*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: Thu, 02 Dec 2010 15:46:25 +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/02/t12913051796gixpaceyccarc8.htm/, Retrieved Thu, 02 Dec 2010 16:52:59 +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/02/t12913051796gixpaceyccarc8.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 «

4 4 4 4 4 3 5 5 4 2 3 4 2 4 4 4 3 4 4 4 4 4 3 4 4 2 2 2 4 4 3 2 3 4 2 2 3 2 2 4 1 3 4 4 4 4 4 5 4 2 4 2 2 2 4 3 4 4 3 3 4 3 4 3 4 2 2 3 2 4 2 4 2 2 4 3 4 4 4 4 4 3 3 3 4 4 4 4 2 5 4 4 4 4 4 4 4 5 4 4 5 4 4 4 4 5 4 4 4 4 4 2 2 4 4 4 4 4 4 5 5 4 4 4 3 4 2 2 2 4 3 4 4 4 4 4 3 4 2 2 4 5 4 4 4 4 4 4 3 4 4 4 3 4 3 4 4 4 4 3 2 4 5 4 3 4 4 3 4 4 4 4 4 4 4 3 5 2 1 3 4 3 4 4 3 4 4 4 4 4 2 4 3 3 4 4 5 4 2 4 4 4 4 4 4 3 4 4 4 4 4 2 4 4 3 4 4 4 4 3 3 3 4 4 4 4 4 4 4 3 3 4 3 4 4 2 4 4 4 4 4 3 4 2 2 4 3 2 2 5 3 4 3 2 3 3 2 3 4 4 4 4 4 4 4 4 4 4 2 3 4 2 2 3 4 5 4 2 2 4 3 4 4 3 4 5 5 4 4 3 3 4 4 4 2 3 3 3 2 4 3 4 4 3 3 3 4 3 2 4 3 4 2 4 3 3 1 2 3 3 3 4 2 4 4 3 4 2 2 4 3 2 2 4 2 2 4 4 3 5 5 5 3 5 4 3 3 4 4 4 4 3 4 4 3 3 4 2 2 3 4 4 4 3 2 4 4 3 3 5 2 4 4 2 3 3 2 4 3 4 4 3 4 4 3 4 4 4 4 4 4 3 4 3 2 4 2 4 5 3 3 2 2 2 4 4 4 4 4 3 3 4 3 3 4 3 4 4 3 4 4 3 3 5 4 4 3 5 1 4 2 3 4 2 4 4 4 4 5 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Goals[t] = + 0.779741026497208 + 0.311165646709790Competent[t] + 0.349589111529403Focus[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) 0.779741026497208 0.426598 1.8278 0.069488 0.034744 Competent 0.311165646709790 0.089064 3.4937 0.00062 0.00031 Focus 0.349589111529403 0.097539 3.5841 0.000452 0.000226 Multiple Linear Regression - Regression Statistics Multiple R 0.415329063708261 R-squared 0.172498231160780 Adjusted R-squared 0.161889234124380 F-TEST (value) 16.2596172445827 F-TEST (DF numerator) 2 F-TEST (DF denominator) 156 p-value 3.85457589291427e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.883248696608336 Sum Squared Residuals 121.700008569411 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 3.42276005945398 0.577239940546016 2 4 3.07317094792458 0.926829052075423 3 5 3.73392570616377 1.26607429383623 4 3 2.8004287660344 0.199571233965598 5 4 2.8004287660344 1.19957123396560 6 3 3.42276005945398 -0.422760059453981 7 4 3.42276005945398 0.577239940546019 8 3 3.42276005945398 -0.422760059453981 9 2 2.72358183639517 -0.723581836395174 10 4 2.8004287660344 1.19957123396560 11 2 2.76200530121479 -0.762005301214788 12 2 2.72358183639517 -0.723581836395174 13 2 2.41241618968538 -0.412416189685384 14 1 3.07317094792458 -2.07317094792458 15 4 3.42276005945398 0.577239940546019 16 4 3.77234917098338 0.227650829016616 17 2 3.42276005945398 -1.42276005945398 18 2 2.10125054297559 -0.101250542975595 19 3 3.42276005945398 -0.422760059453981 20 3 3.07317094792458 -0.0731709479245774 21 3 3.42276005945398 -0.422760059453981 22 4 2.41241618968538 1.58758381031462 23 3 2.10125054297559 0.898749457024405 24 2 3.42276005945398 -1.42276005945398 25 2 2.8004287660344 -0.800428766034402 26 4 3.11159441274419 0.888405587255809 27 4 3.42276005945398 0.577239940546019 28 3 2.76200530121479 0.237994698785212 29 4 3.42276005945398 0.577239940546019 30 2 3.77234917098338 -1.77234917098338 31 4 3.42276005945398 0.577239940546019 32 4 3.42276005945398 0.577239940546019 33 5 3.42276005945398 1.57723994054602 34 5 3.42276005945398 1.57723994054602 35 4 3.42276005945398 0.577239940546019 36 4 3.73392570616377 0.266074293836230 37 4 3.42276005945398 0.577239940546019 38 2 2.8004287660344 -0.800428766034402 39 4 3.42276005945398 0.577239940546019 40 4 3.77234917098338 0.227650829016616 41 4 3.73392570616377 0.266074293836230 42 3 3.42276005945398 -0.422760059453981 43 2 2.10125054297559 -0.101250542975595 44 3 3.42276005945398 -0.422760059453981 45 4 3.42276005945398 0.577239940546019 46 3 3.42276005945398 -0.422760059453981 47 2 2.8004287660344 -0.800428766034402 48 4 3.73392570616377 0.266074293836230 49 4 3.42276005945398 0.577239940546019 50 3 3.42276005945398 -0.422760059453981 51 4 3.07317094792458 0.926829052075423 52 3 3.42276005945398 -0.422760059453981 53 4 3.42276005945398 0.577239940546019 54 2 3.11159441274419 -1.11159441274419 55 4 3.38433659463437 0.615663405365633 56 4 3.07317094792458 0.926829052075423 57 4 3.42276005945398 0.577239940546019 58 4 3.42276005945398 0.577239940546019 59 3 3.77234917098338 -0.772349170983384 60 1 2.450839654505 -1.45083965450500 61 3 3.42276005945398 -0.422760059453981 62 3 3.42276005945398 -0.422760059453981 63 4 3.42276005945398 0.577239940546019 64 2 3.42276005945398 -1.42276005945398 65 3 3.11159441274419 -0.111594412744191 66 5 3.42276005945398 1.57723994054602 67 4 2.8004287660344 1.19957123396560 68 4 3.42276005945398 0.577239940546019 69 3 3.42276005945398 -0.422760059453981 70 4 3.42276005945398 0.577239940546019 71 2 3.42276005945398 -1.42276005945398 72 3 3.42276005945398 -0.422760059453981 73 4 3.42276005945398 0.577239940546019 74 3 2.76200530121479 0.237994698785212 75 4 3.42276005945398 0.577239940546019 76 4 3.42276005945398 0.577239940546019 77 3 3.07317094792458 -0.0731709479245774 78 3 3.42276005945398 -0.422760059453981 79 2 3.42276005945398 -1.42276005945398 80 4 3.42276005945398 0.577239940546019 81 3 3.42276005945398 -0.422760059453981 82 2 2.8004287660344 -0.800428766034402 83 2 2.41241618968538 -0.412416189685384 84 3 3.73392570616377 -0.73392570616377 85 2 2.76200530121479 -0.762005301214788 86 2 2.76200530121479 -0.762005301214788 87 4 3.42276005945398 0.577239940546019 88 4 3.42276005945398 0.577239940546019 89 4 3.42276005945398 0.577239940546019 90 2 3.07317094792458 -1.07317094792458 91 2 2.72358183639517 -0.723581836395174 92 4 3.46118352427359 0.538816475726405 93 2 2.72358183639517 -0.723581836395174 94 3 3.42276005945398 -0.422760059453981 95 3 3.42276005945398 -0.422760059453981 96 5 3.73392570616377 1.26607429383623 97 3 3.07317094792458 -0.0731709479245774 98 4 3.42276005945398 0.577239940546019 99 3 2.450839654505 0.549160345495002 100 2 3.11159441274419 -1.11159441274419 101 4 3.11159441274419 0.888405587255809 102 3 2.76200530121479 0.237994698785212 103 3 2.72358183639517 0.276418163604826 104 3 3.42276005945398 -0.422760059453981 105 4 2.450839654505 1.54916034549500 106 1 2.41241618968538 -1.41241618968538 107 3 2.76200530121479 0.237994698785212 108 2 3.42276005945398 -1.42276005945398 109 3 3.42276005945398 -0.422760059453981 110 2 2.8004287660344 -0.800428766034402 111 2 2.41241618968538 -0.412416189685384 112 2 2.72358183639517 -0.723581836395174 113 4 3.07317094792458 0.926829052075423 114 5 4.08351481769317 0.916485182306826 115 5 3.11159441274419 1.88840558725581 116 3 3.11159441274419 -0.111594412744191 117 4 3.42276005945398 0.577239940546019 118 4 3.11159441274419 0.888405587255809 119 3 3.11159441274419 -0.111594412744191 120 2 2.450839654505 -0.450839654504998 121 4 3.42276005945398 0.577239940546019 122 2 3.11159441274419 -1.11159441274419 123 3 3.07317094792458 -0.0731709479245774 124 2 3.73392570616377 -1.73392570616377 125 2 3.07317094792458 -1.07317094792458 126 2 3.11159441274419 -1.11159441274419 127 4 3.11159441274419 0.888405587255809 128 4 3.11159441274419 0.888405587255809 129 4 3.11159441274419 0.888405587255809 130 4 3.42276005945398 0.577239940546019 131 3 3.42276005945398 -0.422760059453981 132 2 3.11159441274419 -1.11159441274419 133 4 3.15001787756381 0.849982122436195 134 3 2.41241618968538 0.587583810314615 135 2 2.8004287660344 -0.800428766034402 136 4 3.42276005945398 0.577239940546019 137 3 3.07317094792458 -0.0731709479245774 138 3 3.07317094792458 -0.0731709479245774 139 3 3.42276005945398 -0.422760059453981 140 3 3.42276005945398 -0.422760059453981 141 3 3.07317094792458 -0.0731709479245774 142 4 3.73392570616377 0.266074293836230 143 5 2.06282707815598 2.93717292184402 144 2 3.07317094792458 -1.07317094792458 145 2 3.42276005945398 -1.42276005945398 146 4 3.42276005945398 0.577239940546019 147 3 3.73392570616377 -0.73392570616377 148 3 3.11159441274419 -0.111594412744191 149 1 2.450839654505 -1.45083965450500 150 2 3.42276005945398 -1.42276005945398 151 4 3.11159441274419 0.888405587255809 152 4 3.42276005945398 0.577239940546019 153 5 3.73392570616377 1.26607429383623 154 2 3.11159441274419 -1.11159441274419 155 4 2.76200530121479 1.23799469878521 156 3 3.11159441274419 -0.111594412744191 157 2 3.73392570616377 -1.73392570616377 158 4 3.07317094792458 0.926829052075423 159 2 2.450839654505 -0.450839654504998 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.533245263965052 0.933509472069895 0.466754736034948 7 0.363755488762697 0.727510977525394 0.636244511237303 8 0.389913094711492 0.779826189422985 0.610086905288508 9 0.420582172719254 0.841164345438508 0.579417827280746 10 0.363681591069359 0.727363182138718 0.636318408930641 11 0.365976445373396 0.731952890746793 0.634023554626604 12 0.274114796381210 0.548229592762419 0.72588520361879 13 0.198514922752275 0.39702984550455 0.801485077247725 14 0.559993767427224 0.880012465145553 0.440006232572776 15 0.478709899801838 0.957419799603676 0.521290100198162 16 0.441255472858144 0.882510945716287 0.558744527141856 17 0.623701242088012 0.752597515823975 0.376298757911988 18 0.551317214765645 0.89736557046871 0.448682785234355 19 0.498574553344609 0.997149106689217 0.501425446655391 20 0.430602516972278 0.861205033944556 0.569397483027722 21 0.38015603256649 0.76031206513298 0.61984396743351 22 0.620758262873202 0.758483474253595 0.379241737126798 23 0.594664702375878 0.810670595248244 0.405335297624122 24 0.678773943964789 0.642452112070422 0.321226056035211 25 0.72705497037553 0.545890059248939 0.272945029624470 26 0.711058499176094 0.577883001647811 0.288941500823906 27 0.683171142580037 0.633657714839926 0.316828857419963 28 0.628038808823095 0.743922382353811 0.371961191176905 29 0.595849544856278 0.808300910287443 0.404150455143722 30 0.746269699170776 0.507460601658449 0.253730300829224 31 0.724566296341397 0.550867407317205 0.275433703658602 32 0.700173030470299 0.599653939059402 0.299826969529701 33 0.795393595643087 0.409212808713826 0.204606404356913 34 0.861153340008717 0.277693319982567 0.138846659991283 35 0.839422920856284 0.321154158287433 0.160577079143716 36 0.808110534863433 0.383778930273134 0.191889465136567 37 0.781117005599828 0.437765988800343 0.218882994400172 38 0.79272012247659 0.414559755046819 0.207279877523410 39 0.765097695255646 0.469804609488707 0.234902304744354 40 0.723523124487196 0.552953751025608 0.276476875512804 41 0.680493135136087 0.639013729727826 0.319506864863913 42 0.647655489830839 0.704689020338323 0.352344510169161 43 0.600043521291715 0.79991295741657 0.399956478708285 44 0.564789537571884 0.870420924856232 0.435210462428116 45 0.530487877251317 0.939024245497367 0.469512122748683 46 0.494902754705875 0.98980550941175 0.505097245294125 47 0.496175530262561 0.992351060525123 0.503824469737439 48 0.44874827810471 0.89749655620942 0.55125172189529 49 0.416162815986054 0.832325631972108 0.583837184013946 50 0.382254656700059 0.764509313400118 0.617745343299941 51 0.381473235810449 0.762946471620898 0.618526764189551 52 0.348839650944909 0.697679301889817 0.651160349055091 53 0.319724103545208 0.639448207090416 0.680275896454792 54 0.350856161495724 0.701712322991448 0.649143838504276 55 0.322839883121668 0.645679766243335 0.677160116878332 56 0.320428092688069 0.640856185376138 0.679571907311931 57 0.293142774034693 0.586285548069386 0.706857225965307 58 0.267053460283087 0.534106920566174 0.732946539716913 59 0.260018499166879 0.520036998333758 0.739981500833121 60 0.329211753133865 0.65842350626773 0.670788246866135 61 0.298890089017116 0.597780178034232 0.701109910982884 62 0.269686604547095 0.539373209094191 0.730313395452905 63 0.246320468876871 0.492640937753742 0.753679531123129 64 0.31402851916914 0.62805703833828 0.68597148083086 65 0.273956219420506 0.547912438841013 0.726043780579494 66 0.361336739059263 0.722673478118527 0.638663260940737 67 0.403862819335745 0.80772563867149 0.596137180664255 68 0.376871053625068 0.753742107250136 0.623128946374932 69 0.344904093823828 0.689808187647657 0.655095906176172 70 0.319750238739884 0.639500477479768 0.680249761260116 71 0.390562976227728 0.781125952455456 0.609437023772272 72 0.357511656259212 0.715023312518424 0.642488343740788 73 0.332544470334542 0.665088940669083 0.667455529665458 74 0.294183449344645 0.588366898689289 0.705816550655355 75 0.271502072605077 0.543004145210154 0.728497927394923 76 0.249942583263690 0.499885166527381 0.75005741673631 77 0.215936768664078 0.431873537328156 0.784063231335922 78 0.191352584019882 0.382705168039763 0.808647415980118 79 0.244664270769777 0.489328541539554 0.755335729230223 80 0.224578754354561 0.449157508709122 0.775421245645439 81 0.198944153743347 0.397888307486695 0.801055846256653 82 0.192006160068654 0.384012320137308 0.807993839931346 83 0.169388793729367 0.338777587458734 0.830611206270633 84 0.160744095864771 0.321488191729542 0.83925590413523 85 0.153527309769326 0.307054619538652 0.846472690230674 86 0.146427245621548 0.292854491243097 0.853572754378452 87 0.132074896442926 0.264149792885852 0.867925103557074 88 0.118864034090909 0.237728068181818 0.881135965909091 89 0.106770623224356 0.213541246448712 0.893229376775644 90 0.116138239931758 0.232276479863516 0.883861760068242 91 0.108511878610056 0.217023757220112 0.891488121389944 92 0.0961079864363127 0.192215972872625 0.903892013563687 93 0.090043724809887 0.180087449619774 0.909956275190113 94 0.0759365907560238 0.151873181512048 0.924063409243976 95 0.0635476950480537 0.127095390096107 0.936452304951946 96 0.082369958074607 0.164739916149214 0.917630041925393 97 0.0660946442958712 0.132189288591742 0.933905355704129 98 0.0588479345876013 0.117695869175203 0.941152065412399 99 0.0504415849781907 0.100883169956381 0.94955841502181 100 0.0564888224377834 0.112977644875567 0.943511177562217 101 0.0566415966531821 0.113283193306364 0.943358403346818 102 0.045132381085195 0.09026476217039 0.954867618914805 103 0.0357540663634678 0.0715081327269356 0.964245933636532 104 0.0287302740093296 0.0574605480186592 0.97126972599067 105 0.0457147217483587 0.0914294434967173 0.954285278251641 106 0.0686733056361501 0.137346611272300 0.93132669436385 107 0.054808023275214 0.109616046550428 0.945191976724786 108 0.0739744759788347 0.147948951957669 0.926025524021165 109 0.0608953794818833 0.121790758963767 0.939104620518117 110 0.0576456857161987 0.115291371432397 0.942354314283801 111 0.0498836501971016 0.0997673003942033 0.950116349802898 112 0.0503158299698922 0.100631659939784 0.949684170030108 113 0.0485583414142632 0.0971166828285264 0.951441658585737 114 0.059783831046211 0.119567662092422 0.940216168953789 115 0.135126736112980 0.270253472225960 0.86487326388702 116 0.109565275899073 0.219130551798147 0.890434724100927 117 0.101476455203096 0.202952910406193 0.898523544796904 118 0.106578463672739 0.213156927345478 0.893421536327261 119 0.0849083132423092 0.169816626484618 0.91509168675769 120 0.075830596827642 0.151661193655284 0.924169403172358 121 0.0711219989256703 0.142243997851341 0.92887800107433 122 0.0751974048451955 0.150394809690391 0.924802595154804 123 0.0583837182448364 0.116767436489673 0.941616281755164 124 0.0902508753016812 0.180501750603362 0.909749124698319 125 0.109225373230169 0.218450746460339 0.89077462676983 126 0.116434650689590 0.232869301379180 0.88356534931041 127 0.119802333600313 0.239604667200625 0.880197666399688 128 0.126416629372403 0.252833258744807 0.873583370627597 129 0.137642131018848 0.275284262037696 0.862357868981152 130 0.129610279321915 0.259220558643831 0.870389720678085 131 0.102635634030899 0.205271268061798 0.8973643659691 132 0.102202563084311 0.204405126168621 0.89779743691569 133 0.195283457056407 0.390566914112814 0.804716542943593 134 0.165388327022466 0.330776654044933 0.834611672977534 135 0.134397175190177 0.268794350380354 0.865602824809823 136 0.134180380537611 0.268360761075222 0.865819619462389 137 0.108176234375973 0.216352468751947 0.891823765624027 138 0.086764702387018 0.173529404774036 0.913235297612982 139 0.0635513339569539 0.127102667913908 0.936448666043046 140 0.0451788639267899 0.0903577278535798 0.95482113607321 141 0.0345429134935076 0.0690858269870151 0.965457086506492 142 0.0246996192495771 0.0493992384991543 0.975300380750423 143 0.0629707119110075 0.125941423822015 0.937029288088992 144 0.071610173929175 0.14322034785835 0.928389826070825 145 0.0871850694358728 0.174370138871746 0.912814930564127 146 0.0739237926483194 0.147847585296639 0.92607620735168 147 0.0613148266714124 0.122629653342825 0.938685173328588 148 0.0400756033733885 0.080151206746777 0.959924396626611 149 0.0717684055801868 0.143536811160374 0.928231594419813 150 0.0969692637475261 0.193938527495052 0.903030736252474 151 0.119684859093457 0.239369718186915 0.880315140906543 152 0.101329759646790 0.202659519293581 0.89867024035321 153 0.281315064171938 0.562630128343875 0.718684935828062 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 1 0.00675675675675676 OK 10% type I error level 10 0.0675675675675676 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/104olr1291304774.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/104olr1291304774.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/1fn6g1291304774.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/1fn6g1291304774.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/2fn6g1291304774.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/2fn6g1291304774.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/38w5i1291304774.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/38w5i1291304774.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/48w5i1291304774.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/48w5i1291304774.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/58w5i1291304774.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/58w5i1291304774.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/60o531291304774.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/60o531291304774.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/7bxm61291304774.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/7bxm61291304774.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/8bxm61291304774.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/8bxm61291304774.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/9bxm61291304774.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t12913051796gixpaceyccarc8/9bxm61291304774.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') }

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Software written by Ed van Stee & Patrick Wessa

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