WS8: model 3

*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: Fri, 26 Nov 2010 13:04:18 +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/26/t1290780355oa6lf6ljqyh1o9g.htm/, Retrieved Fri, 26 Nov 2010 15:05:59 +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/26/t1290780355oa6lf6ljqyh1o9g.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2 14 2 18 2 11 1 12 2 16 2 18 2 14 2 14 2 15 2 15 1 17 2 19 1 10 2 16 2 18 1 14 1 14 2 17 1 14 2 16 1 18 2 11 2 14 2 12 1 17 2 9 1 16 2 14 2 15 1 11 2 16 1 13 2 17 2 15 1 14 1 16 1 9 1 15 2 17 1 13 1 15 2 16 1 16 1 12 2 12 2 11 2 15 2 15 2 17 1 13 2 16 1 14 1 11 2 12 1 12 2 15 2 16 2 15 1 12 2 12 1 8 1 13 2 11 2 14 2 15 1 10 2 11 1 12 2 15 1 15 1 14 2 16 2 15 1 15 1 13 2 12 2 17 2 13 1 15 1 13 1 15 1 16 2 15 1 16 2 15 2 14 1 15 2 14 2 13 2 7 2 17 2 13 2 15 2 14 2 13 2 16 2 12 2 14 1 17 1 15 2 17 1 12 2 16 1 11 2 15 1 9 2 16 1 15 1 10 2 10 2 15 2 11 2 13 1 14 2 18 1 16 2 14 2 14 2 14 2 14 2 12 2 14 2 15 2 15 2 15 2 13 1 17 2 17 2 19 2 15 1 13 1 9 2 15 1 15 1 15 2 16 1 11 1 14 2 11 2 15 1 13 2 15 1 16 2 14 1 15 2 16 2 16 1 11 1 12 1 9 2 16 2 13 1 16 2 12 2 9 2 13 2 13 2 14 2 19 2 13 2 12 2 13

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 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation y[t] = + 13.4283031142472 + 0.832897843710754x[t] -1.31091204200039M1[t] -0.365009421819613M2[t] + 0.926100187197648M3[t] -0.866154643520036M4[t] -0.348823451910686M5[t] -1.49822113977123M6[t] + 0.49863090992441M7[t] -0.431904701871787M8[t] + 0.983814030091073M9[t] -0.844090480737548M10[t] -0.261872578116706M11[t] -0.00539532330297578t + 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) 13.4283031142472 0.923422 14.5419 0 0 x 0.832897843710754 0.367901 2.2639 0.025033 0.012516 M1 -1.31091204200039 0.86543 -1.5148 0.131968 0.065984 M2 -0.365009421819613 0.864442 -0.4222 0.673456 0.336728 M3 0.926100187197648 0.864388 1.0714 0.285736 0.142868 M4 -0.866154643520036 0.86529 -1.001 0.318461 0.159231 M5 -0.348823451910686 0.864331 -0.4036 0.687107 0.343554 M6 -1.49822113977123 0.86528 -1.7315 0.085449 0.042724 M7 0.49863090992441 0.880616 0.5662 0.572095 0.286048 M8 -0.431904701871787 0.881885 -0.4898 0.625035 0.312517 M9 0.983814030091073 0.880066 1.1179 0.265427 0.132713 M10 -0.844090480737548 0.880495 -0.9587 0.339296 0.169648 M11 -0.261872578116706 0.881806 -0.297 0.766903 0.383452 t -0.00539532330297578 0.003778 -1.428 0.155389 0.077694 Multiple Linear Regression - Regression Statistics Multiple R 0.391457433269082 R-squared 0.153238922061618 Adjusted R-squared 0.0788612598102736 F-TEST (value) 2.06028150688278 F-TEST (DF numerator) 13 F-TEST (DF denominator) 148 p-value 0.0197505101968209 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.24355168996005 Sum Squared Residuals 744.961579457345 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 13.7777914363653 0.222208563634675 2 18 14.7182987332431 3.2817012667569 3 11 16.0040130189574 -5.00401301895738 4 12 13.373465021226 -1.37346502122596 5 16 14.7182987332431 1.28170126675691 6 18 13.5635057220796 4.43649427792042 7 14 15.5549624484722 -1.55496244847224 8 14 14.6190315133731 -0.619031513373067 9 15 16.029354922033 -1.02935492203295 10 15 14.1960550879014 0.803944912098647 11 17 13.9399798235085 3.06002017649153 12 19 15.029354922033 3.97064507796705 13 10 12.8801497130188 -2.88014971301883 14 16 14.6535548536074 1.34644514639261 15 18 15.9392691393217 2.06073086067833 16 14 13.3087211415903 0.691278858409743 17 14 13.8206570098966 0.179342990103369 18 17 13.4987618424439 3.50123815755613 19 14 14.6573207251258 -0.657320725125775 20 16 14.5542876337374 1.44571236626264 21 18 15.1317131986865 2.86828680131351 22 11 14.1313112082656 -3.13131120826564 23 14 14.7081337875835 -0.70813378758351 24 12 14.9646110423972 -2.96461104239724 25 17 12.8154058333831 4.18459416661688 26 9 14.5888109739717 -5.58881097397168 27 16 15.0416274159752 0.958372584024793 28 14 14.0768751056653 -0.0768751056653012 29 15 14.5888109739717 0.411189026028324 30 11 12.6011201190974 -1.6011201190974 31 16 15.4254746892008 0.57452531079918 32 13 13.6566459103909 -0.656645910390893 33 17 15.8998671627615 1.10013283723847 34 15 14.0665673286299 0.933432671370065 35 14 13.810492064237 0.189507935762953 36 16 14.0669693190508 1.93303068094922 37 9 12.7506619537474 -3.75066195374741 38 15 13.6911692506252 1.30883074937479 39 17 15.8097813800503 1.19021861994975 40 13 13.1792333823188 -0.179233382318837 41 15 13.6911692506252 1.30883074937479 42 16 13.3692740831724 2.63072591682755 43 16 14.5278329658544 1.47216703414564 44 12 13.5919020307552 -1.59190203075518 45 12 15.8351232831258 -3.83512328312582 46 11 14.0018234489942 -3.00182344899422 47 15 14.5786460283121 0.421353971687908 48 15 14.8351232831258 0.164876716874178 49 17 13.5188159178225 3.48118408217755 50 13 13.6264253709895 -0.626425370989503 51 16 15.7450375004145 0.254962499585457 52 14 13.1144895026831 0.885510497316871 53 11 13.6264253709895 -2.6264253709895 54 12 13.3045302035367 -1.30453020353674 55 12 14.4630890862186 -2.46308908621865 56 15 14.3600559948302 0.639944005169771 57 16 15.7703794034901 0.229620596509888 58 15 13.9370795693585 1.06292043064148 59 12 13.6810043049656 -1.68100430496563 60 12 14.7703794034901 -2.77037940349011 61 8 12.621174194476 -4.62117419447599 62 13 13.5616814913538 -0.561681491353793 63 11 15.6802936207788 -4.68029362077883 64 14 13.8826434667582 0.117356533241827 65 15 14.3945793350645 0.605420664935452 66 10 12.4068884801903 -2.40688848019028 67 11 15.2312430502937 -4.23124305029369 68 12 13.4624142714838 -1.46241427148376 69 15 15.7056355238544 -0.705635523854403 70 15 13.0394378460121 1.96056215398795 71 14 13.6162604253299 0.383739574670082 72 16 14.7056355238544 1.2943644761456 73 15 13.389328158551 1.61067184144897 74 15 13.4969376117181 1.50306238828192 75 13 14.7826518974324 -1.78265189743237 76 12 13.8178995871225 -1.81789958712246 77 17 14.3298354554288 2.67016454457116 78 13 13.1750424442653 -0.175042444265321 79 15 14.3336013269472 0.666398673052771 80 13 13.3976703918481 -0.397670391848056 81 15 14.8079938005079 0.192006199492061 82 16 12.9746939663763 3.02530603362366 83 15 14.384414389405 0.615585610595036 84 16 13.8079938005079 2.19200619949206 85 15 13.3245842789153 1.67541572108468 86 14 14.2650915757931 -0.265091575793129 87 15 14.7179080177967 0.28209198220334 88 14 13.7531557074868 0.246844292513246 89 13 14.2650915757931 -1.26509157579313 90 7 13.1102985646296 -6.11029856462961 91 17 15.1017552910223 1.89824470897773 92 13 14.1658243559231 -1.1658243559231 93 15 15.576147764583 -0.576147764582984 94 14 13.7428479304514 0.257152069548612 95 13 14.3196705097693 -1.31967050976925 96 16 14.576147764583 1.42385223541702 97 12 13.2598403992796 -1.25984039927961 98 14 14.2003476961574 -0.200347696157419 99 17 14.653164138161 2.34683586183905 100 15 12.8555139841403 2.14448601585971 101 17 14.2003476961574 2.79965230384258 102 12 12.2126568412831 -0.212656841283147 103 16 15.0370114113866 0.962988588613436 104 11 13.2681826325766 -2.26818263257664 105 15 15.5114038849473 -0.511403884947275 106 9 12.8452062071049 -3.84520620710493 107 16 14.2549266301335 1.74507336986646 108 15 13.6785060412365 1.32149395876348 109 10 12.3621986759332 -2.36219867593315 110 10 14.1356038165217 -4.13560381652171 111 15 15.421318102236 -0.421318102235996 112 11 13.6236679482153 -2.62366794821533 113 13 14.1356038165217 -1.13560381652171 114 14 12.1479129616474 1.85208703835256 115 18 14.9722675317509 3.02773246824915 116 16 13.2034387529409 2.79656124705907 117 14 15.4466600053116 -1.44666000531157 118 14 13.61336017118 0.386639828820031 119 14 14.1901827504978 -0.190182750497835 120 14 14.4466600053116 -0.446660005311566 121 12 13.1303526400082 -1.13035264000819 122 14 14.070859936886 -0.0708599368860008 123 15 15.3565742226003 -0.356574222600287 124 15 13.5589240685796 1.44107593142037 125 15 14.070859936886 0.929140063113999 126 13 12.9160669257225 0.0839330742775167 127 17 14.0746258084044 2.92537419159561 128 17 13.971592717016 3.02840728298403 129 19 15.3819161256759 3.61808387432414 130 15 13.5486162915443 1.45138370845574 131 13 13.2925410271514 -0.292541027151372 132 9 13.5490182819651 -4.5490182819651 133 15 13.0656087603725 1.93439123962751 134 15 13.1732182135395 1.82678178646046 135 15 14.4589324992538 0.541067500746177 136 16 13.4941801889439 2.50581981105608 137 11 13.1732182135395 -2.17321821353954 138 14 12.018425202376 1.98157479762398 139 11 14.8427797724794 -3.84277977247944 140 15 13.9068488373803 1.09315116261974 141 13 14.4842744023294 -1.48427440232939 142 15 13.4838724119085 1.51612758809145 143 16 13.2277971475157 2.77220285248434 144 14 14.3171722460401 -0.317172246040147 145 15 12.167967037026 2.83203296297398 146 16 13.9413721776146 2.05862782238542 147 16 15.2270864633289 0.772913536671132 148 11 12.5965384655975 -1.59653846559745 149 12 13.1084743339038 -1.10847433390383 150 9 11.9536813227403 -2.95368132274031 151 16 14.7780358928437 1.22196410715627 152 13 13.8421049577446 -0.842104957744553 153 16 14.4195305226937 1.58046947730632 154 12 13.4191285322728 -1.41912853227284 155 9 13.9959511115907 -4.9959511115907 156 13 14.2524283664044 -1.25242836640444 157 13 12.9361210011011 0.0638789988989338 158 14 13.8766282979789 0.123371702021128 159 19 15.1623425836932 3.83765741630684 160 13 13.3646924296725 -0.364692429672498 161 12 13.8766282979789 -1.87662829797887 162 13 12.7218352868154 0.278164713184645 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.775705067824097 0.448589864351806 0.224294932175903 18 0.746128161482611 0.507743677034777 0.253871838517389 19 0.687775784365806 0.624448431268388 0.312224215634194 20 0.573468452384091 0.853063095231818 0.426531547615909 21 0.663895747754116 0.672208504491767 0.336104252245884 22 0.779605055524588 0.440789888950823 0.220394944475412 23 0.78560816082384 0.428783678352319 0.21439183917616 24 0.90336718461727 0.193265630765461 0.0966328153827306 25 0.959230153041746 0.0815396939165085 0.0407698469582542 26 0.99343330600238 0.0131333879952384 0.00656669399761918 27 0.99009753291555 0.0198049341689004 0.00990246708445019 28 0.989604646725386 0.0207907065492291 0.0103953532746145 29 0.984265508843814 0.0314689823123727 0.0157344911561863 30 0.992827571666648 0.0143448566667038 0.00717242833335192 31 0.991407697786918 0.0171846044261647 0.00859230221308233 32 0.986865291940192 0.0262694161196157 0.0131347080598078 33 0.98148583112875 0.0370283377425002 0.0185141688712501 34 0.97819640356281 0.0436071928743788 0.0218035964371894 35 0.968925804442966 0.0621483911140675 0.0310741955570338 36 0.962294464023785 0.0754110719524299 0.037705535976215 37 0.970217659857038 0.0595646802859232 0.0297823401429616 38 0.964650523317504 0.0706989533649929 0.0353494766824964 39 0.96099782766173 0.0780043446765415 0.0390021723382708 40 0.94684130970796 0.106317380584081 0.0531586902920403 41 0.933607973129286 0.132784053741427 0.0663920268707137 42 0.929821612639292 0.140356774721416 0.070178387360708 43 0.920914786358303 0.158170427283395 0.0790852136416974 44 0.905480484235834 0.189039031528331 0.0945195157641656 45 0.93162770613833 0.136744587723339 0.0683722938616693 46 0.927730672242662 0.144538655514675 0.0722693277573375 47 0.90891960232965 0.1821607953407 0.0910803976703502 48 0.88523040943257 0.229539181134859 0.11476959056743 49 0.933547654149544 0.132904691700912 0.0664523458504561 50 0.914576876045954 0.170846247908093 0.0854231239540463 51 0.893924306132448 0.212151387735103 0.106075693867552 52 0.875445194216066 0.249109611567869 0.124554805783934 53 0.880035646738371 0.239928706523258 0.119964353261629 54 0.876117969990171 0.247764060019658 0.123882030009829 55 0.866686648545383 0.266626702909235 0.133313351454617 56 0.846521241959971 0.306957516080058 0.153478758040029 57 0.817821392478256 0.364357215043488 0.182178607521744 58 0.808311969804006 0.383376060391988 0.191688030195994 59 0.787275925243038 0.425448149513924 0.212724074756962 60 0.791714693935467 0.416570612129067 0.208285306064533 61 0.858014885913894 0.283970228172211 0.141985114086106 62 0.82925053753759 0.341498924924819 0.17074946246241 63 0.882759227359489 0.234481545281023 0.117240772640512 64 0.860031789966087 0.279936420067827 0.139968210033913 65 0.838174420516746 0.323651158966508 0.161825579483254 66 0.834459391537125 0.33108121692575 0.165540608462875 67 0.880006995328139 0.239986009343722 0.119993004671861 68 0.862418422209325 0.27516315558135 0.137581577790675 69 0.836532983449763 0.326934033100474 0.163467016550237 70 0.849255047687933 0.301489904624134 0.150744952312067 71 0.822563971338465 0.35487205732307 0.177436028661535 72 0.809661338853261 0.380677322293478 0.190338661146739 73 0.809688247358831 0.380623505282337 0.190311752641169 74 0.80017428448782 0.39965143102436 0.19982571551218 75 0.790512725905708 0.418974548188584 0.209487274094292 76 0.771068819803299 0.457862360393403 0.228931180196701 77 0.797771230780874 0.404457538438252 0.202228769219126 78 0.76338431478437 0.47323137043126 0.23661568521563 79 0.746359663275116 0.507280673449767 0.253640336724884 80 0.711375845891983 0.577248308216035 0.288624154108017 81 0.672508875852806 0.654982248294388 0.327491124147194 82 0.711957869223218 0.576084261553564 0.288042130776782 83 0.676336958887917 0.647326082224165 0.323663041112082 84 0.681335019470443 0.637329961059114 0.318664980529557 85 0.671432165325336 0.657135669349328 0.328567834674664 86 0.62575327341195 0.748493453176101 0.374246726588051 87 0.589044252375461 0.821911495249078 0.410955747624539 88 0.543314838660362 0.913370322679276 0.456685161339638 89 0.503252526963437 0.993494946073125 0.496747473036563 90 0.752453476560812 0.495093046878375 0.247546523439188 91 0.74579082256473 0.508418354870541 0.254209177435271 92 0.721066803438634 0.557866393122732 0.278933196561366 93 0.682609940792148 0.634780118415704 0.317390059207852 94 0.638425509761525 0.72314898047695 0.361574490238475 95 0.602588429207486 0.794823141585029 0.397411570792514 96 0.585129431772118 0.829741136455764 0.414870568227882 97 0.55071936788194 0.89856126423612 0.44928063211806 98 0.501075699707451 0.997848600585099 0.498924300292549 99 0.499404250461685 0.99880850092337 0.500595749538315 100 0.497843813947472 0.995687627894944 0.502156186052528 101 0.550549318162319 0.898901363675362 0.449450681837681 102 0.499188823631218 0.998377647262436 0.500811176368782 103 0.457277226433694 0.914554452867389 0.542722773566306 104 0.48074110271396 0.96148220542792 0.51925889728604 105 0.434443040619576 0.868886081239151 0.565556959380424 106 0.537196912721978 0.925606174556044 0.462803087278022 107 0.528555356746264 0.942889286507473 0.471444643253736 108 0.521048242264607 0.957903515470786 0.478951757735393 109 0.552687999976195 0.89462400004761 0.447312000023805 110 0.706095977352789 0.587808045294422 0.293904022647211 111 0.683074056428136 0.633851887143729 0.316925943571864 112 0.73090844998207 0.538183100035859 0.26909155001793 113 0.689991414814767 0.620017170370466 0.310008585185233 114 0.658529721148596 0.682940557702807 0.341470278851404 115 0.674207208843383 0.651585582313233 0.325792791156617 116 0.656840784360349 0.686318431279301 0.343159215639651 117 0.671411482753607 0.657177034492785 0.328588517246393 118 0.622219457023196 0.755561085953608 0.377780542976804 119 0.564167977514539 0.871664044970922 0.435832022485461 120 0.511241071257948 0.977517857484105 0.488758928742052 121 0.542704460216928 0.914591079566143 0.457295539783072 122 0.530109731518392 0.939780536963216 0.469890268481608 123 0.565338401823267 0.869323196353465 0.434661598176733 124 0.511117788407934 0.977764423184132 0.488882211592066 125 0.452975123840713 0.905950247681427 0.547024876159287 126 0.409366073569435 0.81873214713887 0.590633926430565 127 0.47077010991975 0.9415402198395 0.52922989008025 128 0.451670263406918 0.903340526813836 0.548329736593082 129 0.441577385010494 0.883154770020987 0.558422614989506 130 0.381072933333326 0.762145866666652 0.618927066666674 131 0.31627648808503 0.632552976170061 0.68372351191497 132 0.418826936106955 0.83765387221391 0.581173063893045 133 0.35437660924695 0.7087532184939 0.64562339075305 134 0.290611502722235 0.58122300544447 0.709388497277765 135 0.277946121308708 0.555892242617416 0.722053878691292 136 0.310059768236725 0.620119536473449 0.689940231763275 137 0.259378291935031 0.518756583870063 0.740621708064969 138 0.247872298225104 0.495744596450208 0.752127701774896 139 0.339946873949267 0.679893747898535 0.660053126050733 140 0.27575765560507 0.551515311210141 0.72424234439493 141 0.2658224440035 0.531644888007001 0.7341775559965 142 0.223806705780232 0.447613411560463 0.776193294219768 143 0.65103016033736 0.69793967932528 0.34896983966264 144 0.527406304056351 0.945187391887298 0.472593695943649 145 0.572119095440641 0.855761809118718 0.427880904559359 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 9 0.0697674418604651 NOK 10% type I error level 15 0.116279069767442 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/10or1i1290776646.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/10or1i1290776646.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/1z8m61290776646.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/1z8m61290776646.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/2z8m61290776646.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/2z8m61290776646.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/3ahm91290776646.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/3ahm91290776646.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/4ahm91290776646.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/4ahm91290776646.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/5ahm91290776646.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/5ahm91290776646.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/6k8lb1290776646.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/6k8lb1290776646.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/7dikf1290776646.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/7dikf1290776646.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/8dikf1290776646.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/8dikf1290776646.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/9dikf1290776646.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290780355oa6lf6ljqyh1o9g/9dikf1290776646.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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Software written by Ed van Stee & Patrick Wessa

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