twowayanova

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Tue, 23 Nov 2010 19:55:57 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2.htm/, Retrieved Tue, 23 Nov 2010 20:55:33 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2.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 12 12 8 13 5 15 10 12 16 6 12 9 7 12 6 10 10 10 11 5 12 12 7 12 3 15 13 16 18 8 9 12 11 11 4 12 12 14 14 4 11 6 6 9 4 11 5 16 14 6 11 12 11 12 6 15 11 16 11 5 7 14 12 12 4 11 14 7 13 6 11 12 13 11 4 10 12 11 12 6 14 11 15 16 6 10 11 7 9 4 6 7 9 11 4 11 9 7 13 2 15 11 14 15 7 11 11 15 10 5 12 12 7 11 4 14 12 15 13 6 15 11 17 16 6 9 11 15 15 7 13 8 14 14 5 13 9 14 14 6 16 12 8 14 4 13 10 8 8 4 12 10 14 13 7 14 12 14 15 7 11 8 8 13 4 9 12 11 11 4 16 11 16 15 6 12 12 10 15 6 10 7 8 9 5 13 11 14 13 6 16 11 16 16 7 14 12 13 13 6 15 9 5 11 3 5 15 8 12 3 8 11 10 12 4 11 11 8 12 6 16 11 13 14 7 17 11 15 14 5 9 15 6 8 4 9 11 12 13 5 13 12 16 16 6 10 12 5 13 6 6 9 15 11 6 12 12 12 14 5 8 12 8 13 4 14 13 13 13 5 12 11 14 13 5 11 9 12 12 4 16 9 16 16 6 8 11 10 15 2 15 11 15 15 8 7 12 8 12 3 16 12 16 14 6 14 9 19 12 6 16 11 14 15 6 9 9 6 12 5 14 12 13 13 5 11 12 15 12 6 13 12 7 12 5 15 12 13 13 6 5 14 4 5 2 15 11 14 13 5 13 12 13 13 5 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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Liked[t] = + 6.44337607583825 + 0.228447260896724Popularity[t] + 0.0600370360974463FindingFriends[t] + 0.110103033300961KnowingPeople[t] + 0.393494049827484Celebrity[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) 6.44337607583825 1.02725 6.2725 0 0 Popularity 0.228447260896724 0.063171 3.6164 0.000407 0.000203 FindingFriends 0.0600370360974463 0.077742 0.7723 0.441168 0.220584 KnowingPeople 0.110103033300961 0.051418 2.1413 0.033851 0.016926 Celebrity 0.393494049827484 0.128921 3.0522 0.002685 0.001342 Multiple Linear Regression - Regression Statistics Multiple R 0.634459073838359 R-squared 0.402538316375828 Adjusted R-squared 0.386711516809625 F-TEST (value) 25.4339681684864 F-TEST (DF numerator) 4 F-TEST (DF denominator) 151 p-value 4.44089209850063e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.70372255642955 Sum Squared Residuals 438.303252942315 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 12.9155965524586 0.0844034475414042 2 13 12.7534821553134 0.246517844686591 3 16 14.1526560488400 1.84734395115998 4 12 12.8567620635476 -0.856762063547592 5 11 12.396719627927 -1.39671962792700 6 12 11.8563910223575 0.143608977642517 7 18 15.5601673899912 2.43983261000883 8 11 12.0049554226986 -1.00495542269864 9 14 13.0206063052917 0.979393694708303 10 9 11.5511125614026 -2.55111256140260 11 14 13.3790939579697 0.62090604203026 12 12 13.2488380441471 -1.24883804414706 13 11 14.2596111683138 -3.25961116831383 14 12 11.7782380064010 0.221761993598952 15 13 12.9284999831381 0.0715000168618957 16 11 12.6820560110940 -1.68205601109401 17 12 13.0203907832503 -1.02039078325033 18 16 14.3145549239436 1.68544507605637 19 9 11.7329535142941 -2.73295351429407 20 11 10.7992223929193 0.200777607080684 21 13 11.0543386033409 1.94566139665906 22 15 14.8263932013669 0.173606798633125 23 10 13.2357190914260 -3.23571909142597 24 11 12.2498850721850 -1.24988507218497 25 13 14.3745919600411 -1.37459196004107 26 16 14.7632082514423 1.23679174855773 27 15 13.5658126692875 1.43418733071251 28 14 13.4023994716261 0.59760052837388 29 14 13.8559305575510 0.144069442448950 30 14 13.2737771490728 0.726222850927177 31 8 12.4683612941878 -4.46836129418776 32 13 14.0810143825793 -1.08101438257926 33 15 14.6579829765676 0.342017023432403 34 13 11.8913927001994 1.10860729980058 35 11 12.0049554226986 -1.00495542269864 36 15 14.8815524790380 0.118447520961963 37 15 13.3671822717428 1.63281772825718 38 9 11.9964024530327 -2.99640245303273 39 13 13.9760046297459 -0.976004629745943 40 16 15.2750465288655 0.724953471134479 41 13 14.1543858934392 -1.15438589343915 42 11 12.1414156301534 -1.14141563015339 43 12 10.5474743376737 1.45252566232628 44 12 11.6063680924035 0.39363190759649 45 12 12.8584919081467 -0.858491908146727 46 14 14.9447374289626 -0.944737428962637 47 14 14.6064026568063 -0.606402656806315 48 8 11.6345513644862 -3.63455136448617 49 13 12.4485154697296 0.551484530270359 50 16 14.2562477324453 1.74375226755469 51 13 12.3597725834446 0.640227416555435 52 11 12.3669027645749 -1.36690276457495 53 14 13.1938942885173 0.806105711482742 54 13 11.4461990618990 1.55380093810097 55 13 13.8209288797091 -0.820928879709113 56 13 13.3540633190217 -0.354063319021735 57 12 12.3918418695007 -0.391841869500712 58 16 14.7614784068431 1.23852159315686 59 15 10.8193799927485 4.18062000725146 60 15 15.3299902844953 -0.32999028449532 61 12 10.8242577511748 1.17574224882517 62 14 14.9415895151355 -0.941589515135483 63 12 14.6348929849526 -2.63489298495258 64 15 14.6613464124361 0.338653587563886 65 12 11.6678231977290 0.33217680227102 66 13 13.7608918436117 -0.760891843611667 67 12 13.6892501773509 -1.68925017735090 68 12 12.8718263829092 -0.871826382909175 69 13 14.3828331543359 -1.38283315433588 70 5 9.65353111854494 -4.65353111854494 71 13 14.0394051017119 -1.03940510171191 72 13 13.5324445827149 -0.532444582714944 73 14 12.7953069582221 1.20469304177787 74 17 13.2189249274653 3.78107507253474 75 13 13.4673142661499 -0.46731426614985 76 13 13.9176974382476 -0.917697438247627 77 12 13.4741373912166 -1.47413739121663 78 13 13.0638491774284 -0.0638491774284345 79 14 12.8168826272794 1.18311737272062 80 11 9.9821103738487 1.01788962615131 81 12 11.1076487677013 0.892351232298652 82 12 13.7941636768545 -1.79416367685447 83 16 14.0943488573417 1.90565114265829 84 12 12.5068226612280 -0.506822661227957 85 12 11.8646322166523 0.135367783347716 86 12 13.6474253744422 -1.64742537444219 87 10 11.6146092866983 -1.61460928669831 88 15 12.7836060747291 2.21639392527093 89 15 15.4483345120911 -0.448334512091082 90 12 11.953159580896 0.0468404191040039 91 16 13.7640397574388 2.23596024256118 92 15 13.1805598137548 1.81944018624519 93 16 15.3350835649630 0.664916435037033 94 13 14.5930681820439 -1.59306818204387 95 12 13.0237542191189 -1.02375421911885 96 11 11.9030935836925 -0.90309358369248 97 13 11.4925898478629 1.50741015213708 98 10 11.0026390148680 -1.00263901486803 99 15 12.9455049498327 2.05449505016733 100 13 13.7057325659405 -0.705732565940505 101 16 15.3851495621665 0.614850437833517 102 15 15.224980531662 -0.224980531662006 103 18 14.7148720988379 3.28512790116211 104 13 11.2876636226639 1.71233637733606 105 10 9.18493571325843 0.815064286741568 106 16 14.6711019292887 1.32889807071132 107 13 11.4913873006763 1.50861269932374 108 15 15.1015430235986 -0.101543023598596 109 14 11.1528370064786 2.84716299352142 110 15 11.2561169147128 3.74388308528724 111 14 12.8453729554256 1.15462704457436 112 13 14.0710433436853 -1.07104334368533 113 13 12.8084259109432 0.191574089056788 114 15 14.1543858934392 0.845614106560848 115 16 14.6662241708624 1.33377582913760 116 14 14.6613464124361 -0.661346412436114 117 14 14.7213834485336 -0.72138344853356 118 16 12.9185289442442 3.08147105575583 119 14 14.3745919600411 -0.374591960041074 120 12 13.1972577243858 -1.19725772438577 121 13 12.8004002386898 0.199599761310226 122 12 14.0311639074171 -2.03116390741711 123 12 11.4962650591025 0.503734940897451 124 14 14.2061817352418 -0.206181735241797 125 14 14.8314864818345 -0.831486481834522 126 14 12.5332760887115 1.46672391128851 127 16 15.5083715481885 0.491628451811471 128 13 13.9176974382476 -0.917697438247627 129 14 12.5050928166288 1.49490718337117 130 4 10.0720558073204 -6.07205580732043 131 16 15.5083715481885 0.491628451811471 132 13 14.2126930849375 -1.21269308493747 133 16 11.9030935836925 4.09690641630752 134 15 13.7657696020380 1.23423039796205 135 14 14.3828331543359 -0.382833154335875 136 13 12.4700911387869 0.52990886121311 137 14 14.3145549239436 -0.314554923943628 138 12 11.3747729176796 0.625227082320367 139 15 15.5168282645247 -0.516828264524693 140 14 13.2940262829243 0.705973717075711 141 13 13.1807753357962 -0.180775335796174 142 14 14.0360416658434 -0.0360416658433889 143 16 13.7059480879819 2.29405191201813 144 6 11.5463310563061 -5.54633105630606 145 13 12.5801941720879 0.419805827912149 146 13 12.3097065862411 0.69029341375895 147 14 11.8396931117265 2.16030688827348 148 15 13.6409140247465 1.35908597525348 149 14 14.6531052181413 -0.653105218141313 150 15 15.2881654815866 -0.288165481586606 151 13 14.1492926129715 -1.14929261297150 152 16 15.224980531662 0.775019468337994 153 12 11.7247123199993 0.275287680000728 154 15 13.9242087879433 1.07579121205670 155 12 14.2044518906427 -2.20445189064267 156 14 11.8432720696364 2.15672793036360 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.0482272034650254 0.0964544069300509 0.951772796534974 9 0.0320183182287707 0.0640366364575414 0.96798168177123 10 0.0122517701204647 0.0245035402409294 0.987748229879535 11 0.0196801925697242 0.0393603851394484 0.980319807430276 12 0.0179007644025317 0.0358015288050633 0.982099235597468 13 0.587011946451649 0.825976107096701 0.412988053548351 14 0.494117157357415 0.98823431471483 0.505882842642585 15 0.398032388618634 0.796064777237268 0.601967611381366 16 0.363779658800202 0.727559317600404 0.636220341199798 17 0.313444820915219 0.626889641830438 0.686555179084781 18 0.283286142687774 0.566572285375548 0.716713857312226 19 0.282322875630855 0.564645751261709 0.717677124369145 20 0.302044810217682 0.604089620435364 0.697955189782318 21 0.500756407713033 0.998487184573935 0.499243592286967 22 0.427095114694097 0.854190229388193 0.572904885305903 23 0.584998173366144 0.830003653267713 0.415001826633856 24 0.533791743700601 0.932416512598798 0.466208256299399 25 0.509724020920573 0.980551958158854 0.490275979079427 26 0.469728355323233 0.939456710646465 0.530271644676767 27 0.460410778878529 0.920821557757057 0.539589221121471 28 0.405877377657276 0.811754755314553 0.594122622342724 29 0.344044059039346 0.688088118078693 0.655955940960653 30 0.303156976151672 0.606313952303344 0.696843023848328 31 0.581216601056026 0.837566797887947 0.418783398943974 32 0.548506274826061 0.902987450347878 0.451493725173939 33 0.489165433969292 0.978330867938583 0.510834566030708 34 0.493764104967472 0.987528209934944 0.506235895032528 35 0.441758540284111 0.883517080568221 0.55824145971589 36 0.38521754644372 0.77043509288744 0.61478245355628 37 0.39299339891277 0.78598679782554 0.60700660108723 38 0.460200881684568 0.920401763369137 0.539799118315432 39 0.423381045611846 0.846762091223692 0.576618954388154 40 0.373075212104365 0.74615042420873 0.626924787895635 41 0.347036241418163 0.694072482836327 0.652963758581837 42 0.313625885380791 0.627251770761582 0.686374114619209 43 0.336193203132848 0.672386406265695 0.663806796867152 44 0.298506283413085 0.59701256682617 0.701493716586915 45 0.260104160414412 0.520208320828823 0.739895839585588 46 0.231013548690325 0.46202709738065 0.768986451309675 47 0.197349989653746 0.394699979307491 0.802650010346254 48 0.315798096000743 0.631596192001486 0.684201903999257 49 0.280459783575738 0.560919567151475 0.719540216424262 50 0.280556738490732 0.561113476981465 0.719443261509268 51 0.262538555527956 0.525077111055913 0.737461444472044 52 0.245895723214386 0.491791446428773 0.754104276785614 53 0.219957530815771 0.439915061631542 0.78004246918423 54 0.234077092707099 0.468154185414198 0.765922907292901 55 0.205446611783886 0.410893223567773 0.794553388216114 56 0.172503672448293 0.345007344896587 0.827496327551707 57 0.144363184097062 0.288726368194124 0.855636815902938 58 0.131655576326106 0.263311152652213 0.868344423673894 59 0.341521162951089 0.683042325902179 0.65847883704891 60 0.298698119478684 0.597396238957367 0.701301880521316 61 0.280898567127941 0.561797134255882 0.719101432872059 62 0.254778221978133 0.509556443956267 0.745221778021867 63 0.317498040342468 0.634996080684936 0.682501959657532 64 0.279372645843141 0.558745291686283 0.720627354156859 65 0.248616569539528 0.497233139079057 0.751383430460472 66 0.218734089653299 0.437468179306598 0.781265910346701 67 0.216413973100506 0.432827946201012 0.783586026899494 68 0.191651799991801 0.383303599983601 0.8083482000082 69 0.179188405528306 0.358376811056613 0.820811594471694 70 0.432625216685786 0.865250433371571 0.567374783314214 71 0.404619757636620 0.809239515273241 0.59538024236338 72 0.364296963137579 0.728593926275159 0.635703036862421 73 0.347067980360357 0.694135960720715 0.652932019639643 74 0.543323639447835 0.91335272110433 0.456676360552165 75 0.499126600514335 0.99825320102867 0.500873399485665 76 0.463768072454965 0.92753614490993 0.536231927545035 77 0.452740299510145 0.905480599020291 0.547259700489855 78 0.406580955329362 0.813161910658723 0.593419044670638 79 0.390641679270858 0.781283358541715 0.609358320729142 80 0.365098144235169 0.730196288470338 0.634901855764831 81 0.335425857541933 0.670851715083866 0.664574142458067 82 0.336736204675409 0.673472409350819 0.66326379532459 83 0.349174977588605 0.69834995517721 0.650825022411395 84 0.310475051779087 0.620950103558174 0.689524948220913 85 0.28362761517333 0.56725523034666 0.71637238482667 86 0.281479062335854 0.562958124671709 0.718520937664146 87 0.286988035978736 0.573976071957473 0.713011964021264 88 0.318626334319817 0.637252668639635 0.681373665680183 89 0.279307983957983 0.558615967915966 0.720692016042017 90 0.243490249123682 0.486980498247364 0.756509750876318 91 0.267577455680672 0.535154911361343 0.732422544319328 92 0.278183186780664 0.556366373561328 0.721816813219336 93 0.246230015046375 0.49246003009275 0.753769984953625 94 0.237230869095685 0.47446173819137 0.762769130904315 95 0.218289853084331 0.436579706168661 0.78171014691567 96 0.205583447787578 0.411166895575156 0.794416552212422 97 0.200699261920811 0.401398523841621 0.79930073807919 98 0.205271880104182 0.410543760208364 0.794728119895818 99 0.251780058621512 0.503560117243023 0.748219941378488 100 0.227456014111821 0.454912028223642 0.77254398588818 101 0.203577966175119 0.407155932350238 0.796422033824881 102 0.171082052131984 0.342164104263969 0.828917947868016 103 0.258604290498478 0.517208580996955 0.741395709501522 104 0.24252702703236 0.48505405406472 0.75747297296764 105 0.210226581891885 0.42045316378377 0.789773418108115 106 0.191404095204565 0.382808190409130 0.808595904795435 107 0.178579904148993 0.357159808297986 0.821420095851007 108 0.151972308926683 0.303944617853365 0.848027691073317 109 0.201590729163252 0.403181458326503 0.798409270836748 110 0.533816260190661 0.932367479618677 0.466183739809339 111 0.548863043772898 0.902273912454205 0.451136956227102 112 0.584446040773573 0.831107918452853 0.415553959226427 113 0.539754911215736 0.920490177568528 0.460245088784264 114 0.495757896182059 0.991515792364118 0.504242103817941 115 0.468398015661354 0.936796031322709 0.531601984338646 116 0.418286193850302 0.836572387700605 0.581713806149698 117 0.389210784368489 0.778421568736978 0.610789215631511 118 0.482424723718845 0.96484944743769 0.517575276281155 119 0.427849180019722 0.855698360039443 0.572150819980279 120 0.430685251832067 0.861370503664134 0.569314748167933 121 0.383572186371925 0.767144372743849 0.616427813628075 122 0.388993096298687 0.777986192597373 0.611006903701313 123 0.345556177273976 0.691112354547953 0.654443822726024 124 0.298649992367959 0.597299984735918 0.701350007632041 125 0.283093244229128 0.566186488458256 0.716906755770872 126 0.242644158132831 0.485288316265662 0.757355841867169 127 0.203937769427835 0.407875538855669 0.796062230572165 128 0.16704724039085 0.3340944807817 0.83295275960915 129 0.428760012887131 0.857520025774262 0.571239987112869 130 0.604344460204629 0.791311079590743 0.395655539795371 131 0.558518036934418 0.882963926131165 0.441481963065582 132 0.515891045019853 0.968217909960294 0.484108954980147 133 0.705638094506496 0.588723810987009 0.294361905493504 134 0.644388978602689 0.711222042794623 0.355611021397311 135 0.588608216386712 0.822783567226577 0.411391783613288 136 0.523284890696006 0.953430218607988 0.476715109303994 137 0.446131390327221 0.892262780654443 0.553868609672779 138 0.37108568619292 0.74217137238584 0.62891431380708 139 0.421079108457023 0.842158216914047 0.578920891542977 140 0.493220032353866 0.986440064707731 0.506779967646134 141 0.410530022147559 0.821060044295118 0.589469977852441 142 0.320469242214911 0.640938484429822 0.679530757785089 143 0.247100878998526 0.494201757997053 0.752899121001474 144 0.80953347583421 0.380933048331579 0.190466524165789 145 0.748205590093663 0.503588819812674 0.251794409906337 146 0.720262206022577 0.559475587954846 0.279737793977423 147 0.66205254168722 0.675894916625559 0.337947458312779 148 0.628690986814005 0.742618026371991 0.371309013185995 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 3 0.0212765957446809 OK 10% type I error level 5 0.0354609929078014 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/10leys1290542145.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/10leys1290542145.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/1xvjy1290542145.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/1xvjy1290542145.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/27mi11290542145.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/27mi11290542145.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/37mi11290542145.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/37mi11290542145.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/47mi11290542145.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/47mi11290542145.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/57mi11290542145.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/57mi11290542145.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/60ehm1290542145.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/60ehm1290542145.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/7bny71290542145.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/7bny71290542145.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/8bny71290542145.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/8bny71290542145.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/9leys1290542145.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905421227nk13gndzkvbgj2/9leys1290542145.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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

Software written by Ed van Stee & Patrick Wessa

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