multiple regression model 1

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Fri, 26 Nov 2010 09:50:58 +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/26/t1290764979tgdn3qc5y068d4e.htm/, Retrieved Fri, 26 Nov 2010 10:49:49 +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/26/t1290764979tgdn3qc5y068d4e.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:

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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 24 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation PersonalStandards[t] = + 7.46043060983698 + 0.328154021465218ConcernoverMistakes[t] -0.362736672389799Doubtsaboutactions[t] + 0.186560236681879ParentalExpectations[t] + 0.0233844134026164ParentalCriticism[t] + 0.401270321441297Organization[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) 7.46043060983698 2.248109 3.3185 0.001131 0.000565 ConcernoverMistakes 0.328154021465218 0.055544 5.908 0 0 Doubtsaboutactions -0.362736672389799 0.107118 -3.3863 9e-04 0.00045 ParentalExpectations 0.186560236681879 0.10114 1.8446 0.067032 0.033516 ParentalCriticism 0.0233844134026164 0.128621 0.1818 0.855973 0.427987 Organization 0.401270321441297 0.071773 5.5908 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.605858798778077 R-squared 0.367064884056814 Adjusted R-squared 0.346380729941024 F-TEST (value) 17.7461878306445 F-TEST (DF numerator) 5 F-TEST (DF denominator) 153 p-value 7.54951656745106e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.40927289715423 Sum Squared Residuals 1778.34067815237 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.0236176333507 0.976382366649325 2 25 22.3963921073235 2.60360789267648 3 30 24.2529863072522 5.74701369274783 4 19 20.2962579947228 -1.29625799472284 5 22 20.5386282852832 1.46137171471677 6 22 23.1227812851809 -1.12278128518095 7 25 22.5736026083869 2.42639739161312 8 23 19.4568594581893 3.54314054181066 9 17 18.7937770436835 -1.79377704368349 10 21 21.6696775851730 -0.669677585173036 11 19 22.8153403514384 -3.81534035143841 12 19 23.3938848919955 -4.39388489199547 13 15 23.2200335336539 -8.22003353365394 14 16 17.0860954231925 -1.08609542319247 15 23 19.4598225179576 3.54017748204243 16 27 24.0748423820553 2.92515761794466 17 22 21.0019432886847 0.99805671131526 18 14 16.535329320714 -2.53532932071399 19 22 24.0873202920243 -2.08732029202430 20 23 24.0090508616482 -1.00905086164818 21 23 21.5688381779423 1.43116182205770 22 21 24.4545998179461 -3.45459981794611 23 19 22.4295524471459 -3.42955244714590 24 18 23.8367869289911 -5.83678692899107 25 20 23.1800605324662 -3.18006053246622 26 23 22.4483525596049 0.55164744039509 27 25 23.3280787328681 1.67192126713187 28 19 23.3532655211774 -4.35326552117744 29 24 23.839829931247 0.160170068753002 30 22 21.5692258736674 0.430774126332576 31 25 25.1649483334544 -0.164948333454417 32 26 23.2232169775374 2.77678302246257 33 29 22.7002038848751 6.29979611512493 34 32 25.1965595373823 6.8034404626177 35 25 21.5830794177202 3.41692058227981 36 29 24.4099495065135 4.59005049348653 37 28 24.9467056041625 3.05329439583750 38 17 17.1062381095522 -0.106238109552165 39 28 26.0751635208601 1.92483647913991 40 29 22.9430722049405 6.05692779505949 41 26 27.5286218564100 -1.52862185640998 42 25 23.4667094578832 1.53329054211676 43 14 19.5469105942640 -5.54691059426405 44 25 22.1055221703104 2.89447782968956 45 26 21.6780393824329 4.32196061756712 46 20 20.3008968098917 -0.300896809891661 47 18 21.4213727878477 -3.42137278784772 48 32 24.6610362298757 7.3389637701243 49 25 25.0045460489836 -0.00454604898359189 50 25 21.6915513577573 3.30844864224273 51 23 20.8454749613068 2.15452503869318 52 21 22.1588588066973 -1.15885880669729 53 20 24.0575114630031 -4.05751146300312 54 15 16.5269290283781 -1.52692902837805 55 30 26.7173902089880 3.28260979101198 56 24 25.3394958960663 -1.33949589606632 57 26 24.3125491844923 1.68745081550774 58 24 21.7172524612978 2.28274753870220 59 22 21.4941504714309 0.505849528569084 60 14 15.6462203516491 -1.64622035164913 61 24 22.255359520076 1.74464047992401 62 24 22.9203756085798 1.07962439142021 63 24 23.3536201567194 0.646379843280558 64 24 19.9850555838132 4.0149444161868 65 19 18.5129061642547 0.487093835745273 66 31 26.8208676764294 4.17913232357061 67 22 26.6010375214530 -4.60103752145305 68 27 21.4697621005205 5.5302378994795 69 19 17.7359069452234 1.26409305477656 70 25 22.3044035896075 2.69559641039245 71 20 24.9772106374541 -4.97721063745406 72 21 21.5026773832730 -0.502677383272962 73 27 27.4823128306108 -0.482312830610753 74 23 24.3803773473337 -1.38037734733372 75 25 25.6982731831007 -0.698273183100734 76 20 22.2330812773097 -2.23308127730969 77 21 19.2454670687402 1.75453293125985 78 22 22.4516157406899 -0.451615740689923 79 23 23.0320339448358 -0.0320339448358424 80 25 24.0521764435639 0.947823556436078 81 25 23.4230855798854 1.57691442011461 82 17 23.8630492300674 -6.86304923006741 83 19 21.4391304477228 -2.43913044772283 84 25 23.9709132955503 1.02908670444972 85 19 22.3733623294629 -3.37336232946291 86 20 23.1407040596382 -3.14070405963825 87 26 22.5238707218134 3.47612927818658 88 23 20.8073842775135 2.19261572248651 89 27 24.4361957884407 2.56380421155931 90 17 20.8970807780462 -3.8970807780462 91 17 23.3435280898338 -6.3435280898338 92 19 20.191563551002 -1.19156355100200 93 17 19.7459731472925 -2.74597314729248 94 22 22.0165688176436 -0.0165688176435780 95 21 23.5510323826098 -2.55103238260976 96 32 28.6372448399853 3.36275516001471 97 21 24.6834795872242 -3.6834795872242 98 21 24.3266944626333 -3.32669446263334 99 18 21.259817450436 -3.259817450436 100 18 21.2889468496438 -3.28894684964376 101 23 22.8395308141606 0.160469185839440 102 19 20.6492902959521 -1.64929029595211 103 20 20.9576947616757 -0.957694761675735 104 21 22.3255043730554 -1.32550437305537 105 20 23.8525057494042 -3.85250574940423 106 17 18.7741072251434 -1.77410722514342 107 18 20.3006604066273 -2.30066040662729 108 19 20.7496791060040 -1.74967910600404 109 22 22.0682765809344 -0.0682765809344147 110 15 18.7664416321540 -3.76644163215395 111 14 18.8510893511519 -4.8510893511519 112 18 26.6429142940773 -8.64291429407725 113 24 21.4114487878798 2.58855121212023 114 35 23.5620327119435 11.4379672880565 115 29 19.2163246027188 9.78367539728123 116 21 21.9816944326307 -0.981694432630686 117 25 20.4953208143283 4.50467918567167 118 20 18.4924302963951 1.50756970360488 119 22 23.2253187184531 -1.22531871845307 120 13 16.8359413686559 -3.83594136865588 121 26 23.2142002181326 2.78579978186736 122 17 16.8872223911238 0.112777608876169 123 25 20.0947136369743 4.90528636302571 124 20 20.7722734892362 -0.772273489236233 125 19 18.1285543931859 0.871445606814115 126 21 22.6212243668162 -1.62122436681623 127 22 21.0704752877172 0.929524712282783 128 24 22.7056739110488 1.29432608895115 129 21 22.9951676639565 -1.99516766395646 130 26 25.482195851486 0.517804148514019 131 24 20.5950930960205 3.40490690397949 132 16 20.2987397994430 -4.29873979944297 133 23 22.3765319512249 0.623468048775058 134 18 20.8107987510593 -2.81079875105926 135 16 22.3793138772619 -6.37931387726185 136 26 24.0698543662375 1.93014563376249 137 19 19.0560620045677 -0.0560620045676737 138 21 16.8666199037581 4.13338009624188 139 21 22.2168258710245 -1.21682587102449 140 22 18.5260173770404 3.47398262295962 141 23 19.7340241912749 3.26597580872508 142 29 24.8124059410788 4.18759405892122 143 21 19.2156508743754 1.78434912562462 144 21 19.9639464131369 1.03605358686309 145 23 21.8927879622684 1.10721203773160 146 27 22.996067272599 4.00393272740102 147 25 25.3746950753506 -0.374695075350646 148 21 21.0001409137780 -0.00014091377804544 149 10 17.1119616413152 -7.1119616413152 150 20 22.6490195793518 -2.64901957935177 151 26 22.5749237282455 3.42507627175453 152 24 23.6474832613484 0.352516738651611 153 29 31.6584752151628 -2.65847521516282 154 19 18.9825826818211 0.0174173181788779 155 24 22.0940161795511 1.90598382044895 156 19 20.7666852307848 -1.76668523078483 157 24 23.4401554227186 0.559844577281405 158 22 21.8244370969672 0.175562903032759 159 17 23.7736200572454 -6.77362005724542 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.303167174871690 0.606334349743380 0.69683282512831 10 0.183271906161378 0.366543812322756 0.816728093838622 11 0.338965752665167 0.677931505330334 0.661034247334833 12 0.289608818137534 0.579217636275067 0.710391181862466 13 0.866047634514266 0.267904730971468 0.133952365485734 14 0.804934375302345 0.390131249395309 0.195065624697655 15 0.759902102105923 0.480195795788155 0.240097897894077 16 0.69717005828316 0.605659883433681 0.302829941716841 17 0.619282751525192 0.761434496949616 0.380717248474808 18 0.591038687395452 0.817922625209095 0.408961312604548 19 0.524025389127916 0.951949221744168 0.475974610872084 20 0.518204023347029 0.963591953305943 0.481795976652971 21 0.497824319669458 0.995648639338917 0.502175680330541 22 0.430879369865434 0.861758739730868 0.569120630134566 23 0.385894677332065 0.77178935466413 0.614105322667935 24 0.434994510379911 0.869989020759822 0.565005489620089 25 0.447721043082056 0.895442086164111 0.552278956917944 26 0.379605715547791 0.759211431095582 0.620394284452209 27 0.329281747759596 0.658563495519192 0.670718252240404 28 0.345291322953479 0.690582645906959 0.65470867704652 29 0.291663451307306 0.583326902614613 0.708336548692694 30 0.238502872434837 0.477005744869674 0.761497127565163 31 0.191952554345429 0.383905108690858 0.808047445654571 32 0.212174113640594 0.424348227281188 0.787825886359406 33 0.362084702521349 0.724169405042698 0.637915297478651 34 0.596683272280861 0.806633455438278 0.403316727719139 35 0.573836653892848 0.852326692214305 0.426163346107152 36 0.633997466898336 0.732005066203328 0.366002533101664 37 0.625046475135516 0.749907049728968 0.374953524864484 38 0.581207101871442 0.837585796257115 0.418792898128558 39 0.549265039489188 0.901469921021624 0.450734960510812 40 0.634014980726027 0.731970038547947 0.365985019273973 41 0.6026968069944 0.794606386011201 0.397303193005600 42 0.557493784028078 0.885012431943844 0.442506215971922 43 0.644045523161668 0.711908953676664 0.355954476838332 44 0.61600099720838 0.76799800558324 0.38399900279162 45 0.639204204427412 0.721591591145176 0.360795795572588 46 0.589703966450402 0.820592067099195 0.410296033549598 47 0.580443349320714 0.839113301358572 0.419556650679286 48 0.691689468145315 0.61662106370937 0.308310531854685 49 0.650493606472394 0.699012787055211 0.349506393527606 50 0.639685672078383 0.720628655843233 0.360314327921617 51 0.601176208528053 0.797647582943893 0.398823791471947 52 0.560223306122016 0.879553387755968 0.439776693877984 53 0.596548010136338 0.806903979727324 0.403451989863662 54 0.563409560023508 0.873180879952984 0.436590439976492 55 0.6148934247036 0.7702131505928 0.3851065752964 56 0.581855444429154 0.836289111141691 0.418144555570846 57 0.54213307683525 0.9157338463295 0.45786692316475 58 0.511041653464183 0.977916693071635 0.488958346535817 59 0.463967143941438 0.927934287882876 0.536032856058562 60 0.422762276607028 0.845524553214057 0.577237723392972 61 0.389856149572536 0.779712299145073 0.610143850427464 62 0.35005358735427 0.70010717470854 0.64994641264573 63 0.309275961404124 0.618551922808247 0.690724038595876 64 0.342214870616303 0.684429741232605 0.657785129383697 65 0.300789340611199 0.601578681222398 0.699210659388801 66 0.314622189809827 0.629244379619654 0.685377810190173 67 0.376722299893159 0.753444599786317 0.623277700106841 68 0.45373581027028 0.90747162054056 0.54626418972972 69 0.415173598595846 0.830347197191692 0.584826401404154 70 0.39896243090014 0.79792486180028 0.60103756909986 71 0.465805133548298 0.931610267096596 0.534194866451702 72 0.420547218514767 0.841094437029534 0.579452781485233 73 0.37942008361566 0.75884016723132 0.62057991638434 74 0.343987947421434 0.687975894842868 0.656012052578566 75 0.311941642730413 0.623883285460826 0.688058357269587 76 0.288322322782675 0.57664464556535 0.711677677217325 77 0.265760054108159 0.531520108216318 0.734239945891841 78 0.229963664211330 0.459927328422660 0.77003633578867 79 0.197609624720245 0.395219249440491 0.802390375279755 80 0.170889702903008 0.341779405806016 0.829110297096992 81 0.149927711996897 0.299855423993793 0.850072288003104 82 0.2439587987738 0.4879175975476 0.7560412012262 83 0.225769628132371 0.451539256264743 0.774230371867629 84 0.196630524503169 0.393261049006338 0.803369475496831 85 0.198635525287207 0.397271050574414 0.801364474712793 86 0.194109087922453 0.388218175844906 0.805890912077547 87 0.201566756712155 0.403133513424309 0.798433243287845 88 0.188441608808055 0.37688321761611 0.811558391191945 89 0.176294099046914 0.352588198093829 0.823705900953086 90 0.181308594520281 0.362617189040562 0.818691405479719 91 0.258552651528515 0.517105303057029 0.741447348471485 92 0.224227745019767 0.448455490039534 0.775772254980233 93 0.207472771899059 0.414945543798118 0.79252722810094 94 0.176647005370815 0.353294010741629 0.823352994629185 95 0.161860531291105 0.32372106258221 0.838139468708895 96 0.165595947642546 0.331191895285093 0.834404052357454 97 0.167373926121473 0.334747852242946 0.832626073878527 98 0.163457638314321 0.326915276628642 0.836542361685679 99 0.156349521556574 0.312699043113148 0.843650478443426 100 0.15119866933871 0.30239733867742 0.84880133066129 101 0.124811279134694 0.249622558269388 0.875188720865306 102 0.104690768274489 0.209381536548977 0.895309231725511 103 0.0848347178153745 0.169669435630749 0.915165282184625 104 0.0691676951931677 0.138335390386335 0.930832304806832 105 0.0739920091905177 0.147984018381035 0.926007990809482 106 0.0610052105173343 0.122010421034669 0.938994789482666 107 0.0539069738399775 0.107813947679955 0.946093026160022 108 0.0472209695484166 0.0944419390968331 0.952779030451583 109 0.0363985089919581 0.0727970179839163 0.963601491008042 110 0.035899257796703 0.071798515593406 0.964100742203297 111 0.0452125173350235 0.090425034670047 0.954787482664976 112 0.18095568318365 0.3619113663673 0.81904431681635 113 0.165054450617798 0.330108901235597 0.834945549382202 114 0.597307230948242 0.805385538103516 0.402692769051758 115 0.874510148678329 0.250979702643343 0.125489851321671 116 0.844979458493553 0.310041083012894 0.155020541506447 117 0.894632713617536 0.210734572764929 0.105367286382464 118 0.87279443800004 0.25441112399992 0.12720556199996 119 0.847689558796054 0.304620882407892 0.152310441203946 120 0.877971708479871 0.244056583040258 0.122028291520129 121 0.857671657384474 0.284656685231053 0.142328342615526 122 0.821949400890632 0.356101198218737 0.178050599109368 123 0.850400725233223 0.299198549533553 0.149599274766777 124 0.812775955862856 0.374448088274287 0.187224044137144 125 0.77727497835217 0.44545004329566 0.22272502164783 126 0.732848303780099 0.534303392439802 0.267151696219901 127 0.699031978855796 0.601936042288408 0.300968021144204 128 0.659625545216796 0.680748909566408 0.340374454783204 129 0.603997811521453 0.792004376957094 0.396002188478547 130 0.542618005847216 0.914763988305569 0.457381994152784 131 0.541396971393464 0.917206057213071 0.458603028606536 132 0.541507306832898 0.916985386334204 0.458492693167102 133 0.492018422002719 0.984036844005439 0.507981577997281 134 0.444298507112975 0.88859701422595 0.555701492887025 135 0.596843113757033 0.806313772485935 0.403156886242967 136 0.560225537119912 0.879548925760177 0.439774462880088 137 0.488060397250346 0.976120794500692 0.511939602749654 138 0.500465747071631 0.999068505856739 0.499534252928369 139 0.428677355797048 0.857354711594096 0.571322644202952 140 0.392394744899588 0.784789489799176 0.607605255100412 141 0.357899121912324 0.715798243824647 0.642100878087676 142 0.417566057793126 0.835132115586252 0.582433942206874 143 0.570950490818347 0.858099018363306 0.429049509181653 144 0.497661935280862 0.995323870561724 0.502338064719138 145 0.41681494841382 0.83362989682764 0.58318505158618 146 0.411934368393863 0.823868736787727 0.588065631606137 147 0.360460923669245 0.72092184733849 0.639539076330755 148 0.251071208740865 0.50214241748173 0.748928791259135 149 0.456567419664046 0.913134839328093 0.543432580335954 150 0.385521341064606 0.771042682129212 0.614478658935394 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 4 0.0281690140845070 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/1036ss1290765033.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/1036ss1290765033.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/1fmap1290765032.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/1fmap1290765032.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/2fmap1290765032.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/2fmap1290765032.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/3fmap1290765032.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/3fmap1290765032.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/48wra1290765032.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/48wra1290765032.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/58wra1290765032.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/58wra1290765032.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/68wra1290765032.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/68wra1290765032.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/7bxb71290765033.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/7bxb71290765033.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/836ss1290765033.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/836ss1290765033.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/936ss1290765033.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290764979tgdn3qc5y068d4e/936ss1290765033.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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