*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: Tue, 28 Dec 2010 09:02:26 +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/28/t1293526805j3pyvc4jozcrbd2.htm/, Retrieved Tue, 28 Dec 2010 10:00:08 +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/28/t1293526805j3pyvc4jozcrbd2.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 «

22 27 5 26 49 35 23 36 4 25 45 34 27 25 4 17 54 13 19 27 3 37 36 35 15 25 3 35 36 28 29 44 3 15 53 32 25 50 4 27 46 35 25 41 4 36 42 36 21 48 5 25 41 27 22 43 4 30 45 29 22 47 2 27 47 27 24 41 3 33 42 28 22 44 2 29 45 29 23 47 5 30 40 28 19 40 3 25 45 30 19 46 3 23 40 25 21 28 3 26 42 15 20 56 3 24 45 33 23 49 4 35 47 31 11 25 4 39 31 37 21 41 4 23 46 37 19 26 3 32 34 34 21 50 5 29 43 32 23 47 4 26 45 21 19 52 2 21 42 25 22 37 5 35 51 32 19 41 3 23 44 28 23 45 4 21 47 22 29 26 4 28 47 25 27 3 30 41 26 18 52 4 21 44 34 30 46 2 29 51 34 26 58 3 28 46 36 20 54 5 19 47 36 22 29 3 26 46 26 20 50 3 33 38 26 21 43 2 34 50 34 18 30 3 33 48 33 21 47 2 40 36 31 27 45 3 24 51 33 48 1 35 35 22 18 48 3 35 49 29 24 26 4 32 38 24 24 46 5 20 47 37 17 3 35 36 32 22 50 3 35 47 23 21 25 4 21 46 29 23 47 2 33 43 35 19 47 2 40 53 20 22 41 3 22 55 28 19 45 2 35 39 26 24 41 4 20 55 36 22 45 5 28 41 26 26 40 3 46 33 33 22 29 4 18 52 25 23 34 5 22 42 29 27 45 5 20 56 32 21 5 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 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation Behoefte_affiliatie[t] = + 59.8331365247396 -0.321873599043689leeftijd[t] -0.0894242784873792opleiding[t] + 0.0106074503726083Neuroticisme[t] -0.3095406594854Extraversie[t] -0.305320732396517`Openheid `[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) 59.8331365247396 7.064592 8.4694 0 0 leeftijd -0.321873599043689 0.062584 -5.1431 1e-06 0 opleiding -0.0894242784873792 0.078225 -1.1432 0.254412 0.127206 Neuroticisme 0.0106074503726083 0.091174 0.1163 0.907504 0.453752 Extraversie -0.3095406594854 0.058358 -5.3042 0 0 `Openheid ` -0.305320732396517 0.074876 -4.0777 6.7e-05 3.3e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.601830538297624 R-squared 0.362199996827607 Adjusted R-squared 0.345326980870666 F-TEST (value) 21.466227362785 F-TEST (DF numerator) 5 F-TEST (DF denominator) 189 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.32437127245557 Sum Squared Residuals 16432.3970294264 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 22 25.117503719148 -3.11750371914802 2 23 23.8429415262079 -0.842941526207933 3 27 30.9245609576659 -3.92456095766588 4 19 29.4370628035319 -10.4370628035319 5 15 32.1968402276497 -17.1968402276497 6 29 19.3856186975295 9.61438130247047 7 25 18.7430646484596 6.25693535154043 8 25 22.6682359987513 2.33176400124867 9 21 23.2664418239135 -2.26644182391349 10 22 23.1694672467477 -1.16946724674772 11 22 22.0205592022521 -0.0205592022521363 12 24 25.168403785293 -1.16840378529302 13 22 23.0158347543062 -1.01583475430618 14 23 23.6455726019091 -0.645572601909105 15 19 23.8661543381066 -4.86615433810661 16 19 24.9880048025088 -5.98800480250884 17 21 33.2476779414074 -12.2476779414074 18 20 17.7896071058454 2.21039289415457 19 23 20.0615401205848 2.9384598794152 20 11 30.949662456511 -19.949662456511 21 21 20.9868557735693 0.0131442264306973 22 19 30.6303012020798 -11.6303012020798 23 21 20.5194394463632 0.480560553636838 24 23 24.2821089082547 -1.28210890825467 25 19 22.5058912670181 -3.50589126701808 26 22 22.2911156602836 -0.291115660283565 27 19 24.4432479625961 -5.44324796259614 28 23 23.9484168031117 -0.948416803111689 29 29 29.2223051403605 -0.222305140360478 30 27 43.0758625085064 -16.0758625085064 31 52 37.4504557023255 14.5495442976745 32 46 38.6743437547082 7.3256562452918 33 58 39.6017002576971 18.3982997423029 34 54 39.1627375515758 14.8372624484242 35 29 42.8759554095259 -13.8759554095259 36 50 41.8598051247369 8.14019487526314 37 43 40.6591807710708 2.34081922892917 38 30 39.7990950120652 -9.79909501206515 39 47 38.1548661818176 8.84513381818242 40 45 32.3920760948634 12.6079239051366 41 1 25.4439476935796 -24.4439476935796 42 3 29.1260721031755 -26.1260721031755 43 4 24.9159080638744 -20.9159080638744 44 5 43.4070457103042 -38.4070457103042 45 35 29.2244787843085 5.7755212156915 46 35 33.9112760055802 1.08872399441979 47 21 27.5185657905591 -6.51856579055908 48 33 27.9052111152754 5.09478888472456 49 40 27.6115848777829 12.3884151222171 50 22 25.2877791951336 -3.28777919513363 51 35 31.297163761819 3.70283623818099 52 20 23.6882451211629 -3.68824512116287 53 28 31.2894928563588 -3.28949285635877 54 46 36.2957084197491 9.70429158025093 55 18 29.0530876863671 -11.0530876863671 56 22 28.5516091100055 -6.55160911000551 57 20 22.1573180340913 -2.15731803409132 58 25 28.1543704591459 -3.15437045914591 59 31 31.5139676779368 -0.513967677936793 60 21 25.9910725730771 -4.99107257307712 61 23 25.3729960749065 -2.3729960749065 62 26 34.1701657726983 -8.1701657726983 63 34 32.1313912291573 1.8686087708427 64 31 32.7573745048708 -1.75737450487082 65 23 24.5593903594388 -1.55939035943877 66 31 25.5075150757564 5.49248492424363 67 26 26.3505567828462 -0.350556782846201 68 36 27.7415338862523 8.2584661137477 69 28 31.4066900418439 -3.40669004184395 70 34 26.7751441404037 7.22485585959629 71 25 29.8403298621303 -4.8403298621303 72 33 36.4018598303324 -3.40185983033239 73 46 34.411648096307 11.588351903693 74 24 30.8806902146584 -6.8806902146584 75 32 34.240882116718 -2.24088211671803 76 33 24.8457235853604 8.15427641463962 77 42 36.7499372059277 5.2500627940723 78 17 24.6725863811359 -7.67258638113595 79 36 28.4048382173346 7.5951617826654 80 40 32.6957231333812 7.30427686661876 81 30 33.8707904565763 -3.87079045657634 82 19 39.1403382599544 -20.1403382599544 83 33 28.7312274136253 4.26877258637471 84 35 26.2421932782159 8.75780672178407 85 23 28.044172588995 -5.04417258899498 86 15 23.5007379467095 -8.50073794670946 87 38 37.7319902629241 0.268009737075917 88 37 28.5978346382849 8.40216536171506 89 23 26.3483891866514 -3.34838918665136 90 41 32.4038973180102 8.59610268198982 91 34 33.0626952372673 0.937304762732664 92 38 30.7097484352265 7.29025156477346 93 45 29.8865534164882 15.1134465835118 94 27 25.5757244534985 1.42427554650147 95 46 36.0046569314304 9.99534306856957 96 26 29.7575110723 -3.75751107230004 97 44 35.7090487155723 8.29095128442775 98 36 27.8633307012742 8.13666929872585 99 20 31.5289118550932 -11.5289118550932 100 44 32.2596022200666 11.7403977799334 101 27 34.1718421836245 -7.17184218362446 102 27 29.5732814086967 -2.57328140869672 103 41 32.6650299923254 8.33497000767465 104 30 28.7033597545219 1.29664024547813 105 33 34.3596217800457 -1.35962178004566 106 37 26.9645385411172 10.0354614588828 107 30 30.6180941559829 -0.618094155982933 108 20 24.2016441672297 -4.20164416722974 109 44 37.3874083635522 6.61259163644775 110 20 24.7570084575151 -4.75700845751505 111 33 28.3388367927594 4.66116320724062 112 31 36.1185594972838 -5.11855949728375 113 23 32.0759972549547 -9.07599725495468 114 33 31.7216259321873 1.27837406781273 115 33 25.7252450972587 7.27475490274133 116 32 28.0191136811288 3.98088631887124 117 25 27.8388646312644 -2.8388646312644 118 37 42.8425156230228 -5.84251562302283 119 48 39.1393976824685 8.86060231753151 120 45 38.4590446944559 6.5409553055441 121 32 41.1596830916966 -9.15968309169657 122 46 41.4326636351029 4.56733636489714 123 20 42.658514607755 -22.658514607755 124 42 37.2210525394832 4.77894746051684 125 45 30.8312465888785 14.1687534111215 126 29 38.7523182355638 -9.75231823556379 127 51 42.1721179609673 8.82788203903274 128 55 38.5806547771155 16.4193452228845 129 50 40.3542386690303 9.64576133096973 130 44 40.1964049541366 3.80359504586339 131 41 34.5084929360706 6.4915070639294 132 40 37.9865421328518 2.01345786714818 133 47 38.0826316980718 8.91736830192823 134 42 34.9518265865393 7.04817341346067 135 40 38.0837237674786 1.91627623252136 136 51 40.5224501630833 10.4775498369167 137 43 40.8654119166818 2.13458808331817 138 45 39.3843979448103 5.61560205518968 139 41 32.8107170009084 8.1892829990916 140 41 38.1256927573231 2.87430724267686 141 37 39.8478435187051 -2.84784351870506 142 46 34.6892134190821 11.3107865809179 143 38 38.7857446711579 -0.785744671157946 144 39 32.5768279394361 6.42317206056392 145 45 28.1156710501322 16.8843289498678 146 28 26.6180752684827 1.38192473151731 147 45 37.1591680253186 7.84083197468137 148 21 27.1314689730685 -6.13146897306851 149 33 35.8654777966963 -2.8654777966963 150 24 21.3875891395787 2.61241086042127 151 16 21.267268615358 -5.26726861535805 152 23 42.383847373134 -19.383847373134 153 40 39.7850955834691 0.214904416530853 154 49 41.538707661304 7.46129233869598 155 38 42.2356109094779 -4.23561090947787 156 32 39.4641123378523 -7.46411233785233 157 46 39.7590443831771 6.24095561682288 158 32 41.8293045142391 -9.82930451423912 159 41 43.8411207733459 -2.84112077334594 160 43 42.7722082651476 0.227791734852425 161 44 41.9629921618101 2.0370078381899 162 47 39.956952012003 7.04304798799703 163 28 42.1311359098207 -14.1311359098207 164 52 41.9411825777961 10.0588174222039 165 27 41.1011942399206 -14.1011942399206 166 45 41.6360493756894 3.36395062431065 167 27 37.2457898800738 -10.2457898800737 168 25 38.4103544268903 -13.4103544268903 169 28 40.0364179431271 -12.0364179431271 170 25 43.9528100691583 -18.9528100691583 171 52 39.5883616994112 12.4116383005888 172 44 43.5772562546508 0.422743745349184 173 43 39.0746000596783 3.92539994032169 174 47 40.9183901930039 6.08160980699606 175 52 40.2724380877629 11.7275619122371 176 40 40.626081177185 -0.626081177185027 177 42 40.1577977447423 1.84220225525766 178 45 40.0484286213844 4.95157137861561 179 45 45.6646677181087 -0.664667718108656 180 50 40.1240311411379 9.87596885886205 181 49 41.6616763756815 7.33832362431851 182 52 38.3584189763525 13.6415810236475 183 48 38.4470047146676 9.55299528533236 184 51 37.1518599262278 13.8481400737722 185 49 41.7266980362053 7.27330196379472 186 31 41.1435026367017 -10.1435026367017 187 43 38.7709424119061 4.22905758809391 188 31 38.8929230361987 -7.89292303619866 189 28 39.4151245301093 -11.4151245301093 190 43 42.2866993284469 0.713300671553054 191 31 43.214605218925 -12.214605218925 192 51 43.0043201526888 7.99567984731121 193 58 39.8029398171137 18.1970601828863 194 25 37.448188012544 -12.448188012544 195 27 38.5622024299982 -11.5622024299982 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.0114589232736245 0.022917846547249 0.988541076726375 10 0.00558025508464657 0.0111605101692931 0.994419744915353 11 0.00383039495138543 0.00766078990277086 0.996169605048615 12 0.00144688169110891 0.00289376338221783 0.99855311830889 13 0.000406829690622745 0.00081365938124549 0.999593170309377 14 0.000110845320022862 0.000221690640045724 0.999889154679977 15 7.2342061789211e-05 0.000144684123578422 0.99992765793821 16 1.75447938266853e-05 3.50895876533707e-05 0.999982455206173 17 5.37635136478093e-06 1.07527027295619e-05 0.999994623648635 18 2.89050727484676e-06 5.78101454969353e-06 0.999997109492725 19 1.20016921465062e-06 2.40033842930125e-06 0.999998799830785 20 9.13359193218518e-07 1.82671838643704e-06 0.999999086640807 21 2.61232875895227e-07 5.22465751790455e-07 0.999999738767124 22 2.52252598181451e-07 5.04505196362902e-07 0.999999747747402 23 7.2864035954946e-08 1.45728071909892e-07 0.999999927135964 24 1.84663738701328e-08 3.69327477402656e-08 0.999999981533626 25 5.44503040070167e-09 1.08900608014033e-08 0.99999999455497 26 4.41030311973867e-09 8.82060623947733e-09 0.999999995589697 27 1.95896596257068e-09 3.91793192514135e-09 0.999999998041034 28 5.15437507545988e-10 1.03087501509198e-09 0.999999999484563 29 1.68819821438689e-09 3.37639642877377e-09 0.999999998311802 30 5.9772883698613e-10 1.19545767397226e-09 0.999999999402271 31 0.000150681664532755 0.00030136332906551 0.999849318335467 32 8.0415756876931e-05 0.000160831513753862 0.999919584243123 33 0.000365907109930215 0.00073181421986043 0.99963409289007 34 0.00164732958504155 0.00329465917008311 0.998352670414958 35 0.00266332112442352 0.00532664224884704 0.997336678875577 36 0.00275854827666059 0.00551709655332117 0.99724145172334 37 0.0045700735963822 0.0091401471927644 0.995429926403618 38 0.0244512042985658 0.0489024085971317 0.975548795701434 39 0.0183419130615764 0.0366838261231528 0.981658086938424 40 0.0146526036778114 0.0293052073556228 0.985347396322189 41 0.0446198354902716 0.0892396709805433 0.955380164509728 42 0.154352659497981 0.308705318995963 0.845647340502019 43 0.194495406489687 0.388990812979374 0.805504593510313 44 0.379424675276356 0.758849350552712 0.620575324723644 45 0.336592955236531 0.673185910473063 0.663407044763469 46 0.78023838126308 0.43952323747384 0.21976161873692 47 0.770510961115485 0.45897807776903 0.229489038884515 48 0.743121907164485 0.51375618567103 0.256878092835515 49 0.84264550533692 0.31470898932616 0.15735449466308 50 0.815705503819519 0.368588992360962 0.184294496180481 51 0.795694369030286 0.408611261939429 0.204305630969714 52 0.774454530019864 0.451090939960273 0.225545469980136 53 0.738658209733368 0.522683580533264 0.261341790266632 54 0.865208577888779 0.269582844222443 0.134791422111221 55 0.85521114506837 0.289577709863258 0.144788854931629 56 0.856080756588507 0.287838486822985 0.143919243411493 57 0.844351110590967 0.311297778818066 0.155648889409033 58 0.818575428099169 0.362849143801662 0.181424571900831 59 0.791391825211841 0.417216349576318 0.208608174788159 60 0.767627451412294 0.464745097175412 0.232372548587706 61 0.76372558428232 0.472548831435361 0.23627441571768 62 0.760727649162135 0.478544701675729 0.239272350837865 63 0.792621319161183 0.414757361677634 0.207378680838817 64 0.785498182201388 0.429003635597224 0.214501817798612 65 0.75886385283467 0.482272294330659 0.24113614716533 66 0.72969852274891 0.54060295450218 0.27030147725109 67 0.697688722205181 0.604622555589638 0.302311277794819 68 0.67050916972791 0.658981660544181 0.329490830272091 69 0.634003336460959 0.731993327078082 0.365996663539041 70 0.599289230414864 0.801421539170271 0.400710769585136 71 0.565225622782044 0.869548754435912 0.434774377217956 72 0.525981248344482 0.948037503311036 0.474018751655518 73 0.557120398905477 0.885759202189046 0.442879601094523 74 0.531071433194677 0.937857133610647 0.468928566805323 75 0.496724543571677 0.993449087143354 0.503275456428323 76 0.497510218661856 0.995020437323713 0.502489781338144 77 0.502629175223135 0.99474164955373 0.497370824776865 78 0.506425799985833 0.987148400028335 0.493574200014167 79 0.534512814701131 0.930974370597737 0.465487185298869 80 0.597339585083252 0.805320829833495 0.402660414916748 81 0.567974395886876 0.864051208226247 0.432025604113124 82 0.660230495497843 0.679539009004315 0.339769504502157 83 0.642377241358703 0.715245517282593 0.357622758641297 84 0.622147061998002 0.755705876003997 0.377852938001998 85 0.611980370395952 0.776039259208096 0.388019629604048 86 0.628844810188592 0.742310379622817 0.371155189811408 87 0.603137017927938 0.793725964144124 0.396862982072062 88 0.582096652166166 0.835806695667669 0.417903347833834 89 0.558679888516547 0.882640222966905 0.441320111483453 90 0.598157096220026 0.803685807559949 0.401842903779974 91 0.570324198017843 0.859351603964313 0.429675801982157 92 0.548274253270091 0.903451493459818 0.451725746729909 93 0.593708865882408 0.812582268235185 0.406291134117592 94 0.552681864005298 0.894636271989403 0.447318135994702 95 0.598964236109576 0.802071527780849 0.401035763890424 96 0.578804637731024 0.842390724537951 0.421195362268976 97 0.597137662109916 0.805724675780167 0.402862337890084 98 0.575726942453607 0.848546115092785 0.424273057546393 99 0.585142003008531 0.829715993982938 0.414857996991469 100 0.636605533662943 0.726788932674113 0.363394466337057 101 0.6150445118132 0.769910976373599 0.384955488186799 102 0.581811070804592 0.836377858390816 0.418188929195408 103 0.568267848201777 0.863464303596445 0.431732151798223 104 0.526728934156501 0.946542131686997 0.473271065843499 105 0.489010152696447 0.978020305392894 0.510989847303553 106 0.484085090515923 0.968170181031847 0.515914909484077 107 0.443251196901721 0.886502393803443 0.556748803098279 108 0.423113051125958 0.846226102251915 0.576886948874042 109 0.420705663313017 0.841411326626033 0.579294336686983 110 0.397812041623197 0.795624083246394 0.602187958376803 111 0.364481751868533 0.728963503737066 0.635518248131467 112 0.331334939643604 0.662669879287209 0.668665060356396 113 0.345232510020782 0.690465020041565 0.654767489979218 114 0.307222544628448 0.614445089256896 0.692777455371552 115 0.285053235851774 0.570106471703549 0.714946764148226 116 0.25677966398057 0.51355932796114 0.74322033601943 117 0.233523774618624 0.467047549237247 0.766476225381376 118 0.217740954102276 0.435481908204553 0.782259045897724 119 0.269191025196724 0.538382050393449 0.730808974803276 120 0.277529935878483 0.555059871756966 0.722470064121517 121 0.277320878782892 0.554641757565783 0.722679121217108 122 0.263975897680145 0.52795179536029 0.736024102319855 123 0.464493586812371 0.928987173624743 0.535506413187629 124 0.455616252820708 0.911232505641415 0.544383747179292 125 0.526686622032022 0.946626755935957 0.473313377967978 126 0.555556359736652 0.888887280526697 0.444443640263349 127 0.548386250229047 0.903227499541907 0.451613749770953 128 0.639028595979682 0.721942808040635 0.360971404020318 129 0.633150145505531 0.733699708988937 0.366849854494469 130 0.599330417263779 0.801339165472442 0.400669582736221 131 0.57152852804158 0.85694294391684 0.42847147195842 132 0.52882821339049 0.94234357321902 0.47117178660951 133 0.510002059293768 0.979995881412465 0.489997940706232 134 0.478171357018699 0.956342714037397 0.521828642981301 135 0.440904601392002 0.881809202784004 0.559095398607998 136 0.443379760096956 0.886759520193912 0.556620239903044 137 0.399074665778718 0.798149331557436 0.600925334221282 138 0.365477951036707 0.730955902073413 0.634522048963293 139 0.347450787487511 0.694901574975021 0.65254921251249 140 0.307377448116169 0.614754896232339 0.69262255188383 141 0.271663303482737 0.543326606965473 0.728336696517264 142 0.285226503807552 0.570453007615104 0.714773496192448 143 0.24970828781133 0.499416575622659 0.75029171218867 144 0.265228817331314 0.530457634662628 0.734771182668686 145 0.411895223048801 0.823790446097602 0.588104776951199 146 0.381116633794084 0.762233267588168 0.618883366205916 147 0.399774874840253 0.799549749680507 0.600225125159747 148 0.359055332719995 0.71811066543999 0.640944667280005 149 0.315050496231318 0.630100992462635 0.684949503768682 150 0.273438453556903 0.546876907113807 0.726561546443097 151 0.237202866961541 0.474405733923083 0.762797133038459 152 0.396279801129488 0.792559602258975 0.603720198870512 153 0.346859501475779 0.693719002951557 0.653140498524222 154 0.316026060615208 0.632052121230417 0.683973939384792 155 0.27269238042869 0.54538476085738 0.72730761957131 156 0.237921187879064 0.475842375758129 0.762078812120936 157 0.240857987269945 0.48171597453989 0.759142012730055 158 0.237286415828547 0.474572831657093 0.762713584171453 159 0.198810899612474 0.397621799224949 0.801189100387526 160 0.162758181212426 0.325516362424851 0.837241818787574 161 0.137037214281066 0.274074428562132 0.862962785718934 162 0.115426928411025 0.230853856822051 0.884573071588975 163 0.121747622768038 0.243495245536075 0.878252377231962 164 0.104749075173166 0.209498150346333 0.895250924826834 165 0.125783960178131 0.251567920356262 0.874216039821869 166 0.114061149506233 0.228122299012467 0.885938850493767 167 0.164948181453491 0.329896362906983 0.835051818546509 168 0.203021562875422 0.406043125750844 0.796978437124578 169 0.195594283216885 0.391188566433771 0.804405716783115 170 0.301937208160486 0.603874416320972 0.698062791839514 171 0.318987246080777 0.637974492161553 0.681012753919223 172 0.259062762326213 0.518125524652425 0.740937237673787 173 0.207231852849931 0.414463705699862 0.792768147150069 174 0.181438398922317 0.362876797844633 0.818561601077683 175 0.185702687127536 0.371405374255073 0.814297312872464 176 0.156347084979167 0.312694169958333 0.843652915020833 177 0.116017415044117 0.232034830088234 0.883982584955883 178 0.102060594096149 0.204121188192298 0.897939405903851 179 0.0901741680289291 0.180348336057858 0.90982583197107 180 0.135166221722372 0.270332443444744 0.864833778277628 181 0.111534490222688 0.223068980445376 0.888465509777312 182 0.0772631105673212 0.154526221134642 0.922736889432679 183 0.0540291440100027 0.108058288020005 0.945970855989997 184 0.0512555479809749 0.10251109596195 0.948744452019025 185 0.0865484004555814 0.173096800911163 0.913451599544419 186 0.0448417369653801 0.0896834739307602 0.95515826303462 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 27 0.151685393258427 NOK 5% type I error level 32 0.179775280898876 NOK 10% type I error level 34 0.191011235955056 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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