Meervoudige regressie: inclusief lineaire trend

*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: Fri, 10 Dec 2010 18:05:35 +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/10/t1292004445ubyrax6rausrfha.htm/, Retrieved Fri, 10 Dec 2010 19:07:37 +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/10/t1292004445ubyrax6rausrfha.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 13 14 13 3 2 12 12 8 13 5 1 15 10 12 16 6 0 12 9 7 12 6 3 10 10 10 11 5 3 12 12 7 12 3 1 15 13 16 18 8 3 9 12 11 11 4 1 12 12 14 14 4 4 11 6 6 9 4 0 11 5 16 14 6 3 11 12 11 12 6 2 15 11 16 11 5 4 7 14 12 12 4 3 11 14 7 13 6 1 11 12 13 11 4 1 10 12 11 12 6 2 14 11 15 16 6 3 10 11 7 9 4 1 6 7 9 11 4 1 11 9 7 13 2 2 15 11 14 15 7 3 11 11 15 10 5 4 12 12 7 11 4 2 14 12 15 13 6 1 15 11 17 16 6 2 9 11 15 15 7 2 13 8 14 14 5 4 13 9 14 14 6 2 16 12 8 14 4 3 13 10 8 8 4 3 12 10 14 13 7 3 14 12 14 15 7 4 11 8 8 13 4 2 9 12 11 11 4 2 16 11 16 15 6 4 12 12 10 15 6 3 10 7 8 9 5 4 13 11 14 13 6 2 16 11 16 16 7 5 14 12 13 13 6 3 15 9 5 11 3 1 5 15 8 12 3 1 8 11 10 12 4 1 11 11 8 12 6 2 16 11 13 14 7 3 17 11 15 14 5 9 9 15 6 8 4 0 9 11 12 13 5 0 13 12 16 16 6 2 10 12 5 13 6 2 6 9 15 11 6 3 12 12 12 14 5 1 8 12 8 13 4 2 14 13 13 13 5 0 12 11 14 13 5 5 11 9 12 12 4 2 16 9 16 16 6 4 8 11 10 15 2 3 15 11 15 15 8 0 7 12 8 12 3 0 16 12 16 14 6 4 14 9 19 12 6 1 16 11 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 20 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 0.0422788742601457 + 0.107901800776091FindingFriends[t] + 0.211040385215400KnowingPeople[t] + 0.359974774820001Liked[t] + 0.606491671344046Celebrity[t] + 0.212457917682306SumFriends[t] -0.000685171025765t + 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) 0.0422788742601457 1.428584 0.0296 0.97643 0.488215 FindingFriends 0.107901800776091 0.096234 1.1212 0.263987 0.131993 KnowingPeople 0.211040385215400 0.063872 3.3041 0.001193 0.000597 Liked 0.359974774820001 0.097099 3.7073 0.000295 0.000147 Celebrity 0.606491671344046 0.155924 3.8897 0.000151 7.5e-05 SumFriends 0.212457917682306 0.120422 1.7643 0.079733 0.039867 t -0.000685171025765 0.003797 -0.1804 0.857055 0.428527 Multiple Linear Regression - Regression Statistics Multiple R 0.713839592799361 R-squared 0.509566964247958 Adjusted R-squared 0.489817982942506 F-TEST (value) 25.8021898125601 F-TEST (DF numerator) 6 F-TEST (DF denominator) 149 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.09754558153579 Sum Squared Residuals 655.55492252643 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 11.3229454283959 1.67705457160413 2 12 10.9486415703074 1.05135842969255 3 15 13.0502724167128 1.94972758328717 4 12 11.0839581726009 0.916041827399105 5 10 10.8578295118334 -0.857829511833381 6 12 9.1619023834809 2.8380976165191 7 15 16.7857053211747 -1.78570532117466 8 9 10.2512104788150 -1.25121047881501 9 12 12.6009445409424 -0.600944540942367 10 11 7.61481993870763 3.38518006129237 11 11 13.2668677888948 -2.26686778889479 12 11 12.0338858299024 -1.03388582990235 13 15 12.4389501733781 2.56104982662194 14 7 11.4588340496126 -4.45883404961262 15 11 11.5509892346533 -0.550989234653334 16 11 10.6678098810397 0.332190118960308 17 10 12.0304599747735 -2.03045997477353 18 14 14.4183915607956 -0.418391560795577 19 10 8.5716607062539 1.42833929374609 20 6 9.28139865219458 -3.28139865219458 21 11 8.79386043692441 2.20613956307559 22 15 14.4511273880012 0.548872611998838 23 11 11.861083303085 -0.861083303085009 24 12 9.60854411922348 2.39145588077652 25 14 13.0166570045667 0.983342995433302 26 15 14.6225330453379 0.37746695466205 27 9 14.4462840004054 -5.44628400040543 28 13 12.7628107596925 0.237189240307485 29 13 13.0516032254223 -0.0516032254222731 30 16 11.1078557204266 4.8921442795734 31 13 8.73151829892865 4.26848170107135 32 12 13.6164243273274 -1.61642432732742 33 14 14.7639502251761 -0.763950225176144 34 11 10.1010751407169 0.89892485928313 35 9 10.4451687788017 -1.44516877880166 36 16 14.4695820104095 1.53041798959049 37 12 13.0980984111851 -1.09809841118513 38 10 9.58194106326637 0.418058936733627 39 13 12.9005803418968 0.0994196581031959 40 16 15.6457656901528 0.354234309847196 41 14 13.0085293330883 0.991470666911728 42 15 8.03147527897429 6.96852472102571 43 5 9.67129684307127 -4.67129684307127 44 8 10.2675769107160 -2.26757691071598 45 11 11.2702522296298 -0.270252229629817 46 16 13.8636681233474 2.13633187665260 47 17 14.3468278861582 2.65317211384182 48 9 8.19992487189338 0.80007512810662 49 9 11.4402403544997 -2.4402403544997 50 13 14.5029503562803 -1.50295035628028 51 10 11.1008966234251 -1.10089662342512 52 6 12.3794182702674 -6.37941827026738 53 12 12.1178341636750 -0.117834163675035 54 8 10.5189789233059 -2.51897892330593 55 14 11.8629733151127 2.13702668488731 56 12 12.9198145161617 -0.919814516161673 57 11 10.6774047739420 0.322595226058038 58 16 14.5986794211105 1.40132057888950 59 8 10.5491561624660 -2.54915616246603 60 15 14.6052491925346 0.394750807465382 61 7 9.12280044459692 -2.12280044459692 62 16 14.1996945896957 1.80030541030429 63 14 13.1511018693010 0.848898130699046 64 16 13.3909426982104 2.60905730178963 65 9 10.4370886011521 -1.43708860115210 66 14 12.1724504684178 1.82754953158221 67 11 13.2652787997115 -2.26527879971149 68 13 10.3324051225716 2.66759487742844 69 15 13.2018024620492 1.79819753795084 70 5 5.78687670633618 -0.78687670633618 71 15 12.9095369507752 2.09046304922480 72 13 12.5932552776278 0.406744722372182 73 11 12.4225623102152 -1.42256231021516 74 11 14.2019052867592 -3.20190528675919 75 12 12.770847449127 -0.770847449126987 76 12 13.4066291176173 -1.40662911761730 77 12 12.3363389159882 -0.336338915988176 78 12 11.9450791306866 0.0549208693134415 79 14 10.8618244224818 3.13817557751819 80 6 7.93369289619485 -1.93369289619485 81 7 9.71700622789257 -2.71700622789257 82 14 12.3979675769200 1.60203242308003 83 14 14.1642325913724 -0.164232591372359 84 10 11.1622582431510 -1.16225824315104 85 13 9.11060893737928 3.88939106262072 86 12 12.3021253599872 -0.302125359987231 87 9 9.3085421542196 -0.308542154219595 88 12 11.9157364811797 0.0842635188202862 89 16 14.7992546829366 1.20074531706335 90 10 10.44993449368 -0.449934493680007 91 14 13.1007142321554 0.899285767844572 92 10 13.5856333596382 -3.58563335963817 93 16 15.5048955088810 0.495104491118956 94 15 13.3895328228167 1.61046717718326 95 12 11.4750810803260 0.524918919673974 96 10 9.34533635521919 0.654663644780811 97 8 10.1063714494618 -2.10637144946177 98 8 8.69927681792892 -0.699276817928916 99 11 12.6492225563186 -1.64922255631859 100 13 12.5460234721373 0.453976527862662 101 16 15.6025527251142 0.397447274885767 102 16 14.9277138096138 1.07228619038624 103 14 15.40097191064 -1.40097191064001 104 11 9.02930394347526 1.97069605652474 105 4 7.13116239143005 -3.13116239143005 106 14 14.7316815286915 -0.731681528691532 107 9 10.5059486593727 -1.50594865937267 108 14 15.2097347363448 -1.20973473634482 109 8 10.2285968715611 -2.22859687156112 110 8 10.6596323591557 -2.65963235915573 111 11 11.8622906426285 -0.862290642628484 112 12 13.1319315935648 -1.13193159356483 113 11 11.0555809548939 -0.0555809548938764 114 14 13.2535455624828 0.746454437517184 115 15 14.4332022877703 0.56679771222969 116 16 13.4202548654152 2.57974513458479 117 16 12.8900977421186 3.10990225788139 118 11 12.7680356448051 -1.76803564480507 119 14 14.1620573736940 -0.162057373694014 120 14 10.8500426008709 3.14995739912905 121 12 11.5296919231236 0.470308076876418 122 14 12.5117833887074 1.48821661129263 123 8 10.8522396851944 -2.85223968519437 124 13 14.0540754016590 -1.05407540165897 125 16 13.9454884298571 2.05451157014288 126 12 10.5891164498195 1.41088355018051 127 16 15.4535526772360 0.546447322764025 128 12 12.7336264712306 -0.733626471230597 129 11 11.4245311098640 -0.42453110986404 130 4 5.94852914306801 -1.94852914306801 131 16 16.0881857461798 -0.0881857461798333 132 15 12.6272365837522 2.37276341624783 133 10 11.3323168190482 -1.33231681904819 134 13 13.9879527607243 -0.98795276072434 135 15 13.0916401138041 1.90835988619594 136 12 10.4613773667263 1.53862263327370 137 14 13.6169066590895 0.383093340910459 138 7 10.3377021193723 -3.33770211937232 139 19 13.8709549749518 5.1290450250482 140 12 12.9018752063590 -0.901875206359016 141 12 11.8273324073292 0.172667592670824 142 13 13.2978843018391 -0.297884301839101 143 15 12.3792495024006 2.62075049759937 144 8 8.78114102917261 -0.781141029172615 145 12 10.8787091303921 1.12129086960788 146 10 10.7202088738558 -0.72020887385583 147 8 11.2092665463915 -3.20926654639153 148 10 14.6134096734128 -4.6134096734128 149 15 13.8197249919958 1.18027500800424 150 16 14.0183644453457 1.98163555465434 151 13 13.2207100056067 -0.220710005606677 152 16 15.0409721154632 0.959027884536796 153 9 9.7693949660099 -0.769394966009893 154 14 13.0117526523669 0.988247347633058 155 14 13.0984994811350 0.901500518865017 156 12 10.1213022656799 1.87869773432008 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0769249686088593 0.153849937217719 0.92307503139114 11 0.113426184645691 0.226852369291381 0.886573815354309 12 0.0702391813723468 0.140478362744694 0.929760818627653 13 0.563585063487147 0.872829873025706 0.436414936512853 14 0.729368248847453 0.541263502305095 0.270631751152547 15 0.659434130151593 0.681131739696815 0.340565869848407 16 0.569035574025244 0.861928851949511 0.430964425974756 17 0.482636716513075 0.96527343302615 0.517363283486925 18 0.461884833940402 0.923769667880804 0.538115166059598 19 0.404155708708348 0.808311417416696 0.595844291291652 20 0.531143257840978 0.937713484318044 0.468856742159022 21 0.548434713400161 0.903130573199679 0.451565286599839 22 0.588785918961769 0.822428162076462 0.411214081038231 23 0.526538933373726 0.946922133252549 0.473461066626274 24 0.541207332809878 0.917585334380243 0.458792667190122 25 0.516147883834627 0.967704232330745 0.483852116165373 26 0.456570764409287 0.913141528818573 0.543429235590713 27 0.680681521294078 0.638636957411844 0.319318478705922 28 0.63386565451101 0.732268690977981 0.366134345488991 29 0.578273166433521 0.843453667132957 0.421726833566479 30 0.730829355354567 0.538341289290866 0.269170644645433 31 0.81176230026992 0.376475399460159 0.188237699730080 32 0.776586940498692 0.446826119002616 0.223413059501308 33 0.730261683521193 0.539476632957615 0.269738316478807 34 0.695603717588639 0.608792564822722 0.304396282411361 35 0.691579099149864 0.616841801700272 0.308420900850136 36 0.688288492493393 0.623423015013214 0.311711507506607 37 0.661300765282161 0.677398469435679 0.338699234717839 38 0.612418860063075 0.77516227987385 0.387581139936925 39 0.563166573043847 0.873666853912307 0.436833426956153 40 0.520027354588786 0.959945290822427 0.479972645411214 41 0.481142698296269 0.962285396592538 0.518857301703731 42 0.770009333350157 0.459981333299687 0.229990666649843 43 0.95101905559329 0.0979618888134217 0.0489809444067109 44 0.95524941073423 0.0895011785315403 0.0447505892657701 45 0.941838204057146 0.116323591885708 0.0581617959428539 46 0.949683263770228 0.100633472459545 0.0503167362297724 47 0.949267860635503 0.101464278728994 0.0507321393644971 48 0.93855244317928 0.122895113641442 0.0614475568207209 49 0.936241146295479 0.127517707409043 0.0637588537045214 50 0.924519038763673 0.150961922472653 0.0754809612363267 51 0.917067898726457 0.165864202547086 0.0829321012735431 52 0.986884755219867 0.0262304895602666 0.0131152447801333 53 0.982764290324557 0.034471419350885 0.0172357096754425 54 0.986455017393267 0.0270899652134659 0.0135449826067330 55 0.991156863376892 0.0176862732462161 0.00884313662310807 56 0.988355336411087 0.0232893271778255 0.0116446635889127 57 0.984322083168263 0.0313558336634737 0.0156779168317368 58 0.98250729027616 0.0349854194476782 0.0174927097238391 59 0.98798338166841 0.0240332366631784 0.0120166183315892 60 0.987072194460296 0.0258556110794081 0.0129278055397041 61 0.98688232031371 0.0262353593725817 0.0131176796862908 62 0.987456880225994 0.0250862395480124 0.0125431197740062 63 0.986031796729663 0.0279364065406739 0.0139682032703370 64 0.98895101497247 0.0220979700550612 0.0110489850275306 65 0.987593675966376 0.024812648067247 0.0124063240336235 66 0.987014291123916 0.0259714177521671 0.0129857088760836 67 0.987387948101294 0.0252241037974117 0.0126120518987058 68 0.990003657441651 0.0199926851166972 0.0099963425583486 69 0.989465938306517 0.0210681233869652 0.0105340616934826 70 0.9862727032158 0.0274545935684006 0.0137272967842003 71 0.986849246248584 0.0263015075028313 0.0131507537514156 72 0.982617473989787 0.0347650520204252 0.0173825260102126 73 0.979414301896697 0.0411713962066070 0.0205856981033035 74 0.985678538657707 0.0286429226845863 0.0143214613422931 75 0.981128602605813 0.037742794788374 0.018871397394187 76 0.977786351747742 0.0444272965045168 0.0222136482522584 77 0.971043897750517 0.0579122044989662 0.0289561022494831 78 0.962237263653105 0.07552547269379 0.037762736346895 79 0.976027939675934 0.0479441206481321 0.0239720603240660 80 0.973996470491219 0.0520070590175623 0.0260035295087812 81 0.976806498669516 0.046387002660967 0.0231935013304835 82 0.976399240281436 0.0472015194371282 0.0236007597185641 83 0.968838090293502 0.0623238194129967 0.0311619097064984 84 0.961553386056901 0.0768932278861977 0.0384466139430989 85 0.987956146651313 0.0240877066973731 0.0120438533486866 86 0.983772162882018 0.0324556742359639 0.0162278371179820 87 0.978493102166136 0.0430137956677281 0.0215068978338641 88 0.972304214559655 0.0553915708806898 0.0276957854403449 89 0.967407048323728 0.0651859033525439 0.0325929516762719 90 0.958365347811157 0.083269304377686 0.041634652188843 91 0.951978662874677 0.0960426742506467 0.0480213371253233 92 0.969609837576824 0.0607803248463525 0.0303901624231762 93 0.96121643984532 0.0775671203093583 0.0387835601546791 94 0.957914140750117 0.0841717184997668 0.0420858592498834 95 0.948718490038674 0.102563019922651 0.0512815099613255 96 0.938664577157452 0.122670845685097 0.0613354228425485 97 0.931685955640147 0.136628088719707 0.0683140443598535 98 0.915502826190057 0.168994347619887 0.0844971738099434 99 0.906208124037952 0.187583751924096 0.093791875962048 100 0.888552545908263 0.222894908183475 0.111447454091737 101 0.864314528118522 0.271370943762955 0.135685471881478 102 0.846373604381371 0.307252791237257 0.153626395618629 103 0.846247427016688 0.307505145966624 0.153752572983312 104 0.897430054103697 0.205139891792605 0.102569945896302 105 0.894070534691886 0.211858930616228 0.105929465308114 106 0.868575815953268 0.262848368093464 0.131424184046732 107 0.842584208671341 0.314831582657317 0.157415791328659 108 0.830949136612741 0.338101726774517 0.169050863387259 109 0.821470409629004 0.357059180741992 0.178529590370996 110 0.844533336245618 0.310933327508765 0.155466663754382 111 0.831661380692579 0.336677238614843 0.168338619307421 112 0.885029484518534 0.229941030962932 0.114970515481466 113 0.855881744120244 0.288236511759512 0.144118255879756 114 0.829589290619283 0.340821418761434 0.170410709380717 115 0.793546722535682 0.412906554928636 0.206453277464318 116 0.7883451801048 0.4233096397904 0.2116548198952 117 0.799437937318468 0.401124125363064 0.200562062681532 118 0.792579079137657 0.414841841724686 0.207420920862343 119 0.748848610315745 0.502302779368509 0.251151389684255 120 0.807636564006685 0.384726871986629 0.192363435993315 121 0.77458882903606 0.450822341927881 0.225411170963941 122 0.748018263896552 0.503963472206895 0.251981736103448 123 0.740448390473104 0.519103219053793 0.259551609526896 124 0.69444469286775 0.611110614264501 0.305555307132251 125 0.69320485591071 0.61359028817858 0.30679514408929 126 0.685370216057684 0.629259567884633 0.314629783942316 127 0.624961492118192 0.750077015763616 0.375038507881808 128 0.58135224128217 0.837295517435661 0.418647758717830 129 0.595087862938056 0.809824274123888 0.404912137061944 130 0.600866750520333 0.798266498959334 0.399133249479667 131 0.537688209587014 0.924623580825971 0.462311790412986 132 0.506754389074648 0.986491221850704 0.493245610925352 133 0.488649664102352 0.977299328204704 0.511350335897648 134 0.414580966842154 0.829161933684309 0.585419033157846 135 0.37427737609642 0.74855475219284 0.62572262390358 136 0.366185057788308 0.732370115576617 0.633814942211692 137 0.293944941019253 0.587889882038507 0.706055058980747 138 0.369583689153775 0.73916737830755 0.630416310846225 139 0.760652911928199 0.478694176143602 0.239347088071801 140 0.742262861666488 0.515474276667025 0.257737138333512 141 0.692243638858141 0.615512722283719 0.307756361141860 142 0.605101613287318 0.789796773425363 0.394898386712682 143 0.532565670799797 0.934868658400407 0.467434329200204 144 0.407376376806561 0.814752753613123 0.592623623193439 145 0.467845343159032 0.935690686318063 0.532154656840968 146 0.721255047136129 0.557489905727742 0.278744952863871 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 31 0.226277372262774 NOK 10% type I error level 45 0.328467153284672 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/10a53h1292004313.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/10a53h1292004313.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/13mo61292004313.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/13mo61292004313.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/2ed591292004313.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/2ed591292004313.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/3ed591292004313.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/3ed591292004313.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/4ed591292004313.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/4ed591292004313.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/57m4c1292004313.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/57m4c1292004313.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/67m4c1292004313.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/67m4c1292004313.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/7zdlw1292004313.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/7zdlw1292004313.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/8zdlw1292004313.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/8zdlw1292004313.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/9a53h1292004313.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/10/t1292004445ubyrax6rausrfha/9a53h1292004313.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by