*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, 14 Dec 2010 11:10:42 +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/14/t1292325014pqlg8ovran0gspl.htm/, Retrieved Tue, 14 Dec 2010 12:12:28 +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/14/t1292325014pqlg8ovran0gspl.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 «

3 3 4 2 5 3 3 2 2 4 4 4 2 4 4 3 3 2 3 3 3 2 2 3 4 3 3 2 1 4 3 4 5 4 4 2 2 4 2 4 3 3 4 2 4 3 4 2 2 2 3 3 4 4 1 3 3 2 3 4 3 4 4 3 3 2 2 4 2 5 3 2 1 3 5 3 3 4 2 5 2 2 3 3 5 3 4 4 3 3 2 2 1 2 4 1 1 2 2 3 2 3 1 1 3 3 4 4 4 3 3 2 4 3 4 3 3 1 2 4 3 3 4 3 4 3 4 5 3 4 2 3 4 4 4 3 3 4 3 3 3 4 4 3 3 4 4 2 2 4 3 4 2 2 4 3 3 4 4 3 3 4 4 4 4 3 3 2 2 4 2 2 3 2 4 3 4 4 3 4 3 3 3 3 4 3 2 2 3 2 3 4 4 3 4 4 4 4 4 3 3 4 3 3 4 3 4 1 1 3 1 2 2 2 5 2 2 4 2 4 3 3 2 3 4 4 4 3 4 3 4 5 4 3 3 2 2 1 2 5 1 3 3 2 4 3 3 4 3 4 3 2 1 3 4 1 2 4 4 4 3 3 3 3 4 2 2 1 2 4 3 4 1 2 4 3 3 4 2 4 2 3 4 2 3 4 4 4 3 3 1 1 2 1 5 3 4 4 5 3 2 2 2 2 4 4 4 4 3 4 3 4 5 4 3 4 4 3 4 4 3 2 2 2 3 3 4 4 3 4 3 2 4 3 4 3 4 2 3 4 3 4 3 3 4 1 1 1 1 5 3 4 4 3 4 3 4 4 3 4 3 3 4 3 4 2 3 4 4 2 3 3 3 3 3 3 3 4 4 4 3 3 3 3 4 2 3 3 3 3 3 4 2 2 4 2 1 1 1 4 2 3 2 2 4 3 4 4 3 3 3 3 3 3 4 2 3 5 2 4 2 4 1 2 5 3 3 3 3 4 2 2 2 2 5 3 3 3 3 3 4 4 4 4 3 2 3 3 2 4 3 4 3 3 4 2 3 4 3 4 4 4 4 4 4 3 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 0.958098198311375 + 0.497466363851451Friends[t] -0.131819434513708Known[t] + 0.303489208454995Nfriends[t] -0.0335165464291636Before[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) 0.958098198311375 0.327385 2.9265 0.003958 0.001979 Friends 0.497466363851451 0.059428 8.3709 0 0 Known -0.131819434513708 0.046904 -2.8104 0.005604 0.002802 Nfriends 0.303489208454995 0.064511 4.7044 6e-06 3e-06 Before -0.0335165464291636 0.062163 -0.5392 0.590564 0.295282 Multiple Linear Regression - Regression Statistics Multiple R 0.70337646006034 R-squared 0.494738444567015 Adjusted R-squared 0.481354032502565 F-TEST (value) 36.9637786243207 F-TEST (DF numerator) 4 F-TEST (DF denominator) 151 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.563332541287094 Sum Squared Residuals 47.9188763630193 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3 2.36261523657507 0.637384763424932 2 3 2.65977065203165 0.340229347968354 3 4 3.76421543279309 0.235784567206915 4 3 2.9967764069158 0.00322359308419623 5 3 2.46579349663519 0.534206503364812 6 3 2.35628144357665 0.64371855642335 7 3 3.36875712925196 -0.36875712925196 8 2 1.89866541915278 0.101334580847222 9 3 2.39613178300423 0.603868216995772 10 3 3.22427010874142 -0.224270108741423 11 3 3.10365983920171 -0.103659839201708 12 3 2.96325986048664 0.0367401395133602 13 3 3.23060390173984 -0.230603901739837 14 2 1.86514887272361 0.134851127276386 15 3 2.56409638471973 0.435903615280266 16 3 2.36261523657506 0.637384763424935 17 2 2.30045751569232 -0.300457515692317 18 3 3.23060390173984 -0.230603901739837 19 2 2.29412372269390 -0.294123722693903 20 1 1.69835447075791 -0.698354470757908 21 2 2.52161742451952 -0.521617424519523 22 3 3.53409311019483 -0.534093110194832 23 3 2.20215462760777 0.797845372392228 24 3 2.79159008654535 0.208409913454647 25 3 2.69962099145922 0.300379008540777 26 3 3.06526792079697 -0.0652679207969651 27 2 3.00311019991422 -1.00311019991422 28 3 2.73313753788839 0.266862462111613 29 3 3.23060390173984 -0.230603901739837 30 4 3.15723701588310 0.842762984116904 31 3 3.15723701588310 -0.157237015883096 32 3 3.03662674634338 -0.0366267463433812 33 3 3.50057656376567 -0.500576563765668 34 3 2.65977065203165 0.340229347968355 35 2 2.03048485366649 -0.0304848536664862 36 3 3.19708735531067 -0.197087355310674 37 3 2.83144042597293 0.168559574027069 38 3 2.53282658949352 0.467173410506484 39 3 3.19708735531067 -0.197087355310674 40 4 3.53409311019483 0.465906889805168 41 3 3.32890678982438 -0.328906789824382 42 3 3.01908378837097 -0.0190837883709731 43 1 2.12878774175103 -1.12878774175103 44 2 1.89866541915278 0.101334580847222 45 3 2.96325986048664 0.0367401395133602 46 4 3.66591254470854 0.33408745529146 47 4 3.72807026559129 0.271929734408712 48 2 2.26060717626474 -0.260607176264739 49 1 2.52795121751794 -1.52795121751794 50 3 2.69962099145922 0.300379008540777 51 3 2.5976129311489 0.402387068851102 52 1 2.50564383606277 -1.50564383606277 53 3 2.83144042597293 0.168559574027069 54 2 2.29412372269390 -0.294123722693903 55 3 3.28905645039680 -0.289056450396804 56 3 2.39613178300423 0.603868216995772 57 2 2.42964832943339 -0.429648329433392 58 4 3.23060390173984 0.769396098260163 59 1 1.32783216944459 -0.327832169444586 60 3 3.83758231864983 -0.837582318649827 61 2 2.16230428818019 -0.162304288180195 62 4 3.19708735531067 0.802912644689326 63 3 3.40227367568112 -0.402273675681123 64 4 3.63239599827938 0.367604001720624 65 3 2.19582083460936 0.804179165390642 66 3 3.19708735531067 -0.197087355310674 67 3 2.20215462760777 0.797845372392228 68 3 3.46072622433809 -0.46072622433809 69 3 3.32890678982438 -0.328906789824382 70 1 1.45965160395829 -0.459651603958294 71 3 3.19708735531067 -0.197087355310674 72 3 3.19708735531067 -0.197087355310674 73 3 2.69962099145922 0.300379008540777 74 2 3.07014329277254 -1.07014329277254 75 3 2.86495697240210 0.135043027597905 76 3 3.00311019991422 -0.00311019991421758 77 3 2.83144042597293 0.168559574027069 78 2 2.86495697240210 -0.864956972402095 79 3 3.15723701588310 -0.157237015883096 80 2 1.49316815038746 0.506831849612542 81 2 2.65977065203165 -0.659770652031645 82 3 3.23060390173984 -0.230603901739837 83 3 2.83144042597293 0.168559574027069 84 2 2.26431234849052 -0.26431234849052 85 2 3.25553990396764 -1.25553990396764 86 3 2.83144042597293 0.168559574027069 87 2 2.12878774175103 -0.128787741751031 88 3 2.86495697240210 0.135043027597905 89 4 3.53409311019483 0.465906889805168 90 2 2.52795121751794 -0.527951217517937 91 3 3.32890678982438 -0.328906789824382 92 2 2.69962099145922 -0.699620991459223 93 4 3.50057656376567 0.499423436234332 94 3 3.23060390173984 -0.230603901739837 95 3 2.65977065203165 0.340229347968355 96 3 2.16230428818019 0.837695711819805 97 3 2.16717966015577 0.832820339844226 98 2 2.26060717626474 -0.260607176264739 99 3 2.2691877204661 0.7308122795339 100 4 2.96325986048664 1.03674013951336 101 4 3.53409311019483 0.465906889805168 102 4 3.63239599827938 0.367604001720624 103 3 2.53428501051635 0.465714989483649 104 3 2.55513397094869 0.444866029051314 105 1 1.52668469681662 -0.526684696816621 106 4 3.23323252251247 0.76676747748753 107 1 2.39613178300423 -1.39613178300423 108 3 3.53409311019483 -0.534093110194832 109 2 2.06400140009565 -0.0640014000956498 110 2 1.93218196558194 0.0678180344180585 111 3 2.73313753788839 0.266862462111613 112 3 2.90480731182967 0.095192688170327 113 2 3.09507929500035 -1.09507929500035 114 3 3.19708735531067 -0.197087355310674 115 3 3.50057656376567 -0.500576563765668 116 4 2.86008160042652 1.13991839957348 117 4 3.46072622433809 0.53927377566191 118 3 2.46579349663519 0.534206503364811 119 3 2.69962099145922 0.300379008540777 120 3 3.02541758136939 -0.0254175813693874 121 3 2.52795121751794 0.472048782482063 122 3 2.92711469328484 0.0728853067151573 123 1 2.16230428818019 -1.16230428818019 124 2 3.46706001733650 -1.46706001733650 125 4 3.19708735531067 0.802912644689326 126 3 2.79159008654535 0.208409913454647 127 4 3.50057656376567 0.499423436234332 128 3 2.69962099145922 0.300379008540777 129 2 2.59498431037626 -0.594984310376264 130 1 1.49316815038746 -0.493168150387458 131 4 3.50057656376567 0.499423436234332 132 3 3.36242333625355 -0.362423336253546 133 3 2.16230428818019 0.837695711819805 134 3 2.49443467108877 0.505565328911227 135 4 3.19708735531067 0.802912644689326 136 3 2.65977065203165 0.340229347968355 137 3 3.23060390173984 -0.230603901739837 138 1 1.89866541915278 -0.898665419152778 139 4 3.82637315367583 0.173626846324168 140 2 2.69962099145922 -0.699620991459223 141 2 2.89359814685568 -0.89359814685568 142 3 2.69962099145922 0.300379008540777 143 3 2.89359814685568 0.106401853144321 144 2 2.03048485366649 -0.0304848536664862 145 3 2.52795121751794 0.472048782482063 146 3 3.06156274857118 -0.0615627485711845 147 2 2.16230428818019 -0.162304288180195 148 2 2.66610444503006 -0.666104445030059 149 3 3.23060390173984 -0.230603901739837 150 4 3.63239599827938 0.367604001720624 151 4 3.16844618085709 0.83155381914291 152 4 3.50057656376567 0.499423436234332 153 2 2.03048485366649 -0.0304848536664862 154 3 3.23060390173984 -0.230603901739837 155 3 3.23060390173984 -0.230603901739837 156 3 2.09264257454923 0.907357425450766 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.0130345641773373 0.0260691283546747 0.986965435822663 9 0.0511455987174925 0.102291197434985 0.948854401282508 10 0.0181952465942219 0.0363904931884438 0.981804753405778 11 0.0418584506914566 0.0837169013829133 0.958141549308543 12 0.0267434372452707 0.0534868744905414 0.97325656275473 13 0.0126915348669953 0.0253830697339907 0.987308465133005 14 0.0118779676398048 0.0237559352796096 0.988122032360195 15 0.0056184730760953 0.0112369461521906 0.994381526923905 16 0.00385138810622494 0.00770277621244988 0.996148611893775 17 0.0105001230074836 0.0210002460149673 0.989499876992516 18 0.00597221991731835 0.0119444398346367 0.994027780082682 19 0.0131755992924072 0.0263511985848143 0.986824400707593 20 0.0219538412285344 0.0439076824570688 0.978046158771466 21 0.0315872447784621 0.0631744895569241 0.968412755221538 22 0.0299623331868863 0.0599246663737727 0.970037666813114 23 0.0543582667613231 0.108716533522646 0.945641733238677 24 0.0369105692914719 0.0738211385829437 0.963089430708528 25 0.0252796233103352 0.0505592466206703 0.974720376689665 26 0.0183354495334467 0.0366708990668935 0.981664550466553 27 0.0631720560470741 0.126344112094148 0.936827943952926 28 0.053787975641766 0.107575951283532 0.946212024358234 29 0.0388934611019506 0.0777869222039013 0.96110653889805 30 0.0488691777188672 0.0977383554377343 0.951130822281133 31 0.0424135748192401 0.0848271496384801 0.95758642518076 32 0.0314091696571541 0.0628183393143083 0.968590830342846 33 0.0295596986852998 0.0591193973705995 0.9704403013147 34 0.0216279477892319 0.0432558955784639 0.978372052210768 35 0.0155908746072287 0.0311817492144574 0.984409125392771 36 0.0116691826435618 0.0233383652871236 0.988330817356438 37 0.00798592720306734 0.0159718544061347 0.992014072796933 38 0.0112663578019954 0.0225327156039909 0.988733642198005 39 0.00807309530779549 0.0161461906155910 0.991926904692205 40 0.0104343776014087 0.0208687552028173 0.989565622398591 41 0.00853496459356752 0.0170699291871350 0.991465035406432 42 0.00585783486999089 0.0117156697399818 0.994142165130009 43 0.0391553314178993 0.0783106628357987 0.9608446685821 44 0.0288556076751749 0.0577112153503499 0.971144392324825 45 0.0209036815831272 0.0418073631662545 0.979096318416873 46 0.0188545259450987 0.0377090518901973 0.981145474054901 47 0.0146138797390726 0.0292277594781452 0.985386120260927 48 0.0117102849300912 0.0234205698601824 0.98828971506991 49 0.104062058418541 0.208124116837081 0.89593794158146 50 0.0882930218951066 0.176586043790213 0.911706978104893 51 0.0798359871953379 0.159671974390676 0.920164012804662 52 0.252164377405133 0.504328754810266 0.747835622594867 53 0.217616979056440 0.435233958112881 0.78238302094356 54 0.191746828073266 0.383493656146532 0.808253171926734 55 0.171225062454845 0.342450124909690 0.828774937545155 56 0.172769888345656 0.345539776691312 0.827230111654344 57 0.161665021301576 0.323330042603151 0.838334978698424 58 0.190451085913222 0.380902171826443 0.809548914086778 59 0.169398223363954 0.338796446727907 0.830601776636046 60 0.200139060608901 0.400278121217801 0.7998609393911 61 0.169851493376705 0.33970298675341 0.830148506623295 62 0.201095276254838 0.402190552509675 0.798904723745162 63 0.183991177239672 0.367982354479343 0.816008822760328 64 0.167899639711387 0.335799279422775 0.832100360288613 65 0.207331483651165 0.414662967302329 0.792668516348835 66 0.179400171646909 0.358800343293817 0.820599828353092 67 0.215769514301506 0.431539028603012 0.784230485698494 68 0.203368503082949 0.406737006165898 0.796631496917051 69 0.181614115942875 0.363228231885751 0.818385884057125 70 0.172515711659917 0.345031423319834 0.827484288340083 71 0.147466147000028 0.294932294000056 0.852533852999972 72 0.124879659099005 0.24975931819801 0.875120340900995 73 0.108233074959875 0.216466149919749 0.891766925040125 74 0.17632247628762 0.35264495257524 0.82367752371238 75 0.149843958105749 0.299687916211497 0.850156041894251 76 0.125937295533086 0.251874591066171 0.874062704466914 77 0.105316787815026 0.210633575630053 0.894683212184973 78 0.139200936405623 0.278401872811246 0.860799063594377 79 0.117064502375354 0.234129004750708 0.882935497624646 80 0.113333838586868 0.226667677173736 0.886666161413132 81 0.121577367121563 0.243154734243125 0.878422632878437 82 0.103619552760358 0.207239105520716 0.896380447239642 83 0.0858299206140278 0.171659841228056 0.914170079385972 84 0.0731915726662953 0.146383145332591 0.926808427333705 85 0.156862934671143 0.313725869342285 0.843137065328857 86 0.132905444127504 0.265810888255007 0.867094555872496 87 0.110116414554418 0.220232829108837 0.889883585445582 88 0.0908035804795388 0.181607160959078 0.90919641952046 89 0.0844839207359597 0.168967841471919 0.91551607926404 90 0.0821671620517223 0.164334324103445 0.917832837948278 91 0.0718542641570665 0.143708528314133 0.928145735842933 92 0.0809217612050825 0.161843522410165 0.919078238794917 93 0.0766484672768176 0.153296934553635 0.923351532723182 94 0.0640949806455766 0.128189961291153 0.935905019354423 95 0.0545866849004882 0.109173369800976 0.945413315099512 96 0.0705038145260872 0.141007629052174 0.929496185473913 97 0.0852199126460257 0.170439825292051 0.914780087353974 98 0.0711067054598074 0.142213410919615 0.928893294540193 99 0.084662125288868 0.169324250577736 0.915337874711132 100 0.132673581684995 0.26534716336999 0.867326418315005 101 0.124064700191129 0.248129400382258 0.87593529980887 102 0.109397177623049 0.218794355246097 0.890602822376951 103 0.102099755370371 0.204199510740743 0.897900244629628 104 0.094497329875615 0.18899465975123 0.905502670124385 105 0.0874684581904226 0.174936916380845 0.912531541809577 106 0.100980966338088 0.201961932676176 0.899019033661912 107 0.255149349050986 0.510298698101972 0.744850650949014 108 0.246252488092018 0.492504976184036 0.753747511907982 109 0.208046907186204 0.416093814372408 0.791953092813796 110 0.174733339724503 0.349466679449006 0.825266660275497 111 0.151967291057837 0.303934582115673 0.848032708942163 112 0.126830773926791 0.253661547853582 0.873169226073209 113 0.218430201508319 0.436860403016637 0.781569798491681 114 0.188610508393755 0.377221016787511 0.811389491606245 115 0.185346674123028 0.370693348246055 0.814653325876972 116 0.278854387363616 0.557708774727233 0.721145612636384 117 0.255448639213784 0.510897278427567 0.744551360786216 118 0.248447117609912 0.496894235219824 0.751552882390088 119 0.220344057660368 0.440688115320737 0.779655942339632 120 0.183137395980538 0.366274791961077 0.816862604019462 121 0.170282485354689 0.340564970709378 0.829717514645311 122 0.136673116004531 0.273346232009062 0.863326883995469 123 0.240670222069715 0.48134044413943 0.759329777930285 124 0.661402894116437 0.677194211767126 0.338597105883563 125 0.692017043530283 0.615965912939433 0.307982956469717 126 0.636082656856576 0.727834686286848 0.363917343143424 127 0.595702039689826 0.808595920620347 0.404297960310174 128 0.548858117692151 0.902283764615697 0.451141882307849 129 0.521270584223325 0.95745883155335 0.478729415776675 130 0.524303716790688 0.951392566418623 0.475696283209312 131 0.504860348542961 0.990279302914077 0.495139651457038 132 0.503771329173895 0.99245734165221 0.496228670826105 133 0.532008497688945 0.93598300462211 0.467991502311055 134 0.525040244192402 0.949919511615196 0.474959755807598 135 0.626912695534294 0.746174608931413 0.373087304465706 136 0.556831111729454 0.886337776541092 0.443168888270546 137 0.502124426389272 0.995751147221456 0.497875573610728 138 0.556665576696273 0.886668846607454 0.443334423303727 139 0.479477560303249 0.958955120606499 0.520522439696751 140 0.52930781912552 0.94138436174896 0.47069218087448 141 0.65523197694526 0.68953604610948 0.34476802305474 142 0.578544245704204 0.842911508591592 0.421455754295796 143 0.474561586421573 0.949123172843147 0.525438413578427 144 0.373298829128348 0.746597658256696 0.626701170871652 145 0.307731591341489 0.615463182682978 0.692268408658511 146 0.211731891571751 0.423463783143501 0.78826810842825 147 0.20825812868739 0.41651625737478 0.79174187131261 148 0.294657157979445 0.589314315958891 0.705342842020555 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.00709219858156028 OK 5% type I error level 24 0.170212765957447 NOK 10% type I error level 37 0.262411347517730 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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