*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 20:51:13 +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/t1292273377k2wegxp4f2bfl3x.htm/, Retrieved Mon, 13 Dec 2010 21:49:37 +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/t1292273377k2wegxp4f2bfl3x.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 «

0 13 13 14 13 3 0 12 12 8 13 5 1 15 10 12 16 6 1 12 9 7 12 6 1 10 10 10 11 5 1 12 12 7 12 3 0 15 13 16 18 8 1 9 12 11 11 4 0 12 12 14 14 4 0 11 6 6 9 4 1 11 5 16 14 6 0 11 12 11 12 6 0 15 11 16 11 5 1 7 14 12 12 4 0 11 14 7 13 6 1 11 12 13 11 4 1 10 12 11 12 6 0 14 11 15 16 6 0 10 11 7 9 4 0 6 7 9 11 4 0 11 9 7 13 2 0 15 11 14 15 7 0 11 11 15 10 5 0 12 12 7 11 4 1 14 12 15 13 6 1 15 11 17 16 6 0 9 11 15 15 7 1 13 8 14 14 5 1 13 9 14 14 6 1 16 12 8 14 4 1 13 10 8 8 4 0 12 10 14 13 7 1 14 12 14 15 7 1 11 8 8 13 4 0 9 12 11 11 4 0 16 11 16 15 6 1 12 12 10 15 6 0 10 7 8 9 5 1 13 11 14 13 6 1 16 11 16 16 7 1 14 12 13 13 6 1 15 9 5 11 3 1 5 15 8 12 3 0 8 11 10 12 4 0 11 11 8 12 6 1 16 11 13 14 7 1 17 11 15 14 5 1 9 15 6 8 4 1 9 11 12 13 5 1 13 12 16 16 6 1 10 12 5 13 6 0 6 9 15 11 6 1 12 12 12 14 5 1 8 12 8 13 4 1 14 13 13 13 5 1 12 11 14 13 5 0 11 9 12 12 4 0 16 9 16 16 6 1 8 11 10 15 2 0 15 11 15 15 8 1 7 12 8 12 3 0 16 12 16 14 6 1 14 9 19 12 6 1 16 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Liked[t] = + 9.25946256471586 -0.235508153221877Gender[t] + 0.202661168726369Popularity[t] -0.0127348359586671FindingFriends[t] + 0.0418507240312587KnowingPeople[t] + 0.228874092442771Celebrity[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) 9.25946256471586 1.093644 8.4666 0 0 Gender -0.235508153221877 0.067227 -3.5032 0.000606 0.000303 Popularity 0.202661168726369 0.064358 3.149 0.001978 0.000989 FindingFriends -0.0127348359586671 0.065811 -0.1935 0.846825 0.423413 KnowingPeople 0.0418507240312587 0.062222 0.6726 0.502236 0.251118 Celebrity 0.228874092442771 0.10593 2.1606 0.032313 0.016157 Multiple Linear Regression - Regression Statistics Multiple R 0.452533389584601 R-squared 0.204786468688928 Adjusted R-squared 0.178279350978559 F-TEST (value) 7.72571619919355 F-TEST (DF numerator) 5 F-TEST (DF denominator) 150 p-value 1.72100968731659e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.42245083732669 Sum Squared Residuals 880.240208889717 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 13.0010373044619 -0.00103730446192066 2 13 13.0177548123922 -0.0177548123921965 3 16 13.8119768258346 2.18802317416544 4 12 13.0074745354578 -1.00747453545783 5 11 12.4860954416974 -1.48609544169744 6 12 12.2826477502535 -0.282647750253518 7 18 14.6344315521910 3.36556844780898 8 11 12.0709412326422 -1.07094123264222 9 14 13.0399850641370 0.960014935863021 10 9 12.5789271189125 -3.57892711891254 11 14 13.2324092268475 0.767590773152538 12 12 13.1695199082024 -1.16951990820238 13 11 13.9732789467800 -2.97327894678004 14 12 11.6819999473034 0.318000052696592 15 13 12.97664734016 0.0233526598399927 16 11 12.5599650181575 -1.55996501815747 17 12 12.7313505862541 -0.731350586254131 18 16 13.9576411464652 2.04235885353482 19 9 12.3544424944241 -3.3544424944241 20 11 11.6784386114158 -0.67843861141581 21 13 12.1248251501823 0.875174849817743 22 15 14.3473256836031 0.652674316396935 23 10 13.1207835478433 -3.12078354784331 24 11 12.7470299959182 -1.74702999591817 25 13 13.7093981572846 -0.70939815728464 26 16 14.0084956100322 1.99150438996781 27 15 13.1732093952761 1.82679060472389 28 14 13.2869515159189 0.713048484081091 29 14 13.503090772403 0.496909227596987 30 14 13.3640172416330 0.635982758366977 31 8 12.7815034073713 -4.78150340737125 32 13 13.7520770133826 -0.752077013382626 33 15 13.8964215256962 1.10357847430385 34 13 12.4016507418358 0.598349258164151 35 11 12.3064493858641 -1.30644938586410 36 15 14.4048142079492 0.59518579205082 37 15 13.0948221996756 1.90517780032439 38 9 12.6761066547328 -3.67610665473280 39 13 13.4776211004857 -0.477621100485679 40 16 14.3981801471701 1.60181985282993 41 13 13.6256967092221 -0.625696709222122 42 11 12.8451343162461 -1.84513431624611 43 12 10.8676657853242 1.13233421467580 44 12 12.0746723290651 -0.0746723290651366 45 12 13.0567025720673 -1.05670257206727 46 14 14.2726279750763 -0.272627975076297 47 14 14.1012424069796 -0.101242406979641 48 8 11.8234831046099 -3.82348310460993 49 13 12.3544008850749 0.645599114925083 50 16 13.5485877125895 2.45141228741047 51 13 12.4802462420666 0.519753757933421 52 11 12.3618214685716 -1.36182146857157 53 14 12.9496495552954 1.05035044470465 54 13 11.7427278918221 1.25727210817793 55 13 13.3840877808207 -0.384087780820684 56 13 13.0460858393165 -0.0460858393165396 57 12 12.7918269552241 -0.791826955224094 58 16 14.4302838798665 1.56971612013349 59 15 11.3814159909577 3.61858400904228 60 15 14.6180505000771 0.381949499922905 61 12 11.3111926306529 0.688807369347064 62 14 14.3920793719905 -0.392079371990512 63 12 13.9150055612857 -1.91500556128568 64 15 14.0856046066648 0.914395393335215 65 12 12.1287662128047 -0.128766212804698 66 13 13.6323307700012 -0.632330770001228 67 12 13.1014146511055 -1.10141465110553 68 12 12.9430571038654 -0.94305710386543 69 13 13.8283578779485 -0.82835787794849 70 5 10.7196317859369 -5.71963178593693 71 13 13.6540693454956 -0.654069345495645 72 13 13.4296696012749 -0.429669601274859 73 14 12.9533806517183 1.04661934828173 74 17 13.1359729428263 3.86402705717372 75 13 13.4395014728773 -0.439501472877338 76 13 13.5395839730538 -0.53958397305378 77 12 13.2561243206211 -1.25612432062108 78 13 13.0424396231613 -0.0424396231612821 79 14 12.9586949041803 1.04130509581971 80 11 10.7959559214213 0.204044078578722 81 12 11.7337241522863 0.266275847713675 82 12 13.937613878196 -1.937613878196 83 16 13.8739396984027 2.12606030159733 84 12 12.5279461657287 -0.527946165728693 85 12 12.6371156241392 -0.637115624139247 86 12 13.4012969650013 -1.40129696500134 87 10 12.193632049729 -2.19363204972899 88 15 12.9714730110574 2.02852698894257 89 15 14.5433527915503 0.456647208449673 90 12 12.4381439424866 -0.438143942486615 91 16 13.5128793730870 2.48712062691299 92 15 13.0632950234972 1.93670497650281 93 16 14.3854453112114 1.61455468878859 94 13 14.2148878751815 -1.21488787518148 95 12 12.9205336672228 -0.920533667222764 96 11 12.3835583824967 -1.38355838249669 97 13 12.3322555135978 0.667744486402205 98 10 11.4592682393894 -1.45926823938938 99 15 12.8816291784662 2.11837082153383 100 13 13.5748422456551 -0.574842245655113 101 16 14.4400308712013 1.55996912879867 102 15 14.5791027404020 0.420897259597975 103 18 13.7676299334298 4.23237006657018 104 13 12.2572629586038 0.742737041396155 105 10 10.3324018078234 -0.332401807823358 106 16 13.9451578860552 2.05484211394478 107 13 11.8675368121168 1.13246318788322 108 15 14.4153893313507 0.584610668649274 109 14 11.8585330725810 2.14146692741897 110 15 11.8482527956467 3.15174720435333 111 14 12.7724580584863 1.22754194151368 112 13 13.5838892561093 -0.583889256109342 113 13 12.7666088588555 0.233391141144536 114 15 13.6256967092221 1.37430329077788 115 16 14.01538124636 1.98461875364000 116 14 14.0856046066648 -0.085604606664785 117 6 10.848503587769 -4.84850358776901 118 14 10.8484901540264 3.15150984597359 119 11 11.8200868585557 -0.82008685855573 120 12 10.5687632595859 1.43123674041407 121 12 12.8285851651662 -0.828585165166163 122 4 12.9676285614340 -8.96762856143401 123 16 12.0570798538064 3.94292014619355 124 12 10.3631408558366 1.63685914416342 125 14 10.9360910553622 3.06390894463781 126 13 11.6555187472788 1.34448125272124 127 5 9.66422037570819 -4.66422037570819 128 16 11.4543170129027 4.54568298709733 129 11 12.4772984013443 -1.47729840134427 130 8 11.4506693930624 -3.45066939306244 131 15 12.6200747968089 2.37992520319106 132 6 11.3256206693923 -5.32562066939232 133 14 10.7767802901235 3.22321970987651 134 12 11.7560058827797 0.24399411722031 135 15 10.7347064240344 4.26529357596557 136 14 11.8812799091658 2.11872009083418 137 4 11.9783028208671 -7.9783028208671 138 15 12.0899268383020 2.91007316169805 139 10 11.7775344920746 -1.77753449207458 140 10 11.9818121789172 -1.98181217891719 141 13 11.7191362224110 1.28086377758898 142 5 12.5801037368533 -7.58010373685326 143 15 11.3444546189613 3.65554538103875 144 12 11.6682801533964 0.331719846603630 145 12 10.6182979148358 1.38170208516416 146 16 12.9305456678489 3.06945433215112 147 4 12.9609945006549 -8.96099450065491 148 14 11.9140118788915 2.08598812110847 149 11 11.3376971338196 -0.337697133819581 150 13 10.1159674636675 2.88403253633253 151 12 9.13904150692783 2.86095849307217 152 10 10.5726775502868 -0.572677550286762 153 9 8.79889162503987 0.201108374960133 154 10 10.3438450671932 -0.343845067193171 155 12 9.77377122242288 2.22622877757712 156 13 11.3310945717857 1.66890542821435 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.0332063795291718 0.0664127590583435 0.966793620470828 10 0.0081826675236302 0.0163653350472604 0.99181733247637 11 0.00635446702022058 0.0127089340404412 0.99364553297978 12 0.00264954584492481 0.00529909168984963 0.997350454155075 13 0.170899060742427 0.341798121484855 0.829100939257573 14 0.105319005154655 0.210638010309310 0.894680994845345 15 0.0616122364176452 0.123224472835290 0.938387763582355 16 0.0534785581274298 0.106957116254860 0.94652144187257 17 0.0387159860315139 0.0774319720630278 0.961284013968486 18 0.0296854016308333 0.0593708032616667 0.970314598369167 19 0.0215444324586011 0.0430888649172022 0.978455567541399 20 0.0259379805081834 0.0518759610163667 0.974062019491817 21 0.0551099618628086 0.110219923725617 0.944890038137191 22 0.0354872029051243 0.0709744058102486 0.964512797094876 23 0.0568666062560085 0.113733212512017 0.943133393743992 24 0.0403942850762976 0.0807885701525951 0.959605714923702 25 0.0323512722984838 0.0647025445969676 0.967648727701516 26 0.0236825469091123 0.0473650938182247 0.976317453090888 27 0.0202372192998835 0.0404744385997669 0.979762780700117 28 0.0134867322235010 0.0269734644470019 0.9865132677765 29 0.00836465084421238 0.0167293016884248 0.991635349155788 30 0.00556914420920341 0.0111382884184068 0.994430855790797 31 0.0195161544635444 0.0390323089270888 0.980483845536456 32 0.0147079915775537 0.0294159831551073 0.985292008422446 33 0.00966171718485873 0.0193234343697175 0.990338282815141 34 0.00877090981650862 0.0175418196330172 0.991229090183491 35 0.00576254210911547 0.0115250842182309 0.994237457890885 36 0.00362769930821658 0.00725539861643316 0.996372300691783 37 0.00321986871908998 0.00643973743817996 0.99678013128091 38 0.00379780686319757 0.00759561372639514 0.996202193136802 39 0.00270070442364543 0.00540140884729086 0.997299295576355 40 0.00174531250814586 0.00349062501629171 0.998254687491854 41 0.00127899621311750 0.00255799242623499 0.998721003786883 42 0.000855770753876636 0.00171154150775327 0.999144229246123 43 0.000779005535089664 0.00155801107017933 0.99922099446491 44 0.000522603127502539 0.00104520625500508 0.999477396872497 45 0.000322543545474865 0.00064508709094973 0.999677456454525 46 0.000209316102880782 0.000418632205761564 0.99979068389712 47 0.000123851580700402 0.000247703161400805 0.9998761484193 48 0.000316099067092517 0.000632198134185035 0.999683900932907 49 0.000199886320452593 0.000399772640905185 0.999800113679547 50 0.000169367189701377 0.000338734379402753 0.999830632810299 51 0.000122704601162935 0.000245409202325871 0.999877295398837 52 8.96692580477432e-05 0.000179338516095486 0.999910330741952 53 5.77686743941312e-05 0.000115537348788262 0.999942231325606 54 5.23465235456143e-05 0.000104693047091229 0.999947653476454 55 3.27209495952781e-05 6.54418991905561e-05 0.999967279050405 56 1.87221918667679e-05 3.74443837335358e-05 0.999981277808133 57 1.07851489024146e-05 2.15702978048293e-05 0.999989214851098 58 8.34591880135242e-06 1.66918376027048e-05 0.999991654081199 59 5.04409808309112e-05 0.000100881961661822 0.99994955901917 60 2.95079815552761e-05 5.90159631105522e-05 0.999970492018445 61 1.95191484788638e-05 3.90382969577275e-05 0.999980480851521 62 1.17670821461057e-05 2.35341642922114e-05 0.999988232917854 63 1.83445296541794e-05 3.66890593083588e-05 0.999981655470346 64 1.09663237563734e-05 2.19326475127468e-05 0.999989033676244 65 6.74626782564889e-06 1.34925356512978e-05 0.999993253732174 66 3.83789395744204e-06 7.67578791488408e-06 0.999996162106043 67 3.24687618326127e-06 6.49375236652255e-06 0.999996753123817 68 1.95585103708257e-06 3.91170207416515e-06 0.999998044148963 69 1.27585840183468e-06 2.55171680366936e-06 0.999998724141598 70 1.47517042337942e-05 2.95034084675885e-05 0.999985248295766 71 9.44108218984345e-06 1.88821643796869e-05 0.99999055891781 72 5.43545077342035e-06 1.08709015468407e-05 0.999994564549227 73 4.29553371975103e-06 8.59106743950205e-06 0.99999570446628 74 1.17963126668169e-05 2.35926253336337e-05 0.999988203687333 75 6.88177136827811e-06 1.37635427365562e-05 0.999993118228632 76 4.05641938029076e-06 8.11283876058153e-06 0.99999594358062 77 2.60084105511261e-06 5.20168211022523e-06 0.999997399158945 78 1.46385175299052e-06 2.92770350598103e-06 0.999998536148247 79 1.07785120421103e-06 2.15570240842205e-06 0.999998922148796 80 7.43047174197283e-07 1.48609434839457e-06 0.999999256952826 81 5.4563401078505e-07 1.0912680215701e-06 0.99999945436599 82 4.10631316449519e-07 8.21262632899038e-07 0.999999589368684 83 4.73785601725248e-07 9.47571203450496e-07 0.999999526214398 84 2.7624757670266e-07 5.5249515340532e-07 0.999999723752423 85 2.03038446977654e-07 4.06076893955308e-07 0.999999796961553 86 1.36072332213164e-07 2.72144664426328e-07 0.999999863927668 87 1.30581862181447e-07 2.61163724362894e-07 0.999999869418138 88 1.12488608225840e-07 2.24977216451679e-07 0.999999887511392 89 6.11976930446247e-08 1.22395386089249e-07 0.999999938802307 90 3.75016314080406e-08 7.50032628160812e-08 0.999999962498369 91 3.89806499851154e-08 7.79612999702309e-08 0.99999996101935 92 3.56015406488215e-08 7.12030812976431e-08 0.99999996439846 93 2.35772970834702e-08 4.71545941669403e-08 0.999999976422703 94 1.41626441015748e-08 2.83252882031497e-08 0.999999985837356 95 8.8430107531714e-09 1.76860215063428e-08 0.99999999115699 96 6.52677823728966e-09 1.30535564745793e-08 0.999999993473222 97 5.07886174784363e-09 1.01577234956873e-08 0.999999994921138 98 5.51534555150793e-09 1.10306911030159e-08 0.999999994484654 99 4.0923835229472e-09 8.1847670458944e-09 0.999999995907616 100 2.18726469888137e-09 4.37452939776274e-09 0.999999997812735 101 1.52345411610492e-09 3.04690823220983e-09 0.999999998476546 102 7.92577505163597e-10 1.58515501032719e-09 0.999999999207422 103 5.12226493247483e-09 1.02445298649497e-08 0.999999994877735 104 5.99477329362574e-09 1.19895465872515e-08 0.999999994005227 105 1.58805599181335e-08 3.17611198362669e-08 0.99999998411944 106 1.09533246334767e-08 2.19066492669535e-08 0.999999989046675 107 6.69160368617817e-09 1.33832073723563e-08 0.999999993308396 108 4.72121536659872e-09 9.44243073319744e-09 0.999999995278785 109 5.79219582562647e-09 1.15843916512529e-08 0.999999994207804 110 6.540929601759e-09 1.3081859203518e-08 0.99999999345907 111 3.35805079432463e-09 6.71610158864927e-09 0.99999999664195 112 2.25095582579562e-09 4.50191165159124e-09 0.999999997749044 113 1.41222952744239e-09 2.82445905488478e-09 0.99999999858777 114 8.98756840744456e-10 1.79751368148891e-09 0.999999999101243 115 9.6101248690528e-10 1.92202497381056e-09 0.999999999038988 116 7.5539302997093e-10 1.51078605994186e-09 0.999999999244607 117 2.53977653479898e-08 5.07955306959795e-08 0.999999974602235 118 5.16106532064725e-08 1.03221306412945e-07 0.999999948389347 119 2.82867593441334e-08 5.65735186882668e-08 0.99999997171324 120 1.47123577463059e-08 2.94247154926117e-08 0.999999985287642 121 9.2627432108212e-09 1.85254864216424e-08 0.999999990737257 122 6.15860540521451e-06 1.23172108104290e-05 0.999993841394595 123 1.51741900564564e-05 3.03483801129128e-05 0.999984825809944 124 1.07215946125291e-05 2.14431892250582e-05 0.999989278405387 125 1.44241477476284e-05 2.88482954952569e-05 0.999985575852252 126 1.21742629134651e-05 2.43485258269301e-05 0.999987825737087 127 0.000122076845392417 0.000244153690784833 0.999877923154608 128 0.000200736913800664 0.000401473827601328 0.9997992630862 129 0.000151945316243837 0.000303890632487673 0.999848054683756 130 0.000170352075734909 0.000340704151469818 0.999829647924265 131 0.000179763418473201 0.000359526836946402 0.999820236581527 132 0.000746447991552074 0.00149289598310415 0.999253552008448 133 0.000569781978781885 0.00113956395756377 0.999430218021218 134 0.000334033599732041 0.000668067199464082 0.999665966400268 135 0.000446168802142328 0.000892337604284655 0.999553831197858 136 0.000472901190290915 0.00094580238058183 0.99952709880971 137 0.0177485055516433 0.0354970111032866 0.982251494448357 138 0.0171325455525961 0.0342650911051923 0.982867454447404 139 0.0105208629457560 0.0210417258915120 0.989479137054244 140 0.00722533937820272 0.0144506787564054 0.992774660621797 141 0.00441741506354484 0.00883483012708968 0.995582584936455 142 0.0325933435043011 0.0651866870086022 0.967406656495699 143 0.0410735450594398 0.0821470901188796 0.95892645494056 144 0.0298254797515881 0.0596509595031762 0.970174520248412 145 0.0211828197573877 0.0423656395147754 0.978817180242612 146 0.109597999969336 0.219195999938673 0.890402000030664 147 0.797101421185557 0.405797157628887 0.202898578814443 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 103 0.741007194244604 NOK 5% type I error level 121 0.870503597122302 NOK 10% type I error level 131 0.942446043165468 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/10prwd1292273462.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/10prwd1292273462.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/1iqh11292273462.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/1iqh11292273462.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/2iqh11292273462.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/2iqh11292273462.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/3shg41292273462.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/3shg41292273462.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/4shg41292273462.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/4shg41292273462.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/5shg41292273462.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/5shg41292273462.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/63qx71292273462.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/63qx71292273462.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/7ezea1292273462.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/7ezea1292273462.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/8ezea1292273462.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/8ezea1292273462.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/9ezea1292273462.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/13/t1292273377k2wegxp4f2bfl3x/9ezea1292273462.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by