*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: Sun, 12 Dec 2010 18:38:54 +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/12/t1292179006m4kafl8s7ugzr0e.htm/, Retrieved Sun, 12 Dec 2010 19:38:57 +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/12/t1292179006m4kafl8s7ugzr0e.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 «

8 350 165 3693 11,5 8 318 150 3436 11 8 302 140 3449 10,5 8 429 198 4341 10 8 440 215 4312 8,5 8 455 225 4425 10 8 383 170 3563 10 8 340 160 3609 8 8 455 225 3086 10 4 113 95 2372 15 6 199 97 2774 15,5 4 97 46 1835 20,5 4 110 87 2672 17,5 4 104 95 2375 17,5 4 121 113 2234 12,5 8 360 215 4615 14 8 307 200 4376 15 8 304 193 4732 18,5 4 97 88 2130 14,5 4 113 95 2228 14 6 250 100 3329 15,5 6 232 100 3288 15,5 8 350 165 4209 12 8 318 150 4096 13 8 400 170 4746 12 8 400 175 5140 12 4 140 72 2408 19 6 250 100 3282 15 4 122 86 2220 14 4 116 90 2123 14 4 88 76 2065 14,5 4 71 65 1773 19 4 97 60 1834 19 4 91 70 1955 20,5 4 97,5 80 2126 17 4 122 86 2226 16,5 8 350 165 4274 12 8 318 150 4135 13,5 8 351 153 4129 13 8 429 208 4633 11 8 350 155 4502 13,5 8 400 190 4422 12,5 3 70 97 2330 13,5 8 307 130 4098 14 8 302 140 4294 16 4 121 112 2933 14,5 4 121 76 2511 18 4 122 86 2395 16 4 120 97 2506 14,5 4 98 80 2164 15 8 350 175 4100 13 8 304 150 3672 11,5 8 302 137 4042 14,5 8 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 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 acceleration [t] = + 17.2587244715863 -0.184751272787248cylinders[t] -0.00730185636427856engine.displacement[t] -0.0732603848551417horsepower[t] + 0.00278578297645537weight[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) 17.2587244715863 0.764212 22.5837 0 0 cylinders -0.184751272787248 0.206326 -0.8954 0.371472 0.185736 engine.displacement -0.00730185636427856 0.004611 -1.5835 0.114653 0.057326 horsepower -0.0732603848551417 0.006727 -10.8911 0 0 weight 0.00278578297645537 0.00036 7.7475 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.768262915498146 R-squared 0.590227907329712 Adjusted R-squared 0.583253063199153 F-TEST (value) 84.6223795516537 F-TEST (DF numerator) 4 F-TEST (DF denominator) 235 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.70721080842101 Sum Squared Residuals 684.923654931535 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11.5 11.4249975927423 0.075002407257699 2 11 12.0416165442772 -1.0416165442772 3 10.5 12.9272652733510 -2.42726527335098 4 10 10.2357456084876 -0.235745608487573 5 8.5 8.82921093962588 -0.329210939625876 6 10 8.30187272194974 1.69812727805026 7 10 10.4555826215061 -0.455582621506065 8 8 11.6303123106384 -3.63031231063841 9 10 4.571709316476 5.42829068352400 10 15 15.3427502701875 -0.342750270187548 11 15.5 15.3186520641099 0.181347935890127 12 20.5 17.5533733715614 2.94662662843859 13 17.5 16.7864738110581 0.713526188941872 14 17.5 15.4168243263954 2.08317567360458 15 12.5 13.5812104411299 -1.08121044112993 16 14 10.2574516906341 3.74254830936585 17 15 11.0775537193952 3.9224462806048 18 18.5 12.6040207220921 5.89597927790786 19 14.5 15.2982431856998 -0.798243185699798 20 14 14.9415975215780 -0.941597521577975 21 15.5 16.2725857868990 -0.772585786898968 22 15.5 16.2898020994213 -0.789802099421313 23 12 12.8624616085931 -0.862461608593136 24 13 13.8802333087377 -0.880233308737719 25 12 13.6270323244600 -1.62703232446003 26 12 14.3583288929077 -2.35832889290774 27 19 16.9308771871727 2.06912281282732 28 15 16.1416539870056 -1.14165398700557 29 14 15.5129380141841 -1.5129380141841 30 14 14.9934866642330 -0.993486664233034 31 14.5 16.0620086177704 -1.56200861777041 32 19 16.1785557802447 2.82144421975527 33 19 16.5249422006130 2.47505779938702 34 20.5 16.1732292303983 4.32677076960167 35 17 15.8695322044530 1.13046779554703 36 16.5 15.5296527120428 0.970347287957169 37 12 13.0435375020627 -1.04353750206273 38 13.5 13.9888788448195 -0.488878844819479 39 13 13.5114217323741 -0.511421732374127 40 11 10.3165903890611 0.68340961093889 41 13.5 14.4112998692460 -0.911299869245975 42 12.5 11.2592309429857 1.24076905701434 43 13.5 15.5779577119174 -2.07795771191736 44 14 15.4313329918005 -1.43133299180053 45 16 15.2812518884558 0.718748111544243 46 14.5 15.6017331265274 -1.10173312652737 47 18 17.0635065652483 0.936493434751694 48 16 16.0004500350638 -0.000450035063788784 49 14.5 15.5184114247723 -1.01841142477233 50 15 15.9717410293761 -0.971741029376135 51 13 11.8262074156081 1.17379258439192 52 11.5 12.8012873158205 -1.30128731582054 53 14.5 14.7990157329544 -0.299015732954429 54 12.5 12.9915685392485 -0.491568539248457 55 12 14.3066492222024 -2.30664922220245 56 13 13.7969930245890 -0.796993024588975 57 11 10.0075971386665 0.992402861333498 58 11 9.76719456756527 1.23280543243473 59 16.5 15.5093874126275 0.99061258737249 60 18 16.1305108550997 1.86948914490026 61 16.5 16.2936892484124 0.206310751587585 62 16 15.8346264771236 0.165373522876367 63 14 15.7914715486532 -1.79147154865316 64 12.5 12.5714328989381 -0.0714328989380675 65 15 14.8996963941701 0.100303605829915 66 19.5 16.9113767063375 2.58862329366251 67 16.5 15.4720204176993 1.02797958230073 68 18.5 15.8369188669202 2.66308113307978 69 14 14.0660234366972 -0.0660234366971941 70 13 13.9738748676861 -0.973874867686137 71 9.5 7.92766280017042 1.57233719982958 72 15.5 16.1898948412361 -0.689894841236096 73 14 16.2135043782995 -2.21350437829946 74 11 11.9385425741483 -0.938542574148328 75 14 14.9877351436653 -0.98773514366534 76 11 10.2453041135978 0.754695886402165 77 16.5 16.3862115064618 0.113788493538204 78 16 15.2117040875331 0.788295912466914 79 16.5 16.5960161908761 -0.0960161908761392 80 21 16.3540601077614 4.64593989223858 81 17 17.5317596922568 -0.531759692256794 82 18 16.3256593292993 1.6743406707007 83 14 14.8550270930581 -0.855027093058085 84 14.5 15.3264010398834 -0.82640103988339 85 16 16.2395612323564 -0.239561232356403 86 15.5 14.4309703570469 1.06902964295307 87 15.5 16.5029189251467 -1.00291892514674 88 14.5 16.5044301402486 -2.00443014024863 89 19 17.0247051278787 1.97529487212131 90 14.5 16.2878122684843 -1.78781226848431 91 14 16.4350437431642 -2.43504374316417 92 15 15.4710531141726 -0.471053114172592 93 16 16.6059928952756 -0.60599289527559 94 16 16.6403582268120 -0.640358226812043 95 19.5 17.8475076738691 1.65249232613093 96 11.5 13.4097412522965 -1.90974125229651 97 14 14.9711851732572 -0.971185173257158 98 13.5 15.3486170682183 -1.84861706821827 99 21 17.2888997696600 3.71110023033995 100 19 16.5986660609919 2.40133393900808 101 19 18.0917511575453 0.90824884245471 102 13.5 14.7819925549445 -1.28199255494454 103 12 12.9531102733500 -0.953110273350026 104 17 16.7685288213273 0.231471178672692 105 16 15.247919266227 0.752080733772994 106 13.5 16.0354592839128 -2.53545928391283 107 16.5 16.8538605395975 -0.353860539597506 108 14.5 16.1081184673653 -1.60811846736530 109 15 16.2251686758776 -1.22516867587762 110 17 17.4341430108500 -0.434143010849979 111 13.5 14.6520768321306 -1.15207683213064 112 17.5 16.9729304967029 0.527069503297121 113 16.9 15.9230510766455 0.97694892335452 114 14.9 15.9225378982085 -1.02253789820852 115 15.3 15.8359140588232 -0.535914058823178 116 13 15.0392694642229 -2.03926946422295 117 13.9 15.8069759246468 -1.90697592464685 118 12.8 13.8242594532044 -1.02425945320443 119 14.5 15.9731426540582 -1.47314265405819 120 17.6 17.1465327138242 0.453467286175763 121 22.2 17.7585899340930 4.44141006590702 122 22.1 17.4369487264790 4.66305127352103 123 17.7 17.3521543144246 0.347845685575438 124 16.2 16.4202893589074 -0.220289358907449 125 17.8 16.2016063754625 1.59839362453748 126 17 16.3145427727599 0.68545722724006 127 16.4 16.3202727632280 0.0797272367719747 128 15.7 16.8731351736911 -1.17313517369110 129 13.2 13.4456511644107 -0.245651164410682 130 16.7 16.7739497531066 -0.0739497531065677 131 12.1 12.2399247247399 -0.139924724739879 132 15 14.8326837549901 0.167316245009903 133 14 12.9302813137664 1.06971868623356 134 14.8 15.8517448498524 -1.05174484985241 135 18.6 16.7778243380922 1.82217566190783 136 16.8 16.1891825388194 0.610817461180553 137 12.5 13.7397302428347 -1.23973024283469 138 13.7 14.3691096839775 -0.669109683977464 139 16.9 16.3124542992843 0.58754570071573 140 17.7 17.293652871919 0.406347128081 141 11.1 11.4291066302931 -0.32910663029309 142 11.4 12.3735852333534 -0.97358523335339 143 14.5 14.3783345649445 0.121665435055500 144 14.5 15.5015482687247 -1.00154826872469 145 18.2 16.6267088906381 1.57329110936189 146 15.8 16.6521173374653 -0.85211733746528 147 15.9 15.5040251899062 0.395974810093818 148 16.4 16.4327727360717 -0.0327727360717458 149 14.5 15.8198675534513 -1.31986755345131 150 12.8 14.8205881650780 -2.02058816507802 151 21.5 17.8758330428694 3.62416695713061 152 14.4 15.9833614139184 -1.58336141391836 153 18.6 16.5374054108764 2.06259458912363 154 13.2 13.6071695027887 -0.407169502788748 155 12.8 13.3376053983572 -0.537605398357211 156 18.2 16.5192542914854 1.68074570851463 157 15.8 16.7225593745103 -0.922559374510269 158 17.2 16.7364962766279 0.463503723372074 159 17.2 16.8051148758092 0.394885124190789 160 16.7 17.0150665870381 -0.315066587038084 161 18.7 16.5331911936030 2.16680880639697 162 13.2 12.4721989885475 0.727801011452502 163 13.4 11.9725468675049 1.42745313249512 164 13.7 14.5682646296658 -0.86826462966585 165 16.5 16.8257936008497 -0.325793600849737 166 14.7 14.9518419879868 -0.251841987986807 167 14.5 16.4707916355479 -1.97079163554795 168 17.6 17.1434167545243 0.456583245475682 169 15.9 15.7163711072187 0.183628892781287 170 13.6 14.5498246866626 -0.949824686662602 171 15.8 14.7159030114644 1.08409698853558 172 14.9 16.2120749624477 -1.31207496244768 173 16.6 16.7700779413206 -0.170077941320628 174 18.2 16.7922039489217 1.40779605107835 175 17.3 17.1014584241419 0.198541575858103 176 16.6 15.8088876197246 0.791112380275368 177 15.4 14.7272046966036 0.672795303396401 178 13.2 14.1256012672980 -0.925601267298019 179 15.2 14.2381208098277 0.961879190172283 180 14.3 14.1083522425465 0.191647757453468 181 15 14.7163181632549 0.283681836745116 182 14 16.0309990689781 -2.03099906897808 183 15.2 16.6317560960245 -1.43175609602454 184 15 17.2134045190841 -2.21340451908414 185 24.8 19.1753180032516 5.62468199674836 186 22.2 16.8161747770905 5.38382522290945 187 14.9 16.6142309217072 -1.71423092170723 188 19.2 16.7644181863293 2.43558181367069 189 16 16.2617449796044 -0.261744979604369 190 11.3 13.6911582494031 -2.39115824940305 191 13.2 15.9441657202885 -2.74416572028846 192 14.7 16.2090669092676 -1.50906690926760 193 15.5 16.5817704269635 -1.08177042696352 194 16.4 16.7543305469886 -0.354330546988576 195 18.1 17.0457427646128 1.05425723538721 196 20.1 17.189410710764 2.91058928923600 197 15.8 16.1924224468856 -0.392422446885625 198 15.5 16.5000936398318 -1.00009363983178 199 15 15.6914388311075 -0.691438831107534 200 15.2 16.5463884706311 -1.34638847063105 201 14.4 15.4884817118950 -1.08848171189505 202 19.2 17.0151386542103 2.18486134578971 203 19.9 18.7610574828212 1.13894251717876 204 13.8 16.1005031724359 -2.30050317243594 205 15.3 16.4674798945579 -1.16747989455793 206 15.1 16.1464364778813 -1.04643647788132 207 15.7 16.3166960548017 -0.616696054801711 208 16.4 16.6038048845593 -0.203804884559282 209 12.6 14.4196119606180 -1.81961196061796 210 12.9 16.0241888422739 -3.12418884227390 211 16.4 16.4264381832341 -0.0264381832341449 212 16.1 16.4356239621837 -0.335623962183735 213 19.4 16.6390579523888 2.76094204761118 214 17.3 17.0385654047313 0.261434595268720 215 14.9 17.3081295091628 -2.40812950916282 216 16.2 16.7391386280051 -0.539138628005072 217 14.2 16.4326207013449 -2.23262070134488 218 14.8 15.6095824710048 -0.809582471004822 219 20.4 18.6274058586136 1.77259414138642 220 13.8 14.4552437440754 -0.655243744075418 221 15.8 15.918294545244 -0.118294545244007 222 17.1 16.7674276027081 0.332572397291897 223 16.6 17.932904453631 -1.33290445363099 224 18.6 16.6094646582279 1.99053534177214 225 18 15.9269478289963 2.07305217100371 226 16 16.4141984589776 -0.414198458977648 227 18 16.4428208730740 1.55717912692603 228 15.3 15.8476062762892 -0.547606276289246 229 17.6 16.3615367447554 1.23846325524456 230 14.7 17.0574090412818 -2.35740904128183 231 14.5 15.2138739786151 -0.713873978615051 232 14.5 16.386543348408 -1.88654334840801 233 15.7 16.4208682147283 -0.72086821472831 234 16.4 14.9740693645239 1.42593063547608 235 17 16.4091334287478 0.590866571252236 236 13.9 15.8593667501412 -1.95936675014119 237 17.3 17.0417642130119 0.258235786988129 238 15.6 16.9694008962066 -1.36940089620664 239 11.6 15.7734683743929 -4.17346837439291 240 18.6 17.1686065263631 1.43139347363693 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.597446407623232 0.805107184753535 0.402553592376768 9 0.466738494429124 0.933476988858247 0.533261505570876 10 0.321899744726942 0.643799489453884 0.678100255273058 11 0.350894288546905 0.701788577093809 0.649105711453095 12 0.269968261233995 0.539936522467991 0.730031738766004 13 0.221492720146526 0.442985440293052 0.778507279853474 14 0.200659259824317 0.401318519648634 0.799340740175683 15 0.349215312759481 0.698430625518962 0.650784687240519 16 0.944552725120053 0.110894549759893 0.0554472748799466 17 0.974493843845538 0.0510123123089236 0.0255061561544618 18 0.996512841585981 0.00697431682803777 0.00348715841401889 19 0.996311790100958 0.00737641979808345 0.00368820989904172 20 0.995948177674056 0.0081036446518873 0.00405182232594365 21 0.994177953017572 0.0116440939648556 0.00582204698242778 22 0.991113448066526 0.0177731038669474 0.0088865519334737 23 0.98786243280204 0.0242751343959224 0.0121375671979612 24 0.982647753425294 0.0347044931494123 0.0173522465747062 25 0.977421545076747 0.0451569098465066 0.0225784549232533 26 0.975188013667534 0.0496239726649321 0.0248119863324660 27 0.985498223229746 0.0290035535405072 0.0145017767702536 28 0.98030358526431 0.0393928294713796 0.0196964147356898 29 0.98082694109455 0.0383461178109011 0.0191730589054505 30 0.978762865281175 0.04247426943765 0.021237134718825 31 0.977651503595605 0.0446969928087892 0.0223484964043946 32 0.986335798054615 0.0273284038907691 0.0136642019453845 33 0.991709082001422 0.0165818359971561 0.00829091799857804 34 0.998093080284634 0.00381383943073315 0.00190691971536657 35 0.99730198099811 0.00539603800378031 0.00269801900189015 36 0.996205941526133 0.00758811694773366 0.00379405847386683 37 0.99486466803945 0.0102706639211006 0.00513533196055029 38 0.992699850671551 0.0146002986568972 0.0073001493284486 39 0.98989733785148 0.0202053242970389 0.0101026621485195 40 0.986760049015006 0.0264799019699881 0.0132399509849940 41 0.982336652794824 0.0353266944103518 0.0176633472051759 42 0.979824678418027 0.0403506431639454 0.0201753215819727 43 0.991327034031614 0.0173459319367712 0.00867296596838558 44 0.989059681597237 0.0218806368055252 0.0109403184027626 45 0.986972440760252 0.0260551184794951 0.0130275592397476 46 0.986913399982049 0.0261732000359022 0.0130866000179511 47 0.98468456546046 0.0306308690790781 0.0153154345395391 48 0.979733908808978 0.0405321823820440 0.0202660911910220 49 0.97760725715512 0.0447854856897585 0.0223927428448793 50 0.974533456020051 0.0509330879598978 0.0254665439799489 51 0.970083683484018 0.0598326330319634 0.0299163165159817 52 0.968830038777815 0.0623399224443707 0.0311699612221853 53 0.960334922799793 0.0793301544004133 0.0396650772002066 54 0.950885781574146 0.0982284368517085 0.0491142184258542 55 0.946878052549548 0.106243894900905 0.0531219474504524 56 0.93474616677482 0.130507666450359 0.0652538332251797 57 0.927135724604817 0.145728550790366 0.0728642753951829 58 0.924701475501536 0.150597048996928 0.0752985244984638 59 0.919986714882534 0.160026570234933 0.0800132851174663 60 0.94056832720377 0.118863345592462 0.0594316727962309 61 0.93315303815646 0.133693923687081 0.0668469618435407 62 0.918980136142252 0.162039727715496 0.081019863857748 63 0.910520210875576 0.178959578248848 0.0894797891244238 64 0.893548848778191 0.212902302443617 0.106451151221809 65 0.873834221128905 0.252331557742189 0.126165778871095 66 0.906805296518643 0.186389406962715 0.0931947034813575 67 0.893667058509668 0.212665882980663 0.106332941490332 68 0.914556719391826 0.170886561216348 0.0854432806081738 69 0.901079592679231 0.197840814641538 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0.0497629687375558 138 0.944932628223895 0.11013474355221 0.0550673717761051 139 0.93448040034251 0.131039199314981 0.0655195996574905 140 0.92739197742244 0.145216045155120 0.0726080225775599 141 0.924311469781321 0.151377060437357 0.0756885302186787 142 0.911570451094918 0.176859097810164 0.0884295489050819 143 0.896091767403165 0.20781646519367 0.103908232596835 144 0.88408194883312 0.231836102333758 0.115918051166879 145 0.884032423236872 0.231935153526255 0.115967576763128 146 0.870198492564545 0.259603014870911 0.129801507435455 147 0.862068143020684 0.275863713958632 0.137931856979316 148 0.843337192749602 0.313325614500796 0.156662807250398 149 0.85560437854195 0.288791242916099 0.144395621458050 150 0.855860579212118 0.288278841575763 0.144139420787882 151 0.926037211342004 0.147925577315991 0.0739627886579956 152 0.919390258382247 0.161219483235506 0.0806097416177529 153 0.934893298664786 0.130213402670429 0.0651067013352143 154 0.92157754211623 0.156844915767540 0.0784224578837699 155 0.906511096786848 0.186977806426304 0.0934889032131521 156 0.89909308168867 0.20181383662266 0.10090691831133 157 0.894179379350038 0.211641241299924 0.105820620649962 158 0.877997050708126 0.244005898583748 0.122002949291874 159 0.857184895722623 0.285630208554754 0.142815104277377 160 0.846114281554312 0.307771436891376 0.153885718445688 161 0.840922124789889 0.318155750420222 0.159077875210111 162 0.845723594427226 0.308552811145549 0.154276405572774 163 0.906543923656312 0.186912152687376 0.0934560763436879 164 0.90207263699407 0.19585472601186 0.09792736300593 165 0.883862848899547 0.232274302200905 0.116137151100453 166 0.883110978791381 0.233778042417237 0.116889021208619 167 0.885871321581864 0.228257356836272 0.114128678418136 168 0.865087822436398 0.269824355127204 0.134912177563602 169 0.84104121463594 0.317917570728121 0.158958785364060 170 0.828628689412721 0.342742621174558 0.171371310587279 171 0.804635000517313 0.390729998965374 0.195364999482687 172 0.784454506435072 0.431090987129856 0.215545493564928 173 0.752794953711204 0.494410092577591 0.247205046288796 174 0.726712396018073 0.546575207963854 0.273287603981927 175 0.690550322577515 0.61889935484497 0.309449677422485 176 0.655720961582992 0.688558076834016 0.344279038417008 177 0.618077938714812 0.763844122570376 0.381922061285188 178 0.581012438474015 0.83797512305197 0.418987561525985 179 0.554336728466788 0.891326543066424 0.445663271533212 180 0.520346715178594 0.959306569642813 0.479653284821406 181 0.481556433251871 0.963112866503743 0.518443566748129 182 0.471720517885808 0.943441035771617 0.528279482114192 183 0.453003857581788 0.906007715163576 0.546996142418212 184 0.534306748376069 0.931386503247862 0.465693251623931 185 0.724085730258896 0.551828539482209 0.275914269741104 186 0.902715828474577 0.194568343050846 0.097284171525423 187 0.89742316433919 0.205153671321621 0.102576835660811 188 0.928694646882606 0.142610706234789 0.0713053531173944 189 0.912540242486435 0.174919515027130 0.0874597575135648 190 0.90478728211224 0.190425435775521 0.0952127178877603 191 0.913764905283865 0.17247018943227 0.086235094716135 192 0.90305790098372 0.193884198032561 0.0969420990162803 193 0.88550765560337 0.228984688793261 0.114492344396630 194 0.859728432995014 0.280543134009972 0.140271567004986 195 0.837071430045814 0.325857139908371 0.162928569954186 196 0.889820817745527 0.220358364508947 0.110179182254473 197 0.863768686178484 0.272462627643031 0.136231313821516 198 0.840624442706512 0.318751114586976 0.159375557293488 199 0.807632699214082 0.384734601571837 0.192367300785918 200 0.785272299512866 0.429455400974269 0.214727700487134 201 0.747104799110547 0.505790401778906 0.252895200889453 202 0.78031604789421 0.43936790421158 0.21968395210579 203 0.744844724701808 0.510310550596383 0.255155275298192 204 0.740219736057955 0.519560527884091 0.259780263942045 205 0.700184011578812 0.599631976842376 0.299815988421188 206 0.657735459594867 0.684529080810267 0.342264540405133 207 0.60433541170661 0.79132917658678 0.39566458829339 208 0.552233588854213 0.895532822291574 0.447766411145787 209 0.535873413188491 0.928253173623019 0.464126586811509 210 0.59231866547143 0.81536266905714 0.40768133452857 211 0.535254992329044 0.929490015341911 0.464745007670956 212 0.474571028594908 0.949142057189817 0.525428971405092 213 0.640129317343546 0.719741365312908 0.359870682656454 214 0.598398255118598 0.803203489762804 0.401601744881402 215 0.614364713233338 0.771270573533324 0.385635286766662 216 0.548770710780822 0.902458578438357 0.451229289219178 217 0.552341706760213 0.895316586479575 0.447658293239787 218 0.495996654241239 0.991993308482477 0.504003345758761 219 0.44455869766909 0.88911739533818 0.55544130233091 220 0.469134446306972 0.938268892613944 0.530865553693028 221 0.410018774332604 0.820037548665208 0.589981225667396 222 0.335725672331551 0.671451344663101 0.66427432766845 223 0.450822029465317 0.901644058930634 0.549177970534683 224 0.409877753651629 0.819755507303257 0.590122246348371 225 0.506285912515665 0.987428174968669 0.493714087484335 226 0.415097422949845 0.83019484589969 0.584902577050155 227 0.551744339044776 0.896511321910447 0.448255660955224 228 0.48050694833634 0.96101389667268 0.51949305166366 229 0.59842051622508 0.80315896754984 0.40157948377492 230 0.583154108180912 0.833691783638176 0.416845891819088 231 0.865704778410308 0.268590443179385 0.134295221589692 232 0.76885290495217 0.46229419009566 0.23114709504783 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.0266666666666667 NOK 5% type I error level 39 0.173333333333333 NOK 10% type I error level 63 0.28 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/10nkjk1292179119.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/10nkjk1292179119.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/19t4c1292179119.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/19t4c1292179119.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/29t4c1292179119.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/29t4c1292179119.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/39t4c1292179119.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/39t4c1292179119.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/4j23w1292179119.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/4j23w1292179119.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/5j23w1292179119.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/5j23w1292179119.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/6j23w1292179119.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/6j23w1292179119.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/7utk01292179119.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/7utk01292179119.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/8nkjk1292179119.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/8nkjk1292179119.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/9nkjk1292179119.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292179006m4kafl8s7ugzr0e/9nkjk1292179119.ps (open in new window)

Parameters (Session):

par1 = 5 ; 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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