include trend

*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: Fri, 03 Dec 2010 14:45:03 +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/03/t1291387413orn8iriqasoksam.htm/, Retrieved Fri, 03 Dec 2010 15:43:33 +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/03/t1291387413orn8iriqasoksam.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 «

4 4 1 4 5 4 2 1 4 4 4 3 2 5 5 4 2 1 3 4 4 2 2 4 3 5 2 1 3 5 4 1 3 4 4 3 1 1 3 4 4 1 1 2 4 4 2 1 4 4 4 2 2 2 4 4 2 4 2 4 4 2 2 2 4 2 2 1 1 3 3 1 1 4 4 4 3 3 4 5 3 2 2 2 4 2 2 2 2 2 4 2 3 3 4 3 2 3 3 4 3 3 1 3 4 4 4 2 4 4 3 2 2 3 4 3 2 2 2 4 4 2 2 2 5 4 1 3 4 4 4 2 2 4 4 4 2 2 3 4 4 2 2 4 4 4 2 2 2 4 5 4 2 4 5 4 2 3 4 4 4 4 2 5 2 4 3 2 5 5 3 1 2 4 4 4 4 2 4 5 3 3 2 4 4 4 2 1 2 4 4 4 2 4 4 3 2 1 4 4 5 3 2 4 5 4 3 2 3 4 3 2 2 2 4 3 1 2 3 5 3 2 2 4 4 4 1 3 3 4 4 2 2 2 4 4 4 2 4 4 4 2 2 4 4 4 2 4 3 4 4 2 1 4 4 4 2 2 3 4 5 2 2 4 5 3 1 1 2 3 3 2 5 4 4 5 3 2 4 5 5 2 2 4 5 4 2 2 4 4 4 1 1 3 5 3 1 2 1 2 4 2 2 3 4 4 2 2 3 4 5 1 2 4 4 4 2 2 2 4 4 1 1 3 4 5 4 1 5 5 4 4 2 4 4 3 1 2 4 4 4 1 1 3 4 4 3 2 4 4 4 4 2 2 3 4 2 1 3 4 4 4 3 4 5 4 4 3 3 5 4 3 3 4 4 3 4 2 4 4 4 2 2 3 5 3 2 2 3 4 5 2 1 2 5 4 2 4 4 3 5 2 3 3 4 5 2 2 2 4 4 2 2 2 4 4 1 2 3 4 4 3 1 2 5 4 3 2 2 4 4 2 3 4 4 5 4 1 4 5 4 4 2 4 3 3 2 2 2 4 4 2 2 2 4 3 1 1 4 5 4 1 1 2 4 4 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 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 neat[t] = + 1.91248932919395 + 0.22582746701983fail[t] -0.0151695182184149performance[t] + 0.0407018900354282goals[t] + 0.408125426799028`organized `[t] -0.108520379228040M1[t] -0.320677772100933M2[t] -0.0523926228821235M3[t] -0.100794438378459M4[t] -0.0408498667731373M5[t] -0.325277806373867M6[t] -0.129584987021746M7[t] -0.168273241267620M8[t] + 0.353475024355944M9[t] + 0.368840159639130M10[t] + 0.0953099758679434M11[t] -0.00910905651160431t + 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) 1.91248932919395 0.506351 3.777 0.000233 0.000116 fail 0.22582746701983 0.070489 3.2037 0.001675 0.000838 performance -0.0151695182184149 0.078959 -0.1921 0.847924 0.423962 goals 0.0407018900354282 0.074355 0.5474 0.584962 0.292481 `organized ` 0.408125426799028 0.086822 4.7007 6e-06 3e-06 M1 -0.108520379228040 0.3161 -0.3433 0.731873 0.365937 M2 -0.320677772100933 0.314246 -1.0205 0.309242 0.154621 M3 -0.0523926228821235 0.320743 -0.1633 0.870477 0.435238 M4 -0.100794438378459 0.321759 -0.3133 0.754542 0.377271 M5 -0.0408498667731373 0.322792 -0.1266 0.899474 0.449737 M6 -0.325277806373867 0.320407 -1.0152 0.311736 0.155868 M7 -0.129584987021746 0.32523 -0.3984 0.690903 0.345452 M8 -0.168273241267620 0.323169 -0.5207 0.603388 0.301694 M9 0.353475024355944 0.320861 1.1016 0.272479 0.136239 M10 0.368840159639130 0.323868 1.1389 0.256679 0.128339 M11 0.0953099758679434 0.320917 0.297 0.766906 0.383453 t -0.00910905651160431 0.00162 -5.6231 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.661871167577602 R-squared 0.438073442470539 Adjusted R-squared 0.374757774016515 F-TEST (value) 6.91887889944086 F-TEST (DF numerator) 16 F-TEST (DF denominator) 142 p-value 1.57234225639513e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.812915986590508 Sum Squared Residuals 93.8382009781274 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 4.88643493745207 -0.886434937452065 2 4 3.80538812722888 0.194611872771119 3 4 4.72404948557196 -0.724049485571957 4 4 3.96635145789272 0.0336485421072819 5 4 3.63459391800442 0.36540608199558 6 5 4.13177540367313 0.86822459632687 7 4 3.69476912629339 0.305230873706614 8 3 3.63660896193731 -0.63660896193731 9 4 4.10854628101384 -0.108546281013841 10 4 4.42203360687611 -0.42203360687611 11 4 4.04282106830405 -0.0428210683040475 12 4 3.90806299948767 0.0919370005123304 13 4 3.82077260018486 0.179227399815144 14 2 3.16584835218432 -1.16584835218432 15 3 3.72942807477700 -0.729428074777004 16 4 4.50135852717092 -0.501358527170923 17 3 3.85200688659334 -0.85200688659334 18 2 2.74221903688295 -0.74221903688295 19 4 3.77058602513854 0.229413974861463 20 3 3.72278871438106 -0.722788714381059 21 3 4.49159442694968 -1.49159442694968 22 4 4.7492103445581 -0.749210344558104 23 3 3.97421428020022 -0.974214280200224 24 3 3.82909335778525 -0.829093357785248 25 4 4.11958934884463 -0.119589348844633 26 4 3.33060426749372 0.669395732506282 27 4 3.83077734543917 0.169222654560832 28 4 3.7325645833958 0.267435416604200 29 4 3.82410198852495 0.175898011475055 30 4 3.44916121234175 0.550838787658245 31 5 4.57692911609182 0.423070883908183 32 4 3.65418192627724 0.345818073722764 33 4 3.85809662408464 0.141903375915358 34 4 4.86290151623348 -0.862901516233478 35 3 3.67978002507657 -0.67978002507657 36 4 4.66096882055554 -0.660968820555541 37 3 3.90938649099704 -0.909386490997039 38 4 3.39605831274027 0.60394168725973 39 4 4.17312360133958 -0.173123601339577 40 3 3.67912731351039 -0.679127313510391 41 5 4.34874620420455 0.651253795795448 42 4 3.60638189125776 0.393618108742238 43 3 3.52643629704302 -0.52643629704302 44 3 3.70163883610017 -0.701638836100169 45 3 4.07268197546836 -1.07268197546836 46 4 3.79723917896627 0.202760821033733 47 4 3.71489503388629 0.285104966113707 48 4 4.14353471561726 -0.143534715617261 49 4 3.57425034583796 0.425749654162042 50 4 3.2819429699812 0.718057030018798 51 4 3.62732950737908 0.372670492620921 52 4 3.51394722711730 0.486052772882704 53 5 4.01361005904547 0.98638994095453 54 3 2.61176048046281 0.388239519537192 55 3 3.45302284431938 -0.45302284431938 56 5 4.08468698203600 0.915313017963995 57 5 4.37149872412813 0.628501275871866 58 4 3.96962937610069 0.0303706238993117 59 4 3.84375572378008 0.156244276219918 60 3 2.41838711271418 0.581612887285822 61 4 3.42423977766328 0.575760222336722 62 4 3.20297332827878 0.79702667172122 63 5 3.27702384400158 1.72297615599842 64 4 3.36393665894262 0.636063341057384 65 4 3.24481611527035 0.755183884729653 66 5 4.11829072708739 0.881709272912612 67 4 3.84087765487503 0.159122345124967 68 3 3.11559794305807 -0.115597943058065 69 4 3.60270478035301 0.397295219646989 70 4 4.08614816498127 -0.0861481649812668 71 4 3.53980718484842 0.460192815151579 72 4 3.44773005348208 0.552269946517916 73 4 4.20024383217973 -0.200243832179727 74 4 3.9382754927598 0.0617245072401984 75 4 3.60420058168358 0.395799418316423 76 3 3.78768669491388 -0.787686694913881 77 4 3.75429081273154 0.245709187268461 78 3 3.05262838982018 -0.0526283898201764 79 5 3.62180520764271 1.37819479235729 80 4 2.79365226870279 1.20634773129721 81 5 3.68888453279676 1.31111546720324 82 5 3.66960823975133 1.33039176024867 83 4 3.38696899946854 0.613031000531463 84 4 3.09742439010459 0.902575609895412 85 4 3.81404294338662 0.185957056613381 86 4 3.16948154898468 0.830518451015322 87 4 3.26906443652449 0.730935563475505 88 5 4.10167296179207 0.898327038207927 89 4 3.32108810506932 0.678911894930681 90 3 2.90261782164550 0.0973821783545034 91 4 3.08920158448601 0.910798415513987 92 3 3.32027553179700 -0.320275531797005 93 4 3.34338553403908 0.656614465960921 94 4 2.96704855782865 1.03295144217135 95 4 3.72648763816374 0.273512361836258 96 4 3.67313334941822 0.326866650581779 97 4 3.73026663706438 0.269733362935619 98 3 3.33706508149928 -0.337065081499283 99 3 3.14939290478664 -0.149392904786644 100 3 3.02084110630645 -0.0208411063064463 101 3 3.61990485372910 -0.619904853729096 102 3 2.83401103354167 0.165988966458327 103 2 2.39983237336713 -0.399832373367134 104 3 2.95762796740630 0.042372032593703 105 5 3.93426401157113 1.06573598842887 106 2 3.06086259209742 -1.06086259209742 107 2 2.81609762464485 -0.816097624644849 108 3 2.47350922423226 0.52649077576774 109 3 2.97183554688786 0.0281644531121445 110 2 2.8064405057572 -0.806440505757201 111 2 2.79908724140915 -0.799087241409148 112 4 2.59998029965744 1.40001970034256 113 3 2.21235135151530 0.787648648484702 114 1 2.27106837394815 -1.27106837394815 115 1 2.72135387663872 -1.72135387663872 116 1 2.07277032570442 -1.07277032570442 117 2 3.53091455714499 -1.53091455714499 118 2 3.35204505893217 -1.35204505893217 119 3 2.30902637330517 0.690973626694833 120 1 2.32067103885238 -1.32067103885238 121 3 2.25410634674676 0.745893653253241 122 1 2.24830451078349 -1.24830451078349 123 2 2.94113840210674 -0.94113840210674 124 1 2.67296958129738 -1.67296958129738 125 2 2.94963256341093 -0.949632563410932 126 2 2.4737976075194 -0.473797607519399 127 3 2.62721471671788 0.372785283282117 128 2 2.80524487298024 -0.805244872980235 129 2 3.31788408209219 -1.31788408209219 130 4 2.50788930726572 1.49211069273428 131 2 3.01596854876397 -1.01596854876397 132 3 3.33484446140187 -0.334844461401867 133 2 2.59362498544196 -0.593624985441963 134 1 2.34682616424045 -1.34682616424045 135 2 2.8469992421859 -0.846999242185903 136 3 2.80267884098176 0.197321159018235 137 1 1.60077808665618 -0.600778086656181 138 2 2.45021359087007 -0.450213590870075 139 2 2.31007570698242 -0.310075706982419 140 3 2.18087461615409 0.819125383845914 141 3 2.73421571530147 0.265784284698527 142 3 1.94975331229201 1.05024668770799 143 4 3.43169756514110 0.568302434858904 144 4 2.99970831624278 1.00029168375721 145 2 3.11073396472818 -1.11073396472818 146 3 2.04005000810359 0.959949991896412 147 3 2.94834851284807 0.0516514871519341 148 2 2.25688474702127 -0.256884747021268 149 1 2.62407905524456 -1.62407905524456 150 2 2.35607443094924 -0.356074430949238 151 2 2.36789547040395 -0.367895470403951 152 4 2.95405105346533 1.04594894653467 153 4 2.94532875505671 1.05467124494329 154 2 2.60563074411679 -0.60563074411679 155 3 2.518479934417 0.481520065583001 156 2 2.69293216010592 -0.69293216010592 157 4 2.59047224258469 1.40952775741531 158 2 1.93074132996434 0.0692586700356638 159 4 3.08003681994706 0.91996318005294 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.428668139044791 0.857336278089582 0.571331860955209 21 0.27733604579056 0.55467209158112 0.72266395420944 22 0.240760948498464 0.481521896996927 0.759239051501536 23 0.177504817986353 0.355009635972706 0.822495182013647 24 0.110388635964664 0.220777271929329 0.889611364035335 25 0.0663546789698085 0.132709357939617 0.933645321030191 26 0.040594807313886 0.081189614627772 0.959405192686114 27 0.107094463047319 0.214188926094638 0.892905536952681 28 0.0913433190798588 0.182686638159718 0.908656680920141 29 0.0607981243245648 0.121596248649130 0.939201875675435 30 0.0429551156120772 0.0859102312241543 0.957044884387923 31 0.0564202079537636 0.112840415907527 0.943579792046236 32 0.0516201859890342 0.103240371978068 0.948379814010966 33 0.0551950762557932 0.110390152511586 0.944804923744207 34 0.0587268071220573 0.117453614244115 0.941273192877943 35 0.0616814206171002 0.123362841234200 0.9383185793829 36 0.0451135458670546 0.0902270917341092 0.954886454132945 37 0.0504656563294614 0.100931312658923 0.949534343670539 38 0.0589836137479877 0.117967227495975 0.941016386252012 39 0.0493370801074684 0.0986741602149368 0.950662919892532 40 0.0439283449328107 0.0878566898656215 0.95607165506719 41 0.0358971065294053 0.0717942130588105 0.964102893470595 42 0.0242539725283055 0.0485079450566111 0.975746027471694 43 0.0203727110987992 0.0407454221975985 0.9796272889012 44 0.0174695897827455 0.0349391795654911 0.982530410217254 45 0.0250953210906046 0.0501906421812091 0.974904678909395 46 0.0207479507553039 0.0414959015106078 0.979252049244696 47 0.0227067729353674 0.0454135458707348 0.977293227064633 48 0.0191027480407725 0.0382054960815451 0.980897251959228 49 0.0157251811807353 0.0314503623614706 0.984274818819265 50 0.0107475666985538 0.0214951333971077 0.989252433301446 51 0.00964806571107034 0.0192961314221407 0.99035193428893 52 0.00732501800696291 0.0146500360139258 0.992674981993037 53 0.00610444692245212 0.0122088938449042 0.993895553077548 54 0.00397833935277452 0.00795667870554904 0.996021660647226 55 0.00663516785581521 0.0132703357116304 0.993364832144185 56 0.00891067101800732 0.0178213420360146 0.991089328981993 57 0.00734653724568696 0.0146930744913739 0.992653462754313 58 0.00523374679184329 0.0104674935836866 0.994766253208157 59 0.00349140367385705 0.00698280734771411 0.996508596326143 60 0.00342898426252641 0.00685796852505282 0.996571015737474 61 0.00239773526910487 0.00479547053820974 0.997602264730895 62 0.00164033808912388 0.00328067617824776 0.998359661910876 63 0.00346486788415394 0.00692973576830787 0.996535132115846 64 0.00243910135660809 0.00487820271321617 0.997560898643392 65 0.00181608434984212 0.00363216869968424 0.998183915650158 66 0.00127867801468335 0.00255735602936669 0.998721321985317 67 0.000826910012984882 0.00165382002596976 0.999173089987015 68 0.000667178392139518 0.00133435678427904 0.99933282160786 69 0.00041763804275479 0.00083527608550958 0.999582361957245 70 0.000287658250046701 0.000575316500093401 0.999712341749953 71 0.000229430975584082 0.000458861951168164 0.999770569024416 72 0.000142061042529593 0.000284122085059186 0.99985793895747 73 0.000133233179246372 0.000266466358492744 0.999866766820754 74 0.000104643290040762 0.000209286580081525 0.99989535670996 75 6.30375019059781e-05 0.000126075003811956 0.999936962498094 76 0.000135959810105757 0.000271919620211514 0.999864040189894 77 0.000111744160806597 0.000223488321613194 0.999888255839193 78 0.000126716325391571 0.000253432650783142 0.999873283674608 79 0.000188490240653453 0.000376980481306905 0.999811509759347 80 0.000218088724568250 0.000436177449136499 0.999781911275432 81 0.000296164942552215 0.00059232988510443 0.999703835057448 82 0.000454270750391256 0.000908541500782511 0.999545729249609 83 0.000311809651934784 0.000623619303869568 0.999688190348065 84 0.00024570790774756 0.00049141581549512 0.999754292092252 85 0.000157796896652786 0.000315593793305572 0.999842203103347 86 0.000145701602624395 0.000291403205248789 0.999854298397376 87 0.000116823307992768 0.000233646615985537 0.999883176692007 88 9.44260565070915e-05 0.000188852113014183 0.999905573943493 89 7.32996667704886e-05 0.000146599333540977 0.99992670033323 90 8.55492302300503e-05 0.000171098460460101 0.99991445076977 91 0.000126259608380383 0.000252519216760766 0.99987374039162 92 0.000141816931177771 0.000283633862355543 0.999858183068822 93 0.000159905055540945 0.000319810111081889 0.99984009494446 94 0.000226322838144948 0.000452645676289897 0.999773677161855 95 0.000191652834197883 0.000383305668395767 0.999808347165802 96 0.000144013557196753 0.000288027114393506 0.999855986442803 97 0.000105976774493026 0.000211953548986052 0.999894023225507 98 0.000121946587779997 0.000243893175559995 0.99987805341222 99 0.000147315032178872 0.000294630064357745 0.999852684967821 100 0.000161054376760928 0.000322108753521856 0.99983894562324 101 0.000205434073910199 0.000410868147820397 0.99979456592609 102 0.000271605803526976 0.000543211607053951 0.999728394196473 103 0.000258717402139155 0.000517434804278311 0.99974128259786 104 0.000203449630371195 0.00040689926074239 0.999796550369629 105 0.00168969576651353 0.00337939153302707 0.998310304233486 106 0.00163330228057279 0.00326660456114558 0.998366697719427 107 0.00160529356022709 0.00321058712045417 0.998394706439773 108 0.00136200991878948 0.00272401983757895 0.99863799008121 109 0.00124823089100913 0.00249646178201826 0.99875176910899 110 0.00200606138637293 0.00401212277274587 0.997993938613627 111 0.00297617065490250 0.00595234130980501 0.997023829345097 112 0.0290680308429418 0.0581360616858836 0.970931969157058 113 0.0604165395427022 0.120833079085404 0.939583460457298 114 0.0859536105648165 0.171907221129633 0.914046389435184 115 0.162174275935195 0.32434855187039 0.837825724064805 116 0.191299108979191 0.382598217958382 0.808700891020809 117 0.196907651078627 0.393815302157254 0.803092348921373 118 0.200545476633576 0.401090953267152 0.799454523366424 119 0.216781844751067 0.433563689502135 0.783218155248933 120 0.243032795154939 0.486065590309878 0.756967204845061 121 0.255914921698472 0.511829843396943 0.744085078301528 122 0.241780185940003 0.483560371880005 0.758219814059997 123 0.210661033105907 0.421322066211814 0.789338966894093 124 0.220715669635189 0.441431339270377 0.779284330364811 125 0.226985464900521 0.453970929801043 0.773014535099479 126 0.178703609551170 0.357407219102339 0.82129639044883 127 0.19851294656647 0.39702589313294 0.80148705343353 128 0.235941071115642 0.471882142231283 0.764058928884358 129 0.246013161633416 0.492026323266831 0.753986838366584 130 0.327680426282546 0.655360852565093 0.672319573717454 131 0.324757351515695 0.64951470303139 0.675242648484305 132 0.249547374513023 0.499094749026046 0.750452625486977 133 0.210585402517729 0.421170805035459 0.78941459748227 134 0.294035378585677 0.588070757171354 0.705964621414323 135 0.442471575604692 0.884943151209384 0.557528424395308 136 0.362325380626252 0.724650761252504 0.637674619373748 137 0.303495369318894 0.606990738637787 0.696504630681106 138 0.197370514893060 0.394741029786120 0.80262948510694 139 0.128228810691926 0.256457621383852 0.871771189308074 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 54 0.45 NOK 5% type I error level 69 0.575 NOK 10% type I error level 77 0.641666666666667 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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