Workshop7

*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, 20 Dec 2010 13:08:41 +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/20/t1292850535yvprq5yusq63rgi.htm/, Retrieved Mon, 20 Dec 2010 14:09:07 +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/20/t1292850535yvprq5yusq63rgi.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:

multiple regression

Dataseries X:

» Textbox « » Textfile « » CSV «

2 5 2 3 3 4 4 2 4 2 4 3 4 4 4 4 2 4 2 5 4 2 4 2 2 2 2 4 3 2 2 2 3 2 4 4 5 1 3 2 4 5 3 5 1 2 1 4 4 3 4 3 3 3 4 3 3 3 2 3 2 4 4 2 4 1 3 2 2 4 4 4 4 3 3 3 4 4 2 2 4 2 4 4 3 3 3 2 2 3 4 3 3 2 2 2 4 2 4 4 1 1 3 4 3 4 5 1 1 1 4 4 3 4 2 3 3 4 3 3 2 2 2 2 2 2 3 4 2 2 3 4 4 4 4 2 3 4 4 3 2 4 1 4 2 4 3 5 4 2 4 3 3 4 4 4 4 3 5 2 3 2 4 2 2 2 4 3 3 5 2 3 2 2 4 4 4 2 4 3 3 4 4 4 2 3 2 4 4 3 4 2 2 2 3 4 4 4 3 1 2 4 4 4 4 2 3 2 4 4 1 4 1 2 3 4 5 4 4 4 4 4 4 4 5 2 1 4 1 4 4 2 4 2 5 3 4 4 4 4 2 2 3 4 3 3 5 2 4 2 5 4 2 5 2 4 1 4 3 4 4 2 2 1 2 4 5 3 2 4 2 4 4 4 4 2 4 2 4 3 4 5 2 2 2 5 5 4 4 2 3 1 4 4 3 4 2 2 2 2 3 4 5 2 4 1 4 3 2 4 2 3 2 4 3 2 5 1 1 2 4 4 4 4 2 2 4 2 4 2 4 1 5 2 5 4 4 4 2 2 2 4 4 4 3 1 4 2 4 4 1 4 1 4 1 4 4 4 4 2 2 2 4 4 2 4 2 2 2 4 5 1 2 1 2 1 3 3 4 3 5 4 5 5 3 3 5 2 3 2 4 5 2 4 2 4 2 4 5 4 4 1 2 2 4 4 3 5 1 3 1 4 4 2 3 2 2 3 2 3 2 5 2 2 1 4 4 3 4 1 3 1 4 4 2 5 1 2 2 4 5 1 4 2 3 3 4 4 3 4 1 2 2 3 4 2 5 1 4 2 4 5 3 4 2 2 2 2 4 3 4 1 5 4 4 3 3 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation mistakes[t] = + 1.98324156116145 -0.0448001902119397standards[t] -0.0356772706903457organization[t] + 0.351017163481253punished[t] + 0.112612004015097secondrate[t] -0.0911763790187378competent[t] -0.0725515712595284neat[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) 1.98324156116145 0.523112 3.7912 0.000216 0.000108 standards -0.0448001902119397 0.075288 -0.595 0.552697 0.276348 organization -0.0356772706903457 0.086798 -0.411 0.681624 0.340812 punished 0.351017163481253 0.079883 4.3941 2.1e-05 1e-05 secondrate 0.112612004015097 0.071574 1.5734 0.117714 0.058857 competent -0.0911763790187378 0.089734 -1.0161 0.311209 0.155604 neat -0.0725515712595284 0.092819 -0.7816 0.435636 0.217818 Multiple Linear Regression - Regression Statistics Multiple R 0.406253173307400 R-squared 0.165041640822333 Adjusted R-squared 0.132082758223214 F-TEST (value) 5.00750109855809 F-TEST (DF numerator) 6 F-TEST (DF denominator) 152 p-value 0.000103787659412546 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.848151185471069 Sum Squared Residuals 109.342785879229 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3 2.10021336518055 0.899786634819452 2 3 2.24850263988602 0.751497360113985 3 2 2.0677258804434 -0.0677258804433997 4 2 2.2056313898933 -0.205631389893299 5 3 2.23218574106205 0.76781425893795 6 2 1.58704425001591 0.412955749984087 7 1 1.59178400747228 -0.591784007472284 8 3 2.51465918039976 0.485340819600239 9 2 2.12676771634932 -0.126767716349325 10 2 1.96722623042714 0.0327737695728583 11 3 2.83950096142828 0.160499038571717 12 2 2.23025680084283 -0.230256800842827 13 2 2.45634925483422 -0.456349254834219 14 2 2.15925885485328 -0.159258854853285 15 3 1.54260065519512 1.45739934480488 16 1 1.43437181324525 -0.434371813245248 17 3 2.16364201691851 0.836357983081492 18 2 2.37728888358111 -0.377288883581106 19 3 1.97847844164388 1.02152155835612 20 4 2.11884182670657 1.88115817329343 21 2 1.97003704766429 0.0299629523357089 22 3 2.20527844826893 0.794721551731066 23 5 3.00322891170655 1.99677108829345 24 2 2.09583020311535 -0.0958302031153507 25 2 2.23776593300611 -0.237765933006109 26 3 2.25007863848087 0.749921361519126 27 2 2.04629025544704 -0.0462902554470395 28 2 2.06965482066262 -0.0696548206626204 29 2 2.1720834108981 -0.172083410898099 30 2 2.04629025544704 -0.0462902554470395 31 3 1.64451008732698 1.35548991267302 32 4 2.86093658642464 1.13906341357536 33 1 1.83443944714963 -0.834439447149635 34 3 2.36111464390111 0.638885356098888 35 3 2.00622982269147 0.993770177308529 36 2 2.07684879996499 -0.0768487999649925 37 1 2.2853769404552 -1.28537694045520 38 1 2.11603100946942 -1.11603100946942 39 2 2.14977933994054 -0.149779339940542 40 2 2.23145383072166 -0.231453830721665 41 2 1.73427303046333 0.265726969536669 42 1 2.04629025544704 -1.04629025544704 43 2 2.23338277094089 -0.233382770940887 44 1 2.19577656003132 -1.19577656003132 45 2 2.20844220713045 -0.208442207130447 46 2 1.52397219366913 0.476027806330873 47 4 2.11603100946942 1.88396899053058 48 2 1.91892110140112 0.0810788985988785 49 2 1.93367825143194 0.0663217485680571 50 2 1.84356236667123 0.156437633328771 51 1 1.94228566661670 -0.942285666616702 52 2 1.93367825143194 0.0663217485680571 53 2 1.95072706059629 0.0492729394037062 54 1 1.95214415024547 -0.952144150245467 55 5 3.22900621283703 1.77099378716297 56 2 1.98286160370911 0.0171383962908947 57 2 2.17595106862649 -0.175951068626487 58 2 1.58266108795069 0.41733891204931 59 1 1.70439601148738 -0.704396011487381 60 3 2.31386023184317 0.686139768156828 61 1 1.98760136116548 -0.987601361165477 62 1 1.74007328217773 -0.740073282177726 63 2 1.56403262642470 0.435967373575305 64 3 2.18069082608286 0.819309173917141 65 2 1.71863765718137 0.281362342818632 66 2 1.78925663445489 0.210743365545111 67 2 2.16083119968136 -0.160831199681358 68 4 2.03784886146745 1.96215113853255 69 1 1.47917200345719 -0.479172003457187 70 2 2.13589063587092 -0.135890635870919 71 2 1.66313854885298 0.336861451147025 72 2 1.67226146837457 0.327738531625431 73 2 2.36163014823795 -0.361630148237947 74 2 2.56541853127178 -0.565418531271781 75 1 2.12322498877179 -1.12322498877179 76 2 2.09583020311535 -0.0958302031153507 77 2 1.74007328217773 0.259926717822274 78 2 2.54679372351257 -0.546793723512572 79 2 1.87024959969401 0.129750400305991 80 1 1.93367825143194 -0.933678251431943 81 4 2.14027379793614 1.85972620206386 82 2 2.12395689911218 -0.123956899112175 83 3 1.94386166521156 1.05613833478844 84 2 2.54453619937571 -0.544536199375711 85 1 1.87604985140840 -0.876049851408404 86 2 1.89906147499962 0.100938525000379 87 2 1.78487347238967 0.215126527610334 88 1 1.45142062240960 -0.451420622409599 89 2 2.74832458240955 -0.748324582409546 90 1 2.05103001290341 -1.05103001290341 91 2 1.93367825143194 0.0663217485680571 92 1 1.68770014394739 -0.687700143947393 93 2 1.82055074308001 0.179449256919988 94 2 1.66313854885298 0.336861451147025 95 3 2.40643033844989 0.593569661550113 96 4 2.80189475051872 1.19810524948128 97 1 2.83792496283342 -1.83792496283342 98 3 2.62727118441486 0.372728815585143 99 1 2.18858258072895 -1.18858258072895 100 1 2.14220639192215 -1.14220639192215 101 2 2.56103536920656 -0.561035369206559 102 1 1.79118922844090 -0.791189228440896 103 3 2.47459874764419 0.525401252355808 104 2 2.09583020311535 -0.0958302031153507 105 2 2.16521436174658 -0.165214361746581 106 1 2.66874870681960 -1.66874870681960 107 2 2.21475796318168 -0.214757963181677 108 2 2.98183107547364 -0.981831075473644 109 1 2.46985899018782 -1.46985899018782 110 2 1.77887652296613 0.221123477033869 111 2 1.59690273364468 0.403097266355323 112 4 2.04629025544704 1.95370974455296 113 3 2.05051450856658 0.949485491433424 114 2 2.63165800024687 -0.631658000246865 115 5 2.29961858614918 2.70038141385082 116 1 2.18226682467772 -1.18226682467772 117 2 2.26274793934679 -0.262747939346788 118 1 1.91526984967628 -0.915269849676284 119 2 2.44368360773509 -0.443683607735091 120 1 1.99059444940951 -0.990594449409508 121 1 1.81262485343725 -0.812624853437255 122 2 2.17788366261249 -0.177883662612494 123 2 2.66294845510520 -0.662948455105203 124 2 1.89642498214674 0.103575017853261 125 3 1.67226146837457 1.32773853162543 126 2 2.28575590917122 -0.285755909171220 127 1 1.97161304625915 -0.97161304625915 128 2 2.18226682467772 -0.182266824677717 129 2 1.83124966119646 0.168750338803536 130 3 2.09109044565898 0.90890955434102 131 2 2.69069983615279 -0.690699836152791 132 2 2.06965482066262 -0.0696548206626204 133 2 1.57985027071354 0.420149729286459 134 1 1.78644947098452 -0.786449470984525 135 2 2.20563138989330 -0.205631389893298 136 2 2.04629025544704 -0.0462902554470395 137 2 1.78049031032444 0.219509689675557 138 3 2.15133296521053 0.848667034789472 139 1 2.44210760914023 -1.44210760914023 140 3 2.82441888124661 0.175581118753392 141 4 2.39240875252624 1.60759124747376 142 2 2.93191215908931 -0.931912159089312 143 5 3.32211518584178 1.67788481415822 144 1 1.67226146837457 -0.672261468374569 145 2 2.36043311835911 -0.360433118359110 146 3 2.20370244967408 0.796297550325924 147 2 2.22075491260521 -0.220754912605212 148 2 2.36623337007350 -0.366233370073505 149 3 1.84110814482523 1.15889185517477 150 2 2.86093658642464 -0.860936586424642 151 1 2.28575590917122 -1.28575590917122 152 2 2.04629025544704 -0.0462902554470395 153 1 2.00835546061983 -1.00835546061983 154 2 1.89029515086918 0.109704849130824 155 3 2.71896306777043 0.281036932229570 156 2 2.14220639192215 -0.142206391922149 157 2 1.99991406664024 8.59333597585943e-05 158 2 2.74832458240955 -0.748324582409546 159 4 3.03890618239689 0.961093817603105 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.352715975565943 0.705431951131887 0.647284024434057 11 0.277963878119080 0.555927756238159 0.72203612188092 12 0.191392937743574 0.382785875487147 0.808607062256426 13 0.171569439567146 0.343138879134293 0.828430560432854 14 0.104949392051952 0.209898784103903 0.895050607948048 15 0.309962060795372 0.619924121590745 0.690037939204628 16 0.285325632406166 0.570651264812333 0.714674367593834 17 0.228960465554080 0.457920931108161 0.77103953444592 18 0.202849121426438 0.405698242852876 0.797150878573562 19 0.198906172088537 0.397812344177073 0.801093827911463 20 0.380874195452934 0.761748390905868 0.619125804547066 21 0.323791842435448 0.647583684870896 0.676208157564552 22 0.262275826422600 0.524551652845201 0.7377241735774 23 0.315538899442759 0.631077798885519 0.68446110055724 24 0.25634593246702 0.51269186493404 0.74365406753298 25 0.265739644390045 0.53147928878009 0.734260355609955 26 0.216172449176573 0.432344898353146 0.783827550823427 27 0.183723952525237 0.367447905050473 0.816276047474763 28 0.142772910485341 0.285545820970683 0.857227089514659 29 0.115602925107619 0.231205850215238 0.884397074892381 30 0.09282291564002 0.18564583128004 0.90717708435998 31 0.227247226223229 0.454494452446459 0.77275277377677 32 0.205710745467017 0.411421490934033 0.794289254532983 33 0.196178554957584 0.392357109915167 0.803821445042416 34 0.160467430250672 0.320934860501345 0.839532569749328 35 0.151572721094488 0.303145442188977 0.848427278905512 36 0.140319277490859 0.280638554981718 0.859680722509141 37 0.291821416618421 0.583642833236842 0.708178583381579 38 0.370101681471218 0.740203362942435 0.629898318528782 39 0.322720718654777 0.645441437309554 0.677279281345223 40 0.285788330608009 0.571576661216018 0.714211669391991 41 0.241778721526182 0.483557443052364 0.758221278473818 42 0.291475304688045 0.58295060937609 0.708524695311955 43 0.253112179028578 0.506224358057156 0.746887820971422 44 0.312632786830447 0.625265573660894 0.687367213169553 45 0.276039610148505 0.552079220297011 0.723960389851495 46 0.240815729362455 0.481631458724911 0.759184270637544 47 0.406877544701012 0.813755089402025 0.593122455298988 48 0.358708194454982 0.717416388909963 0.641291805545018 49 0.312941240044693 0.625882480089385 0.687058759955308 50 0.271795561717541 0.543591123435083 0.728204438282459 51 0.281585701795328 0.563171403590657 0.718414298204672 52 0.242013194465550 0.484026388931099 0.75798680553445 53 0.207687572759024 0.415375145518047 0.792312427240977 54 0.208004149561892 0.416008299123784 0.791995850438108 55 0.26710505100312 0.53421010200624 0.73289494899688 56 0.231150572816907 0.462301145633815 0.768849427183093 57 0.198478568416999 0.396957136833998 0.801521431583001 58 0.175110907148329 0.350221814296657 0.824889092851671 59 0.162648643269964 0.325297286539928 0.837351356730036 60 0.150860188080797 0.301720376161594 0.849139811919203 61 0.176595837815979 0.353191675631957 0.823404162184021 62 0.164893177623181 0.329786355246363 0.835106822376819 63 0.146495074699753 0.292990149399506 0.853504925300247 64 0.142211737935220 0.284423475870440 0.85778826206478 65 0.120871514609047 0.241743029218093 0.879128485390953 66 0.101289883276544 0.202579766553088 0.898710116723456 67 0.0843420417589644 0.168684083517929 0.915657958241036 68 0.224903794163126 0.449807588326251 0.775096205836874 69 0.199703054563544 0.399406109127089 0.800296945436455 70 0.170330212858117 0.340660425716233 0.829669787141883 71 0.147757189279436 0.295514378558872 0.852242810720564 72 0.126977791172763 0.253955582345526 0.873022208827237 73 0.116476071292291 0.232952142584583 0.883523928707709 74 0.111513845364528 0.223027690729056 0.888486154635472 75 0.131294660681711 0.262589321363421 0.86870533931829 76 0.109245629762387 0.218491259524773 0.890754370237613 77 0.09091278165218 0.18182556330436 0.90908721834782 78 0.0831038694515817 0.166207738903163 0.916896130548418 79 0.0669585920189706 0.133917184037941 0.93304140798103 80 0.0730142995906573 0.146028599181315 0.926985700409343 81 0.161597472052288 0.323194944104576 0.838402527947712 82 0.137946743664369 0.275893487328737 0.862053256335631 83 0.161641711589859 0.323283423179717 0.838358288410141 84 0.153689771163911 0.307379542327823 0.846310228836089 85 0.151844735594494 0.303689471188987 0.848155264405506 86 0.127305570538416 0.254611141076832 0.872694429461584 87 0.106764849843906 0.213529699687811 0.893235150156094 88 0.0901117461389476 0.180223492277895 0.909888253861052 89 0.090305562986289 0.180611125972578 0.90969443701371 90 0.101808604105203 0.203617208210405 0.898191395894797 91 0.08232245826905 0.1646449165381 0.91767754173095 92 0.0758198256511452 0.151639651302290 0.924180174348855 93 0.0612271039650575 0.122454207930115 0.938772896034943 94 0.0498262439651128 0.0996524879302256 0.950173756034887 95 0.0447029985387487 0.0894059970774975 0.955297001461251 96 0.0667511441620525 0.133502288324105 0.933248855837947 97 0.143777626128969 0.287555252257938 0.856222373871031 98 0.127427385939969 0.254854771879939 0.87257261406003 99 0.151628072711570 0.303256145423140 0.84837192728843 100 0.178278331765886 0.356556663531772 0.821721668234114 101 0.158583781849215 0.317167563698431 0.841416218150785 102 0.157914949453463 0.315829898906927 0.842085050546536 103 0.137950928633337 0.275901857266673 0.862049071366663 104 0.114342973548493 0.228685947096986 0.885657026451507 105 0.092834013403872 0.185668026807744 0.907165986596128 106 0.154832112230900 0.309664224461799 0.8451678877691 107 0.135955701434288 0.271911402868575 0.864044298565712 108 0.151203801079506 0.302407602159012 0.848796198920494 109 0.207572983787708 0.415145967575417 0.792427016212292 110 0.183597106085566 0.367194212171133 0.816402893914434 111 0.158778734986541 0.317557469973081 0.84122126501346 112 0.399617241391685 0.799234482783369 0.600382758608315 113 0.402964735556398 0.805929471112796 0.597035264443602 114 0.361152486379275 0.72230497275855 0.638847513620725 115 0.801500541855713 0.396998916288574 0.198499458144287 116 0.817603888578167 0.364792222843665 0.182396111421833 117 0.78676933250307 0.426461334993859 0.213230667496929 118 0.835795253310034 0.328409493379932 0.164204746689966 119 0.800895915395927 0.398208169208146 0.199104084604073 120 0.88539658159547 0.229206836809060 0.114603418404530 121 0.88260146855642 0.234797062887161 0.117398531443580 122 0.870665836917677 0.258668326164647 0.129334163082323 123 0.855399045863073 0.289201908273853 0.144600954136927 124 0.82178328383578 0.356433432328438 0.178216716164219 125 0.887962295755088 0.224075408489824 0.112037704244912 126 0.855360633798462 0.289278732403077 0.144639366201538 127 0.860790577384936 0.278418845230129 0.139209422615064 128 0.821359236928516 0.357281526142967 0.178640763071484 129 0.78194308070384 0.436113838592319 0.218056919296159 130 0.854692180903269 0.290615638193462 0.145307819096731 131 0.873839554623619 0.252320890752762 0.126160445376381 132 0.833533629922564 0.332932740154872 0.166466370077436 133 0.836330870200716 0.327338259598567 0.163669129799284 134 0.807996426363343 0.384007147273315 0.192003573636657 135 0.752412452359531 0.495175095280939 0.247587547640469 136 0.704715710304391 0.590568579391217 0.295284289695609 137 0.634069440671403 0.731861118657193 0.365930559328597 138 0.570579583786858 0.858840832426284 0.429420416213142 139 0.629843995684016 0.740312008631968 0.370156004315984 140 0.562173537024349 0.875652925951303 0.437826462975651 141 0.734037177382132 0.531925645235736 0.265962822617868 142 0.75494226671308 0.49011546657384 0.24505773328692 143 0.717399590928025 0.565200818143949 0.282600409071975 144 0.74923458451143 0.501530830977138 0.250765415488569 145 0.710073023074733 0.579853953850533 0.289926976925267 146 0.796597528256857 0.406804943486285 0.203402471743143 147 0.687244937080654 0.625510125838693 0.312755062919346 148 0.543311030323723 0.913377939352553 0.456688969676277 149 0.456480885930606 0.912961771861213 0.543519114069394 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 0 0 OK 10% type I error level 2 0.0142857142857143 OK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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Software written by Ed van Stee & Patrick Wessa

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