*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, 23 Nov 2010 20:29:46 +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/Nov/23/t12905452502qviomya2rkvhvk.htm/, Retrieved Tue, 23 Nov 2010 21:47:30 +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/Nov/23/t12905452502qviomya2rkvhvk.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 «

24 11 12 26 14 25 7 8 23 11 17 17 8 25 6 18 10 8 23 12 18 12 9 19 8 16 12 7 29 10 20 11 4 25 10 16 11 11 21 11 18 12 7 22 16 17 13 7 25 11 23 14 12 24 13 30 16 10 18 12 23 11 10 22 8 18 10 8 15 12 15 11 8 22 11 12 15 4 28 4 21 9 9 20 9 15 11 8 12 8 20 17 7 24 8 31 17 11 20 14 27 11 9 21 15 34 18 11 20 16 21 14 13 21 9 31 10 8 23 14 19 11 8 28 11 16 15 9 24 8 20 15 6 24 9 21 13 9 24 9 22 16 9 23 9 17 13 6 23 9 24 9 6 29 10 25 18 16 24 16 26 18 5 18 11 25 12 7 25 8 17 17 9 21 9 32 9 6 26 16 33 9 6 22 11 13 12 5 22 16 32 18 12 22 12 25 12 7 23 12 29 18 10 30 14 22 14 9 23 9 18 15 8 17 10 17 16 5 23 9 20 10 8 23 10 15 11 8 25 12 20 14 10 24 14 33 9 6 24 14 29 12 8 23 10 23 17 7 21 14 26 5 4 24 16 18 12 8 24 9 20 12 8 28 10 11 6 4 16 6 28 24 20 20 8 26 12 8 29 13 22 12 8 27 10 17 14 6 22 8 12 7 4 28 7 14 13 8 16 15 17 12 9 25 9 21 13 6 24 10 19 14 7 28 12 18 8 9 24 13 10 11 5 23 10 29 9 5 30 11 31 11 8 24 8 19 13 8 21 9 9 10 6 25 13 20 11 8 25 11 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 9 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation D[t] = + 6.49442505844273 + 0.199709095209500CM[t] -0.152437526053681PE[t] + 0.153754981742715PC[t] + 0.0350480394488463O[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) 6.49442505844273 1.608182 4.0384 8.5e-05 4.2e-05 CM 0.199709095209500 0.038561 5.1791 1e-06 0 PE -0.152437526053681 0.075086 -2.0302 0.044061 0.022031 PC 0.153754981742715 0.095961 1.6023 0.111147 0.055573 O 0.0350480394488463 0.053919 0.65 0.516652 0.258326 Multiple Linear Regression - Regression Statistics Multiple R 0.427261498314918 R-squared 0.182552387942309 Adjusted R-squared 0.161319982434317 F-TEST (value) 8.59781939797614 F-TEST (DF numerator) 4 F-TEST (DF denominator) 154 p-value 2.73614794954469e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.56470383287756 Sum Squared Residuals 1012.96668555803 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 12.3669393634628 1.63306063653715 2 11 12.4562345175697 -1.45623451756966 3 6 9.40428257425454 -3.40428257425454 4 12 10.6009582729421 1.39904172705789 5 8 10.3096460447821 -2.30964604478208 6 10 9.95319828536611 0.046801714633887 7 10 10.3030150892343 -0.303015089234263 8 11 10.4402714227999 0.559728577200115 9 16 10.1072801996432 5.89271980035681 10 11 9.86027769672655 1.13972230327345 11 13 11.6398216111946 1.36017838880540 12 12 12.2151120253752 -0.215112025375229 13 8 11.7195281469725 -3.71952814697252 14 12 10.3205739573513 1.67942604264866 15 11 9.81434542181109 1.18565457818891 16 4 8.20073634169008 -4.20073634169008 17 9 11.4011339480205 -2.40113394802047 18 8 9.46386502732262 -1.46386502732262 19 8 9.81460683869148 -1.81460683869148 20 14 12.4862346551715 1.51376534482854 21 15 12.3295615066190 2.67043849338104 22 16 12.9329244147463 3.06707558525372 23 9 11.2890142841718 -2.28901428417177 24 14 13.1971765106656 0.802823489334384 25 11 10.8234700393422 0.176529960657836 26 8 9.62815547344627 -1.62815547344627 27 9 9.96572690905612 -0.965726909056124 28 9 10.9315760016011 -1.93157600160113 29 9 10.6389244792007 -1.63892447920074 30 9 9.63642663608614 -0.636426636086139 31 10 11.8544286434604 -1.85442864346044 32 16 12.0445096243697 3.95549037563026 33 11 10.3426256837163 0.657374316283711 34 8 11.6103879844562 -3.61038798445623 35 9 9.41784539820187 -0.417845398201869 36 16 13.3469572867899 2.65304271321009 37 11 13.4064742242040 -2.40647422420402 38 16 8.80122476011026 7.19877523988974 39 12 12.7573572849677 -0.757357284967684 40 12 11.5402919055585 0.459708094441463 41 14 12.1311043514445 1.86889564855548 42 9 10.9437995313081 -1.94379953130811 43 10 9.62848240598063 0.371517594019369 44 9 9.02535907618238 -0.0253590761823804 45 10 11.0003764633611 -1.00037646336111 46 12 9.91948954015762 2.08051045984238 47 14 10.7331843620807 3.26681563791933 48 14 13.4765703031017 0.523429696898287 49 10 12.4928832681393 -2.49288326813925 50 14 10.3085900059734 3.69140999402656 51 16 12.3808467773645 3.61915322263549 52 9 10.3311312602836 -1.33113126028360 53 10 10.8707416084980 -0.870741608497983 54 6 8.95238850757755 -2.95238850757755 55 8 12.2038395228516 -4.20383952285163 56 13 12.1040442192038 0.89595578079617 57 10 11.2351117594681 -1.23511175946814 58 8 9.44894107058361 -1.44894107058361 59 7 9.42023655011952 -2.42023655011952 60 15 9.09947303780115 5.90052696219885 61 9 10.3202251862657 -1.32022518626566 62 10 10.4703110563730 -0.470311056372986 63 12 10.2124024794384 1.78759752056159 64 13 11.0946363462410 1.90536365375896 65 10 8.38958303998428 1.61041696001572 66 11 12.7342671772141 -1.73426717721407 67 8 13.0797870240608 -5.07978702406078 68 9 10.2732587110929 -1.27325871109288 69 13 8.56616253146887 4.43383746853113 70 11 10.9180350162051 0.081964983794875 71 8 12.1043711517382 -4.10437115173819 72 9 10.7993499124626 -1.79934991246258 73 9 12.4941788852770 -3.49417888527697 74 15 12.0395230570453 2.96047694295469 75 9 11.1990295197620 -2.19902951976197 76 10 11.2245326179846 -1.22453261798456 77 14 8.90768633414583 5.09231366585417 78 12 10.7791384755475 1.22086152445255 79 12 11.0109556048447 0.98904439515531 80 11 11.7981786439418 -0.798178643941795 81 14 11.5898932921094 2.41010670789061 82 6 10.5536648652350 -4.55366486523497 83 12 10.7077249409607 1.29227505903928 84 8 10.4283093099733 -2.42830930997330 85 14 11.5833060136642 2.41669398633578 86 11 10.1667534599547 0.833246540045342 87 10 10.6214311267376 -0.621431126737633 88 14 10.3645567500604 3.63544324993963 89 12 12.5709059197225 -0.570905919722476 90 10 10.2719412554038 -0.271941255403843 91 14 11.6239289698522 2.37607103014776 92 5 9.03569863933689 -4.03569863933689 93 11 9.89271266334865 1.10728733665135 94 10 10.2249529416797 -0.224952941679739 95 9 11.0959319633787 -2.09593196337875 96 10 12.2405277693925 -2.24052776939253 97 16 12.8112774670913 3.1887225329087 98 13 12.1231819598903 0.876818040109663 99 9 10.2719412554038 -1.27194125540384 100 10 10.8022899178237 -0.802289917823686 101 10 11.0747300033089 -1.07473000330895 102 7 9.31934989282313 -2.31934989282313 103 9 9.6906124162215 -0.690612416221491 104 8 10.1112325667103 -2.11123256671029 105 14 11.9648644231144 2.03513557688556 106 14 11.1048351525360 2.89516484746398 107 8 10.8360423401348 -2.83604234013482 108 9 11.3690259139327 -2.36902591393273 109 14 11.6279031754707 2.37209682452934 110 14 9.71876808324213 4.28123191675787 111 8 9.00359060524915 -1.00359060524915 112 8 12.3334920351347 -4.33349203513474 113 8 11.7086439115059 -3.7086439115059 114 7 11.0303984395142 -4.03039843951424 115 6 9.56971641339212 -3.56971641339212 116 8 9.31801059858277 -1.31801059858277 117 6 9.41817233073623 -3.41817233073623 118 11 10.1059845825055 0.894015417494522 119 14 11.4255373303318 2.57446266966823 120 11 10.3397511940092 0.660248805990849 121 11 12.6050029319880 -1.60500293198795 122 11 9.09815558211211 1.90184441788789 123 14 11.1111173369982 2.88888266300185 124 8 10.3741672069406 -2.3741672069406 125 20 11.0218835174140 8.97811648258605 126 11 9.93331378098535 1.06668621901465 127 8 9.4218590997916 -1.42185909979160 128 11 10.9530830556540 0.0469169443460286 129 10 10.2501072688166 -0.250107268816644 130 14 13.5142532539286 0.485746746071372 131 11 11.2285068236030 -0.228506823602986 132 9 9.82656895151806 -0.826568951518058 133 9 9.89269082479732 -0.892690824797324 134 8 9.73895768160593 -1.73895768160593 135 10 10.8952105064633 -0.895210506463252 136 13 10.9467176981179 2.05328230188211 137 13 9.88342913900278 3.11657086099722 138 12 9.94692028203532 2.05307971796468 139 8 10.2851771468168 -2.28517714681681 140 13 11.5833101947956 1.41668980520444 141 14 12.9882275682129 1.01177243178710 142 12 12.5077417092243 -0.507741709224296 143 14 11.0545227475252 2.94547725247484 144 15 11.2311812309524 3.76881876904764 145 13 10.5592397819741 2.44076021802585 146 16 12.3728588701563 3.62714112984365 147 9 12.1436766522372 -3.14367665223718 148 9 10.5890398372182 -1.58903983721818 149 9 9.69993961767 -0.699939617670003 150 8 10.9924103947043 -2.99241039470428 151 7 10.9666458796013 -3.9666458796013 152 16 11.7184721081639 4.28152789183612 153 11 12.974860645492 -1.97486064549199 154 9 10.0970061521426 -1.09700615214265 155 11 10.1396319931913 0.860368006808658 156 9 9.56633055718845 -0.566330557188446 157 14 12.4806597384323 1.51934026156772 158 13 10.9100689475483 2.08993105245171 159 16 12.9501345117777 3.04986548822233 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.266943462013504 0.533886924027009 0.733056537986496 9 0.901954408063652 0.196091183872697 0.0980455919363483 10 0.84120872940062 0.317582541198761 0.158791270599381 11 0.795473416748 0.409053166504001 0.204526583252000 12 0.713160726175516 0.573678547648969 0.286839273824484 13 0.793032126280613 0.413935747438774 0.206967873719387 14 0.73023619472965 0.5395276105407 0.26976380527035 15 0.649130602786605 0.701738794426791 0.350869397213395 16 0.703372068420992 0.593255863158015 0.296627931579008 17 0.721833712058824 0.556332575882353 0.278166287941176 18 0.675108111010295 0.64978377797941 0.324891888989705 19 0.605039978855001 0.789920042289997 0.394960021144999 20 0.568599499212746 0.862801001574508 0.431400500787254 21 0.549409070953311 0.901181858093377 0.450590929046689 22 0.529833097659981 0.940333804680039 0.470166902340019 23 0.516146091271241 0.967707817457519 0.483853908728759 24 0.452891594662862 0.905783189325725 0.547108405337138 25 0.385837191593568 0.771674383187135 0.614162808406432 26 0.328594122558107 0.657188245116215 0.671405877441893 27 0.272330371021031 0.544660742042061 0.727669628978969 28 0.245195083675243 0.490390167350485 0.754804916324757 29 0.208008061415369 0.416016122830737 0.791991938584631 30 0.165197986766982 0.330395973533965 0.834802013233018 31 0.154289603266888 0.308579206533775 0.845710396733112 32 0.190621780503349 0.381243561006698 0.809378219496651 33 0.156967956668402 0.313935913336803 0.843032043331598 34 0.195545798652670 0.391091597305341 0.80445420134733 35 0.157014837918836 0.314029675837672 0.842985162081164 36 0.155445993317861 0.310891986635722 0.844554006682139 37 0.168007219959708 0.336014439919415 0.831992780040292 38 0.61720933180285 0.765581336394301 0.382790668197150 39 0.57354018682399 0.85291962635202 0.42645981317601 40 0.521133244308242 0.957733511383515 0.478866755691758 41 0.496610587189841 0.993221174379681 0.503389412810159 42 0.47327463673176 0.94654927346352 0.52672536326824 43 0.420845507143845 0.84169101428769 0.579154492856155 44 0.370663172702910 0.741326345405819 0.62933682729709 45 0.327192489702158 0.654384979404316 0.672807510297842 46 0.317341906441762 0.634683812883525 0.682658093558238 47 0.341708372737378 0.683416745474757 0.658291627262622 48 0.297583540625526 0.595167081251052 0.702416459374474 49 0.296412751620691 0.592825503241381 0.70358724837931 50 0.341593804274304 0.683187608548607 0.658406195725696 51 0.396199607040796 0.792399214081592 0.603800392959204 52 0.360959147573184 0.721918295146368 0.639040852426816 53 0.319160930198697 0.638321860397394 0.680839069801303 54 0.325600755786337 0.651201511572674 0.674399244213663 55 0.409688756145579 0.819377512291158 0.590311243854421 56 0.366857394618443 0.733714789236885 0.633142605381557 57 0.33197380484914 0.66394760969828 0.66802619515086 58 0.301167377584529 0.602334755169059 0.69883262241547 59 0.292435671898158 0.584871343796316 0.707564328101842 60 0.485591215897926 0.971182431795851 0.514408784102074 61 0.44823186455589 0.89646372911178 0.55176813544411 62 0.402776585385587 0.805553170771173 0.597223414614413 63 0.382280156246296 0.764560312492591 0.617719843753704 64 0.363037020723486 0.726074041446972 0.636962979276514 65 0.335771029141442 0.671542058282884 0.664228970858558 66 0.311128355371483 0.622256710742967 0.688871644628517 67 0.438182951985538 0.876365903971076 0.561817048014462 68 0.404018479469565 0.80803695893913 0.595981520530435 69 0.491017622734873 0.982035245469746 0.508982377265127 70 0.444314480884517 0.888628961769035 0.555685519115483 71 0.514766492265663 0.970467015468675 0.485233507734337 72 0.491946157825673 0.983892315651346 0.508053842174327 73 0.529354435750658 0.941291128498684 0.470645564249342 74 0.545989355972811 0.908021288054378 0.454010644027189 75 0.532891013564184 0.934217972871632 0.467108986435816 76 0.497959362161447 0.995918724322894 0.502040637838553 77 0.636751044141421 0.726497911717157 0.363248955858579 78 0.602579249939475 0.79484150012105 0.397420750060525 79 0.563692611128743 0.872614777742514 0.436307388871257 80 0.524708589350052 0.950582821299895 0.475291410649948 81 0.517722732947798 0.964554534104404 0.482277267052202 82 0.613989521334723 0.772020957330554 0.386010478665277 83 0.579806682008273 0.840386635983455 0.420193317991727 84 0.572590039115187 0.854819921769627 0.427409960884813 85 0.562898579087373 0.874202841825254 0.437101420912627 86 0.52248909128569 0.95502181742862 0.47751090871431 87 0.478767751473561 0.957535502947122 0.521232248526439 88 0.527878904429524 0.944242191140951 0.472121095570476 89 0.48562455815122 0.97124911630244 0.51437544184878 90 0.439542197399378 0.879084394798755 0.560457802600622 91 0.431067765083482 0.862135530166964 0.568932234916518 92 0.488497477538327 0.976994955076654 0.511502522461673 93 0.451803837276169 0.903607674552338 0.548196162723831 94 0.405494350360568 0.810988700721135 0.594505649639432 95 0.389574627770356 0.779149255540712 0.610425372229644 96 0.384556624734488 0.769113249468975 0.615443375265512 97 0.397233327031846 0.794466654063691 0.602766672968154 98 0.355696818143441 0.711393636286882 0.644303181856559 99 0.321511673060832 0.643023346121664 0.678488326939168 100 0.283717061080594 0.567434122161187 0.716282938919406 101 0.251614859457286 0.503229718914571 0.748385140542714 102 0.239815987885699 0.479631975771399 0.7601840121143 103 0.205509852370687 0.411019704741373 0.794490147629313 104 0.193125476574919 0.386250953149839 0.80687452342508 105 0.176385350120233 0.352770700240466 0.823614649879767 106 0.182532378397733 0.365064756795466 0.817467621602267 107 0.186675712980515 0.373351425961030 0.813324287019485 108 0.182324803684197 0.364649607368395 0.817675196315803 109 0.172728076676227 0.345456153352455 0.827271923323773 110 0.234421741247915 0.468843482495829 0.765578258752085 111 0.200542976038619 0.401085952077239 0.79945702396138 112 0.289012607497829 0.578025214995658 0.710987392502171 113 0.364571051827908 0.729142103655816 0.635428948172092 114 0.452055183160643 0.904110366321285 0.547944816839357 115 0.543411951220094 0.913176097559813 0.456588048779906 116 0.498632544756084 0.997265089512168 0.501367455243916 117 0.520010496262856 0.959979007474289 0.479989503737144 118 0.471300531771797 0.942601063543595 0.528699468228203 119 0.455595168808777 0.911190337617554 0.544404831191223 120 0.409649416594959 0.819298833189918 0.590350583405041 121 0.381700913736434 0.763401827472867 0.618299086263566 122 0.365131724288328 0.730263448576656 0.634868275711672 123 0.355021348388556 0.710042696777112 0.644978651611444 124 0.371459151418386 0.742918302836772 0.628540848581614 125 0.887952835668909 0.224094328662183 0.112047164331091 126 0.864201926744787 0.271596146510426 0.135798073255213 127 0.831573830644998 0.336852338710004 0.168426169355002 128 0.788801445411546 0.422397109176909 0.211198554588454 129 0.74035777406828 0.519284451863441 0.259642225931721 130 0.687187328087875 0.625625343824251 0.312812671912125 131 0.635832133968744 0.728335732062513 0.364167866031256 132 0.578030385896483 0.843939228207034 0.421969614103517 133 0.514878770086379 0.970242459827241 0.485121229913621 134 0.467079020921857 0.934158041843714 0.532920979078143 135 0.416371331924013 0.832742663848027 0.583628668075987 136 0.381288213454773 0.762576426909546 0.618711786545227 137 0.43001062586582 0.86002125173164 0.56998937413418 138 0.416667319593665 0.83333463918733 0.583332680406335 139 0.433683969524689 0.867367939049378 0.566316030475311 140 0.361930385280691 0.723860770561382 0.638069614719309 141 0.291348819524459 0.582697639048918 0.708651180475541 142 0.244863416280756 0.489726832561513 0.755136583719244 143 0.230389479735933 0.460778959471867 0.769610520264067 144 0.243546868651770 0.487093737303541 0.75645313134823 145 0.214242132733454 0.428484265466909 0.785757867266546 146 0.288490070469898 0.576980140939796 0.711509929530102 147 0.320521564479434 0.641043128958869 0.679478435520566 148 0.230791746774715 0.46158349354943 0.769208253225285 149 0.149543067561754 0.299086135123508 0.850456932438246 150 0.164930279804287 0.329860559608573 0.835069720195713 151 0.496848004841617 0.993696009683235 0.503151995158383 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/10d2yi1290544173.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/10d2yi1290544173.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/16ii61290544173.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/16ii61290544173.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/26ii61290544173.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/26ii61290544173.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/3zs0r1290544173.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/3zs0r1290544173.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/4zs0r1290544173.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/4zs0r1290544173.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/5zs0r1290544173.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/5zs0r1290544173.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/6sjzu1290544173.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/6sjzu1290544173.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/72sgx1290544173.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/72sgx1290544173.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/82sgx1290544173.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/82sgx1290544173.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/92sgx1290544173.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905452502qviomya2rkvhvk/92sgx1290544173.ps (open in new window)

Parameters (Session):

par1 = 3 ; 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') }

Copyright

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

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

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.

FreeStatistics.org is powered by