Workshop 7 - regression model

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 23 Nov 2010 09:58:23 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m.htm/, Retrieved Tue, 23 Nov 2010 10:57:55 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

24 3 4 4 4 3 2 4 25 4 4 4 3 2 4 4 30 4 5 5 4 4 4 4 19 2 2 3 4 2 3 3 22 2 2 4 4 4 4 2 22 3 4 3 4 2 2 4 25 2 4 4 4 3 4 4 23 3 4 3 4 4 2 3 17 3 4 2 2 1 3 2 21 3 2 4 4 2 3 3 19 3 3 2 3 2 3 3 19 4 4 2 2 2 3 2 15 2 3 2 2 2 2 2 16 2 4 1 3 1 3 2 23 1 4 4 4 2 4 4 27 1 4 4 5 4 5 4 22 3 4 2 4 2 4 3 14 2 2 2 2 2 2 2 22 2 4 3 4 3 3 3 23 3 4 3 3 2 4 4 23 4 4 3 4 3 2 3 21 4 3 4 2 2 3 3 19 3 2 3 2 3 2 4 18 2 4 2 4 2 2 2 20 3 2 2 4 3 2 4 23 4 3 4 4 3 3 2 25 3 4 4 4 4 3 3 19 2 3 3 3 2 3 3 24 1 4 4 4 4 3 4 22 3 4 2 5 3 3 2 25 2 4 4 4 4 3 4 26 4 4 4 4 3 3 4 29 4 4 5 4 4 4 4 32 5 4 5 4 4 5 5 25 2 4 4 4 3 4 4 29 4 5 4 4 5 4 3 28 4 4 4 4 4 4 4 17 2 2 2 4 2 3 2 28 4 4 4 4 4 4 4 29 4 4 4 5 4 4 4 26 2 5 4 4 5 2 4 25 3 4 3 4 4 4 3 14 2 2 2 2 2 2 2 25 4 4 3 4 4 3 3 26 3 4 4 4 4 3 4 20 1 4 3 4 1 4 3 18 2 2 2 4 2 2 4 32 5 5 4 4 5 4 5 25 2 4 4 4 4 3 4 25 4 4 3 4 2 4 4 23 4 4 4 3 3 2 3 21 2 4 3 4 4 2 2 20 2 4 4 4 2 2 2 15 2 3 2 4 1 1 2 30 4 5 4 3 4 5 5 24 3 4 4 3 2 4 4 26 4 4 4 4 4 2 4 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 32 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Yt[t] = + 5.65277449152099e-15 + 0.999999999999998X1t[t] + 1.00000000000000X2t[t] + 1X3t[t] + 1X4t[t] + 1X5t[t] + 1X6t[t] + 1.00000000000000X7t[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) 5.65277449152099e-15 0 2.1714 0.031474 0.015737 X1t 0.999999999999998 0 2295304619726722 0 0 X2t 1.00000000000000 0 1737088925487035 0 0 X3t 1 0 1680838988880423 0 0 X4t 1 0 1690597273108607 0 0 X5t 1 0 1979753070537650 0 0 X6t 1 0 1907175258011070 0 0 X7t 1.00000000000000 0 1659750307323752 0 0 Multiple Linear Regression - Regression Statistics Multiple R 1 R-squared 1 Adjusted R-squared 1 F-TEST (value) 1.59029440260596e+31 F-TEST (DF numerator) 7 F-TEST (DF denominator) 150 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.02271080728302e-15 Sum Squared Residuals 3.78414357803965e-27 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.9999999999999 5.4679233911816e-14 2 25 25.0000000000000 -2.34466723732491e-14 3 30 30 4.40060569066426e-15 4 19 19 -6.162445547409e-15 5 22 22 -6.95001114635409e-16 6 22 22 -5.18669161073777e-15 7 25 25 2.07099882053762e-15 8 23 23 2.12019517737531e-15 9 17 17 9.6944945555234e-16 10 21 21 7.77436210298879e-16 11 19 19 4.38141436319459e-16 12 19 19 7.12315530563665e-16 13 15 15 -3.73653379795946e-16 14 16 16 1.34092654939325e-15 15 23 23 -2.95342082814583e-16 16 27 27 4.63216986012391e-16 17 22 22 6.56439306485443e-16 18 14 14 5.40082240803923e-16 19 22 22 -4.67453343341134e-16 20 23 23 2.16539268495076e-16 21 23 23 -1.16667692028670e-15 22 21 21 3.66942880131265e-16 23 19 19 -1.385016727195e-16 24 18 18 -3.62226921603343e-16 25 20 20 -3.46285400048605e-16 26 23 23 1.02214280119796e-15 27 25 25 -1.20146484791471e-15 28 19 19 8.71717219850532e-17 29 24 24 -1.75460259035751e-15 30 22 22 -4.31016926757548e-16 31 25 25 -1.04784318713914e-15 32 26 26 -7.24343648051878e-16 33 29 29 -1.35638899308394e-16 34 32 32 -2.58269908054916e-16 35 25 25 -5.28756467219368e-17 36 29 29 -1.76325283274044e-16 37 28 28 1.19194075351474e-16 38 17 17 1.32978507811277e-15 39 28 28 1.19194075351474e-16 40 29 29 1.65441480513277e-16 41 26 26 -3.12307980184998e-15 42 25 25 -2.73792413445623e-17 43 14 14 5.40082240803923e-16 44 25 25 -2.2599468222865e-16 45 26 26 -1.28477335485215e-15 46 20 20 6.458702439866e-16 47 18 18 -3.11196079984962e-16 48 32 32 -1.13498397717451e-15 49 25 25 -1.04784318713914e-15 50 25 25 8.58523774412738e-16 51 23 23 -1.60653517818652e-15 52 21 21 -7.129785620458e-16 53 20 20 -1.81558244185446e-15 54 15 15 -1.2287797014343e-15 55 30 30 1.16088935041905e-15 56 24 24 7.11106835457189e-16 57 26 26 -2.16340039831914e-15 58 24 24 2.2839261784989e-17 59 22 22 -2.04919174317775e-15 60 14 14 3.97073410775532e-16 61 24 24 6.46046537787993e-16 62 24 24 3.18297824888136e-16 63 24 24 2.2839261784989e-17 64 24 24 2.19860134884790e-16 65 19 19 4.86689791810069e-16 66 31 31 -6.27729222140305e-16 67 22 22 -3.02797614858376e-16 68 27 27 3.81947828900892e-16 69 19 19 -6.06449295311223e-16 70 25 25 3.96531757615815e-16 71 20 20 1.53178949344847e-15 72 21 21 -3.43166177506857e-16 73 27 27 3.56124243064482e-16 74 23 23 1.28192278000074e-15 75 25 25 -5.30012838651923e-16 76 20 20 -1.81558244185446e-15 77 21 21 -3.69604675937102e-16 78 22 22 4.38955063764887e-16 79 23 23 1.83467728186949e-16 80 25 25 -5.28756467219368e-17 81 25 25 -6.36044127085785e-16 82 17 17 1.32978507811277e-15 83 19 19 2.37877032938004e-15 84 25 25 -2.12177931580617e-16 85 19 19 4.38141436319459e-16 86 20 20 8.67345083381545e-16 87 26 26 2.37550122262004e-16 88 23 23 -1.61578293218882e-15 89 27 27 3.56124243064482e-16 90 17 17 -2.97452024302629e-16 91 17 17 1.07515356352717e-15 92 19 19 -1.06275845822984e-15 93 17 17 -6.36140748408697e-16 94 22 22 -4.67453343341134e-16 95 21 21 -1.88098814184504e-15 96 32 32 -1.25099729366568e-15 97 21 21 -3.69604675937102e-16 98 21 21 9.52989789784179e-16 99 18 18 -6.89940385366812e-16 100 18 18 -1.56503167576656e-16 101 23 23 8.71717219850532e-17 102 19 19 -6.03477925834168e-17 103 20 20 -3.43166177506857e-16 104 21 21 -2.7137233371064e-16 105 20 20 3.8740123706713e-16 106 17 17 7.81102892466329e-16 107 18 18 -1.26529090409144e-15 108 19 19 -2.01221420158322e-15 109 22 22 -1.85204654553362e-16 110 15 15 -8.58368178089289e-16 111 14 14 -8.85982709039911e-16 112 18 18 -4.17320388550468e-16 113 24 24 -9.23917275843618e-16 114 35 35 7.46141745770695e-17 115 29 29 -1.09847858098335e-15 116 21 21 -2.3705594404562e-15 117 25 25 -1.48475568927335e-15 118 20 20 1.39860867927233e-15 119 22 22 1.35597572495392e-15 120 13 13 1.61876993845633e-16 121 26 26 -5.5871432562863e-16 122 17 17 1.07722196656207e-15 123 25 25 2.49679571505464e-16 124 20 20 1.87412014690547e-15 125 19 19 8.10163784511347e-16 126 21 21 -9.31659726921099e-16 127 22 22 -4.61856279439127e-16 128 24 24 -1.19432992028941e-15 129 21 21 -1.28477335485215e-15 130 26 26 -1.36401985913911e-16 131 24 24 -1.70001156246394e-15 132 16 16 -7.13551212464841e-16 133 23 23 -1.27755875474837e-15 134 18 18 2.85632355932166e-16 135 16 16 -1.28477335485215e-15 136 26 26 1.97255783690882e-15 137 19 19 8.14333699301813e-16 138 21 21 -7.16017700782112e-16 139 21 21 8.88336680079244e-16 140 22 22 1.6803345918565e-15 141 23 23 -2.67185608551446e-16 142 29 29 -3.33351947284590e-16 143 21 21 -1.72572187981651e-15 144 21 21 -1.14348170687555e-15 145 23 23 2.58013733520171e-16 146 27 27 -6.81721525080088e-16 147 25 25 -5.30455275752571e-16 148 21 21 -7.36848301521211e-16 149 10 10 -6.14042652104326e-16 150 20 20 1.22726050535130e-15 151 26 26 -2.1283110782555e-15 152 24 24 -1.33027470068247e-15 153 29 29 3.40334549005982e-16 154 19 19 2.18554800890698e-15 155 24 24 -1.17441156338223e-15 156 19 19 -1.05042300688226e-15 157 24 24 7.70453382242686e-17 158 22 22 4.12462447823937e-16 159 17 NA NA Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.198727293869551 0.397454587739102 0.80127270613045 12 0.000490491475111996 0.000980982950223991 0.999509508524888 13 1.94688890818687e-06 3.89377781637374e-06 0.999998053111092 14 0.0576826627588537 0.115365325517707 0.942317337241146 15 0.000132972044698631 0.000265944089397262 0.999867027955301 16 2.70906270740679e-08 5.41812541481358e-08 0.999999972909373 17 7.82291503356155e-13 1.56458300671231e-12 0.999999999999218 18 5.43588848424815e-11 1.08717769684963e-10 0.99999999994564 19 4.86549774806163e-08 9.73099549612327e-08 0.999999951345023 20 2.26872957874386e-11 4.53745915748772e-11 0.999999999977313 21 1.21659006195967e-07 2.43318012391935e-07 0.999999878340994 22 4.71127242425764e-09 9.42254484851528e-09 0.999999995288728 23 0.92141888939187 0.157162221216260 0.0785811106081302 24 8.15931656494636e-06 1.63186331298927e-05 0.999991840683435 25 2.33936528157533e-07 4.67873056315065e-07 0.999999766063472 26 0.000130694976904984 0.000261389953809967 0.999869305023095 27 0.687779047889801 0.624441904220398 0.312220952110199 28 4.7555550200333e-17 9.5111100400666e-17 1 29 0.996943909981371 0.00611218003725717 0.00305609001862858 30 1.18640835779094e-06 2.37281671558188e-06 0.999998813591642 31 0.0023797936960184 0.0047595873920368 0.997620206303982 32 1 2.17032219948718e-36 1.08516109974359e-36 33 1.21346827995270e-05 2.42693655990539e-05 0.9999878653172 34 0.00722537188835583 0.0144507437767117 0.992774628111644 35 0.0010254375061223 0.0020508750122446 0.998974562493878 36 3.47798144082734e-24 6.95596288165467e-24 1 37 3.56528677374145e-15 7.1305735474829e-15 0.999999999999996 38 3.48854217370139e-21 6.97708434740277e-21 1 39 7.6418565557708e-20 1.52837131115416e-19 1 40 0.995817963597323 0.00836407280535362 0.00418203640267681 41 0.126771523269821 0.253543046539643 0.873228476730179 42 0.861520941281004 0.276958117437991 0.138479058718996 43 1.52260053609570e-06 3.04520107219141e-06 0.999998477399464 44 0.488263059251034 0.976526118502068 0.511736940748966 45 6.05105651649973e-15 1.21021130329995e-14 0.999999999999994 46 0.00144273143076962 0.00288546286153925 0.99855726856923 47 5.910425385906e-17 1.1820850771812e-16 1 48 4.26411668105976e-23 8.52823336211952e-23 1 49 1.95143593707703e-21 3.90287187415406e-21 1 50 0.93977842986939 0.120443140261219 0.0602215701306094 51 0.999430794348792 0.00113841130241621 0.000569205651208105 52 0.0112149623793594 0.0224299247587189 0.98878503762064 53 2.03010174963882e-06 4.06020349927764e-06 0.99999796989825 54 2.05309699349572e-46 4.10619398699143e-46 1 55 1 7.14505104207465e-17 3.57252552103733e-17 56 0.0309415835724505 0.0618831671449009 0.96905841642755 57 1 1.00327916640463e-32 5.01639583202317e-33 58 5.45616859408648e-21 1.09123371881730e-20 1 59 0.999926307198345 0.000147385603310179 7.36928016550894e-05 60 0.778253145839155 0.44349370832169 0.221746854160845 61 1 6.57638899936315e-33 3.28819449968158e-33 62 1.73056098794098e-06 3.46112197588196e-06 0.999998269439012 63 2.48310030101095e-36 4.9662006020219e-36 1 64 2.15316826675274e-17 4.30633653350548e-17 1 65 0.913740611574031 0.172518776851938 0.0862593884259692 66 1 1.19301945875477e-36 5.96509729377384e-37 67 0.997800207710883 0.00439958457823412 0.00219979228911706 68 1 2.65526352413373e-38 1.32763176206687e-38 69 1.59887962088185e-19 3.1977592417637e-19 1 70 0.296520250852007 0.593040501704013 0.703479749147993 71 0.146624026886372 0.293248053772744 0.853375973113628 72 1 1.17993338638020e-69 5.89966693190098e-70 73 4.72341726308488e-45 9.44683452616976e-45 1 74 4.01124780059783e-13 8.02249560119567e-13 0.9999999999996 75 2.73421917446137e-23 5.46843834892273e-23 1 76 3.0629804335193e-15 6.1259608670386e-15 0.999999999999997 77 1.05803165581653e-44 2.11606331163306e-44 1 78 0.999999999999236 1.52730932080693e-12 7.63654660403465e-13 79 1.49191426289055e-37 2.98382852578111e-37 1 80 3.90789497978888e-07 7.81578995957775e-07 0.999999609210502 81 1 1.99430642065003e-95 9.97153210325013e-96 82 0.999999989917556 2.01648890094061e-08 1.00824445047030e-08 83 1.40309893562625e-33 2.80619787125249e-33 1 84 1 2.96674520049018e-16 1.48337260024509e-16 85 0.999999998596866 2.80626892269445e-09 1.40313446134722e-09 86 0.999894643418962 0.000210713162076471 0.000105356581038236 87 1 5.46741031049254e-29 2.73370515524627e-29 88 3.15633442070998e-05 6.31266884141996e-05 0.999968436655793 89 0.0156973704222820 0.0313947408445640 0.984302629577718 90 3.37200759402839e-08 6.74401518805677e-08 0.999999966279924 91 1 6.01706842051864e-25 3.00853421025932e-25 92 0.999448105415294 0.00110378916941253 0.000551894584706264 93 0.999999999977055 4.58900846909031e-11 2.29450423454516e-11 94 0.99999999987145 2.57098416524765e-10 1.28549208262382e-10 95 0.999997481584117 5.03683176636401e-06 2.51841588318200e-06 96 0.999999999989658 2.06845786084223e-11 1.03422893042111e-11 97 0.00097201802617477 0.00194403605234954 0.999027981973825 98 1 7.49059524779674e-38 3.74529762389837e-38 99 2.53653331870966e-07 5.07306663741932e-07 0.999999746346668 100 1 8.49598251502897e-56 4.24799125751449e-56 101 0.999999985290239 2.941952254783e-08 1.4709761273915e-08 102 1 9.7653925436888e-18 4.8826962718444e-18 103 1.37044041150991e-17 2.74088082301982e-17 1 104 1 7.1771670206962e-45 3.5885835103481e-45 105 1 1.31631077905512e-15 6.58155389527561e-16 106 1.08318025860870e-16 2.16636051721740e-16 1 107 0.997458272238597 0.00508345552280653 0.00254172776140327 108 0.00079351766375589 0.00158703532751178 0.999206482336244 109 1 8.95310763600885e-18 4.47655381800442e-18 110 5.3106178648092e-30 1.06212357296184e-29 1 111 1 1.28390320646231e-18 6.41951603231153e-19 112 1 1.10400558791487e-18 5.52002793957433e-19 113 1 6.21493048831439e-17 3.10746524415720e-17 114 1.72747190175854e-18 3.45494380351709e-18 1 115 5.42040149392627e-41 1.08408029878525e-40 1 116 0.948973807599695 0.102052384800609 0.0510261924003046 117 0.00282315310769563 0.00564630621539125 0.997176846892304 118 0.128367495950330 0.256734991900660 0.87163250404967 119 0.999999999909306 1.81387424317920e-10 9.06937121589602e-11 120 0.616004902619715 0.76799019476057 0.383995097380285 121 1 3.81318743666095e-29 1.90659371833048e-29 122 1 3.27713339019568e-27 1.63856669509784e-27 123 0.999910243601812 0.000179512796376129 8.97563981880647e-05 124 0.99985591576006 0.000288168479877699 0.000144084239938849 125 0.999998333692969 3.33261406264709e-06 1.66630703132354e-06 126 1 4.92231723801526e-29 2.46115861900763e-29 127 0.99999999999113 1.77414281440152e-11 8.87071407200762e-12 128 1 1.0641748143815e-23 5.3208740719075e-24 129 0.993319338373864 0.0133613232522721 0.00668066162613604 130 0.999999847325628 3.05348744952807e-07 1.52674372476404e-07 131 1.78194535966749e-05 3.56389071933499e-05 0.999982180546403 132 0.765405281759343 0.469189436481315 0.234594718240657 133 0.999999999865671 2.68658115532553e-10 1.34329057766277e-10 134 1 7.30904477198118e-16 3.65452238599059e-16 135 0.999999931616854 1.36766292885816e-07 6.8383146442908e-08 136 0.99999987122409 2.57551820504207e-07 1.28775910252103e-07 137 0.999999762458179 4.75083642392734e-07 2.37541821196367e-07 138 1 1.68954833573697e-18 8.44774167868483e-19 139 0.999999999999982 3.64195639708312e-14 1.82097819854156e-14 140 0.999999961254138 7.74917233687675e-08 3.87458616843838e-08 141 0.999999997257455 5.48508918887605e-09 2.74254459443803e-09 142 0.9999999971593 5.68139785080545e-09 2.84069892540273e-09 143 0.999999999887272 2.25456084643568e-10 1.12728042321784e-10 144 0.866627065186277 0.266745869627445 0.133372934813723 145 0.999620545141225 0.00075890971754979 0.000379454858774895 146 0.999999936696689 1.26606622515509e-07 6.33033112577543e-08 147 0.996742931865387 0.00651413626922547 0.00325706813461274 148 0.382786192682766 0.765572385365533 0.617213807317234 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 115 0.833333333333333 NOK 5% type I error level 119 0.86231884057971 NOK 10% type I error level 120 0.869565217391304 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/10j7521290506270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/10j7521290506270.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/1u6q81290506270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/1u6q81290506270.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/2ngqb1290506270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/2ngqb1290506270.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/3ngqb1290506270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/3ngqb1290506270.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/4ngqb1290506270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/4ngqb1290506270.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/5ngqb1290506270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/5ngqb1290506270.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/6g77d1290506270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/6g77d1290506270.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/7ry6h1290506270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/7ry6h1290506270.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/8ry6h1290506270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/8ry6h1290506270.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/9ry6h1290506270.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905062647mfzrimp07s4i6m/9ry6h1290506270.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

Copyright

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

Software written by Ed van Stee & Patrick Wessa

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