Multiple Regression Analysis

*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, 15 Dec 2010 00:08:12 +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/15/t1292372740wtnetgr7szn910g.htm/, Retrieved Wed, 15 Dec 2010 01:25:43 +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/15/t1292372740wtnetgr7szn910g.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 «

13 26 9 15 25 25 16 20 9 15 25 24 19 21 9 14 19 21 15 31 14 10 18 23 14 21 8 10 18 17 13 18 8 12 22 19 19 26 11 18 29 18 15 22 10 12 26 27 14 22 9 14 25 23 15 29 15 18 23 23 16 15 14 9 23 29 16 16 11 11 23 21 16 24 14 11 24 26 17 17 6 17 30 25 15 19 20 8 19 25 15 22 9 16 24 23 20 31 10 21 32 26 18 28 8 24 30 20 16 38 11 21 29 29 16 26 14 14 17 24 19 25 11 7 25 23 16 25 16 18 26 24 17 29 14 18 26 30 17 28 11 13 25 22 16 15 11 11 23 22 15 18 12 13 21 13 14 21 9 13 19 24 15 25 7 18 35 17 12 23 13 14 19 24 14 23 10 12 20 21 16 19 9 9 21 23 14 18 9 12 21 24 7 18 13 8 24 24 10 26 16 5 23 24 14 18 12 10 19 23 16 18 6 11 17 26 16 28 14 11 24 24 16 17 14 12 15 21 14 29 10 12 25 23 20 12 4 15 27 28 14 25 12 12 29 23 14 28 12 16 27 22 11 20 14 14 18 24 15 17 9 17 25 21 16 17 9 13 22 23 14 20 10 10 26 23 16 31 14 17 23 20 14 21 10 12 16 23 12 19 9 13 27 21 16 23 14 13 25 27 9 15 8 11 14 12 14 24 9 13 19 15 16 28 8 12 20 22 16 16 9 12 16 21 15 19 9 12 18 21 16 21 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 7 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Learning[t] = + 12.3537171110201 + 0.0061848539683367Concern[t] -0.277968257641376Doubts[t] + 0.107111545991711Expectations[t] + 0.0278119768219914Standards[t] + 0.156915805748762Organization[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) 12.3537171110201 1.434908 8.6094 0 0 Concern 0.0061848539683367 0.037642 0.1643 0.86972 0.43486 Doubts -0.277968257641376 0.06854 -4.0556 8.2e-05 4.1e-05 Expectations 0.107111545991711 0.054197 1.9764 0.050026 0.025013 Standards 0.0278119768219914 0.048586 0.5724 0.567929 0.283964 Organization 0.156915805748762 0.048636 3.2263 0.001552 0.000776 Multiple Linear Regression - Regression Statistics Multiple R 0.455153141765681 R-squared 0.20716438245917 Adjusted R-squared 0.179635367961225 F-TEST (value) 7.52531052190885 F-TEST (DF numerator) 5 F-TEST (DF denominator) 144 p-value 2.64790903370393e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.05867599198798 Sum Squared Residuals 610.293144958229 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.237676749569 -3.23767674956899 2 16 16.0436518200102 -0.0436518200102288 3 19 15.3051058498086 3.69489415019138 4 15 13.8346865519938 1.1653134480062 5 14 14.4991527236661 -0.499152723666114 6 13 15.11990077253 -2.11990077253001 7 19 15.015912139308 3.98408786069198 8 15 15.9552780263987 -0.955278026398673 9 14 15.7919941762064 -1.79199417620643 10 15 14.5403008384594 0.459699161540607 11 16 14.7091720611112 1.29082793888877 12 16 14.508158333997 1.49184166600298 13 16 14.5361233983854 1.46387660161461 14 17 17.3692008128715 -0.369200812871485 15 15 12.2200792548616 2.7799207451384 16 15 15.9784052913679 -0.97840529136786 17 20 16.9849016812223 3.01509831877772 18 18 16.8464994844386 1.1535005155614 19 16 17.1375388881396 -1.13753888813958 20 16 14.3613122950457 1.63868770495427 21 19 14.5048314008867 4.49516859911328 22 16 14.4779449011594 1.52205509884059 23 17 16.0001156668081 0.999884333191923 24 17 15.0091394329932 1.99086056700677 25 16 14.6588892857774 1.34111071422255 26 15 13.1458324766417 1.85416752335834 27 14 15.6687417210632 -1.6687417210632 28 15 16.1315563710884 -1.13155637108838 29 12 14.6763499444261 -2.67634994442608 30 14 14.8530961849425 -0.85309618494249 31 16 15.1266339770549 0.873366022945099 32 14 15.5986995668105 -1.59869956681046 33 7 14.1418162827441 -7.14181628274409 34 10 13.0082437267695 -3.00824372676953 35 14 14.3380319425102 -0.338031942510166 36 16 16.5280764979524 -0.528076497952433 37 16 14.2470312027612 1.75296879723879 38 16 13.565054146457 2.43494585354299 39 14 15.34309680436 -1.34309680435999 40 20 18.0673014531094 1.93269854689056 41 14 14.8736687804919 -0.873668780491858 42 14 15.108129766971 -1.10812976697097 43 11 14.3520151480577 -3.3520151480577 44 15 15.7685729328424 -0.768572932842354 45 16 15.5705224299071 0.429477570092938 46 14 15.1010220034835 -1.10102200348353 47 16 14.2527798407994 1.74722015920055 48 14 15.0433101812154 -1.04331018121537 49 12 15.4081204104562 -3.40812041045617 50 16 14.9288894189712 1.07111058102877 51 9 13.673328209816 -4.67332820981603 52 14 14.2750540312293 -0.275054031229348 53 16 15.5968727758157 0.403127224184315 54 16 14.9765225575175 1.02347744248246 55 15 15.0507010730665 -0.0507010730665349 56 16 14.6960682445673 1.30393175543272 57 12 13.4138868529087 -1.41388685290866 58 16 16.4524072391691 -0.452407239169051 59 16 16.1207526067982 -0.12075260679821 60 14 16.3828093530209 -2.38280935302086 61 16 12.4482077844049 3.55179221559515 62 17 16.0090764099168 0.990923590083235 63 18 14.5845673118244 3.41543268817564 64 18 15.396959538259 2.60304046174096 65 12 14.4904952319956 -2.49049523199564 66 16 15.8328664490569 0.167133550943142 67 10 14.3182316106513 -4.31823161065129 68 14 12.5632518673365 1.43674813266347 69 18 15.3445478155233 2.65545218447667 70 18 16.2374444281417 1.76255557185832 71 16 15.5298333475318 0.470166652468223 72 16 15.4941531841508 0.505846815849227 73 16 14.7267817886006 1.27321821139936 74 13 14.695053449334 -1.69505344933404 75 16 15.0296604558526 0.970339544147362 76 16 14.7682325149164 1.23176748508362 77 20 15.9685202920334 4.03147970796663 78 16 15.2578667533836 0.742133246616405 79 15 12.6781168976852 2.32188310231477 80 15 15.3452887554362 -0.345288755436168 81 16 15.84878601265 0.151213987349972 82 14 14.1044637626414 -0.10446376264139 83 15 13.2278422445353 1.77215775546466 84 12 14.8664806881124 -2.8664806881124 85 17 16.0140744788799 0.985925521120118 86 16 15.2161849265094 0.783815073490602 87 15 12.9992695660541 2.0007304339459 88 13 14.4158407684455 -1.4158407684455 89 16 15.9752929983482 0.0247070016518326 90 16 15.3006055492998 0.699394450700157 91 16 16.2412567081343 -0.241256708134275 92 16 15.8777713568705 0.122228643129508 93 14 15.6097101492979 -1.60971014929793 94 16 14.226652417437 1.77334758256299 95 16 15.2184260085378 0.781573991462233 96 20 16.4287316236433 3.57126837635668 97 15 15.5416876056774 -0.54168760567739 98 16 14.1305514539328 1.86944854606722 99 13 14.3489714691489 -1.34897146914894 100 17 15.9329522632788 1.06704773672119 101 16 14.2862281951954 1.7137718048046 102 12 13.3344846738315 -1.33448467383146 103 16 15.0669541168445 0.933045883155495 104 16 15.3749042516497 0.625095748350275 105 17 15.5413292769015 1.45867072309846 106 13 13.1969179746937 -0.196917974693656 107 12 15.8841708509294 -3.88417085092944 108 18 15.8548587319919 2.14514126800808 109 14 13.7807154719128 0.219284528087229 110 14 14.5468809554179 -0.546880955417902 111 13 13.8035393596059 -0.803539359605925 112 16 15.4601551324916 0.539844867508437 113 13 12.6215505513634 0.378449448636596 114 16 15.367797834869 0.632202165131008 115 13 14.8762945057604 -1.87629450576037 116 16 15.8704829704835 0.129517029516503 117 15 14.782731170255 0.217268829745022 118 16 15.4043203272014 0.595679672798566 119 15 14.9516011720379 0.0483988279620662 120 17 15.6717021473854 1.32829785261461 121 15 15.8851225166506 -0.885122516650605 122 12 13.6514492823763 -1.6514492823763 123 16 14.4408949925792 1.55910500742083 124 10 14.2264598280807 -4.22645982808073 125 16 14.3244427790839 1.67555722091608 126 14 14.7449208386032 -0.744920838603168 127 15 16.4749559248351 -1.4749559248351 128 13 14.5210053366415 -1.52100533664155 129 15 15.4337746836742 -0.433774683674172 130 11 13.7744896650045 -2.7744896650045 131 12 14.2703404373367 -2.27034043733666 132 8 14.6012988711791 -6.60129887117906 133 16 16.2835266176361 -0.283526617636069 134 15 14.8894380543754 0.110561945624628 135 17 15.3197770758723 1.68022292412767 136 16 15.4619518205776 0.538048179422432 137 10 15.0690118825599 -5.06901188255991 138 18 13.8990484520381 4.1009515479619 139 13 13.9545025069759 -0.954502506975867 140 15 14.3165551093662 0.683444890633833 141 16 14.6588892857774 1.34111071422255 142 16 15.0253844245968 0.974615575403246 143 14 13.4643186970832 0.535681302916778 144 10 13.1271356772014 -3.12713567720144 145 17 16.0140744788799 0.985925521120118 146 13 14.4004669878333 -1.40046698783329 147 15 15.8851225166506 -0.885122516650605 148 16 15.9714096625069 0.0285903374931292 149 12 15.3026117423253 -3.30261174232529 150 13 13.5543242505955 -0.554324250595498 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.542937923805889 0.914124152388222 0.457062076194111 10 0.878242484064457 0.243515031871086 0.121757515935543 11 0.805471577314012 0.389056845371977 0.194528422685989 12 0.713622598297131 0.572754803405738 0.286377401702869 13 0.623316918361144 0.753366163277711 0.376683081638856 14 0.552760488360424 0.894479023279151 0.447239511639576 15 0.504913599239875 0.99017280152025 0.495086400760125 16 0.428671042182649 0.857342084365298 0.571328957817351 17 0.501123441348738 0.997753117302523 0.498876558651262 18 0.421571652688251 0.843143305376503 0.578428347311749 19 0.350804434195236 0.701608868390472 0.649195565804764 20 0.289081488759066 0.578162977518133 0.710918511240934 21 0.481059739783455 0.96211947956691 0.518940260216545 22 0.432152894650588 0.864305789301175 0.567847105349412 23 0.375237660525749 0.750475321051497 0.624762339474251 24 0.317079470267044 0.634158940534088 0.682920529732956 25 0.260141747067839 0.520283494135678 0.739858252932161 26 0.2298577607525 0.459715521505001 0.7701422392475 27 0.185466920342036 0.370933840684072 0.814533079657964 28 0.254791735149358 0.509583470298716 0.745208264850642 29 0.335602146563614 0.671204293127228 0.664397853436386 30 0.289502817254976 0.579005634509952 0.710497182745024 31 0.250485393038421 0.500970786076841 0.74951460696158 32 0.214109802020969 0.428219604041938 0.78589019797903 33 0.909426185018366 0.181147629963269 0.0905738149816343 34 0.94419770025212 0.111604599495761 0.0558022997478807 35 0.926292924036293 0.147414151927415 0.0737070759637074 36 0.911064457825953 0.177871084348094 0.0889355421740472 37 0.89884047458533 0.202319050829339 0.10115952541467 38 0.891769084973123 0.216461830053754 0.108230915026877 39 0.872404243577225 0.25519151284555 0.127595756422775 40 0.895122020853726 0.209755958292547 0.104877979146274 41 0.872393088615957 0.255213822768086 0.127606911384043 42 0.856689438027999 0.286621123944002 0.143310561972001 43 0.915086612230865 0.16982677553827 0.0849133877691349 44 0.898829687261274 0.202340625477452 0.101170312738726 45 0.874888080978087 0.250223838043826 0.125111919021913 46 0.85105448607621 0.297891027847578 0.148945513923789 47 0.83291377608919 0.334172447821619 0.16708622391081 48 0.805989276927003 0.388021446145993 0.194010723072997 49 0.853638196167488 0.292723607665024 0.146361803832512 50 0.830447320887573 0.339105358224853 0.169552679112427 51 0.92172223048686 0.156555539026282 0.0782777695131409 52 0.902644030594762 0.194711938810476 0.097355969405238 53 0.884067766349561 0.231864467300878 0.115932233650439 54 0.86865281892337 0.26269436215326 0.13134718107663 55 0.841153212445802 0.317693575108395 0.158846787554198 56 0.830085636673044 0.339828726653913 0.169914363326956 57 0.811426693444093 0.377146613111813 0.188573306555907 58 0.777313479235043 0.445373041529913 0.222686520764957 59 0.738897720550812 0.522204558898377 0.261102279449188 60 0.740863706078396 0.518272587843208 0.259136293921604 61 0.802734603796781 0.394530792406438 0.197265396203219 62 0.780064123757039 0.439871752485922 0.219935876242961 63 0.835373364767057 0.329253270465886 0.164626635232943 64 0.858263078183253 0.283473843633493 0.141736921816747 65 0.872054031203344 0.255891937593313 0.127945968796656 66 0.845918405301685 0.308163189396629 0.154081594698315 67 0.92110275898926 0.157794482021481 0.0788972410107406 68 0.909780132539447 0.180439734921107 0.0902198674605535 69 0.928537110338736 0.142925779322527 0.0714628896612637 70 0.927351289838899 0.145297420322202 0.072648710161101 71 0.910099056949653 0.179801886100694 0.0899009430503471 72 0.890314524022223 0.219370951955555 0.109685475977777 73 0.877287961680415 0.245424076639169 0.122712038319585 74 0.867980332025085 0.264039335949829 0.132019667974915 75 0.847109406507455 0.30578118698509 0.152890593492545 76 0.827694549462457 0.344610901075087 0.172305450537543 77 0.901637754542174 0.196724490915651 0.0983622454578256 78 0.882273269674707 0.235453460650586 0.117726730325293 79 0.888970330969545 0.222059338060911 0.111029669030455 80 0.864741677646265 0.270516644707471 0.135258322353735 81 0.836751778304778 0.326496443390443 0.163248221695222 82 0.809133582140433 0.381732835719134 0.190866417859567 83 0.809290431525817 0.381419136948366 0.190709568474183 84 0.839015156593465 0.321969686813071 0.160984843406535 85 0.814682122123909 0.370635755752183 0.185317877876091 86 0.785879499832503 0.428241000334994 0.214120500167497 87 0.790846892207134 0.418306215585733 0.209153107792866 88 0.770998334377145 0.45800333124571 0.229001665622855 89 0.731964366161471 0.536071267677058 0.268035633838529 90 0.695825801706555 0.608348396586891 0.304174198293445 91 0.652700145916509 0.694599708166983 0.347299854083491 92 0.606352113918735 0.78729577216253 0.393647886081265 93 0.591266815450365 0.81746636909927 0.408733184549635 94 0.603500771745819 0.792998456508362 0.396499228254181 95 0.567386517700287 0.865226964599426 0.432613482299713 96 0.659728219451359 0.680543561097282 0.340271780548641 97 0.613282943477555 0.773434113044889 0.386717056522445 98 0.633368925368596 0.733262149262809 0.366631074631404 99 0.601756103401759 0.796487793196483 0.398243896598241 100 0.574888403900847 0.850223192198306 0.425111596099153 101 0.595235696164164 0.809528607671673 0.404764303835836 102 0.560927723980292 0.878144552039416 0.439072276019708 103 0.524434901778949 0.951130196442102 0.475565098221051 104 0.502367623942266 0.995264752115468 0.497632376057734 105 0.509942902664223 0.980114194671554 0.490057097335777 106 0.457759600355051 0.915519200710101 0.542240399644949 107 0.598110377803215 0.80377924439357 0.401889622196785 108 0.609947582109585 0.78010483578083 0.390052417890415 109 0.61273970534223 0.77452058931554 0.38726029465777 110 0.562745612606525 0.87450877478695 0.437254387393475 111 0.509686695587908 0.980626608824185 0.490313304412092 112 0.457585795175883 0.915171590351766 0.542414204824117 113 0.429721444199351 0.859442888398701 0.570278555800649 114 0.391684839501555 0.78336967900311 0.608315160498445 115 0.375124202346405 0.75024840469281 0.624875797653595 116 0.320362498211981 0.640724996423962 0.679637501788019 117 0.29360363404872 0.587207268097441 0.70639636595128 118 0.296591452479692 0.593182904959384 0.703408547520308 119 0.245727890925742 0.491455781851484 0.754272109074258 120 0.21531342346389 0.43062684692778 0.78468657653611 121 0.179592184155114 0.359184368310228 0.820407815844886 122 0.164129007226705 0.32825801445341 0.835870992773295 123 0.155755616796569 0.311511233593138 0.844244383203431 124 0.207757779101591 0.415515558203182 0.792242220898409 125 0.16960563341694 0.33921126683388 0.83039436658306 126 0.133229688815761 0.266459377631521 0.86677031118424 127 0.10260941026088 0.205218820521759 0.89739058973912 128 0.0791126415369807 0.158225283073961 0.920887358463019 129 0.0578319745875705 0.115663949175141 0.94216802541243 130 0.0486812666505442 0.0973625333010885 0.951318733349456 131 0.0371988114039727 0.0743976228079453 0.962801188596027 132 0.241994223126728 0.483988446253455 0.758005776873272 133 0.180504696332892 0.361009392665783 0.819495303667108 134 0.131222507673446 0.262445015346892 0.868777492326554 135 0.137096213245877 0.274192426491755 0.862903786754123 136 0.100014035517835 0.20002807103567 0.899985964482165 137 0.444485793800294 0.888971587600589 0.555514206199705 138 0.694165943625938 0.611668112748124 0.305834056374062 139 0.576879323753421 0.846241352493157 0.423120676246579 140 0.461809008842616 0.923618017685232 0.538190991157384 141 0.333076697503629 0.666153395007259 0.66692330249637 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 0.0150375939849624 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/10k8i51292371681.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/10k8i51292371681.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/13g481292371681.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/13g481292371681.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/2e84c1292371681.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/2e84c1292371681.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/3e84c1292371681.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/3e84c1292371681.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/4oy2e1292371681.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/4oy2e1292371681.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/5oy2e1292371681.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/5oy2e1292371681.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/6oy2e1292371681.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/6oy2e1292371681.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/7zqkz1292371681.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/7zqkz1292371681.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/8zqkz1292371681.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/8zqkz1292371681.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/9shj21292371681.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292372740wtnetgr7szn910g/9shj21292371681.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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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