BEL20-MR1

*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 15:44:40 +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/t129303522624nzf5nsq8teqx3.htm/, Retrieved Wed, 22 Dec 2010 17:27:17 +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/t129303522624nzf5nsq8teqx3.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:

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3,04 493 9 3.030 9.026 25,64 104,8 3,28 481 11 2.803 9.787 27,97 105,2 3,51 462 13 2.768 9.536 27,62 105,6 3,69 457 12 2.883 9.490 23,31 105,8 3,92 442 13 2.863 9.736 29,07 106,1 4,29 439 15 2.897 9.694 29,58 106,5 4,31 488 13 3.013 9.647 28,63 106,71 4,42 521 16 3.143 9.753 29,92 106,68 4,59 501 10 3.033 10.070 32,68 107,41 4,76 485 14 3.046 10.137 31,54 107,15 4,83 464 14 3.111 9.984 32,43 107,5 4,83 460 45 3.013 9.732 26,54 107,22 4,76 467 13 2.987 9.103 25,85 107,11 4,99 460 8 2.996 9.155 27,60 107,57 4,78 448 7 2.833 9.308 25,71 107,81 5,06 443 3 2.849 9.394 25,38 108,75 4,65 436 3 2.795 9.948 28,57 109,43 4,54 431 4 2.845 10.177 27,64 109,62 4,51 484 4 2.915 10.002 25,36 109,54 4,49 510 0 2.893 9.728 25,90 109,53 3,99 513 -4 2.604 10.002 26,29 109,84 3,97 503 -14 2.642 10.063 21,74 109,67 3,51 471 -18 2.660 10.018 19,20 109,79 3,34 471 -8 2.639 9.960 19,32 109,56 3,29 476 -1 2.720 10.236 19,82 110,22 3,28 475 1 2.746 10.893 20,36 110,4 3,26 470 2 2.736 10.756 24,31 110,69 3,32 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 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation BEL20[t] = -6.52694269803798 + 0.38134548609792Eonia[t] + 0.0066331019909006Werkloosheid[t] + 0.0339479944182582Consumentenvertrouwen[t] -0.0176233167337368Goudprijs[t] + 0.00861723790694973Olieprijs[t] + 0.0406391768418570CPI[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) -6.52694269803798 2.38488 -2.7368 0.007116 0.003558 Eonia 0.38134548609792 0.064267 5.9338 0 0 Werkloosheid 0.0066331019909006 0.001316 5.0403 2e-06 1e-06 Consumentenvertrouwen 0.0339479944182582 0.006971 4.8699 3e-06 2e-06 Goudprijs -0.0176233167337368 0.022191 -0.7942 0.42861 0.214305 Olieprijs 0.00861723790694973 0.003943 2.1856 0.030722 0.015361 CPI 0.0406391768418570 0.024786 1.6396 0.103616 0.051808 Multiple Linear Regression - Regression Statistics Multiple R 0.821004574068137 R-squared 0.674048510640803 Adjusted R-squared 0.658276664381487 F-TEST (value) 42.7374512506842 F-TEST (DF numerator) 6 F-TEST (DF denominator) 124 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.443811783973242 Sum Squared Residuals 24.4241435495955 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.03 2.52886246710014 0.501137532899857 2 2.803 2.63160663973489 0.171393360265108 3 2.768 2.67884624251629 0.0891537574837057 4 2.883 2.65217313820033 0.230826861799671 5 2.863 2.73182577203769 0.131174227962309 6 2.897 2.94231092612984 -0.0453109261298374 7 3.013 3.20823999158108 -0.195239991581082 8 3.143 3.57895333402728 -0.435953334027283 9 3.033 3.35529564464951 -0.322295644649509 10 3.046 3.42821612369081 -0.382216123690813 11 3.111 3.34020458700085 -0.229204587000851 12 3.013 4.3083665810325 -1.29536658103250 13 2.987 3.24243715217481 -0.255437152174809 14 2.996 3.14683270316400 -0.150832703163997 15 2.833 2.94397538811202 -0.110975388112018 16 2.849 2.91563616907485 -0.0666361690748498 17 2.795 2.75821311754354 0.0367868824564586 18 2.845 2.71271927135099 0.132280728649011 19 2.915 3.03301895613899 -0.118018956138994 20 2.893 3.07113642599380 -0.178136425993797 21 2.604 2.77570109006415 -0.171701090064148 22 2.642 2.31507110139011 0.326928898609894 23 2.66 1.77538290259360 0.884617097406401 24 2.639 2.0427433243853 0.596256675614701 25 2.72 2.32074396121330 0.399256038786698 26 2.746 2.37858323440516 0.367416765594839 27 2.736 2.41997665455607 0.316023345443931 28 2.812 2.32754457691911 0.484455423080892 29 2.799 2.32068242989377 0.478317570106226 30 2.555 2.29091897230156 0.264081027698440 31 2.305 2.67672989992180 -0.371729899921805 32 2.215 2.66082224946506 -0.445822249465058 33 2.066 2.68646593848017 -0.620465938480174 34 1.94 2.63971624795032 -0.699716247950316 35 2.042 2.51314735381025 -0.471147353810252 36 1.995 2.34075676879281 -0.345756768792811 37 1.947 2.27731516979939 -0.330315169799387 38 1.766 2.16750911477274 -0.401509114772736 39 1.635 1.94932252581049 -0.314322525810488 40 1.833 2.06133507586850 -0.228335075868503 41 1.91 2.06531652356652 -0.155316523566523 42 1.96 1.96783418640435 -0.00783418640434615 43 1.97 2.24318894228212 -0.273188942282121 44 2.061 2.40753719200839 -0.346537192008392 45 2.093 2.54982783286232 -0.456827832862316 46 2.121 2.13125322539307 -0.0102532253930704 47 2.175 2.30269572913065 -0.127695729130647 48 2.197 2.39521749977699 -0.198217499776989 49 2.35 2.55283678509818 -0.202836785098181 50 2.44 2.63824164372342 -0.198241643723416 51 2.409 2.54239917372659 -0.133399173726592 52 2.473 2.48727537695453 -0.0142753769545326 53 2.408 2.41205113061827 -0.00405113061826799 54 2.455 2.64208456826422 -0.187084568264222 55 2.448 2.8938820671105 -0.445882067110501 56 2.498 3.10151427871375 -0.60351427871375 57 2.646 3.12993179137956 -0.483931791379559 58 2.757 3.0772604088016 -0.320260408801600 59 2.849 2.87701643611857 -0.0280164361185700 60 2.921 2.85342411070563 0.0675758892943694 61 2.982 2.88973361096918 0.0922663890308174 62 3.081 3.01535605812902 0.0656439418709842 63 3.106 3.10986675820726 -0.00386675820725781 64 3.119 2.95103797346697 0.167962026533034 65 3.061 2.69707852713291 0.363921472867087 66 3.097 2.73984893339747 0.357151066602535 67 3.162 3.13919013770657 0.0228098622934251 68 3.257 3.27800536751436 -0.0210053675143613 69 3.277 3.1420321005045 0.134967899495502 70 3.295 3.17246104419478 0.122538955805216 71 3.364 2.99799396374254 0.366006036257458 72 3.494 3.21613360312913 0.27786639687087 73 3.667 3.38493811406359 0.282061885936408 74 3.813 3.33743267116482 0.47556732883518 75 3.918 3.24445629209607 0.673543707903935 76 3.896 3.32895502916185 0.567044970838153 77 3.801 3.2681595671291 0.532840432870902 78 3.57 3.46266672569636 0.107333274303636 79 3.702 3.85764514853185 -0.155645148531854 80 3.862 3.96758405557747 -0.105584055577467 81 3.97 3.86608594539865 0.103914054601354 82 4.139 3.83792827718991 0.301071722810089 83 4.2 3.67199631415098 0.52800368584902 84 4.291 3.41051099303483 0.880489006965169 85 4.444 3.63088505813174 0.81311494186826 86 4.503 3.66470368917874 0.838296310821256 87 4.357 3.56846432133214 0.788535678667865 88 4.591 3.74753046033778 0.843469539662219 89 4.697 3.63488006261796 1.06211993738204 90 4.621 3.61228197144169 1.00871802855831 91 4.563 4.01994528937295 0.543054710627052 92 4.203 4.00793265948259 0.195067340517414 93 4.296 3.88130591979074 0.41469408020926 94 4.435 3.84307933643781 0.591920663562193 95 4.105 3.65206317241614 0.452936827583862 96 4.117 3.75712488355986 0.359875116440137 97 3.844 3.76782140566508 0.0761785943349186 98 3.721 3.85309626671009 -0.132096266710090 99 3.674 3.88954341116678 -0.215543411166777 100 3.858 3.79347512693928 0.0645248730607213 101 3.801 3.76684792776853 0.0341520722314743 102 3.504 3.86283777376056 -0.358837773760565 103 3.033 4.2358899442194 -1.2028899442194 104 3.047 4.20228495580579 -1.15528495580579 105 2.962 4.02778282004451 -1.06578282004451 106 2.198 3.25381164883254 -1.05581164883254 107 2.014 2.60415942852153 -0.590159428521525 108 1.863 2.22344393493199 -0.360443934931989 109 1.905 2.21079346409249 -0.305793464092489 110 1.811 1.85654968154084 -0.0455496815408419 111 1.67 1.8116048573789 -0.141604857378901 112 1.864 1.86393738779001 6.26122099874546e-05 113 2.052 1.90893604083542 0.143063959164578 114 2.03 2.08139440319924 -0.0513944031992398 115 2.071 2.29810846050504 -0.227108460505042 116 2.293 2.64124405962976 -0.348244059629764 117 2.443 2.47677443292429 -0.0337744329242888 118 2.513 2.36314204383208 0.149857956167918 119 2.467 2.41176816408873 0.0552318359112712 120 2.503 2.32940611752455 0.173593882475448 121 2.54 2.39599373999704 0.144006260002959 122 2.483 2.34932085260560 0.133679147394396 123 2.626 2.39554497625331 0.230455023746685 124 2.656 2.54069648842171 0.115303511578291 125 2.447 2.16836987759470 0.278630122405305 126 2.467 2.31021806504714 0.156781934952857 127 2.462 2.83746925148891 -0.375469251488915 128 2.505 2.95937767668005 -0.454377676680048 129 2.579 2.85115799954385 -0.272157999543846 130 2.649 2.92893610743094 -0.279936107430943 131 2.637 2.86283904555191 -0.225839045551909 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.000878723581651672 0.00175744716330334 0.999121276418348 11 0.000615358272501805 0.00123071654500361 0.999384641727498 12 0.000206265559376606 0.000412531118753212 0.999793734440623 13 0.000221007060854818 0.000442014121709636 0.999778992939145 14 4.71259844848096e-05 9.42519689696192e-05 0.999952874015515 15 9.00616697596201e-06 1.80123339519240e-05 0.999990993833024 16 1.73030505214405e-06 3.46061010428809e-06 0.999998269694948 17 3.65545430783622e-07 7.31090861567244e-07 0.99999963445457 18 1.39548733097121e-07 2.79097466194241e-07 0.999999860451267 19 2.30153054991982e-08 4.60306109983964e-08 0.999999976984695 20 7.47544960303117e-09 1.49508992060623e-08 0.99999999252455 21 3.98377021393674e-08 7.96754042787349e-08 0.999999960162298 22 8.79613583082916e-09 1.75922716616583e-08 0.999999991203864 23 8.67518727119655e-09 1.73503745423931e-08 0.999999991324813 24 2.80595923888905e-09 5.6119184777781e-09 0.99999999719404 25 1.44509635548742e-09 2.89019271097484e-09 0.999999998554904 26 5.04217689203774e-10 1.00843537840755e-09 0.999999999495782 27 1.31953193165719e-10 2.63906386331437e-10 0.999999999868047 28 5.76717683575943e-11 1.15343536715189e-10 0.999999999942328 29 1.76875382461664e-11 3.53750764923327e-11 0.999999999982312 30 1.66760542193812e-11 3.33521084387624e-11 0.999999999983324 31 4.14879514602423e-10 8.29759029204845e-10 0.99999999958512 32 1.18712006636003e-09 2.37424013272006e-09 0.99999999881288 33 6.46080540198683e-09 1.29216108039737e-08 0.999999993539195 34 5.17214660795943e-08 1.03442932159189e-07 0.999999948278534 35 8.67148857002095e-08 1.73429771400419e-07 0.999999913285114 36 7.22392259002392e-08 1.44478451800478e-07 0.999999927760774 37 2.98424106293431e-08 5.96848212586862e-08 0.99999997015759 38 1.17777933364393e-08 2.35555866728786e-08 0.999999988222207 39 4.73820144124059e-09 9.47640288248118e-09 0.999999995261799 40 4.88743918498313e-09 9.77487836996627e-09 0.99999999511256 41 2.84311663633253e-09 5.68623327266506e-09 0.999999997156883 42 1.03235783760647e-08 2.06471567521294e-08 0.999999989676422 43 4.55525824298141e-08 9.11051648596281e-08 0.999999954447418 44 1.21866330095137e-07 2.43732660190273e-07 0.99999987813367 45 1.35009733581721e-07 2.70019467163442e-07 0.999999864990266 46 2.2333647090806e-07 4.4667294181612e-07 0.999999776663529 47 3.06822292808928e-07 6.13644585617855e-07 0.999999693177707 48 4.48516944038307e-07 8.97033888076613e-07 0.999999551483056 49 2.1088194129996e-06 4.2176388259992e-06 0.999997891180587 50 1.47882523602673e-05 2.95765047205347e-05 0.99998521174764 51 5.15177380113457e-05 0.000103035476022691 0.999948482261989 52 0.000164565775424614 0.000329131550849227 0.999835434224575 53 0.00049394746016683 0.00098789492033366 0.999506052539833 54 0.00158062897915926 0.00316125795831852 0.99841937102084 55 0.0047459748477082 0.0094919496954164 0.995254025152292 56 0.016438106073818 0.032876212147636 0.983561893926182 57 0.0526395731298754 0.105279146259751 0.947360426870125 58 0.101002542836081 0.202005085672162 0.898997457163919 59 0.179453009278977 0.358906018557954 0.820546990721023 60 0.335138832842899 0.670277665685799 0.664861167157101 61 0.498660151648292 0.997320303296584 0.501339848351708 62 0.65258496565341 0.69483006869318 0.34741503434659 63 0.773989474203105 0.45202105159379 0.226010525796895 64 0.857539910984313 0.284920178031374 0.142460089015687 65 0.880038952926756 0.239922094146487 0.119961047073244 66 0.898177818759918 0.203644362480164 0.101822181240082 67 0.877017538100424 0.245964923799152 0.122982461899576 68 0.848782527213123 0.302434945573754 0.151217472786877 69 0.829055092251293 0.341889815497414 0.170944907748707 70 0.80963961931093 0.38072076137814 0.19036038068907 71 0.79240614714809 0.415187705703819 0.207593852851909 72 0.803719474337616 0.392561051324768 0.196280525662384 73 0.872830717258066 0.254338565483868 0.127169282741934 74 0.878518191946193 0.242963616107613 0.121481808053807 75 0.860692190136325 0.278615619727349 0.139307809863675 76 0.864444671980724 0.271110656038551 0.135555328019276 77 0.892639959372465 0.214720081255070 0.107360040627535 78 0.986035992345747 0.0279280153085061 0.0139640076542530 79 0.996012425082256 0.00797514983548776 0.00398757491774388 80 0.997625560359799 0.00474887928040306 0.00237443964020153 81 0.99805761573492 0.00388476853015968 0.00194238426507984 82 0.999460814934272 0.00107837013145645 0.000539185065728224 83 0.999832534068288 0.000334931863423922 0.000167465931711961 84 0.999810158629765 0.000379682740469761 0.000189841370234880 85 0.999839222400774 0.000321555198452334 0.000160777599226167 86 0.999797627413853 0.000404745172293666 0.000202372586146833 87 0.999657305314763 0.000685389370474297 0.000342694685237149 88 0.999468365632934 0.00106326873413212 0.000531634367066058 89 0.999399541861348 0.00120091627730413 0.000600458138652066 90 0.999134451368837 0.00173109726232502 0.000865548631162511 91 0.99951945211794 0.00096109576412044 0.00048054788206022 92 0.999318349988928 0.00136330002214366 0.00068165001107183 93 0.99907733106634 0.00184533786731935 0.000922668933659677 94 0.999226854041798 0.00154629191640355 0.000773145958201775 95 0.999610205003309 0.00077958999338241 0.000389794996691205 96 0.999831590283322 0.000336819433356223 0.000168409716678112 97 0.999910446257232 0.000179107485536182 8.95537427680908e-05 98 0.999953594958624 9.28100827521577e-05 4.64050413760788e-05 99 0.999971933527522 5.6132944955891e-05 2.80664724779455e-05 100 0.99999082247386 1.83550522807422e-05 9.1775261403711e-06 101 0.99999952845077 9.43098461443915e-07 4.71549230721957e-07 102 0.999999789030433 4.21939134837489e-07 2.10969567418744e-07 103 0.99999996576447 6.84710584228158e-08 3.42355292114079e-08 104 0.99999995339989 9.32002214404243e-08 4.66001107202121e-08 105 0.999999957520574 8.49588514838488e-08 4.24794257419244e-08 106 0.999999989934453 2.01310944525951e-08 1.00655472262975e-08 107 0.999999981524716 3.69505688458387e-08 1.84752844229194e-08 108 0.99999994330389 1.13392221562619e-07 5.66961107813096e-08 109 0.99999993595287 1.28094260290691e-07 6.40471301453456e-08 110 0.999999936273068 1.27453864478889e-07 6.37269322394447e-08 111 0.99999971111534 5.77769320118724e-07 2.88884660059362e-07 112 0.999998805002148 2.38999570331684e-06 1.19499785165842e-06 113 0.99999896243481 2.07513037799125e-06 1.03756518899562e-06 114 0.999996546619171 6.90676165800907e-06 3.45338082900453e-06 115 0.999998704238816 2.59152236717197e-06 1.29576118358599e-06 116 0.999999936871317 1.26257366764203e-07 6.31286833821014e-08 117 0.999999297635776 1.40472844721956e-06 7.02364223609781e-07 118 0.999995325479443 9.34904111482786e-06 4.67452055741393e-06 119 0.99997938151032 4.12369793587486e-05 2.06184896793743e-05 120 0.999770801046404 0.000458397907191199 0.000229198953595599 121 0.997942672799135 0.00411465440172924 0.00205732720086462 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 89 0.794642857142857 NOK 5% type I error level 91 0.8125 NOK 10% type I error level 91 0.8125 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/10brlw1293032668.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/10brlw1293032668.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/14qol1293032668.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/14qol1293032668.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/24qol1293032668.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/24qol1293032668.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/3xz551293032668.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/3xz551293032668.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/4xz551293032668.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/4xz551293032668.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/5xz551293032668.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/5xz551293032668.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/68qmr1293032668.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/68qmr1293032668.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/70hlb1293032668.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/70hlb1293032668.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/8brlw1293032668.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/8brlw1293032668.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/9brlw1293032668.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t129303522624nzf5nsq8teqx3/9brlw1293032668.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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