Meervoudige lineaire regressie

*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, 22 Dec 2010 18:58:15 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp.htm/, Retrieved Wed, 22 Dec 2010 19:57:27 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp.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 «

14 12 24 24 11 8 25 25 6 8 30 17 12 8 19 18 8 9 22 18 10 7 22 16 10 4 25 20 11 11 23 16 16 7 17 18 11 7 21 17 13 12 19 23 12 10 19 30 8 10 15 23 12 8 16 18 11 8 23 15 4 4 27 12 9 9 22 21 8 8 14 15 8 7 22 20 14 11 23 31 15 9 23 27 16 11 21 34 9 13 19 21 14 8 18 31 11 8 20 19 8 9 23 16 9 6 25 20 9 9 19 21 9 9 24 22 9 6 22 17 10 6 25 24 16 16 26 25 11 5 29 26 8 7 32 25 9 9 25 17 16 6 29 32 11 6 28 33 16 5 17 13 12 12 28 32 12 7 29 25 14 10 26 29 9 9 25 22 10 8 14 18 9 5 25 17 10 8 26 20 12 8 20 15 14 10 18 20 14 6 32 33 10 8 25 29 14 7 25 23 16 4 23 26 9 8 21 18 10 8 20 20 6 4 15 11 8 20 30 28 13 8 24 26 10 8 26 22 8 6 24 17 7 4 22 12 15 8 14 14 9 9 24 17 10 6 24 21 12 7 24 19 13 9 24 18 10 5 19 10 11 5 31 29 8 8 22 31 9 8 27 19 13 6 19 9 11 8 25 20 8 7 20 28 9 7 21 19 9 9 27 30 15 11 23 29 9 6 25 26 10 8 20 23 14 6 21 13 12 9 22 21 12 8 23 19 11 6 25 28 14 10 25 23 6 8 17 18 12 8 19 21 8 10 25 20 14 5 19 23 11 7 20 21 10 5 26 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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation CM[t] = -2.63961096398292 + 0.772391502321592DA[t] + 0.419767875666413PC[t] + 0.558040238534683PS[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) -2.63961096398292 2.498439 -1.0565 0.292382 0.146191 DA 0.772391502321592 0.130373 5.9245 0 0 PC 0.419767875666413 0.135981 3.087 0.002396 0.001198 PS 0.558040238534683 0.086292 6.4669 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.62120705296726 R-squared 0.385898202656269 Adjusted R-squared 0.374012361417358 F-TEST (value) 32.4670500723958 F-TEST (DF numerator) 3 F-TEST (DF denominator) 155 p-value 2.22044604925031e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.52785891001842 Sum Squared Residuals 3177.73347790015 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 26.6040503013487 -2.60405030134868 2 25 23.165844530253 1.83415546974703 3 17 22.0940882113184 -5.09408821131842 4 18 20.5899946013665 -2.58999460136646 5 18 19.5943171833506 -1.59431718335056 6 16 20.2995644366609 -4.29956443666092 7 20 20.7143815252657 -0.714381525265727 8 16 23.3090676801828 -7.30906768018284 9 18 22.1437122579171 -4.14371225791705 10 17 20.5139157004478 -3.51391570044783 11 23 23.0414576063537 -0.0414576063537089 12 30 21.4295303526993 8.5704696473007 13 23 16.1078033892742 6.89219661072581 14 18 18.9158738857624 -0.915873885762416 15 15 22.0497640531836 -7.0497640531836 16 12 17.1961129884055 -5.19611298840554 17 21 20.3667086856722 0.63329131432785 18 15 14.7102273994067 0.289772600593319 19 20 18.7547814320177 1.24521856798227 20 31 25.6262421871476 5.37375781285238 21 27 25.5590979381364 1.44090206186361 22 34 26.0549447147214 7.94505528527856 23 21 20.3716594727338 0.628340527266247 24 31 21.576737367475 9.42326263252503 25 19 20.3756433375796 -1.37564333757956 26 16 20.1523574218852 -4.15235742188524 27 20 20.781525774277 -0.781525774276961 28 21 18.6925879700681 2.3074120299319 29 22 21.4827891627415 0.517210837258484 30 17 19.1074050586729 -2.10740505867291 31 24 21.5539172765986 2.44608272340145 32 25 30.9439852857269 -5.94398528572692 33 26 24.1387018573925 1.86129814260754 34 25 24.3351838173646 0.664816182635437 35 17 22.0408294012762 -5.0408294012762 36 32 28.4204272446668 3.57957275533316 37 33 24.0004294945242 8.9995705054758 38 13 21.3041765065842 -8.30417650658423 39 32 27.2914282508443 4.70857174915574 40 25 25.7506291110469 -0.750629111046883 41 29 26.8805950270853 2.11940497291474 42 22 22.0408294012762 -0.0408294012761991 43 18 16.2550104040499 1.74498959595014 44 17 20.3617578986105 -3.36175789861055 45 20 22.9514932664661 -2.95149326646606 46 15 21.1480348399012 -6.14803483990115 47 20 22.4162731188078 -2.41627311880779 48 33 28.5497649556277 4.4502350443723 49 29 22.3934530279314 6.60654697206862 50 23 25.0632511615513 -2.06325116155133 51 26 24.2326500621259 1.76734993787409 52 18 19.3889005714711 -1.38890057147105 53 20 19.603251835258 0.396748164742037 54 11 12.0444131306325 -1.04441313063253 55 28 28.6760857239586 -0.676085723958564 56 26 24.1525872963615 1.84741270363853 57 22 22.9514932664661 -0.951493266466062 58 17 19.4510940334207 -2.45109403342068 59 12 16.7230863026969 -4.7230863026969 60 14 20.1169679156578 -6.11696791565783 61 17 21.4827891627415 -4.48278916274152 62 21 20.9958770380639 0.00412296193613052 63 19 22.9604279183735 -3.96042791837347 64 18 24.5723551720279 -6.57235517202789 65 10 17.785907969724 -7.78590796972404 66 29 25.2547823344618 3.74521766553817 67 31 19.1745493076841 11.8254506923159 68 19 22.7371420026792 -3.73714200267915 69 9 20.5228503523552 -11.5228503523552 70 20 23.165844530253 -3.16584453025297 71 28 17.6387009549484 10.3612990450516 72 19 18.9691326958046 0.0308673041953589 73 30 23.1569098783456 6.84309012165443 74 29 26.3986336894692 2.60136631053079 75 26 20.781525774277 5.21847422572304 76 23 19.603251835258 3.39674816474204 77 13 22.4113223317462 -9.4113223317462 78 21 22.6838831926369 -1.68388319263693 79 19 22.8221555555052 -3.8221555555052 80 28 22.3263087789201 5.67369122107986 81 23 26.3225547885506 -3.32255478855057 82 18 14.8395651103675 3.16043488963246 83 21 20.5899946013665 0.410005398633535 84 20 21.688205774621 -1.68820577462102 85 23 20.8754739790104 2.12452602098959 86 21 19.9558754619131 1.04412453808686 87 21 21.6921896394668 -0.692189639466823 88 15 24.3669385601484 -9.36693856014838 89 28 27.5729237636424 0.427076236357593 90 19 17.5093632439875 1.4906367560125 91 26 21.0186971289403 4.98130287105972 92 10 14.3437183337825 -4.34371833378249 93 16 17.4422189949763 -1.44221899497627 94 22 19.8797965609945 2.1202034390055 95 19 20.2284363228039 -1.22843632280388 96 31 27.9788062003398 3.02119379966019 97 31 25.2154089633886 5.78459103661139 98 29 24.1575380834231 4.84246191657693 99 19 17.2950119802006 1.70498801979941 100 22 18.4871713581886 3.5128286418114 101 23 22.1169083021948 0.883091697805162 102 15 15.8885013384257 -0.888501338425677 103 20 19.6703960842692 0.329603915730803 104 18 19.4560448204823 -1.45604482048229 105 23 23.5323535958772 -0.532353595877158 106 25 19.759393501941 5.24060649805895 107 21 16.522620477879 4.477379522121 108 24 19.1123558457345 4.88764415426549 109 25 25.0682019486129 -0.0682019486129373 110 17 19.0630809005381 -2.06308090053809 111 13 14.2904595237403 -1.29045952374027 112 28 18.6214598562111 9.37854014378894 113 21 21.5499334117528 -0.54993341175275 114 25 26.9159845333127 -1.91598453331267 115 9 22.795351599783 -13.795351599783 116 16 17.3572054421502 -1.35720544215022 117 19 19.303887018645 -0.303887018645008 118 17 19.5361075862467 -2.53610758624673 119 25 24.2286661972801 0.771333802719888 120 20 14.7902901651711 5.20970983482888 121 29 22.044813266122 6.955186733878 122 14 18.2817547463091 -4.28175474630909 123 22 26.742322664217 -4.74232266421699 124 15 17.218933079282 -2.21893307928195 125 19 26.3493587442728 -7.34935874427279 126 20 20.9336835761142 -0.933683576114239 127 15 17.4954778050185 -2.49547780501849 128 20 22.6078042917183 -2.60780429171829 129 18 20.5810599494591 -2.58105994945906 130 33 26.0410592757524 6.95894072424757 131 22 23.8671079187175 -1.86710791871753 132 16 16.5986993787976 -0.59869937879764 133 17 19.2456774215412 -2.24567742154118 134 16 15.2633168508798 0.736683149120239 135 21 17.3710908811192 3.62890911888077 136 26 26.1082035247637 -0.108203524763664 137 18 20.5228503523552 -2.52285035235523 138 18 22.1258429541022 -4.12584295410224 139 17 19.0362769448159 -2.03627694481587 140 22 25.1353461976242 -3.13534619762417 141 30 24.7867064358148 5.2132935641852 142 30 27.0099327380461 2.99006726195388 143 24 28.288072591076 -4.28807259107597 144 21 22.7639459584014 -1.76394595840137 145 21 24.853850684826 -3.85385068482603 146 29 27.3043467675975 1.69565323240253 147 31 22.0408294012762 8.9591705987238 148 20 18.9691326958046 1.03086730419536 149 16 13.670225823256 2.32977417674405 150 22 18.8980045819476 3.1019954180524 151 20 21.0540866351677 -1.0540866351677 152 28 26.4697618033263 1.53023819667375 153 38 24.9782376087253 13.0217623912747 154 22 17.4332843430689 4.56671565693114 155 20 24.7066436700504 -4.70664367005035 156 17 17.4332843430689 -0.433284343068862 157 28 24.9249787986831 3.07502120131693 158 22 23.8760425706249 -1.87604257062493 159 31 25.9216231389148 5.07837686108523 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.249445492688399 0.498890985376797 0.750554507311601 8 0.248913537819918 0.497827075639836 0.751086462180082 9 0.195565458081761 0.391130916163522 0.80443454191824 10 0.113753732219148 0.227507464438297 0.886246267780852 11 0.118519866007289 0.237039732014579 0.88148013399271 12 0.578651702824571 0.842696594350858 0.421348297175429 13 0.532839615249157 0.934320769501686 0.467160384750843 14 0.460227508752618 0.920455017505236 0.539772491247382 15 0.471119169252794 0.942238338505588 0.528880830747206 16 0.409940110766888 0.819880221533776 0.590059889233112 17 0.336090936522085 0.67218187304417 0.663909063477915 18 0.298221545805888 0.596443091611776 0.701778454194112 19 0.254880941316553 0.509761882633107 0.745119058683447 20 0.366182239431312 0.732364478862623 0.633817760568688 21 0.334171734597087 0.668343469194175 0.665828265402913 22 0.452374492572973 0.904748985145947 0.547625507427027 23 0.393506702453209 0.787013404906418 0.606493297546791 24 0.568074641436503 0.863850717126993 0.431925358563497 25 0.507918880838688 0.984162238322623 0.492081119161312 26 0.469407327700054 0.938814655400108 0.530592672299946 27 0.419391782294758 0.838783564589516 0.580608217705242 28 0.370698819890991 0.741397639781983 0.629301180109008 29 0.322186416733026 0.644372833466051 0.677813583266974 30 0.270495416766811 0.540990833533623 0.729504583233189 31 0.272651216478215 0.54530243295643 0.727348783521785 32 0.317181813843737 0.634363627687474 0.682818186156263 33 0.316205083169298 0.632410166338596 0.683794916830702 34 0.312298460302082 0.624596920604165 0.687701539697918 35 0.300460281515826 0.600920563031652 0.699539718484174 36 0.28011332867869 0.56022665735738 0.71988667132131 37 0.460740735006478 0.921481470012957 0.539259264993522 38 0.679963717874554 0.640072564250892 0.320036282125446 39 0.681192626182062 0.637614747635875 0.318807373817938 40 0.63258095657867 0.734838086842659 0.367419043421329 41 0.58814983693556 0.82370032612888 0.41185016306444 42 0.535795038303561 0.928409923392878 0.464204961696439 43 0.49116089750327 0.98232179500654 0.50883910249673 44 0.459647675518113 0.919295351036227 0.540352324481887 45 0.42593343494374 0.85186686988748 0.57406656505626 46 0.469359709850048 0.938719419700096 0.530640290149952 47 0.436973124355942 0.873946248711884 0.563026875644058 48 0.430458485544768 0.860916971089536 0.569541514455232 49 0.491832743134936 0.983665486269872 0.508167256865064 50 0.454815777365918 0.909631554731836 0.545184222634082 51 0.411062616291425 0.82212523258285 0.588937383708575 52 0.365757486411424 0.731514972822848 0.634242513588576 53 0.321104654808723 0.642209309617445 0.678895345191277 54 0.280618842971023 0.561237685942045 0.719381157028977 55 0.2414533933519 0.482906786703801 0.7585466066481 56 0.20963617560906 0.41927235121812 0.79036382439094 57 0.177078360762939 0.354156721525878 0.822921639237061 58 0.153187177643339 0.306374355286679 0.84681282235666 59 0.148991735543892 0.297983471087785 0.851008264456108 60 0.175875019295915 0.351750038591829 0.824124980704085 61 0.172289890840493 0.344579781680987 0.827710109159506 62 0.143775096731864 0.287550193463727 0.856224903268136 63 0.137299008428432 0.274598016856865 0.862700991571568 64 0.170779249289487 0.341558498578974 0.829220750710513 65 0.224470009713255 0.448940019426509 0.775529990286745 66 0.213090891370544 0.426181782741087 0.786909108629457 67 0.479584340934018 0.959168681868035 0.520415659065982 68 0.463721458448322 0.927442916896644 0.536278541551678 69 0.694174143130542 0.611651713738916 0.305825856869458 70 0.672877461643777 0.654245076712445 0.327122538356223 71 0.832523867821863 0.334952264356273 0.167476132178137 72 0.802610485150496 0.394779029699008 0.197389514849504 73 0.838570178043654 0.322859643912692 0.161429821956346 74 0.818534543145451 0.362930913709097 0.181465456854549 75 0.828182204631837 0.343635590736325 0.171817795368163 76 0.815743390044065 0.36851321991187 0.184256609955935 77 0.899440385173265 0.201119229653469 0.100559614826735 78 0.8808521260568 0.238295747886401 0.1191478739432 79 0.874722897277273 0.250554205445454 0.125277102722727 80 0.887184360590313 0.225631278819374 0.112815639409687 81 0.877255873156658 0.245488253686684 0.122744126843342 82 0.865580616953166 0.268838766093669 0.134419383046834 83 0.839701178558465 0.32059764288307 0.160298821441535 84 0.814403687548952 0.371192624902096 0.185596312451048 85 0.790682153885253 0.418635692229494 0.209317846114747 86 0.757936068412936 0.484127863174128 0.242063931587064 87 0.721776608954689 0.556446782090622 0.278223391045311 88 0.841531730219913 0.316936539560174 0.158468269780087 89 0.812142607955377 0.375714784089245 0.187857392044623 90 0.782948548363337 0.434102903273325 0.217051451636663 91 0.787823891503364 0.424352216993272 0.212176108496636 92 0.786331351423752 0.427337297152497 0.213668648576248 93 0.758595078268757 0.482809843462487 0.241404921731243 94 0.727236373512461 0.545527252975078 0.272763626487539 95 0.689752699927862 0.620494600144276 0.310247300072138 96 0.668755977206709 0.662488045586582 0.331244022793291 97 0.69004951586869 0.619900968262621 0.309950484131311 98 0.698247993241249 0.603504013517502 0.301752006758751 99 0.66027054676135 0.679458906477301 0.339729453238651 100 0.639767466236746 0.720465067526507 0.360232533763254 101 0.595690390711235 0.80861921857753 0.404309609288765 102 0.552434104940603 0.895131790118794 0.447565895059397 103 0.50432361741225 0.9913527651755 0.49567638258775 104 0.460467209553848 0.920934419107697 0.539532790446152 105 0.412968142201529 0.825936284403059 0.587031857798471 106 0.417902129487051 0.835804258974102 0.582097870512949 107 0.410727213813859 0.821454427627717 0.589272786186141 108 0.419426705736974 0.838853411473948 0.580573294263026 109 0.371588597837157 0.743177195674314 0.628411402162843 110 0.338799433630477 0.677598867260954 0.661200566369523 111 0.298884729203604 0.597769458407209 0.701115270796396 112 0.484017902103863 0.968035804207727 0.515982097896137 113 0.435500862567474 0.871001725134948 0.564499137432526 114 0.390463261071346 0.780926522142692 0.609536738928654 115 0.798904845015963 0.402190309968074 0.201095154984037 116 0.770710577994918 0.458578844010163 0.229289422005082 117 0.736044248463625 0.52791150307275 0.263955751536375 118 0.711428205701328 0.577143588597343 0.288571794298672 119 0.664550885142805 0.67089822971439 0.335449114857195 120 0.702495086681328 0.595009826637344 0.297504913318672 121 0.728384388961717 0.543231222076567 0.271615611038283 122 0.713972493312134 0.572055013375731 0.286027506687866 123 0.726995194625641 0.546009610748718 0.273004805374359 124 0.698470371957245 0.603059256085509 0.301529628042755 125 0.770682894507768 0.458634210984465 0.229317105492232 126 0.728363804661094 0.543272390677813 0.271636195338906 127 0.718488091390232 0.563023817219537 0.281511908609768 128 0.705946230567985 0.58810753886403 0.294053769432015 129 0.679968398362855 0.64006320327429 0.320031601637145 130 0.710714472888155 0.57857105422369 0.289285527111845 131 0.672387148603661 0.655225702792678 0.327612851396339 132 0.614012653480107 0.771974693039787 0.385987346519893 133 0.61403863885504 0.771922722289919 0.38596136114496 134 0.557146646738897 0.885706706522206 0.442853353261103 135 0.52288823229967 0.95422353540066 0.47711176770033 136 0.460986506841044 0.921973013682087 0.539013493158956 137 0.438102764773249 0.876205529546498 0.561897235226751 138 0.460601715219903 0.921203430439807 0.539398284780097 139 0.436634787786742 0.873269575573484 0.563365212213258 140 0.402488782063243 0.804977564126486 0.597511217936757 141 0.378580930195194 0.757161860390387 0.621419069804806 142 0.308641404210443 0.617282808420886 0.691358595789557 143 0.26705673710574 0.534113474211479 0.73294326289426 144 0.244359739124237 0.488719478248474 0.755640260875763 145 0.271627088503909 0.543254177007819 0.728372911496091 146 0.223595422381496 0.447190844762993 0.776404577618504 147 0.302908234873074 0.605816469746149 0.697091765126925 148 0.224038010971399 0.448076021942798 0.7759619890286 149 0.160661131519145 0.321322263038289 0.839338868480855 150 0.122824456955706 0.245648913911412 0.877175543044294 151 0.0765079447683091 0.153015889536618 0.92349205523169 152 0.0642757852221568 0.128551570444314 0.935724214777843 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/Dec/22/t12930442442xqa52wnlvepbgp/10yh181293044284.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/10yh181293044284.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/19y4e1293044284.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/19y4e1293044284.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/29y4e1293044284.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/29y4e1293044284.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/328lz1293044284.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/328lz1293044284.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/428lz1293044284.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/428lz1293044284.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/528lz1293044284.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/528lz1293044284.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/6dzl21293044284.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/6dzl21293044284.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/7dzl21293044284.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/7dzl21293044284.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/8oqkn1293044284.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/8oqkn1293044284.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/9oqkn1293044284.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930442442xqa52wnlvepbgp/9oqkn1293044284.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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

Software written by Ed van Stee & Patrick Wessa

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