Multiple Regression G Minitutorial

*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 22:51:32 +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/t1290552638grcyesj6i1pc9h5.htm/, Retrieved Tue, 23 Nov 2010 23:50:41 +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/t1290552638grcyesj6i1pc9h5.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:

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7 7 1 7 7 1 7 7 1 5 6 1 5 5 1 5 5 1 6 6 2 5 6 1 4 5 1 4 5 2 5 6 2 5 6 2 5 6 2 5 6 2 5 6 1 6 7 1 7 5 1 6 7 1 7 7 1 7 7 1 7 6 2 6 7 1 5 6 1 5 7 1 6 7 1 3 7 2 7 7 1 6 6 1 6 6 1 5 6 1 5 4 1 7 7 1 4 7 2 5 6 1 6 7 1 6 7 2 4 6 1 5 6 1 4 5 1 6 7 1 3 6 1 6 6 1 6 6 1 7 7 1 7 7 1 5 6 2 5 6 3 6 6 2 3 4 1 7 7 1 4 7 1 7 7 1 7 7 1 6 7 2 3 7 1 7 7 1 6 7 2 5 6 2 6 7 2 6 6 1 3 3 1 5 5 1 4 4 2 5 7 1 7 7 NA 5 7 1 2 5 1 4 5 1 2 6 1 6 7 1 7 6 1 6 7 2 3 6 1 7 7 2 5 7 1 6 5 1 7 6 1 6 5 1 6 5 1 7 6 1 6 5 1 5 6 1 3 6 1 5 7 1 5 5 1 7 6 1 5 6 2 7 6 1 5 6 1 5 6 1 6 6 1 7 6 1 6 6 2 5 5 1 5 5 1 6 6 1 5 4 4 5 3 6 5 1 1 4 5 3 4 3 3 4 5 2 4 4 1 5 5 1 6 7 2 6 6 2 6 6 2 5 5 2 5 6 1 7 7 1 5 7 1 5 7 1 5 7 1 5 5 2 7 7 1 7 7 1 7 7 2 5 7 1 7 6 1 5 6 1 5 7 1 6 7 1 5 7 1 6 5 1 6 7 1 7 6 1 5 6 2 7 6 2 5 6 1 6 6 1 7 6 2 7 5 2 7 3 1 6 5 1 6 6 2 5 6 4 6 6 4 3 6 1 5 5 1 4 6 2 4 5 2 5 4 3 7 7 3 6 7 2 6 6 2 5 6 2 5 6 1 2 6 3 6 7 2 4 7 2 4 6 2 5 6 2 4 5 1 4 5 1 3 5 1 6 5 1 6 6 2 7 7 1 5 7 1 3 5 1 6 4 1 4 3 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 9 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Q1_7[t] = + 3.06528780326958 + 0.164175161185608Q1_2[t] -0.0765245287154905Q1_3[t] + 0.243401719833989Q1_5[t] + 0.419839287888058Q1_8[t] -0.303558928060235Q1_12[t] + 0.085748375843493Q1_16[t] -0.161019595095292Q1_22[t] + 0.306324782495529GENDER[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) 3.06528780326958 0.816055 3.7562 0.000245 0.000122 Q1_2 0.164175161185608 0.085825 1.9129 0.057629 0.028814 Q1_3 -0.0765245287154905 0.088532 -0.8644 0.388735 0.194367 Q1_5 0.243401719833989 0.127181 1.9138 0.05751 0.028755 Q1_8 0.419839287888058 0.119876 3.5023 0.000605 0.000302 Q1_12 -0.303558928060235 0.103292 -2.9388 0.003805 0.001903 Q1_16 0.085748375843493 0.104048 0.8241 0.411153 0.205577 Q1_22 -0.161019595095292 0.106772 -1.5081 0.133601 0.0668 GENDER 0.306324782495529 0.176177 1.7387 0.084093 0.042046 Multiple Linear Regression - Regression Statistics Multiple R 0.450959020796799 R-squared 0.203364038438007 Adjusted R-squared 0.161709870513197 F-TEST (value) 4.8822014355226 F-TEST (DF numerator) 8 F-TEST (DF denominator) 153 p-value 2.21235956312515e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.06402597940044 Sum Squared Residuals 173.219146580378 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7 6.3369862852835 0.663013714716503 2 5 5.39602435435525 -0.396024354355251 3 5 6.13769214741941 -1.13769214741941 4 5 5.81336098894718 -0.813360988947182 5 5 5.59468683892177 -0.59468683892177 6 7 5.24738417247828 1.75261582752172 7 7 6.80433066287432 0.195669337125685 8 5 5.58147508452284 -0.581475084522841 9 3 5.86925219603765 -2.86925219603765 10 6 5.81901920833362 0.180980791666376 11 7 6.2872892040238 0.7127107959762 12 6 6.3057368982798 -0.305736898279805 13 5 5.56594010521421 -0.565940105214208 14 3 5.82824305546163 -2.82824305546163 15 7 6.24933565281338 0.750664347186624 16 5 5.68320106920056 -0.683201069200558 17 7 5.65261409915705 1.34738590084295 18 7 6.55756269193553 0.44243730806447 19 7 5.9008620471931 1.0991379528069 20 6 6.10027450265332 -0.100274502653322 21 5 5.67884361987783 -0.678843619877834 22 7 7.56175867688814 -0.561758676888145 23 4 2.97354824286186 1.02645175713814 24 7 5.28175448950933 1.71824551049067 25 7 6.1423117079879 0.8576882920121 26 7 6.1423117079879 0.8576882920121 27 7 9.49382445205272 -2.49382445205272 28 3 2.03769335835904 0.962306641640964 29 7 7.98319436951923 -0.983194369519232 30 5 4.21109236667265 0.788907633327353 31 7 7.39727766381894 -0.397277663818941 32 5 4.56588373559208 0.434116264407923 33 5 5.56895713630856 -0.568957136308561 34 4 4.45493221874906 -0.454932218749061 35 5 5.2262063776982 -0.2262063776982 36 6 4.91366373994078 1.08633626005922 37 7 8.4655031839114 -1.46550318391141 38 5 4.64331106777902 0.356688932220977 39 7 5.57831951843253 1.42168048156747 40 7 6.8371392112253 0.162860788774708 41 6 6.48687977662416 -0.486879776624159 42 6 4.59468683892177 1.40531316107823 43 7 6.1543014095512 0.845698590448803 44 7 7.18500182611667 -0.185001826116668 45 6 5.30287567078229 0.697124329217706 46 6 7.8094056495506 -1.8094056495506 47 4 3.3384715392583 0.661528460741705 48 7 7.75886200010738 -0.758862000107379 49 5 4.82495917464374 0.175040825356262 50 6 6.50578289698796 -0.505782896987962 51 5 7.39412209772863 -2.39412209772863 52 3 2.32124062096038 0.67875937903962 53 7 5.96065008715856 1.03934991284144 54 6 6.55440712584521 -0.554407125845215 55 6 6.09562099238533 -0.0956209923853308 56 5 5.81586364224331 -0.815863642243308 57 5 4.24808234334968 0.751917656650315 58 7 5.96310490606365 1.03689509393635 59 7 6.77871220426027 0.221287795739735 60 7 7.39506311974298 -0.39506311974298 61 6 6.13052138306137 -0.130521383061368 62 6 4.8923881709588 1.1076118290412 63 7 6.60043223845072 0.399567761549281 64 7 6.54578990475935 0.454210095240646 65 5 4.04881946211366 0.951180537886337 66 7 6.90753343861241 0.0924665613875884 67 6 7.3057368982798 -1.3057368982798 68 5 5.07468333503607 -0.0746833350360746 69 6 6.28175448950933 -0.281754489509331 70 5 5.83713921122529 -0.837139211225291 71 5 5.46991205946541 -0.469912059465413 72 6 5.7433582774268 0.256641722573196 73 6 5.03883003526388 0.961169964736119 74 6 4.78350382019416 1.21649617980584 75 7 6.1624681378154 0.837531862184606 76 6 6.23899266653088 -0.238992666530884 77 5 4.16509982194149 0.834900178058513 78 7 6.55756269193553 0.44243730806447 79 7 5.42919855050459 1.57080144949541 80 6 5.37818024280562 0.621819757194375 81 7 6.98003880342892 0.0199611965710835 82 6 5.98129211289261 0.0187078871073924 83 6 4.66406789427602 1.33593210572398 84 7 6.15282201115803 0.847177988841974 85 6 5.45179205657374 0.548207943426255 86 7 5.86002834890965 1.13997165109035 87 7 7.02367345923255 -0.023673459232553 88 5 7.94195693749092 -2.94195693749092 89 3 2.43366724382648 0.566332756173522 90 6 5.77108255628838 0.22891744371162 91 6 7.69856002751253 -1.69856002751253 92 5 4.64096448722922 0.359035512770785 93 6 6.24808234334968 -0.248082343349685 94 6 5.57179770123741 0.428202298762586 95 6 4.83713921122529 1.16286078877471 96 7 7.37211196176794 -0.372111961767939 97 6 5.71595060290473 0.28404939709527 98 6 5.6197563270976 0.380243672902398 99 6 5.48008525412388 0.519914745876117 100 7 6.4919221954261 0.508077804573901 101 6 7.20668349111864 -1.20668349111864 102 5 5.92113490466636 -0.921134904666362 103 5 4.74059242299151 0.259407577008491 104 6 5.77887366556627 0.22112633443373 105 6 4.94465758559865 1.05534241440135 106 6 6.55454129615442 -0.554541296154416 107 5 5.01182409687694 -0.0118240968769383 108 6 8.00863596291228 -2.00863596291228 109 4 3.90476758417712 0.095232415822883 110 6 5.00863596291228 0.991364037087722 111 7 5.86002834890965 1.13997165109035 112 7 7.05270959518268 -0.052709595182682 113 5 5.0014485427201 -0.00144854272010161 114 5 4.08706274825439 0.912937251745607 115 7 9.66650605734698 -2.66650605734698 116 3 1.75853430874304 1.24146569125696 117 7 6.75002485899052 0.249975141009482 118 5 3.71601442740713 1.28398557259287 119 7 8.05828872355003 -1.05828872355003 120 5 4.50703620645165 0.492963793548347 121 3 4.0592653620773 -1.0592653620773 122 6 6.66098538770463 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-0.241952042021315 147 5 4.7055047029411 0.294495297058905 148 6 4.99531824139173 1.00468175860827 149 6 6.61010481188055 -0.610104811880548 150 6 5.61932865900855 0.38067134099145 151 5 3.89587142841345 1.10412857158655 152 6 5.47913590659341 0.520864093406585 153 7 7.13456783795716 -0.134567837957156 154 7 6.78473126158948 0.215268738410524 155 6 5.18790973120844 0.81209026879156 156 6 4.63631763566393 1.36368236433607 157 6 5.64096448722922 0.359035512770785 158 7 7.9016120180868 -0.901612018086801 159 6 6.76964981843827 -0.769649818438267 160 5 5.8923881709588 -0.892388170958799 161 5 5.90981000297906 -0.909810002979057 162 5 6.46910391473786 -1.46910391473786 163 4 NA NA 164 4 NA NA Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.327917860295575 0.655835720591149 0.672082139704425 13 0.548823856796558 0.902352286406884 0.451176143203442 14 0.903800919266921 0.192398161466157 0.0961990807330785 15 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0.122004766755267 0.0610023833776335 33 0.921528828384667 0.156942343230667 0.0784711716153334 34 0.916375854683192 0.167248290633617 0.0836241453168083 35 0.891252339136098 0.217495321727805 0.108747660863902 36 0.891038794696747 0.217922410606505 0.108961205303253 37 0.897077446892025 0.205845106215949 0.102922553107975 38 0.871169700105041 0.257660599789918 0.128830299894959 39 0.908266555750708 0.183466888498584 0.0917334442492921 40 0.884342337921846 0.231315324156308 0.115657662078154 41 0.866467636924173 0.267064726151653 0.133532363075827 42 0.886045397692188 0.227909204615624 0.113954602307812 43 0.872578620600011 0.254842758799977 0.127421379399988 44 0.8444125273072 0.311174945385601 0.1555874726928 45 0.821075565331398 0.357848869337203 0.178924434668602 46 0.85626456349909 0.287470873001819 0.14373543650091 47 0.831210532816003 0.337578934367995 0.168789467183997 48 0.81258911137302 0.374821777253959 0.187410888626979 49 0.781249530708795 0.43750093858241 0.218750469291205 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0.865716063574372 103 0.11173865046015 0.223477300920301 0.88826134953985 104 0.0916005525705022 0.183201105141004 0.908399447429498 105 0.0923702897936378 0.184740579587276 0.907629710206362 106 0.0770165077403165 0.154033015480633 0.922983492259684 107 0.0610316595124207 0.122063319024841 0.93896834048758 108 0.0987794669801699 0.19755893396034 0.90122053301983 109 0.0788020431351747 0.157604086270349 0.921197956864825 110 0.0767916645959381 0.153583329191876 0.923208335404062 111 0.075930059335053 0.151860118670106 0.924069940664947 112 0.0610796592385986 0.122159318477197 0.938920340761401 113 0.0485437858231791 0.0970875716463581 0.951456214176821 114 0.04586102192156 0.09172204384312 0.95413897807844 115 0.150815029061095 0.30163005812219 0.849184970938905 116 0.155454915782918 0.310909831565836 0.844545084217082 117 0.134958169757762 0.269916339515525 0.865041830242238 118 0.15197461237501 0.30394922475002 0.84802538762499 119 0.146432282040981 0.292864564081961 0.85356771795902 120 0.126543443796296 0.253086887592593 0.873456556203704 121 0.121767089028497 0.243534178056994 0.878232910971503 122 0.0990384975351056 0.198076995070211 0.900961502464894 123 0.0876076289285626 0.175215257857125 0.912392371071437 124 0.0671530023928754 0.134306004785751 0.932846997607125 125 0.0544048673942543 0.108809734788509 0.945595132605746 126 0.256987893388333 0.513975786776665 0.743012106611667 127 0.214634247116803 0.429268494233605 0.785365752883197 128 0.173920437237641 0.347840874475281 0.82607956276236 129 0.13963460769945 0.279269215398899 0.86036539230055 130 0.111614275164114 0.223228550328228 0.888385724835886 131 0.343389552749515 0.68677910549903 0.656610447250485 132 0.290613068468512 0.581226136937024 0.709386931531488 133 0.342204481414239 0.684408962828478 0.657795518585761 134 0.386523352524824 0.773046705049648 0.613476647475176 135 0.344256471015982 0.688512942031963 0.655743528984018 136 0.466602965793652 0.933205931587303 0.533397034206348 137 0.422481373749491 0.844962747498981 0.577518626250509 138 0.350008924553949 0.700017849107897 0.649991075446051 139 0.723947107390342 0.552105785219317 0.276052892609658 140 0.654807707494753 0.690384585010495 0.345192292505247 141 0.632447241942376 0.735105516115248 0.367552758057624 142 0.628857659585733 0.742284680828534 0.371142340414267 143 0.55764896236793 0.884702075264139 0.442351037632069 144 0.488164154359083 0.976328308718165 0.511835845640917 145 0.571667930450284 0.856664139099432 0.428332069549716 146 0.568068706254014 0.863862587491972 0.431931293745986 147 0.484130017125987 0.968260034251975 0.515869982874013 148 0.365165524438764 0.730331048877527 0.634834475561236 149 0.258679194169434 0.517358388338868 0.741320805830566 150 0.154013255904754 0.308026511809509 0.845986744095246 151 0.752771670267674 0.494456659464651 0.247228329732326 152 0.566113444098601 0.867773111802798 0.433886555901399 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 3 0.0212765957446809 OK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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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