Faillissementen over de laatste 4 maanden

*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, 18 Dec 2010 13:37:07 +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/18/t1292679695il88z8rxdmyp7g7.htm/, Retrieved Sat, 18 Dec 2010 14:41:46 +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/18/t1292679695il88z8rxdmyp7g7.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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58 59 66 62 46 61 58 59 66 62 41 61 58 59 66 27 41 61 58 59 58 27 41 61 58 70 58 27 41 61 49 70 58 27 41 59 49 70 58 27 44 59 49 70 58 36 44 59 49 70 72 36 44 59 49 45 72 36 44 59 56 45 72 36 44 54 56 45 72 36 53 54 56 45 72 35 53 54 56 45 61 35 53 54 56 52 61 35 53 54 47 52 61 35 53 51 47 52 61 35 52 51 47 52 61 63 52 51 47 52 74 63 52 51 47 45 74 63 52 51 51 45 74 63 52 64 51 45 74 63 36 64 51 45 74 30 36 64 51 45 55 30 36 64 51 64 55 30 36 64 39 64 55 30 36 40 39 64 55 30 63 40 39 64 55 45 63 40 39 64 59 45 63 40 39 55 59 45 63 40 40 55 59 45 63 64 40 55 59 45 27 64 40 55 59 28 27 64 40 55 45 28 27 64 40 57 45 28 27 64 45 57 45 28 27 69 45 57 45 28 60 69 45 57 45 56 60 69 45 57 58 56 60 69 45 50 58 56 60 69 51 50 58 56 60 53 51 50 58 56 37 53 51 50 58 22 37 53 51 50 55 22 37 53 51 70 55 22 37 53 62 70 55 22 37 58 62 70 55 22 39 58 62 70 55 49 39 58 62 70 58 49 39 58 62 47 58 49 39 58 42 47 58 49 39 62 42 47 58 49 39 62 42 47 58 40 39 62 42 47 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 16 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation faillissementen[t] = + 44.9943140478135 + 0.119676240683047`Y-1`[t] + 0.118023330461420`Y-2`[t] -0.114070297649060`Y-3`[t] -0.0825692584978275`Y-4`[t] + 0.889367993868057M1[t] + 14.1736152636581M2[t] -8.39507896223981M3[t] -16.831064932218M4[t] + 15.0692743531417M5[t] + 17.4087369750493M6[t] -3.7535077827975M7[t] + 7.3282567821366M8[t] + 5.64905477660003M9[t] + 2.49342334199798M10[t] + 17.1748580182210M11[t] + 0.00847982563409131t + 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) 44.9943140478135 15.291612 2.9424 0.00489 0.002445 `Y-1` 0.119676240683047 0.140334 0.8528 0.397759 0.198879 `Y-2` 0.118023330461420 0.139463 0.8463 0.401354 0.200677 `Y-3` -0.114070297649060 0.138079 -0.8261 0.412581 0.20629 `Y-4` -0.0825692584978275 0.144016 -0.5733 0.568938 0.284469 M1 0.889367993868057 5.962993 0.1491 0.882025 0.441013 M2 14.1736152636581 5.836522 2.4284 0.01873 0.009365 M3 -8.39507896223981 5.188471 -1.618 0.111826 0.055913 M4 -16.831064932218 6.524153 -2.5798 0.01281 0.006405 M5 15.0692743531417 7.271138 2.0725 0.043294 0.021647 M6 17.4087369750493 5.930643 2.9354 0.004985 0.002493 M7 -3.7535077827975 6.381471 -0.5882 0.559002 0.279501 M8 7.3282567821366 7.257272 1.0098 0.317367 0.158684 M9 5.64905477660003 5.630819 1.0032 0.320482 0.160241 M10 2.49342334199798 5.641326 0.442 0.660363 0.330182 M11 17.1748580182210 5.830963 2.9455 0.004849 0.002424 t 0.00847982563409131 0.052189 0.1625 0.871567 0.435784 Multiple Linear Regression - Regression Statistics Multiple R 0.80610013552331 R-squared 0.649797428490698 Adjusted R-squared 0.539929955076015 F-TEST (value) 5.91437491274698 F-TEST (DF numerator) 16 F-TEST (DF denominator) 51 p-value 5.17198614380376e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.26768004305843 Sum Squared Residuals 3486.08119801372 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 58 49.8720555329274 8.12794446707255 2 61 60.441553747877 0.558446252122982 3 41 38.5905597887531 2.40944021124695 4 27 28.8156539292661 -1.81565392926611 5 58 56.4288974270195 1.57110257298047 6 70 62.8681748867635 7.13182511323652 7 49 50.0576174240948 -1.05761742409475 8 59 57.6707311177047 1.32926888229526 9 44 50.7897908197215 -6.78979081972154 10 36 48.4323740537784 -12.4323740537784 11 72 60.9877801252136 11.0122198747864 12 45 48.0709218332826 -3.07092183328265 13 56 52.1374523096136 3.86254769038645 14 54 60.1140114827093 -6.11401148270931 15 53 38.7201059667579 14.2798940332421 16 35 30.9114736261095 4.08852637389046 17 61 59.8679758261691 1.13202417383088 18 52 63.4822893978091 -11.4822893978091 19 47 46.4558795076269 0.544120492373131 20 51 54.4059516347124 -3.40595163471238 21 52 51.503649723133 0.496350276866989 22 63 50.2617424914195 12.7382575085805 23 74 66.3426840731445 7.65731592685548 24 45 51.3466538315063 -6.34665383150633 25 51 48.7348047736383 2.26519522636174 26 64 57.1598776121637 6.8401223878363 27 36 39.2633711118947 -3.26337111189466 28 30 30.7293202349663 -0.729320234966344 29 55 56.6370992285174 -1.63709922851738 30 64 63.3893756840686 0.610624315931397 31 39 49.2596412033724 -10.2596412033724 32 40 56.0638476607776 -16.0638476607776 33 63 48.4713543187355 14.5286456812645 34 45 50.3034136906851 -5.30341369068506 35 59 67.5038536256567 -8.50385362565667 36 55 47.1823367499006 7.81766325009939 37 40 49.4079786453635 -9.40797864536349 38 64 60.3227312945703 3.67726870542972 39 27 38.1647082854049 -11.1647082854049 40 28 30.1830726655894 -2.18307266558940 41 45 56.3455565240837 -11.3455565240837 42 57 63.084957202766 -6.08495720276593 43 45 48.3146960433645 -3.31469604336451 44 69 57.3633411927413 11.6366588072587 45 60 54.3760478574431 5.62395214255686 46 56 53.3623824832166 2.63761751678336 47 58 64.7645260065853 -6.76452600658531 48 50 46.4103774484125 3.58962255158754 49 51 47.7862665204498 3.21373347955025 50 53 60.3566196515587 -7.35661965155874 51 37 38.9012049273193 -1.90120492731928 52 22 29.3414093633028 -7.34140936330281 53 55 57.2560017228723 -2.25600172287228 54 70 63.4428964014225 6.55710359857752 55 62 51.0112075853835 10.9887924146165 56 58 60.388611062457 -2.38861106245705 57 39 52.8591572809668 -13.8591572809668 58 49 46.6400872809004 2.35991271909964 59 58 61.4011561693998 -3.40115616939985 60 47 48.989710136898 -1.98971013689797 61 42 50.0614422180075 -8.0614422180075 62 62 59.605206211121 2.39479378887905 63 39 39.3600499198702 -0.360049919870194 64 40 32.0190701807658 7.9809298192342 65 72 59.464469271338 12.5355307286620 66 70 66.7323064271704 3.26769357282964 67 54 50.900958236158 3.09904176384200 68 65 56.1075173316069 8.89248266839315 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.499775094575356 0.999550189150712 0.500224905424644 21 0.329358084977960 0.658716169955921 0.67064191502204 22 0.678483764558413 0.643032470883175 0.321516235441587 23 0.647087399647295 0.70582520070541 0.352912600352705 24 0.576068197602718 0.847863604794563 0.423931802397282 25 0.48934015967609 0.97868031935218 0.51065984032391 26 0.449535992807091 0.899071985614182 0.550464007192909 27 0.532078332542743 0.935843334914513 0.467921667457257 28 0.43533910013304 0.87067820026608 0.56466089986696 29 0.349282770173304 0.698565540346607 0.650717229826696 30 0.2697338047305 0.539467609461 0.7302661952695 31 0.250029620382113 0.500059240764226 0.749970379617887 32 0.367891504095873 0.735783008191746 0.632108495904127 33 0.614607349882864 0.770785300234272 0.385392650117136 34 0.561448165581717 0.877103668836566 0.438551834418283 35 0.537619591289099 0.924760817421802 0.462380408710901 36 0.545942934279772 0.908114131440456 0.454057065720228 37 0.518731104688556 0.962537790622888 0.481268895311444 38 0.54210055479825 0.9157988904035 0.45789944520175 39 0.561473762930726 0.877052474138549 0.438526237069274 40 0.466363688841631 0.932727377683262 0.533636311158369 41 0.529912147077173 0.940175705845653 0.470087852922826 42 0.437363828339427 0.874727656678855 0.562636171660573 43 0.41329455719516 0.82658911439032 0.58670544280484 44 0.516032344182979 0.967935311634042 0.483967655817021 45 0.552415202377455 0.89516959524509 0.447584797622545 46 0.457292846751372 0.914585693502744 0.542707153248628 47 0.339954065172612 0.679908130345224 0.660045934827388 48 0.258525613650123 0.517051227300246 0.741474386349877 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 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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