*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 16:02:12 +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/t12913920844a42e8ahwz9l2ab.htm/, Retrieved Fri, 03 Dec 2010 17:01:24 +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/t12913920844a42e8ahwz9l2ab.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 13 13 14 13 3 1 12 12 8 13 5 0 15 10 12 16 6 3 12 9 7 12 6 3 10 10 10 11 5 1 12 12 7 12 3 3 15 13 16 18 8 1 9 12 11 11 4 4 12 12 14 14 4 0 11 6 6 9 4 3 11 5 16 14 6 2 11 12 11 12 6 4 15 11 16 11 5 3 7 14 12 12 4 1 11 14 7 13 6 1 11 12 13 11 4 2 10 12 11 12 6 3 14 11 15 16 6 1 10 11 7 9 4 1 6 7 9 11 4 2 11 9 7 13 2 3 15 11 14 15 7 4 11 11 15 10 5 2 12 12 7 11 4 1 14 12 15 13 6 2 15 11 17 16 6 2 9 11 15 15 7 4 13 8 14 14 5 2 13 9 14 14 6 3 16 12 8 14 4 3 13 10 8 8 4 3 12 10 14 13 7 4 14 12 14 15 7 2 11 8 8 13 4 2 9 12 11 11 4 4 16 11 16 15 6 3 12 12 10 15 6 4 10 7 8 9 5 2 13 11 14 13 6 5 16 11 16 16 7 3 14 12 13 13 6 1 15 9 5 11 3 1 5 15 8 12 3 1 8 11 10 12 4 2 11 11 8 12 6 3 16 11 13 14 7 9 17 11 15 14 5 0 9 15 6 8 4 0 9 11 12 13 5 2 13 12 16 16 6 2 10 12 5 13 6 3 6 9 15 11 6 1 12 12 12 14 5 2 8 12 8 13 4 0 14 13 13 13 5 5 12 11 14 13 5 2 11 9 12 12 4 4 16 9 16 16 6 3 8 11 10 15 2 0 15 11 15 15 8 0 7 12 8 12 3 4 16 12 16 14 6 1 14 9 19 12 6 1 16 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 aantalVrienden[t] = + 1.23901678587798 + 0.0963160831939473Popularity[t] -0.064095320981191FindingFriends[t] + 0.128730344656522KnowingPeople[t] -0.0742946234905387Liked[t] + 0.0388673886095459`Celebrity `[t] -0.000136327489515622t + 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) 1.23901678587798 0.956507 1.2954 0.197201 0.0986 Popularity 0.0963160831939473 0.054592 1.7643 0.079733 0.039867 FindingFriends -0.064095320981191 0.064855 -0.9883 0.324617 0.162309 KnowingPeople 0.128730344656522 0.043287 2.9739 0.003431 0.001715 Liked -0.0742946234905387 0.068054 -1.0917 0.27673 0.138365 `Celebrity ` 0.0388673886095459 0.11014 0.3529 0.724668 0.362334 t -0.000136327489515622 0.002557 -0.0533 0.957552 0.478776 Multiple Linear Regression - Regression Statistics Multiple R 0.404585261523168 R-squared 0.163689233841770 Adjusted R-squared 0.130012290238083 F-TEST (value) 4.86057273391784 F-TEST (DF numerator) 6 F-TEST (DF denominator) 149 p-value 0.000145740995116217 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.41229152671296 Sum Squared Residuals 297.190536107357 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 2.61074725279724 -0.610747252797238 2 1 1.88374287237493 -0.883742872374926 3 0 2.63165033319365 -2.63165033319365 4 3 2.06018784778303 0.939812152216968 5 3 2.22494230177499 0.775057698225012 6 1 1.75102706403179 -0.751027064031788 7 3 2.88288596915612 0.117114030843882 8 1 2.08988955019709 -1.08988955019709 9 4 2.54200863578736 1.45799136421264 10 0 2.17175851119156 -2.17175851119156 11 3 3.22928261101486 -0.229282611014857 12 2 2.28541656035547 -0.285416560355473 13 4 3.41371884478654 0.586281155213461 14 3 1.8226844980757 1.1773155019243 15 1 1.56760093380792 -0.567600933807918 16 1 2.5388917859819 -1.5388917859819 17 2 2.18841883971395 -0.188418839713948 18 3 2.85538505064534 0.144614949354656 19 1 1.88246922034254 -0.882469220342544 20 1 1.86232128633397 -0.86232128633397 21 2 1.73179001933860 0.268209980661404 22 3 2.93558749132479 0.064412508675208 23 4 2.97265551594961 1.02734448405039 24 2 1.86173518132059 0.138264818679408 25 1 3.01321930770916 -2.01321930770916 26 2 3.20807120323621 -1.20807120323621 27 2 2.48573969937005 -0.485739699370052 28 4 2.93098316921482 1.06901683078518 29 2 2.90561890935366 -0.905618909353663 30 3 2.15202802334419 0.847971976655807 31 3 2.43690182917845 0.56309817082155 32 3 2.85796053481006 0.142039465189937 33 4 2.77367648476498 1.22632351523502 34 2 2.00057820483170 -0.000578204831697277 35 2 2.08620870798017 -0.086208707980166 36 4 3.24858829036902 0.751411709630982 37 3 2.02671024118339 0.973289758816608 38 4 2.30385801523258 1.69614198476742 39 2 2.85035961598666 -0.850359615986663 40 5 3.21261574552996 1.78738425447004 41 3 2.75357737856387 0.246422621436133 42 1 2.04418742111214 -1.04418742111214 43 1 1.00821474627503 -0.00821474627502893 44 1 1.84973603021471 -0.849736030214708 45 2 1.95882204021308 0.0411779597869168 46 3 2.97419599360438 0.0258040063956187 47 9 3.25010166140276 5.74989833859724 48 0 1.47138263486190 -1.47138263486190 49 0 2.16740393039313 -2.16740393039313 50 2 2.81934151146223 -0.819341511462228 51 2 1.33710701364075 0.662892986359253 52 3 2.57988500986531 0.420114990134689 53 1 2.31741692554518 -1.31741692554518 54 2 1.45252212153478 0.547477878465221 55 0 2.64870608411991 -2.64870608411991 56 5 2.71285857686140 2.28714142313860 57 2 2.52256335370827 -0.522563353708273 58 4 3.29948510407152 0.700514895928482 59 3 1.54707247018127 1.45292752981873 60 0 3.09800477998927 -3.09800477998927 61 0 1.39067898079522 -1.39067898079522 62 4 3.25524307815096 0.74475692184904 63 1 3.78954082816776 -2.78954082816776 64 1 2.98731043134954 -1.98731043134954 65 4 1.59532588807467 2.40467411192533 66 2 2.71130180271643 -0.71130180271643 67 4 2.7928399270582 1.2071600729418 68 1 1.91662562009486 -0.91662562009486 69 4 2.84607629205138 1.15392370794862 70 2 1.03490282223744 0.965097177762564 71 5 2.99976191410051 2.00023808589949 72 4 2.61416775458539 1.38583224541461 73 4 2.15373926888559 1.84626073111441 74 4 2.67625409840952 1.32374590159048 75 4 2.5557703748383 1.4442296251617 76 3 2.81363443935597 0.186365560644031 77 3 2.65609968110973 0.343900318890267 78 3 2.77341499037911 0.226585009620888 79 2 1.95271580997003 0.0472841900299665 80 1 1.06973922086842 -0.0697392208684202 81 1 1.29808947495793 -0.298089474957927 82 5 3.20685450087141 1.79314549912859 83 4 2.58906307451379 1.41093692548621 84 2 2.26860815126924 -0.268608151269237 85 3 1.57911258624096 1.42088741375904 86 2 2.43627943300060 -0.436279433000595 87 2 1.83131858902752 0.168681410972482 88 2 2.43009710017103 -0.430097100171026 89 2 3.06163702133074 -1.06163702133074 90 3 1.90736678742836 1.09263321257164 91 2 2.20178142062810 -0.201781420628095 92 3 2.27686641782289 0.723133582177106 93 4 3.14129506760444 0.858704932395556 94 3 3.35704978074543 -0.357049780745433 95 3 2.39564539429127 0.604354605708731 96 0 1.78801778034409 -1.78801778034409 97 1 1.32995004298457 -0.329950042984567 98 2 1.43771452822045 0.562285471779551 99 2 2.65437712758078 -0.654377127580781 100 3 2.39175728417545 0.608242715824546 101 4 3.33303011332603 0.666969886673968 102 4 3.08563239903282 0.91436760096718 103 1 2.76038269342491 -1.76038269342491 104 2 1.43778621602411 0.56221378397589 105 2 0.818723443382513 1.18127655661749 106 3 2.14928064354207 0.85071935645793 107 3 2.0171271351068 0.9828728648932 108 3 2.99514497729857 0.00485502270143094 109 1 1.71751342878676 -0.717513428786761 110 1 1.74550548470330 -0.745505484703303 111 1 2.34138448992171 -1.34138448992171 112 1 3.10397532226772 -2.10397532226772 113 0 1.68243148179777 -1.68243148179777 114 1 2.59503622484815 -1.59503622484815 115 3 2.52705840101507 0.472941598984934 116 3 3.05451602538526 -0.0545160253852636 117 0 2.99028437691456 -2.99028437691456 118 2 1.58759631853510 0.412403681464903 119 5 2.92610990020415 2.07389009979585 120 2 2.67473232948825 -0.674732329488248 121 3 2.34357389113911 0.656426108860891 122 3 3.22824844174485 -0.22824844174485 123 5 1.71023581388645 3.28976418611355 124 4 2.76501685858144 1.23498314141856 125 4 3.11792410165495 0.882075898345047 126 0 1.53508295087141 -1.53508295087141 127 3 2.91806663225742 0.0819333677425846 128 0 2.80654540990116 -2.80654540990116 129 2 2.20966054775976 -0.209660547759764 130 0 1.72446910558237 -1.72446910558237 131 6 2.91752132229935 3.08247867770065 132 3 2.77285263653656 0.227147363463439 133 1 1.41150054577932 -0.411500545779323 134 6 2.17443758156966 3.82556241843034 135 2 2.76278405425281 -0.762784054252807 136 1 1.95533794482681 -0.955337944826809 137 3 2.98775132637406 0.0122486736259372 138 1 2.02383348738512 -1.02383348738512 139 2 3.33066914289304 -1.33066914289304 140 4 2.69120776523274 1.30879223476726 141 1 2.91986404095607 -1.91986404095607 142 2 2.69792794009482 -0.697927940094825 143 0 2.66409975479303 -2.66409975479303 144 5 2.34596634318757 2.65403365681243 145 2 2.08284134207769 -0.0828413420776901 146 1 1.13133023649905 -0.131330236499050 147 1 1.40441643012883 -0.404416430128833 148 4 2.2703114837983 1.7296885162017 149 3 3.21116182435034 -0.211161824350344 150 0 2.73176503417605 -2.73176503417605 151 3 2.61649763645742 0.383502363542584 152 3 3.0045214010665 -0.0045214010665006 153 0 1.80246207239493 -1.80246207239493 154 2 2.58904342257338 -0.589043422573384 155 5 3.00515633388734 1.99484366611266 156 2 2.1221380046211 -0.122138004621100 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.868498361736535 0.26300327652693 0.131501638263465 11 0.776573187216813 0.446853625566374 0.223426812783187 12 0.678445880634021 0.643108238731958 0.321554119365979 13 0.588960543091486 0.822078913817027 0.411039456908514 14 0.476213813251186 0.952427626502371 0.523786186748814 15 0.374375534853299 0.748751069706599 0.6256244651467 16 0.398478607977216 0.796957215954431 0.601521392022784 17 0.307286126137239 0.614572252274478 0.692713873862761 18 0.261794712321611 0.523589424643221 0.73820528767839 19 0.193974424390319 0.387948848780638 0.806025575609681 20 0.141129739758082 0.282259479516164 0.858870260241918 21 0.161440118953599 0.322880237907197 0.838559881046401 22 0.115930719797995 0.231861439595989 0.884069280202005 23 0.0915782096953282 0.183156419390656 0.908421790304672 24 0.0656489817016864 0.131297963403373 0.934351018298314 25 0.122892556152686 0.245785112305372 0.877107443847314 26 0.107360481545101 0.214720963090202 0.892639518454899 27 0.0829838334513259 0.165967666902652 0.917016166548674 28 0.0941314666738324 0.188262933347665 0.905868533326168 29 0.07348593901096 0.14697187802192 0.92651406098904 30 0.071672263289031 0.143344526578062 0.928327736710969 31 0.0568606665349212 0.113721333069842 0.943139333465079 32 0.0404641392784202 0.0809282785568404 0.95953586072158 33 0.0365682954762461 0.0731365909524923 0.963431704523754 34 0.0252891728692645 0.0505783457385291 0.974710827130735 35 0.0181581419844450 0.0363162839688899 0.981841858015555 36 0.0127374625292575 0.025474925058515 0.987262537470743 37 0.00928959209370844 0.0185791841874169 0.990710407906292 38 0.0109333349233127 0.0218666698466254 0.989066665076687 39 0.0113978562026664 0.0227957124053327 0.988602143797334 40 0.0118535774907575 0.0237071549815151 0.988146422509242 41 0.0082099064935534 0.0164198129871068 0.991790093506447 42 0.0085583603848342 0.0171167207696684 0.991441639615166 43 0.00619725474484487 0.0123945094896897 0.993802745255155 44 0.0057593182896588 0.0115186365793176 0.994240681710341 45 0.00384640032728877 0.00769280065457753 0.996153599672711 46 0.00260929195577162 0.00521858391154324 0.997390708044228 47 0.172199165342915 0.344398330685831 0.827800834657085 48 0.193277423756223 0.386554847512446 0.806722576243777 49 0.281974696872211 0.563949393744422 0.718025303127789 50 0.279931828766966 0.559863657533932 0.720068171233034 51 0.251701882306207 0.503403764612415 0.748298117693793 52 0.215085356681531 0.430170713363062 0.784914643318469 53 0.232541745671247 0.465083491342494 0.767458254328753 54 0.202055249586743 0.404110499173486 0.797944750413257 55 0.364956259661258 0.729912519322515 0.635043740338742 56 0.407188018409381 0.814376036818762 0.592811981590619 57 0.375802032443456 0.751604064886912 0.624197967556544 58 0.333321090867896 0.666642181735791 0.666678909132104 59 0.32492487049837 0.64984974099674 0.67507512950163 60 0.554528814290128 0.890942371419745 0.445471185709872 61 0.566555645396125 0.86688870920775 0.433444354603875 62 0.52155300196041 0.95689399607918 0.47844699803959 63 0.69152661254454 0.616946774910919 0.308473387455459 64 0.750998150460793 0.498003699078415 0.249001849539207 65 0.806633905303116 0.386732189393768 0.193366094696884 66 0.789440129879252 0.421119740241496 0.210559870120748 67 0.775148510433077 0.449702979133845 0.224851489566923 68 0.764579877162291 0.470840245675417 0.235420122837709 69 0.742889677831266 0.514220644337468 0.257110322168734 70 0.71747618733059 0.565047625338819 0.282523812669410 71 0.73044309294734 0.539113814105319 0.269556907052659 72 0.710231386165092 0.579537227669815 0.289768613834908 73 0.712707274800285 0.57458545039943 0.287292725199715 74 0.694348206682506 0.611303586634988 0.305651793317494 75 0.677149661134245 0.64570067773151 0.322850338865755 76 0.634066901503644 0.731866196992711 0.365933098496356 77 0.588478304900057 0.823043390199886 0.411521695099943 78 0.544334705026634 0.911330589946732 0.455665294973366 79 0.501190247772525 0.99761950445495 0.498809752227475 80 0.459296723410264 0.918593446820528 0.540703276589736 81 0.423641576163133 0.847283152326267 0.576358423836867 82 0.447860417381202 0.895720834762404 0.552139582618798 83 0.433142926806649 0.866285853613299 0.56685707319335 84 0.394879640390983 0.789759280781967 0.605120359609017 85 0.383092454483286 0.766184908966571 0.616907545516714 86 0.355137229501316 0.710274459002632 0.644862770498684 87 0.312276130488306 0.624552260976613 0.687723869511694 88 0.287651665014636 0.575303330029272 0.712348334985364 89 0.280387457250966 0.560774914501932 0.719612542749034 90 0.255124938974764 0.510249877949528 0.744875061025236 91 0.222080043418358 0.444160086836716 0.777919956581642 92 0.190465881604331 0.380931763208663 0.809534118395669 93 0.166269588842120 0.332539177684241 0.83373041115788 94 0.14289804736667 0.28579609473334 0.85710195263333 95 0.120223728875531 0.240447457751063 0.879776271124469 96 0.149807031520925 0.299614063041850 0.850192968479075 97 0.124723747413419 0.249447494826839 0.87527625258658 98 0.101619798987313 0.203239597974625 0.898380201012687 99 0.0878427854794147 0.175685570958829 0.912157214520585 100 0.0706658811085584 0.141331762217117 0.929334118891442 101 0.0590612351088533 0.118122470217707 0.940938764891147 102 0.0501881223966285 0.100376244793257 0.949811877603371 103 0.0659809072693731 0.131961814538746 0.934019092730627 104 0.0581029264237964 0.116205852847593 0.941897073576204 105 0.05273631184077 0.10547262368154 0.94726368815923 106 0.0426757440400503 0.0853514880801005 0.95732425595995 107 0.0399046455090613 0.0798092910181226 0.960095354490939 108 0.0302065451282026 0.0604130902564052 0.969793454871797 109 0.0244950509477374 0.0489901018954748 0.975504949052263 110 0.0204601368730113 0.0409202737460226 0.979539863126989 111 0.0183180826730065 0.036636165346013 0.981681917326994 112 0.0250543766749511 0.0501087533499021 0.974945623325049 113 0.028572655049232 0.057145310098464 0.971427344950768 114 0.0327745521764338 0.0655491043528675 0.967225447823566 115 0.0243325204874719 0.0486650409749438 0.975667479512528 116 0.0176976057486303 0.0353952114972606 0.98230239425137 117 0.051026685892464 0.102053371784928 0.948973314107536 118 0.0385427508237056 0.0770855016474112 0.961457249176294 119 0.0407369589654044 0.0814739179308089 0.959263041034596 120 0.0313422766656189 0.0626845533312378 0.968657723334381 121 0.0236203074594015 0.047240614918803 0.976379692540599 122 0.01706003044804 0.03412006089608 0.98293996955196 123 0.056976874085964 0.113953748171928 0.943023125914036 124 0.0471229431470613 0.0942458862941226 0.952877056852939 125 0.0392303746069709 0.0784607492139418 0.96076962539303 126 0.0345800263364107 0.0691600526728215 0.96541997366359 127 0.0244935237964153 0.0489870475928306 0.975506476203585 128 0.0788659876339943 0.157731975267989 0.921134012366006 129 0.0614852171904676 0.122970434380935 0.938514782809532 130 0.111022944337545 0.222045888675089 0.888977055662455 131 0.192886885132545 0.38577377026509 0.807113114867455 132 0.148764351038975 0.29752870207795 0.851235648961025 133 0.117043611447656 0.234087222895311 0.882956388552344 134 0.651476310038078 0.697047379923843 0.348523689961922 135 0.579635398779735 0.840729202440529 0.420364601220264 136 0.509405024737291 0.98118995052542 0.49059497526271 137 0.451558528686305 0.90311705737261 0.548441471313695 138 0.434080706779878 0.868161413559755 0.565919293220122 139 0.370926924329184 0.741853848658367 0.629073075670816 140 0.669150609644766 0.661698780710467 0.330849390355234 141 0.650156312410736 0.699687375178529 0.349843687589264 142 0.541638265245033 0.916723469509934 0.458361734754967 143 0.502817886794039 0.994364226411923 0.497182113205961 144 0.396545903807507 0.793091807615014 0.603454096192493 145 0.271590293505361 0.543180587010722 0.728409706494639 146 0.39483223847893 0.78966447695786 0.60516776152107 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0145985401459854 NOK 5% type I error level 20 0.145985401459854 NOK 10% type I error level 35 0.255474452554745 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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