Paper

*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: Sun, 12 Dec 2010 11:09:09 +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/12/t12921529213uu1rmmh782mwtw.htm/, Retrieved Sun, 12 Dec 2010 12:22:04 +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/12/t12921529213uu1rmmh782mwtw.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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14,2754 0 12,5621 13,3181 16,8622 25,2609 12,2961 0 14,2754 12,5621 13,3181 16,8622 10,0871 0 12,2961 14,2754 12,5621 13,3181 13,5117 0 10,0871 12,2961 14,2754 12,5621 13,9921 0 13,5117 10,0871 12,2961 14,2754 13,6932 0 13,9921 13,5117 10,0871 12,2961 14,4211 0 13,6932 13,9921 13,5117 10,0871 15,3397 0 14,4211 13,6932 13,9921 13,5117 16,5182 0 15,3397 14,4211 13,6932 13,9921 15,2809 0 16,5182 15,3397 14,4211 13,6932 15,6204 0 15,2809 16,5182 15,3397 14,4211 15,5698 0 15,6204 15,2809 16,5182 15,3397 15,9458 0 15,5698 15,6204 15,2809 16,5182 16,4063 0 15,9458 15,5698 15,6204 15,2809 17,55 0 16,4063 15,9458 15,5698 15,6204 17,0353 0 17,55 16,4063 15,9458 15,5698 16,0591 0 17,0353 17,55 16,4063 15,9458 16,3643 0 16,0591 17,0353 17,55 16,4063 14,6527 0 16,3643 16,0591 17,0353 17,55 13,4664 0 14,6527 16,3643 16,0591 17,0353 13,3266 0 13,4664 14,6527 16,3643 16,0591 13,1823 0 13,3266 13,4664 14,6527 16,3643 12,113 0 13,1823 13,3266 13,4664 14,6527 13,354 0 12,113 13,1823 13,3266 13,4664 13,45 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 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Prijs[t] = + 0.661625634076359 + 0.0186165752279153Crisis[t] + 1.27491177408209`1`[t] -0.241331945276682`2`[t] -0.0900126281803489`3`[t] + 0.00689405840870922`4`[t] -0.111842600882872M1[t] -0.301474301122538M2[t] -0.680435234824421M3[t] + 0.00209725839635172M4[t] -0.888811409648947M5[t] -1.10179193392374M6[t] -1.32154900924288M7[t] -1.45903436067523M8[t] + 0.097912846691725M9[t] -0.477649825427485M10[t] + 0.203399810894763M11[t] + 0.00850067172102355t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 0.661625634076359 0.557429 1.1869 0.236286 0.118143 Crisis 0.0186165752279153 0.737815 0.0252 0.979888 0.489944 `1` 1.27491177408209 0.060492 21.0757 0 0 `2` -0.241331945276682 0.098076 -2.4607 0.014486 0.007243 `3` -0.0900126281803489 0.097819 -0.9202 0.358282 0.179141 `4` 0.00689405840870922 0.060472 0.114 0.909319 0.454659 M1 -0.111842600882872 0.689448 -0.1622 0.871252 0.435626 M2 -0.301474301122538 0.689053 -0.4375 0.662079 0.33104 M3 -0.680435234824421 0.690774 -0.985 0.325477 0.162738 M4 0.00209725839635172 0.692586 0.003 0.997586 0.498793 M5 -0.888811409648947 0.696948 -1.2753 0.203287 0.101643 M6 -1.10179193392374 0.701067 -1.5716 0.117199 0.058599 M7 -1.32154900924288 0.702553 -1.8811 0.061023 0.030512 M8 -1.45903436067523 0.705661 -2.0676 0.039615 0.019808 M9 0.097912846691725 0.708556 0.1382 0.890195 0.445097 M10 -0.477649825427485 0.700792 -0.6816 0.496077 0.248038 M11 0.203399810894763 0.701598 0.2899 0.772105 0.386052 t 0.00850067172102355 0.002918 2.9137 0.003867 0.001933 Multiple Linear Regression - Regression Statistics Multiple R 0.990086226149054 R-squared 0.980270735210076 Adjusted R-squared 0.979046656737709 F-TEST (value) 800.823441747244 F-TEST (DF numerator) 17 F-TEST (DF denominator) 274 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.40437877940115 Sum Squared Residuals 1584.00422426467 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14.2754 12.0161091028756 2.25929089712439 2 12.2961 14.4628439946977 -2.16674399469775 3 10.0871 11.1990931509317 -1.11199315093172 4 13.5117 9.39208398219395 4.11961601780605 5 13.9921 13.5988146997364 0.393285300263597 6 13.6932 13.3655295694992 0.327670430500822 7 14.4211 12.3337799486257 2.08732005137425 8 15.3397 13.1853049935606 2.15439500643941 9 16.5182 15.7764379855761 0.74176201442386 10 15.2809 16.4225911598917 -1.1416911598917 11 15.6204 15.1726160172239 0.447783982776142 12 15.5698 15.6094024409855 -0.0396024409855272 13 15.9458 15.4791150533159 0.466684946684097 14 16.4063 15.7504729425468 0.655827057453202 15 17.55 15.8832639129224 1.66673608707761 16 17.0353 17.8870867255307 -0.851786725530675 17 16.0591 16.033611643958 0.0254883560419734 18 16.3643 14.6090037408266 1.75529625917342 19 14.6527 15.0766528899839 -0.423952889983881 20 13.4664 12.7761966638219 0.690203336178111 21 13.3266 13.2080786289126 0.118521371087368 22 13.1823 12.9052457301993 0.277054269800679 23 12.113 13.5395465856302 -1.42654658563023 24 13.354 12.0206138300633 1.33338616993671 25 13.4537 13.7695186945026 -0.315818694502564 26 13.2715 13.5112591164564 -0.239759116456415 27 13.1959 12.7653716460655 0.430528353934532 28 13.5542 13.4035734287717 0.150626571228304 29 12.124 13.0132986546418 -0.889298654641758 30 10.967 10.9045196040515 0.0624803959484841 31 10.9201 9.53057051048242 1.38952948951758 32 12.5971 9.75221973120313 2.84488026879687 33 14.3177 13.5612978521288 0.756402147871219 34 14.2471 14.77938054467 -0.53228054467003 35 16.0926 14.8124118276222 1.28018817237777 36 17.1334 16.8440860107578 0.28931398924218 37 16.5866 17.6405109595001 -1.05391095950006 38 16.361 16.3444748584389 0.0165251415611361 39 15.8494 15.7373926492855 0.112007350714458 40 15.5932 15.8870196785422 -0.293819678542157 41 16.6387 14.8179818866812 1.82071811331879 42 16.8312 16.0527466993102 0.778453300689787 43 16.5044 15.854132498494 0.650267501505962 44 16.5556 15.1661757910201 1.38942420897995 45 16.7469 16.865646739799 -0.118746739799041 46 15.9543 16.5608623993176 -0.60656239931761 47 15.5888 16.1868892092412 -0.598089209241184 48 14.3945 15.7004230764864 -1.30592307648637 49 13.8889 14.2353236840062 -0.346423684006235 50 12.9999 13.7252553896608 -0.725355389660801 51 14.1022 12.4483982955403 1.65380170445974 52 19.6245 14.7965876192542 4.82791238074582 53 24.7658 20.7651403001858 4.00065969981416 54 25.9843 25.6773072123504 0.306992787649639 55 22.9635 25.2892934592039 -2.32579345920385 56 19.6288 20.5902814505125 -0.961481450512484 57 17.3363 18.5590606119197 -1.22276061191966 58 13.311 16.1543435647306 -2.84334356473064 59 14.6359 12.54458453266 2.09131546733995 60 15.834 15.1936138158178 0.640386184182174 61 16.2415 16.644526192199 -0.403026192199047 62 15.9808 16.5467735235941 -0.56597352359414 63 16.9726 15.6468908025727 1.32570919742734 64 16.8708 17.6368763285787 -0.766076328578684 65 16.923 16.4116049112956 0.511395088704394 66 18.1138 16.2071712397217 1.90662876027834 67 16.7716 17.5174830618356 -0.745883061835586 68 14.0299 15.3845332441788 -1.35463324417877 69 13.822 13.671644081428 0.150355918571978 70 14.2537 13.63021211186 0.623487888139996 71 14.3985 15.1578491616834 -0.75934916168343 72 15.2454 15.0431864320804 0.202213567919631 73 15.6683 15.944330692384 -0.276030692383954 74 16.1721 16.0879181651243 0.0841818348756693 75 14.8679 16.1824657401202 -1.31456574012016 76 14.1948 15.0569481728826 -0.862148172882569 77 14.7056 13.5887093196773 1.11689068032273 78 15.3819 14.3187626299895 1.06313737001051 79 15.5001 14.8980529706073 0.60204702939268 80 14.7886 14.7059312268124 0.082668773187557 81 14.563 15.2783998873061 -0.715399887306113 82 15.5528 14.5894484287903 0.96335157120974 83 15.9781 16.6602097603286 -0.682109760328631 84 15.5139 16.7840619655968 -1.27016196559683 85 15.3603 15.89561771563 -0.535317715629993 86 15.0512 15.5992278958576 -0.548027895857615 87 14.7874 14.916476896345 -0.129076896345021 88 14.9624 15.3564097573442 -0.394009757344163 89 13.9188 14.7875386646472 -0.868738664647212 90 14.5146 13.2319421720978 1.28265782790221 91 13.7115 14.0145613590488 -0.303061359048762 92 12.0738 12.8130530995668 -0.739253099566786 93 12.5688 12.4235674882671 0.145232511732949 94 12.2547 12.9592127645107 -0.704512764510669 95 11.8741 13.2707310342657 -1.39663103426572 96 13.0261 12.6105561874825 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-1.54908232688061 118 13.362 14.1091403758184 -0.74714037581842 119 14.5735 14.5033673067168 0.0701326932831996 120 15.8357 15.9119952733264 -0.0762952733264367 121 14.9927 17.141045567816 -2.14834556781598 122 14.5078 15.4702621240522 -0.962462124052167 123 15.2648 14.5797781851601 0.685021814839939 124 15.7163 16.4375237494262 -0.721223749426169 125 17.7969 15.9858855686916 1.81101443130838 126 19.0408 18.2535432915457 0.78725670845428 127 17.8571 19.0906124989776 -1.23351249897762 128 18.815 16.9681543387351 1.84684566126486 129 19.0961 19.942881899572 -0.846781899572 130 17.6215 19.6181491957194 -1.99664919571942 131 17.0163 18.2654925984116 -1.24919259841162 132 15.8286 17.6361862088366 -1.80758620883661 133 16.7818 16.2993562002123 0.482443799787665 134 15.8726 17.6644106901991 -1.79181069019912 135 16.6621 16.0074987473259 0.654601252674056 136 17.5709 17.8305056521976 -0.259605652197574 137 16.9914 18.0046168033799 -1.01321680337993 138 18.0412 16.7646700580245 1.27652994197545 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27.1826 31.4943742016725 -4.3117742016725 204 22.8764 27.4986667862896 -4.62226678628963 205 21.938 22.4097090153794 -0.471709015379405 206 23.3076 22.3182161630184 0.989383836981614 207 24.9572 24.2898564404154 0.667343559584643 208 26.4694 26.8082364915969 -0.338836491596883 209 23.9297 27.3258982231446 -3.39619822314459 210 24.7033 23.3795400412574 1.3237599587426 211 24.646 24.6427214699251 0.00327853007493407 212 24.0496 24.4930202196081 -0.443420219608069 213 24.2096 25.2247964277969 -1.01519642779693 214 24.0717 25.0161416505946 -0.944441650594601 215 26.6673 25.5445570156476 1.12274298435238 216 27.6457 28.6735849155912 -1.02788491559121 217 30.8791 29.2047312598026 1.67436874019741 218 29.3278 32.6751933179828 -3.3473933179828 219 30.7268 29.4764655716048 1.25033442839525 220 34.1204 32.0411768699839 2.07922313001614 221 35.0205 35.3096139172974 -0.289113917297383 222 39.3565 35.2970756434702 4.05942435652978 223 34.4724 40.1007917410695 -5.62839174106946 224 29.9762 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-6.47160672549526 246 47.6976 46.9025868570941 0.795013142905878 247 46.7381 45.3181527755978 1.41994722440217 248 47.4282 45.2591774969207 2.16902250307927 249 42.2269 48.1168404622988 -5.8899404622988 250 44.9066 40.8205867881196 4.08601321188043 251 47.2648 46.1130254603878 1.15177453961219 252 50.2325 48.7508663257588 1.48163367424116 253 50.2504 51.5849061694528 -1.33450616945284 254 52.5685 50.5166014762356 2.05189852376443 255 55.2325 52.8463214478226 2.38617855217744 256 52.3674 56.3931362676683 -4.02573626766827 257 55.1692 51.006535375465 4.16266462453503 258 57.7252 54.8417309632714 2.88346903672862 259 62.8232 57.4892461625512 5.33395383744879 260 62.7599 62.9709677066007 -0.211067706600685 261 62.4387 63.0146469085893 -0.575946908589304 262 64.0862 61.6307129685491 2.45548703145089 263 66.1209 64.539039954347 1.58186004565307 264 69.8474 66.569085084329 3.27831491567105 265 80.1039 70.5751535957415 9.52874640425847 266 85.9319 82.3990409506921 3.5328590493079 267 85.2843 86.6621406930615 -1.37784069306151 268 77.0383 84.2235346037636 -7.18523460376354 269 69.9981 72.5306059991534 -2.53250599915339 270 55.2039 65.438986245874 -10.2350862458739 271 43.1188 48.8032347750371 -5.68443477503712 272 32.077 37.4139853784557 -5.33698537845567 273 34.2974 29.101762396164 5.19563760383603 274 34.5613 35.016073106206 -0.454773106205948 275 36.5235 36.4168052327038 0.106694767296177 276 39.0474 38.3838636225265 0.663536377473495 277 42.8033 41.0162832116625 1.78701678833754 278 49.5164 44.8396921817335 4.6767078182665 279 46.459 51.8891515709957 -5.4301515709957 280 51.1313 46.7415054798572 4.38979452014281 281 46.9331 51.9753456748054 -5.04224567480537 282 49.7654 45.612441077286 4.15295892271397 283 52.0729 49.5836331672553 2.48926683274465 284 51.6425 52.123085062361 -0.480585062361049 285 53.9784 52.2990520473515 1.67934795264849 286 54.4891 54.6257476313836 -0.1366476313836 287 59.0665 55.4573175664257 3.60918243357429 288 63.9929 60.7617236565769 3.23117634342306 289 61.6167 65.8045686267688 -4.18786862676882 290 62.1816 60.9965915368619 1.18500846313814 291 58.9178 61.5079005559188 -2.5901005559188 292 59.9151 58.1493991531515 1.76570084684853 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.441984457106752 0.883968914213504 0.558015542893248 22 0.32496436415149 0.649928728302981 0.67503563584851 23 0.211569306027234 0.423138612054467 0.788430693972766 24 0.17065073044106 0.341301460882121 0.82934926955894 25 0.125998706785029 0.251997413570057 0.874001293214971 26 0.0878905118613512 0.175781023722702 0.912109488138649 27 0.0500760242558651 0.10015204851173 0.949923975744135 28 0.027373868843222 0.0547477376864439 0.972626131156778 29 0.0156397542820077 0.0312795085640154 0.984360245717992 30 0.00981807368919141 0.0196361473783828 0.990181926310809 31 0.00520225428655282 0.0104045085731056 0.994797745713447 32 0.00424806773948254 0.00849613547896508 0.995751932260518 33 0.00294500523587494 0.00589001047174988 0.997054994764125 34 0.00170141706957953 0.00340283413915906 0.99829858293042 35 0.00183042065620253 0.00366084131240506 0.998169579343797 36 0.000959663811941066 0.00191932762388213 0.99904033618806 37 0.000484680034262357 0.000969360068524713 0.999515319965738 38 0.000263025229734213 0.000526050459468425 0.999736974770266 39 0.000123296943634685 0.00024659388726937 0.999876703056365 40 5.68144626080608e-05 0.000113628925216122 0.999943185537392 41 6.84889710057791e-05 0.000136977942011558 0.999931511028994 42 3.42398203712728e-05 6.84796407425455e-05 0.999965760179629 43 2.01393133099754e-05 4.02786266199507e-05 0.99997986068669 44 9.35866583232377e-06 1.87173316646475e-05 0.999990641334168 45 4.24019789363078e-06 8.48039578726156e-06 0.999995759802106 46 1.83645228430888e-06 3.67290456861776e-06 0.999998163547716 47 8.2831559657551e-07 1.65663119315102e-06 0.999999171684403 48 6.263719370493e-07 1.2527438740986e-06 0.999999373628063 49 3.16219577837365e-07 6.3243915567473e-07 0.999999683780422 50 1.45818424215487e-07 2.91636848430973e-07 0.999999854181576 51 1.18488275968318e-07 2.36976551936635e-07 0.999999881511724 52 4.06102281101579e-06 8.12204562203157e-06 0.99999593897719 53 3.56217675852157e-05 7.12435351704315e-05 0.999964378232415 54 1.947564298864e-05 3.895128597728e-05 0.999980524357011 55 1.3013899600472e-05 2.60277992009439e-05 0.9999869861004 56 7.15610825826488e-06 1.43122165165298e-05 0.999992843891742 57 3.74576479757412e-06 7.49152959514824e-06 0.999996254235202 58 2.90813245833798e-06 5.81626491667596e-06 0.999997091867542 59 4.18877468037541e-06 8.37754936075082e-06 0.99999581122532 60 2.32283329716138e-06 4.64566659432275e-06 0.999997677166703 61 1.25186571631027e-06 2.50373143262053e-06 0.999998748134284 62 6.3252323578707e-07 1.26504647157414e-06 0.999999367476764 63 3.60925655191494e-07 7.21851310382989e-07 0.999999639074345 64 4.41180772890756e-07 8.82361545781511e-07 0.999999558819227 65 2.27469155525075e-07 4.5493831105015e-07 0.999999772530844 66 1.41326581990587e-07 2.82653163981174e-07 0.999999858673418 67 9.22609529080083e-08 1.84521905816017e-07 0.999999907739047 68 9.82159562395928e-08 1.96431912479186e-07 0.999999901784044 69 4.9150752886882e-08 9.8301505773764e-08 0.999999950849247 70 2.65186381796402e-08 5.30372763592805e-08 0.999999973481362 71 1.9313963888313e-08 3.86279277766261e-08 0.999999980686036 72 9.71490763694468e-09 1.94298152738894e-08 0.999999990285092 73 5.3153381627554e-09 1.06306763255108e-08 0.999999994684662 74 2.78789443770011e-09 5.57578887540022e-09 0.999999997212106 75 2.82310538735412e-09 5.64621077470824e-09 0.999999997176895 76 1.97197850849061e-09 3.94395701698122e-09 0.999999998028022 77 1.01261482656667e-09 2.02522965313334e-09 0.999999998987385 78 5.33550143505433e-10 1.06710028701087e-09 0.99999999946645 79 2.64482447559537e-10 5.28964895119073e-10 0.999999999735518 80 1.46445100594709e-10 2.92890201189418e-10 0.999999999853555 81 7.18934154729491e-11 1.43786830945898e-10 0.999999999928107 82 5.72108112686186e-11 1.14421622537237e-10 0.99999999994279 83 3.32643631819141e-11 6.65287263638282e-11 0.999999999966736 84 1.62517303488265e-11 3.2503460697653e-11 0.999999999983748 85 7.51005446817597e-12 1.50201089363519e-11 0.99999999999249 86 3.35227488088555e-12 6.7045497617711e-12 0.999999999996648 87 1.53800178534172e-12 3.07600357068345e-12 0.999999999998462 88 8.45606112946412e-13 1.69121222589282e-12 0.999999999999154 89 6.55815184886626e-13 1.31163036977325e-12 0.999999999999344 90 3.36668394649785e-13 6.7333678929957e-13 0.999999999999663 91 1.85980518524856e-13 3.71961037049713e-13 0.999999999999814 92 1.13463085941468e-13 2.26926171882936e-13 0.999999999999887 93 4.98717083440266e-14 9.97434166880533e-14 0.99999999999995 94 2.37871827723624e-14 4.75743655447247e-14 0.999999999999976 95 1.51374378917373e-14 3.02748757834745e-14 0.999999999999985 96 7.07081023003154e-15 1.41416204600631e-14 0.999999999999993 97 3.21740594666885e-15 6.4348118933377e-15 0.999999999999997 98 1.36251120612822e-15 2.72502241225644e-15 0.999999999999999 99 5.75107896443818e-16 1.15021579288764e-15 1 100 4.81632735850257e-16 9.63265471700515e-16 1 101 2.32263916542185e-16 4.6452783308437e-16 1 102 1.10133440585682e-16 2.20266881171365e-16 1 103 6.563563096533e-17 1.3127126193066e-16 1 104 3.11093534439583e-17 6.22187068879166e-17 1 105 1.24894757860082e-17 2.49789515720163e-17 1 106 5.24231203191492e-18 1.04846240638298e-17 1 107 3.87217660120621e-18 7.74435320241242e-18 1 108 1.83343769473551e-18 3.66687538947102e-18 1 109 8.29592217588289e-19 1.65918443517658e-18 1 110 3.70016234471112e-19 7.40032468942224e-19 1 111 1.76052247367953e-19 3.52104494735907e-19 1 112 7.14641596229363e-20 1.42928319245873e-19 1 113 2.94735571983167e-20 5.89471143966333e-20 1 114 1.95429343187327e-20 3.90858686374654e-20 1 115 1.15680515124678e-20 2.31361030249356e-20 1 116 5.98259397256529e-21 1.19651879451306e-20 1 117 2.8226237080463e-21 5.6452474160926e-21 1 118 1.18027260397414e-21 2.36054520794828e-21 1 119 4.93801531629108e-22 9.87603063258216e-22 1 120 2.02910331669608e-22 4.05820663339215e-22 1 121 1.08601589525981e-22 2.17203179051961e-22 1 122 4.58045443754556e-23 9.16090887509112e-23 1 123 2.28705479982762e-23 4.57410959965525e-23 1 124 8.64471335779579e-24 1.72894267155916e-23 1 125 2.33676100543505e-23 4.67352201087011e-23 1 126 1.1199937296683e-23 2.23998745933661e-23 1 127 4.06854467277726e-24 8.13708934555452e-24 1 128 1.32703581764546e-23 2.65407163529092e-23 1 129 4.86684757969807e-24 9.73369515939615e-24 1 130 1.90359821015004e-24 3.80719642030008e-24 1 131 6.98972974027952e-25 1.3979459480559e-24 1 132 3.36056325557561e-25 6.72112651115121e-25 1 133 3.2857016569053e-25 6.5714033138106e-25 1 134 1.4564062256099e-25 2.91281245121979e-25 1 135 1.36247443656436e-25 2.72494887312872e-25 1 136 5.01235178764589e-26 1.00247035752918e-25 1 137 1.9384506374411e-26 3.87690127488221e-26 1 138 1.63353922461197e-26 3.26707844922394e-26 1 139 6.45623652291113e-27 1.29124730458223e-26 1 140 2.32261270023293e-27 4.64522540046586e-27 1 141 1.29595025162829e-27 2.59190050325657e-27 1 142 4.6958959129343e-28 9.3917918258686e-28 1 143 2.54216235914236e-28 5.08432471828471e-28 1 144 8.71965606387456e-29 1.74393121277491e-28 1 145 3.4514751706049e-29 6.9029503412098e-29 1 146 1.48876698916517e-29 2.97753397833033e-29 1 147 5.55478566294184e-30 1.11095713258837e-29 1 148 4.93883025019184e-30 9.87766050038368e-30 1 149 1.76590495671335e-30 3.5318099134267e-30 1 150 1.80965092559433e-30 3.61930185118865e-30 1 151 6.40229078146793e-31 1.28045815629359e-30 1 152 4.67169006401349e-31 9.34338012802698e-31 1 153 1.65901564141412e-31 3.31803128282825e-31 1 154 7.04850808952563e-32 1.40970161790513e-31 1 155 5.46647545837656e-32 1.09329509167531e-31 1 156 2.20049864355548e-32 4.40099728711095e-32 1 157 9.01477362745882e-33 1.80295472549176e-32 1 158 5.22394637438534e-33 1.04478927487707e-32 1 159 8.23614787968446e-33 1.64722957593689e-32 1 160 2.70323367935875e-33 5.4064673587175e-33 1 161 9.13979705463894e-33 1.82795941092779e-32 1 162 4.58321476495492e-33 9.16642952990984e-33 1 163 1.02154161070719e-30 2.04308322141439e-30 1 164 8.97628283268059e-31 1.79525656653612e-30 1 165 3.73199502380142e-31 7.46399004760283e-31 1 166 7.2130278001918e-30 1.44260556003836e-29 1 167 2.57781825513688e-30 5.15563651027375e-30 1 168 1.69507602986949e-29 3.39015205973899e-29 1 169 1.5764012680633e-24 3.1528025361266e-24 1 170 6.3888095941148e-25 1.27776191882296e-24 1 171 2.6342533314448e-25 5.2685066628896e-25 1 172 4.4924699012122e-25 8.9849398024244e-25 1 173 3.20587673388667e-24 6.41175346777335e-24 1 174 1.46189990096795e-24 2.9237998019359e-24 1 175 1.72955987799429e-24 3.45911975598857e-24 1 176 2.34126185598544e-19 4.68252371197088e-19 1 177 1.25121859794183e-19 2.50243719588365e-19 1 178 3.01315920355484e-19 6.02631840710968e-19 1 179 2.41773087606649e-19 4.83546175213297e-19 1 180 2.80501162795987e-19 5.61002325591975e-19 1 181 2.99668358899583e-19 5.99336717799167e-19 1 182 1.59848739063012e-19 3.19697478126024e-19 1 183 2.17778766811536e-19 4.35557533623073e-19 1 184 1.08933699694702e-19 2.17867399389405e-19 1 185 7.42421390765344e-20 1.48484278153069e-19 1 186 5.43357868173468e-19 1.08671573634694e-18 1 187 2.51549696081426e-19 5.03099392162852e-19 1 188 1.44978631161833e-19 2.89957262323666e-19 1 189 8.82971331452787e-20 1.76594266290557e-19 1 190 4.61793351097899e-20 9.23586702195797e-20 1 191 1.87693946366727e-19 3.75387892733453e-19 1 192 8.79426622510885e-20 1.75885324502177e-19 1 193 6.57285053318425e-20 1.31457010663685e-19 1 194 8.6984908894843e-20 1.73969817789686e-19 1 195 4.12120357267784e-20 8.24240714535569e-20 1 196 1.94201109128922e-20 3.88402218257843e-20 1 197 2.09556549845545e-20 4.19113099691091e-20 1 198 1.06052386111325e-20 2.1210477222265e-20 1 199 1.52610884837591e-20 3.05221769675182e-20 1 200 2.10148274739357e-19 4.20296549478714e-19 1 201 9.57366854379656e-20 1.91473370875931e-19 1 202 7.84932027484652e-20 1.5698640549693e-19 1 203 4.14883385682176e-19 8.29766771364352e-19 1 204 4.52272337162255e-18 9.0454467432451e-18 1 205 2.24976624413716e-18 4.49953248827431e-18 1 206 1.37875604775112e-18 2.75751209550224e-18 1 207 7.58222779837163e-19 1.51644555967433e-18 1 208 3.46705043526281e-19 6.93410087052563e-19 1 209 5.48131390647802e-19 1.0962627812956e-18 1 210 3.13798994130577e-19 6.27597988261154e-19 1 211 1.34895166506304e-19 2.69790333012608e-19 1 212 5.83909437466646e-20 1.16781887493329e-19 1 213 3.80483022694635e-20 7.6096604538927e-20 1 214 2.21548795588016e-20 4.43097591176032e-20 1 215 1.69121668349302e-20 3.38243336698603e-20 1 216 1.49699983016354e-20 2.99399966032708e-20 1 217 1.4153415931395e-20 2.830683186279e-20 1 218 1.37599624143006e-19 2.75199248286012e-19 1 219 8.76055922803037e-20 1.75211184560607e-19 1 220 6.78624129795191e-20 1.35724825959038e-19 1 221 2.85699947450754e-20 5.71399894901507e-20 1 222 2.18555817455634e-19 4.37111634911267e-19 1 223 1.31374777440662e-17 2.62749554881323e-17 1 224 2.57664081316578e-17 5.15328162633157e-17 1 225 4.15676867164098e-17 8.31353734328196e-17 1 226 2.15997310852666e-17 4.31994621705332e-17 1 227 8.0088132190147e-17 1.60176264380294e-16 1 228 1.76280164467595e-16 3.5256032893519e-16 1 229 6.01824144962783e-16 1.20364828992557e-15 1 230 1.08211022155611e-14 2.16422044311222e-14 0.99999999999999 231 5.57420969309252e-15 1.1148419386185e-14 0.999999999999994 232 6.53513142433404e-15 1.30702628486681e-14 0.999999999999993 233 3.06488784906519e-15 6.12977569813038e-15 0.999999999999997 234 3.13663562746179e-15 6.27327125492358e-15 0.999999999999997 235 1.72624751003129e-15 3.45249502006259e-15 0.999999999999998 236 1.27809464705435e-15 2.55618929410871e-15 0.999999999999999 237 2.07226916651286e-15 4.14453833302573e-15 0.999999999999998 238 1.78599714713447e-15 3.57199429426893e-15 0.999999999999998 239 1.05074761828323e-15 2.10149523656646e-15 1 240 2.03357848885156e-15 4.06715697770312e-15 0.999999999999998 241 4.08059185073576e-15 8.16118370147151e-15 0.999999999999996 242 3.71745035099927e-15 7.43490070199854e-15 0.999999999999996 243 2.01721396212135e-14 4.03442792424269e-14 0.99999999999998 244 1.14610154363694e-14 2.29220308727388e-14 0.999999999999989 245 8.80224635597465e-13 1.76044927119493e-12 0.99999999999912 246 4.32550359965161e-13 8.65100719930321e-13 0.999999999999567 247 2.0102368954104e-13 4.0204737908208e-13 0.999999999999799 248 1.54918916550948e-13 3.09837833101896e-13 0.999999999999845 249 2.13400086449224e-11 4.26800172898448e-11 0.99999999997866 250 1.82759728902284e-11 3.65519457804568e-11 0.999999999981724 251 7.898551360062e-12 1.5797102720124e-11 0.999999999992101 252 9.9132213309722e-12 1.98264426619444e-11 0.999999999990087 253 2.84685729815182e-11 5.69371459630363e-11 0.999999999971531 254 6.61949092194962e-11 1.32389818438992e-10 0.999999999933805 255 4.39514907704175e-11 8.79029815408349e-11 0.999999999956048 256 1.65439515131452e-09 3.30879030262903e-09 0.999999998345605 257 1.06426556614982e-09 2.12853113229964e-09 0.999999998935734 258 6.92470656863751e-10 1.3849413137275e-09 0.99999999930753 259 1.04830313728865e-09 2.09660627457729e-09 0.999999998951697 260 4.17250815906727e-10 8.34501631813454e-10 0.99999999958275 261 9.97951004766283e-09 1.99590200953257e-08 0.99999999002049 262 4.78889990295073e-09 9.57779980590147e-09 0.9999999952111 263 1.81739078083518e-09 3.63478156167036e-09 0.99999999818261 264 7.10277923716223e-10 1.42055584743245e-09 0.999999999289722 265 5.1364836516066e-06 1.02729673032132e-05 0.999994863516348 266 1.62030365953473e-05 3.24060731906946e-05 0.999983796963405 267 0.000286904724446622 0.000573809448893244 0.999713095275553 268 0.000336533274078928 0.000673066548157856 0.999663466725921 269 0.110677729485441 0.221355458970882 0.889322270514559 270 0.0971420133233432 0.194284026646686 0.902857986676657 271 0.206420122400535 0.412840244801069 0.793579877599465 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 237 0.944223107569721 NOK 5% type I error level 240 0.95617529880478 NOK 10% type I error level 241 0.9601593625498 NOK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

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

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

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

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