Mini-Tutorial Multiple Regression Interaction Effects

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 23 Nov 2010 02:24:42 +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/Nov/23/t1290479371ui8ntsxpg4t8ibw.htm/, Retrieved Tue, 23 Nov 2010 03:29:34 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290479371ui8ntsxpg4t8ibw.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 «

0 13 26 0 9 0 6 0 25 0 25 0 0 16 20 0 9 0 6 0 25 0 24 0 0 19 21 0 9 0 13 0 19 0 21 0 1 15 31 31 14 14 8 8 18 18 23 23 0 14 21 0 8 0 7 0 18 0 17 0 0 13 18 0 8 0 9 0 22 0 19 0 0 19 26 0 11 0 5 0 29 0 18 0 0 15 22 0 10 0 8 0 26 0 27 0 0 14 22 0 9 0 9 0 25 0 23 0 0 15 29 0 15 0 11 0 23 0 23 0 1 16 15 15 14 14 8 8 23 23 29 29 0 16 16 0 11 0 11 0 23 0 21 0 1 16 24 24 14 14 12 12 24 24 26 26 0 17 17 0 6 0 8 0 30 0 25 0 1 15 19 19 20 20 7 7 19 19 25 25 1 15 22 22 9 9 9 9 24 24 23 23 0 20 31 0 10 0 12 0 32 0 26 0 1 18 28 28 8 8 20 20 30 30 20 20 0 16 38 0 11 0 7 0 29 0 29 0 1 16 26 26 14 14 8 8 17 17 24 24 0 19 25 0 11 0 8 0 25 0 23 0 0 16 25 0 16 0 16 0 26 0 24 0 1 17 29 29 14 14 10 10 26 26 30 30 0 17 28 0 11 0 6 0 25 0 22 0 1 16 15 15 11 11 8 8 23 23 22 22 0 15 18 0 12 0 9 0 21 0 13 0 1 14 21 21 9 9 9 9 19 19 24 24 0 15 25 0 7 0 11 0 35 0 17 0 1 12 23 23 13 13 12 12 19 19 24 24 0 14 23 0 10 0 8 0 20 0 21 0 0 16 19 0 9 0 7 0 21 0 23 0 1 14 18 18 9 9 8 8 21 21 24 24 1 7 18 18 13 13 9 9 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 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Selfconfidence[t] = + 13.6904599062833 -3.23857734904733Gender[t] + 0.00877329489010884ConcernMistakes[t] + 0.0239140039291088ConcernMistakes_G[t] -0.212820358169707DoubtsActions[t] -0.186727182614101DoubtsActions_G[t] + 0.0272883965522743ParentalCriticism[t] + 0.0569766005229586ParentalCriticism_G[t] + 0.0323243960587162PersonalStandards[t] -0.038112033503889PersonalStandards_G[t] + 0.117975229950911Organization[t] + 0.20126225687406Organization_G[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) 13.6904599062833 1.818071 7.5302 0 0 Gender -3.23857734904733 2.978129 -1.0875 0.278732 0.139366 ConcernMistakes 0.00877329489010884 0.047808 0.1835 0.854666 0.427333 ConcernMistakes_G 0.0239140039291088 0.077534 0.3084 0.758218 0.379109 DoubtsActions -0.212820358169707 0.09557 -2.2269 0.027578 0.013789 DoubtsActions_G -0.186727182614101 0.146837 -1.2717 0.205631 0.102815 ParentalCriticism 0.0272883965522743 0.087395 0.3122 0.755329 0.377665 ParentalCriticism_G 0.0569766005229586 0.144895 0.3932 0.694759 0.34738 PersonalStandards 0.0323243960587162 0.061268 0.5276 0.598631 0.299316 PersonalStandards_G -0.038112033503889 0.104694 -0.364 0.716391 0.358195 Organization 0.117975229950911 0.063028 1.8718 0.063354 0.031677 Organization_G 0.20126225687406 0.114274 1.7612 0.080416 0.040208 Multiple Linear Regression - Regression Statistics Multiple R 0.478100989985447 R-squared 0.228580556625065 Adjusted R-squared 0.16709060099373 F-TEST (value) 3.71736414961047 F-TEST (DF numerator) 11 F-TEST (DF denominator) 138 p-value 0.000117570465484218 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.07435659787837 Sum Squared Residuals 593.80783073229 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 15.9244033794531 -2.92440337945306 2 16 15.7537883801615 0.246211619838472 3 19 15.4057083847125 3.59429161528748 4 15 13.7839279492215 1.21607205077851 5 14 14.9505730477062 -0.950573047706224 6 13 15.3440780002771 -2.34407800027713 7 19 14.7749452411399 4.22505475886011 8 15 15.999341490788 -0.99934149078803 9 14 15.7352249296477 -1.73522492964765 10 15 14.5096438458473 0.490356154152711 11 16 15.147417901838 0.852582098162033 12 16 15.0109219850529 0.98907801494712 13 16 14.8151634815918 1.18483651840823 14 17 16.7001035733494 0.299896426650644 15 15 11.5428174578176 3.45718254218244 16 15 15.5370191361718 -0.537019136171766 17 20 16.2634258774095 3.7365741225905 18 18 16.0671671525525 1.93283284744751 19 16 16.2325291023858 -0.232529102385761 20 16 13.9455165793955 2.05448342060446 21 19 15.3086157014263 3.69138429857371 22 16 14.6131207090056 1.38687929099442 23 17 16.0754446539469 0.924555346053067 24 17 15.1623835630412 1.83761643695884 25 16 14.1113981164146 1.88860188358541 26 15 13.7526207918341 1.24737920816588 27 14 15.8525075114034 -1.85250751140338 28 15 15.8571549046436 -0.857154904643638 29 12 14.5724869371323 -2.57248693713228 30 14 15.1063170296204 -1.10631702962038 31 16 15.5250306676379 0.474969332362088 32 14 15.6586053429802 -1.65860534298015 33 7 14.1273172645846 -7.12731726458463 34 10 12.774635684856 -2.77463568485596 35 14 14.1523005086941 -0.152300508694102 36 16 16.4066349494271 -0.406634949427065 37 16 13.9703777149178 2.02962228508223 38 16 12.5366637102876 3.46333628971245 39 14 15.5565292391564 -1.55652923915643 40 20 18.3653833883118 1.6346166116882 41 14 14.2389702289017 -0.238970228901665 42 14 15.2325191694071 -1.23251916940708 43 11 14.5725694031111 -3.57256940311107 44 15 15.4554079952953 -0.455407995295286 45 16 15.5125200773641 0.487479922635864 46 14 14.9762567257839 -0.976256725783944 47 16 14.3860851039445 1.61391489605552 48 14 15.0668203990549 -1.06682039905489 49 12 14.6988543566534 -2.69885435665342 50 16 15.1790857500451 0.820914249954856 51 9 12.1697546075229 -3.16975460752286 52 14 14.6423117000206 -0.64231170002056 53 16 15.666511053809 0.333488946191029 54 16 15.1284267393245 0.871573260675543 55 15 14.6666780965847 0.333321903415258 56 16 15.2755527567287 0.724447243271338 57 12 13.1065870035093 -1.10658700350926 58 16 16.033474846882 -0.0334748468819896 59 16 16.0260662005621 -0.0260662005620591 60 14 16.382009611696 -2.38200961169597 61 16 13.6148836362444 2.38511636375564 62 17 16.8238241036963 0.176175896303671 63 18 14.796944482711 3.20305551728899 64 18 16.0772621786825 1.92273782131755 65 12 15.0086158419986 -3.00861584199858 66 16 16.0120576157256 -0.0120576157256189 67 10 13.9285122580368 -3.92851225803681 68 14 13.179433058654 0.820566941345987 69 18 15.879095513538 2.12090448646198 70 18 17.1956789531862 0.80432104681376 71 16 15.171226792168 0.828773207831987 72 16 15.6043664588382 0.395633541161823 73 16 14.6619737067197 1.33802629328028 74 13 14.5023013137842 -1.50230131378418 75 16 15.1146969118119 0.885303088188091 76 16 14.6869259484412 1.31307405155878 77 20 16.8175350964247 3.18246490357525 78 16 15.2578670109011 0.742132989098926 79 15 11.1225136152367 3.87748638476326 80 15 15.5863505207698 -0.586350520769762 81 16 15.7119394975354 0.288060502464623 82 14 13.6902099260435 0.309790073956472 83 15 13.7792420513741 1.22075794862592 84 12 14.9870395642523 -2.98703956425231 85 17 16.4435075479248 0.556492452075229 86 16 15.5006996868776 0.499300313122432 87 15 13.7996608748901 1.20033912510991 88 13 14.3893691806829 -1.38936918068286 89 16 15.582204868988 0.41779513101199 90 16 15.3177938214201 0.682206178579898 91 16 15.9487319563102 0.0512680436898163 92 16 16.4773001309686 -0.477300130968617 93 14 15.2449713483551 -1.24497134835508 94 16 14.3564846291403 1.64351537085972 95 16 13.8230304036733 2.17696959632668 96 20 16.0757623245403 3.92423767545967 97 15 16.1749351449768 -1.17493514497681 98 16 14.419096168496 1.58090383150398 99 13 13.0649088565378 -0.0649088565377565 100 17 15.9058237546064 1.09417624539357 101 16 13.918983115302 2.08101688469799 102 12 13.3258665170576 -1.32586651705765 103 16 14.9896405037922 1.01035949620776 104 16 15.2453599519217 0.75464004807832 105 17 15.342283663855 1.65771633614501 106 13 11.8302166483025 1.16978335169754 107 12 15.6929676906234 -3.69296769062342 108 18 16.0000227516948 1.99997724830517 109 14 14.407654319102 -0.407654319101987 110 14 14.696283475394 -0.696283475394039 111 13 14.2191130615465 -1.21911306154654 112 16 15.4597860142233 0.540213985776681 113 13 13.3858924291833 -0.385892429183331 114 16 15.0149411238257 0.98505887617433 115 13 15.1798782726753 -2.17987827267529 116 16 15.8928564590829 0.10714354091714 117 15 14.7471229731149 0.252877026885079 118 16 15.5672752636237 0.432724736376266 119 15 14.4371022084823 0.562897791517722 120 17 15.7711922826 1.22880771740001 121 15 16.0576682223147 -1.05766822231465 122 12 14.1003992829567 -2.10039928295671 123 16 14.2452537355041 1.75474626449588 124 10 14.5407968772968 -4.54079687729676 125 16 14.9916672073607 1.00833279263933 126 14 14.2729181932461 -0.272918193246106 127 15 16.2239857707387 -1.22398577073869 128 13 13.9311249183268 -0.931124918326784 129 15 14.605647372226 0.394352627774 130 11 14.2537990121 -3.25379901210002 131 12 14.4104160847048 -2.41041608470483 132 8 13.9681560904257 -5.96815609042569 133 16 15.9742547043547 0.025745295645268 134 15 15.5948091988777 -0.594809198877692 135 17 15.5428877887217 1.45711221127833 136 16 14.8790947982401 1.12090520175987 137 10 15.2055609650956 -5.20556096509563 138 18 14.1616858341785 3.83831416582149 139 13 13.7430386209006 -0.743038620900636 140 15 14.7419604605995 0.258039539400483 141 16 14.1113981164146 1.88860188358541 142 16 15.1089926020232 0.891007397976815 143 14 14.2015700030607 -0.201570003060701 144 10 13.9523220553945 -3.95232205539449 145 17 16.4435075479248 0.556492452075229 146 13 15.1489044608854 -2.14890446088543 147 15 16.0576682223147 -1.05766822231465 148 16 15.7749295779837 0.225070422016346 149 12 15.5326927633043 -3.53269276330432 150 13 14.0179669199171 -1.01796691991715 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.925254089848804 0.149491820302391 0.0747459101511956 16 0.85818947737465 0.283621045250699 0.14181052262535 17 0.784345153699594 0.431309692600813 0.215654846300406 18 0.69213703725387 0.615725925492261 0.307862962746131 19 0.584219948475781 0.831560103048437 0.415780051524219 20 0.484634882636314 0.969269765272629 0.515365117363686 21 0.642420080915322 0.715159838169356 0.357579919084678 22 0.651353413045579 0.697293173908842 0.348646586954421 23 0.584431947411197 0.831136105177605 0.415568052588803 24 0.530680636161421 0.938638727677158 0.469319363838579 25 0.47595492799861 0.95190985599722 0.52404507200139 26 0.434494451061421 0.868988902122841 0.56550554893858 27 0.386262921554637 0.772525843109275 0.613737078445363 28 0.579825891232321 0.840348217535359 0.420174108767679 29 0.600543643877045 0.79891271224591 0.399456356122955 30 0.550894315694996 0.898211368610009 0.449105684305004 31 0.493281594379401 0.986563188758802 0.506718405620599 32 0.433179628910959 0.866359257821919 0.56682037108904 33 0.967513573694358 0.0649728526112841 0.0324864263056421 34 0.973740299541029 0.0525194009179427 0.0262597004589713 35 0.963032736042512 0.0739345279149765 0.0369672639574882 36 0.952322772754245 0.0953544544915092 0.0476772272457546 37 0.951317726188006 0.0973645476239889 0.0486822738119944 38 0.966970787558677 0.066058424882646 0.033029212441323 39 0.963226705099636 0.0735465898007276 0.0367732949003638 40 0.97728840585724 0.0454231882855185 0.0227115941427592 41 0.968298721982585 0.0634025560348293 0.0317012780174147 42 0.966004601111864 0.0679907977762715 0.0339953988881357 43 0.98151848604972 0.0369630279005596 0.0184815139502798 44 0.974490820257012 0.0510183594859759 0.025509179742988 45 0.966260358508043 0.0674792829839135 0.0337396414919567 46 0.956616513312828 0.0867669733743436 0.0433834866871718 47 0.947658633317503 0.104682733364994 0.052341366682497 48 0.935650101415385 0.128699797169229 0.0643498985846147 49 0.943153675039884 0.113692649920233 0.0568463249601164 50 0.927994290252675 0.144011419494651 0.0720057097473255 51 0.941690660771955 0.11661867845609 0.0583093392280449 52 0.92606344744373 0.147873105112541 0.0739365525562703 53 0.907643487481896 0.184713025036208 0.0923565125181039 54 0.892563784126474 0.214872431747052 0.107436215873526 55 0.870755419331386 0.258489161337228 0.129244580668614 56 0.84473688569058 0.310526228618841 0.155263114309421 57 0.81765686827891 0.364686263442182 0.182343131721091 58 0.783789388568891 0.432421222862218 0.216210611431109 59 0.744997731793408 0.510004536413184 0.255002268206592 60 0.755217265379425 0.48956546924115 0.244782734620575 61 0.757865144120109 0.484269711759782 0.242134855879891 62 0.716177701992742 0.567644596014516 0.283822298007258 63 0.76490913259024 0.470181734819519 0.23509086740976 64 0.760763445926961 0.478473108146078 0.239236554073039 65 0.810138542998531 0.379722914002937 0.189861457001469 66 0.77595061078263 0.448098778434741 0.224049389217371 67 0.860957174774246 0.278085650451508 0.139042825225754 68 0.836340735180344 0.327318529639311 0.163659264819656 69 0.84021697668632 0.319566046627361 0.15978302331368 70 0.813199547594263 0.373600904811475 0.186800452405737 71 0.783890091677019 0.432219816645962 0.216109908322981 72 0.746610747460151 0.506778505079698 0.253389252539849 73 0.721556810116908 0.556886379766185 0.278443189883092 74 0.705996694970594 0.588006610058813 0.294003305029406 75 0.686268160130571 0.627463679738857 0.313731839869429 76 0.655802245254893 0.688395509490214 0.344197754745107 77 0.720779204923739 0.558441590152523 0.279220795076261 78 0.68370996226852 0.63258007546296 0.31629003773148 79 0.78450444846926 0.43099110306148 0.21549555153074 80 0.748772051906274 0.502455896187453 0.251227948093726 81 0.707198567373538 0.585602865252924 0.292801432626462 82 0.70815535716805 0.583689285663899 0.29184464283195 83 0.680295405347957 0.639409189304086 0.319704594652043 84 0.735328121184529 0.529343757630942 0.264671878815471 85 0.695619906344379 0.608760187311242 0.304380093655621 86 0.652873489783573 0.694253020432854 0.347126510216427 87 0.62642980622222 0.74714038755556 0.37357019377778 88 0.600676963621478 0.798646072757044 0.399323036378522 89 0.553331822339662 0.893336355320676 0.446668177660338 90 0.508026385928306 0.983947228143388 0.491973614071694 91 0.455982018962008 0.911964037924016 0.544017981037992 92 0.425034065191444 0.850068130382887 0.574965934808556 93 0.440137523358535 0.880275046717069 0.559862476641465 94 0.441105800396944 0.882211600793888 0.558894199603056 95 0.437415716647415 0.87483143329483 0.562584283352585 96 0.590751366041495 0.81849726791701 0.409248633958505 97 0.549769078059126 0.900461843881748 0.450230921940874 98 0.556615354760942 0.886769290478116 0.443384645239058 99 0.506639996599345 0.98672000680131 0.493360003400655 100 0.477757605029646 0.95551521005929 0.522242394970354 101 0.473484940590007 0.946969881180014 0.526515059409993 102 0.44759724568268 0.895194491365361 0.55240275431732 103 0.413636180162316 0.827272360324633 0.586363819837683 104 0.392296295270274 0.784592590540549 0.607703704729726 105 0.406680507944709 0.813361015889417 0.593319492055291 106 0.430856763274346 0.861713526548692 0.569143236725654 107 0.54758168134385 0.9048366373123 0.45241831865615 108 0.598187419643846 0.803625160712308 0.401812580356154 109 0.575479375285098 0.849041249429805 0.424520624714902 110 0.520627326781922 0.958745346436156 0.479372673218078 111 0.46986387566669 0.93972775133338 0.53013612433331 112 0.416762011879355 0.83352402375871 0.583237988120645 113 0.371935713918518 0.743871427837036 0.628064286081482 114 0.36192475432827 0.723849508656539 0.63807524567173 115 0.349405062210559 0.698810124421117 0.650594937789441 116 0.290837049844612 0.581674099689224 0.709162950155388 117 0.267867326619525 0.53573465323905 0.732132673380475 118 0.263528568908791 0.527057137817581 0.73647143109121 119 0.254935884065091 0.509871768130182 0.745064115934909 120 0.231280060436479 0.462560120872959 0.76871993956352 121 0.187506233762298 0.375012467524595 0.812493766237703 122 0.164770265308406 0.329540530616811 0.835229734691594 123 0.173964337109354 0.347928674218708 0.826035662890646 124 0.252015073030027 0.504030146060054 0.747984926969973 125 0.196259428395544 0.392518856791089 0.803740571604456 126 0.148415986340889 0.296831972681778 0.851584013659111 127 0.107486237223407 0.214972474446814 0.892513762776593 128 0.096171535467252 0.192343070934504 0.903828464532748 129 0.0630616551263485 0.126123310252697 0.936938344873651 130 0.0490195071451278 0.0980390142902556 0.950980492854872 131 0.0351791673202444 0.0703583346404888 0.964820832679756 132 0.0289185356943467 0.0578370713886934 0.971081464305653 133 0.015359781853913 0.030719563707826 0.984640218146087 134 0.00702237965933809 0.0140447593186762 0.992977620340662 135 0.0124805011868111 0.0249610023736221 0.987519498813189 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 5 0.0413223140495868 OK 10% type I error level 20 0.165289256198347 NOK

Charts produced by software:

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Parameters (Session):

par1 = 0 ; par2 = 36 ;

Parameters (R input):

par1 = 2 ; 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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