Workshop 7, tutorial Multiple Regression

*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: Mon, 22 Nov 2010 21:19:35 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v.htm/, Retrieved Mon, 22 Nov 2010 22:19:55 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v.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 «

5,6 5,5 6 12 4,4 3,5 4 11 2,4 8,5 4 14 4,8 5 4 12 3,2 6 4,5 21 4 6 3,5 12 4 5,5 2 22 4,4 5,5 5,5 11 6,4 6 3,5 10 4,4 6,5 3,5 13 5,2 7 6 10 4,8 8 5 8 3,2 5,5 5 15 4,8 5 4 14 4,4 5,5 4 10 1,6 7,5 2 14 3,6 4,5 4,5 14 3,2 5,5 4 11 3,2 8,5 3,5 10 5,6 8,5 5,5 13 6 5,5 4,5 7 6,4 9 5,5 14 3,6 7 6,5 12 5,6 5 4 14 4,4 5,5 4 11 3,2 7,5 4,5 9 3,6 7,5 3 11 3,6 6,5 4,5 15 3,6 8 4,5 14 3,6 6,5 3 13 4 4,5 3 9 6,4 9 8 15 4,4 9 2,5 10 3,2 6 3,5 11 3,6 8,5 4,5 13 6,4 4,5 3 8 4,4 4,5 3 20 6,4 6 2,5 12 4,8 9 6 10 4,8 6 3,5 10 5,6 9 5 9 3,6 7 4,5 14 4 7,5 4 8 3,6 8 2,5 14 4 5 4 11 4,8 5,5 4 13 5,6 7 5 9 5,6 4,5 3 11 4 6 4 15 5,6 8,5 3,5 11 6,4 2,5 2 10 3,6 6 4 14 4 6 4 18 2,4 3 2 14 3,2 12 10 11 5,2 6 4 12 4 6 4 13 3,2 7 3 9 2,8 3,5 2 10 6 6,5 4 15 3,6 6 4,5 20 4 6,5 3 12 4,8 7 3,5 12 5,2 4 4,5 14 4 5,5 2,5 13 4,4 4,5 2,5 11 3,2 5,5 4 17 3,6 6,5 4 12 5,2 5 3 13 4,4 5,5 4 14 3,2 6 3,5 13 3,6 4,5 3,5 15 3,6 7,5 4,5 13 6 9 5,5 10 3,6 7,5 3 11 4 6 4 19 5,6 6,5 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Depression[t] = + 14.2746162191590 -0.199901806823605Doubts[t] -0.054501555912315Expect[t] -0.038947120698009Criticism[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) 14.2746162191590 1.365305 10.4553 0 0 Doubts -0.199901806823605 0.228178 -0.8761 0.382343 0.191172 Expect -0.054501555912315 0.182095 -0.2993 0.76511 0.382555 Criticism -0.038947120698009 0.23449 -0.1661 0.8683 0.43415 Multiple Linear Regression - Regression Statistics Multiple R 0.0855457044326433 R-squared 0.00731806754687717 Adjusted R-squared -0.0118951311457638 F-TEST (value) 0.380887517167045 F-TEST (DF numerator) 3 F-TEST (DF denominator) 155 p-value 0.766914280365275 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.16405509068659 Sum Squared Residuals 1551.74291561946 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 12.621724819241 -0.621724819240985 2 11 13.0485043406500 -2.04850434064998 3 14 13.1758001747356 0.824199825264388 4 12 12.8867912840521 -0.88679128405206 5 21 13.1326590587085 7.86734094129149 6 12 13.0116847339476 -1.01168473394764 7 22 13.0973561929508 8.9026438070492 8 11 12.8810805477783 -1.88108054777833 9 10 12.5319203975710 -2.53192039757098 10 13 12.9044732332620 0.0955267667379638 11 10 12.6199332081020 -2.61993320810197 12 8 12.6843394956171 -4.68433949561711 13 15 13.1404362763157 1.85956372368434 14 14 12.8867912840521 1.11320871594794 15 10 12.9395012288253 -2.93950122882535 16 14 13.4681174175028 0.53188258249717 17 14 13.1344506698475 0.865549330152459 18 11 13.1793833970137 -2.17938339701367 19 10 13.0353522896257 -3.03535228962573 20 13 12.4776937118531 0.522306288146938 21 7 12.6001847775586 -5.60018477755857 22 14 12.2905214884380 1.70947851156198 23 12 12.9203025386707 -0.920302538670735 24 14 12.7268698385932 1.27313016140682 25 11 12.9395012288253 -1.93950122882535 26 9 13.0509067248400 -4.05090672484004 27 11 13.0293666831576 -2.02936668315761 28 15 13.0254475580229 1.97455244197709 29 14 12.9436952241544 1.05630477584556 30 13 13.0838682390699 -0.083868239069925 31 9 13.1129106281651 -4.11291062816511 32 15 12.193153686693 2.80684631330700 33 10 12.8071664641793 -2.80716646417926 34 11 13.1716061794065 -2.17160617940652 35 13 12.9164444461983 0.0835555538017188 36 8 12.6331462917885 -4.63314629178846 37 20 13.0329499054357 6.96705009456433 38 12 12.570867518269 -0.570867518268993 39 10 12.5908908190068 -2.59089081900678 40 10 12.8517632884888 -2.85176328848875 41 9 12.4699164942459 -3.46991649424591 42 14 12.9981967800668 1.00180321993325 43 8 12.9104588397302 -4.91045883973016 44 14 13.0215894655505 0.978410534449543 45 11 13.0467127295109 -2.04671272951095 46 13 12.8595405060959 0.140459493904095 47 9 12.5789196060705 -3.57891960607054 48 11 12.7930677372473 -1.79306773724734 49 15 12.9922111735986 2.00778882640137 50 11 12.5555879532491 -1.55558795324908 51 10 12.7810965243111 -2.7810965243111 52 14 13.0721718963281 0.927828103671927 53 18 12.9922111735986 5.00778882640137 54 14 13.5534529736494 0.446547026350637 55 11 12.5914405593956 -1.59144055939557 56 12 12.7523290054103 -0.752329005410305 57 13 12.9922111735986 0.00778882640136876 58 9 13.1365781838432 -4.13657818384321 59 10 13.4462414729638 -3.44624147296376 60 15 12.5651567819953 2.43484321800474 61 20 13.0526983359791 6.94730166402093 62 12 13.0039075163405 -1.00390751634048 63 12 12.7972617325764 -0.797261732576437 64 14 12.8418585568859 1.15814144311407 65 13 13.0778826326018 -0.0778826326018025 66 11 13.0524234657847 -2.05242346578468 67 17 13.1793833970137 3.82061660298633 68 12 13.0449211183719 -1.04492111837192 69 13 12.8457776820206 0.154222317979371 70 14 12.9395012288253 1.06049877117465 71 13 13.1716061794065 -0.17160617940652 72 15 13.1733977905456 1.82660220945445 73 13 12.9709460021106 0.0290539978894038 74 10 12.3704822111675 -2.37048221116746 75 11 13.0293666831576 -2.02936668315761 76 19 12.9922111735986 6.00778882640137 77 13 12.6840646254227 0.315935374577285 78 17 12.7583146118784 4.24168538812157 79 13 12.8867912840521 0.113208715947938 80 9 12.9239467936110 -3.92394679361104 81 11 12.6061703840267 -1.60617038402670 82 10 13.3393048424726 -3.33930484247256 83 9 12.8050389501836 -3.80503895018359 84 12 13.0041823865349 -1.00418238653488 85 12 12.8397920755525 -0.839792075552507 86 13 12.8227208993936 0.177279100606436 87 13 13.0778826326018 -0.0778826326018025 88 12 12.7541206165493 -0.754120616549335 89 15 12.6064452542211 2.39355474577891 90 22 13.0116847339476 8.98831526605236 91 13 12.6178667267685 0.382133273231452 92 15 13.5399650197685 1.46003498023152 93 13 13.0524234657847 -0.0524234657846753 94 15 12.9494059604282 2.05059403957183 95 10 13.0604755535862 -3.06047555358622 96 11 12.6690599305972 -1.66905993059720 97 16 12.4384717209607 3.56152827903934 98 11 12.5109300962773 -1.51093009627734 99 11 13.0916454566771 -2.09164545667708 100 10 12.9649603956425 -2.96496039564247 101 10 12.8715117190321 -2.87151171903215 102 16 13.2710404624850 2.72895953751503 103 12 12.8424693299370 -0.842469329936962 104 11 13.0314331644910 -2.03143316449103 105 16 12.660671939939 3.33932806006099 106 19 12.7580397416840 6.24196025831596 107 11 13.2261077353188 -2.22610773531883 108 16 13.0059739976739 2.99402600232609 109 15 12.5321952677654 2.46780473223462 110 24 12.7113154033789 11.2886845966211 111 14 13.1716061794065 0.82839382059348 112 15 12.9652352658369 2.03476473416313 113 11 13.1754642718790 -2.17546427187897 114 15 13.010167993003 1.989832006997 115 12 13.3626364952940 -1.36263649529402 116 10 13.1833025221484 -3.18330252214837 117 14 13.1758001747356 0.824199825264388 118 13 13.0329499054357 -0.0329499054356707 119 9 12.5711423884634 -3.57114238846339 120 15 13.0991478040898 1.90085219591016 121 15 13.126398582046 1.87360141795401 122 14 12.9317240112182 1.06827598878181 123 11 12.5594460457215 -1.55944604572153 124 8 13.3545844074925 -5.35458440749247 125 11 12.3210806184778 -1.32108061847785 126 11 12.7759965610884 -1.77599656108840 127 8 13.2845284163659 -5.28452841636585 128 10 12.9395012288253 -2.93950122882535 129 11 12.9182360573373 -1.91823605733731 130 13 12.6996190606370 0.300380939362979 131 11 12.8265789918660 -1.82657899186602 132 20 13.0721718963281 6.92782810367193 133 10 13.1578433553312 -3.15784335533124 134 15 13.311779194322 1.68822080567799 135 12 12.9922111735986 -0.992211173598631 136 14 12.4953756610630 1.50462433893696 137 23 12.7912761261083 10.2087238738917 138 14 12.7855653898346 1.21443461016541 139 16 13.1326590587085 2.86734094129149 140 11 12.6549612036653 -1.65496120366528 141 12 12.7346470562003 -0.734647056200331 142 10 12.7115902735733 -2.71159027357327 143 14 12.1116762230189 1.88832377698108 144 12 12.7870821307792 -0.787082130779222 145 12 12.5576544345825 -0.557654434582504 146 11 12.5786447358761 -1.57864473587615 147 12 12.9164444461983 -0.916444446198281 148 13 13.1188962346332 -0.118896234633235 149 11 13.0526983359791 -2.05269833597907 150 19 13.0586839424472 5.94131605755281 151 12 13.2398705593941 -1.23987055939411 152 17 12.4034437253973 4.59655627460265 153 9 12.6864670096128 -3.68646700961278 154 12 13.0566174611138 -1.05661746111377 155 19 12.5968764254749 6.4031235745251 156 18 13.0838682390699 4.91613176093007 157 15 12.6996190606370 2.30038093936298 158 14 12.6316295508438 1.36837044915618 159 11 12.1659029087368 -1.16590290873684 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.976394534322343 0.047210931355314 0.023605465677657 8 0.951903386473852 0.0961932270522953 0.0480966135261477 9 0.91986285096968 0.160274298060641 0.0801371490303206 10 0.873498134910829 0.253003730178342 0.126501865089171 11 0.812066070024099 0.375867859951802 0.187933929975901 12 0.787588045557719 0.424823908884563 0.212411954442281 13 0.710785546943447 0.578428906113106 0.289214453056553 14 0.627513994637113 0.744972010725774 0.372486005362887 15 0.65500430365723 0.689991392685539 0.344995696342770 16 0.723185586279466 0.553628827441068 0.276814413720534 17 0.654820272702685 0.69035945459463 0.345179727297315 18 0.671761928492559 0.656476143014882 0.328238071507441 19 0.648164279953095 0.70367144009381 0.351835720046905 20 0.680104363237949 0.639791273524102 0.319895636762051 21 0.723983109251041 0.552033781497918 0.276016890748959 22 0.775713522373843 0.448572955252315 0.224286477626157 23 0.721378411229249 0.557243177541502 0.278621588770751 24 0.680923814105871 0.638152371788258 0.319076185894129 25 0.640954701922063 0.718090596155874 0.359045298077937 26 0.670988404431302 0.658023191137396 0.329011595568698 27 0.639738613068442 0.720522773863115 0.360261386931558 28 0.607490711163808 0.785018577672384 0.392509288836192 29 0.559087494711717 0.881825010576565 0.440912505288282 30 0.498827205162897 0.997654410325795 0.501172794837103 31 0.552115623552737 0.895768752894526 0.447884376447263 32 0.587547937127836 0.824904125744328 0.412452062872164 33 0.559270668049349 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0.136798437146626 0.931600781426687 104 0.0599471534027872 0.119894306805574 0.940052846597213 105 0.0602354306592319 0.120470861318464 0.939764569340768 106 0.103229356050117 0.206458712100235 0.896770643949883 107 0.0920132622354364 0.184026524470873 0.907986737764564 108 0.0887288354770994 0.177457670954199 0.9112711645229 109 0.0791138836175985 0.158227767235197 0.920886116382401 110 0.469495517498109 0.938991034996219 0.530504482501891 111 0.422601212941633 0.845202425883266 0.577398787058367 112 0.390118575475749 0.780237150951497 0.609881424524251 113 0.358204890458748 0.716409780917496 0.641795109541252 114 0.324430903406466 0.648861806812933 0.675569096593534 115 0.284101187740825 0.56820237548165 0.715898812259175 116 0.286555843389544 0.573111686779087 0.713444156610456 117 0.244894626674674 0.489789253349348 0.755105373325326 118 0.205392778984916 0.410785557969831 0.794607221015085 119 0.222061136792562 0.444122273585124 0.777938863207438 120 0.198184961737775 0.396369923475551 0.801815038262225 121 0.179147871348368 0.358295742696736 0.820852128651632 122 0.148882284826899 0.297764569653797 0.851117715173101 123 0.127405813631577 0.254811627263155 0.872594186368423 124 0.165855250402198 0.331710500804396 0.834144749597802 125 0.137990332677587 0.275980665355174 0.862009667322413 126 0.122720030492509 0.245440060985019 0.87727996950749 127 0.185498757440324 0.370997514880648 0.814501242559676 128 0.187085528829706 0.374171057659412 0.812914471170294 129 0.173231281788721 0.346462563577441 0.82676871821128 130 0.137811807341951 0.275623614683902 0.862188192658049 131 0.123452485953459 0.246904971906917 0.876547514046541 132 0.221672627715068 0.443345255430136 0.778327372284932 133 0.241648622422646 0.483297244845292 0.758351377577354 134 0.197335687546180 0.394671375092359 0.80266431245382 135 0.166414078240956 0.332828156481911 0.833585921759044 136 0.130123211166473 0.260246422332947 0.869876788833527 137 0.59495868211983 0.81008263576034 0.40504131788017 138 0.527551394236181 0.944897211527637 0.472448605763819 139 0.488535085834113 0.977070171668226 0.511464914165887 140 0.447976322557999 0.895952645115998 0.552023677442001 141 0.379257995471569 0.758515990943138 0.620742004528431 142 0.387257939715211 0.774515879430423 0.612742060284789 143 0.316592306749893 0.633184613499786 0.683407693250107 144 0.248631282647622 0.497262565295245 0.751368717352378 145 0.198210025648444 0.396420051296887 0.801789974351556 146 0.16885831478444 0.33771662956888 0.83114168521556 147 0.125888632990712 0.251777265981425 0.874111367009288 148 0.0864737044462057 0.172947408892411 0.913526295553794 149 0.0938770751296552 0.187754150259310 0.906122924870345 150 0.115922567769026 0.231845135538052 0.884077432230974 151 0.112701268950409 0.225402537900817 0.887298731049591 152 0.354598120010481 0.709196240020963 0.645401879989519 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 1 0.00684931506849315 OK 10% type I error level 2 0.0136986301369863 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/10w5xw1290460765.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/10w5xw1290460765.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/174ik1290460765.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/174ik1290460765.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/2hvzn1290460765.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/2hvzn1290460765.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/3hvzn1290460765.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/3hvzn1290460765.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/4hvzn1290460765.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/4hvzn1290460765.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/5amy81290460765.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/5amy81290460765.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/6amy81290460765.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/6amy81290460765.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/73wgb1290460765.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/73wgb1290460765.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/83wgb1290460765.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/83wgb1290460765.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/9w5xw1290460765.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/22/t1290460784wzimxo3d1rsgr1v/9w5xw1290460765.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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