956 38 0.780594305418258 0.438811389163483 0.219405694581741 39 0.774989139581518 0.450021720836964 0.225010860418482 40 0.733367820350589 0.533264359298823 0.266632179649411 41 0.710191137649806 0.579617724700389 0.289808862350194 42 0.661503861337903 0.676992277324194 0.338496138662097 43 0.614373674165386 0.771252651669227 0.385626325834614 44 0.599750468509982 0.800499062980037 0.400249531490018 45 0.565947561996052 0.868104876007896 0.434052438003948 46 0.587894140057009 0.824211719885982 0.412105859942991 47 0.546384137900854 0.907231724198292 0.453615862099146 48 0.536591409475937 0.926817181048125 0.463408590524063 49 0.599832799760325 0.80033440047935 0.400167200239675 50 0.578909157964415 0.84218168407117 0.421090842035585 51 0.543206096839558 0.913587806320885 0.456793903160442 52 0.494007802937747 0.988015605875494 0.505992197062253 53 0.456160085713159 0.912320171426319 0.543839914286841 54 0.408477504633944 0.816955009267888 0.591522495366056 55 0.364122037763876 0.728244075527751 0.635877962236124 56 0.334695554507234 0.669391109014468 0.665304445492766 57 0.290444656409196 0.580889312818392 0.709555343590804 58 0.265027586866105 0.530055173732209 0.734972413133895 59 0.244192746044807 0.488385492089615 0.755807253955193 60 0.304860264003553 0.609720528007106 0.695139735996447 61 0.292214977719332 0.584429955438664 0.707785022280668 62 0.255056941768284 0.510113883536567 0.744943058231716 63 0.241958636777053 0.483917273554106 0.758041363222947 64 0.276548658878426 0.553097317756852 0.723451341121574 65 0.351375121563765 0.70275024312753 0.648624878436235 66 0.351107811415878 0.702215622831756 0.648892188584122 67 0.68417734571236 0.631645308575281 0.31582265428764 68 0.677217950546536 0.645564098906928 0.322782049453464 69 0.84910831563478 0.301783368730439 0.15089168436522 70 0.830406690773575 0.33918661845285 0.169593309226425 71 0.93121602893771 0.137567942124578 0.0687839710622892 72 0.91505195468036 0.169896090639279 0.0849480453196393 73 0.938614753233633 0.122770493532733 0.0613852467663667 74 0.926515464837545 0.14696907032491 0.0734845351624548 75 0.927269776527218 0.145460446945565 0.0727302234727823 76 0.921295900002674 0.157408199994653 0.0787040999973264 77 0.969310364472374 0.0613792710552513 0.0306896355276256 78 0.961595359451175 0.0768092810976501 0.0384046405488251 79 0.95440889935429 0.0911822012914208 0.0455911006457104 80 0.956088309375481 0.0878233812490372 0.0439116906245186 81 0.948653948853465 0.102692102293071 0.0513460511465355 82 0.947289976246263 0.105420047507474 0.0527100237537368 83 0.933976520125412 0.132046959749176 0.0660234798745881 84 0.921043301440931 0.157913397118138 0.078956698559069 85 0.912589063842091 0.174821872315817 0.0874109361579086 86 0.896860308723345 0.20627938255331 0.103139691276655 87 0.875559700157106 0.248880599685789 0.124440299842894 88 0.919676458647418 0.160647082705164 0.0803235413525821 89 0.903047813078362 0.193904373843276 0.0969521869216378 90 0.883250400779371 0.233499198441257 0.116749599220629 91 0.885873439894257 0.228253120211485 0.114126560105743 92 0.873778036059214 0.252443927881572 0.126221963940786 93 0.851261904425356 0.297476191149289 0.148738095574644 94 0.823598899881724 0.352802200236553 0.176401100118276 95 0.790569183028185 0.41886163394363 0.209430816971815 96 0.761714449281901 0.476571101436198 0.238285550718099 97 0.781517470685154 0.436965058629691 0.218482529314846 98 0.777135073996202 0.445729852007597 0.222864926003798 99 0.741672483209814 0.516655033580372 0.258327516790186 100 0.715567649170053 0.568864701659894 0.284432350829947 101 0.673362216376691 0.653275567246619 0.326637783623309 102 0.636066706692136 0.727866586615729 0.363933293307864 103 0.595619656179181 0.808760687641638 0.404380343820819 104 0.554506496977988 0.890987006044024 0.445493503022012 105 0.508461237893369 0.983077524213262 0.491538762106631 106 0.485442498060947 0.970884996121894 0.514557501939053 107 0.484570895065951 0.969141790131902 0.515429104934049 108 0.49133624194656 0.98267248389312 0.50866375805344 109 0.441094256714162 0.882188513428324 0.558905743285838 110 0.416783443911544 0.833566887823088 0.583216556088456 111 0.376938148427725 0.75387629685545 0.623061851572275 112 0.602586560115651 0.794826879768697 0.397413439884349 113 0.596580270904186 0.806839458191628 0.403419729095814 114 0.572536239675484 0.854927520649033 0.427463760324516 115 0.772152537892129 0.455694924215742 0.227847462107871 116 0.75488220363888 0.490235592722241 0.24511779636112 117 0.736441242429285 0.52711751514143 0.263558757570715 118 0.705429016363231 0.589141967273538 0.294570983636769 119 0.655836780318508 0.688326439362983 0.344163219681491 120 0.678128609240408 0.643742781519185 0.321871390759592 121 0.736336963165258 0.527326073669483 0.263663036834742 122 0.727961306478301 0.544077387043398 0.272038693521699 123 0.72898819311443 0.542023613771141 0.271011806885571 124 0.676552099471697 0.646895801056606 0.323447900528303 125 0.719064286019384 0.561871427961232 0.280935713980616 126 0.685699128156418 0.628601743687163 0.314300871843582 127 0.682503487307807 0.634993025384387 0.317496512692193 128 0.644344272199422 0.711311455601155 0.355655727800578 129 0.612361745026848 0.775276509946304 0.387638254973152 130 0.686113678363333 0.627772643273333 0.313886321636667 131 0.633423826299745 0.73315234740051 0.366576173700255 132 0.572068634421696 0.855862731156607 0.427931365578304 133 0.562229210973165 0.87554157805367 0.437770789026835 134 0.505084176724888 0.989831646550224 0.494915823275112 135 0.45534806895603 0.91069613791206 0.54465193104397 136 0.42175373716162 0.84350747432324 0.57824626283838 137 0.438572900787355 0.87714580157471 0.561427099212645 138 0.508820180950987 0.982359638098027 0.491179819049013 139 0.433280192381418 0.866560384762836 0.566719807618582 140 0.355669923067759 0.711339846135519 0.64433007693224 141 0.424681998118506 0.849363996237012 0.575318001881494 142 0.370325180293534 0.740650360587067 0.629674819706466 143 0.304711630377864 0.609423260755727 0.695288369622136 144 0.228558708684983 0.457117417369967 0.771441291315017 145 0.368224064359684 0.736448128719367 0.631775935640316 146 0.270276284106354 0.540552568212709 0.729723715893646 147 0.39371901078636 0.78743802157272 0.60628098921364 148 0.336492835922942 0.672985671845885 0.663507164077058 149 0.252960816433276 0.505921632866552 0.747039183566724 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 4 0.0285714285714286 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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