multiple regression - model 2

*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 16:37:19 +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/t1291223247yzvd40mevpd2vd2.htm/, Retrieved Wed, 01 Dec 2010 18:07:38 +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/t1291223247yzvd40mevpd2vd2.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 9 15 10 12 16 6 3 9 12 9 7 12 6 3 9 10 10 10 11 5 1 9 12 12 7 12 3 3 9 15 13 16 18 8 1 9 9 12 11 11 4 4 9 12 12 14 14 4 0 9 11 6 6 9 4 3 9 11 5 16 14 6 2 9 11 12 11 12 6 4 9 15 11 16 11 5 3 9 7 14 12 12 4 1 9 11 14 7 13 6 1 9 11 12 13 11 4 2 9 10 12 11 12 6 3 9 14 11 15 16 6 1 9 10 11 7 9 4 1 9 6 7 9 11 4 2 9 11 9 7 13 2 3 9 15 11 14 15 7 4 9 11 11 15 10 5 2 9 12 12 7 11 4 1 9 14 12 15 13 6 2 9 15 11 17 16 6 2 9 9 11 15 15 7 4 9 13 8 14 14 5 2 9 13 9 14 14 6 3 9 16 12 8 14 4 3 9 13 10 8 8 4 3 9 12 10 14 13 7 4 9 14 12 14 15 7 2 9 11 8 8 13 4 2 9 9 12 11 11 4 4 9 16 11 16 15 6 3 9 12 12 10 15 6 4 9 10 7 8 9 5 2 9 13 11 14 13 6 5 9 16 11 16 16 7 3 9 14 12 13 13 6 1 9 15 9 5 11 3 1 9 5 15 8 12 3 1 9 8 11 10 12 4 2 9 11 11 8 12 6 3 9 16 11 13 14 7 9 9 17 11 15 14 5 0 9 9 15 6 8 4 0 9 9 11 12 13 5 2 9 13 12 16 16 6 2 9 10 12 5 13 6 3 9 6 9 15 11 6 1 9 12 12 12 14 5 2 10 8 12 8 13 4 0 10 14 13 13 13 5 5 10 12 11 14 13 5 2 10 11 9 12 12 4 4 10 16 9 16 16 6 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 12 seconds R Server 'George Udny Yule' @ 72.249.76.132 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation aantalVrienden[t] = + 0.766368778596676 + 0.048718031746747maand[t] + 0.0991533235522943Popularity[t] -0.0609920300506682FindingFriends[t] + 0.128326230337218KnowingPeople[t] -0.076124742332118Liked[t] + 0.0313954332780401`Celebrity `[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) 0.766368778596676 2.451766 0.3126 0.755044 0.377522 maand 0.048718031746747 0.24646 0.1977 0.843575 0.421788 Popularity 0.0991533235522943 0.054995 1.803 0.073444 0.036722 FindingFriends -0.0609920300506682 0.065252 -0.9347 0.351469 0.175734 KnowingPeople 0.128326230337218 0.043992 2.917 0.004089 0.002045 Liked -0.076124742332118 0.068512 -1.1111 0.268335 0.134168 `Celebrity ` 0.0313954332780401 0.113138 0.2775 0.781788 0.390894 Multiple Linear Regression - Regression Statistics Multiple R 0.402657535519121 R-squared 0.162133090910332 Adjusted R-squared 0.127934441559734 F-TEST (value) 4.74092088398498 F-TEST (DF numerator) 6 F-TEST (DF denominator) 147 p-value 0.000191518186576811 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.41891364789336 Sum Squared Residuals 295.957443206173 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0 2.59250210349606 -2.59250210349606 2 3 2.01890198053226 0.981098019467736 3 3 2.18931130344274 0.810688696557262 4 1 1.74173959054614 -0.74173959054614 5 3 2.83337231658481 0.166627683415192 6 1 2.06510471684829 -1.06510471684829 7 4 2.51916915152047 1.48083084847953 8 0 2.13998187723503 -2.13998187723503 9 3 3.16640336555337 -0.166403365553368 10 2 2.25007748817684 -0.250077488176837 11 4 3.39404327317685 0.60595672682315 12 3 1.79701549764746 1.20298450235254 13 1 1.53866376439451 -0.538663764394512 14 1 2.52006382462731 -1.52006382462731 15 2 2.15092416462454 -0.150924164624543 16 3 2.81733544090479 0.182664559095212 17 1 1.86419463376661 -0.864194633766614 18 1 1.81595243577031 -0.815952435770309 19 2 1.71804218153569 0.281957818464308 20 3 2.89568270973002 0.104317290269977 21 4 2.94522849096257 1.05477150903743 22 2 1.8492597661563 0.150740233843702 23 1 2.98471763785047 -1.98471763785047 24 2 3.17314122513152 -1.17314122513152 25 2 2.42908899875347 -0.429088998753474 26 4 2.89368602855348 1.10631397144652 27 2 2.86408943178085 -0.864089431780848 28 3 2.14582506370634 0.85417493629366 29 3 2.4270976071435 0.5729023928565 30 3 2.81146425378804 0.188535746211956 31 4 2.73553735612706 1.26446264387294 32 2 1.97015130847966 0.0298486915203416 33 2 2.06510471684829 -0.0651047168482865 34 4 3.22009306067871 0.779906939321287 35 3 1.99253035439556 1.00746964560444 36 4 2.26788441758454 1.73211558241546 37 2 2.81823011401163 -0.81823011401163 38 5 3.17536375162463 1.82463624837537 39 3 2.72806517717604 0.271934822823962 40 1 2.04164793301271 -1.04164793301271 41 1 0.993016465865293 0.00698353413470687 42 1 1.82249245067732 -0.822492450677325 43 2 1.92609082721585 0.073909172784148 44 3 2.94263454527722 0.0573654547227828 45 9 3.23564946294787 5.76435053705213 46 0 1.46887170200655 -1.46887170200655 47 0 2.13356892584998 -2.13356892584998 48 2 2.78551631763904 -0.785516317639044 49 2 1.30484204026912 0.695157959730882 50 3 2.52671662424836 0.473283375751640 51 1 2.29391212412407 -1.29391212412407 52 2 1.47744124936685 0.52255875063315 53 0 2.68439574559408 -2.68439574559408 54 5 2.73639938892804 2.26360061107196 55 2 2.54730697385673 -0.547306973856727 56 4 3.31467041019468 0.685329589805322 57 3 1.58004538887164 1.41995461112836 58 0 3.10412240509203 -3.10412240509203 59 0 1.42301723486863 -1.42301723486863 60 4 3.28394380470691 0.71605619529309 61 1 3.80584142343022 -2.80584142343022 62 1 3.01215863175102 -2.01215863175102 63 4 1.61043837800687 2.38956162199313 64 2 2.74538777564474 -0.745387775644745 65 4 2.81210044127246 1.18789955872754 66 1 1.95240181240126 -0.952401812401262 67 4 2.87593653247508 1.12406346752492 68 2 1.09089936936062 0.909100630639377 69 5 3.03385935958493 1.96614064041507 70 4 2.64623445209245 1.35376554790755 71 4 2.17614263203198 1.82385736796802 72 4 2.66910267957866 1.33089732042134 73 4 2.57213439158232 1.42786560841768 74 3 2.83512902249263 0.164870977507368 75 3 2.69054007115882 0.309459928841176 76 3 2.79104924874283 0.208950751257171 77 2 1.9962364483485 0.00376355165150205 78 1 1.11194075969598 -0.111940759695981 79 1 1.32608643780946 -0.326086437809456 80 5 3.21886013155891 1.78113986844109 81 4 2.6094010119771 1.3905989880229 82 2 2.29023082319459 -0.290230823194586 83 3 1.63295848517075 1.36704151482925 84 2 2.46528304376243 -0.465283043762429 85 2 1.86596082996617 0.134039170033834 86 2 2.44313933345483 -0.443139333454826 87 2 3.07494949830710 -1.07494949830710 88 3 1.94119089919144 1.05880910080856 89 2 2.22442232096545 -0.224422320965446 90 3 2.28891246010004 0.71108753989996 91 4 3.16308975332071 0.836910246679286 92 3 3.38289928358807 -0.382899283588070 93 3 2.42754544024851 0.572454559751493 94 0 1.82799738113567 -1.82799738113567 95 1 1.3318873448274 -0.331887344827399 96 2 1.48510178269728 0.514898217302723 97 2 2.66797267086352 -0.667972670863517 98 3 2.42097742469606 0.579022575303945 99 4 3.3524080137086 0.6475919862914 100 4 3.11088826531561 0.889111734684386 101 1 2.78748035850973 -1.78748035850973 102 2 1.48051115583538 0.519488844164624 103 2 0.855090454350411 1.14490954564959 104 3 2.16522912742019 0.83477087257981 105 3 2.05216189075409 0.947838109245906 106 3 3.00496908153973 -0.00496908153973336 107 1 1.74855759453246 -0.748557594532464 108 1 1.75847814529317 -0.758478145293173 109 1 2.36546089241986 -1.36546089241986 110 1 3.11049257597335 -2.11049257597335 111 0 1.70936585624260 -1.70936585624260 112 1 2.62453372425855 -1.62453372425855 113 3 2.55063150841955 0.449368491580452 114 3 3.08828337408314 -0.088283374083142 115 0 3.02729134403247 -3.02729134403247 116 2 1.60931785958346 0.390682140416541 117 5 2.9573109272651 2.04268907273490 118 2 2.72278288441227 -0.722782884412273 119 3 2.3873594649249 0.612640535075101 120 3 3.26748323903918 -0.267483239039185 121 5 1.74288425208685 3.25711574791315 122 4 2.79716557366214 1.20283442633786 123 4 3.15561757436969 0.844382425630308 124 0 1.57267277384751 -1.57267277384751 125 3 2.93783272592432 0.0621672740756817 126 0 2.83512902249263 -2.83512902249263 127 2 2.23079249184676 -0.230792491846763 128 0 1.75326629567497 -1.75326629567497 129 6 2.93783272592432 3.06216727407568 130 3 2.80860233218853 0.19139766781147 131 1 1.44737366947508 -0.447373669475085 132 6 2.20773590998115 3.79226409001885 133 2 2.79981179014296 -0.799811790142962 134 1 2.00238077391325 -1.00238077391325 135 3 3.01830295731577 -0.0183029573157713 136 1 2.06464838655472 -1.06464838655472 137 2 3.37695280269446 -1.37695280269446 138 4 2.72126667664659 1.27873332335341 139 1 2.96165641632444 -1.96165641632444 140 2 2.72983137337559 -0.729831373375591 141 0 2.71309766925986 -2.71309766925986 142 5 2.38895096646745 2.61104903353255 143 2 2.13070700425046 -0.130707004250463 144 1 1.16424181162798 -0.164241811627979 145 1 1.43271194031277 -0.432711940312772 146 4 2.30159680057180 1.69840319942820 147 3 3.24578251120528 -0.245782511205283 148 0 2.757305007582 -2.757305007582 149 3 2.64169111836198 0.358308881638018 150 3 3.03476352298350 -0.0347635229834959 151 0 1.84203757563915 -1.84203757563915 152 2 2.61819155402267 -0.618191554022668 153 5 3.04222621164279 1.95777378835721 154 2 2.18110965575015 -0.181109655750151 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.863877656553283 0.272244686893435 0.136122343446717 11 0.796478096381642 0.407043807236715 0.203521903618358 12 0.690294275320577 0.619411449358846 0.309705724679423 13 0.580540385911347 0.838919228177305 0.419459614088653 14 0.629926030131743 0.740147939736515 0.370073969868257 15 0.532139055859901 0.935721888280198 0.467860944140099 16 0.43554139051357 0.87108278102714 0.56445860948643 17 0.345595010638954 0.691190021277908 0.654404989361046 18 0.270899697501195 0.541799395002389 0.729100302498805 19 0.258820823963766 0.517641647927532 0.741179176036234 20 0.195788378813396 0.391576757626792 0.804211621186604 21 0.16245638947496 0.32491277894992 0.83754361052504 22 0.126602663038369 0.253205326076738 0.873397336961631 23 0.190759356080609 0.381518712161218 0.809240643919391 24 0.169820947383655 0.339641894767309 0.830179052616346 25 0.134017372335032 0.268034744670064 0.865982627664968 26 0.143859000387219 0.287718000774439 0.85614099961278 27 0.112927067001129 0.225854134002258 0.88707293299887 28 0.108785590988613 0.217571181977225 0.891214409011387 29 0.0924096285446096 0.184819257089219 0.90759037145539 30 0.0704941604535975 0.140988320907195 0.929505839546402 31 0.0731564044768805 0.146312808953761 0.92684359552312 32 0.0544632467898823 0.108926493579765 0.945536753210118 33 0.0385377559104195 0.077075511820839 0.96146224408958 34 0.0299060393666153 0.0598120787332306 0.970093960633385 35 0.0266294879467879 0.0532589758935757 0.973370512053212 36 0.0427563541451614 0.0855127082903227 0.957243645854839 37 0.0349839778958687 0.0699679557917374 0.965016022104131 38 0.0450004862980937 0.0900009725961873 0.954999513701906 39 0.0325052387392796 0.0650104774785592 0.96749476126072 40 0.0271364056437966 0.0542728112875933 0.972863594356203 41 0.0190410860306250 0.0380821720612501 0.980958913969375 42 0.0148209475575167 0.0296418951150334 0.985179052442483 43 0.0101606067434809 0.0203212134869619 0.98983939325652 44 0.00684277041151251 0.0136855408230250 0.993157229588488 45 0.366406362970681 0.732812725941362 0.633593637029319 46 0.347625068917505 0.69525013783501 0.652374931082495 47 0.383498602540241 0.766997205080482 0.616501397459759 48 0.356600004422329 0.713200008844658 0.643399995577671 49 0.344971288861002 0.689942577722005 0.655028711138998 50 0.320082798696386 0.640165597392771 0.679917201303614 51 0.303074753808899 0.606149507617798 0.696925246191101 52 0.259646775709827 0.519293551419654 0.740353224290173 53 0.382793410837067 0.765586821674135 0.617206589162933 54 0.480733877770576 0.961467755541152 0.519266122229424 55 0.437339531004032 0.874679062008064 0.562660468995968 56 0.396475409508385 0.79295081901677 0.603524590491615 57 0.398112601297592 0.796225202595183 0.601887398702408 58 0.566856696324476 0.866286607351048 0.433143303675524 59 0.550683357869335 0.898633284261331 0.449316642130665 60 0.517774325609138 0.964451348781723 0.482225674390862 61 0.628985354369616 0.742029291260769 0.371014645630384 62 0.647586213613529 0.704827572772942 0.352413786386471 63 0.768914450056416 0.462171099887167 0.231085549943584 64 0.736015181007075 0.52796963798585 0.263984818992925 65 0.739478366905362 0.521043266189277 0.260521633094638 66 0.71028859235421 0.579422815291579 0.289711407645790 67 0.70307669875761 0.59384660248478 0.29692330124239 68 0.686386066774133 0.627227866451733 0.313613933225866 69 0.72462938544534 0.550741229109319 0.275370614554659 70 0.7197793985979 0.560441202804199 0.280220601402099 71 0.741164141546244 0.517671716907512 0.258835858453756 72 0.734373659502854 0.531252680994292 0.265626340497146 73 0.731008636842113 0.537982726315775 0.268991363157887 74 0.690066857916723 0.619866284166554 0.309933142083277 75 0.647486144659 0.705027710682 0.352513855341 76 0.604569354430721 0.790861291138558 0.395430645569279 77 0.559472300285479 0.881055399429043 0.440527699714521 78 0.513257956690262 0.973484086619476 0.486742043309738 79 0.469617350826338 0.939234701652677 0.530382649173662 80 0.510843153476286 0.978313693047427 0.489156846523714 81 0.508070069390029 0.983859861219942 0.491929930609971 82 0.463149413833457 0.926298827666914 0.536850586166543 83 0.46130569370232 0.92261138740464 0.53869430629768 84 0.423968009462162 0.847936018924324 0.576031990537838 85 0.377402963540973 0.754805927081947 0.622597036459027 86 0.344225895223147 0.688451790446293 0.655774104776853 87 0.324560794052601 0.649121588105202 0.675439205947399 88 0.304777026561221 0.609554053122442 0.695222973438779 89 0.265956662429988 0.531913324859975 0.734043337570012 90 0.233583407039258 0.467166814078515 0.766416592960742 91 0.209484876067957 0.418969752135914 0.790515123932043 92 0.178946905420861 0.357893810841721 0.82105309457914 93 0.153839137726459 0.307678275452917 0.846160862273541 94 0.176998975818013 0.353997951636026 0.823001024181987 95 0.147531093747641 0.295062187495282 0.85246890625236 96 0.122084764906054 0.244169529812108 0.877915235093946 97 0.103810291765184 0.207620583530368 0.896189708234816 98 0.0855900034351003 0.171180006870201 0.9144099965649 99 0.0733253800375625 0.146650760075125 0.926674619962437 100 0.0639276244614359 0.127855248922872 0.936072375538564 101 0.0781395648986159 0.156279129797232 0.921860435101384 102 0.0703668801763407 0.140733760352681 0.929633119823659 103 0.065512587491255 0.13102517498251 0.934487412508745 104 0.0540165655942251 0.108033131188450 0.945983434405775 105 0.0502335771468472 0.100467154293694 0.949766422853153 106 0.0383773175390741 0.0767546350781482 0.961622682460926 107 0.0306370218563422 0.0612740437126843 0.969362978143658 108 0.0249632963474509 0.0499265926949018 0.97503670365255 109 0.0220505036333621 0.0441010072667242 0.977949496366638 110 0.0288542648785874 0.0577085297571747 0.971145735121413 111 0.0313697961687218 0.0627395923374436 0.968630203831278 112 0.033325248472774 0.066650496945548 0.966674751527226 113 0.0250975363907924 0.0501950727815848 0.974902463609208 114 0.0184388154122338 0.0368776308244676 0.981561184587766 115 0.0437174085191495 0.087434817038299 0.95628259148085 116 0.0329603637457304 0.0659207274914609 0.96703963625427 117 0.0392521321265268 0.0785042642530537 0.960747867873473 118 0.0297264419042338 0.0594528838084675 0.970273558095766 119 0.0235247515213249 0.0470495030426498 0.976475248478675 120 0.0166926378174624 0.0333852756349247 0.983307362182538 121 0.062406805390272 0.124813610780544 0.937593194609728 122 0.0518491369271731 0.103698273854346 0.948150863072827 123 0.0422569308695831 0.0845138617391663 0.957743069130417 124 0.0379339875982633 0.0758679751965265 0.962066012401737 125 0.0271143615500080 0.0542287231000161 0.972885638449992 126 0.0763272455037649 0.152654491007530 0.923672754496235 127 0.0620195439028811 0.124039087805762 0.937980456097119 128 0.0868137180292053 0.173627436058411 0.913186281970795 129 0.192833191447199 0.385666382894398 0.8071668085528 130 0.150953151502791 0.301906303005581 0.84904684849721 131 0.121786361474164 0.243572722948328 0.878213638525836 132 0.594832620585329 0.810334758829343 0.405167379414671 133 0.521287936365176 0.957424127269649 0.478712063634824 134 0.445129886515827 0.890259773031655 0.554870113484173 135 0.364353718047331 0.728707436094661 0.63564628195267 136 0.389536168973082 0.779072337946163 0.610463831026918 137 0.313713451373548 0.627426902747096 0.686286548626452 138 0.364480143078096 0.728960286156192 0.635519856921904 139 0.49649054360313 0.99298108720626 0.50350945639687 140 0.429523193244493 0.859046386488985 0.570476806755507 141 0.501418843033881 0.997162313932239 0.498581156966119 142 0.391630500387687 0.783261000775374 0.608369499612313 143 0.266867571030782 0.533735142061563 0.733132428969218 144 0.292232696723876 0.584465393447752 0.707767303276124 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 9 0.0666666666666667 NOK 10% type I error level 30 0.222222222222222 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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