transport

*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: Sat, 20 Dec 2008 01:48:40 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/20/t1229763324i7vnclqwrg0hp2p.htm/, Retrieved Sat, 20 Dec 2008 09:55:34 +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/2008/Dec/20/t1229763324i7vnclqwrg0hp2p.htm/}, year = {2008}, } @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 = {2008}, 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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124.9 11554.5 132 13182.1 151.4 14800.1 108.9 12150.7 121.3 14478.2 123.4 13253.9 90.3 12036.8 79.3 12653.2 117.2 14035.4 116.9 14571.4 120.8 15400.9 96.1 14283.2 100.8 14485.3 105.3 14196.3 116.1 15559.1 112.8 13767.4 114.5 14634 117.2 14381.1 77.1 12509.9 80.1 12122.3 120.3 13122.3 133.4 13908.7 109.4 13456.5 93.2 12441.6 91.2 12953 99.2 13057.2 108.2 14350.1 101.5 13830.2 106.9 13755.5 104.4 13574.4 77.9 12802.6 60 11737.3 99.5 13850.2 95 15081.8 105.6 13653.3 102.5 14019.1 93.3 13962 97.3 13768.7 127 14747.1 111.7 13858.1 96.4 13188 133 13693.1 72.2 12970 95.8 11392.8 124.1 13985.2 127.6 14994.7 110.7 13584.7 104.6 14257.8 112.7 13553.4 115.3 14007.3 139.4 16535.8 119 14721.4 97.4 13664.6 154 16405.9 81.5 13829.4 88.8 13735.6 127.7 15870.5 105.1 15962.4 114.9 15744.1 106.4 16083.7 104.5 14863.9 121.6 15533.1 141.4 17473.1 99 15925.5 126.7 15573.7 134.1 17495 81.3 14155.8 88.6 14913.9 132.7 17250.4 132.9 15879.8 134.4 17647.8 103.7 17749.9

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation transport[t] = + 54.9985096492864 + 0.00311260210866943Invoer[t] + 7.3549953429037M1[t] + 13.3408353823988M2[t] + 27.0981087061434M3[t] + 10.1103238103206M4[t] + 11.2871096412385M5[t] + 26.6165486678778M6[t] -15.5703016190040M7[t] -12.6127705975196M8[t] + 19.5408533168305M9[t] + 16.5889077671826M10[t] + 14.5450972375246M11[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) 54.9985096492864 17.758212 3.0971 0.00299 0.001495 Invoer 0.00311260210866943 0.001155 2.695 0.009156 0.004578 M1 7.3549953429037 6.922864 1.0624 0.292374 0.146187 M2 13.3408353823988 6.842687 1.9496 0.055976 0.027988 M3 27.0981087061434 6.830554 3.9672 2e-04 1e-04 M4 10.1103238103206 6.829354 1.4804 0.144081 0.072041 M5 11.2871096412385 6.806381 1.6583 0.102562 0.051281 M6 26.6165486678778 6.772161 3.9303 0.000225 0.000113 M7 -15.5703016190040 7.069044 -2.2026 0.031542 0.015771 M8 -12.6127705975196 7.17287 -1.7584 0.083866 0.041933 M9 19.5408533168305 6.773582 2.8849 0.00546 0.00273 M10 16.5889077671826 6.778843 2.4472 0.017395 0.008698 M11 14.5450972375246 6.773321 2.1474 0.03588 0.01794 Multiple Linear Regression - Regression Statistics Multiple R 0.82573390130504 R-squared 0.681836475764443 Adjusted R-squared 0.617125250496194 F-TEST (value) 10.5366027754537 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 1.02019281911225e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.7297225778502 Sum Squared Residuals 8117.59711344646 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 124.9 98.3180660568106 26.5819339431894 2 132 109.369977288376 22.6300227116235 3 151.4 128.163440823948 23.2365591760517 4 108.9 102.929127901417 5.97087209858339 5 121.3 111.350495140263 9.94950485973734 6 123.4 122.869175405258 0.530824594742055 7 90.3 76.8939770919146 13.4060229080854 8 79.3 81.7701160531828 -2.47011605318282 9 117.2 118.225978602136 -1.02597860213591 10 116.9 116.942387782735 -0.0423877827347017 11 120.8 117.480480702218 3.31951929778194 12 96.1 99.4564280878336 -3.35642808783365 13 100.8 107.440480316899 -6.64048031689942 14 105.3 112.526778346989 -7.22677834698903 15 116.1 130.525905824428 -14.4259058244284 16 112.8 107.961271730503 4.8387282694975 17 114.5 111.835438548793 2.66456145120662 18 117.2 126.37770050215 -9.17770050215014 19 77.1 78.3665491495261 -1.26654914952614 20 80.1 80.1176355936903 -0.0176355936902604 21 120.3 115.383861616710 4.91613838329018 22 133.4 114.879666365319 18.5203336346805 23 109.4 111.428337162121 -2.0283371621212 24 93.2 93.724260044508 -0.524260044507987 25 91.2 102.671040105785 -11.4710401057852 26 99.2 108.981213285004 -9.78121328500368 27 108.2 126.762769875047 -18.5627698750470 28 101.5 108.156743142927 -6.65674314292694 29 106.9 109.101017596327 -2.20101759632728 30 104.4 123.866764381086 -19.4667643810865 31 77.9 79.2776077867337 -1.37760778673368 32 60 78.9192837818525 -18.9192837818525 33 99.5 117.649524691610 -18.1495246916103 34 95 118.531059899000 -23.5310598989996 35 105.6 112.040897257107 -6.44089725710735 36 102.5 98.634389870934 3.86561012906598 37 93.3 105.811655633433 -12.5116556334327 38 97.3 111.195829685322 -13.8958296853220 39 127 127.998472912189 -0.998472912188807 40 111.7 108.243584741759 3.45641525824119 41 96.4 107.334615899657 -10.9346158996574 42 133 124.236230251386 8.76376974861444 43 72.2 79.798657379725 -7.59865737972495 44 95.8 77.8469923554159 17.9530076445841 45 124.1 118.069725976281 6.03027402371932 46 127.6 118.259952255334 9.3400477446655 47 110.7 111.827372752453 -1.12737275245262 48 104.6 99.3773679942734 5.22263200572658 49 112.7 104.539846411830 8.16015358816964 50 115.3 111.938496548451 3.36150345154950 51 139.4 133.565984303966 5.83401569603419 52 119 110.930694142173 8.06930585782687 53 97.4 108.818082064649 -11.4180820646492 54 154 132.680097251784 21.319902748216 55 81.5 82.4736276319155 -0.973627631915457 56 88.8 85.1391965756066 3.66080342439335 57 127.7 123.937914731755 3.76208526824484 58 105.1 121.272017315894 -16.1720173158939 59 114.9 118.548725745913 -3.64872574591339 60 106.4 105.060668184493 1.33933181550707 61 104.5 108.618911475242 -4.11891147524166 62 121.6 116.687704845858 4.91229515414167 63 141.4 136.483426260422 4.91657373957833 64 99 114.678578341222 -15.678578341222 65 126.7 114.76035075031 11.9396492496900 66 134.1 136.070032208336 -1.97003220833587 67 81.3 83.4895809601852 -2.18958096018516 68 88.6 88.8067756402518 -0.206775640251839 69 132.7 128.232994381508 4.46700561849188 70 132.9 121.014916381718 11.8850836182822 71 134.4 124.474186380187 9.92581361981262 72 103.7 110.246885817958 -6.54688581795794 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.873751910565766 0.252496178868468 0.126248089434234 17 0.783228607972259 0.433542784055483 0.216771392027741 18 0.678622785806653 0.642754428386694 0.321377214193347 19 0.584188542026142 0.831622915947716 0.415811457973858 20 0.466014030456996 0.932028060913992 0.533985969543004 21 0.368159192842796 0.736318385685592 0.631840807157204 22 0.378648834918873 0.757297669837746 0.621351165081127 23 0.520374933863221 0.959250132273558 0.479625066136779 24 0.478117395396814 0.956234790793629 0.521882604603186 25 0.563658029860577 0.872683940278846 0.436341970139423 26 0.628544035871448 0.742911928257104 0.371455964128552 27 0.777919604412079 0.444160791175842 0.222080395587921 28 0.71595802278514 0.56808395442972 0.28404197721486 29 0.675338658944108 0.649322682111785 0.324661341055892 30 0.753016416912015 0.49396716617597 0.246983583087985 31 0.685109018884561 0.629781962230878 0.314890981115439 32 0.79425639740813 0.411487205183741 0.205743602591870 33 0.859452812524858 0.281094374950284 0.140547187475142 34 0.94965514302596 0.100689713948079 0.0503448569740393 35 0.938954619473872 0.122090761052256 0.061045380526128 36 0.915359688739643 0.169280622520713 0.0846403112603565 37 0.911553812631417 0.176892374737166 0.088446187368583 38 0.930508443895573 0.138983112208855 0.0694915561044275 39 0.906672230451227 0.186655539097546 0.093327769548773 40 0.87333592767397 0.253328144652059 0.126664072326029 41 0.887910236124765 0.224179527750470 0.112089763875235 42 0.869962201589547 0.260075596820906 0.130037798410453 43 0.834561643099469 0.330876713801063 0.165438356900531 44 0.842676003530396 0.314647992939209 0.157323996469604 45 0.792772573142498 0.414454853715005 0.207227426857502 46 0.767702971676678 0.464594056646644 0.232297028323322 47 0.704369721358702 0.591260557282596 0.295630278641298 48 0.627498487989288 0.745003024021424 0.372501512010712 49 0.576068717376676 0.847862565246648 0.423931282623324 50 0.476844064264627 0.953688128529254 0.523155935735373 51 0.393597699703782 0.787195399407564 0.606402300296218 52 0.465565221008086 0.931130442016172 0.534434778991914 53 0.540519848514846 0.918960302970308 0.459480151485154 54 0.684114701635689 0.631770596728622 0.315885298364311 55 0.535649180832118 0.928701638335763 0.464350819167882 56 0.378580599604900 0.757161199209801 0.6214194003951 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 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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