ws 7 4

*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: Wed, 24 Nov 2010 13:33:12 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu.htm/, Retrieved Wed, 24 Nov 2010 14:34:01 +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/24/t1290605629tpo6mafqislrwxu.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 «

9 26 24 14 11 12 24 9 23 25 11 7 8 25 9 25 17 6 17 8 30 9 23 18 12 10 8 19 9 19 18 8 12 9 22 10 29 16 10 12 7 22 10 25 20 10 11 4 25 10 21 16 11 11 11 23 10 22 18 16 12 7 17 10 25 17 11 13 7 21 10 24 23 13 14 12 19 10 18 30 12 16 10 19 10 22 23 8 11 10 15 10 15 18 12 10 8 16 10 22 15 11 11 8 23 10 28 12 4 15 4 27 10 20 21 9 9 9 22 10 12 15 8 11 8 14 10 24 20 8 17 7 22 10 20 31 14 17 11 23 10 21 27 15 11 9 23 10 20 34 16 18 11 21 10 21 21 9 14 13 19 10 23 31 14 10 8 18 10 28 19 11 11 8 20 10 24 16 8 15 9 23 10 24 20 9 15 6 25 10 24 21 9 13 9 19 10 23 22 9 16 9 24 10 23 17 9 13 6 22 10 29 24 10 9 6 25 10 24 25 16 18 16 26 10 18 26 11 18 5 29 10 25 25 8 12 7 32 10 21 17 9 17 9 25 10 26 32 16 9 6 29 10 22 33 11 9 6 28 10 22 13 16 12 5 17 10 22 32 12 18 12 28 10 23 25 12 12 7 29 10 30 29 14 18 10 26 10 23 22 9 14 9 25 10 17 18 10 15 8 14 10 23 17 9 16 5 25 10 23 20 10 10 8 26 10 25 15 12 11 8 20 10 24 20 14 14 10 18 10 24 33 14 9 6 32 10 23 29 10 12 8 25 10 21 23 14 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation O[t] = + 17.5320115250951 -0.139909328473949maand[t] -0.070363411108702CM[t] + 0.218463701335249D[t] -0.147631760526752PE[t] -0.256721327474915PC[t] + 0.421989595060317PS[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 17.5320115250951 16.370606 1.0709 0.285892 0.142946 maand -0.139909328473949 1.626397 -0.086 0.93156 0.46578 CM -0.070363411108702 0.063231 -1.1128 0.267555 0.133777 D 0.218463701335249 0.113039 1.9326 0.055141 0.02757 PE -0.147631760526752 0.105729 -1.3963 0.164654 0.082327 PC -0.256721327474915 0.132088 -1.9436 0.053795 0.026897 PS 0.421989595060317 0.076385 5.5245 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.47160366663133 R-squared 0.222410018380114 Adjusted R-squared 0.191715677000382 F-TEST (value) 7.24596158062454 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 8.09619131958428e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.51076676883417 Sum Squared Residuals 1873.47346238284 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 26 23.0657425068685 2.93425749313151 2 23 24.3793899388211 -1.37938993882106 3 25 24.4836090910485 0.516390908951501 4 23 22.1155646659751 0.884435334024934 5 19 21.9556937972866 -2.95569379728661 6 29 22.9068813486504 6.09311865134962 7 25 24.8091922323480 0.190807767651953 8 21 22.6680810956730 -1.66808109567305 9 22 21.9669887591429 0.0330112408571081 10 25 22.4853602832899 2.51463971671013 11 24 20.2248896312862 3.77511036871381 12 18 19.7320611860864 -1.73206118608635 13 22 18.4009506808988 3.59904931910124 14 15 20.7096865523202 -5.70968655232017 15 22 23.5086084892065 -1.50860848920649 16 28 24.3147694612198 3.68523053878023 17 20 22.2660532184021 -2.26605321840206 18 12 19.0553110296579 -7.05531102965789 19 24 21.4503414989113 2.54965850108868 20 20 21.3822304698878 -1.38223046988775 21 21 23.2813810337682 -2.28138103376815 22 20 20.6164566885848 -0.61645668858476 23 21 19.2350403206877 1.76495967931231 24 23 21.0758688006982 1.92413119930183 25 28 21.9611860595907 6.03881394040927 26 24 21.9356056045101 2.06439439548988 27 24 23.4867588339559 0.513241166044059 28 24 20.4095573911141 3.59044260888591 29 23 22.0062466737267 0.993753326273276 30 23 22.7271438031546 0.272856196845402 31 29 24.3095594540169 4.69044054598311 32 24 22.0760687264901 1.92393127350990 33 18 25.0032901961102 -7.00329019611016 34 25 26.0565791966047 -1.05657919660475 35 21 22.6324215638038 -1.6324215638038 36 26 26.7453927534000 -0.745392753400043 37 22 25.1607212405548 -3.16072124055478 38 22 22.8322484696362 -0.832248469636231 39 22 22.5805345434085 -0.580534543408475 40 23 25.6644652167648 -2.66446521676479 41 30 22.8980156442343 7.10198435576573 42 23 22.7234997898405 0.276500210159454 43 17 18.6906211568953 -1.69062115689527 44 23 23.8069386342302 -0.80693863423021 45 23 24.3519282780354 -1.35192827803544 46 25 22.4611034053608 2.53889659463921 47 24 20.7458966258371 3.25410337416294 48 24 27.5040707248018 -3.50407072480179 49 23 23.0014044619433 -0.00140446194329844 50 21 23.8160022587777 -2.81600225877766 51 24 25.7396053467472 -1.73960534674719 52 24 21.8689799025625 2.1310200974375 53 28 21.5247271866200 6.47527281337997 54 16 21.0868709790159 -5.08687097901593 55 20 19.8925513896631 0.107448610336903 56 29 23.4458962042148 5.55410379578516 57 27 23.9159379347645 3.08406206523547 58 22 23.2050275314132 -1.20502753141323 59 28 24.0412666741380 3.95873332586205 60 16 20.3596568290598 -4.35965682905983 61 25 22.9485907713772 2.05140922862276 62 24 23.5081330501757 0.491866949824326 63 28 23.6814341870619 4.31856581293809 64 24 24.3426092077165 -0.342609207716546 65 23 22.7241674455982 0.275832554401772 66 30 26.9648649976454 3.03513500235455 67 24 21.3054132124012 2.69458678759881 68 21 24.1829223012890 -3.18292230128895 69 25 23.3408323937645 1.65916760623548 70 25 24.0007706237836 0.999229376216382 71 22 20.7816138225548 1.21838617744517 72 23 22.4982331005090 0.50176689949103 73 26 22.8569399305648 3.14306006943519 74 23 21.5937892329137 1.40621076708634 75 25 23.0645783673037 1.93542163269627 76 21 21.3136369532939 -0.313636953293923 77 25 23.6789263592053 1.32107364079466 78 24 22.1832855197740 1.81671448022596 79 29 23.5932503066337 5.40674969336631 80 22 23.6560424688103 -1.65604246881033 81 27 23.6363653184599 3.36363468154007 82 26 19.6732621788422 6.32673782115776 83 22 21.3216698225948 0.678330177405243 84 24 22.0937780621943 1.90622193780572 85 27 23.1261931881064 3.87380681189365 86 24 21.3390217622145 2.66097823778552 87 24 24.9040970888247 -0.904097088824728 88 29 24.4592631142657 4.54073688573425 89 22 22.2218194588866 -0.221819458886641 90 21 20.5858431400227 0.414156859977307 91 24 20.4151692190744 3.58483078092564 92 24 21.8180228930273 2.18197710697268 93 23 21.9717350112141 1.02826498878587 94 20 22.2985269278928 -2.29852692789283 95 27 21.4328055970307 5.56719440296928 96 26 23.4590336505077 2.54096634949231 97 25 21.9315166189677 3.0684833810323 98 21 20.0561613126476 0.943838687352392 99 21 20.7893690337478 0.210630966252239 100 19 20.3923894137552 -1.39238941375524 101 21 21.6232678019448 -0.623267801944792 102 21 21.3126061980473 -0.312606198047303 103 16 19.7593985066477 -3.75939850664769 104 22 20.6941782646972 1.30582173530283 105 29 21.8216808642118 7.17831913578816 106 15 21.6985918941881 -6.69859189418806 107 17 20.7254420312486 -3.72544203124861 108 15 19.9417458303131 -4.94174583031307 109 21 21.6776848625332 -0.677684862533154 110 21 21.0131669049354 -0.0131669049353742 111 19 19.3051274188235 -0.305127418823454 112 24 18.0635009529526 5.93649904704739 113 20 22.3781260522376 -2.37812605223761 114 17 25.1914084073903 -8.19140840739028 115 23 25.0431393186999 -2.04313931869988 116 24 22.4137752453426 1.58622475465735 117 14 22.0930249650556 -8.09302496505556 118 19 22.9106190578115 -3.91061905781147 119 24 22.191127517483 1.80887248251702 120 13 20.4066760745397 -7.40667607453972 121 22 25.4069018708723 -3.40690187087228 122 16 21.1561238969015 -5.15612389690145 123 19 23.3023756415670 -4.30237564156697 124 25 22.8388500576034 2.16114994239662 125 25 24.2049863856028 0.79501361439717 126 23 21.4270216803818 1.57297831961816 127 24 23.6057448605668 0.394255139433163 128 26 23.5787810287233 2.4212189712767 129 26 21.5354587553693 4.46454124463067 130 25 24.1634269784366 0.836573021563442 131 18 22.3726267030276 -4.37262670302765 132 21 19.8997587494783 1.10024125052168 133 26 23.7011182467433 2.29888175325667 134 23 21.9950548297436 1.00494517025638 135 23 19.7664053952701 3.23359460472994 136 22 22.5953786551716 -0.595378655171626 137 20 22.4122981727327 -2.41229817273269 138 13 22.1200179185666 -9.12001791856658 139 24 21.4641582848610 2.53584171513896 140 15 21.5997640211544 -6.59976402115444 141 14 23.1470906201603 -9.1470906201603 142 22 24.0995888972163 -2.09958889721628 143 10 17.6868808865665 -7.68688088656654 144 24 24.4769946623064 -0.476994662306395 145 22 21.8674008796395 0.132599120360474 146 24 25.817240275552 -1.81724027555201 147 19 21.6473338082820 -2.64733380828197 148 20 22.1326061683468 -2.13260616834676 149 13 17.1110998516415 -4.1110998516415 150 20 20.1383667857288 -0.138366785728794 151 22 23.2921840860280 -1.29218408602802 152 24 23.3700334438962 0.629966556103828 153 29 23.2025913262756 5.79740867372435 154 12 20.9617262019034 -8.96172620190338 155 20 20.9664885466080 -0.966488546607962 156 21 21.4611750179736 -0.461175017973646 157 24 23.6712648438594 0.328735156140567 158 22 21.9270327219989 0.0729672780010754 159 20 17.7083501437683 2.29164985623173 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.733977919159224 0.532044161681552 0.266022080840776 11 0.59360893700997 0.81278212598006 0.40639106299003 12 0.556783308280779 0.886433383438441 0.443216691719221 13 0.533599958788348 0.932800082423304 0.466400041211652 14 0.75731503332551 0.485369933348979 0.242684966674489 15 0.700450899570969 0.599098200858063 0.299549100429031 16 0.642562248259424 0.714875503481153 0.357437751740576 17 0.584414155702067 0.831171688595865 0.415585844297932 18 0.694648742857737 0.610702514284526 0.305351257142263 19 0.620656734426268 0.758686531147464 0.379343265573732 20 0.629892561782802 0.740214876434397 0.370107438217199 21 0.582650978481448 0.834698043037105 0.417349021518552 22 0.511964498628973 0.976071002742054 0.488035501371027 23 0.449180341777389 0.898360683554779 0.55081965822261 24 0.446323790554778 0.892647581109556 0.553676209445222 25 0.581306208195706 0.837387583608587 0.418693791804294 26 0.516610670529969 0.966778658940063 0.483389329470031 27 0.452040354328003 0.904080708656005 0.547959645671997 28 0.441703989037654 0.883407978075308 0.558296010962346 29 0.378585195746722 0.757170391493444 0.621414804253278 30 0.318638210318513 0.637276420637025 0.681361789681487 31 0.329552280098855 0.65910456019771 0.670447719901145 32 0.276178173847759 0.552356347695518 0.723821826152241 33 0.505281898447016 0.989436203105968 0.494718101552984 34 0.466830587945646 0.933661175891292 0.533169412054354 35 0.432321707668986 0.864643415337972 0.567678292331014 36 0.374814603645248 0.749629207290496 0.625185396354752 37 0.353533380908847 0.707066761817694 0.646466619091153 38 0.301568620612193 0.603137241224387 0.698431379387807 39 0.254308890961731 0.508617781923462 0.745691109038269 40 0.23054065160102 0.46108130320204 0.76945934839898 41 0.38670498835897 0.77340997671794 0.61329501164103 42 0.334771707871647 0.669543415743293 0.665228292128353 43 0.300659903948624 0.601319807897248 0.699340096051376 44 0.256510226428865 0.513020452857729 0.743489773571135 45 0.222833501330865 0.445667002661729 0.777166498669135 46 0.199578125750874 0.399156251501747 0.800421874249126 47 0.185813987709651 0.371627975419303 0.814186012290348 48 0.172247282258227 0.344494564516454 0.827752717741773 49 0.140929276090566 0.281858552181132 0.859070723909434 50 0.130162096677748 0.260324193355496 0.869837903322252 51 0.10763916999168 0.21527833998336 0.89236083000832 52 0.0909577716660183 0.181915543332037 0.909042228333982 53 0.148405862597768 0.296811725195536 0.851594137402232 54 0.182009538929390 0.364019077858780 0.81799046107061 55 0.174813273592978 0.349626547185956 0.825186726407022 56 0.230947311565686 0.461894623131372 0.769052688434314 57 0.220298261119905 0.44059652223981 0.779701738880095 58 0.189386631653744 0.378773263307488 0.810613368346256 59 0.197984909434763 0.395969818869525 0.802015090565237 60 0.226381017453841 0.452762034907681 0.773618982546159 61 0.198893445376701 0.397786890753403 0.801106554623299 62 0.167022898718333 0.334045797436666 0.832977101281667 63 0.1810976336219 0.3621952672438 0.8189023663781 64 0.153334529458645 0.306669058917290 0.846665470541355 65 0.126525809106944 0.253051618213887 0.873474190893056 66 0.121699039729004 0.243398079458009 0.878300960270996 67 0.110881898182298 0.221763796364596 0.889118101817702 68 0.111763712087129 0.223527424174258 0.888236287912871 69 0.09463098016003 0.18926196032006 0.90536901983997 70 0.0770917818149238 0.154183563629848 0.922908218185076 71 0.0626473843656424 0.125294768731285 0.937352615634358 72 0.0494721220510656 0.0989442441021311 0.950527877948934 73 0.0462758658512578 0.0925517317025156 0.953724134148742 74 0.0370892500650546 0.0741785001301091 0.962910749934945 75 0.0308733614070777 0.0617467228141554 0.969126638592922 76 0.0237075036080355 0.0474150072160709 0.976292496391965 77 0.0185765295724801 0.0371530591449602 0.98142347042752 78 0.0148243237015234 0.0296486474030468 0.985175676298477 79 0.0217866831477679 0.0435733662955358 0.978213316852232 80 0.0173361514188484 0.0346723028376968 0.982663848581152 81 0.0167860461485907 0.0335720922971815 0.98321395385141 82 0.0297616209584065 0.059523241916813 0.970238379041593 83 0.022897702844581 0.045795405689162 0.97710229715542 84 0.0190371000112952 0.0380742000225903 0.980962899988705 85 0.0208656180393237 0.0417312360786474 0.979134381960676 86 0.018557463657087 0.037114927314174 0.981442536342913 87 0.0141104525322401 0.0282209050644802 0.98588954746776 88 0.0181493546633150 0.0362987093266299 0.981850645336685 89 0.0143570001957524 0.0287140003915049 0.985642999804248 90 0.0107174169582959 0.0214348339165918 0.989282583041704 91 0.0108507989301548 0.0217015978603095 0.989149201069845 92 0.00943730756873828 0.0188746151374766 0.990562692431262 93 0.00722070342850107 0.0144414068570021 0.9927792965715 94 0.00594441011835978 0.0118888202367196 0.99405558988164 95 0.0107764759066595 0.0215529518133189 0.98922352409334 96 0.00972571262909135 0.0194514252581827 0.99027428737091 97 0.00927338032304567 0.0185467606460913 0.990726619676954 98 0.00707702013636055 0.0141540402727211 0.99292297986364 99 0.00520923017220676 0.0104184603444135 0.994790769827793 100 0.00398259107638168 0.00796518215276337 0.996017408923618 101 0.0029464389941767 0.0058928779883534 0.997053561005823 102 0.00209347688238093 0.00418695376476186 0.99790652311762 103 0.00223750343843133 0.00447500687686266 0.997762496561569 104 0.00174884288662551 0.00349768577325101 0.998251157113375 105 0.00742464920578417 0.0148492984115683 0.992575350794216 106 0.0166599083383909 0.0333198166767819 0.98334009166161 107 0.0166501106081609 0.0333002212163218 0.983349889391839 108 0.021251359233092 0.042502718466184 0.978748640766908 109 0.0163882377213784 0.0327764754427567 0.983611762278622 110 0.0119344101884850 0.0238688203769700 0.988065589811515 111 0.00861747116182453 0.0172349423236491 0.991382528838175 112 0.0213303532973868 0.0426607065947735 0.978669646702613 113 0.0196933607323615 0.039386721464723 0.980306639267639 114 0.0563052526614859 0.112610505322972 0.943694747338514 115 0.0484177645845321 0.0968355291690642 0.951582235415468 116 0.0392235578048461 0.0784471156096923 0.960776442195154 117 0.115895014148471 0.231790028296941 0.88410498585153 118 0.111430121528750 0.222860243057499 0.88856987847125 119 0.098786569216521 0.197573138433042 0.901213430783479 120 0.172338142426747 0.344676284853493 0.827661857573253 121 0.164432930147093 0.328865860294186 0.835567069852907 122 0.196170260434800 0.392340520869600 0.8038297395652 123 0.189868464437356 0.379736928874713 0.810131535562644 124 0.188675379899246 0.377350759798492 0.811324620100754 125 0.171360012076945 0.342720024153889 0.828639987923055 126 0.139531415398660 0.279062830797319 0.86046858460134 127 0.109132481967157 0.218264963934314 0.890867518032843 128 0.112414558222421 0.224829116444842 0.887585441777579 129 0.160846263288343 0.321692526576685 0.839153736711657 130 0.13856315456797 0.27712630913594 0.86143684543203 131 0.121454860099208 0.242909720198415 0.878545139900792 132 0.105201637132710 0.210403274265419 0.89479836286729 133 0.0964123362806631 0.192824672561326 0.903587663719337 134 0.0787077122510166 0.157415424502033 0.921292287748983 135 0.107288843621677 0.214577687243353 0.892711156378323 136 0.0795883173944661 0.159176634788932 0.920411682605534 137 0.0580822234184984 0.116164446836997 0.941917776581502 138 0.148141437938321 0.296282875876642 0.85185856206168 139 0.209464939747946 0.418929879495891 0.790535060252054 140 0.190498855311627 0.380997710623254 0.809501144688373 141 0.409057540473872 0.818115080947745 0.590942459526128 142 0.359313516622146 0.718627033244292 0.640686483377854 143 0.668662754938432 0.662674490123135 0.331337245061568 144 0.607530267717217 0.784939464565567 0.392469732282783 145 0.496932909225936 0.993865818451872 0.503067090774064 146 0.425898167970874 0.851796335941748 0.574101832029126 147 0.43593643957613 0.87187287915226 0.56406356042387 148 0.305355085611884 0.610710171223768 0.694644914388116 149 0.212989052643738 0.425978105287475 0.787010947356262 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0357142857142857 NOK 5% type I error level 37 0.264285714285714 NOK 10% type I error level 44 0.314285714285714 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/10w19s1290605581.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/10w19s1290605581.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/18iug1290605581.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/18iug1290605581.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/28iug1290605581.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/28iug1290605581.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/3iatj1290605581.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/3iatj1290605581.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/4iatj1290605581.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/4iatj1290605581.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/5iatj1290605581.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/5iatj1290605581.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/6t1sm1290605581.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/6t1sm1290605581.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/74as71290605581.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/74as71290605581.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/84as71290605581.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/84as71290605581.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/94as71290605581.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/24/t1290605629tpo6mafqislrwxu/94as71290605581.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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