WS7 - Minitutorail blog 4 linear trend

*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: Tue, 23 Nov 2010 19:49:15 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290541716awssfspfemeegzc.htm/, Retrieved Tue, 23 Nov 2010 20:48:36 +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/23/t1290541716awssfspfemeegzc.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 «

12 6 15 4 7 2 2 2 2 11 6 15 3 5 4 1 2 2 14 13 14 5 7 7 4 3 4 12 8 10 3 3 3 1 2 3 21 7 10 6 7 7 5 4 4 12 9 12 5 7 2 1 2 3 22 5 18 6 7 7 1 2 3 11 8 12 6 1 2 1 3 4 10 9 14 5 4 1 1 2 3 13 11 18 5 5 2 1 2 4 10 8 9 3 6 6 2 3 3 8 11 11 5 4 1 1 2 2 15 12 11 7 7 1 3 3 3 10 8 17 5 6 1 1 1 3 14 7 8 5 2 2 1 3 3 14 9 16 3 2 2 1 1 2 11 12 21 5 6 2 1 3 3 10 20 24 6 7 1 1 2 2 13 7 21 5 5 7 2 3 4 7 8 14 2 2 1 4 4 5 12 8 7 5 7 2 1 3 3 14 16 18 4 4 4 2 3 3 11 10 18 6 5 2 1 1 1 9 6 13 3 5 1 2 2 4 11 8 11 5 5 1 3 1 3 15 9 13 4 3 5 1 3 4 13 9 13 5 5 2 1 3 3 9 11 18 2 1 1 1 2 3 15 12 14 2 1 3 1 2 1 10 8 12 5 3 1 1 3 4 11 7 9 2 2 2 2 2 4 13 8 12 2 3 5 1 2 2 8 9 8 2 2 2 1 2 2 20 4 5 5 5 6 1 1 1 12 8 10 5 2 4 1 2 3 10 8 11 1 3 1 1 3 4 10 8 11 5 4 3 1 1 1 9 6 12 2 6 6 1 2 3 14 8 12 6 2 7 2 3 3 8 4 15 1 7 4 1 2 2 14 7 12 4 6 1 2 1 4 11 14 16 3 5 5 1 1 3 13 10 14 2 3 3 1 3 3 11 9 17 5 3 2 2 3 2 11 8 10 3 4 2 1 3 3 10 11 17 4 5 2 1 3 2 14 8 12 3 2 2 1 2 1 18 8 13 6 7 1 1 3 3 14 10 13 4 6 2 1 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 26 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Depression[t] = + 7.13203448823286 + 0.0467973554484997CriticParents[t] -0.0610624420846635ExpecParents[t] + 0.586113320938374FutureWorrying[t] + 0.214967677788581SleepDepri[t] + 0.335209949039189ChangesLastYear[t] -0.0864177319112125FreqSmoking[t] + 0.284315482532366FreqHighAlc[t] + 0.192320018536851`FreqBeerOrWine `[t] + 0.00645640371582369t + 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) 7.13203448823286 1.486388 4.7982 4e-06 2e-06 CriticParents 0.0467973554484997 0.115867 0.4039 0.686934 0.343467 ExpecParents -0.0610624420846635 0.086747 -0.7039 0.4827 0.24135 FutureWorrying 0.586113320938374 0.168218 3.4843 0.000666 0.000333 SleepDepri 0.214967677788581 0.141718 1.5169 0.131638 0.065819 ChangesLastYear 0.335209949039189 0.136435 2.4569 0.015282 0.007641 FreqSmoking -0.0864177319112125 0.275507 -0.3137 0.754258 0.377129 FreqHighAlc 0.284315482532366 0.315102 0.9023 0.368507 0.184253 `FreqBeerOrWine ` 0.192320018536851 0.294925 0.6521 0.515447 0.257723 t 0.00645640371582369 0.006255 1.0321 0.30386 0.15193 Multiple Linear Regression - Regression Statistics Multiple R 0.460266065223322 R-squared 0.211844850796159 Adjusted R-squared 0.15930117418257 F-TEST (value) 4.03178582941739 F-TEST (DF numerator) 9 F-TEST (DF denominator) 135 p-value 0.000136292636910840 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.89896684527411 Sum Squared Residuals 1134.5411839498 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 11.8034208580377 0.196579141962334 2 11 11.5506662152276 -0.550666215227555 3 14 14.9632607176114 -0.96326071761145 4 12 11.3896606579000 0.61033934209998 5 21 15.7236502322503 5.27634976774972 6 12 13.0241333406027 -1.02413334060272 7 22 14.7391887361509 7.26081126384911 8 11 12.7631915478620 -1.76319154786198 9 10 11.9412646851759 -1.94126468517594 10 13 12.5395636768147 0.460436323185273 11 10 13.3443485570999 -3.34434855709992 12 8 12.0450959149375 -4.04509591493755 13 15 14.2192793865912 0.780720613408847 14 10 11.8891818950974 -1.88918189509736 15 14 12.4423731250763 1.55762687492375 16 14 10.1207470775334 3.87925292246656 17 11 12.7553316738041 -1.75533167380410 18 10 12.9422151434725 -2.94221514347248 19 13 14.1012420580262 -1.10124205802625 20 7 10.471230258614 -3.47123025861401 21 12 13.6638097338473 -1.66380973384726 22 14 12.7259439300828 1.27405606991716 23 11 12.3015373524674 -1.30153735246739 24 9 11.1074244391899 -2.10742443918993 25 11 11.9387738468684 -0.938773846868396 26 15 13.1284802889286 1.87151971107138 27 13 12.9530355035056 0.0469644964944373 28 9 9.51003830215407 -0.510038302154067 29 15 10.0933216906617 4.90667830933828 30 10 12.4138445152097 -2.4138445152097 31 11 10.5478599837229 0.45214001627708 32 13 11.3403016363769 1.65969836362309 33 8 10.4172076389737 -2.41720763897374 34 20 13.6403118829695 6.35968811703054 35 12 12.8822780862179 -0.882278086217913 36 10 10.1691920958358 -0.169192095835807 37 10 12.2598983384968 -2.2598983384968 38 9 12.4578783487166 -3.45787834871664 39 14 14.5756197355890 -0.575619735588976 40 8 10.9601235592323 -2.96012355923227 41 14 11.8418086160867 2.15819138391332 42 11 12.3654532504075 -1.36545325040751 43 13 11.1890075069695 1.81099249303052 44 11 12.1098714923107 -1.10987149231069 45 11 11.8184464215306 -0.818446421530552 46 10 12.1466187771893 -2.14661877718933 47 14 10.6103434696096 3.38965653039036 48 18 13.7226613535657 4.27733864643429 49 14 12.4864126150200 1.51358738497998 50 11 12.9670372099912 -1.96703720999121 51 12 11.4246719766547 0.575328023345259 52 13 13.0819133275888 -0.0819133275888192 53 9 13.6882139190418 -4.68821391904182 54 10 12.2390407889505 -2.23904078895049 55 15 13.4839668625129 1.51603313748708 56 20 14.1097729893239 5.89022701067606 57 12 11.6725921879785 0.327407812021524 58 12 11.9845671611827 0.0154328388173484 59 14 11.3368204586236 2.66317954137641 60 13 14.9342063362509 -1.93420633625086 61 11 14.3339567919935 -3.33395679199350 62 17 13.1768012688317 3.82319873116826 63 12 12.2082127195663 -0.208212719566292 64 13 12.8267565218183 0.173243478181712 65 14 13.7952789289943 0.204721071005673 66 13 10.7283395619145 2.27166043808553 67 15 13.7954029674143 1.20459703258573 68 13 11.9109387612743 1.08906123872567 69 10 13.5677501317880 -3.56775013178802 70 11 11.273139121698 -0.273139121697992 71 13 12.7314620715271 0.268537928472890 72 17 14.1397036225824 2.86029637741759 73 13 12.8670398050245 0.132960194975543 74 9 12.0549466343081 -3.05494663430812 75 11 12.3397040899440 -1.33970408994403 76 10 10.2967752046680 -0.296775204668031 77 9 10.3058972499947 -1.30589724999465 78 12 11.2841401005794 0.715859899420595 79 12 12.4348775095511 -0.434877509551113 80 13 12.3637336548888 0.636266345111186 81 13 12.4234991526585 0.57650084734154 82 22 14.512220941371 7.48777905862899 83 13 11.9205907468917 1.07940925310831 84 15 13.7390295626360 1.26097043736396 85 13 14.1015011530776 -1.10150115307764 86 15 11.5946402649398 3.40535973506017 87 10 11.6874586748402 -1.68745867484024 88 11 10.8750542243480 0.124945775652039 89 16 14.1837910355097 1.81620896449035 90 11 12.0425833932396 -1.04258339323962 91 11 12.4255241935236 -1.42552419352357 92 10 12.7072587998349 -2.70725879983489 93 10 14.5620910104904 -4.56209101049043 94 16 14.2255723382278 1.77442766177225 95 12 13.3892112914856 -1.38921129148557 96 11 13.9185426575266 -2.91854265752657 97 16 14.4210525468873 1.57894745311269 98 19 14.9904390611284 4.00956093887163 99 11 14.8959736676309 -3.89597366763086 100 15 12.7672596931523 2.23274030684774 101 24 16.571589722843 7.428410277157 102 14 11.6953526889516 2.30464731104837 103 15 13.6526776275226 1.34732237247740 104 11 14.9179142605919 -3.91791426059188 105 15 13.5618988422876 1.43810115771242 106 12 12.9351808535059 -0.935180853505916 107 10 10.8477922441472 -0.847792244147166 108 14 13.9971501977574 0.00284980224257205 109 9 12.9089923937108 -3.90899239371078 110 15 10.7201602693727 4.27983973062725 111 15 9.79877947006756 5.20122052993244 112 14 13.1668567400140 0.833143259986041 113 11 14.2205243292760 -3.22052432927598 114 8 14.4197763322497 -6.4197763322497 115 11 14.3117863018382 -3.31178630183823 116 8 11.8963645932459 -3.89636459324589 117 10 11.3260138183465 -1.32601381834645 118 11 13.7110640088442 -2.71106400884425 119 13 14.1597410318982 -1.15974103189823 120 11 13.8537558806655 -2.85375588066549 121 20 12.7745649493019 7.22543505069813 122 10 12.2969965736639 -2.29699657366387 123 12 11.0701418180347 0.92985818196535 124 14 12.6762041235299 1.32379587647015 125 23 14.1250790331462 8.87492096685384 126 14 13.1385635147755 0.861436485224494 127 16 15.3459235257493 0.654076474250725 128 11 13.5617021817485 -2.56170218174851 129 12 14.3748513742172 -2.37485137421721 130 10 13.7930867095764 -3.7930867095764 131 14 13.9165352062806 0.0834647937194315 132 12 9.99551526151993 2.00448473848007 133 12 13.8351566065299 -1.83515660652989 134 11 10.3673615487187 0.632638451281277 135 12 12.5532725501845 -0.553272550184466 136 13 15.9200443612809 -2.92004436128085 137 17 16.4628398674848 0.537160132515228 138 11 12.6683474667565 -1.66834746675647 139 12 13.8583047626368 -1.85830476263683 140 19 15.2869993557498 3.71300064425025 141 15 14.107044574438 0.892955425562008 142 14 13.6469730267066 0.353026973293381 143 11 13.8724741017398 -2.87247410173984 144 9 10.7776270678648 -1.77762706786479 145 18 12.0135143157458 5.98648568425415 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.402671123218951 0.805342246437902 0.597328876781049 14 0.533270412555893 0.933459174888214 0.466729587444107 15 0.516580081089885 0.96683983782023 0.483419918910115 16 0.640498739051791 0.719002521896419 0.359501260948209 17 0.531050458821396 0.937899082357208 0.468949541178604 18 0.441004927557038 0.882009855114077 0.558995072442962 19 0.581190520850798 0.837618958298404 0.418809479149202 20 0.504890125441824 0.990219749116352 0.495109874558176 21 0.427808788919080 0.855617577838159 0.57219121108092 22 0.456837564948535 0.91367512989707 0.543162435051465 23 0.511995152816762 0.976009694366475 0.488004847183238 24 0.43369630294148 0.86739260588296 0.56630369705852 25 0.364335547240132 0.728671094480264 0.635664452759868 26 0.329058861882457 0.658117723764914 0.670941138117543 27 0.273275018916258 0.546550037832516 0.726724981083742 28 0.230824072439464 0.461648144878928 0.769175927560536 29 0.283463863453706 0.566927726907413 0.716536136546294 30 0.241161683391162 0.482323366782324 0.758838316608838 31 0.195245517807672 0.390491035615343 0.804754482192328 32 0.157538363678278 0.315076727356556 0.842461636321722 33 0.15460319223178 0.30920638446356 0.84539680776822 34 0.170320148674268 0.340640297348536 0.829679851325732 35 0.177678787613773 0.355357575227545 0.822321212386227 36 0.17541508727267 0.35083017454534 0.82458491272733 37 0.224813329982337 0.449626659964675 0.775186670017663 38 0.269532193637579 0.539064387275158 0.730467806362421 39 0.274689952996456 0.549379905992912 0.725310047003544 40 0.248398175948942 0.496796351897884 0.751601824051058 41 0.290628552023277 0.581257104046554 0.709371447976723 42 0.253980427532261 0.507960855064521 0.746019572467739 43 0.263739451911075 0.527478903822149 0.736260548088925 44 0.221773067441902 0.443546134883805 0.778226932558098 45 0.186522137217062 0.373044274434123 0.813477862782938 46 0.162151707184911 0.324303414369822 0.837848292815089 47 0.172410639605071 0.344821279210142 0.827589360394929 48 0.273253416509989 0.546506833019977 0.726746583490012 49 0.247998952398139 0.495997904796278 0.752001047601861 50 0.223080047841007 0.446160095682015 0.776919952158993 51 0.187193833772047 0.374387667544095 0.812806166227953 52 0.152886600911436 0.305773201822873 0.847113399088564 53 0.227737137228514 0.455474274457027 0.772262862771486 54 0.220055461329851 0.440110922659703 0.779944538670149 55 0.201443843273614 0.402887686547229 0.798556156726386 56 0.288793352872919 0.577586705745839 0.71120664712708 57 0.247582684180814 0.495165368361627 0.752417315819186 58 0.212954125408914 0.425908250817827 0.787045874591086 59 0.194357158458752 0.388714316917504 0.805642841541248 60 0.216919936787527 0.433839873575053 0.783080063212473 61 0.269897397489615 0.539794794979231 0.730102602510385 62 0.305164025002802 0.610328050005604 0.694835974997198 63 0.262481244065422 0.524962488130844 0.737518755934578 64 0.222693743055660 0.445387486111321 0.77730625694434 65 0.187233517375458 0.374467034750915 0.812766482624542 66 0.172485630892524 0.344971261785047 0.827514369107476 67 0.146126361814526 0.292252723629051 0.853873638185474 68 0.121995310566522 0.243990621133043 0.878004689433478 69 0.133984989783259 0.267969979566518 0.866015010216741 70 0.108705052307732 0.217410104615464 0.891294947692268 71 0.0869915730080343 0.173983146016069 0.913008426991966 72 0.0892423661981333 0.178484732396267 0.910757633801867 73 0.0708755909812244 0.141751181962449 0.929124409018776 74 0.0724592239096161 0.144918447819232 0.927540776090384 75 0.0598788165938048 0.119757633187610 0.940121183406195 76 0.0477608472605966 0.0955216945211933 0.952239152739403 77 0.0418745039159361 0.0837490078318722 0.958125496084064 78 0.0320187500230407 0.0640375000460813 0.96798124997696 79 0.0244182395834017 0.0488364791668033 0.975581760416598 80 0.0184051854345944 0.0368103708691887 0.981594814565406 81 0.0139045825444571 0.0278091650889143 0.986095417455543 82 0.0659997439974944 0.131999487994989 0.934000256002506 83 0.0518138432605953 0.103627686521191 0.948186156739405 84 0.040321744735627 0.080643489471254 0.959678255264373 85 0.0328151943462775 0.065630388692555 0.967184805653723 86 0.0334241716437087 0.0668483432874175 0.966575828356291 87 0.028570510523537 0.057141021047074 0.971429489476463 88 0.0211853854978990 0.0423707709957979 0.978814614502101 89 0.0184896677268707 0.0369793354537413 0.98151033227313 90 0.0144400452973548 0.0288800905947097 0.985559954702645 91 0.0116860357337379 0.0233720714674758 0.988313964266262 92 0.0115685459439798 0.0231370918879596 0.98843145405602 93 0.0176145094850588 0.0352290189701177 0.982385490514941 94 0.0137599998101145 0.0275199996202291 0.986240000189885 95 0.0108337348641421 0.0216674697282841 0.989166265135858 96 0.0118201733511398 0.0236403467022796 0.98817982664886 97 0.009975170552696 0.019950341105392 0.990024829447304 98 0.0151825124393321 0.0303650248786642 0.984817487560668 99 0.0178203524223689 0.0356407048447378 0.982179647577631 100 0.0141480859613225 0.0282961719226451 0.985851914038677 101 0.0690155142356918 0.138031028471384 0.930984485764308 102 0.0620600435545498 0.124120087109100 0.93793995644545 103 0.0516527470095528 0.103305494019106 0.948347252990447 104 0.0530853169311383 0.106170633862277 0.946914683068862 105 0.0445332668259305 0.089066533651861 0.95546673317407 106 0.0333650139268554 0.0667300278537107 0.966634986073145 107 0.0263383472861093 0.0526766945722185 0.97366165271389 108 0.0190960004053130 0.0381920008106259 0.980903999594687 109 0.0178981913546507 0.0357963827093013 0.98210180864535 110 0.0270168894872160 0.0540337789744319 0.972983110512784 111 0.0415455591031522 0.0830911182063045 0.958454440896848 112 0.0341426802884413 0.0682853605768827 0.965857319711559 113 0.0302078238031110 0.0604156476062219 0.96979217619689 114 0.0539784627196432 0.107956925439286 0.946021537280357 115 0.0506360980142687 0.101272196028537 0.949363901985731 116 0.076084919097917 0.152169838195834 0.923915080902083 117 0.0580716836609768 0.116143367321954 0.941928316339023 118 0.0505787428201364 0.101157485640273 0.949421257179864 119 0.0380493884522973 0.0760987769045947 0.961950611547703 120 0.078777940659504 0.157555881319008 0.921222059340496 121 0.181057099691235 0.362114199382469 0.818942900308765 122 0.379188054510414 0.758376109020828 0.620811945489586 123 0.330995224498295 0.66199044899659 0.669004775501705 124 0.258364879987658 0.516729759975315 0.741635120012342 125 0.502726585656352 0.994546828687296 0.497273414343648 126 0.828209672295613 0.343580655408774 0.171790327704387 127 0.787320259179968 0.425359481640064 0.212679740820032 128 0.704622346002689 0.590755307994622 0.295377653997311 129 0.634359688280721 0.731280623438557 0.365640311719279 130 0.592248877960882 0.815502244078236 0.407751122039118 131 0.569248570896568 0.861502858206864 0.430751429103432 132 0.466622727475853 0.933245454951706 0.533377272524147 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 18 0.15 NOK 10% type I error level 33 0.275 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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Software written by Ed van Stee & Patrick Wessa

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