Meervoudige regressie met tijdvertraging: Faillissementen

*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, 11 Dec 2010 12:31:50 +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/11/t1292070786d3lizvbc72h4atp.htm/, Retrieved Sat, 11 Dec 2010 13:33:18 +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/11/t1292070786d3lizvbc72h4atp.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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27 41 61 58 59 66 62 46 58 27 41 61 58 59 66 62 70 58 27 41 61 58 59 66 49 70 58 27 41 61 58 59 59 49 70 58 27 41 61 58 44 59 49 70 58 27 41 61 36 44 59 49 70 58 27 41 72 36 44 59 49 70 58 27 45 72 36 44 59 49 70 58 56 45 72 36 44 59 49 70 54 56 45 72 36 44 59 49 53 54 56 45 72 36 44 59 35 53 54 56 45 72 36 44 61 35 53 54 56 45 72 36 52 61 35 53 54 56 45 72 47 52 61 35 53 54 56 45 51 47 52 61 35 53 54 56 52 51 47 52 61 35 53 54 63 52 51 47 52 61 35 53 74 63 52 51 47 52 61 35 45 74 63 52 51 47 52 61 51 45 74 63 52 51 47 52 64 51 45 74 63 52 51 47 36 64 51 45 74 63 52 51 30 36 64 51 45 74 63 52 55 30 36 64 51 45 74 63 64 55 30 36 64 51 45 74 39 64 55 30 36 64 51 45 40 39 64 55 30 36 64 51 63 40 39 64 55 30 36 64 45 63 40 39 64 55 30 36 59 45 63 40 39 64 55 30 55 59 45 63 40 39 64 55 40 55 59 45 63 40 39 64 64 40 55 59 45 63 40 39 27 64 40 55 59 45 63 40 28 27 64 40 55 59 45 63 45 28 27 64 40 55 59 45 57 45 28 27 64 40 55 59 45 57 45 28 27 64 40 55 69 45 57 45 28 27 64 40 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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Yt[t] = + 54.1289882375707 + 0.0743007158608039`Yt-1`[t] + 0.0785777695501799`Yt-2`[t] -0.161410948493399`Yt-3`[t] -0.0651190403399635`Yt-4`[t] -0.0877429693266317`Yt-5`[t] -0.116882268075762`Yt-6`[t] -0.0333284658880138`Yt-7`[t] -6.96007335314391M1[t] + 24.4760936488194M2[t] + 25.2621720483599M3[t] + 5.75978078634362M4[t] + 17.1927602981443M5[t] + 11.9528555928096M6[t] + 8.5129331116677M7[t] + 26.9648752251198M8[t] + 10.6154076472889M9[t] + 8.92522966959725M10[t] + 23.8060185192799M11[t] + 0.00905195872685246t + 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) 54.1289882375707 26.324613 2.0562 0.045589 0.022795 `Yt-1` 0.0743007158608039 0.152033 0.4887 0.627417 0.313709 `Yt-2` 0.0785777695501799 0.151406 0.519 0.606313 0.303157 `Yt-3` -0.161410948493399 0.150009 -1.076 0.287659 0.143829 `Yt-4` -0.0651190403399635 0.157392 -0.4137 0.681031 0.340515 `Yt-5` -0.0877429693266317 0.157252 -0.558 0.579625 0.289813 `Yt-6` -0.116882268075762 0.155699 -0.7507 0.456744 0.228372 `Yt-7` -0.0333284658880138 0.158656 -0.2101 0.834564 0.417282 M1 -6.96007335314391 7.519101 -0.9257 0.359564 0.179782 M2 24.4760936488194 8.155344 3.0012 0.004375 0.002187 M3 25.2621720483599 6.04489 4.1791 0.000133 6.7e-05 M4 5.75978078634362 7.66477 0.7515 0.456287 0.228144 M5 17.1927602981443 8.936198 1.9239 0.0607 0.03035 M6 11.9528555928096 7.32759 1.6312 0.109826 0.054913 M7 8.5129331116677 7.461836 1.1409 0.259962 0.129981 M8 26.9648752251198 8.368565 3.2222 0.002367 0.001184 M9 10.6154076472889 5.971208 1.7778 0.0822 0.0411 M10 8.92522966959725 6.805117 1.3115 0.196326 0.098163 M11 23.8060185192799 7.018994 3.3917 0.001457 0.000728 t 0.00905195872685246 0.061558 0.147 0.88375 0.441875 Multiple Linear Regression - Regression Statistics Multiple R 0.811379738044797 R-squared 0.658337079309643 Adjusted R-squared 0.514079401684825 F-TEST (value) 4.56361900558133 F-TEST (DF numerator) 19 F-TEST (DF denominator) 45 p-value 1.44195929475677e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.58721839245433 Sum Squared Residuals 3318.31438738677 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 27 27.2428357162288 -0.242835716228843 2 58 55.2705917174992 2.72940828250075 3 70 61.0744223249019 8.92557767509808 4 49 48.5576891750165 0.442310824983464 5 59 56.7278070567268 2.27219294327316 6 44 50.1002682101377 -6.10026821013769 7 36 48.5317551012895 -12.5317551012895 8 72 60.7633998456986 11.2366001543014 9 45 47.645994361605 -2.64599436160503 10 56 50.2327782569202 5.7672217430798 11 54 59.3757049816912 -5.3757049816912 12 53 40.4301957284209 12.5698042715791 13 35 31.5066499719619 3.49335002803808 14 61 59.5703169790504 1.42968302094963 15 52 62.1653389304528 -10.1653389304528 16 47 46.8064808747382 0.193519125261784 17 51 54.1001612860111 -3.10016128601111 18 52 50.2961386904283 1.70386130957168 19 63 48.5028981563607 14.4971018436393 20 74 65.890389420239 8.10961057976096 21 45 51.4338651770292 -6.43386517702917 22 51 47.1551300454501 3.84486995454986 23 64 57.3315602427127 6.66843975728733 24 36 37.7212088739993 -1.72120887399933 25 30 28.3470588412163 1.65294115878368 26 55 55.5494674237535 -0.549467423753461 27 64 63.9001229281046 0.099877071895396 28 39 48.9563064278479 -9.95630642784788 29 40 56.3408233183445 -16.3408233183445 30 63 49.5050437694402 13.4949562305598 31 45 50.7517862508023 -5.75178625080228 32 59 67.6374485666409 -8.63744856664092 33 55 47.4536944352803 7.54630556471968 34 40 50.5174710112122 -10.5174710112122 35 64 61.5891205353327 2.41087946466728 36 27 36.9884346576492 -9.98843465764918 37 28 31.9647181737141 -3.96471817371411 38 45 56.9943157283964 -11.9943157283964 39 57 64.8575592417146 -7.85755924171456 40 45 49.6203607760424 -4.62036077604241 41 69 59.245854145702 9.75414585429799 42 60 55.2483480456154 4.75165195438461 43 56 53.8147809387266 2.18521906127337 44 58 65.1056952866532 -7.10569528665319 45 50 47.5731560842657 2.42684391573433 46 51 45.5833093969619 5.41669060303809 47 53 58.2409369099814 -5.2409369099814 48 37 36.4352281666435 0.564771833356541 49 22 29.4040915584221 -7.40409155842212 50 55 58.6911076130842 -3.69110761308419 51 70 63.9924903902232 6.00750960977677 52 62 51.6440566132173 10.3559433867827 53 58 60.4573677121149 -2.45736771211495 54 39 52.8502012843783 -13.8502012843783 55 49 47.3987795528208 1.60122044717917 56 58 61.6030668807683 -3.60306688076827 57 47 47.8932899418198 -0.893289941819812 58 42 46.5113112894556 -4.51131128945557 59 62 60.462677330282 1.53732266971797 60 39 40.4249325732871 -1.42493257328708 61 40 33.5346457384567 6.46535426154332 62 72 59.9242005382163 12.0757994617837 63 70 67.0100661846029 2.98993381539714 64 54 50.4151061331377 3.58489386686232 65 65 55.1279864811006 9.87201351889938 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 23 0.813102860224024 0.373794279551952 0.186897139775976 24 0.798852893690574 0.402294212618853 0.201147106309426 25 0.74474295149927 0.510514097001459 0.255257048500729 26 0.713642566884737 0.572714866230526 0.286357433115263 27 0.629132964686915 0.741734070626171 0.370867035313085 28 0.557068759749914 0.885862480500173 0.442931240250087 29 0.651918411467033 0.696163177065934 0.348081588532967 30 0.802595111463643 0.394809777072714 0.197404888536357 31 0.728800378845895 0.54239924230821 0.271199621154105 32 0.693831082593061 0.612337834813877 0.306168917406939 33 0.694049056694841 0.611901886610318 0.305950943305159 34 0.717200186849811 0.565599626300378 0.282799813150189 35 0.65522032660536 0.68955934678928 0.34477967339464 36 0.614436448264173 0.771127103471655 0.385563551735827 37 0.519997864254213 0.960004271491575 0.480002135745787 38 0.573079277518022 0.853841444963955 0.426920722481978 39 0.459965686204521 0.919931372409042 0.540034313795479 40 0.426314586167301 0.852629172334603 0.573685413832699 41 0.396759034122893 0.793518068245786 0.603240965877107 42 0.502000006633369 0.995999986733262 0.497999993366631 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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