Lineaire trend 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, 18 Dec 2010 13:10:54 +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/t12926778162lwz4ly85eqbw3a.htm/, Retrieved Sat, 18 Dec 2010 14:10:27 +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/t12926778162lwz4ly85eqbw3a.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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46 62 66 59 58 61 41 27 58 70 49 59 44 36 72 45 56 54 53 35 61 52 47 51 52 63 74 45 51 64 36 30 55 64 39 40 63 45 59 55 40 64 27 28 45 57 45 69 60 56 58 50 51 53 37 22 55 70 62 58 39 49 58 47 42 62 39 40 72 70 54 65

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 Faillissementen[t] = + 57.275 -6.40535714285716M1[t] -5.23214285714285M2[t] + 7.44107142857144M3[t] -6.88571428571428M4[t] -7.37916666666667M5[t] + 2.62738095238096M6[t] -18.1994047619048M7[t] -26.6928571428571M8[t] + 0.647023809523812M9[t] + 6.8202380952381M10[t] -7.67321428571428M11[t] -0.00654761904761901t + 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) 57.275 3.86125 14.8333 0 0 M1 -6.40535714285716 4.727887 -1.3548 0.180645 0.090323 M2 -5.23214285714285 4.723019 -1.1078 0.272446 0.136223 M3 7.44107142857144 4.718609 1.577 0.120151 0.060076 M4 -6.88571428571428 4.71466 -1.4605 0.14946 0.07473 M5 -7.37916666666667 4.711173 -1.5663 0.122624 0.061312 M6 2.62738095238096 4.708149 0.558 0.578922 0.289461 M7 -18.1994047619048 4.705588 -3.8676 0.000277 0.000138 M8 -26.6928571428571 4.703492 -5.6751 0 0 M9 0.647023809523812 4.701861 0.1376 0.891017 0.445509 M10 6.8202380952381 4.700696 1.4509 0.152104 0.076052 M11 -7.67321428571428 4.699997 -1.6326 0.107879 0.05394 t -0.00654761904761901 0.046811 -0.1399 0.889236 0.444618 Multiple Linear Regression - Regression Statistics Multiple R 0.788766683784605 R-squared 0.622152881448563 Adjusted R-squared 0.54530262004827 F-TEST (value) 8.09565081643555 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 1.05415345341697e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.14022956487382 Sum Squared Residuals 3909.5369047619 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 46 50.8630952380953 -4.8630952380953 2 62 52.0297619047619 9.97023809523812 3 66 64.6964285714286 1.30357142857142 4 59 50.3630952380953 8.63690476190474 5 58 49.8630952380953 8.13690476190475 6 61 59.8630952380952 1.13690476190478 7 41 39.0297619047619 1.97023809523810 8 27 30.5297619047619 -3.52976190476191 9 58 57.8630952380952 0.136904761904763 10 70 64.0297619047619 5.9702380952381 11 49 49.5297619047619 -0.529761904761905 12 59 57.1964285714286 1.80357142857143 13 44 50.7845238095238 -6.7845238095238 14 36 51.9511904761905 -15.9511904761905 15 72 64.6178571428571 7.38214285714286 16 45 50.2845238095238 -5.2845238095238 17 56 49.7845238095238 6.21547619047619 18 54 59.7845238095238 -5.78452380952381 19 53 38.9511904761905 14.0488095238095 20 35 30.4511904761905 4.54880952380952 21 61 57.7845238095238 3.21547619047619 22 52 63.9511904761905 -11.9511904761905 23 47 49.4511904761905 -2.45119047619047 24 51 57.1178571428571 -6.11785714285714 25 52 50.7059523809524 1.29404761904763 26 63 51.8726190476191 11.1273809523809 27 74 64.5392857142857 9.46071428571428 28 45 50.2059523809524 -5.20595238095237 29 51 49.7059523809524 1.29404761904762 30 64 59.7059523809524 4.29404761904762 31 36 38.8726190476191 -2.87261904761905 32 30 30.3726190476190 -0.372619047619048 33 55 57.7059523809524 -2.70595238095238 34 64 63.872619047619 0.127380952380954 35 39 49.3726190476191 -10.3726190476191 36 40 57.0392857142857 -17.0392857142857 37 63 50.6273809523810 12.3726190476190 38 45 51.7940476190476 -6.79404761904762 39 59 64.4607142857143 -5.46071428571429 40 55 50.1273809523809 4.87261904761905 41 40 49.6273809523809 -9.62738095238095 42 64 59.627380952381 4.37261904761904 43 27 38.7940476190476 -11.7940476190476 44 28 30.2940476190476 -2.29404761904762 45 45 57.627380952381 -12.6273809523810 46 57 63.7940476190476 -6.79404761904762 47 45 49.2940476190476 -4.29404761904762 48 69 56.9607142857143 12.0392857142857 49 60 50.5488095238095 9.45119047619048 50 56 51.7154761904762 4.28452380952381 51 58 64.3821428571429 -6.38214285714286 52 50 50.0488095238095 -0.0488095238095161 53 51 49.5488095238095 1.45119047619048 54 53 59.5488095238095 -6.54880952380953 55 37 38.7154761904762 -1.71547619047619 56 22 30.2154761904762 -8.21547619047619 57 55 57.5488095238095 -2.54880952380953 58 70 63.7154761904762 6.2845238095238 59 62 49.2154761904762 12.7845238095238 60 58 56.8821428571429 1.11785714285715 61 39 50.4702380952381 -11.4702380952381 62 49 51.6369047619048 -2.63690476190476 63 58 64.3035714285714 -6.30357142857143 64 47 49.9702380952381 -2.97023809523809 65 42 49.4702380952381 -7.47023809523809 66 62 59.4702380952381 2.5297619047619 67 39 38.6369047619048 0.363095238095237 68 40 30.1369047619048 9.86309523809524 69 72 57.4702380952381 14.5297619047619 70 70 63.6369047619048 6.36309523809523 71 54 49.1369047619048 4.86309523809524 72 65 56.8035714285714 8.19642857142857 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.732908727843819 0.534182544312363 0.267091272156181 17 0.631003933477688 0.737992133044624 0.368996066522312 18 0.488125797563982 0.976251595127964 0.511874202436018 19 0.673963118555837 0.652073762888326 0.326036881444163 20 0.659490685854953 0.681018628290095 0.340509314145047 21 0.58096779692689 0.83806440614622 0.41903220307311 22 0.625590025101047 0.748819949797907 0.374409974898953 23 0.524313972051933 0.951372055896135 0.475686027948067 24 0.436530453392634 0.873060906785268 0.563469546607366 25 0.439927496985149 0.879854993970298 0.560072503014851 26 0.571787650543135 0.85642469891373 0.428212349456865 27 0.601740266554453 0.796519466891093 0.398259733445547 28 0.539797737989977 0.920404524020047 0.460202262010023 29 0.502296256634934 0.995407486730132 0.497703743365066 30 0.473926491919632 0.947852983839264 0.526073508080368 31 0.459139191357033 0.918278382714065 0.540860808642967 32 0.385693243894581 0.771386487789162 0.614306756105419 33 0.314758926147807 0.629517852295614 0.685241073852193 34 0.258396865800558 0.516793731601116 0.741603134199442 35 0.237209928500533 0.474419857001065 0.762790071499468 36 0.383047870256918 0.766095740513835 0.616952129743082 37 0.589507313061928 0.820985373876143 0.410492686938072 38 0.534981934200494 0.930036131599012 0.465018065799506 39 0.49596354433266 0.99192708866532 0.50403645566734 40 0.494713758346348 0.989427516692696 0.505286241653652 41 0.470411590767585 0.94082318153517 0.529588409232415 42 0.473422178619643 0.946844357239285 0.526577821380357 43 0.467131634558849 0.934263269117697 0.532868365441151 44 0.381538540937047 0.763077081874094 0.618461459062953 45 0.442794561069322 0.885589122138644 0.557205438930678 46 0.426861064453727 0.853722128907455 0.573138935546273 47 0.453798957218836 0.907597914437671 0.546201042781164 48 0.533426515180371 0.933146969639258 0.466573484819629 49 0.773547723846288 0.452904552307424 0.226452276153712 50 0.757596585262114 0.484806829475771 0.242403414737886 51 0.678317374167358 0.643365251665284 0.321682625832642 52 0.606006291861958 0.787987416276085 0.393993708138043 53 0.67579927934054 0.648401441318918 0.324200720659459 54 0.554229059479104 0.891541881041793 0.445770940520896 55 0.423749258028762 0.847498516057524 0.576250741971238 56 0.441613575689106 0.883227151378212 0.558386424310894 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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