workshop 4

*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: Wed, 01 Dec 2010 15:30:25 +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/01/t1291217364624ite3ah6zxdqi.htm/, Retrieved Wed, 01 Dec 2010 16:29:35 +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/01/t1291217364624ite3ah6zxdqi.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

5 6 5 7 3 2 6 2 3 3 6 6 6 5 3 6 4 4 5 2 6 2 6 3 3 5 7 3 4 4 5 6 5 4 4 6 5 3 5 2 6 6 5 5 3 5 7 4 5 3 5 7 1 6 1 5 4 6 5 1 6 1 6 2 3 5 6 6 5 3 5 4 4 4 3 6 5 6 6 3 6 5 5 5 3 4 6 3 6 2 5 4 5 5 3 5 6 4 2 2 5 3 5 3 3 6 3 6 5 2 5 5 3 6 2 7 5 4 5 3 6 5 5 4 2 6 5 4 5 4 6 5 5 5 1 6 2 6 5 1 4 6 7 5 2 5 7 2 6 2 6 2 4 6 4 4 3 6 6 3 5 6 5 6 3 5 5 5 4 3 5 7 5 4 3 7 5 6 3 3 7 6 6 5 4 6 5 1 6 4 7 3 4 4 3 6 7 2 6 1 5 5 3 3 3 6 5 4 2 3 4 6 5 5 3 6 2 4 5 3 5 3 3 6 0 6 6 4 4 3 6 7 6 3 1 5 5 4 3 4 6 4 5 4 4 5 6 4 5 3 5 7 5 4 1 5 2 6 3 2 6 2 6 4 3 6 2 4 4 1 5 5 4 4 2 7 2 6 3 3 6 5 4 6 3 5 6 2 5 4 5 2 6 5 3 6 4 5 6 4 5 6 6 6 2 5 4 6 4 2 6 3 5 5 4 6 3 5 4 3 3 3 5 6 2 5 6 5 5 3 5 6 3 5 3 6 5 4 5 2 5 3 1 5 3 5 3 5 2 3 4 2 2 5 3 5 3 6 5 3 5 3 5 5 2 2 5 2 2 3 6 3 6 6 2 6 5 5 4 3 6 2 6 4 3 6 5 3 6 3 5 6 4 6 3 5 6 4 4 3 6 5 4 2 3 5 2 4 4 2 5 6 5 5 3 6 7 2 7 3 3 5 3 7 3 6 5 5 5 4 3 2 6 5 2 5 5 5 5 3 5 6 6 4 4 6 5 3 6 3 5 5 4 5 4 6 4 4 4 2 6 5 3 6 1 6 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation handgebruik[t] = + 4.14821985603947 -0.0935744572405169ontmoeting[t] + 0.181694835293119extravert[t] + 0.0616746589819732blozen[t] + 0.149405325426724populariteit[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) 4.14821985603947 0.603354 6.8753 0 0 ontmoeting -0.0935744572405169 0.055498 -1.6861 0.093842 0.046921 extravert 0.181694835293119 0.06265 2.9001 0.004287 0.002144 blozen 0.0616746589819732 0.072346 0.8525 0.395292 0.197646 populariteit 0.149405325426724 0.101545 1.4713 0.143287 0.071644 Multiple Linear Regression - Regression Statistics Multiple R 0.314528747220300 R-squared 0.0989283328279716 Adjusted R-squared 0.0750588846909643 F-TEST (value) 4.14455886286673 F-TEST (DF numerator) 4 F-TEST (DF denominator) 151 p-value 0.00325211903668698 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.06408114994983 Sum Squared Residuals 170.972572745462 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 5 5.37518587821598 -0.375185878215982 2 2 4.58340273640871 -2.58340273640871 3 6 5.43353139554513 0.566468604454869 4 6 5.1078853140132 0.892114685986802 5 6 5.68447990654325 0.315520093456752 6 5 4.88260309887 0.117396901129995 7 5 5.33956722669676 -0.33956722669676 8 6 4.83261602147956 1.16738397852044 9 6 5.25183656025201 0.748163439747991 10 5 4.97656726771837 0.0234327322816268 11 5 4.19434676996754 0.80565323003246 12 5 5.32186965917271 -0.321869659172713 13 6 5.71637970480179 0.283620295198209 14 5 5.43353139554513 -0.433531395545128 15 5 5.19561598045795 -0.195615980457949 16 6 5.58878051176762 0.411219488232382 17 6 5.34541101749253 0.654588982507475 18 4 4.80071622322102 -0.800716223221019 19 5 5.43898547473304 -0.438985474733042 20 5 4.73571242258625 0.264287577413754 21 5 5.40921061400961 -0.409210614009612 22 6 5.56484944183995 0.435150558160047 23 5 4.89429068046154 0.105709319538464 24 7 5.16371618219941 1.83628381780059 25 6 5.13433103308383 0.865668966916172 26 6 5.31312150762613 0.68687849237387 27 6 5.04660036663908 0.953399633360923 28 6 5.50901857365375 0.490981426346254 29 4 5.46582090541152 -1.46582090541152 30 5 4.52544693068738 0.474553069312617 31 6 5.65551953832965 0.344480461670347 32 4 5.77592942624865 -1.77592942624865 33 5 5.31351121923398 -0.313511219233982 34 5 5.28373635851055 -0.283736358510552 35 5 5.09658744402952 -0.0965874440295194 36 7 5.4037565348217 1.59624346517830 37 7 5.58293672097185 1.41706327902815 38 6 4.82971166072874 1.17028833927126 39 7 5.28919043769847 1.71080956230153 40 6 4.37604160526066 1.62395839473934 41 5 4.85867202894234 0.14132797105766 42 6 4.97869220525349 1.02130779474651 43 4 5.25183656025201 -1.25183656025201 44 6 5.44443955392096 0.555560446079045 45 5 4.78262894408912 0.21737105591088 46 6 5.00846706597692 0.991532934023083 47 6 4.91779696948722 1.08220303051278 48 5 5.18977218966218 -0.189772189662184 49 6 5.52671614117779 0.473283858822207 50 5 5.07014172495889 -0.0701417249588896 51 5 4.79777679317607 0.202223206823929 52 5 5.53507458111652 -0.535074581116523 53 6 5.74615456552522 0.253845434474779 54 6 5.08395424408553 0.916045755914466 55 5 4.95263619779071 0.0473638022092915 56 7 5.68447990654325 1.31552009345675 57 6 5.22539084118138 0.77460915881862 58 5 4.85615737979937 0.143842620200625 59 5 5.80782922450719 -0.807829224507194 60 6 5.65006545914174 0.349934540858261 61 5 5.34580072910038 -0.345800729100378 62 5 5.40960032561746 -0.409600325617464 63 6 5.68196525740028 0.318034742599718 64 6 5.47088527299158 0.529114727008415 65 3 5.44482926552881 -2.44482926552881 66 5 5.25183656025201 -0.251836560252009 67 5 4.88844688966577 0.111553110334230 68 6 5.01431085677268 0.985689143227318 69 5 4.80578059080108 0.194219409198920 70 5 5.34753595502764 -0.347535955027639 71 4 5.08104988333472 -1.08104988333472 72 5 5.71425476726668 -0.714254767266678 73 5 5.38315460654683 -0.383154606546834 74 2 4.61530253466725 -2.61530253466725 75 6 5.62652410082193 0.373475899178073 76 6 5.28373635851055 0.716263641489448 77 6 5.74615456552522 0.253845434474779 78 6 5.04369600588826 0.95630399411174 79 5 5.13181638394086 -0.131816383940863 80 5 5.00846706597692 -0.00846706597691644 81 6 4.97869220525349 1.02130779474651 82 5 5.23335956951226 -0.233359569512258 83 5 5.25183656025201 -0.251836560252009 84 6 4.73652691509608 1.26347308490392 85 3 5.10537066487023 -2.10537066487023 86 6 5.49481634291925 0.50518365708075 87 3 5.65842389908047 -2.65842389908047 88 5 5.34541101749253 -0.345411017492525 89 5 5.52126206198988 -0.52126206198988 90 6 5.04369600588826 0.95630399411174 91 5 5.31312150762613 -0.31312150762613 92 6 5.04621065503123 0.953789344968775 93 6 4.74488535503481 1.25511464496519 94 6 5.19561598045795 0.80438401954205 95 5 5.13978511227174 -0.139785112271741 96 3 4.80032651161317 -1.80032651161317 97 4 5.62280524756127 -1.62280524756127 98 7 5.41215004405456 1.58784995594544 99 6 5.43898547473304 0.561014525266958 100 6 5.53255993197356 0.467440068026442 101 5 5.4070856764745 -0.407085676474499 102 4 5.04660036663908 -1.04660036663908 103 6 5.5321702203657 0.467829779634294 104 6 4.80032651161317 1.19967348838683 105 6 5.62613438921407 0.373865610785925 106 5 4.73904156423905 0.260958435760954 107 6 5.80782922450719 0.192170775492806 108 6 5.83972902276574 0.160270977234263 109 2 4.42776390857836 -2.42776390857836 110 6 5.98952405980031 0.0104759401996865 111 5 5.55861593943634 -0.558615939436336 112 5 5.52710585278564 -0.527105852785645 113 3 5.62068031002616 -2.62068031002616 114 4 5.83176029443486 -1.83176029443486 115 6 4.73904156423905 1.26095843576095 116 5 5.5967492400985 -0.596749240098497 117 6 5.5833264325797 0.416673567420295 118 4 5.47339992213455 -1.47339992213455 119 6 5.16038704054661 0.839612959453394 120 4 5.32147994756486 -1.32147994756486 121 3 5.14601861467536 -2.14601861467536 122 6 5.34541101749253 0.654588982507475 123 5 5.25144684864416 -0.251446848644157 124 7 5.25729063943992 1.74270936056008 125 6 5.71425476726668 0.285745232733322 126 6 5.95723454993392 0.0427654500660817 127 5 5.00846706597692 -0.00846706597691644 128 5 5.65509475742767 -0.65509475742767 129 2 4.95012154864774 -2.95012154864774 130 5 4.92073639953217 0.0792636004678346 131 3 4.86996989892602 -1.86996989892602 132 6 5.01431085677268 0.985689143227318 133 5 5.21954705038561 -0.219547050385614 134 5 4.98202134690629 0.0179786530937135 135 5 4.9874754260942 0.0125245739058002 136 2 5.07053143656674 -3.07053143656674 137 5 5.16038704054661 -0.160387040546606 138 5 5.19561598045795 -0.195615980457949 139 6 5.65045517074959 0.349544829250409 140 6 5.55861593943634 0.441384060563664 141 5 4.71433107109568 0.285668928904323 142 5 5.34541101749253 -0.345411017492525 143 5 5.22206169952858 -0.222061699528579 144 6 5.62613438921407 0.373865610785925 145 6 5.59423459095553 0.405765409044469 146 6 5.50278507125013 0.497214928749872 147 6 5.07014172495889 0.92985827504111 148 6 5.61522623083825 0.384773769161752 149 7 5.65219039667685 1.34780960332315 150 6 5.44150012387601 0.558499876123993 151 6 5.0755958041468 0.924404195853197 152 6 5.01470056838053 0.985299431619466 153 7 5.80782922450719 1.19217077549281 154 1 4.64256274624771 -3.64256274624771 155 6 5.68447990654325 0.315520093456752 156 5 5.29503422849423 -0.295034228494231 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.841734456544736 0.316531086910527 0.158265543455264 9 0.748982780632802 0.502034438734396 0.251017219367198 10 0.625943147895837 0.748113704208327 0.374056852104163 11 0.510961779971296 0.978076440057408 0.489038220028704 12 0.56583920110263 0.86832159779474 0.43416079889737 13 0.466458016112008 0.932916032224015 0.533541983887992 14 0.378936449050603 0.757872898101205 0.621063550949397 15 0.298664746569703 0.597329493139407 0.701335253430297 16 0.223837816905661 0.447675633811322 0.776162183094339 17 0.170135689133455 0.34027137826691 0.829864310866545 18 0.193561216110984 0.387122432221969 0.806438783889016 19 0.170503899038528 0.341007798077056 0.829496100961472 20 0.142169073840270 0.284338147680541 0.85783092615973 21 0.105599833864011 0.211199667728021 0.89440016613599 22 0.0736835947310574 0.147367189462115 0.926316405268943 23 0.0498326565850808 0.0996653131701617 0.95016734341492 24 0.123607329422616 0.247214658845233 0.876392670577384 25 0.105979246162304 0.211958492324607 0.894020753837697 26 0.0907147449362214 0.181429489872443 0.909285255063779 27 0.0725040436792848 0.145008087358570 0.927495956320715 28 0.053397457860212 0.106794915720424 0.946602542139788 29 0.0928632731975344 0.185726546395069 0.907136726802466 30 0.0697011085869588 0.139402217173918 0.930298891413041 31 0.0528814696556269 0.105762939311254 0.947118530344373 32 0.135216719183497 0.270433438366995 0.864783280816503 33 0.106477874488640 0.212955748977281 0.89352212551136 34 0.0817699722199387 0.163539944439877 0.918230027780061 35 0.0611168854502775 0.122233770900555 0.938883114549723 36 0.100832656030060 0.201665312060121 0.89916734396994 37 0.131923406360629 0.263846812721257 0.868076593639372 38 0.128620031103084 0.257240062206167 0.871379968896916 39 0.161692202045171 0.323384404090342 0.838307797954829 40 0.188567328137965 0.377134656275930 0.811432671862035 41 0.154199188313867 0.308398376627735 0.845800811686133 42 0.144296657550888 0.288593315101775 0.855703342449112 43 0.165099257081045 0.33019851416209 0.834900742918955 44 0.135804206770044 0.271608413540088 0.864195793229956 45 0.114042365870033 0.228084731740067 0.885957634129967 46 0.106258075710221 0.212516151420441 0.89374192428978 47 0.106773412424534 0.213546824849068 0.893226587575466 48 0.0875739163470957 0.175147832694191 0.912426083652904 49 0.0705999145317673 0.141199829063535 0.929400085468233 50 0.0554569578849365 0.110913915769873 0.944543042115064 51 0.0434470297205382 0.0868940594410764 0.956552970279462 52 0.0384754929361465 0.0769509858722931 0.961524507063853 53 0.0289992365260993 0.0579984730521985 0.9710007634739 54 0.0248069413108635 0.0496138826217269 0.975193058689137 55 0.0189050516680608 0.0378101033361217 0.98109494833194 56 0.0209282323502195 0.041856464700439 0.97907176764978 57 0.0175114670692392 0.0350229341384785 0.98248853293076 58 0.0129326144751332 0.0258652289502665 0.987067385524867 59 0.0126186403455572 0.0252372806911143 0.987381359654443 60 0.0093022622386835 0.018604524477367 0.990697737761316 61 0.00687301330087511 0.0137460266017502 0.993126986699125 62 0.00532265927159053 0.0106453185431811 0.99467734072841 63 0.00374747232977235 0.00749494465954469 0.996252527670228 64 0.00273102599315486 0.00546205198630972 0.997268974006845 65 0.017120891969731 0.034241783939462 0.982879108030269 66 0.0128926446487052 0.0257852892974104 0.987107355351295 67 0.00958164128426924 0.0191632825685385 0.99041835871573 68 0.00910377437566213 0.0182075487513243 0.990896225624338 69 0.00690680685822775 0.0138136137164555 0.993093193141772 70 0.00554542441542013 0.0110908488308403 0.99445457558458 71 0.006916421187771 0.013832842375542 0.993083578812229 72 0.00579299184813674 0.0115859836962735 0.994207008151863 73 0.00433163863364988 0.00866327726729975 0.99566836136635 74 0.0291221732460852 0.0582443464921705 0.970877826753915 75 0.0228413749253349 0.0456827498506698 0.977158625074665 76 0.0196351472537021 0.0392702945074042 0.980364852746298 77 0.0148574171417200 0.0297148342834401 0.98514258285828 78 0.0138964428667979 0.0277928857335957 0.986103557133202 79 0.0104167999198890 0.0208335998397779 0.98958320008011 80 0.00766361229722304 0.0153272245944461 0.992336387702777 81 0.00771509501475797 0.0154301900295159 0.992284904985242 82 0.00568549520969398 0.0113709904193880 0.994314504790306 83 0.00417010454730063 0.00834020909460127 0.9958298954527 84 0.00499443707080507 0.00998887414161014 0.995005562929195 85 0.0134670349959174 0.0269340699918347 0.986532965004083 86 0.0106605568649373 0.0213211137298746 0.989339443135063 87 0.0469587801140001 0.0939175602280002 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0.970419105998442 105 0.0230944470552769 0.0461888941105538 0.976905552944723 106 0.0199095338313878 0.0398190676627756 0.980090466168612 107 0.0147688505446988 0.0295377010893976 0.985231149455301 108 0.0107914643804130 0.0215829287608259 0.989208535619587 109 0.0294748696381991 0.0589497392763982 0.970525130361801 110 0.0219472219438964 0.0438944438877927 0.978052778056104 111 0.0183082890725141 0.0366165781450281 0.981691710927486 112 0.0141267356898461 0.0282534713796922 0.985873264310154 113 0.0551720695504918 0.110344139100984 0.944827930449508 114 0.100288256004930 0.200576512009860 0.89971174399507 115 0.159651366601288 0.319302733202577 0.840348633398712 116 0.141121698218969 0.282243396437938 0.858878301781031 117 0.115776495106327 0.231552990212653 0.884223504893673 118 0.164153526776662 0.328307053553325 0.835846473223337 119 0.148113617446217 0.296227234892434 0.851886382553783 120 0.163901747936584 0.327803495873168 0.836098252063416 121 0.257608881713367 0.515217763426734 0.742391118286633 122 0.233587711102778 0.467175422205555 0.766412288897222 123 0.192252039523463 0.384504079046925 0.807747960476538 124 0.289384301620902 0.578768603241804 0.710615698379098 125 0.242765696230259 0.485531392460518 0.757234303769741 126 0.214636747231099 0.429273494462197 0.785363252768901 127 0.184436387029927 0.368872774059855 0.815563612970073 128 0.277444116309323 0.554888232618646 0.722555883690677 129 0.469359766177593 0.938719532355186 0.530640233822407 130 0.426626532741909 0.853253065483817 0.573373467258091 131 0.58517063929563 0.82965872140874 0.41482936070437 132 0.613155750979514 0.773688498040972 0.386844249020486 133 0.569223235772971 0.861553528454059 0.430776764227029 134 0.53208832565611 0.935823348687779 0.467911674343889 135 0.466471992204508 0.932943984409015 0.533528007795492 136 0.85022004108229 0.299559917835419 0.149779958917709 137 0.803394250804885 0.39321149839023 0.196605749195115 138 0.740929314467937 0.518141371064127 0.259070685532063 139 0.669696672921884 0.660606654156232 0.330303327078116 140 0.588312474776394 0.823375050447211 0.411687525223606 141 0.558721143988303 0.882557712023395 0.441278856011697 142 0.477541302100029 0.955082604200058 0.522458697899971 143 0.386868889429102 0.773737778858203 0.613131110570898 144 0.293640760323686 0.587281520647372 0.706359239676314 145 0.205659330866445 0.411318661732891 0.794340669133555 146 0.132688510577856 0.265377021155711 0.867311489422144 147 0.178170586389522 0.356341172779045 0.821829413610478 148 0.102617441251603 0.205234882503205 0.897382558748397 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.0354609929078014 NOK 5% type I error level 43 0.304964539007092 NOK 10% type I error level 62 0.439716312056738 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/10qlhm1291217414.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/10qlhm1291217414.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/1cb2v1291217414.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/1cb2v1291217414.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/2cb2v1291217414.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/2cb2v1291217414.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/3cb2v1291217414.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/3cb2v1291217414.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/4nkjy1291217414.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/4nkjy1291217414.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/5nkjy1291217414.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/5nkjy1291217414.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/6nkjy1291217414.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/6nkjy1291217414.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/7yc0j1291217414.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/7yc0j1291217414.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/8qlhm1291217414.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/8qlhm1291217414.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/9qlhm1291217414.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/01/t1291217364624ite3ah6zxdqi/9qlhm1291217414.ps (open in new window)

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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