*The author of this computation has been verified*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 05 Dec 2008 02:59:14 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/05/t1228471629zz53asfw3z5xpue.htm/, Retrieved Fri, 05 Dec 2008 10:07:09 +0000

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/2008/Dec/05/t1228471629zz53asfw3z5xpue.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0,24 0,23 0,23 0,24 0,23 0,23 0,25 0,21 0,26 0,25 0,24 0,24 0,27 0,25 0,26 0,29 0,24 0,26 0,24 0,26 0,25 0,26 0,24 0,21 0,20 0,22 0,20 0,21 0,20 0,19 0,20 0,20 0,21 0,24 0,22 0,19 0,23 0,23 0,23 0,22 0,23 0,25 0,25 0,22 0,25 0,25 0,24 0,19 0,24 0,26 0,24 0,24 0,25 0,23 0,27 0,24 0,26 0,27 0,29 0,28 0,32 0,29 0,27 0,26 0,28 0,31 0,29 0,31 0,31 0,32 0,32 0,26 0,31 0,31 0,31 0,31 0,29 0,27 0,30 0,27 0,27 0,30 0,28 0,24 0,28 0,28 0,33 0,28 0,29 0,25 0,31 0,29 0,37 0,31 0,29 0,28 0,30 0,32 0,31 0,28 0,29 0,29 0,28 0,26 0,28 0,30 0,33 0,31 0,37 0,36 0,37 0,37 0,36 0,33 0,33 0,40 0,32 0,39 0,39 0,37 0,37 0,30 0,33 0,33 0,34 0,35 0,34 0,37 0,37 0,37 0,36 0,32 0,33 0,35 0,36 0,35 0,37 0,35 0,32 0,33 0,28 0,32 0,35 0,30 0,32 0,32 0,32 0,32 0,36 0,31 0,26 0,33 0,31 0,34 0,33 0,38 0,32 0,30 0,32 0,33 0,34 0,29 0,33 0,36 0,32 0,32 0,32 0,31 0,30 0,34 0,34 0,30 0,28 0,25 0,27 0,33 0,28 0,33 0,32 0,27 0,27 0,28 0,27 0,27 0,25 0,25 0,22 0,27

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation X[t] = + 0.232134597594820 + 0.00612345339962998Q1[t] + 0.00578442992599445Q2[t] + 0.00629647028214616Q3[t] + 0.000551789431082331t + 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) 0.232134597594820 0.007443 31.1872 0 0 Q1 0.00612345339962998 0.007886 0.7765 0.438434 0.219217 Q2 0.00578442992599445 0.007885 0.7336 0.464117 0.232059 Q3 0.00629647028214616 0.007884 0.7986 0.425549 0.212775 t 0.000551789431082331 5.1e-05 10.7408 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.622847105294973 R-squared 0.387938516574328 Adjusted R-squared 0.374560123493985 F-TEST (value) 28.9973926049715 F-TEST (DF numerator) 4 F-TEST (DF denominator) 183 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0382194765515835 Sum Squared Residuals 0.267313294981499 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.24 0.238809840425531 0.0011901595744685 2 0.23 0.239022606382979 -0.00902260638297874 3 0.23 0.240086436170213 -0.0100864361702128 4 0.24 0.234341755319149 0.00565824468085105 5 0.23 0.241016998149861 -0.0110169981498612 6 0.23 0.241229764107308 -0.0112297641073080 7 0.25 0.242293593894542 0.0077064061054579 8 0.21 0.236548913043478 -0.0265489130434783 9 0.26 0.243224155874191 0.0167758441258094 10 0.25 0.243436921831637 0.00656307816836263 11 0.24 0.244500751618871 -0.00450075161887143 12 0.24 0.238756070767808 0.0012439292321924 13 0.27 0.24543131359852 0.0245686864014801 14 0.25 0.245644079555967 0.0043559204440333 15 0.26 0.246707909343201 0.0132920906567993 16 0.29 0.240963228492137 0.0490367715078631 17 0.24 0.247638471322849 -0.00763847132284924 18 0.26 0.247851237280296 0.0121487627197040 19 0.24 0.24891506706753 -0.00891506706753008 20 0.26 0.243170386216466 0.0168296137835338 21 0.25 0.249845629047179 0.000154370952821448 22 0.26 0.250058395004625 0.00994160499537466 23 0.24 0.251122224791859 -0.0111222247918594 24 0.21 0.245377543940796 -0.0353775439407956 25 0.2 0.252052786771508 -0.0520527867715079 26 0.22 0.252265552728955 -0.0322655527289547 27 0.2 0.253329382516189 -0.0533293825161887 28 0.21 0.247584701665125 -0.0375847016651249 29 0.2 0.254259944495837 -0.0542599444958372 30 0.19 0.254472710453284 -0.064472710453284 31 0.2 0.255536540240518 -0.055536540240518 32 0.2 0.249791859389454 -0.0497918593894542 33 0.21 0.256467102220167 -0.0464671022201665 34 0.24 0.256679868177613 -0.0166798681776133 35 0.22 0.257743697964847 -0.0377436979648474 36 0.19 0.251999017113784 -0.0619990171137835 37 0.23 0.258674259944496 -0.0286742599444958 38 0.23 0.258887025901943 -0.0288870259019426 39 0.23 0.259950855689177 -0.0299508556891767 40 0.22 0.254206174838113 -0.0342061748381129 41 0.23 0.260881417668825 -0.0308814176688252 42 0.25 0.261094183626272 -0.0110941836262720 43 0.25 0.262158013413506 -0.0121580134135060 44 0.22 0.256413332562442 -0.0364133325624422 45 0.25 0.263088575393155 -0.0130885753931545 46 0.25 0.263301341350601 -0.0133013413506013 47 0.24 0.264365171137835 -0.0243651711378354 48 0.19 0.258620490286772 -0.0686204902867715 49 0.24 0.265295733117484 -0.0252957331174838 50 0.26 0.265508499074931 -0.00550849907493061 51 0.24 0.266572328862165 -0.0265723288621647 52 0.24 0.260827648011101 -0.0208276480111008 53 0.25 0.267502890841813 -0.0175028908418131 54 0.23 0.26771565679926 -0.0377156567992599 55 0.27 0.268779486586494 0.00122051341350603 56 0.24 0.26303480573543 -0.0230348057354302 57 0.26 0.269710048566143 -0.00971004856614247 58 0.27 0.269922814523589 7.71854764107524e-05 59 0.29 0.270986644310823 0.0190133556891767 60 0.28 0.265241963459759 0.0147580365402405 61 0.32 0.271917206290472 0.0480827937095282 62 0.29 0.272129972247919 0.0178700277520814 63 0.27 0.273193802035153 -0.00319380203515262 64 0.26 0.267449121184089 -0.0074491211840888 65 0.28 0.274124364014801 0.0058756359851989 66 0.31 0.274337129972248 0.0356628700277521 67 0.29 0.275400959759482 0.014599040240518 68 0.31 0.269656278908418 0.0403437210915819 69 0.31 0.276331521739130 0.0336684782608696 70 0.32 0.276544287696577 0.0434557123034228 71 0.32 0.277608117483811 0.0423918825161887 72 0.26 0.271863436632747 -0.0118634366327475 73 0.31 0.27853867946346 0.0314613205365402 74 0.31 0.278751445420907 0.0312485545790934 75 0.31 0.279815275208141 0.0301847247918594 76 0.31 0.274070594357077 0.0359294056429232 77 0.29 0.280745837187789 0.00925416281221089 78 0.27 0.280958603145236 -0.0109586031452359 79 0.3 0.28202243293247 0.0179775670675300 80 0.27 0.276277752081406 -0.00627775208140609 81 0.27 0.282952994912118 -0.0129529949121184 82 0.3 0.283165760869565 0.0168342391304348 83 0.28 0.284229590656799 -0.00422959065679924 84 0.24 0.278484909805735 -0.0384849098057354 85 0.28 0.285160152636448 -0.00516015263644772 86 0.28 0.285372918593895 -0.00537291859389452 87 0.33 0.286436748381129 0.0435632516188714 88 0.28 0.280692067530065 -0.000692067530064733 89 0.29 0.287367310360777 0.00263268963922291 90 0.25 0.287580076318224 -0.0375800763182239 91 0.31 0.288643906105458 0.0213560938945421 92 0.29 0.282899225254394 0.0071007747456059 93 0.37 0.289574468085106 0.0804255319148936 94 0.31 0.289787234042553 0.0202127659574468 95 0.29 0.290851063829787 -0.00085106382978726 96 0.28 0.285106382978723 -0.00510638297872338 97 0.3 0.291781625809436 0.00821837419056427 98 0.32 0.291994391766883 0.0280056082331175 99 0.31 0.293058221554117 0.0169417784458834 100 0.28 0.287313540703053 -0.0073135407030527 101 0.29 0.293988783533765 -0.00398878353376506 102 0.29 0.294201549491212 -0.00420154949121186 103 0.28 0.295265379278446 -0.0152653792784459 104 0.26 0.289520698427382 -0.0295206984273821 105 0.28 0.296195941258094 -0.0161959412580943 106 0.3 0.296408707215541 0.00359129278445882 107 0.33 0.297472537002775 0.0325274629972248 108 0.31 0.291727856151711 0.0182721438482886 109 0.37 0.298403098982424 0.0715969010175763 110 0.36 0.298615864939870 0.0613841350601295 111 0.37 0.299679694727105 0.0703203052728955 112 0.37 0.293935013876041 0.0760649861239593 113 0.36 0.300610256706753 0.059389743293247 114 0.33 0.3008230226642 0.0291769773358002 115 0.33 0.301886852451434 0.0281131475485662 116 0.4 0.29614217160037 0.10385782839963 117 0.32 0.302817414431082 0.0171825855689177 118 0.39 0.303030180388529 0.0869698196114709 119 0.39 0.304094010175763 0.0859059898242368 120 0.37 0.298349329324699 0.0716506706753006 121 0.37 0.305024572155412 0.0649754278445883 122 0.3 0.305237338112858 -0.00523733811285847 123 0.33 0.306301167900093 0.0236988320999075 124 0.33 0.300556487049029 0.0294435129509713 125 0.34 0.307231729879741 0.0327682701202590 126 0.35 0.307444495837188 0.0425555041628122 127 0.34 0.308508325624422 0.0314916743755782 128 0.37 0.302763644773358 0.067236355226642 129 0.37 0.309438887604070 0.0605611123959297 130 0.37 0.309651653561517 0.0603483464384829 131 0.36 0.310715483348751 0.0492845166512488 132 0.32 0.304970802497687 0.0150291975023127 133 0.33 0.311646045328400 0.0183539546716004 134 0.35 0.311858811285846 0.0381411887141535 135 0.36 0.312922641073080 0.0470773589269195 136 0.35 0.307177960222017 0.0428220397779833 137 0.37 0.313853203052729 0.056146796947271 138 0.35 0.314065969010176 0.0359340309898242 139 0.32 0.31512979879741 0.0048702012025902 140 0.33 0.309385117946346 0.0206148820536540 141 0.28 0.316060360777058 -0.0360603607770583 142 0.32 0.316273126734505 0.00372687326549492 143 0.35 0.317336956521739 0.0326630434782609 144 0.3 0.311592275670675 -0.0115922756706753 145 0.32 0.318267518501388 0.00173248149861239 146 0.32 0.318480284458834 0.00151971554116559 147 0.32 0.319544114246068 0.000455885753931549 148 0.32 0.313799433395005 0.00620056660499538 149 0.36 0.320474676225717 0.039525323774283 150 0.31 0.320687442183164 -0.0106874421831637 151 0.26 0.321751271970398 -0.0617512719703978 152 0.33 0.316006591119334 0.0139934088806661 153 0.31 0.322681833950046 -0.0126818339500463 154 0.34 0.322894599907493 0.0171054000925070 155 0.33 0.323958429694727 0.00604157030527291 156 0.38 0.318213748843663 0.0617862511563367 157 0.32 0.324888991674376 -0.00488899167437558 158 0.3 0.325101757631822 -0.0251017576318224 159 0.32 0.326165587419056 -0.00616558741905642 160 0.33 0.320420906567993 0.00957909343200742 161 0.34 0.327096149398705 0.0129038506012951 162 0.29 0.327308915356152 -0.0373089153561517 163 0.33 0.328372745143386 0.00162725485661426 164 0.36 0.322628064292322 0.0373719357076781 165 0.32 0.329303307123034 -0.00930330712303423 166 0.32 0.329516073080481 -0.00951607308048103 167 0.32 0.330579902867715 -0.0105799028677151 168 0.31 0.324835222016651 -0.0148352220166512 169 0.3 0.331510464847364 -0.0315104648473636 170 0.34 0.331723230804810 0.00827676919518966 171 0.34 0.332787060592044 0.00721293940795562 172 0.3 0.327042379740981 -0.0270423797409806 173 0.28 0.333717622571693 -0.0537176225716929 174 0.25 0.33393038852914 -0.0839303885291397 175 0.27 0.334994218316374 -0.0649942183163737 176 0.33 0.32924953746531 0.000750462534690122 177 0.28 0.335924780296022 -0.0559247802960222 178 0.33 0.336137546253469 -0.00613754625346899 179 0.32 0.337201376040703 -0.0172013760407031 180 0.27 0.331456695189639 -0.0614566951896392 181 0.27 0.338131938020352 -0.0681319380203515 182 0.28 0.338344703977798 -0.0583447039777983 183 0.27 0.339408533765032 -0.0694085337650324 184 0.27 0.333663852913969 -0.0636638529139685 185 0.25 0.340339095744681 -0.0903390957446809 186 0.25 0.340551861702128 -0.0905518617021277 187 0.22 0.341615691489362 -0.121615691489362 188 0.27 0.335871010638298 -0.0658710106382979 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.0656649105898685 0.131329821179737 0.934335089410132 9 0.047639766537891 0.095279533075782 0.952360233462109 10 0.0196456593197535 0.0392913186395070 0.980354340680247 11 0.00741875133765383 0.0148375026753077 0.992581248662346 12 0.00250852125498888 0.00501704250997775 0.997491478745011 13 0.00103807954353198 0.00207615908706396 0.998961920456468 14 0.000312152512982536 0.000624305025965073 0.999687847487017 15 9.16155367664095e-05 0.000183231073532819 0.999908384463234 16 0.000623786423840114 0.00124757284768023 0.99937621357616 17 0.00114828198593287 0.00229656397186575 0.998851718014067 18 0.000460167012673279 0.000920334025346557 0.999539832987327 19 0.000365733990423199 0.000731467980846399 0.999634266009577 20 0.000146161685430748 0.000292323370861497 0.99985383831457 21 8.22895054797856e-05 0.000164579010959571 0.99991771049452 22 3.14970949477591e-05 6.29941898955181e-05 0.999968502905052 23 2.08217765189514e-05 4.16435530379029e-05 0.999979178223481 24 0.000152241304299332 0.000304482608598665 0.9998477586957 25 0.000905449383066492 0.00181089876613298 0.999094550616934 26 0.000798488996392935 0.00159697799278587 0.999201511003607 27 0.00126882005367030 0.00253764010734061 0.99873117994633 28 0.00104174140867689 0.00208348281735378 0.998958258591323 29 0.00109926501051470 0.00219853002102939 0.998900734989485 30 0.00160393660199483 0.00320787320398966 0.998396063398005 31 0.00128309618835240 0.00256619237670481 0.998716903811648 32 0.000975339035398215 0.00195067807079643 0.999024660964602 33 0.000625414824892061 0.00125082964978412 0.999374585175108 34 0.000513642223195416 0.00102728444639083 0.999486357776805 35 0.000328056433132806 0.000656112866265613 0.999671943566867 36 0.000309137111854393 0.000618274223708787 0.999690862888146 37 0.000234806931608059 0.000469613863216117 0.999765193068392 38 0.000162237367053204 0.000324474734106409 0.999837762632947 39 0.000124454835104431 0.000248909670208862 0.999875545164896 40 8.50402062743735e-05 0.000170080412548747 0.999914959793726 41 6.36295203248859e-05 0.000127259040649772 0.999936370479675 42 6.94634244616076e-05 0.000138926848923215 0.999930536575538 43 8.41114372859404e-05 0.000168222874571881 0.999915888562714 44 5.92415227028426e-05 0.000118483045405685 0.999940758477297 45 6.41945934508712e-05 0.000128389186901742 0.99993580540655 46 5.58600710650061e-05 0.000111720142130012 0.999944139928935 47 4.43578005508643e-05 8.87156011017285e-05 0.99995564219945 48 6.84677792884433e-05 0.000136935558576887 0.999931532220712 49 5.74493168326042e-05 0.000114898633665208 0.999942550683167 50 6.39210211300437e-05 0.000127842042260087 0.99993607897887 51 5.39418707050595e-05 0.000107883741410119 0.999946058129295 52 5.46408656245064e-05 0.000109281731249013 0.999945359134376 53 5.11149244281496e-05 0.000102229848856299 0.999948885075572 54 4.45560433127285e-05 8.9112086625457e-05 0.999955443956687 55 7.39610014853121e-05 0.000147922002970624 0.999926038998515 56 7.33795190630281e-05 0.000146759038126056 0.999926620480937 57 7.77686510458294e-05 0.000155537302091659 0.999922231348954 58 8.82753346579807e-05 0.000176550669315961 0.999911724665342 59 0.000205510575199033 0.000411021150398066 0.9997944894248 60 0.000406226879977928 0.000812453759955856 0.999593773120022 61 0.00202221489455302 0.00404442978910605 0.997977785105447 62 0.00224176478888926 0.00448352957777853 0.99775823521111 63 0.00195784433551475 0.00391568867102951 0.998042155664485 64 0.00181207469721955 0.00362414939443910 0.99818792530278 65 0.0016059429549187 0.0032118859098374 0.998394057045081 66 0.00229323540368029 0.00458647080736059 0.99770676459632 67 0.00218694633826837 0.00437389267653674 0.997813053661732 68 0.00386951957195163 0.00773903914390326 0.996130480428048 69 0.00427639608603222 0.00855279217206444 0.995723603913968 70 0.00512499921591695 0.0102499984318339 0.994875000784083 71 0.00620458683567426 0.0124091736713485 0.993795413164326 72 0.00569498048122614 0.0113899609624523 0.994305019518774 73 0.00514128358369802 0.0102825671673960 0.994858716416302 74 0.00432778758732072 0.00865557517464144 0.99567221241268 75 0.00374774969024908 0.00749549938049817 0.99625225030975 76 0.00376339898645068 0.00752679797290136 0.99623660101355 77 0.00288216348236163 0.00576432696472326 0.997117836517638 78 0.0027664291973617 0.0055328583947234 0.997233570802638 79 0.00211577138427192 0.00423154276854384 0.997884228615728 80 0.00192740149289559 0.00385480298579119 0.998072598507104 81 0.00198008199724962 0.00396016399449925 0.99801991800275 82 0.00148205219532096 0.00296410439064192 0.99851794780468 83 0.00133890614780160 0.00267781229560319 0.998661093852198 84 0.00298054601148867 0.00596109202297735 0.997019453988511 85 0.00287819108768193 0.00575638217536386 0.997121808912318 86 0.00281288523043703 0.00562577046087405 0.997187114769563 87 0.00275422663373695 0.0055084532674739 0.997245773366263 88 0.00278011323990501 0.00556022647981003 0.997219886760095 89 0.00255577305571208 0.00511154611142417 0.997444226944288 90 0.00683790597189923 0.0136758119437985 0.9931620940281 91 0.00575840712641251 0.0115168142528250 0.994241592873587 92 0.00596313337766486 0.0119262667553297 0.994036866622335 93 0.0126661283513147 0.0253322567026294 0.987333871648685 94 0.0107843644775259 0.0215687289550518 0.989215635522474 95 0.0113899003992872 0.0227798007985744 0.988610099600713 96 0.0147260161791991 0.0294520323583983 0.9852739838208 97 0.0141573065444364 0.0283146130888728 0.985842693455564 98 0.0121833417082131 0.0243666834164262 0.987816658291787 99 0.0110383811110442 0.0220767622220884 0.988961618888956 100 0.0171257831256755 0.034251566251351 0.982874216874325 101 0.0219580480776633 0.0439160961553266 0.978041951922337 102 0.0294603059610526 0.0589206119221052 0.970539694038947 103 0.0535449975017497 0.107089995003499 0.94645500249825 104 0.172462099997794 0.344924199995588 0.827537900002206 105 0.299606107033756 0.599212214067513 0.700393892966244 106 0.378877914616572 0.757755829233144 0.621122085383428 107 0.391260498189144 0.782520996378287 0.608739501810856 108 0.502640507119123 0.994718985761754 0.497359492880877 109 0.542035115707389 0.915929768585223 0.457964884292611 110 0.550020657292158 0.899958685415684 0.449979342707842 111 0.569927604063862 0.860144791872276 0.430072395936138 112 0.622594128159013 0.754811743681973 0.377405871840987 113 0.608239683847166 0.783520632305667 0.391760316152834 114 0.606413297430836 0.787173405138328 0.393586702569164 115 0.60689567804385 0.7862086439123 0.39310432195615 116 0.728267288576548 0.543465422846903 0.271732711423452 117 0.745957244134511 0.508085511730977 0.254042755865489 118 0.783681072047953 0.432637855904094 0.216318927952047 119 0.81446772387204 0.371064552255919 0.185532276127959 120 0.809701593807048 0.380596812385905 0.190298406192952 121 0.79516182745035 0.409676345099300 0.204838172549650 122 0.861313689450376 0.277372621099248 0.138686310549624 123 0.85278506833473 0.294429863330541 0.147214931665270 124 0.854805598251273 0.290388803497454 0.145194401748727 125 0.833571197304366 0.332857605391268 0.166428802695634 126 0.805500552863342 0.388998894273316 0.194499447136658 127 0.780586266512359 0.438827466975282 0.219413733487641 128 0.762753573400455 0.47449285319909 0.237246426599545 129 0.7439267582364 0.5121464835272 0.2560732417636 130 0.723477553200949 0.553044893598102 0.276522446799051 131 0.688510506414645 0.622978987170709 0.311489493585355 132 0.702392621060754 0.595214757878493 0.297607378939246 133 0.676947227540178 0.646105544919645 0.323052772459822 134 0.63336170883025 0.7332765823395 0.36663829116975 135 0.598114718856175 0.80377056228765 0.401885281143825 136 0.551743441916358 0.896513116167284 0.448256558083642 137 0.550452288352589 0.899095423294822 0.449547711647411 138 0.509216484301505 0.98156703139699 0.490783515698495 139 0.494731763933235 0.98946352786647 0.505268236066765 140 0.463595242594774 0.927190485189548 0.536404757405226 141 0.642329953224136 0.715340093551728 0.357670046775864 142 0.627189056689575 0.74562188662085 0.372810943310425 143 0.5865658420717 0.8268683158566 0.4134341579283 144 0.68611192488928 0.62777615022144 0.31388807511072 145 0.672125424434631 0.655749151130737 0.327874575565369 146 0.656075861167963 0.687848277664074 0.343924138832037 147 0.6374539340321 0.7250921319358 0.3625460659679 148 0.656010792900656 0.687978414198688 0.343989207099344 149 0.632324667312367 0.735350665375265 0.367675332687633 150 0.643782901158629 0.712434197682741 0.356217098841371 151 0.930880166140337 0.138239667719326 0.0691198338596628 152 0.933036141742815 0.133927716514371 0.0669638582571855 153 0.940048381113379 0.119903237773243 0.0599516188866215 154 0.920884501414802 0.158230997170396 0.0791154985851978 155 0.906768634999782 0.186462730000435 0.0932313650002177 156 0.904160797034108 0.191678405931784 0.0958392029658918 157 0.88659544552953 0.226809108940942 0.113404554470471 158 0.91327142236364 0.173457155272720 0.0867285776363601 159 0.905781324704276 0.188437350591448 0.0942186752957242 160 0.891136347831936 0.217727304336128 0.108863652168064 161 0.863506849408056 0.272986301183889 0.136493150591944 162 0.929488722054916 0.141022555890167 0.0705112779450837 163 0.907047257068277 0.185905485863445 0.0929527429317225 164 0.887315654543338 0.225368690913324 0.112684345456662 165 0.853874274693156 0.292251450613688 0.146125725306844 166 0.817769722675325 0.364460554649350 0.182230277324675 167 0.771012096814631 0.457975806370738 0.228987903185369 168 0.745310695640438 0.509378608719123 0.254689304359562 169 0.698439409851868 0.603121180296265 0.301560590148132 170 0.661252870159149 0.677494259681701 0.338747129840851 171 0.673832879822475 0.65233424035505 0.326167120177525 172 0.619902428395978 0.760195143208044 0.380097571604022 173 0.570535472647507 0.858929054704986 0.429464527352493 174 0.867057821373801 0.265884357252398 0.132942178626199 175 0.940323851013236 0.119352297973529 0.0596761489867643 176 0.895960547762568 0.208078904474863 0.104039452237432 177 0.863745365458876 0.272509269082248 0.136254634541124 178 0.819904894848578 0.360190210302844 0.180095105151422 179 0.904204740191582 0.191590519616835 0.0957952598084175 180 0.906793502134957 0.186412995730086 0.0932064978650429 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 74 0.427745664739884 NOK 5% type I error level 92 0.531791907514451 NOK 10% type I error level 94 0.543352601156069 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Quarterly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Quarterly Dummies ; par3 = Linear Trend ;

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

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

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