workshop 7

*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 16:59:41 +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/t1290531511rc29thnmeejxceh.htm/, Retrieved Tue, 23 Nov 2010 17:58:33 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh.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 15 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Personal-Standards[t] = + 7.46043060983698 + 0.328154021465218`Concern(Mistakes)`[t] -0.362736672389800`Doubts(actions)`[t] + 0.186560236681879`Parental-Expectations`[t] + 0.0233844134026156`Parental-Criticism`[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 `Concern(Mistakes)` 0.328154021465218 0.055544 5.908 0 0 `Doubts(actions)` -0.362736672389800 0.107118 -3.3863 9e-04 0.00045 `Parental-Expectations` 0.186560236681879 0.10114 1.8446 0.067032 0.033516 `Parental-Criticism` 0.0233844134026156 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 23.0236176333508 0.976382366649192 2 25 22.3963921073235 2.60360789267647 3 30 24.2529863072522 5.74701369274783 4 19 20.2962579947228 -1.29625799472283 5 22 20.5386282852832 1.46137171471678 6 22 23.1227812851809 -1.12278128518093 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 -3.8153403514384 12 19 23.3938848919955 -4.39388489199547 13 15 23.2200335336539 -8.22003353365394 14 16 17.0860954231925 -1.08609542319246 15 23 19.4598225179576 3.54017748204243 16 27 24.0748423820553 2.92515761794465 17 22 21.0019432886847 0.998056711315263 18 14 16.535329320714 -2.53532932071400 19 22 24.0873202920243 -2.08732029202431 20 23 24.0090508616482 -1.00905086164818 21 23 21.5688381779423 1.4311618220577 22 21 24.4545998179461 -3.45459981794611 23 19 22.4295524471459 -3.42955244714589 24 18 23.8367869289911 -5.83678692899107 25 20 23.1800605324662 -3.18006053246622 26 23 22.4483525596049 0.551647440395091 27 25 23.3280787328681 1.67192126713187 28 19 23.3532655211774 -4.35326552117744 29 24 23.839829931247 0.160170068753002 30 22 21.5692258736674 0.430774126332574 31 25 25.1649483334544 -0.164948333454416 32 26 23.2232169775374 2.77678302246258 33 29 22.7002038848751 6.29979611512492 34 32 25.1965595373823 6.8034404626177 35 25 21.5830794177202 3.41692058227981 36 29 24.4099495065135 4.59005049348653 37 28 24.9467056041625 3.0532943958375 38 17 17.1062381095522 -0.106238109552166 39 28 26.0751635208601 1.92483647913992 40 29 22.9430722049405 6.05692779505949 41 26 27.52862185641 -1.52862185640998 42 25 23.4667094578832 1.53329054211676 43 14 19.5469105942641 -5.54691059426405 44 25 22.1055221703104 2.89447782968955 45 26 21.6780393824329 4.32196061756713 46 20 20.3008968098917 -0.300896809891658 47 18 21.4213727878477 -3.42137278784772 48 32 24.6610362298757 7.33896377012431 49 25 25.0045460489836 -0.00454604898359165 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 -1.52692902837806 55 30 26.717390208988 3.28260979101198 56 24 25.3394958960663 -1.33949589606632 57 26 24.3125491844923 1.68745081550775 58 24 21.7172524612978 2.28274753870219 59 22 21.4941504714309 0.505849528569085 60 14 15.6462203516491 -1.64622035164913 61 24 22.255359520076 1.74464047992401 62 24 22.9203756085798 1.07962439142021 63 24 23.3536201567194 0.646379843280559 64 24 19.9850555838132 4.01494441618681 65 19 18.5129061642547 0.487093835745272 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 -0.50267738327296 73 27 27.4823128306108 -0.482312830610752 74 23 24.3803773473337 -1.38037734733371 75 25 25.6982731831007 -0.698273183100738 76 20 22.2330812773097 -2.23308127730969 77 21 19.2454670687402 1.75453293125985 78 22 22.4516157406899 -0.451615740689920 79 23 23.0320339448358 -0.0320339448358371 80 25 24.0521764435639 0.947823556436075 81 25 23.4230855798854 1.57691442011462 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 -0.0165688176435826 95 21 23.5510323826098 -2.55103238260975 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 0.160469185839441 102 19 20.6492902959521 -1.64929029595212 103 20 20.9576947616757 -0.957694761675737 104 21 22.3255043730554 -1.32550437305537 105 20 23.8525057494042 -3.85250574940422 106 17 18.7741072251434 -1.77410722514342 107 18 20.3006604066273 -2.30066040662729 108 19 20.7496791060040 -1.74967910600404 109 22 22.0682765809344 -0.0682765809344119 110 15 18.7664416321540 -3.76644163215395 111 14 18.8510893511519 -4.85108935115190 112 18 26.6429142940772 -8.64291429407725 113 24 21.4114487878798 2.58855121212023 114 35 23.5620327119435 11.4379672880565 115 29 19.2163246027188 9.78367539728123 116 21 21.9816944326307 -0.981694432630689 117 25 20.4953208143283 4.50467918567166 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 -0.77227348923623 125 19 18.1285543931859 0.871445606814121 126 21 22.6212243668162 -1.62122436681623 127 22 21.0704752877172 0.929524712282782 128 24 22.7056739110488 1.29432608895116 129 21 22.9951676639565 -1.99516766395646 130 26 25.482195851486 0.517804148514021 131 24 20.5950930960205 3.40490690397949 132 16 20.2987397994430 -4.29873979944297 133 23 22.3765319512249 0.623468048775057 134 18 20.8107987510593 -2.81079875105926 135 16 22.3793138772619 -6.37931387726185 136 26 24.0698543662375 1.93014563376249 137 19 19.0560620045677 -0.0560620045676752 138 21 16.8666199037581 4.13338009624188 139 21 22.2168258710245 -1.21682587102449 140 22 18.5260173770404 3.47398262295963 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 25.3746950753507 -0.374695075350650 148 21 21.0001409137780 -0.000140913778046401 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 -2.65847521516283 154 19 18.9825826818211 0.017417318178872 155 24 22.0940161795511 1.90598382044895 156 19 20.7666852307848 -1.76668523078483 157 24 23.4401554227186 0.559844577281407 158 22 21.8244370969672 0.175562903032760 159 17 23.7736200572454 -6.77362005724542 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.303167174871691 0.606334349743382 0.696832825128309 10 0.183271906161378 0.366543812322756 0.816728093838622 11 0.338965752665167 0.677931505330333 0.661034247334833 12 0.289608818137534 0.579217636275068 0.710391181862466 13 0.866047634514266 0.267904730971468 0.133952365485734 14 0.804934375302346 0.390131249395308 0.195065624697654 15 0.759902102105923 0.480195795788155 0.240097897894077 16 0.69717005828316 0.60565988343368 0.30282994171684 17 0.619282751525191 0.761434496949617 0.380717248474809 18 0.591038687395453 0.817922625209095 0.408961312604548 19 0.524025389127915 0.95194922174417 0.475974610872085 20 0.518204023347026 0.963591953305947 0.481795976652974 21 0.497824319669455 0.99564863933891 0.502175680330545 22 0.430879369865434 0.861758739730868 0.569120630134566 23 0.385894677332064 0.771789354664128 0.614105322667936 24 0.43499451037991 0.86998902075982 0.56500548962009 25 0.447721043082056 0.895442086164112 0.552278956917944 26 0.379605715547792 0.759211431095584 0.620394284452208 27 0.329281747759595 0.658563495519189 0.670718252240405 28 0.345291322953478 0.690582645906957 0.654708677046522 29 0.291663451307304 0.583326902614608 0.708336548692696 30 0.238502872434837 0.477005744869673 0.761497127565163 31 0.191952554345429 0.383905108690857 0.808047445654571 32 0.212174113640594 0.424348227281188 0.787825886359406 33 0.362084702521348 0.724169405042695 0.637915297478652 34 0.596683272280863 0.806633455438274 0.403316727719137 35 0.573836653892848 0.852326692214304 0.426163346107152 36 0.633997466898335 0.73200506620333 0.366002533101665 37 0.625046475135514 0.749907049728972 0.374953524864486 38 0.581207101871441 0.837585796257118 0.418792898128559 39 0.54926503948919 0.90146992102162 0.45073496051081 40 0.634014980726026 0.731970038547949 0.365985019273974 41 0.6026968069944 0.794606386011199 0.397303193005599 42 0.557493784028079 0.885012431943843 0.442506215971921 43 0.644045523161667 0.711908953676666 0.355954476838333 44 0.616000997208378 0.767998005583244 0.383999002791622 45 0.639204204427411 0.721591591145178 0.360795795572589 46 0.589703966450402 0.820592067099196 0.410296033549598 47 0.580443349320715 0.83911330135857 0.419556650679285 48 0.691689468145315 0.61662106370937 0.308310531854685 49 0.650493606472396 0.699012787055209 0.349506393527605 50 0.639685672078383 0.720628655843235 0.360314327921617 51 0.601176208528055 0.79764758294389 0.398823791471945 52 0.560223306122013 0.879553387755974 0.439776693877987 53 0.59654801013634 0.806903979727321 0.403451989863660 54 0.563409560023509 0.873180879952981 0.436590439976491 55 0.6148934247036 0.7702131505928 0.3851065752964 56 0.581855444429155 0.83628911114169 0.418144555570845 57 0.542133076835251 0.915733846329498 0.457866923164749 58 0.511041653464181 0.977916693071639 0.488958346535819 59 0.463967143941438 0.927934287882877 0.536032856058562 60 0.422762276607028 0.845524553214056 0.577237723392972 61 0.389856149572537 0.779712299145074 0.610143850427463 62 0.350053587354272 0.700107174708545 0.649946412645728 63 0.309275961404122 0.618551922808244 0.690724038595878 64 0.342214870616303 0.684429741232606 0.657785129383697 65 0.300789340611201 0.601578681222403 0.699210659388799 66 0.314622189809826 0.629244379619651 0.685377810190174 67 0.376722299893158 0.753444599786315 0.623277700106842 68 0.453735810270280 0.907471620540561 0.54626418972972 69 0.415173598595846 0.830347197191692 0.584826401404154 70 0.398962430900143 0.797924861800286 0.601037569099857 71 0.465805133548298 0.931610267096597 0.534194866451702 72 0.420547218514767 0.841094437029534 0.579452781485233 73 0.379420083615661 0.758840167231322 0.620579916384339 74 0.343987947421435 0.68797589484287 0.656012052578565 75 0.311941642730412 0.623883285460823 0.688058357269588 76 0.288322322782673 0.576644645565346 0.711677677217327 77 0.265760054108160 0.531520108216319 0.73423994589184 78 0.229963664211329 0.459927328422658 0.770036335788671 79 0.197609624720245 0.395219249440491 0.802390375279755 80 0.170889702903008 0.341779405806016 0.829110297096992 81 0.149927711996899 0.299855423993797 0.850072288003101 82 0.243958798773799 0.487917597547599 0.7560412012262 83 0.225769628132371 0.451539256264742 0.774230371867629 84 0.196630524503168 0.393261049006336 0.803369475496832 85 0.198635525287207 0.397271050574414 0.801364474712793 86 0.194109087922453 0.388218175844906 0.805890912077547 87 0.201566756712154 0.403133513424309 0.798433243287846 88 0.188441608808055 0.37688321761611 0.811558391191945 89 0.176294099046913 0.352588198093826 0.823705900953087 90 0.181308594520281 0.362617189040561 0.81869140547972 91 0.258552651528514 0.517105303057029 0.741447348471486 92 0.224227745019767 0.448455490039533 0.775772254980233 93 0.207472771899061 0.414945543798122 0.792527228100939 94 0.176647005370814 0.353294010741628 0.823352994629186 95 0.161860531291105 0.32372106258221 0.838139468708895 96 0.165595947642546 0.331191895285092 0.834404052357454 97 0.167373926121472 0.334747852242944 0.832626073878528 98 0.163457638314322 0.326915276628644 0.836542361685678 99 0.156349521556575 0.312699043113149 0.843650478443425 100 0.15119866933871 0.30239733867742 0.84880133066129 101 0.124811279134694 0.249622558269388 0.875188720865306 102 0.104690768274489 0.209381536548978 0.895309231725511 103 0.0848347178153746 0.169669435630749 0.915165282184625 104 0.0691676951931689 0.138335390386338 0.930832304806831 105 0.0739920091905175 0.147984018381035 0.926007990809482 106 0.0610052105173347 0.122010421034669 0.938994789482665 107 0.0539069738399774 0.107813947679955 0.946093026160023 108 0.0472209695484173 0.0944419390968347 0.952779030451583 109 0.0363985089919587 0.0727970179839174 0.963601491008041 110 0.0358992577967031 0.0717985155934063 0.964100742203297 111 0.0452125173350232 0.0904250346700465 0.954787482664977 112 0.180955683183649 0.361911366367299 0.81904431681635 113 0.165054450617797 0.330108901235595 0.834945549382203 114 0.597307230948238 0.805385538103524 0.402692769051762 115 0.874510148678328 0.250979702643343 0.125489851321672 116 0.844979458493553 0.310041083012893 0.155020541506447 117 0.894632713617535 0.210734572764929 0.105367286382465 118 0.87279443800004 0.254411123999921 0.127205561999960 119 0.847689558796055 0.304620882407890 0.152310441203945 120 0.877971708479872 0.244056583040257 0.122028291520128 121 0.857671657384474 0.284656685231052 0.142328342615526 122 0.821949400890632 0.356101198218736 0.178050599109368 123 0.850400725233224 0.299198549533553 0.149599274766776 124 0.812775955862856 0.374448088274287 0.187224044137144 125 0.77727497835217 0.445450043295661 0.222725021647830 126 0.732848303780098 0.534303392439803 0.267151696219902 127 0.699031978855796 0.601936042288408 0.300968021144204 128 0.659625545216797 0.680748909566407 0.340374454783204 129 0.603997811521454 0.792004376957092 0.396002188478546 130 0.542618005847216 0.914763988305567 0.457381994152784 131 0.541396971393463 0.917206057213074 0.458603028606537 132 0.541507306832898 0.916985386334204 0.458492693167102 133 0.492018422002719 0.984036844005439 0.507981577997281 134 0.444298507112976 0.888597014225952 0.555701492887024 135 0.596843113757033 0.806313772485935 0.403156886242967 136 0.560225537119912 0.879548925760177 0.439774462880088 137 0.488060397250348 0.976120794500695 0.511939602749652 138 0.500465747071631 0.999068505856738 0.499534252928369 139 0.428677355797048 0.857354711594096 0.571322644202952 140 0.392394744899589 0.784789489799177 0.607605255100411 141 0.357899121912323 0.715798243824647 0.642100878087677 142 0.417566057793126 0.835132115586252 0.582433942206874 143 0.570950490818346 0.858099018363308 0.429049509181654 144 0.497661935280862 0.995323870561723 0.502338064719138 145 0.41681494841382 0.83362989682764 0.58318505158618 146 0.411934368393863 0.823868736787726 0.588065631606137 147 0.360460923669245 0.720921847338491 0.639539076330754 148 0.251071208740865 0.502142417481731 0.748928791259135 149 0.456567419664047 0.913134839328095 0.543432580335953 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/23/t1290531511rc29thnmeejxceh/10xwlq1290531562.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/10xwlq1290531562.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/18v6w1290531562.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/18v6w1290531562.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/28v6w1290531562.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/28v6w1290531562.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/3145h1290531562.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/3145h1290531562.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/4145h1290531562.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/4145h1290531562.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/5145h1290531562.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/5145h1290531562.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/6td421290531562.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/6td421290531562.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/745m51290531562.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/745m51290531562.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/845m51290531562.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/845m51290531562.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/945m51290531562.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290531511rc29thnmeejxceh/945m51290531562.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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