Multiple Regression Learning

*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: Thu, 16 Dec 2010 21:34:13 +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/16/t1292535162tcm8is9j4paksxt.htm/, Retrieved Thu, 16 Dec 2010 22:32:52 +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/16/t1292535162tcm8is9j4paksxt.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 «

0 13 26 9 15 25 25 0 16 20 9 15 25 24 0 19 21 9 14 19 21 1 15 31 14 10 18 23 0 14 21 8 10 18 17 0 13 18 8 12 22 19 0 19 26 11 18 29 18 0 15 22 10 12 26 27 0 14 22 9 14 25 23 0 15 29 15 18 23 23 1 16 15 14 9 23 29 0 16 16 11 11 23 21 1 16 24 14 11 24 26 0 17 17 6 17 30 25 1 15 19 20 8 19 25 1 15 22 9 16 24 23 0 20 31 10 21 32 26 1 18 28 8 24 30 20 0 16 38 11 21 29 29 1 16 26 14 14 17 24 0 19 25 11 7 25 23 0 16 25 16 18 26 24 1 17 29 14 18 26 30 0 17 28 11 13 25 22 1 16 15 11 11 23 22 0 15 18 12 13 21 13 1 14 21 9 13 19 24 0 15 25 7 18 35 17 1 12 23 13 14 19 24 0 14 23 10 12 20 21 0 16 19 9 9 21 23 1 14 18 9 12 21 24 1 10 26 16 5 23 24 1 14 18 12 10 19 23 0 16 18 6 11 17 26 1 16 28 14 11 24 24 1 16 17 14 12 15 21 0 14 29 10 12 25 23 1 20 12 4 15 27 28 1 14 25 12 12 29 23 0 14 28 12 16 27 22 0 11 20 14 14 18 24 0 15 17 9 17 25 21 0 16 17 9 13 22 23 1 14 20 10 10 26 23 0 16 31 14 17 23 20 1 14 21 10 12 16 23 1 12 19 9 13 27 21 0 16 23 14 13 25 27 1 9 15 8 11 14 12 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 13 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Learning[t] = + 11.9745252985294 -0.250678126239298Gender[t] -0.00527530208529847Concern[t] -0.229925046900135Doubts[t] + 0.093052852418534Expectations[t] + 0.0350326972003534Standards[t] + 0.170810919044308Organization[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) 11.9745252985294 1.330306 9.0013 0 0 Gender -0.250678126239298 0.351994 -0.7122 0.477538 0.238769 Concern -0.00527530208529847 0.034977 -0.1508 0.88033 0.440165 Doubts -0.229925046900135 0.064658 -3.556 0.000513 0.000257 Expectations 0.093052852418534 0.050898 1.8282 0.069631 0.034815 Standards 0.0350326972003534 0.045465 0.7705 0.442272 0.221136 Organization 0.170810919044308 0.046887 3.643 0.000378 0.000189 Multiple Linear Regression - Regression Statistics Multiple R 0.471230317353798 R-squared 0.222058011993361 Adjusted R-squared 0.188954097610100 F-TEST (value) 6.70790799609013 F-TEST (DF numerator) 6 F-TEST (DF denominator) 141 p-value 2.88931438152673e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.90311823362478 Sum Squared Residuals 510.682120572871 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.3099252146050 -3.30992521460496 2 16 16.1707661080725 -0.170766108072492 3 19 15.3498090132336 3.65019098676638 4 15 13.8311303628548 1.16886963714521 5 14 14.4892462770820 -0.48924627708203 6 13 15.1729305150650 -2.17293051506502 7 19 15.0736880335516 3.9263119664484 8 15 16.1985973540794 -1.19859735407944 9 14 15.8963517324391 -1.89635173243905 10 15 14.7820203517146 0.217979648285414 11 16 15.0225113440686 0.977488655931356 12 16 14.7773076614057 1.22269233859435 13 16 14.6837392702055 1.31626072979455 14 17 17.4084472649119 -0.408447264911936 15 15 12.7054325369295 2.29456746307054 16 15 15.7967466138365 -0.796746613836472 17 20 17.0279805712364 2.97201942876363 18 18 16.4372060936423 1.56279390635772 19 16 17.168463075271 -1.16846307527101 20 16 14.3654965047994 1.63450349520063 21 19 14.7693057654532 4.23069423454685 22 16 14.8491055238010 1.15089447619899 23 17 16.0620417972866 0.93795820271336 24 17 15.1409860546642 1.85901394533585 25 16 14.7027157562960 1.29728424370404 26 15 13.2863849684168 1.71361503158318 27 14 15.5185107917087 -1.51851079170871 28 15 16.0380487873953 -1.03804878739525 29 12 14.6813128523561 -2.68131285235611 30 14 14.9582603545262 -0.95826035452617 31 16 15.3067825878009 0.693217412199134 32 14 15.5113492399468 -1.51134923994678 33 10 13.2783669224344 -3.27836692243441 34 14 14.3945920809643 -0.394592080964290 35 16 16.5602407037551 -0.560240703755147 36 16 14.3210162237756 1.67898377622436 37 16 13.6443703671964 2.35562963280364 38 14 15.4433938661048 -1.44339386610476 39 20 17.8652247035942 2.13477529640580 40 14 14.8940976432078 -0.894097643207803 41 14 15.2602849594203 -1.26028495942033 42 11 14.6828591407508 -3.68285914075081 43 15 15.8602649620325 -0.860264962032533 44 16 15.7245772988460 0.275422701154047 45 14 15.0891204509964 -1.08912045099644 46 16 14.3959091848927 1.60409081510733 47 14 14.9196238817447 -0.919623881744672 48 12 15.2968902163492 -3.29689021634921 49 16 15.3316420196118 0.66835798038822 50 9 13.3690874317501 -4.3690874317501 51 14 14.2160647402933 -0.21606474029334 52 16 15.5625448569443 0.437455143055744 53 16 15.0849817272220 0.915018272778019 54 15 14.8885430891275 0.111456910872505 55 16 14.8188319236977 1.1811680763023 56 12 13.6507087901974 -1.65070879019740 57 16 16.2310206419693 -0.231020641969338 58 16 16.4317402158784 -0.43174021587843 59 14 16.5111958867373 -2.51119588673732 60 16 12.6318961533638 3.36810384663616 61 17 16.089504752222 0.910495247777996 62 18 14.6449012765407 3.35509872345932 63 18 15.5543130819463 2.44568691805375 64 12 14.7861941530335 -2.78619415303346 65 16 15.7925335526774 0.207466447322556 66 10 14.5537665909205 -4.55376659092046 67 14 12.8849149127881 1.11508508721194 68 18 15.5852394266749 2.41476057332514 69 18 16.2558632575438 1.74413674245625 70 16 15.4637492308103 0.536250769189659 71 16 15.7394405705425 0.260559429457469 72 16 14.8301832130255 1.16981678697447 73 13 14.5968180999253 -1.59681809992529 74 16 14.8681442387592 1.13185576124076 75 16 14.8801253749277 1.11987462507231 76 20 15.9254538425759 4.07454615742413 77 16 15.3425170033828 0.657482996617167 78 15 12.5095554452116 2.49044455478844 79 15 15.6452937454864 -0.64529374548635 80 16 16.0598298622116 -0.0598298622116237 81 14 14.1902116084183 -0.19021160841833 82 15 13.6707994109951 1.32920058900490 83 12 14.9190454478887 -2.91904544788869 84 17 16.2365194745385 0.763480525461452 85 16 15.5095155236424 0.490484476357604 86 15 13.1736847632481 1.82631523675194 87 13 14.6789879150201 -1.67898791502007 88 16 16.1088339477026 -0.108833947702615 89 16 15.5713163459339 0.428683654066055 90 16 16.3517269689131 -0.351726968913115 91 16 15.6146752045199 0.385324795480149 92 14 15.4045270884693 -1.40452708846931 93 16 14.5771085183073 1.42289148169266 94 16 15.1274111029253 0.872588897074726 95 20 16.4937440073912 3.50625599260884 96 15 15.6013819706196 -0.601381970619554 97 16 14.3772335144113 1.62276648558866 98 13 14.1196774365896 -1.11967743658962 99 17 16.1697626940922 0.830237305907778 100 16 14.3887955861149 1.61120441388509 101 12 13.3060316815757 -1.30603168157571 102 16 15.1419486892235 0.85805131077653 103 16 15.4603221531166 0.539677846883446 104 17 15.4447888947497 1.55521110525026 105 13 13.4464977951823 -0.446497795182297 106 12 15.9294891322532 -3.92948913225319 107 18 15.8352589221029 2.16474107789714 108 14 14.2116670457304 -0.211667045730435 109 14 14.7937953866117 -0.793795386611682 110 13 14.0890181080076 -1.08901810800760 111 16 15.4386805362045 0.561319463795501 112 13 12.8049931044696 0.195006895530407 113 16 15.4579039029873 0.542096097012691 114 13 14.9751802334197 -1.97518023341971 115 16 15.9972277151715 0.00277228482849207 116 15 15.0202090907344 -0.0202090907344012 117 16 15.7592774487257 0.240722551274252 118 15 14.9896974438655 0.0103025561345184 119 17 15.8567053117054 1.14329468829461 120 15 15.9518156513104 -0.951815651310364 121 12 13.8166603395711 -1.81666033957112 122 16 14.4719494852158 1.52805051478422 123 10 14.4055034480777 -4.40550344807769 124 16 14.3537289714158 1.64627102858422 125 14 14.623585345027 -0.623585345027007 126 15 16.5297003197088 -1.52970031970883 127 13 14.4871138129197 -1.48711381291969 128 15 15.3354018850243 -0.335401885024273 129 11 14.0634828217611 -3.06348282176115 130 12 14.2862291014697 -2.28622910146967 131 16 16.2063127103063 -0.206312710306301 132 15 15.0613165406223 -0.0613165406222636 133 17 15.3207050289504 1.67929497104955 134 16 15.3728519523644 0.627148047635605 135 10 15.2267468972319 -5.2267468972319 136 18 13.8072354397495 4.19276456025045 137 13 14.1707445408875 -1.17074454088750 138 15 14.4543614937984 0.545638506201642 139 16 14.7027157562960 1.29728424370404 140 16 15.2775647212672 0.722435278732803 141 14 13.7995791508668 0.200420849133171 142 10 13.3189603960459 -3.31896039604592 143 17 16.2365194745385 0.763480525461452 144 13 14.612426335268 -1.61242633526800 145 15 15.9518156513104 -0.951815651310364 146 16 16.0955558696753 -0.0955558696753403 147 12 15.4474354493558 -3.44743544935584 148 13 13.5082981916654 -0.508298191665398 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.93937100511491 0.121257989770178 0.0606289948850891 11 0.885837527663351 0.228324944673297 0.114162472336648 12 0.826478460462177 0.347043079075646 0.173521539537823 13 0.739295952313943 0.521408095372114 0.260704047686057 14 0.638318213832233 0.723363572335535 0.361681786167767 15 0.564808147598309 0.870383704803382 0.435191852401691 16 0.639074013597093 0.721851972805814 0.360925986402907 17 0.716176117868343 0.567647764263313 0.283823882131657 18 0.658157437648765 0.683685124702471 0.341842562351235 19 0.586686553715977 0.826626892568046 0.413313446284023 20 0.518839097802795 0.96232180439441 0.481160902197205 21 0.719720955452265 0.56055808909547 0.280279044547735 22 0.6681490970882 0.6637018058236 0.3318509029118 23 0.609867856746298 0.780264286507405 0.390132143253702 24 0.549904003810022 0.900191992379956 0.450095996189978 25 0.482867688756695 0.96573537751339 0.517132311243305 26 0.443257046396639 0.886514092793278 0.556742953603361 27 0.385964247315845 0.77192849463169 0.614035752684155 28 0.500811662173546 0.998376675652908 0.499188337826454 29 0.601992123803617 0.796015752392766 0.398007876196383 30 0.55343893571883 0.89312212856234 0.44656106428117 31 0.506105974378531 0.987788051242938 0.493894025621469 32 0.458499931004029 0.916999862008058 0.541500068995971 33 0.737013974193717 0.525972051612565 0.262986025806283 34 0.686129774540415 0.62774045091917 0.313870225459585 35 0.646276440474293 0.707447119051415 0.353723559525707 36 0.622230021734641 0.755539956530719 0.377769978265359 37 0.617002096373459 0.765995807253082 0.382997903626541 38 0.589844515368886 0.820310969262228 0.410155484631114 39 0.662838574513448 0.674322850973105 0.337161425486552 40 0.627599280546352 0.744801438907296 0.372400719453648 41 0.615276039514088 0.769447920971824 0.384723960485912 42 0.7825973555406 0.434805288918799 0.217402644459399 43 0.756154335485098 0.487691329029804 0.243845664514902 44 0.712812274477971 0.574375451044058 0.287187725522029 45 0.684323239421458 0.631353521157085 0.315676760578542 46 0.657655625601629 0.684688748796742 0.342344374398371 47 0.615529425618358 0.768941148763284 0.384470574381642 48 0.71233539860674 0.575329202786521 0.287664601393260 49 0.669867008485462 0.660265983029076 0.330132991514538 50 0.811719114752394 0.376561770495213 0.188280885247606 51 0.777162624060042 0.445674751879916 0.222837375939958 52 0.747829096338377 0.504341807323246 0.252170903661623 53 0.7193858949992 0.561228210001598 0.280614105000799 54 0.680929197004082 0.638141605991836 0.319070802995918 55 0.656096133892161 0.687807732215678 0.343903866107839 56 0.644781236069639 0.710437527860723 0.355218763930361 57 0.598145057247573 0.803709885504854 0.401854942752427 58 0.551802769547911 0.896394460904178 0.448197230452089 59 0.577648647535316 0.844702704929369 0.422351352464684 60 0.661140476853337 0.677719046293325 0.338859523146663 61 0.63285215765555 0.7342956846889 0.36714784234445 62 0.719582704591247 0.560834590817507 0.280417295408753 63 0.753060807920929 0.493878384158142 0.246939192079071 64 0.799141150712504 0.401717698574992 0.200858849287496 65 0.764491836246447 0.471016327507105 0.235508163753553 66 0.902527964047064 0.194944071905873 0.0974720359529364 67 0.887372687141252 0.225254625717495 0.112627312858748 68 0.906057957509856 0.187884084980289 0.0939420424901446 69 0.90582425678542 0.188351486429160 0.09417574321458 70 0.885358548355926 0.229282903288149 0.114641451644074 71 0.860533074507527 0.278933850984947 0.139466925492473 72 0.844404125526573 0.311191748946854 0.155595874473427 73 0.835155666352279 0.329688667295443 0.164844333647721 74 0.814590647493919 0.370818705012163 0.185409352506081 75 0.790797563905181 0.418404872189637 0.209202436094819 76 0.89102518351169 0.21794963297662 0.10897481648831 77 0.869656157223617 0.260687685552767 0.130343842776384 78 0.887237834442942 0.225524331114116 0.112762165557058 79 0.864728029900536 0.270543940198929 0.135271970099464 80 0.836201186305655 0.327597627388691 0.163798813694345 81 0.805701047474026 0.388597905051947 0.194298952525974 82 0.799047326846765 0.40190534630647 0.200952673153235 83 0.841535488420837 0.316929023158326 0.158464511579163 84 0.813154967733024 0.373690064533952 0.186845032266976 85 0.782068760958866 0.435862478082268 0.217931239041134 86 0.79095992176477 0.418080156470458 0.209040078235229 87 0.780997861050405 0.438004277899189 0.219002138949595 88 0.742555790551796 0.514888418896408 0.257444209448204 89 0.7042909139881 0.591418172023802 0.295709086011901 90 0.661974432183687 0.676051135632625 0.338025567816313 91 0.616058417459113 0.767883165081775 0.383941582540887 92 0.602307217836764 0.795385564326471 0.397692782163236 93 0.60955652243305 0.7808869551339 0.39044347756695 94 0.566776728832926 0.866446542334149 0.433223271167074 95 0.67718534587258 0.645629308254839 0.322814654127419 96 0.632226486846328 0.735547026307344 0.367773513153672 97 0.654725677274444 0.690548645451112 0.345274322725556 98 0.633368249600607 0.733263500798786 0.366631750399393 99 0.613750213585911 0.772499572828177 0.386249786414089 100 0.614185537053514 0.771628925892972 0.385814462946486 101 0.586615952423471 0.826768095153059 0.413384047576529 102 0.549820960895163 0.900358078209674 0.450179039104837 103 0.519919171406899 0.960161657186202 0.480080828593101 104 0.524072512413468 0.951854975173065 0.475927487586532 105 0.47030438512785 0.9406087702557 0.529695614872149 106 0.655210035040472 0.689579929919057 0.344789964959528 107 0.672603499960365 0.654793000079269 0.327396500039635 108 0.672652842511041 0.654694314977918 0.327347157488959 109 0.62326643104175 0.753467137916501 0.376733568958250 110 0.574345817604756 0.851308364790487 0.425654182395244 111 0.521614503546045 0.95677099290791 0.478385496453955 112 0.492164498823473 0.984328997646946 0.507835501176527 113 0.443028068478606 0.886056136957211 0.556971931521394 114 0.43233530080244 0.86467060160488 0.56766469919756 115 0.372742231129891 0.745484462259781 0.62725776887011 116 0.332597357609637 0.665194715219274 0.667402642390363 117 0.352305006885277 0.704610013770554 0.647694993114723 118 0.298597996106908 0.597195992213815 0.701402003893092 119 0.277701870928855 0.555403741857709 0.722298129071145 120 0.235975177403743 0.471950354807486 0.764024822596257 121 0.216606112165278 0.433212224330557 0.783393887834722 122 0.196624610266666 0.393249220533333 0.803375389733334 123 0.316381028287953 0.632762056575906 0.683618971712047 124 0.26369583079331 0.52739166158662 0.73630416920669 125 0.236084540521773 0.472169081043545 0.763915459478227 126 0.187993160377712 0.375986320755424 0.812006839622288 127 0.18535481044951 0.37070962089902 0.81464518955049 128 0.149708260967608 0.299416521935215 0.850291739032392 129 0.135364996628200 0.270729993256400 0.8646350033718 130 0.118360420766738 0.236720841533476 0.881639579233262 131 0.0808184796477773 0.161636959295555 0.919181520352223 132 0.0527532512544164 0.105506502508833 0.947246748745584 133 0.0581041062971944 0.116208212594389 0.941895893702806 134 0.03485397319856 0.06970794639712 0.96514602680144 135 0.294627575123429 0.589255150246857 0.705372424876571 136 0.480435530571623 0.960871061143246 0.519564469428377 137 0.375624463318191 0.751248926636381 0.624375536681809 138 0.260246796918173 0.520493593836347 0.739753203081827 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 1 0.00775193798449612 OK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

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

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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Software written by Ed van Stee & Patrick Wessa

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