Workshop 8 Regression Analysis of Time Series

*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: Sat, 27 Nov 2010 09:27:19 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox.htm/, Retrieved Sat, 27 Nov 2010 10:26:06 +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/27/t1290849966zdamsrymgzk8rox.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 «

24 14 11 12 24 26 25 11 7 8 25 23 17 6 17 8 30 25 18 12 10 8 19 23 18 8 12 9 22 19 16 10 12 7 22 29 20 10 11 4 25 25 16 11 11 11 23 21 18 16 12 7 17 22 17 11 13 7 21 25 23 13 14 12 19 24 30 12 16 10 19 18 23 8 11 10 15 22 18 12 10 8 16 15 15 11 11 8 23 22 12 4 15 4 27 28 21 9 9 9 22 20 15 8 11 8 14 12 20 8 17 7 22 24 31 14 17 11 23 20 27 15 11 9 23 21 34 16 18 11 21 20 21 9 14 13 19 21 31 14 10 8 18 23 19 11 11 8 20 28 16 8 15 9 23 24 20 9 15 6 25 24 21 9 13 9 19 24 22 9 16 9 24 23 17 9 13 6 22 23 24 10 9 6 25 29 25 16 18 16 26 24 26 11 18 5 29 18 25 8 12 7 32 25 17 9 17 9 25 21 32 16 9 6 29 26 33 11 9 6 28 22 13 16 12 5 17 22 32 12 18 12 28 22 25 12 12 7 29 23 29 14 18 10 26 30 22 9 14 9 25 23 18 10 15 8 14 17 17 9 16 5 25 23 20 10 10 8 26 23 15 12 11 8 20 25 20 14 14 10 18 24 33 14 9 6 32 24 29 10 12 8 25 23 23 14 17 7 25 21 26 16 5 4 23 24 18 9 12 8 21 24 20 10 12 8 20 28 11 6 6 4 15 16 28 8 24 20 30 20 26 13 12 8 24 29 22 10 12 8 26 27 17 8 14 6 24 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Concernovermistakes[t] = -0.125352338445453 + 0.770919334854652Doubtsaboutactions[t] + 0.295573231590158Parentalexpectations[t] + 0.202170447707957Parentalcritism[t] + 0.543024225850058Personalstandards[t] -0.106005802041174Organization[t] + 0.710976996869086M1[t] -3.28910468985948M2[t] -1.88963794952092M3[t] -2.50928059794326M4[t] -3.67319749042358M5[t] -3.05184560496288M6[t] -2.23347749338627M7[t] -3.60826296671053M8[t] -2.67397849068801M9[t] -1.16907499510196M10[t] -2.84270762453105M11[t] + 0.00455965834326353t + 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) -0.125352338445453 3.415074 -0.0367 0.970772 0.485386 Doubtsaboutactions 0.770919334854652 0.13919 5.5386 0 0 Parentalexpectations 0.295573231590158 0.134921 2.1907 0.030115 0.015058 Parentalcritism 0.202170447707957 0.177244 1.1406 0.255957 0.127978 Personalstandards 0.543024225850058 0.096938 5.6018 0 0 Organization -0.106005802041174 0.108083 -0.9808 0.328378 0.164189 M1 0.710976996869086 1.74407 0.4077 0.684146 0.342073 M2 -3.28910468985948 1.725559 -1.9061 0.058671 0.029335 M3 -1.88963794952092 1.731896 -1.0911 0.277098 0.138549 M4 -2.50928059794326 1.779088 -1.4104 0.160615 0.080307 M5 -3.67319749042358 1.758558 -2.0888 0.038527 0.019264 M6 -3.05184560496288 1.773031 -1.7213 0.087397 0.043699 M7 -2.23347749338627 1.806722 -1.2362 0.218438 0.109219 M8 -3.60826296671053 1.765463 -2.0438 0.042834 0.021417 M9 -2.67397849068801 1.755091 -1.5236 0.129859 0.06493 M10 -1.16907499510196 1.749617 -0.6682 0.505105 0.252553 M11 -2.84270762453105 1.799076 -1.5801 0.116326 0.058163 t 0.00455965834326353 0.007937 0.5745 0.566566 0.283283 Multiple Linear Regression - Regression Statistics Multiple R 0.680421219467895 R-squared 0.462973035902178 Adjusted R-squared 0.398225104060596 F-TEST (value) 7.15039110492259 F-TEST (DF numerator) 17 F-TEST (DF denominator) 141 p-value 2.60091947978935e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.43942823848552 Sum Squared Residuals 2778.90175493744 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 27.3368364920501 -3.33683649205006 2 25 19.8986233738820 5.10137662611804 3 17 22.9068949393601 -5.90689493936005 4 18 19.0870604570095 -1.08706045700949 5 18 17.6904386800570 0.309561319943035 6 16 18.3937899777426 -2.39378997774259 7 20 20.3677290586633 -0.367729058663296 8 16 20.5215904689572 -4.52159046895723 9 18 21.4377715612131 -3.43777156121308 10 17 21.242290769736 -4.242290769736 11 23 21.4414392888305 1.55856071116952 12 30 24.3406276168616 5.65937238313841 13 23 17.8985006631396 5.10149933686039 14 18 17.5718066873051 0.428193312694878 15 15 21.5596159493846 -6.55961594938464 16 12 17.457770842005 -5.45777084200499 17 21 17.5233484182191 3.47665158178087 18 15 14.2711692521697 0.728830747830263 19 20 19.7374901462290 0.262509853771029 20 31 24.7685095652225 6.23149043477753 21 27 24.1944869474449 2.80551305255513 22 34 27.9681803031169 6.03181969688309 23 21 18.9326657033625 2.06733429663749 24 31 22.6863486656773 8.31365133432273 25 19 21.9407199894101 -2.94071998941006 26 16 19.0699992162443 -3.06999921624426 27 20 21.724482058357 -1.72448205835698 28 21 17.8666185931211 3.13338140687888 29 22 20.415107985046 1.58489201495400 30 17 18.4617400392555 -1.46174003925550 31 24 19.8663320829725 4.13366791702748 32 25 28.8765390745664 -3.87653907456635 33 26 26.0020190996686 -0.00201909966857823 34 25 24.7166578181709 0.283342181829144 35 17 22.3235648625207 -5.32356486252067 36 32 29.2382381867268 2.76176181327322 37 33 25.9801771499805 7.01982285001949 38 13 20.5505345585803 -7.55053455858034 39 32 28.0327826256908 3.96721737430916 40 25 25.0704264313399 -0.0704264313399201 41 29 25.4617453077386 3.53825469226141 42 22 21.0476131916389 0.95238680836113 43 18 17.397631408192 0.602368591808006 44 17 20.2827798189262 -3.28277981892623 45 20 21.3686394675797 -1.36863946757965 46 15 21.2453575636257 -6.24535756362572 47 20 21.4291412027766 -1.42914120277664 48 33 29.5921996987692 3.40780030123084 49 29 24.8199558258401 4.18004417415995 50 23 25.3958184511985 -2.39581845119854 51 26 22.7842275395603 3.21577246043974 52 18 18.5643551657614 -0.564355165761443 53 20 17.2088698324643 2.79113016753572 54 11 10.7259313517207 0.274068648279334 55 28 29.3670833028862 -1.36708330288617 56 26 21.6663324371301 4.33366756286987 57 22 21.5904786227144 0.409521377285568 58 17 21.1888892332046 -4.18888923320459 59 12 14.5534601467699 -2.55346014676993 60 14 23.0780791065479 -9.07807910654787 61 17 23.5508870088801 -6.55088700888012 62 21 20.1213520058569 0.878647994143073 63 19 23.1409375453815 -4.14093754538147 64 18 22.3516986041967 -4.35169860419672 65 10 16.3485059422252 -6.34850594222523 66 29 22.928440453616 6.07155954638399 67 31 18.3850848048726 12.6149151951274 68 19 21.4100633233004 -2.41006332330042 69 9 19.3733071919333 -10.3733071919333 70 20 23.2989911582597 -3.29899115825969 71 28 17.0134592433653 10.9865407566347 72 19 20.1819445901327 -1.18194459013272 73 30 26.0153894792788 3.98461052072125 74 29 26.0823645529310 2.91763544706896 75 26 21.8373398567925 4.16266014320754 76 23 19.2196994811279 3.78030051887212 77 13 21.1542529402690 -8.15425294026904 78 21 21.7894404169690 -0.789440416968963 79 19 21.2409000284644 -2.24090002846443 80 28 21.4102227439717 6.58977725602832 81 23 24.9404776635274 -1.94047766352738 82 18 15.0489107752639 2.95108922473605 83 21 20.1065719363512 0.893428063648838 84 20 24.2073562210113 -4.20735622101126 85 23 22.5968080328666 0.403191967133399 86 21 19.9184963800281 1.0815036199719 87 21 21.9275417455889 -0.927541745588918 88 15 22.2523992871160 -7.25239928711596 89 28 25.7473762083369 2.2526237916631 90 19 16.9097265656558 2.09027343434418 91 26 21.2916311797590 4.70836882024095 92 10 11.8913995178294 -1.89139951782944 93 16 16.5691197955464 -0.569119795546397 94 22 22.3164119872438 -0.316411987243773 95 19 18.2177437056362 0.782256294363788 96 31 31.2752758210745 -0.275275821074489 97 31 28.0735438388503 2.92645616114969 98 29 23.9780912835502 5.02190871644975 99 19 17.8850760371826 1.11492396281744 100 22 18.7506676653386 3.24933233466140 101 23 21.0899073149657 1.91009268503429 102 15 15.5355624652032 -0.535562465203189 103 20 21.8510765528512 -1.85107655285122 104 18 18.4346278902580 -0.434627890257954 105 23 21.5316302672527 1.46836973274726 106 25 21.8852497336685 3.11475026633147 107 21 16.0304410390483 4.96955896095174 108 24 21.896894524604 2.10310547539602 109 25 28.253382630281 -3.25338263028099 110 17 18.5591190876350 -1.55911908763502 111 13 15.2087873031292 -2.20878730312918 112 28 18.4289173711449 9.57108262885511 113 21 18.6805456314338 2.31945436856619 114 25 27.4869808151687 -2.48698081516871 115 9 20.6890767669850 -11.6890767669850 116 16 16.6753334845747 -0.675333484574669 117 19 21.0932981425276 -2.09329814252763 118 17 20.4432810831369 -3.44328108313686 119 25 24.0229362907741 0.977063709225948 120 20 17.7564264992159 2.24357350078408 121 29 24.2816526405183 4.7183473594817 122 14 18.1193248928042 -4.11932489280418 123 22 27.2621139507390 -5.26211395073904 124 15 15.2949209187737 -0.294920918773672 125 19 23.6368883879306 -4.63688838793065 126 20 21.4849155058446 -1.48491550584459 127 15 17.5544092830465 -2.55440928304646 128 20 20.4752333426692 -0.475233342669169 129 18 20.1029756071086 -2.10297560710856 130 33 26.4283528892695 6.57164711073049 131 22 23.300171882512 -1.30017188251202 132 16 19.041304708039 -3.04130470803901 133 17 22.1258973592819 -5.12589735928187 134 16 14.1690353620269 1.83096463797312 135 21 17.7242534643202 3.27574653567981 136 26 27.727103287484 -1.72710328748400 137 18 19.8053204329258 -1.80532043292579 138 18 22.3904862825775 -4.39048628257748 139 17 18.6680996590357 -1.66809965903566 140 22 23.4582287533804 -1.45822875338038 141 30 24.1216207648897 5.87837923511026 142 30 28.4749540251296 1.52504597487039 143 24 29.9574591028377 -5.9574591028377 144 21 24.0342628393382 -3.0342628393382 145 21 28.674775882773 -7.67477588277303 146 29 26.1678055301888 2.83219446981117 147 31 23.9993278760587 7.00067212394134 148 20 18.9283618955813 1.07163810441868 149 16 13.2376929183879 2.76230708161209 150 22 18.5742036824379 3.42579631756214 151 20 20.5834557260427 -0.583455726042652 152 28 26.1291395792139 1.87086042078611 153 38 26.6741748685937 11.3258251314063 154 22 20.742472660174 1.25752733982601 155 20 25.670945595215 -5.67094559521501 156 17 20.6710415220018 -3.67104152200176 157 28 27.4514730068497 0.548526993150266 158 22 23.3976286177686 -1.39762861776856 159 31 27.0066191084548 3.99338089154524 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.853541397703838 0.292917204592323 0.146458602296162 22 0.786135183894209 0.427729632211582 0.213864816105791 23 0.686989434980851 0.626021130038297 0.313010565019149 24 0.599706651668467 0.800586696663065 0.400293348331533 25 0.578986005872523 0.842027988254954 0.421013994127477 26 0.625357501253916 0.749284997492168 0.374642498746084 27 0.562425286461923 0.875149427076154 0.437574713538077 28 0.491896048626596 0.983792097253191 0.508103951373404 29 0.408278786275982 0.816557572551963 0.591721213724018 30 0.333318252761067 0.666636505522133 0.666681747238933 31 0.267296066991961 0.534592133983921 0.73270393300804 32 0.346146649957842 0.692293299915684 0.653853350042158 33 0.275302468299582 0.550604936599164 0.724697531700418 34 0.214178541557106 0.428357083114213 0.785821458442894 35 0.270658315959940 0.541316631919879 0.72934168404006 36 0.235026975556277 0.470053951112555 0.764973024443723 37 0.280034492059835 0.560068984119669 0.719965507940165 38 0.361717913707915 0.723435827415831 0.638282086292085 39 0.337904149106561 0.675808298213121 0.662095850893439 40 0.289034660702140 0.578069321404279 0.71096533929786 41 0.273944000772723 0.547888001545447 0.726055999227277 42 0.222885723258573 0.445771446517147 0.777114276741427 43 0.218454802654117 0.436909605308233 0.781545197345883 44 0.186353232324969 0.372706464649939 0.81364676767503 45 0.160942076066611 0.321884152133221 0.83905792393339 46 0.193013620819504 0.386027241639007 0.806986379180496 47 0.153710270931096 0.307420541862193 0.846289729068904 48 0.143572517380447 0.287145034760895 0.856427482619553 49 0.125516021376845 0.25103204275369 0.874483978623155 50 0.102577906613671 0.205155813227341 0.89742209338633 51 0.114831137251217 0.229662274502433 0.885168862748783 52 0.0893235383537857 0.178647076707571 0.910676461646214 53 0.0741497900498414 0.148299580099683 0.925850209950159 54 0.055919271589059 0.111838543178118 0.94408072841094 55 0.0666926143178879 0.133385228635776 0.933307385682112 56 0.0828910641687744 0.165782128337549 0.917108935831226 57 0.0649039712588781 0.129807942517756 0.935096028741122 58 0.0595825401864331 0.119165080372866 0.940417459813567 59 0.0475594298682258 0.0951188597364516 0.952440570131774 60 0.198382044164398 0.396764088328796 0.801617955835602 61 0.249286550658369 0.498573101316738 0.750713449341631 62 0.226001431378477 0.452002862756954 0.773998568621523 63 0.208564461712293 0.417128923424586 0.791435538287707 64 0.214522763994547 0.429045527989093 0.785477236005453 65 0.262409107737905 0.52481821547581 0.737590892262095 66 0.28353671084978 0.56707342169956 0.71646328915022 67 0.611437525222839 0.777124949554321 0.388562474777161 68 0.572336311383722 0.855327377232556 0.427663688616278 69 0.747755389492159 0.504489221015682 0.252244610507841 70 0.729129525916492 0.541740948167017 0.270870474083508 71 0.905927758702307 0.188144482595386 0.094072241297693 72 0.885052805250189 0.229894389499623 0.114947194749811 73 0.882811350765758 0.234377298468484 0.117188649234242 74 0.871164876774947 0.257670246450105 0.128835123225053 75 0.878149221641464 0.243701556717072 0.121850778358536 76 0.871728575778322 0.256542848443357 0.128271424221678 77 0.933514656481871 0.132970687036258 0.066485343518129 78 0.916106885324286 0.167786229351427 0.0838931146757137 79 0.90505116018402 0.189897679631960 0.0949488398159798 80 0.929151294379137 0.141697411241726 0.070848705620863 81 0.916702616346391 0.166594767307217 0.0832973836536085 82 0.910391979121988 0.179216041756024 0.0896080208780122 83 0.88873103959612 0.222537920807759 0.111268960403880 84 0.88398904045554 0.232021919088919 0.116010959544459 85 0.858305558670786 0.283388882658428 0.141694441329214 86 0.832658707278392 0.334682585443216 0.167341292721608 87 0.802169280007564 0.395661439984872 0.197830719992436 88 0.873435042852608 0.253129914294784 0.126564957147392 89 0.849570173280281 0.300859653439437 0.150429826719719 90 0.8243738496526 0.351252300694799 0.175626150347400 91 0.848205301261775 0.30358939747645 0.151794698738225 92 0.821117752247388 0.357764495505224 0.178882247752612 93 0.8025369587929 0.394926082414202 0.197463041207101 94 0.775394618049482 0.449210763901036 0.224605381950518 95 0.735096266729865 0.529807466540269 0.264903733270135 96 0.690021845842233 0.619956308315534 0.309978154157767 97 0.682249765892215 0.63550046821557 0.317750234107785 98 0.716322786269792 0.567354427460416 0.283677213730208 99 0.671628957471354 0.656742085057291 0.328371042528646 100 0.636052208830126 0.727895582339747 0.363947791169874 101 0.596739204939635 0.806521590120731 0.403260795060365 102 0.544575664301798 0.910848671396404 0.455424335698202 103 0.539962528541592 0.920074942916816 0.460037471458408 104 0.485185902310077 0.970371804620154 0.514814097689923 105 0.439519600869878 0.879039201739756 0.560480399130122 106 0.403710424279773 0.807420848559545 0.596289575720227 107 0.444752739498529 0.889505478997058 0.555247260501471 108 0.474076314297376 0.948152628594751 0.525923685702624 109 0.452334085807561 0.904668171615123 0.547665914192438 110 0.400197188759114 0.800394377518229 0.599802811240886 111 0.369543056909671 0.739086113819342 0.630456943090329 112 0.73473187219126 0.530536255617479 0.265268127808739 113 0.789850487167907 0.420299025664187 0.210149512832093 114 0.782985199762379 0.434029600475242 0.217014800237621 115 0.850283731394281 0.299432537211438 0.149716268605719 116 0.80877091928843 0.382458161423139 0.191229080711569 117 0.786711079166848 0.426577841666305 0.213288920833152 118 0.791051817816709 0.417896364366582 0.208948182183291 119 0.780971421186068 0.438057157627865 0.219028578813932 120 0.850632729302538 0.298734541394923 0.149367270697462 121 0.95428149911416 0.091437001771682 0.045718500885841 122 0.936510902458654 0.126978195082692 0.0634890975413462 123 0.960871461014576 0.078257077970848 0.039128538985424 124 0.940544774691477 0.118910450617047 0.0594552253085233 125 0.93737161215445 0.125256775691101 0.0626283878455503 126 0.909200516109647 0.181598967780706 0.0907994838903531 127 0.870088356116329 0.259823287767343 0.129911643883671 128 0.81952712465077 0.360945750698461 0.180472875349231 129 0.955921879403166 0.0881562411936676 0.0440781205968338 130 0.959408608688669 0.0811827826226628 0.0405913913113314 131 0.953789672860244 0.0924206542795115 0.0462103271397557 132 0.937433485221183 0.125133029557633 0.0625665147788167 133 0.900384752072575 0.199230495854851 0.0996152479274253 134 0.855487416651143 0.289025166697713 0.144512583348857 135 0.777503181216328 0.444993637567344 0.222496818783672 136 0.66797969060019 0.664040618799621 0.332020309399811 137 0.630043585809385 0.73991282838123 0.369956414190615 138 0.703815294791996 0.592369410416008 0.296184705208004 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 0 0 OK 10% type I error level 6 0.0508474576271186 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/10jku41290850027.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/10jku41290850027.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/1u1fs1290850027.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/1u1fs1290850027.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/2u1fs1290850027.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/2u1fs1290850027.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/35aev1290850027.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/35aev1290850027.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/45aev1290850027.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/45aev1290850027.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/55aev1290850027.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/55aev1290850027.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/6gjvg1290850027.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/6gjvg1290850027.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/7rbv11290850027.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/7rbv11290850027.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/8rbv11290850027.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/8rbv11290850027.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/9rbv11290850027.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/27/t1290849966zdamsrymgzk8rox/9rbv11290850027.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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