ws 7 deterministische 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: Tue, 23 Nov 2010 15:23:13 +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/t12905258211bk6hwg42fb95hb.htm/, Retrieved Tue, 23 Nov 2010 16:23:57 +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/t12905258211bk6hwg42fb95hb.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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Celebrity [t] = + 0.417809867381582 + 0.154188016815281Popularity[t] -0.0205821634162743FindingFriends[t] + 0.103572657945756KnowingPeople[t] + 0.145905397542057Liked[t] + 0.000485950422142418t + 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) 0.417809867381582 0.708265 0.5899 0.556141 0.278071 Popularity 0.154188016815281 0.038463 4.0088 9.6e-05 4.8e-05 FindingFriends -0.0205821634162743 0.04805 -0.4284 0.66901 0.334505 KnowingPeople 0.103572657945756 0.030955 3.3459 0.001037 0.000518 Liked 0.145905397542057 0.049024 2.9762 0.003403 0.001702 t 0.000485950422142418 0.001895 0.2564 0.79798 0.39899 Multiple Linear Regression - Regression Statistics Multiple R 0.677621027970981 R-squared 0.459170257548449 Adjusted R-squared 0.441142599466730 F-TEST (value) 25.4703220721769 F-TEST (DF numerator) 5 F-TEST (DF denominator) 150 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.04697227686073 Sum Squared Residuals 164.422642277242 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3 5.50195929127812 -2.50195929127812 2 5 4.74740344062673 0.252596559373271 3 6 6.10362459273646 -0.103624592736458 4 6 4.56064377623203 1.43935622376797 5 5 4.39698410590254 0.603015894097457 6 3 4.49986918682749 -1.49986918682749 7 8 6.74992333104334 1.25007666895666 8 4 4.30666227146690 -0.306662271466895 9 4 5.51814643879832 -1.51814643879832 10 4 3.9298291016265 0.0701708983735044 11 6 5.71615078263275 0.283849217367246 12 6 4.76288750432808 1.23711249567192 13 5 5.77266557761435 -0.772665577614346 14 4 4.20951566902445 -0.209515669024452 15 6 4.454795794521 1.54520420547900 16 4 4.82607122436611 -0.826071224366108 17 6 4.61112923962351 1.38887076037649 18 6 6.2468616426743 -0.246861642674306 19 4 3.78067647947488 0.21932352052512 20 4 3.74569512727662 0.254304872723378 21 2 4.56062231413522 -2.56062231413522 22 7 6.15351540569034 0.846484594309657 23 5 4.91129495908683 0.0887050409131663 24 4 4.36271089688399 -0.362710896883994 25 6 5.79196493958686 0.208035060413142 26 6 6.61208257875824 -0.612082578758238 27 7 5.33438971485513 1.66561028514487 28 5 5.7638961672994 -0.763896167299403 29 6 5.74379995430527 0.256200045694729 30 4 5.5236675172499 -1.5236675172499 31 4 4.22732135880640 -0.227321358806405 32 7 5.42458222779809 1.57541777220191 33 7 5.98409068010236 1.01590931989764 34 4 4.6910944909851 -0.691094490985104 35 4 4.31978293286474 -0.319782932864741 36 6 6.52165204430713 -0.52165204430713 37 6 5.26336781637734 0.73663218362266 38 5 3.97581084910644 1.02418915089356 39 6 5.56158973415209 0.438410265847911 40 7 6.66950124353776 0.330498756462243 41 6 5.59259483044962 0.407405169550375 42 3 4.68862322928571 -1.68862322928571 43 3 3.48035940243672 -0.480359402436723 44 4 4.23288337286132 -0.232883372861317 45 6 4.48878805783779 1.51121194216221 46 7 6.06988817714923 0.93011182285077 47 5 6.43170746027817 -1.43170746027816 48 4 3.30877431574882 0.69122568425118 49 5 4.74255185522088 0.257448144779122 50 6 6.19121453389706 -0.191214533897064 51 6 4.15212100384388 1.84787899615612 52 6 4.34151716162716 1.65848283837284 53 5 5.33238294148107 -0.332382941481073 54 4 4.15592079531701 -0.155920795317012 55 5 5.57881597294334 -0.578815972943344 56 5 5.41566287451323 -0.415662874513229 57 4 4.95007442151907 -0.950074421519071 58 6 6.71941267796887 -0.719412677968869 59 2 4.67788882181962 -2.67788882181962 60 8 6.27555417967751 1.72444582032249 61 3 3.85922903391467 -0.859229033914671 62 6 6.3677991943245 -0.367799194324501 63 6 6.14056278011806 -0.140562780118058 64 6 6.3281133402356 -0.328113340235606 65 5 4.02415004359111 0.975849956408886 66 5 5.60474359100319 -0.604743591003185 67 6 5.20390540932894 0.79609459067106 68 5 4.6841861298156 0.315813870184402 69 6 5.76038945908489 0.239610540915107 70 2 2.07843381267342 -0.0784338126734208 71 5 5.88551618129121 -0.885516181291208 72 5 5.45347127672076 -0.453471276720759 73 5 5.10492343857916 -0.104923438579159 74 6 5.95675437254611 0.0432456274538886 75 6 5.2383327800587 0.761667219941302 76 6 5.50837237748556 0.491627622514441 77 5 5.23879810900361 -0.238798109003615 78 5 5.38452761610343 -0.38452761610343 79 4 5.23910305430431 -1.23910305430432 80 2 3.36122336168653 -1.36122336168653 81 4 3.76537538441176 0.234624615588236 82 6 5.59010638071305 0.409893619286947 83 6 6.07130310422205 -0.0713031042220515 84 5 4.68485224473961 0.315147755260394 85 3 4.48530197110051 -1.48530197110051 86 6 5.03602634691138 0.963973653088615 87 4 3.90901114685310 0.0909888531469036 88 5 5.49463476293373 -0.494634762933731 89 8 6.34026210078917 1.65973789921083 90 4 4.46004046796467 -0.460040467964674 91 6 5.76447273376192 0.235527266238076 92 6 5.31301919321815 0.686980806781847 93 7 6.67467445249503 0.325325547504970 94 6 6.12442052030827 -0.124420520308270 95 5 4.97799156959746 0.0220084304025405 96 4 4.19289595159344 -0.192895951593442 97 6 3.86543684876748 2.13456315123252 98 3 3.61543159990308 -0.615431599903077 99 5 5.63592801118301 -0.635928011183009 100 6 5.25993257264924 0.740067427350765 101 7 6.8027168772342 0.1972831227658 102 7 6.4295699508065 0.570430049193501 103 6 6.72537704928321 -0.725377049283214 104 3 4.37322871986526 -1.37322871986526 105 2 2.75310970200851 -0.753109702008507 106 8 5.73059766326151 2.26940233673849 107 3 4.68774648517566 -1.68774648517566 108 8 6.14469178312507 1.85530821687493 109 3 4.57686310880096 -1.57686310880096 110 4 4.68142828906823 -0.681428289068229 111 5 5.2475443759826 -0.247544375982601 112 7 5.60819524634778 1.39180475365222 113 6 4.5435832627235 1.45641673727650 114 6 5.91988000635013 0.080119993649865 115 7 6.11688671318386 0.88311328681614 116 6 6.20747736464496 -0.207477364644955 117 6 6.18738115165082 -0.187381151650823 118 6 5.08730186540614 0.91269813459386 119 6 5.9835496768103 0.0164503231896983 120 4 5.40208902172734 -1.40208902172734 121 4 5.2195221726447 -1.2195221726447 122 5 5.81735155435465 -0.817351554354645 123 4 4.16770079826481 -0.167700798264812 124 6 5.81120924868946 0.188790751310541 125 6 6.29484141297372 -0.294841412973718 126 5 4.74642137462294 0.253578625377065 127 8 6.48405145095636 1.51594854904364 128 6 5.53364179943696 0.466358200563035 129 5 5.0903104945222 -0.090310494522202 130 4 2.13813572003379 1.86186427996621 131 8 6.48599525264493 1.51400474735507 132 6 5.70801384115038 0.291986158849616 133 4 4.940403104923 -0.940403104922996 134 6 5.54768351866992 0.452316481330083 135 6 5.93836758448835 0.0616324155116501 136 4 4.91609345513957 -0.91609345513957 137 6 6.01287894782514 -0.0128789478251396 138 3 4.41451050614842 -1.41451050614842 139 6 6.91011416687161 -0.910114166871612 140 5 5.62297027093152 -0.622970270931524 141 4 5.66411397628685 -1.66411397628685 142 6 5.73696586175854 0.263034138241459 143 4 6.33763864089536 -2.33763864089536 144 4 3.42662819323949 0.573371806760509 145 4 5.02403966688461 -1.02403966688461 146 6 4.07413147258538 1.92586852741462 147 5 4.34701958211831 0.652980417881686 148 6 5.46504907908454 0.534950920915458 149 6 6.27647102765189 -0.276471027651885 150 8 6.14217759723207 1.85782240276793 151 7 5.40887086554053 1.59112913445947 152 7 6.59977286945568 0.400227130544323 153 4 4.33646732774437 -0.336467327744365 154 6 5.87690969212262 0.123090307877375 155 6 5.62624260239383 0.373757397606167 156 2 5.29944534043226 -3.29944534043226 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.586990387188991 0.826019225622018 0.413009612811009 10 0.494474023387247 0.988948046774495 0.505525976612752 11 0.672041461363218 0.655917077273564 0.327958538636782 12 0.792897964169486 0.414204071661027 0.207102035830514 13 0.80527609963227 0.389447800735459 0.194723900367729 14 0.743430421889213 0.513139156221574 0.256569578110787 15 0.668643689961552 0.662712620076895 0.331356310038448 16 0.612224585388514 0.775550829222972 0.387775414611486 17 0.559819936593463 0.880360126813073 0.440180063406537 18 0.610907469041091 0.778185061917818 0.389092530958909 19 0.540362083656504 0.919275832686991 0.459637916343496 20 0.545395922673352 0.909208154653296 0.454604077326648 21 0.94803710151131 0.103925796977380 0.0519628984886898 22 0.94150156381605 0.116996872367901 0.0584984361839504 23 0.921177245646137 0.157645508707726 0.078822754353863 24 0.89717550487333 0.205648990253341 0.102824495126671 25 0.86579846197126 0.268403076057481 0.134201538028740 26 0.840376292070865 0.319247415858270 0.159623707929135 27 0.848802424844586 0.302395150310828 0.151197575155414 28 0.832945777262507 0.334108445474985 0.167054222737493 29 0.791440509610162 0.417118980779676 0.208559490389838 30 0.807443480297584 0.385113039404832 0.192556519702416 31 0.772887300501254 0.454225398997492 0.227112699498746 32 0.807788184634145 0.38442363073171 0.192211815365855 33 0.79198819421294 0.416023611574118 0.208011805787059 34 0.782420225588514 0.435159548822973 0.217579774411487 35 0.752545399153768 0.494909201692463 0.247454600846232 36 0.712683747600031 0.574632504799938 0.287316252399969 37 0.673456335377602 0.653087329244797 0.326543664622399 38 0.662993659747389 0.674012680505222 0.337006340252611 39 0.61479282511188 0.770414349776241 0.385207174888120 40 0.563645671323623 0.872708657352753 0.436354328676377 41 0.513615007599107 0.972769984801785 0.486384992400893 42 0.568099802800535 0.86380039439893 0.431900197199465 43 0.575910770487865 0.84817845902427 0.424089229512135 44 0.535454124210463 0.929091751579074 0.464545875789537 45 0.582915971237058 0.834168057525883 0.417084028762942 46 0.568929984130881 0.862140031738238 0.431070015869119 47 0.609803908858468 0.780392182283065 0.390196091141532 48 0.580186206872387 0.839627586255225 0.419813793127613 49 0.535100255243177 0.929799489513646 0.464899744756823 50 0.494369484356615 0.98873896871323 0.505630515643385 51 0.559203020230376 0.881593959539248 0.440796979769624 52 0.596399691980289 0.807200616039422 0.403600308019711 53 0.564600165955523 0.870799668088953 0.435399834044477 54 0.53850734855889 0.92298530288222 0.46149265144111 55 0.503667247646517 0.992665504706966 0.496332752353483 56 0.468361499953993 0.936722999907987 0.531638500046007 57 0.473098907579654 0.946197815159308 0.526901092420346 58 0.444762999754546 0.889525999509091 0.555237000245454 59 0.732397177936408 0.535205644127184 0.267602822063592 60 0.80048684916323 0.399026301673538 0.199513150836769 61 0.79001420910216 0.419971581795679 0.209985790897839 62 0.757198936745185 0.485602126509629 0.242801063254815 63 0.718677306518001 0.562645386963997 0.281322693481999 64 0.68106177637425 0.6378764472515 0.31893822362575 65 0.672075676376287 0.655848647247426 0.327924323623713 66 0.64154555799521 0.716908884009582 0.358454442004791 67 0.622826595162709 0.754346809674581 0.377173404837291 68 0.582459016329134 0.835081967341731 0.417540983670866 69 0.538614593922247 0.922770812155506 0.461385406077753 70 0.493373030362131 0.986746060724261 0.506626969637869 71 0.480161933248131 0.960323866496262 0.519838066751869 72 0.441881136380282 0.883762272760565 0.558118863619718 73 0.396008932718499 0.792017865436997 0.603991067281501 74 0.351996066104635 0.703992132209269 0.648003933895365 75 0.330103346337968 0.660206692675936 0.669896653662032 76 0.298114144707276 0.596228289414553 0.701885855292724 77 0.260142828910523 0.520285657821047 0.739857171089477 78 0.228372577919728 0.456745155839457 0.771627422080272 79 0.249089014671352 0.498178029342703 0.750910985328648 80 0.276591457832071 0.553182915664141 0.723408542167929 81 0.240267110214552 0.480534220429105 0.759732889785448 82 0.209886748895103 0.419773497790207 0.790113251104897 83 0.178345936861481 0.356691873722963 0.821654063138519 84 0.151316731261453 0.302633462522907 0.848683268738547 85 0.213588208325276 0.427176416650551 0.786411791674724 86 0.204619753819274 0.409239507638547 0.795380246180726 87 0.173631986509011 0.347263973018021 0.82636801349099 88 0.151653996035381 0.303307992070763 0.848346003964619 89 0.190346589122399 0.380693178244798 0.8096534108776 90 0.168753892179627 0.337507784359253 0.831246107820373 91 0.143848350958472 0.287696701916944 0.856151649041528 92 0.133358192427458 0.266716384854915 0.866641807572542 93 0.111008270651269 0.222016541302537 0.888991729348731 94 0.090557757874856 0.181115515749712 0.909442242125144 95 0.0730196163365946 0.146039232673189 0.926980383663405 96 0.0605897737760498 0.121179547552100 0.93941022622395 97 0.109814718513314 0.219629437026627 0.890185281486686 98 0.105899668837867 0.211799337675733 0.894100331162133 99 0.0917918604779402 0.183583720955880 0.90820813952206 100 0.0779875255136837 0.155975051027367 0.922012474486316 101 0.0624280681206013 0.124856136241203 0.937571931879399 102 0.0509949099823053 0.101989819964611 0.949005090017695 103 0.0434154249037856 0.0868308498075713 0.956584575096214 104 0.0656324612454417 0.131264922490883 0.934367538754558 105 0.0639073224574633 0.127814644914927 0.936092677542537 106 0.110664526182551 0.221329052365101 0.88933547381745 107 0.148109991635173 0.296219983270345 0.851890008364827 108 0.223783175166953 0.447566350333906 0.776216824833047 109 0.260872571195525 0.52174514239105 0.739127428804475 110 0.231433210459840 0.462866420919679 0.76856678954016 111 0.196256043492041 0.392512086984082 0.803743956507959 112 0.260528164086071 0.521056328172143 0.739471835913929 113 0.257028246676857 0.514056493353715 0.742971753323143 114 0.216060053045368 0.432120106090735 0.783939946954632 115 0.201849222665184 0.403698445330369 0.798150777334816 116 0.166820070124587 0.333640140249174 0.833179929875413 117 0.136669183141036 0.273338366282072 0.863330816858964 118 0.128557792940733 0.257115585881466 0.871442207059267 119 0.103655230427275 0.207310460854551 0.896344769572725 120 0.137778887918912 0.275557775837824 0.862221112081088 121 0.156521824576953 0.313043649153906 0.843478175423047 122 0.146219312161022 0.292438624322045 0.853780687838978 123 0.117125508313735 0.234251016627470 0.882874491686265 124 0.0906346272420705 0.181269254484141 0.90936537275793 125 0.0761538226568265 0.152307645313653 0.923846177343174 126 0.063984515154338 0.127969030308676 0.936015484845662 127 0.0753998971270602 0.150799794254120 0.92460010287294 128 0.0606175796693381 0.121235159338676 0.939382420330662 129 0.0494705009076544 0.0989410018153088 0.950529499092346 130 0.0687426906231696 0.137485381246339 0.93125730937683 131 0.112673196913382 0.225346393826763 0.887326803086618 132 0.0883788255175056 0.176757651035011 0.911621174482494 133 0.067260709319296 0.134521418638592 0.932739290680704 134 0.051258645737293 0.102517291474586 0.948741354262707 135 0.0360902862929718 0.0721805725859435 0.963909713707028 136 0.0329686824405001 0.0659373648810003 0.9670313175595 137 0.0278336205519666 0.0556672411039331 0.972166379448034 138 0.0213321460933189 0.0426642921866377 0.97866785390668 139 0.0211494894050197 0.0422989788100394 0.97885051059498 140 0.0191407149233276 0.0382814298466551 0.980859285076672 141 0.0131993524584073 0.0263987049168147 0.986800647541593 142 0.00860795809431559 0.0172159161886312 0.991392041905684 143 0.0384674210084373 0.0769348420168746 0.961532578991563 144 0.0217751930612494 0.0435503861224988 0.97822480693875 145 0.170476380233895 0.340952760467791 0.829523619766105 146 0.164705002218442 0.329410004436884 0.835294997781558 147 0.0913393542934282 0.182678708586856 0.908660645706572 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 6 0.0431654676258993 OK 10% type I error level 12 0.0863309352517986 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/10sxzw1290525782.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/10sxzw1290525782.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/1v5151290525782.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/1v5151290525782.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/2v5151290525782.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/2v5151290525782.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/3v5151290525782.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/3v5151290525782.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/4oej81290525782.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/4oej81290525782.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/5oej81290525782.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/5oej81290525782.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/6oej81290525782.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/6oej81290525782.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/7hn0b1290525782.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/7hn0b1290525782.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/8sxzw1290525782.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/8sxzw1290525782.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/9sxzw1290525782.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905258211bk6hwg42fb95hb/9sxzw1290525782.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 5 ; 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