Paper TSA MR 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 19:23:16 +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/t1292700139vhp98lxq136t82x.htm/, Retrieved Sat, 18 Dec 2010 20:22:20 +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/t1292700139vhp98lxq136t82x.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:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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67 189 342 432 517 623 605 716 677 710 839 886 891 917 820 793 932 906 844 801 957 1159 1264 1097 1240 1411 1535 1862 1894 2239 2465 2423 2692 2856 3450 4162 4260 4225 4092 4160 3896 3628 3754 3749 3907 4449 5272 6197 6446 7157 7559 7674 6929 7156 6805 7095 7222 7593 7910

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Faillissementen[t] = -1116.53126826417 + 137.414319111631t + 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) -1116.53126826417 216.919568 -5.1472 3e-06 2e-06 t 137.414319111631 6.288184 21.8528 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.94518097525683 R-squared 0.89336707598745 Adjusted R-squared 0.891496322934599 F-TEST (value) 477.544096280167 F-TEST (DF numerator) 1 F-TEST (DF denominator) 57 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 822.527174207404 Sum Squared Residuals 38563404.2816482 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 67 -979.116949152542 1046.11694915254 2 189 -841.702630040915 1030.70263004091 3 342 -704.288310929281 1046.28831092928 4 432 -566.87399181765 998.87399181765 5 517 -429.45967270602 946.45967270602 6 623 -292.045353594390 915.04535359439 7 605 -154.631034482758 759.631034482758 8 716 -17.2167153711282 733.216715371128 9 677 120.197603740503 556.802396259497 10 710 257.611922852133 452.388077147867 11 839 395.026241963764 443.973758036236 12 886 532.440561075395 353.559438924605 13 891 669.854880187025 221.145119812975 14 917 807.269199298656 109.730800701344 15 820 944.683518410286 -124.683518410286 16 793 1082.09783752192 -289.097837521917 17 932 1219.51215663355 -287.512156633548 18 906 1356.92647574518 -450.926475745178 19 844 1494.34079485681 -650.340794856809 20 801 1631.75511396844 -830.75511396844 21 957 1769.16943308007 -812.16943308007 22 1159 1906.5837521917 -747.583752191701 23 1264 2043.99807130333 -779.998071303331 24 1097 2181.41239041496 -1084.41239041496 25 1240 2318.82670952659 -1078.82670952659 26 1411 2456.24102863822 -1045.24102863822 27 1535 2593.65534774985 -1058.65534774985 28 1862 2731.06966686148 -869.069666861485 29 1894 2868.48398597312 -974.483985973115 30 2239 3005.89830508475 -766.898305084746 31 2465 3143.31262419638 -678.312624196376 32 2423 3280.72694330801 -857.726943308007 33 2692 3418.14126241964 -726.141262419638 34 2856 3555.55558153127 -699.555581531268 35 3450 3692.9699006429 -242.969900642899 36 4162 3830.38421975453 331.615780245471 37 4260 3967.79853886616 292.20146113384 38 4225 4105.21285797779 119.787142022209 39 4092 4242.62717708942 -150.627177089421 40 4160 4380.04149620105 -220.041496201052 41 3896 4517.45581531268 -621.455815312683 42 3628 4654.87013442431 -1026.87013442431 43 3754 4792.28445353594 -1038.28445353594 44 3749 4929.69877264757 -1180.69877264757 45 3907 5067.1130917592 -1160.11309175920 46 4449 5204.52741087084 -755.527410870836 47 5272 5341.94172998247 -69.9417299824663 48 6197 5479.3560490941 717.643950905903 49 6446 5616.77036820573 829.229631794272 50 7157 5754.18468731736 1402.81531268264 51 7559 5891.59900642899 1667.40099357101 52 7674 6029.01332554062 1644.98667445938 53 6929 6166.42764465225 762.57235534775 54 7156 6303.84196376388 852.15803623612 55 6805 6441.25628287551 363.743717124489 56 7095 6578.67060198714 516.329398012858 57 7222 6716.08492109877 505.915078901228 58 7593 6853.4992402104 739.500759789597 59 7910 6990.91355932203 919.086440677966 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 4.42271496312226e-05 8.84542992624453e-05 0.999955772850369 6 1.90762692546178e-06 3.81525385092355e-06 0.999998092373075 7 4.79758078960742e-06 9.59516157921484e-06 0.99999520241921 8 5.4329239113529e-07 1.08658478227058e-06 0.999999456707609 9 5.48037715144814e-07 1.09607543028963e-06 0.999999451962285 10 2.60316508013353e-07 5.20633016026707e-07 0.999999739683492 11 3.96599541294006e-08 7.93199082588011e-08 0.999999960340046 12 6.83266171073095e-09 1.36653234214619e-08 0.999999993167338 13 2.07781253226046e-09 4.15562506452092e-09 0.999999997922188 14 8.1061629245219e-10 1.62123258490438e-09 0.999999999189384 15 3.47116487799495e-09 6.9423297559899e-09 0.999999996528835 16 1.05528798238545e-08 2.11057596477090e-08 0.99999998944712 17 4.17282536463961e-09 8.34565072927921e-09 0.999999995827175 18 2.43155410333443e-09 4.86310820666886e-09 0.999999997568446 19 2.91522993851115e-09 5.83045987702229e-09 0.99999999708477 20 4.34579521009899e-09 8.69159042019798e-09 0.999999995654205 21 1.32041948983619e-09 2.64083897967239e-09 0.99999999867958 22 3.80887523644684e-10 7.61775047289368e-10 0.999999999619112 23 1.45119517810022e-10 2.90239035620043e-10 0.99999999985488 24 3.58390415284385e-11 7.1678083056877e-11 0.999999999964161 25 7.08902366188324e-12 1.41780473237665e-11 0.999999999992911 26 2.68794526214162e-12 5.37589052428323e-12 0.999999999997312 27 1.85408511608094e-12 3.70817023216188e-12 0.999999999998146 28 4.42458851643153e-11 8.84917703286306e-11 0.999999999955754 29 1.28008636165601e-10 2.56017272331201e-10 0.999999999871991 30 4.24486507461142e-09 8.48973014922283e-09 0.999999995755135 31 9.2268313608535e-08 1.8453662721707e-07 0.999999907731686 32 1.91178110060626e-07 3.82356220121252e-07 0.99999980882189 33 7.47608528771833e-07 1.49521705754367e-06 0.999999252391471 34 2.24543969288755e-06 4.4908793857751e-06 0.999997754560307 35 5.14586780493138e-05 0.000102917356098628 0.99994854132195 36 0.00412650645896617 0.00825301291793235 0.995873493541034 37 0.0300897637321575 0.060179527464315 0.969910236267842 38 0.0707872896808718 0.141574579361744 0.929212710319128 39 0.0873877744650838 0.174775548930168 0.912612225534916 40 0.0950176630048566 0.190035326009713 0.904982336995143 41 0.0696201023164294 0.139240204632859 0.93037989768357 42 0.0491845691876802 0.0983691383753604 0.95081543081232 43 0.0387534250252959 0.0775068500505919 0.961246574974704 44 0.0504411758652126 0.100882351730425 0.949558824134787 45 0.137778380513187 0.275556761026374 0.862221619486813 46 0.437541155771487 0.875082311542975 0.562458844228513 47 0.794190131139567 0.411619737720867 0.205809868860433 48 0.894942986631059 0.210114026737883 0.105057013368941 49 0.94806142287045 0.1038771542591 0.05193857712955 50 0.945549615663684 0.108900768672631 0.0544503843363156 51 0.957780914301864 0.0844381713962718 0.0422190856981359 52 0.995792780349283 0.00841443930143434 0.00420721965071717 53 0.988567053527849 0.0228658929443029 0.0114329464721515 54 0.999166717460474 0.00166656507905257 0.000833282539526286 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 34 0.68 NOK 5% type I error level 35 0.7 NOK 10% type I error level 39 0.78 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 1 ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ; par4 = 1 ;

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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