*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, 10 Dec 2010 15:14:43 +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/10/t12919940012io920fgctv588a.htm/, Retrieved Fri, 10 Dec 2010 16:13:32 +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/10/t12919940012io920fgctv588a.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 «

23 13 14 22 11 23 8 1 6 15 20 12 7 20 22 24 4 2 5 23 26 26 22 25 23 24 7 2 20 26 19 16 12 23 21 21 4 2 12 19 17 18 15 20 19 21 4 2 11 19 17 12 9 22 12 19 5 2 12 16 21 18 20 18 24 12 15 1 11 23 18 20 10 22 21 21 5 1 9 22 16 18 12 23 21 25 7 2 13 19 26 24 23 28 26 27 4 2 9 24 20 17 10 19 18 21 4 1 14 19 14 19 11 26 21 27 7 1 12 25 22 12 20 27 22 20 8 1 18 23 23 25 11 23 26 16 4 2 9 31 25 23 22 27 20 26 8 1 15 29 24 22 19 23 20 24 4 2 12 18 24 23 20 23 26 25 5 2 12 17 16 16 16 19 27 25 16 1 12 22 16 16 12 21 27 27 7 1 15 21 20 15 14 25 16 23 4 2 11 24 20 24 14 22 26 22 6 1 13 22 15 18 9 13 20 10 4 1 10 16 22 23 19 12 25 25 5 2 17 22 20 18 17 20 16 18 4 1 13 21 20 19 14 24 20 21 4 1 17 25 24 17 19 23 20 20 6 1 15 22 27 22 20 25 24 18 4 1 13 24 25 22 20 28 24 25 4 1 17 25 13 8 9 24 22 28 4 1 21 29 15 12 10 18 18 27 8 1 12 19 19 22 6 19 21 20 5 2 12 29 20 16 15 24 17 20 4 1 15 25 11 12 9 22 15 20 10 2 8 19 28 28 24 28 28 27 4 2 15 27 21 15 11 24 23 23 4 1 16 25 25 17 4 28 19 23 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 16 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation E/Introjected[t] = + 7.23124359254075 -0.156662461706075`I/ToKnow`[t] + 0.684714728855979`I/Accomp.`[t] -0.0407110067422431`I/Exp.Stimulation`[t] + 0.0328194315356129`E/Identified`[t] + 0.189562104249828`E/Ext.Regulation`[t] + 0.250551965087687Amotivation[t] -0.644346153149622gender[t] + 0.150792391144349PE[t] -0.141157422196598PS[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) 7.23124359254075 3.237739 2.2334 0.027131 0.013565 `I/ToKnow` -0.156662461706075 0.112935 -1.3872 0.16762 0.08381 `I/Accomp.` 0.684714728855979 0.082709 8.2786 0 0 `I/Exp.Stimulation` -0.0407110067422431 0.076596 -0.5315 0.595923 0.297962 `E/Identified` 0.0328194315356129 0.109841 0.2988 0.765549 0.382774 `E/Ext.Regulation` 0.189562104249828 0.088347 2.1456 0.033651 0.016826 Amotivation 0.250551965087687 0.115841 2.1629 0.032272 0.016136 gender -0.644346153149622 0.634932 -1.0148 0.311964 0.155982 PE 0.150792391144349 0.090626 1.6639 0.098401 0.049201 PS -0.141157422196598 0.073709 -1.9151 0.057555 0.028777 Multiple Linear Regression - Regression Statistics Multiple R 0.624933873306455 R-squared 0.390542346005808 Adjusted R-squared 0.350795107701839 F-TEST (value) 9.82564733225276 F-TEST (DF numerator) 9 F-TEST (DF denominator) 138 p-value 1.53219659182469e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.46774715378046 Sum Squared Residuals 1659.48730451224 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 17.1887628270360 -6.18876282703598 2 22 14.4563299894549 7.54367001054511 3 23 25.2458629755851 -2.24586297558509 4 21 18.2982447415279 2.70175525847212 5 19 19.6096154166741 -0.609615416674066 6 12 16.2569243613851 -4.25692436138505 7 24 19.8435008151467 4.15649918485333 8 21 21.2614173788212 -0.261417378821210 9 21 21.7983582877648 -0.798358287764784 10 26 22.3748097650295 3.62519023497049 11 18 19.7223722314581 -1.72237223145814 12 21 22.9613006787073 -1.96130067870733 13 22 16.6921046805205 5.30789531947951 14 26 20.7806617001083 5.21933829989173 15 20 23.5106082182199 -3.51060821821988 16 20 22.0480874938838 -2.04808749388376 17 26 23.2733627075316 2.72663729246839 18 27 22.4598562581461 4.54014374185394 19 27 21.4060302665264 5.59396973347362 20 16 16.9636291069249 -0.96362910692488 21 26 24.5673909777789 1.43260902222108 22 20 18.7693132416373 1.23068675836266 23 25 23.314559735533 1.68544026446699 24 16 19.153135796367 -3.15313579636700 25 20 20.6984874601326 -0.698487460132645 26 20 18.8994630005762 1.1005369994238 27 24 20.4138493507099 3.58615064929007 28 24 22.6145794408585 1.38542055914148 29 22 15.8322923139104 6.16770768608959 30 18 18.8872871677340 -0.887287167734022 31 21 21.1689370678466 -0.168937067846635 32 17 18.1124853802839 -1.11248538028394 33 15 17.6125792301426 -2.61257923014258 34 28 25.2409148305753 2.75908516942467 35 23 18.1534309205847 4.84656907941531 36 19 17.8948872580436 1.10511274195636 37 15 17.6477378428373 -2.6477378428373 38 26 23.4961507746566 2.50384922534336 39 20 24.9812770994927 -4.98127709949271 40 11 14.9543741856871 -3.95437418568707 41 17 19.5076319547439 -2.50763195474392 42 16 18.0159081532637 -2.01590815326374 43 21 22.5267747024960 -1.52677470249604 44 18 17.2604132937167 0.739586706283348 45 17 17.6482452784581 -0.648245278458144 46 21 21.5993958166478 -0.599395816647835 47 18 21.3327762174706 -3.33277621747061 48 16 14.408715768842 1.591284231158 49 13 15.7811597303024 -2.78115973030241 50 28 26.9252065337475 1.07479346625247 51 25 18.0224066576685 6.97759334233148 52 24 21.3148288677740 2.68517113222596 53 15 18.1465145756053 -3.14651457560527 54 21 22.1150334611454 -1.11503346114539 55 11 17.3055435446565 -6.30554354465651 56 27 22.4873160608003 4.51268393919967 57 23 20.779840457241 2.22015954275900 58 21 23.0554336647138 -2.05543366471380 59 16 16.7927628387478 -0.79276283874781 60 20 19.4038867827854 0.596113217214579 61 21 22.8359293892082 -1.83592938920819 62 10 16.5624004427194 -6.56240044271935 63 18 24.950439502491 -6.95043950249101 64 20 19.7994979719089 0.200502028091068 65 21 26.7991340167883 -5.79913401678832 66 24 21.2536920497936 2.74630795020637 67 26 23.4234156694060 2.57658433059402 68 23 21.3755221230489 1.62447787695114 69 22 21.4302156175096 0.569784382490431 70 13 15.6755620232162 -2.67556202321618 71 27 25.3416057808712 1.6583942191288 72 24 20.9864430479559 3.01355695204411 73 19 22.8976974155697 -3.89769741556970 74 17 19.0422683298177 -2.04226832981766 75 16 20.2335138850657 -4.23351388506566 76 20 19.2550767843741 0.744923215625898 77 8 14.119714762494 -6.119714762494 78 16 20.0472167220481 -4.04721672204815 79 17 19.1298674151291 -2.12986741512906 80 23 23.5329828397716 -0.532982839771556 81 18 18.6175506623624 -0.617550662362426 82 24 23.5123371937705 0.487662806229457 83 17 16.8018494441569 0.198150555843109 84 20 21.1964205354342 -1.19642053543419 85 22 20.2869921084884 1.71300789151159 86 22 19.7153419994461 2.28465800055394 87 20 20.3920587044841 -0.392058704484145 88 18 22.659226099686 -4.65922609968601 89 21 18.7646190618474 2.23538093815263 90 23 19.1102805206258 3.88971947937421 91 28 22.4080097430397 5.59199025696031 92 19 21.1431661016515 -2.14316610165151 93 22 18.7306914407520 3.26930855924803 94 17 20.630582557575 -3.630582557575 95 25 23.7600210053301 1.23997899466989 96 22 22.0333878398901 -0.0333878398900595 97 21 20.4517074116339 0.54829258836611 98 15 20.2664311077195 -5.26643110771953 99 20 19.9515446522506 0.0484553477493742 100 25 19.0250251537319 5.97497484626807 101 21 19.5885006445898 1.41149935541024 102 24 25.1898300578726 -1.18983005787262 103 23 22.1355319133634 0.864468086636633 104 22 23.9847330929990 -1.98473309299895 105 14 19.0529206292084 -5.05292062920841 106 11 20.9949953105267 -9.99499531052673 107 22 20.1124819689373 1.88751803106270 108 22 22.1018216029887 -0.101821602988680 109 6 13.7634887169726 -7.76348871697257 110 15 21.2973529597553 -6.29735295975528 111 26 21.7036420005457 4.29635799945426 112 26 21.8530142143818 4.14698578561819 113 20 15.9781361683029 4.0218638316971 114 26 24.0211342812475 1.97886571875252 115 15 16.7611299546477 -1.76112995464770 116 25 21.0607484198997 3.93925158010031 117 22 22.9548358783562 -0.954835878356176 118 20 21.3716323893948 -1.37163238939482 119 18 20.6186987124349 -2.61869871243485 120 23 16.5215149542846 6.47848504571544 121 22 20.036048986228 1.96395101377202 122 23 20.1396142235334 2.86038577646658 123 17 20.8876850950878 -3.8876850950878 124 20 17.6302127629929 2.36978723700714 125 21 21.4433052748186 -0.443305274818585 126 23 24.2748336348976 -1.27483363489764 127 25 23.5323518672976 1.46764813270237 128 25 22.2975893978394 2.70241060216059 129 21 18.5787052829325 2.42129471706754 130 22 20.2230201587073 1.77697984129266 131 18 18.0548836246437 -0.054883624643704 132 18 24.0087645771665 -6.00876457716654 133 18 21.5994312412264 -3.59943124122642 134 21 19.4943913104839 1.50560868951609 135 21 17.9213815095301 3.07861849046989 136 25 20.4607148431681 4.53928515683194 137 24 19.9346551576881 4.06534484231186 138 24 23.3651848063123 0.634815193687677 139 28 25.3361942093787 2.66380579062131 140 24 22.9009407464159 1.0990592535841 141 22 22.2477233066586 -0.247723306658584 142 22 21.7992582536119 0.200741746388102 143 20 21.8750954544727 -1.87509545447273 144 25 21.9842849504339 3.01571504956611 145 13 17.8906191366642 -4.89061913666421 146 21 19.7457024157972 1.25429758420276 147 23 19.0952148228556 3.90478517714438 148 18 21.0318426087169 -3.03184260871692 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.677995706129739 0.644008587740522 0.322004293870261 14 0.602711736700602 0.794576526598796 0.397288263299398 15 0.750646666826606 0.498706666346788 0.249353333173394 16 0.652281766550503 0.695436466898993 0.347718233449497 17 0.799807751914372 0.400384496171257 0.200192248085628 18 0.803855147201332 0.392289705597336 0.196144852798668 19 0.858849323649409 0.282301352701182 0.141150676350591 20 0.884345291451866 0.231309417096268 0.115654708548134 21 0.86586321669207 0.268273566615861 0.134136783307930 22 0.818681029167776 0.362637941664447 0.181318970832224 23 0.816043327710909 0.367913344578182 0.183956672289091 24 0.815269601535404 0.369460796929192 0.184730398464596 25 0.75970832124439 0.48058335751122 0.24029167875561 26 0.706831633879938 0.586336732240124 0.293168366120062 27 0.718121304155873 0.563757391688254 0.281878695844127 28 0.675458420331932 0.649083159336136 0.324541579668068 29 0.660160238069538 0.679679523860925 0.339839761930462 30 0.614820136109636 0.770359727780728 0.385179863890364 31 0.599775409027212 0.800449181945576 0.400224590972788 32 0.575313374102829 0.849373251794342 0.424686625897171 33 0.566894734657509 0.866210530684982 0.433105265342491 34 0.524005182365892 0.951989635268216 0.475994817634108 35 0.533964995988525 0.93207000802295 0.466035004011475 36 0.475357723402363 0.950715446804727 0.524642276597637 37 0.523197519552449 0.953604960895102 0.476802480447551 38 0.47439058236237 0.94878116472474 0.52560941763763 39 0.513095127676726 0.973809744646547 0.486904872323274 40 0.592692713130364 0.814614573739271 0.407307286869636 41 0.637334447841147 0.725331104317705 0.362665552158853 42 0.600656514403622 0.798686971192755 0.399343485596378 43 0.553454254319301 0.893091491361399 0.446545745680699 44 0.500287830401348 0.999424339197305 0.499712169598652 45 0.447354303783001 0.894708607566003 0.552645696216999 46 0.392921401815876 0.785842803631751 0.607078598184124 47 0.37093251550116 0.74186503100232 0.62906748449884 48 0.355720278553454 0.711440557106908 0.644279721446546 49 0.357700217326045 0.715400434652091 0.642299782673954 50 0.31816188803583 0.63632377607166 0.68183811196417 51 0.457132614387387 0.914265228774773 0.542867385612613 52 0.43264988527883 0.86529977055766 0.56735011472117 53 0.423541160462101 0.847082320924201 0.576458839537899 54 0.378011410661518 0.756022821323036 0.621988589338482 55 0.488837054663702 0.977674109327404 0.511162945336298 56 0.493002674452922 0.986005348905843 0.506997325547078 57 0.473129789753619 0.946259579507238 0.526870210246381 58 0.453936753654826 0.907873507309652 0.546063246345174 59 0.40708252822896 0.81416505645792 0.59291747177104 60 0.358039676558185 0.71607935311637 0.641960323441815 61 0.34552167432854 0.69104334865708 0.65447832567146 62 0.451770641213938 0.903541282427876 0.548229358786062 63 0.553299590859882 0.893400818280236 0.446700409140118 64 0.504432348775989 0.991135302448022 0.495567651224011 65 0.611847848958909 0.776304302082182 0.388152151041091 66 0.596720518276061 0.806558963447878 0.403279481723939 67 0.603291074850699 0.793417850298602 0.396708925149301 68 0.564298977161421 0.871402045677157 0.435701022838579 69 0.517299617496567 0.965400765006866 0.482700382503433 70 0.505369732283409 0.989260535433183 0.494630267716591 71 0.464909185605657 0.929818371211314 0.535090814394343 72 0.463982117853419 0.927964235706837 0.536017882146582 73 0.476940950811564 0.953881901623127 0.523059049188436 74 0.439467010114985 0.87893402022997 0.560532989885015 75 0.474139284246975 0.948278568493951 0.525860715753025 76 0.426213840130159 0.852427680260318 0.573786159869841 77 0.551250174475276 0.897499651049448 0.448749825524724 78 0.561677773793450 0.876644452413101 0.438322226206550 79 0.530507832739866 0.938984334520269 0.469492167260134 80 0.489594468987761 0.979188937975522 0.510405531012239 81 0.440642684601365 0.88128536920273 0.559357315398635 82 0.391967153698413 0.783934307396825 0.608032846301587 83 0.344349272297088 0.688698544594176 0.655650727702912 84 0.301667094791423 0.603334189582845 0.698332905208577 85 0.266486653343634 0.532973306687268 0.733513346656366 86 0.239001371489229 0.478002742978458 0.760998628510771 87 0.201825181279095 0.403650362558191 0.798174818720905 88 0.227048191419849 0.454096382839699 0.772951808580151 89 0.203967554535923 0.407935109071845 0.796032445464077 90 0.210271404476831 0.420542808953662 0.789728595523169 91 0.277128056437941 0.554256112875882 0.722871943562059 92 0.252018901874282 0.504037803748565 0.747981098125718 93 0.256319185287164 0.512638370574328 0.743680814712836 94 0.274540000138981 0.549080000277963 0.725459999861019 95 0.236158197674978 0.472316395349955 0.763841802325023 96 0.200039811730385 0.400079623460769 0.799960188269615 97 0.166063231826463 0.332126463652926 0.833936768173537 98 0.205854798677417 0.411709597354834 0.794145201322583 99 0.169928622989791 0.339857245979581 0.83007137701021 100 0.261165029292854 0.522330058585708 0.738834970707146 101 0.225011052977849 0.450022105955697 0.774988947022151 102 0.195880694919925 0.391761389839849 0.804119305080075 103 0.161203106414377 0.322406212828754 0.838796893585623 104 0.147515472224250 0.295030944448501 0.85248452777575 105 0.162569154956694 0.325138309913387 0.837430845043306 106 0.528763159178827 0.942473681642345 0.471236840821173 107 0.479537366612390 0.959074733224781 0.520462633387609 108 0.451500775952409 0.903001551904818 0.548499224047591 109 0.736207538735695 0.527584922528611 0.263792461264305 110 0.874485947372708 0.251028105254585 0.125514052627292 111 0.87155083162123 0.256898336757541 0.128449168378770 112 0.90922515601068 0.181549687978640 0.0907748439893198 113 0.89805576283295 0.203888474334098 0.101944237167049 114 0.886063853200895 0.227872293598209 0.113936146799105 115 0.90953140575044 0.180937188499120 0.0904685942495602 116 0.888454940212255 0.22309011957549 0.111545059787745 117 0.852138083336423 0.295723833327154 0.147861916663577 118 0.83914299744667 0.321714005106659 0.160857002553329 119 0.83992568049047 0.320148639019059 0.160074319509530 120 0.904857249881138 0.190285500237724 0.0951427501188618 121 0.873831875244355 0.252336249511289 0.126168124755645 122 0.871113137342259 0.257773725315483 0.128886862657741 123 0.862227902649604 0.275544194700792 0.137772097350396 124 0.817090098081669 0.365819803836662 0.182909901918331 125 0.75362543456736 0.492749130865281 0.246374565432640 126 0.715611478472783 0.568777043054435 0.284388521527217 127 0.637962539994239 0.724074920011523 0.362037460005761 128 0.558612751489568 0.882774497020864 0.441387248510432 129 0.470752795323139 0.941505590646277 0.529247204676861 130 0.42922912248375 0.8584582449675 0.57077087751625 131 0.327137270241885 0.654274540483771 0.672862729758115 132 0.251334008456016 0.502668016912032 0.748665991543984 133 0.482198632732593 0.964397265465186 0.517801367267407 134 0.620791054297009 0.758417891405981 0.379208945702991 135 0.596598956247213 0.806802087505573 0.403401043752787 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/10yiww1291994066.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/10yiww1291994066.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/19zz21291994066.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/19zz21291994066.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/29zz21291994066.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/29zz21291994066.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/3k9gn1291994066.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/3k9gn1291994066.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/4k9gn1291994066.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/4k9gn1291994066.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/5k9gn1291994066.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/5k9gn1291994066.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/6dif81291994066.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/6dif81291994066.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/7n9xb1291994066.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/7n9xb1291994066.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/8n9xb1291994066.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/8n9xb1291994066.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/9n9xb1291994066.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t12919940012io920fgctv588a/9n9xb1291994066.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 5 ; 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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