*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: Thu, 02 Dec 2010 18:53:16 +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/02/t1291315911428wtpswg8c5gi1.htm/, Retrieved Thu, 02 Dec 2010 19:52:01 +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/Dec/02/t1291315911428wtpswg8c5gi1.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 «

2 4 1 2 2 11 2 1 1 1 2 7 4 5 2 4 2 17 2 3 1 2 2 10 3 3 2 2 2 12 4 3 1 2 2 12 3 2 3 2 1 11 3 3 1 2 2 11 3 4 1 1 3 12 2 4 1 4 2 13 4 4 2 2 2 14 4 2 4 3 3 16 3 2 2 2 2 11 3 2 1 2 2 10 4 4 1 1 1 11 4 4 3 3 1 15 3 3 2 1 NA 9 3 2 2 2 2 11 3 5 3 4 2 17 4 4 3 4 2 17 2 3 1 3 2 11 5 4 2 2 5 18 4 3 2 3 2 14 2 2 2 2 2 10 3 2 2 2 2 11 4 3 3 3 2 15 4 4 2 3 2 15 3 4 2 2 2 13 4 5 2 4 1 16 4 4 2 2 1 13 1 3 2 2 1 9 4 4 3 3 4 18 5 4 2 5 2 18 2 4 2 2 2 12 4 5 2 3 3 17 3 2 2 1 1 9 2 2 2 2 1 9 4 4 1 2 1 12 5 5 2 4 2 18 4 3 1 2 2 12 4 5 2 4 3 18 4 2 2 3 3 14 3 4 2 2 4 15 4 4 2 4 2 16 2 2 2 2 2 10 2 2 3 2 2 11 4 4 2 2 2 14 2 2 2 2 1 9 4 2 2 2 2 12 4 4 4 3 2 17 1 1 1 1 1 5 4 2 2 2 2 12 2 4 2 2 2 12 1 1 1 1 2 6 4 5 5 5 5 24 3 4 2 2 1 12 2 4 2 2 2 12 4 4 2 2 2 14 3 1 1 1 1 7 2 4 2 2 3 13 2 4 2 2 2 12 3 4 2 2 2 13 2 4 2 4 2 14 1 2 2 2 1 8 3 4 1 1 2 11 2 3 1 2 1 9 3 2 2 2 2 11 3 4 2 2 2 13 3 4 1 1 1 10 2 3 2 2 2 11 3 3 2 2 2 12 2 2 1 2 2 9 4 4 3 3 1 15 4 4 3 3 4 18 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 Parental[t] = -2.65680401101486e-14 + 1.00000000000000Standards[t] + 0.999999999999999Best[t] + 1.00000000000000Performance[t] + 1Excellence[t] + 0.999999999999999Expectations[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) -2.65680401101486e-14 0 -5.3371 0 0 Standards 1.00000000000000 0 686969967432572 0 0 Best 0.999999999999999 0 773225989758168 0 0 Performance 1.00000000000000 0 535281692331932 0 0 Excellence 1 0 562060524160205 0 0 Expectations 0.999999999999999 0 590173590393371 0 0 Multiple Linear Regression - Regression Statistics Multiple R 1 R-squared 1 Adjusted R-squared 1 F-TEST (value) 1.55470383404813e+30 F-TEST (DF numerator) 5 F-TEST (DF denominator) 152 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.54714534346309e-14 Sum Squared Residuals 3.63836124497528e-26 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 11.0000000000002 -1.86691117805923e-13 2 7 7 -6.12608115143102e-15 3 17 17 1.18067665896588e-14 4 10 10 -8.4413608287485e-16 5 12 12 -2.42434767179544e-15 6 12 12 -4.95846266774762e-16 7 11 11 -4.35847577622514e-15 8 11 11 3.49362523962373e-15 9 12 12 6.82367421107632e-15 10 13 13 7.16936328542979e-15 11 14 14 1.08352229214418e-15 12 16 16 -6.05291802281138e-15 13 11 11 -3.90593651259474e-16 14 10 10 2.2402834060974e-15 15 11 11 2.88464340642885e-15 16 15 15 -2.32301929615634e-15 17 9 9 -3.90593651259474e-16 18 11 11 1.84735807748512e-15 19 17 17 -1.12897142312900e-15 20 17 17 5.74672842080907e-15 21 11 11 1.49110957992390e-15 22 18 18 -5.2788244698472e-16 23 14 14 1.66893037016780e-15 24 10 10 -3.90593651259474e-16 25 11 11 -2.96793992198415e-15 26 15 15 1.05852629392916e-15 27 15 15 2.94528783731010e-15 28 13 13 1.65069534592632e-15 29 16 16 -1.07766003482552e-16 30 13 13 4.47398897902955e-15 31 9 9 6.12467351564397e-16 32 18 18 -1.40834275997939e-15 33 18 18 4.67001022787386e-15 34 12 12 3.61417872554474e-15 35 17 17 -1.58811097123877e-15 36 9 9 4.98458756252793e-16 37 9 9 2.13800244220747e-15 38 12 12 3.69595432843291e-16 39 18 18 1.49308181637967e-15 40 12 12 3.64469387856098e-15 41 18 18 -1.14504749719689e-15 42 14 14 5.66093133595112e-15 43 15 15 1.22781932502354e-15 44 16 16 1.66893037016780e-15 45 10 10 -8.0582157435116e-16 46 11 11 1.08352229214418e-15 47 14 14 4.98458756252793e-16 48 9 9 -2.14480634091483e-15 49 12 12 -3.62729962676029e-15 50 17 17 3.46091363864431e-15 51 5 5 -2.14480634091483e-15 52 12 12 4.67001022787386e-15 53 12 12 4.45791290496164e-15 54 6 6 -1.95627619255832e-15 55 24 24 1.83726626853026e-15 56 12 12 4.67001022787386e-15 57 12 12 1.08352229214418e-15 58 14 14 -1.26181817385017e-15 59 7 7 5.77629707317773e-15 60 13 13 4.67001022787386e-15 61 12 12 2.94528783731010e-15 62 13 13 4.007660844424e-15 63 14 14 2.66553563319064e-15 64 8 8 5.60463033983395e-15 65 11 11 4.21961364039418e-15 66 9 9 -3.90593651259474e-16 67 11 11 2.94528783731010e-15 68 13 13 4.82967567844166e-15 69 10 10 3.33860583792857e-15 70 11 11 1.33112352078059e-15 71 12 12 4.07429337564769e-15 72 9 9 -2.32301929615634e-15 73 15 15 6.12467351564397e-16 74 18 18 -1.07897942669896e-15 75 15 15 4.67001022787386e-15 76 12 12 2.20084832893404e-15 77 13 13 1.08352229214418e-15 78 14 14 2.2402834060974e-15 79 10 10 -7.9941649816154e-15 80 13 13 2.42250705870786e-15 81 13 13 -3.90593651259474e-16 82 11 11 4.24483885799875e-15 83 13 13 2.56166830799615e-15 84 16 16 2.74422720194282e-15 85 8 8 1.22781932502354e-15 86 16 16 -8.0582157435116e-16 87 11 11 5.88652953075434e-15 88 9 9 1.22781932502354e-15 89 16 16 -2.52525642732676e-16 90 12 12 1.08352229214418e-15 91 14 14 1.18833361404518e-15 92 8 8 4.07429337564769e-15 93 9 9 4.47894500439334e-15 94 15 15 -3.90593651259474e-16 95 11 11 -4.03591515428926e-15 96 21 21 5.25170071388139e-15 97 14 14 -7.51897450068611e-16 98 18 18 1.18122809793941e-15 99 12 12 -1.58732112635287e-15 100 13 13 2.21929943653966e-15 101 15 15 -2.52525642732676e-16 102 12 12 3.42246330903420e-16 103 19 19 2.78388766326633e-15 104 15 15 -3.90593651259474e-16 105 11 11 6.80302164762539e-15 106 11 11 1.16277699033379e-15 107 10 10 5.77629707317773e-15 108 13 13 -1.07897942669896e-15 109 15 15 4.67001022787386e-15 110 12 12 1.49308181637967e-15 111 12 12 1.93796087111563e-15 112 16 16 3.91233508004863e-15 113 9 9 3.69595432843291e-16 114 18 18 4.30012078984046e-15 115 8 8 2.94528783731010e-15 116 13 13 -1.88491435141932e-15 117 17 17 3.91233508004863e-15 118 9 9 -1.55539937025935e-15 119 15 15 6.57657474451254e-16 120 8 8 -1.26181817385017e-15 121 7 7 -2.52525642732676e-16 122 12 12 2.97580299032634e-15 123 14 14 1.12730330801270e-15 124 6 6 -1.04435688974773e-17 125 8 8 -1.06976158596646e-16 126 17 17 6.32100850739869e-16 127 10 10 -3.90593651259474e-16 128 11 11 2.49741581819231e-15 129 14 14 -3.90593651259474e-16 130 11 11 -5.86153175616588e-16 131 13 13 1.83726626853026e-15 132 12 12 -3.78157733029553e-17 133 11 11 -2.51020147807165e-15 134 9 9 4.67001022787386e-15 135 12 12 -9.36652126334298e-16 136 20 20 4.67001022787386e-15 137 12 12 -5.86153175616588e-16 138 13 13 -2.52525642732676e-16 139 12 12 7.69469621799674e-16 140 12 12 4.98458756252793e-16 141 9 9 6.23244782449735e-15 142 15 15 -3.15466750034976e-15 143 24 24 2.71371204892658e-15 144 7 7 -4.13344237450995e-15 145 17 17 -3.90593651259474e-16 146 11 11 1.47999320781359e-15 147 17 17 -3.90593651259474e-16 148 11 11 1.90248718879454e-15 149 12 12 1.08352229214418e-15 150 14 14 -3.78157733029553e-17 151 11 11 2.56166830799615e-15 152 16 16 -5.55789665505415e-15 153 21 21 1.08352229214418e-15 154 14 14 -2.07920588466979e-15 155 20 20 2.94528783731010e-15 156 13 13 -3.90593651259474e-16 157 11 11 1.05852629392916e-15 158 15 15 -2.63408316971069e-15 159 19 NA NA Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.000666224684031311 0.00133244936806262 0.999333775315969 10 0.0115244029645687 0.0230488059291375 0.988475597035431 11 0.00153021217789343 0.00306042435578687 0.998469787822106 12 0.00221530628902060 0.00443061257804120 0.99778469371098 13 0.0017026935850312 0.0034053871700624 0.998297306414969 14 1.33213774753360e-07 2.66427549506721e-07 0.999999866786225 15 5.69819777668368e-09 1.13963955533674e-08 0.999999994301802 16 1.07055242362315e-14 2.14110484724629e-14 0.99999999999999 17 4.54358849776291e-11 9.08717699552581e-11 0.999999999954564 18 9.4503051272602e-14 1.89006102545204e-13 0.999999999999906 19 5.59859453874227e-12 1.11971890774845e-11 0.9999999999944 20 3.04186332258892e-07 6.08372664517784e-07 0.999999695813668 21 0.535717883370869 0.928564233258262 0.464282116629131 22 1.00702468622744e-10 2.01404937245489e-10 0.999999999899298 23 3.00437210878664e-15 6.00874421757328e-15 0.999999999999997 24 6.98427516624282e-05 0.000139685503324856 0.999930157248338 25 1.70942557174713e-13 3.41885114349426e-13 0.999999999999829 26 1.41050510355805e-18 2.82101020711611e-18 1 27 3.32471193124165e-07 6.6494238624833e-07 0.999999667528807 28 1.31598892615038e-19 2.63197785230075e-19 1 29 0.99999999999911 1.77922350605650e-12 8.89611753028252e-13 30 3.20481090617697e-09 6.40962181235394e-09 0.99999999679519 31 6.218533232402e-11 1.2437066464804e-10 0.999999999937815 32 7.07673762244338e-05 0.000141534752448868 0.999929232623776 33 0.283944637722693 0.567889275445385 0.716055362277307 34 0.999999995711524 8.57695174713783e-09 4.28847587356891e-09 35 1.07380598771954e-20 2.14761197543909e-20 1 36 3.55822249519096e-33 7.11644499038191e-33 1 37 9.27584800643776e-05 0.000185516960128755 0.999907241519936 38 1.10901374120808e-23 2.21802748241615e-23 1 39 2.21349287881445e-05 4.42698575762889e-05 0.999977865071212 40 0.972188887484956 0.0556222250300887 0.0278111125150444 41 0.000735663372890554 0.00147132674578111 0.99926433662711 42 4.65656290656921e-15 9.31312581313842e-15 0.999999999999995 43 6.01121768029407e-09 1.20224353605881e-08 0.999999993988782 44 3.09014841975990e-24 6.18029683951979e-24 1 45 5.99123960212877e-12 1.19824792042575e-11 0.999999999994009 46 0.999999999999963 7.38708709982437e-14 3.69354354991219e-14 47 5.9158145171579e-14 1.18316290343158e-13 0.99999999999994 48 7.92776261543991e-09 1.58555252308798e-08 0.999999992072237 49 3.74219588174663e-18 7.48439176349327e-18 1 50 0.999998913938082 2.17212383655960e-06 1.08606191827980e-06 51 1.83766228940365e-05 3.6753245788073e-05 0.999981623377106 52 0.998254839891785 0.00349032021643016 0.00174516010821508 53 0.999993984743956 1.20305120878462e-05 6.01525604392312e-06 54 5.79283674955538e-22 1.15856734991108e-21 1 55 5.6452979269295e-06 1.1290595853859e-05 0.999994354702073 56 5.23709400560721e-10 1.04741880112144e-09 0.99999999947629 57 6.33325353062766e-09 1.26665070612553e-08 0.999999993666747 58 2.88484006987951e-30 5.76968013975903e-30 1 59 1 3.49853746504322e-20 1.74926873252161e-20 60 0.00172247365966474 0.00344494731932948 0.998277526340335 61 0.999999999999865 2.70383262038728e-13 1.35191631019364e-13 62 0.00552794804168146 0.0110558960833629 0.994472051958319 63 1.18107245907214e-15 2.36214491814428e-15 0.999999999999999 64 6.75722776764388e-47 1.35144555352878e-46 1 65 0.999501173341646 0.000997653316707268 0.000498826658353634 66 3.09952957835378e-05 6.19905915670757e-05 0.999969004704216 67 5.64992261872775e-15 1.12998452374555e-14 0.999999999999994 68 0.996681646306375 0.00663670738724962 0.00331835369362481 69 0.596824733191774 0.806350533616452 0.403175266808226 70 0.0209282134644016 0.0418564269288032 0.979071786535598 71 1.08638006564165e-31 2.17276013128331e-31 1 72 0.999965519446022 6.89611079563952e-05 3.44805539781976e-05 73 1.79490050411299e-72 3.58980100822598e-72 1 74 1.04517154407862e-12 2.09034308815725e-12 0.999999999998955 75 0.999999999999879 2.42639288073833e-13 1.21319644036916e-13 76 0.00281627168275108 0.00563254336550217 0.997183728317249 77 7.87200434166436e-39 1.57440086833287e-38 1 78 1 2.58993171204631e-51 1.29496585602315e-51 79 0.999997930842236 4.13831552758221e-06 2.06915776379110e-06 80 4.81071051417498e-43 9.62142102834997e-43 1 81 1 3.87715571283853e-33 1.93857785641927e-33 82 0.981621525339221 0.0367569493215576 0.0183784746607788 83 0.99804249677896 0.00391500644208085 0.00195750322104043 84 1 1.75823948399623e-64 8.79119741998113e-65 85 1 4.07331118603039e-43 2.03665559301519e-43 86 7.66819454319872e-19 1.53363890863974e-18 1 87 0.999999990211025 1.95779498920523e-08 9.78897494602615e-09 88 0.999768630017897 0.000462739964206426 0.000231369982103213 89 1.97300104527200e-06 3.94600209054399e-06 0.999998026998955 90 1.53169089566197e-17 3.06338179132395e-17 1 91 0.999999997168683 5.66263417594927e-09 2.83131708797464e-09 92 0.0446084870228063 0.0892169740456125 0.955391512977194 93 0.999999964194846 7.1610307346585e-08 3.58051536732925e-08 94 1 3.21518104225792e-27 1.60759052112896e-27 95 1 2.42423022762367e-35 1.21211511381184e-35 96 1 3.95650342684721e-25 1.97825171342361e-25 97 0.965858994812188 0.0682820103756231 0.0341410051878116 98 1.25050959236739e-11 2.50101918473477e-11 0.999999999987495 99 1.15746185188430e-08 2.31492370376861e-08 0.999999988425381 100 0.999999996372407 7.2551864214854e-09 3.6275932107427e-09 101 1 4.42857421297135e-22 2.21428710648567e-22 102 0.999999999967236 6.55283376743271e-11 3.27641688371636e-11 103 0.999999999999831 3.37132285092664e-13 1.68566142546332e-13 104 1 4.89436055401629e-30 2.44718027700814e-30 105 3.61677298513517e-08 7.23354597027034e-08 0.99999996383227 106 0.99993608589299 0.000127828214020494 6.3914107010247e-05 107 0.000124202445695585 0.000248404891391170 0.999875797554304 108 4.01330776508591e-33 8.02661553017182e-33 1 109 1 4.67941946814384e-18 2.33970973407192e-18 110 1 3.50320966198872e-16 1.75160483099436e-16 111 0.999999990320773 1.93584540327106e-08 9.6792270163553e-09 112 0.99999975391838 4.9216323981864e-07 2.4608161990932e-07 113 0.999999999999994 1.18913102476947e-14 5.94565512384737e-15 114 0.946007365898016 0.107985268203968 0.0539926341019838 115 1 4.4408115856297e-26 2.22040579281485e-26 116 0.999999999999824 3.52326296740756e-13 1.76163148370378e-13 117 0.999942510809054 0.000114978381891319 5.74891909456597e-05 118 0.0164558068785331 0.0329116137570662 0.983544193121467 119 1 1.97622225235386e-36 9.88111126176928e-37 120 0.919009232303574 0.161981535392851 0.0809907676964256 121 1 6.96865285271432e-23 3.48432642635716e-23 122 1 5.76350193630122e-16 2.88175096815061e-16 123 0.999999999999313 1.37343076211827e-12 6.86715381059137e-13 124 0.999998314897548 3.3702049050245e-06 1.68510245251225e-06 125 0.99999999659679 6.80641867444525e-09 3.40320933722262e-09 126 0.143406150206575 0.286812300413150 0.856593849793425 127 0.00274053628443465 0.00548107256886930 0.997259463715565 128 0.999990462492026 1.90750159482805e-05 9.53750797414027e-06 129 4.31371288288625e-30 8.62742576577249e-30 1 130 1 5.83199629911265e-20 2.91599814955632e-20 131 0.346470404213288 0.692940808426575 0.653529595786712 132 1 2.19443606097777e-18 1.09721803048889e-18 133 0.999999999957276 8.544755065743e-11 4.2723775328715e-11 134 0.999999999998103 3.79389036876307e-12 1.89694518438154e-12 135 0.999997252583497 5.49483300560415e-06 2.74741650280208e-06 136 0.999999999999991 1.70672325510816e-14 8.5336162755408e-15 137 0.253670928045803 0.507341856091606 0.746329071954197 138 0.999999924556037 1.50887925836799e-07 7.54439629183993e-08 139 0.999988227005767 2.35459884657689e-05 1.17729942328844e-05 140 0.999999999476728 1.04654471689541e-09 5.23272358447707e-10 141 0.99993561399821 0.000128772003581256 6.43860017906282e-05 142 0.999999999999877 2.46565586437393e-13 1.23282793218696e-13 143 0.999999924204296 1.51591407448704e-07 7.5795703724352e-08 144 0.99999873206182 2.53587635859775e-06 1.26793817929887e-06 145 0.99999725032264 5.49935471965006e-06 2.74967735982503e-06 146 0.889991847315873 0.220016305368253 0.110008152684127 147 0.999999777091868 4.45816262870783e-07 2.22908131435392e-07 148 0.997031001478745 0.00593799704251037 0.00296899852125518 149 0.999344702060008 0.00131059587998402 0.000655297939992008 150 0.765442377698045 0.46911524460391 0.234557622301955 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 124 0.873239436619718 NOK 5% type I error level 129 0.908450704225352 NOK 10% type I error level 132 0.929577464788732 NOK

Charts produced by software:

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Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 6 ; 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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Software written by Ed van Stee & Patrick Wessa

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