Mini tutorial -

*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: Thu, 02 Dec 2010 15:06:31 +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/02/t1291302308ta3t4buzzm5x2ys.htm/, Retrieved Thu, 02 Dec 2010 16:05:19 +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/02/t1291302308ta3t4buzzm5x2ys.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:

Trend extra

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2 13 13 14 13 3 5 1 3 12 12 8 13 5 6 1 3 15 10 12 16 6 4 1 3 12 9 7 12 6 6 2 3 10 10 10 11 5 3 1 3 12 12 7 12 3 10 1 2 15 13 16 18 8 8 2 3 9 12 11 11 4 3 1 3 12 12 14 14 4 4 1 4 11 6 6 9 4 3 1 3 11 5 16 14 6 5 2 3 11 12 11 12 6 5 2 2 15 11 16 11 5 6 1 3 7 14 12 12 4 5 1 3 11 14 7 13 6 3 1 3 11 12 13 11 4 4 2 3 10 12 11 12 6 8 1 3 14 11 15 16 6 8 2 2 10 11 7 9 4 8 2 4 6 7 9 11 4 5 1 3 11 9 7 13 2 8 2 2 15 11 14 15 7 2 1 3 11 11 15 10 5 0 1 3 12 12 7 11 4 5 2 2 14 12 15 13 6 2 1 2 15 11 17 16 6 7 1 4 9 11 15 15 7 5 1 2 13 8 14 14 5 2 1 3 13 9 14 14 6 12 2 2 16 12 8 14 4 7 1 4 13 10 8 8 4 0 2 3 12 10 14 13 7 2 1 2 14 12 14 15 7 3 1 3 11 8 8 13 4 0 2 3 9 12 11 11 4 9 2 1 16 11 16 15 6 2 2 3 12 12 10 15 6 3 1 3 10 7 8 9 5 1 2 3 13 11 14 13 6 10 2 2 16 11 16 16 7 1 1 3 14 12 13 13 6 4 1 15 9 5 11 3 6 1 5 5 15 8 12 3 6 1 4 8 11 10 12 4 4 2 3 11 11 8 12 6 4 2 2 16 11 13 14 7 7 1 2 17 11 15 14 5 7 2 3 9 15 6 8 4 7 2 4 9 11 12 13 5 0 1 2 13 12 16 16 6 3 2 3 10 12 5 13 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation NotPopular[t] = -0.897130299603902 -0.0394487100113876Popularity[t] + 0.506639399645459FindingFriends[t] + 0.341104470528959KnowingPeople[t] -0.41203603377187Liked[t] -0.0763187735029738Celebrity[t] -0.220036383087809WeightedSum[t] + 1.08469284012130Gender[t] + 0.0251347382005958t + 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) -0.897130299603902 1.748825 -0.513 0.608728 0.304364 Popularity -0.0394487100113876 0.109012 -0.3619 0.717965 0.358983 FindingFriends 0.506639399645459 0.067878 7.464 0 0 KnowingPeople 0.341104470528959 0.088231 3.866 0.000166 8.3e-05 Liked -0.41203603377187 0.094158 -4.376 2.3e-05 1.1e-05 Celebrity -0.0763187735029738 0.071209 -1.0718 0.285583 0.142791 WeightedSum -0.220036383087809 0.124401 -1.7688 0.079006 0.039503 Gender 1.08469284012130 0.240032 4.5189 1.3e-05 6e-06 t 0.0251347382005958 0.006372 3.9445 0.000123 6.2e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.875372522073427 R-squared 0.766277052401192 Adjusted R-squared 0.753557436205339 F-TEST (value) 60.243724386196 F-TEST (DF numerator) 8 F-TEST (DF denominator) 147 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.42923828943667 Sum Squared Residuals 867.476204029183 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2 4.3760321563839 -2.37603215638390 2 3 1.51467545168307 1.48532454831693 3 3 0.900249034031469 2.09975096596853 4 3 1.12433235900913 1.87566764099087 5 3 2.82208844488184 0.177911555118155 6 3 0.958637982383089 2.04136201761691 7 2 3.11296176110645 -1.11296176110645 8 3 4.36764341281784 -1.36764341281784 9 3 3.84160094816772 -0.841600948167725 10 4 0.41772878622244 3.58227121377756 11 3 1.77907118814756 1.22092881185244 12 3 4.46923143876531 -1.46923143876531 13 2 4.71907987398542 -2.71907987398542 14 3 5.09962373191658 -2.09962373191658 15 3 3.13684046282462 -0.136840462824622 16 3 6.03668929649123 -3.03668929649123 17 3 2.88955185039495 0.110448149605048 18 3 3.05121893605419 -0.0512189360541913 19 2 3.5422025334777 -1.54220253347770 20 4 1.13212769579832 2.86787230420168 21 3 1.04423791249506 1.95576208750494 22 2 3.34244742699068 -1.34244742699068 23 3 6.5193719578067 -3.51937195780669 24 3 3.93165528582305 -0.931655285823046 25 2 5.20543506282498 -3.20543506282498 26 2 3.030400615672 -1.030400615672 27 4 3.38580869932752 0.61419130067248 28 2 2.61690865805847 -0.616908658058469 29 3 1.95669303164476 1.04330696835524 30 2 1.50489963789751 0.495100362102495 31 4 5.73226543120852 -1.73226543120852 32 3 4.02957360692908 -1.02957360692908 33 2 3.94498127376627 -1.94498127376627 34 3 2.81310809768282 0.186891902317180 35 3 4.81075588582837 -1.81075588582837 36 1 5.49810560646981 -4.49810560646981 37 3 2.83631853797856 0.163681462021435 38 3 3.79824533934783 -0.798245339347827 39 3 4.07342801288912 -1.07342801288912 40 2 4.24563329496387 -2.24563329496387 41 3 4.48530916680098 -1.48530916680098 42 15 9.5982435639497 5.40175643605031 43 5 10.163015871426 -5.16301587142599 44 8 9.79509653898804 -1.79509653898804 45 11 6.89818757023268 4.10181242976732 46 16 9.7177722765255 6.2822277234745 47 17 12.4449143385942 4.55508566140576 48 9 7.20260169065957 1.79739830934043 49 9 10.3037361030174 -1.30373610301743 50 13 13.5629572441280 -0.562957244128046 51 10 7.91488053033595 2.08511946966405 52 6 11.3578536138461 -5.35785361384609 53 12 12.1121287615502 -0.112128761550237 54 8 9.02062585078764 -1.02062585078764 55 14 11.2890303278593 2.71096967214067 56 12 13.5097062029492 -1.50970620294916 57 11 10.1967303508700 0.80326964912996 58 16 15.3397480499820 0.660251950017969 59 8 10.8584914775033 -2.85849147750332 60 15 13.1903114650456 1.80968853495444 61 7 8.56440160882829 -1.56440160882829 62 16 13.1734452240562 2.82655477594384 63 14 13.2225800570540 0.777419942945966 64 16 12.7525465661338 3.24745343386615 65 9 8.03062866495148 0.96937133504852 66 14 11.5286423845743 2.47135761542570 67 11 11.8139154177650 -0.813915417764983 68 13 7.49487201996735 5.50512798003265 69 15 12.4967397886133 2.50326021138668 70 5 4.55682642709225 0.443173572907753 71 15 12.5730781153279 2.42692188467212 72 13 12.9930999744081 0.00690002559190916 73 11 10.3687609606215 0.631239039378527 74 11 14.1797015958454 -3.17970159584545 75 12 11.1351133980729 0.864886601927082 76 12 13.1355003297079 -1.13550032970793 77 12 12.3038846539797 -0.30388465397972 78 12 11.2086363369176 0.791363663082398 79 14 11.4653054213888 2.53469457861123 80 6 10.2779200162553 -4.27792001625531 81 7 8.157340876844 -1.15734087684399 82 14 10.5496934945178 3.45030650548215 83 14 13.9877070185229 0.0122929814770966 84 10 11.2308932994876 -1.23089329948763 85 13 8.97028622475755 4.02971377524245 86 12 11.1137024021434 0.886297597856591 87 9 9.70571401836452 -0.705714018364521 88 12 10.9304863127719 1.06951368722808 89 16 13.1747032152873 2.82529678471266 90 10 10.7410102531608 -0.741010253160765 91 14 12.5925479516883 1.40745204831168 92 10 11.7123494489778 -1.71234944897783 93 16 13.1381021754394 2.86189782456061 94 15 13.7918685694720 1.20813143052798 95 12 11.6968830301917 0.303116969808286 96 10 10.2335824226875 -0.233582422687455 97 8 8.84692134889893 -0.846921348898932 98 8 8.72400251255341 -0.724002512553412 99 11 14.2389633404637 -3.23896334046371 100 13 9.87321581021047 3.12678418978953 101 16 14.1142245112099 1.88577548879008 102 16 13.1522710855949 2.8477289144051 103 14 16.1487668990251 -2.14876689902506 104 11 11.9519951104391 -0.951995110439108 105 4 6.54559165919482 -2.54559165919482 106 14 12.0665995371307 1.93340046286926 107 9 12.3725385655714 -3.37253856557135 108 14 14.7694528287679 -0.769452828767913 109 8 13.5620023360651 -5.56200233606515 110 8 12.1195381747932 -4.11953817479322 111 11 13.0983795716071 -2.09837957160709 112 12 13.5571533906941 -1.55715339069414 113 11 9.55445780494846 1.44554219505154 114 14 12.0643074949525 1.93569250504752 115 15 11.7408275907736 3.25917240922637 116 16 12.2521617743997 3.74783822560030 117 16 12.1526090916648 3.84739090833518 118 11 9.49861126795903 1.50138873204097 119 14 12.8710754521385 1.12892454786147 120 14 13.2439269186239 0.756073081376064 121 12 13.5707174173421 -1.57071741734210 122 14 15.6118169324415 -1.61181693244152 123 8 11.0362251992596 -3.03622519925961 124 13 13.5589306837328 -0.558930683732803 125 16 14.3266131045512 1.67338689544879 126 12 8.82298128300247 3.17701871699753 127 16 14.0336551488330 1.96634485116698 128 12 14.0609128486240 -2.06091284862404 129 11 14.5657727771045 -3.56577277710446 130 4 6.31126272484161 -2.31126272484161 131 16 12.6679073939992 3.33209260600076 132 15 12.6899022499226 2.31009775007745 133 10 10.0980741579090 -0.0980741579090252 134 13 12.5315687537015 0.46843124629847 135 15 13.5736016246874 1.42639837531263 136 12 12.1988639709057 -0.198863970905742 137 14 15.5997339660851 -1.5997339660851 138 7 11.7282442252924 -4.72824422529235 139 19 13.8675122336854 5.13248776631464 140 12 15.6963022983277 -3.69630229832766 141 12 14.3678566882992 -2.36785668829918 142 13 13.3915277347035 -0.391527734703509 143 15 16.8633728412394 -1.86337284123943 144 8 9.8434796048674 -1.84347960486741 145 12 12.4738033733387 -0.47380337333872 146 10 9.7565925497357 0.243407450264293 147 8 9.12675919737866 -1.12675919737866 148 10 13.8227412004506 -3.82274120045061 149 15 13.8659306138014 1.13406938619864 150 16 12.4267842865153 3.57321571348475 151 13 10.9749445028928 2.02505549710717 152 16 15.2754239432533 0.72457605674665 153 9 11.6376297982715 -2.63762979827154 154 14 13.6592490473931 0.34075095260693 155 14 13.6349004632863 0.365099536713684 156 12 13.2331396915687 -1.23313969156869 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 7.36296561677173e-05 0.000147259312335435 0.999926370343832 13 2.45093529440490e-06 4.90187058880979e-06 0.999997549064706 14 6.16922004002754e-07 1.23384400800551e-06 0.999999383077996 15 5.37274866835186e-06 1.07454973367037e-05 0.999994627251332 16 6.063788588944e-07 1.2127577177888e-06 0.99999939362114 17 6.56107551534248e-08 1.31221510306850e-07 0.999999934389245 18 6.47275907396734e-09 1.29455181479347e-08 0.99999999352724 19 2.73037407447581e-07 5.46074814895162e-07 0.999999726962593 20 4.54255087549158e-08 9.08510175098317e-08 0.999999954574491 21 1.23430952533667e-08 2.46861905067334e-08 0.999999987656905 22 1.21314641036168e-08 2.42629282072335e-08 0.999999987868536 23 3.00292421747277e-09 6.00584843494555e-09 0.999999996997076 24 5.87978243507212e-10 1.17595648701442e-09 0.999999999412022 25 1.70280545820092e-10 3.40561091640185e-10 0.99999999982972 26 3.00012067269478e-11 6.00024134538956e-11 0.999999999969999 27 2.72887469479433e-11 5.45774938958866e-11 0.999999999972711 28 3.30007960039896e-11 6.60015920079793e-11 0.999999999967 29 9.17563845882922e-12 1.83512769176584e-11 0.999999999990824 30 1.71334983620567e-12 3.42669967241134e-12 0.999999999998287 31 8.18115113330363e-12 1.63623022666073e-11 0.999999999991819 32 1.71523665606786e-12 3.43047331213572e-12 0.999999999998285 33 6.08957521880222e-13 1.21791504376044e-12 0.99999999999939 34 1.65860404809251e-13 3.31720809618502e-13 0.999999999999834 35 3.23126079078295e-14 6.4625215815659e-14 0.999999999999968 36 8.81656816849453e-14 1.76331363369891e-13 0.999999999999912 37 2.20682298146298e-14 4.41364596292596e-14 0.999999999999978 38 7.43961139362273e-15 1.48792227872455e-14 0.999999999999993 39 3.12800755499881e-15 6.25601510999761e-15 0.999999999999997 40 5.2121277185154e-15 1.04242554370308e-14 0.999999999999995 41 7.0672991546869e-14 1.41345983093738e-13 0.99999999999993 42 0.00159216493288379 0.00318432986576757 0.998407835067116 43 0.00797408594188002 0.0159481718837600 0.99202591405812 44 0.00877779430151145 0.0175555886030229 0.991222205698489 45 0.0982857437981197 0.196571487596239 0.90171425620188 46 0.792277622954593 0.415444754090814 0.207722377045407 47 0.935218724333923 0.129562551332154 0.0647812756660772 48 0.91811590316533 0.163768193669341 0.0818840968346704 49 0.917955776360747 0.164088447278506 0.0820442236392528 50 0.92072287726014 0.158554245479720 0.0792771227398602 51 0.900239478499217 0.199521043001565 0.0997605215007825 52 0.988888833401673 0.0222223331966537 0.0111111665983268 53 0.98481537460316 0.03036925079368 0.01518462539684 54 0.986348441621076 0.0273031167578473 0.0136515583789236 55 0.989561286762665 0.0208774264746708 0.0104387132373354 56 0.986219208914224 0.0275615821715522 0.0137807910857761 57 0.981977962416825 0.0360440751663491 0.0180220375831746 58 0.981190616333469 0.0376187673330625 0.0188093836665312 59 0.98276134957888 0.0344773008422408 0.0172386504211204 60 0.98250943280667 0.0349811343866609 0.0174905671933304 61 0.980447106493732 0.0391057870125364 0.0195528935062682 62 0.98514692730788 0.0297061453842389 0.0148530726921195 63 0.98117719334537 0.0376456133092609 0.0188228066546304 64 0.984791808917104 0.0304163821657915 0.0152081910828958 65 0.97979278545267 0.0404144290946597 0.0202072145473298 66 0.978456816619617 0.043086366760766 0.021543183380383 67 0.978691714072193 0.0426165718556141 0.0213082859278071 68 0.989200537897582 0.0215989242048361 0.0107994621024181 69 0.987550999861562 0.0248980002768762 0.0124490001384381 70 0.984061253337505 0.0318774933249907 0.0159387466624953 71 0.984994122573136 0.0300117548537285 0.0150058774268642 72 0.980766011588879 0.0384679768222427 0.0192339884111213 73 0.97460720288666 0.050785594226681 0.0253927971133405 74 0.984969778523913 0.0300604429521745 0.0150302214760873 75 0.979741079091615 0.0405178418167706 0.0202589209083853 76 0.977664395600066 0.0446712087998688 0.0223356043999344 77 0.971040277014071 0.0579194459718573 0.0289597229859286 78 0.962473551983661 0.075052896032678 0.037526448016339 79 0.968320949064974 0.0633581018700524 0.0316790509350262 80 0.985032248187527 0.0299355036249451 0.0149677518124725 81 0.984427799218547 0.0311444015629055 0.0155722007814527 82 0.988342226253087 0.0233155474938258 0.0116577737469129 83 0.984221034518426 0.0315579309631479 0.0157789654815740 84 0.981494567079375 0.0370108658412509 0.0185054329206254 85 0.99427418825155 0.0114516234968976 0.0057258117484488 86 0.992116350543315 0.0157672989133693 0.00788364945668463 87 0.98990489212724 0.0201902157455219 0.0100951078727609 88 0.98838043519628 0.0232391296074415 0.0116195648037207 89 0.985323672588688 0.0293526548226231 0.0146763274113115 90 0.981372454435815 0.0372550911283695 0.0186275455641847 91 0.976666631210344 0.0466667375793125 0.0233333687896563 92 0.981906008976577 0.0361879820468469 0.0180939910234234 93 0.980603296301584 0.0387934073968319 0.0193967036984160 94 0.97713951615755 0.0457209676849021 0.0228604838424510 95 0.970595441873456 0.0588091162530881 0.0294045581265440 96 0.96260097029435 0.0747980594113006 0.0373990297056503 97 0.960283791160245 0.0794324176795101 0.0397162088397551 98 0.949101480808774 0.101797038382452 0.0508985191912259 99 0.95449530956651 0.091009380866981 0.0455046904334905 100 0.948707017202004 0.102585965595992 0.0512929827979962 101 0.938845905895283 0.122308188209435 0.0611540941047174 102 0.92819236654602 0.143615266907959 0.0718076334539797 103 0.933666650765482 0.132666698469035 0.0663333492345176 104 0.94528455089549 0.109430898209020 0.0547154491045102 105 0.950708744876924 0.098582510246153 0.0492912551230765 106 0.938171615500698 0.123656768998604 0.0618283844993022 107 0.938942294894656 0.122115410210687 0.0610577051053436 108 0.941091119230062 0.117817761539877 0.0589088807699385 109 0.964330801665606 0.0713383966687876 0.0356691983343938 110 0.97224859017575 0.0555028196484987 0.0277514098242494 111 0.969709309715106 0.0605813805697885 0.0302906902848942 112 0.978130750612484 0.0437384987750324 0.0218692493875162 113 0.970210361333786 0.0595792773324282 0.0297896386662141 114 0.961051036492188 0.0778979270156232 0.0389489635078116 115 0.95386634748489 0.0922673050302176 0.0461336525151088 116 0.95270922088592 0.0945815582281617 0.0472907791140808 117 0.964380689778851 0.0712386204422979 0.0356193102211489 118 0.95531160171447 0.0893767965710588 0.0446883982855294 119 0.93855430586194 0.122891388276118 0.0614456941380589 120 0.946007536163495 0.107984927673010 0.0539924638365052 121 0.929870015639792 0.140259968720416 0.0701299843602082 122 0.913836366951636 0.172327266096729 0.0861636330483643 123 0.904339980974954 0.191320038050091 0.0956600190250455 124 0.875148675731081 0.249702648537837 0.124851324268919 125 0.870176973887877 0.259646052224246 0.129823026112123 126 0.881334826522498 0.237330346955004 0.118665173477502 127 0.84531480742661 0.30937038514678 0.15468519257339 128 0.818968594754854 0.362062810490292 0.181031405245146 129 0.897957323483439 0.204085353033122 0.102042676516561 130 0.894974454335403 0.210051091329195 0.105025545664597 131 0.863195733340257 0.273608533319485 0.136804266659743 132 0.822029058726413 0.355941882547174 0.177970941273587 133 0.769505270020402 0.460989459959196 0.230494729979598 134 0.699633447505987 0.600733104988027 0.300366552494013 135 0.625108812039143 0.749782375921713 0.374891187960856 136 0.581966810694238 0.836066378611524 0.418033189305762 137 0.515433423394028 0.969133153211943 0.484566576605972 138 0.539724323439038 0.920551353121923 0.460275676560962 139 0.870855283132126 0.258289433735748 0.129144716867874 140 0.947269825487822 0.105460349024356 0.052730174512178 141 0.91180537210646 0.176389255787080 0.0881946278935399 142 0.8542727646253 0.291454470749399 0.145727235374699 143 0.775671260209266 0.448657479581468 0.224328739790734 144 0.625057195395932 0.749885609208136 0.374942804604068 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 31 0.233082706766917 NOK 5% type I error level 73 0.548872180451128 NOK 10% type I error level 91 0.68421052631579 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/10twd61291302380.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/10twd61291302380.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/15dgc1291302380.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/15dgc1291302380.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/25dgc1291302380.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/25dgc1291302380.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/3x5yx1291302380.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/3x5yx1291302380.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/4x5yx1291302380.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/4x5yx1291302380.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/5x5yx1291302380.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/5x5yx1291302380.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/6qwx01291302380.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/6qwx01291302380.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/715w31291302380.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/715w31291302380.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/815w31291302380.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/815w31291302380.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/915w31291302380.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291302308ta3t4buzzm5x2ys/915w31291302380.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 = 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