*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 10:06:33 +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/t1292234735rinfzma1iw08ihn.htm/, Retrieved Mon, 13 Dec 2010 11:06:03 +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/t1292234735rinfzma1iw08ihn.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 24 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Popularity[t] = + 1.70905089015761 -0.520810039433372Gender[t] + 0.0376773966790884Happiness[t] + 0.426493049447179Liked[t] + 0.93554501323377Celebrity[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) 1.70905089015761 1.699409 1.0057 0.31615 0.158075 Gender -0.520810039433372 0.370385 -1.4061 0.1617 0.08085 Happiness 0.0376773966790884 0.077883 0.4838 0.629236 0.314618 Liked 0.426493049447179 0.097686 4.3659 2.3e-05 1.2e-05 Celebrity 0.93554501323377 0.148498 6.3 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.678310490940214 R-squared 0.460105122119554 Adjusted R-squared 0.446081878538244 F-TEST (value) 32.8101782909031 F-TEST (DF numerator) 4 F-TEST (DF denominator) 154 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.22173210448981 Sum Squared Residuals 760.15840579459 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15 12.9110815231266 2.08891847687345 2 12 9.44013097825671 2.55986902174329 3 15 12.7037323431031 2.29626765689694 4 12 11.0282334210122 0.971766578987806 5 14 11.1035882143704 2.89641178562964 6 8 7.49605271441626 0.503947285583741 7 11 10.4699929814767 0.530007018523322 8 15 9.13842819449359 5.86157180550641 9 4 7.21790269570018 -3.21790269570017 10 13 10.9528786276540 2.04712137234598 11 19 13.8017450187000 5.19825498130003 12 10 12.9487589198056 -2.94875891980561 13 15 16.9146367968300 -1.91463679682995 14 6 11.3488984014033 -5.34889840140334 15 7 9.71563083065712 -2.71563083065712 16 14 12.2772392936559 1.72276070634412 17 16 12.8167645331403 3.18323546685968 18 16 15.0507508913436 0.949249108656351 19 14 16.1746828879729 -2.17468288797286 20 15 13.5943958386765 1.40560416132349 21 14 14.7749674286128 -0.774967428612823 22 12 11.0023140999799 0.99768590002011 23 9 8.31136141663153 0.688638583368469 24 12 9.52003972628044 2.47996027371956 25 14 13.7640676220209 0.235932377979124 26 12 12.8357267297683 -0.83572672976834 27 14 14.1905606714681 -0.190560671468056 28 10 12.8357267297683 -2.83572672976834 29 14 12.4469110770002 1.55308892299975 30 16 14.6242578418965 1.37574215810353 31 10 10.2246827944437 -0.224682794443708 32 8 10.4932621361933 -2.4932621361933 33 8 9.89709730340175 -1.89709730340175 34 12 12.08856869993 -0.088568699930013 35 11 12.9110815231265 -1.91108152312652 36 8 9.8666240277039 -1.86662402770390 37 13 12.8544419298194 0.145558070180587 38 11 10.1421238801043 0.857876119895703 39 12 9.23249818790283 2.76750181209717 40 16 12.7414097397821 3.25859026021785 41 16 13.8394224153791 2.16057758462095 42 13 14.1905606714681 -1.19056067146806 43 14 15.5974802518093 -1.59748025180933 44 5 5.04776005178519 -0.047760051785188 45 14 13.1679027892293 0.832097210770673 46 13 8.75681666270673 4.24318333729327 47 16 14.9753960979855 1.02460390201453 48 15 12.8544419298194 2.14555807018059 49 15 12.8544419298194 2.14555807018059 50 15 14.0398510847517 0.960148915248298 51 11 12.4020295593399 -1.40202955933993 52 15 12.9110815231265 2.08891847687348 53 16 13.2245423825364 2.77545761746357 54 13 12.4773843526981 0.522615647301896 55 11 11.9637784342460 -0.963778434245965 56 12 13.363493893606 -1.36349389360600 57 12 12.7908452121080 -0.790845212108018 58 10 13.8394224153791 -3.83942241537905 59 8 12.7226945397311 -4.72269453973108 60 9 9.08899272216771 -0.088992722167713 61 12 11.9755365098927 0.0244634901072524 62 14 12.8167645331403 1.18323546685968 63 12 12.6096623496938 -0.60966234969381 64 11 10.5945362505838 0.405463749416217 65 14 14.4850593342500 -0.485059334249955 66 7 10.2057205978157 -3.20572059781569 67 16 13.714632149695 2.28536785030499 68 16 15.9486185078983 0.0513814921016704 69 11 12.3525940870141 -1.35259408701406 70 16 13.9644962913935 2.03550370860647 71 13 13.7263902253418 -0.726390225341788 72 11 12.2513199726236 -1.25131997262357 73 11 12.4020295593399 -1.40202955933993 74 13 12.9487589198056 0.0512410801943945 75 14 12.5599432670375 1.44005673296249 76 15 12.3571480416796 2.64285195832039 77 10 9.6357220826334 0.364277917366609 78 15 15.6351576484884 -0.635157648488416 79 11 13.6697506320347 -2.66975063203468 80 6 8.35359276797617 -2.35359276797617 81 11 9.20657886687053 1.79342113312947 82 12 10.3684718705093 1.63152812949075 83 13 12.8167645331403 0.183235466859676 84 12 13.6510354319836 -1.65103543198361 85 8 11.8435421232275 -3.84354212322747 86 9 10.6134984472118 -1.6134984472118 87 10 12.3948254383587 -2.39482543835869 88 16 13.4882841592900 2.51171584070995 89 15 11.9755365098927 3.02446349010725 90 14 12.0014558309251 1.99854416907495 91 12 13.8089491396812 -1.80894913968120 92 12 12.5222658703584 -0.522265870358426 93 10 9.33401929887026 0.66598070112974 94 12 11.0399914966590 0.960008503341022 95 8 8.37951208900848 -0.379512089008474 96 16 15.5221254584511 0.47787454154885 97 11 9.44705148890752 1.55294851109248 98 12 10.9646367033008 1.0353632966992 99 9 11.9378591132137 -2.93785911321366 100 14 11.4170490737803 2.58295092621971 101 15 14.1411251991422 0.858874800857815 102 8 10.4061492671883 -2.40614926718834 103 12 12.3643521626608 -0.364352162660839 104 10 10.4887081815278 -0.488708181527751 105 16 15.6351576484884 0.364842351511585 106 17 12.2513199726236 4.74868002737642 107 8 9.35036794293607 -1.35036794293607 108 9 11.5490434604456 -2.54904346044557 109 8 11.8553001988742 -3.85530019887425 110 11 11.8812195199066 -0.881219519906555 111 16 15.1637830813809 0.836216918619086 112 13 12.7037323431031 0.296267656896941 113 5 9.64027603729894 -4.64027603729894 114 5 9.64027603729894 -4.64027603729894 115 15 11.2355826010357 3.76441739896435 116 15 12.8734041264474 2.12659587355257 117 12 11.4736886670874 0.526311332912609 118 12 11.9261010375669 0.0738989624331232 119 16 15.0884282880227 0.911571711977263 120 12 12.9864363164847 -0.986436316484694 121 10 12.3715562836421 -2.37155628364207 122 12 12.4397069560190 -0.439706956019016 123 4 7.20155405163436 -3.20155405163436 124 11 12.6283775497449 -1.62837754974488 125 16 13.1679027892293 2.83209721077067 126 7 9.15714339454466 -2.15714339454466 127 9 10.2246827944437 -1.22468279444371 128 14 10.0926884077784 3.90731159222157 129 11 10.1493280010855 0.85067199891447 130 10 11.3983338737292 -1.39833387372921 131 6 9.59084056497307 -3.59084056497307 132 14 12.9864363164847 1.01356368351531 133 11 12.4469110770002 -1.44691107700025 134 11 10.6511758438909 0.348824156109113 135 9 14.1788025958213 -5.17880259582127 136 16 11.3534523560689 4.64654764393111 137 7 10.1303658044575 -3.13036580445751 138 8 9.8289466310248 -1.82894663102481 139 10 9.8666240277039 0.133375972296104 140 14 11.9001817165346 2.09981828346543 141 9 10.3377149844810 -1.33771498448097 142 13 13.6959169496439 -0.695916949643932 143 13 9.15714339454466 3.84285660545534 144 12 11.7305099331902 0.269490066809799 145 11 12.3077125693537 -1.30771256935374 146 10 13.2809349792666 -3.28093497926659 147 12 11.9755365098927 0.0244634901072524 148 14 14.0775284814308 -0.0775284814307909 149 11 14.1339210781610 -3.13392107816095 150 13 9.58363644399184 3.41636355600816 151 14 12.7414097397821 1.25859026021785 152 13 11.9378591132137 1.06214088678634 153 16 15.9109411112192 0.0890588887807586 154 13 12.9110815231265 0.0889184768734832 155 13 12.7980493330893 0.201950666910748 156 12 11.5041619427852 0.495838057214754 157 9 10.0667690867461 -1.06676908674612 158 14 11.3911297527480 2.60887024725202 159 15 15.1261056847018 -0.126105684701826 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.117022957898373 0.234045915796746 0.882977042101627 9 0.875366583629224 0.249266832741552 0.124633416370776 10 0.802551585273372 0.394896829453257 0.197448414726628 11 0.734949577844629 0.530100844310742 0.265050422155371 12 0.968578613028364 0.0628427739432728 0.0314213869716364 13 0.98403103272071 0.0319379345585824 0.0159689672792912 14 0.99417027796259 0.0116594440748220 0.00582972203741101 15 0.999062426282993 0.00187514743401420 0.000937573717007098 16 0.99853068465497 0.00293863069005988 0.00146931534502994 17 0.998339730237715 0.00332053952457045 0.00166026976228523 18 0.997074946244829 0.00585010751034249 0.00292505375517124 19 0.997104559857467 0.00579088028506654 0.00289544014253327 20 0.995284404932728 0.00943119013454411 0.00471559506727206 21 0.99281570916122 0.0143685816775592 0.00718429083877958 22 0.98883095930083 0.0223380813983411 0.0111690406991705 23 0.983205700327352 0.0335885993452967 0.0167942996726483 24 0.977424849491003 0.0451503010179941 0.0225751505089970 25 0.96746811863414 0.0650637627317203 0.0325318813658601 26 0.95576316783957 0.0884736643208616 0.0442368321604308 27 0.941320574005848 0.117358851988303 0.0586794259941517 28 0.945249370793865 0.109501258412269 0.0547506292061347 29 0.939046536322016 0.121906927355968 0.060953463677984 30 0.92698408508488 0.146031829830242 0.073015914915121 31 0.905729281849082 0.188541436301836 0.0942707181509178 32 0.930295372965562 0.139409254068875 0.0697046270344377 33 0.937805397924414 0.124389204151172 0.0621946020755861 34 0.918691650731514 0.162616698536972 0.081308349268486 35 0.911488671307599 0.177022657384802 0.088511328692401 36 0.90773899285847 0.184522014283062 0.0922610071415309 37 0.883469923515087 0.233060152969826 0.116530076484913 38 0.856375240960171 0.287249518079658 0.143624759039829 39 0.851335171620405 0.297329656759191 0.148664828379595 40 0.868670213505928 0.262659572988144 0.131329786494072 41 0.858789211223208 0.282421577553585 0.141210788776792 42 0.839056042324372 0.321887915351255 0.160943957675628 43 0.81838956786289 0.363220864274221 0.181610432137111 44 0.782317908081396 0.435364183837208 0.217682091918604 45 0.744808915077059 0.510382169845882 0.255191084922941 46 0.844764155966944 0.310471688066113 0.155235844033056 47 0.820776518847311 0.358446962305378 0.179223481152689 48 0.807364719695337 0.385270560609326 0.192635280304663 49 0.793319725094214 0.413360549811572 0.206680274905786 50 0.7626882569182 0.474623486163599 0.237311743081800 51 0.743655959445945 0.512688081108109 0.256344040554055 52 0.733682640081382 0.532634719837236 0.266317359918618 53 0.75174017257826 0.496519654843479 0.248259827421739 54 0.712382546095195 0.575234907809609 0.287617453904805 55 0.686651430100419 0.626697139799163 0.313348569899581 56 0.666233751375146 0.667532497249708 0.333766248624854 57 0.631056372599224 0.737887254801551 0.368943627400776 58 0.724615423157843 0.550769153684315 0.275384576842157 59 0.838655591402943 0.322688817194113 0.161344408597057 60 0.81000860078246 0.37998279843508 0.18999139921754 61 0.77600339851182 0.447993202976359 0.223996601488180 62 0.747617946993527 0.504764106012945 0.252382053006473 63 0.709716575109862 0.580566849780276 0.290283424890138 64 0.673163237289821 0.653673525420358 0.326836762710179 65 0.635024654597792 0.729950690804416 0.364975345402208 66 0.695239939247145 0.60952012150571 0.304760060752855 67 0.696311079300799 0.607377841398403 0.303688920699201 68 0.654113201425619 0.691773597148762 0.345886798574381 69 0.628325508472785 0.743348983054429 0.371674491527214 70 0.618048880023651 0.763902239952697 0.381951119976349 71 0.578137140176232 0.843725719647537 0.421862859823768 72 0.547577107396785 0.90484578520643 0.452422892603215 73 0.520491409120933 0.959017181758134 0.479508590879067 74 0.473927790411028 0.947855580822055 0.526072209588972 75 0.447415693071004 0.894831386142009 0.552584306928996 76 0.458441692224173 0.916883384448346 0.541558307775827 77 0.416014915873465 0.83202983174693 0.583985084126535 78 0.374292380859551 0.748584761719102 0.625707619140449 79 0.396706954186317 0.793413908372633 0.603293045813683 80 0.405014205360689 0.810028410721378 0.594985794639311 81 0.386009849411029 0.772019698822058 0.613990150588971 82 0.367776307524758 0.735552615049516 0.632223692475242 83 0.325972129870440 0.651944259740881 0.67402787012956 84 0.307705024709621 0.615410049419242 0.692294975290379 85 0.389537865200776 0.779075730401552 0.610462134799224 86 0.367984576987833 0.735969153975667 0.632015423012167 87 0.381145271822431 0.762290543644862 0.618854728177569 88 0.386824936398778 0.773649872797557 0.613175063601222 89 0.421446176483536 0.842892352967073 0.578553823516464 90 0.420074183145019 0.840148366290039 0.57992581685498 91 0.402563266601944 0.805126533203887 0.597436733398056 92 0.359871696975684 0.719743393951368 0.640128303024316 93 0.323280474406548 0.646560948813095 0.676719525593452 94 0.28891493009873 0.57782986019746 0.71108506990127 95 0.253656707305723 0.507313414611446 0.746343292694277 96 0.218510624712279 0.437021249424558 0.78148937528772 97 0.208844183137506 0.417688366275013 0.791155816862494 98 0.182765456296621 0.365530912593243 0.817234543703379 99 0.204346503768907 0.408693007537814 0.795653496231093 100 0.225566710237538 0.451133420475076 0.774433289762462 101 0.199167906032606 0.398335812065212 0.800832093967394 102 0.198020401087853 0.396040802175706 0.801979598912147 103 0.167137896918016 0.334275793836033 0.832862103081984 104 0.140371081071323 0.280742162142646 0.859628918928677 105 0.115582205368704 0.231164410737407 0.884417794631296 106 0.209591281930237 0.419182563860475 0.790408718069763 107 0.187814953103796 0.375629906207593 0.812185046896204 108 0.191263475835972 0.382526951671944 0.808736524164028 109 0.284031868428463 0.568063736856926 0.715968131571537 110 0.246470342853927 0.492940685707855 0.753529657146073 111 0.211889819730184 0.423779639460369 0.788110180269815 112 0.180780518813185 0.36156103762637 0.819219481186815 113 0.342790929841416 0.685581859682831 0.657209070158584 114 0.609279198907792 0.781441602184415 0.390720801092208 115 0.751779282318004 0.496441435363992 0.248220717681996 116 0.766588350435933 0.466823299128134 0.233411649564067 117 0.72520975837673 0.549580483246539 0.274790241623270 118 0.72795971074073 0.544080578518541 0.272040289259271 119 0.691855951710108 0.616288096579784 0.308144048289892 120 0.645133594206722 0.709732811586557 0.354866405793278 121 0.630936070767471 0.738127858465057 0.369063929232529 122 0.583614054114862 0.832771891770275 0.416385945885138 123 0.55692229139687 0.88615541720626 0.44307770860313 124 0.512723574855681 0.974552850288638 0.487276425144319 125 0.624890680187594 0.750218639624812 0.375109319812406 126 0.631786475527553 0.736427048944894 0.368213524472447 127 0.604508421057932 0.790983157884137 0.395491578942068 128 0.80804921762646 0.383901564747079 0.191950782373540 129 0.763576541013386 0.472846917973227 0.236423458986614 130 0.761443254183278 0.477113491633445 0.238556745816722 131 0.805153809288102 0.389692381423796 0.194846190711898 132 0.808165453549723 0.383669092900554 0.191834546450277 133 0.764737477192736 0.470525045614527 0.235262522807264 134 0.70999673880831 0.58000652238338 0.29000326119169 135 0.759956160363853 0.480087679272294 0.240043839636147 136 0.819343116746409 0.361313766507182 0.180656883253591 137 0.862167460937796 0.275665078124408 0.137832539062204 138 0.928283007140865 0.143433985718270 0.0717169928591349 139 0.953727572548835 0.0925448549023303 0.0462724274511651 140 0.938301300443195 0.123397399113610 0.0616986995568051 141 0.921551108157321 0.156897783685358 0.0784488918426788 142 0.909246049310076 0.181507901379847 0.0907539506899236 143 0.927534833496354 0.144930333007292 0.0724651665036461 144 0.903614532554572 0.192770934890857 0.0963854674454284 145 0.860348007396059 0.279303985207882 0.139651992603941 146 0.890826746733686 0.218346506532627 0.109173253266314 147 0.827137103277276 0.345725793445449 0.172862896722724 148 0.732200605162746 0.535598789674508 0.267799394837254 149 0.88396256534339 0.232074869313221 0.116037434656610 150 0.838449023503258 0.323101952993484 0.161550976496742 151 0.697398140280238 0.605203719439523 0.302601859719762 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.0416666666666667 NOK 5% type I error level 12 0.0833333333333333 NOK 10% type I error level 16 0.111111111111111 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/10h4991292234768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/10h4991292234768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/1slvx1292234768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/1slvx1292234768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/22uci1292234768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/22uci1292234768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/32uci1292234768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/32uci1292234768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/42uci1292234768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/42uci1292234768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/5dlt31292234768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/5dlt31292234768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/6dlt31292234768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/6dlt31292234768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/7ova61292234768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/7ova61292234768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/8ova61292234768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/8ova61292234768.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/9h4991292234768.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292234735rinfzma1iw08ihn/9h4991292234768.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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Software written by Ed van Stee & Patrick Wessa

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