*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: Mon, 13 Dec 2010 10:03:31 +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/Dec/13/t1292234563mbp4a3sdrr4vokx.htm/, Retrieved Mon, 13 Dec 2010 11:02:47 +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/Dec/13/t1292234563mbp4a3sdrr4vokx.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 «

1 15 15 13 6 2 9 12 11 4 2 12 15 14 6 2 15 12 12 5 2 17 14 12 5 2 14 8 6 4 1 9 11 10 5 1 12 15 11 3 2 11 4 10 2 2 13 13 12 5 1 16 19 15 6 1 16 10 13 6 1 15 15 18 8 2 10 6 11 6 1 16 7 12 3 2 12 14 13 6 2 15 16 14 6 1 13 16 16 7 1 18 14 16 8 2 13 15 16 6 1 17 14 15 7 1 14 12 13 4 2 13 9 8 4 1 13 12 14 2 1 15 14 15 6 1 13 12 13 6 1 15 14 16 6 1 13 10 13 6 1 14 14 12 6 1 13 16 15 7 1 16 10 11 4 1 14 8 14 3 2 12 8 14 3 1 18 12 13 5 1 15 11 13 6 2 9 8 12 4 2 16 13 14 6 1 16 11 13 3 2 17 12 12 3 2 13 16 14 6 1 17 16 15 6 1 15 13 16 6 1 14 14 15 8 2 10 5 5 2 2 13 14 15 6 1 11 13 8 4 1 11 16 16 7 2 16 15 14 6 2 16 15 14 6 1 11 15 16 6 1 15 11 14 5 1 15 15 13 6 1 12 16 14 6 1 17 13 14 5 2 15 11 12 6 2 16 12 13 7 1 14 12 15 5 1 17 10 15 6 1 10 8 13 6 2 11 9 10 4 1 15 12 13 5 2 15 14 14 6 1 7 12 13 6 2 17 11 13 4 2 14 14 18 6 2 18 7 12 4 2 14 16 14 7 1 12 16 16 8 2 14 11 13 6 1 9 16 16 6 1 14 13 15 6 1 11 11 14 5 1 15 11 14 5 1 16 13 13 6 1 17 14 1 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 8 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Happiness[t] = + 14.1776102759824 -0.662395540767814Gender[t] + 0.0402732610028032Popularity[t] + 0.063572774662549Liked[t] -0.107430080189719Celebrity[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) 14.1776102759824 1.342391 10.5615 0 0 Gender -0.662395540767814 0.381668 -1.7355 0.084647 0.042324 Popularity 0.0402732610028032 0.083249 0.4838 0.629236 0.314618 Liked 0.063572774662549 0.106941 0.5945 0.553073 0.276537 Celebrity -0.107430080189719 0.171962 -0.6247 0.533072 0.266536 Multiple Linear Regression - Regression Statistics Multiple R 0.167199882635009 R-squared 0.0279558007531608 Adjusted R-squared 0.00270789947402217 F-TEST (value) 1.10725245809875 F-TEST (DF numerator) 4 F-TEST (DF denominator) 154 p-value 0.355215089174953 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.29699286024406 Sum Squared Residuals 812.53113480188 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 14.3011792397315 0.698820760268548 2 9 13.6056785270096 -4.60567852700957 3 12 13.7023564736262 -1.70235647362619 4 15 13.5618212214824 1.4381787785176 5 17 13.642367743488 3.35763225651199 6 14 13.1267216096856 0.873278390314383 7 9 14.0567979519223 -5.05679795192232 8 12 14.4963239309755 -2.49632393097552 9 11 13.434779824704 -2.43477982470404 10 13 13.6020944824852 -0.602094482485208 11 16 14.5894178330678 1.41058216693223 12 16 14.0998129347174 1.90018706528256 13 15 14.4041829526648 0.595817047335234 14 10 13.1491788006133 -3.14917880061332 15 16 14.2377106176156 1.76228938238436 16 12 13.5985104379608 -1.59851043796084 17 15 13.742629734629 1.257370265371 18 13 14.4247407445322 -1.42474074453219 19 18 14.2367641423369 3.76323585766314 20 13 13.8295020229513 -0.829502022951292 21 17 14.280621447864 2.71937855213597 22 14 14.3952196171025 -0.395219617102488 23 13 13.2941404200135 -0.294140420013519 24 13 14.6736525521445 -1.67365255214448 25 15 14.3880515280538 0.611948471946246 26 13 14.180359456723 -1.18035945672305 27 15 14.4516243027163 0.548375697283697 28 13 14.0998129347174 -1.09981293471744 29 14 14.1973332040661 -0.197333204066107 30 13 14.3611679698696 -1.36116796986964 31 16 14.1875275457718 1.81247245422822 32 14 14.4051294279435 -0.405129427943544 33 12 13.7427338871757 -1.74273388717573 34 18 14.2877895369128 3.71221046308723 35 15 14.1400861957202 0.859913804279754 36 9 13.5081582576609 -4.50815825766091 37 16 13.6218099516206 2.37819004837941 38 16 14.4623764362894 1.5376235637106 39 17 13.7766813818618 3.22331861813816 40 13 13.742629734629 -0.742629734628997 41 17 14.4685980500594 2.53140194994064 42 15 14.4113510417135 0.5886489582865 43 14 14.1731913676743 -0.173191367674315 44 10 13.1571892123941 -3.1571892123941 45 13 13.7256559872859 -0.72565598728594 46 11 14.1176290047925 -3.11762900479255 47 11 14.4247407445322 -3.42474074453219 48 16 13.7023564736262 2.29764352637381 49 16 13.7023564736262 2.29764352637381 50 11 14.4918975637191 -3.49189756371911 51 15 14.3110890505725 0.688910949427485 52 15 14.3011792397315 0.698820760268541 53 12 14.4050252753968 -2.40502527539681 54 17 14.3916355725781 2.60836442742188 55 15 13.4141178802899 1.58588211971012 56 16 13.4105338357655 2.58946616423448 57 14 14.4149350862379 -0.414935086237867 58 17 14.2269584840425 2.77304151595746 59 10 14.0192664127118 -4.01926641271184 60 11 13.4212859693386 -2.42128596933862 61 15 14.2877895369128 0.712210463087231 62 15 13.6620832126234 1.33791678737661 63 7 14.180359456723 -7.18035945672305 64 17 13.6925508153319 3.30744918466813 65 14 13.9163743112736 0.0836256887264133 66 18 13.4678849966581 4.53211500334189 67 14 13.6351996544393 0.364800345560722 68 12 14.3173106643425 -2.31731066434247 69 14 13.4776906549524 0.522309345047568 70 9 14.5321708247219 -5.53217082472191 71 14 14.347778267051 -0.347778267050951 72 11 14.3110890505725 -3.31108905057251 73 15 14.3110890505725 0.688910949427485 74 16 14.2206327177259 1.77936728227415 75 17 14.1973332040661 2.80266679593389 76 16 14.7067577240985 1.29324227590146 77 12 13.2905563754892 -1.29055637548915 78 15 14.2134646286771 0.786535371322881 79 15 13.6684089789401 1.33159102105992 80 16 14.24129466214 1.75870533785999 81 16 14.5698065164791 1.43019348352088 82 11 13.7328240763347 -2.73282407633467 83 15 13.6218099516206 1.37819004837941 84 12 14.3075050060481 -2.30750500604815 85 14 13.5278737267963 0.472126273203709 86 15 14.2108270594315 0.789172940568471 87 17 14.5053914190845 2.49460858091547 88 19 14.4050252753968 4.59497472460319 89 15 14.4086093199212 0.591390680078822 90 16 13.5349376632983 2.46506233670171 91 14 14.0729293765333 -0.0729293765333301 92 16 14.1167866820605 1.8832133179395 93 15 14.0603819964467 0.939618003553315 94 15 14.3952196171025 0.604780382897512 95 17 13.4884427885255 3.51155721147447 96 12 14.2537378896799 -2.25373788967992 97 18 14.1006552574495 3.89934474255051 98 13 14.3952196171025 -1.39521961710249 99 14 14.1669697539044 -0.166969753904359 100 14 13.7059405181506 0.294059481849439 101 14 13.658499168099 0.341500831900977 102 12 13.5717310323235 -1.57173103232346 103 14 14.3513623115753 -0.351362311575318 104 12 13.4177019248142 -1.41770192481425 105 15 14.2537378896799 0.746262110320078 106 11 14.5527286165893 -3.55272861658933 107 11 13.913736742028 -2.913736742028 108 15 14.1033969792418 0.89660302075819 109 14 14.3612721224164 -0.361272122416374 110 15 13.6486935098047 1.3513064901953 111 16 14.4247407445322 1.57525925546781 112 12 13.6218099516206 -1.62180995162059 113 14 14.15716409561 -0.157164095610036 114 14 14.15716409561 -0.157164095610036 115 18 14.2814637705961 3.71853622940392 116 14 14.3011792397315 -0.301179239731459 117 13 14.2242167622502 -1.22421676225022 118 14 13.4543911412927 0.545608858707314 119 14 14.4247407445322 -0.42474074453219 120 17 14.180359456723 2.81964054327695 121 12 14.0362401600549 -2.03624016005489 122 16 14.3513623115753 1.64863768842468 123 15 13.5008785571171 1.49912144288288 124 10 13.541263429615 -3.54126342961498 125 13 13.8062025092915 -0.806202509291546 126 15 13.5753150768478 1.42468492315217 127 16 14.147254284769 1.85274571523102 128 15 13.7497978236777 1.25020217632227 129 14 14.2278008067746 -0.227800806774587 130 11 14.1436702402446 -3.14367024024461 131 13 13.3640389609928 -0.364038960992756 132 17 14.2609059787287 2.73909402127134 133 14 14.0765134210577 -0.0765134210576972 134 16 14.2913735814371 1.70862641856286 135 15 13.4168596020822 1.5831403979178 136 12 14.6198854357763 -2.61988543577625 137 16 13.4678849966581 2.53211500334189 138 8 13.5081582576609 -5.50815825766091 139 9 13.5887047796665 -4.58870477966652 140 13 14.3683360589184 -1.36833605891838 141 19 14.147254284769 4.85274571523102 142 11 14.1132026375361 -3.11320263753613 143 15 13.8169546428646 1.18304535713535 144 11 13.6889667708075 -2.6889667708075 145 15 13.7122662844672 1.28773371553275 146 16 13.5645629432747 2.43543705672527 147 15 14.2877895369128 0.712210463087231 148 12 14.4516243027163 -2.4516243027163 149 16 13.7319817536026 2.26801824639737 150 15 13.8805274175272 1.1194725824728 151 13 13.6620832126234 -0.66208321262339 152 14 14.3280627979156 -0.328062797915572 153 11 14.3173106643425 -3.31731066434247 154 15 14.2206327177259 0.779367282274147 155 12 14.2206327177259 -2.22063271772585 156 16 14.458792391765 1.54120760823496 157 14 14.3818299142838 -0.381829914283797 158 13 14.5393389137706 -1.53933891377064 159 15 14.3844674835294 0.615532516470613 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.916517523601469 0.166964952797062 0.0834824763985309 9 0.947372526293377 0.105254947413245 0.0526274737066226 10 0.906062222104135 0.187875555791731 0.0939377778958654 11 0.884606109401722 0.230787781196555 0.115393890598278 12 0.883347980075297 0.233304039849406 0.116652019924703 13 0.836677860798444 0.326644278403112 0.163322139201556 14 0.85693756150765 0.286124876984701 0.143062438492351 15 0.89490763454055 0.210184730918899 0.10509236545945 16 0.863093954267721 0.273812091464559 0.136906045732279 17 0.82586762552428 0.34826474895144 0.17413237447572 18 0.800217885568126 0.399564228863747 0.199782114431874 19 0.834995014443003 0.330009971113995 0.165004985556998 20 0.792486806636305 0.415026386727389 0.207513193363695 21 0.777714137306805 0.444571725386391 0.222285862693195 22 0.719917908880198 0.560164182239603 0.280082091119802 23 0.670032370889255 0.65993525822149 0.329967629110745 24 0.611331729166522 0.777336541666955 0.388668270833478 25 0.544785478162984 0.910429043674032 0.455214521837016 26 0.503321410480371 0.993357179039257 0.496678589519629 27 0.437740585393837 0.875481170787673 0.562259414606163 28 0.391533267929411 0.783066535858822 0.608466732070589 29 0.331184622399546 0.662369244799092 0.668815377600454 30 0.313580239863103 0.627160479726207 0.686419760136897 31 0.323429932146693 0.646859864293387 0.676570067853307 32 0.27035051728106 0.54070103456212 0.72964948271894 33 0.230468590545967 0.460937181091934 0.769531409454033 34 0.322007754801385 0.64401550960277 0.677992245198615 35 0.274025129205287 0.548050258410574 0.725974870794713 36 0.359808797767573 0.719617595535146 0.640191202232427 37 0.382725791807669 0.765451583615339 0.617274208192331 38 0.370136583145373 0.740273166290746 0.629863416854627 39 0.47776340014141 0.95552680028282 0.52223659985859 40 0.429625123233833 0.859250246467666 0.570374876766167 41 0.419256151543545 0.83851230308709 0.580743848456455 42 0.368636316717372 0.737272633434743 0.631363683282628 43 0.325748296610064 0.651496593220129 0.674251703389935 44 0.33198685848625 0.6639737169725 0.66801314151375 45 0.289478072417788 0.578956144835576 0.710521927582212 46 0.323481610925858 0.646963221851716 0.676518389074142 47 0.424545918115704 0.849091836231408 0.575454081884296 48 0.425383058522936 0.850766117045872 0.574616941477064 49 0.421756134302929 0.843512268605859 0.57824386569707 50 0.509425426204262 0.981149147591477 0.490574573795738 51 0.465342307862578 0.930684615725156 0.534657692137422 52 0.419761037623067 0.839522075246134 0.580238962376933 53 0.429913916518165 0.859827833036329 0.570086083481835 54 0.44714670558422 0.89429341116844 0.55285329441578 55 0.425658581965752 0.851317163931503 0.574341418034248 56 0.433957776362046 0.867915552724092 0.566042223637954 57 0.387820064001914 0.775640128003829 0.612179935998086 58 0.408939149126727 0.817878298253454 0.591060850873273 59 0.501511900303274 0.996976199393451 0.498488099696726 60 0.504589789138352 0.990820421723295 0.495410210861648 61 0.463450044664814 0.926900089329629 0.536549955335186 62 0.428588363192715 0.85717672638543 0.571411636807285 63 0.799421445298274 0.401157109403453 0.200578554701726 64 0.830380424672391 0.339239150655218 0.169619575327609 65 0.80808229851113 0.383835402977739 0.19191770148887 66 0.887600543145031 0.224798913709938 0.112399456854969 67 0.86467580047022 0.27064839905956 0.13532419952978 68 0.863729878175724 0.272540243648552 0.136270121824276 69 0.8376304634058 0.3247390731884 0.1623695365942 70 0.936693753796136 0.126612492407728 0.063306246203864 71 0.92102137547445 0.157957249051101 0.0789786245255505 72 0.936372352282055 0.12725529543589 0.063627647717945 73 0.922779750546855 0.154440498906289 0.0772202494531447 74 0.917863483532581 0.164273032934837 0.0821365164674187 75 0.928480306360818 0.143039387278363 0.0715196936391817 76 0.917789390320111 0.164421219359778 0.0822106096798892 77 0.907875650721738 0.184248698556524 0.0921243492782619 78 0.890627115969184 0.218745768061633 0.109372884030816 79 0.878312893407238 0.243374213185524 0.121687106592762 80 0.870480131458969 0.259039737082063 0.129519868541031 81 0.854978485769694 0.290043028460611 0.145021514230306 82 0.868858332848172 0.262283334303656 0.131141667151828 83 0.852419815625732 0.295160368748536 0.147580184374268 84 0.849451805490875 0.301096389018249 0.150548194509125 85 0.82231201524778 0.355375969504439 0.17768798475222 86 0.795007874246348 0.409984251507304 0.204992125753652 87 0.811288686415557 0.377422627168886 0.188711313584443 88 0.898368733751902 0.203262532496197 0.101631266248098 89 0.87776762478371 0.24446475043258 0.12223237521629 90 0.879232842098237 0.241534315803526 0.120767157901763 91 0.853889150319081 0.292221699361837 0.146110849680919 92 0.845359838889697 0.309280322220607 0.154640161110303 93 0.821408113636772 0.357183772726456 0.178591886363228 94 0.791421022875315 0.417157954249369 0.208578977124685 95 0.825677146565666 0.348645706868668 0.174322853434334 96 0.819935091654255 0.36012981669149 0.180064908345745 97 0.867476457762478 0.265047084475043 0.132523542237522 98 0.849142658061848 0.301714683876305 0.150857341938152 99 0.819064092145169 0.361871815709663 0.180935907854831 100 0.787642842778139 0.424714314443723 0.212357157221861 101 0.754873882968361 0.490252234063277 0.245126117031639 102 0.732267766843857 0.535464466312285 0.267732233156143 103 0.690731308927555 0.61853738214489 0.309268691072445 104 0.663906938662599 0.672186122674802 0.336093061337401 105 0.626170906696004 0.747658186607992 0.373829093303996 106 0.677594507198714 0.644810985602572 0.322405492801286 107 0.702871830847811 0.594256338304377 0.297128169152189 108 0.663509025844355 0.67298194831129 0.336490974155645 109 0.617991123574527 0.764017752850945 0.382008876425473 110 0.589116021044608 0.821767957910784 0.410883978955392 111 0.576889895286914 0.846220209426172 0.423110104713086 112 0.543039848363538 0.913920303272923 0.456960151636462 113 0.496101054169217 0.992202108338435 0.503898945830783 114 0.452291978944344 0.904583957888689 0.547708021055656 115 0.560465441414001 0.879069117171999 0.439534558585999 116 0.510079153245433 0.979841693509133 0.489920846754567 117 0.46879670482731 0.93759340965462 0.53120329517269 118 0.431530500634597 0.863061001269193 0.568469499365403 119 0.38169861407142 0.76339722814284 0.61830138592858 120 0.422745488060726 0.845490976121452 0.577254511939274 121 0.405170925519302 0.810341851038604 0.594829074480698 122 0.376569251821813 0.753138503643627 0.623430748178187 123 0.340681348365251 0.681362696730502 0.659318651634749 124 0.388106285661167 0.776212571322333 0.611893714338833 125 0.336460137349904 0.672920274699807 0.663539862650096 126 0.29094044545937 0.581880890918739 0.70905955454063 127 0.2665275499981 0.5330550999962 0.7334724500019 128 0.260730144878905 0.52146028975781 0.739269855121095 129 0.214346600186301 0.428693200372602 0.785653399813699 130 0.253678798959335 0.507357597918669 0.746321201040665 131 0.216672020448312 0.433344040896624 0.783327979551688 132 0.290937562704582 0.581875125409163 0.709062437295418 133 0.239408110844986 0.478816221689972 0.760591889155014 134 0.215117530589269 0.430235061178537 0.784882469410731 135 0.181471441509914 0.362942883019827 0.818528558490086 136 0.165480410388757 0.330960820777514 0.834519589611243 137 0.164937782707484 0.329875565414968 0.835062217292516 138 0.476222437355046 0.952444874710092 0.523777562644954 139 0.859887949042942 0.280224101914115 0.140112050957058 140 0.809836111669372 0.380327776661256 0.190163888330628 141 0.910818177961916 0.178363644076169 0.0891818220380843 142 0.903204872824901 0.193590254350198 0.0967951271750989 143 0.872065869438474 0.255868261123052 0.127934130561526 144 0.954454594383692 0.0910908112326162 0.0455454056163081 145 0.923872916414025 0.152254167171949 0.0761270835859746 146 0.87744831030936 0.245103379381281 0.122551689690641 147 0.827099380666134 0.345801238667731 0.172900619333866 148 0.812638334909077 0.374723330181846 0.187361665090923 149 0.715085480478561 0.569829039042878 0.284914519521439 150 0.586387073309303 0.827225853381395 0.413612926690697 151 0.417021280550932 0.834042561101863 0.582978719449068 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 1 0.00694444444444444 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/1086vr1292234599.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/1086vr1292234599.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/1kngf1292234599.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/1kngf1292234599.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/2kngf1292234599.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/2kngf1292234599.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/3cwx01292234599.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/3cwx01292234599.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/4cwx01292234599.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/4cwx01292234599.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/5cwx01292234599.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/5cwx01292234599.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/6n6f31292234599.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/6n6f31292234599.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/7gfw61292234599.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/7gfw61292234599.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/8gfw61292234599.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/8gfw61292234599.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/9gfw61292234599.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234563mbp4a3sdrr4vokx/9gfw61292234599.ps (open in new window)

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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') }

Copyright

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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