Paper: MR Faillissementen (verleden)

*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: Sun, 19 Dec 2010 14:49:23 +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/19/t129277017827rq0qm4z8nqss0.htm/, Retrieved Sun, 19 Dec 2010 15:49:38 +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/19/t129277017827rq0qm4z8nqss0.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:

» Textbox « » Textfile « » CSV «

627 0 724 590 722 803 608 696 0 627 724 590 722 651 825 0 696 627 724 590 691 677 0 825 696 627 724 627 656 0 677 825 696 627 634 785 0 656 677 825 696 731 412 0 785 656 677 825 475 352 0 412 785 656 677 337 839 0 352 412 785 656 803 729 0 839 352 412 785 722 696 0 729 839 352 412 590 641 0 696 729 839 352 724 695 0 641 696 729 839 627 638 0 695 641 696 729 696 762 0 638 695 641 696 825 635 0 762 638 695 641 677 721 0 635 762 638 695 656 854 0 721 635 762 638 785 418 0 854 721 635 762 412 367 0 418 854 721 635 352 824 0 367 418 854 721 839 687 0 824 367 418 854 729 601 0 687 824 367 418 696 676 0 601 687 824 367 641 740 0 676 601 687 824 695 691 0 740 676 601 687 638 683 0 691 740 676 601 762 594 0 683 691 740 676 635 729 0 594 683 691 740 721 731 0 729 594 683 691 854 386 0 731 729 594 683 418 331 0 386 731 729 594 367 706 0 331 386 731 729 824 715 0 706 331 386 731 687 657 0 715 706 331 386 601 653 0 657 715 706 331 676 642 0 653 657 715 706 740 643 0 642 653 657 715 691 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation faillissement[t] = + 179.312954050889 + 44.3969724913641crisis[t] -0.0454083334947606`t-1`[t] -0.0256592317941664`t-2`[t] -0.0949712023846764`t-3`[t] -0.0338903746825824`t-4`[t] + 0.92150086492774`t-12`[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) 179.312954050889 160.671133 1.116 0.26852 0.13426 crisis 44.3969724913641 29.457847 1.5071 0.136621 0.06831 `t-1` -0.0454083334947606 0.103766 -0.4376 0.663125 0.331563 `t-2` -0.0256592317941664 0.117178 -0.219 0.827354 0.413677 `t-3` -0.0949712023846764 0.104231 -0.9112 0.365575 0.182788 `t-4` -0.0338903746825824 0.108255 -0.3131 0.755238 0.377619 `t-12` 0.92150086492774 0.116617 7.902 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.763216614162312 R-squared 0.582499600133384 Adjusted R-squared 0.543961101684158 F-TEST (value) 15.1147456069369 F-TEST (DF numerator) 6 F-TEST (DF denominator) 65 p-value 9.60155288609599e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 115.626264491174 Sum Squared Residuals 869013.147611892 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 627 595.78772072634 31.2122792736601 2 696 651.659848270873 44.3401517291266 3 825 679.623041679433 145.376958320567 4 677 617.689720733283 59.3102792667165 5 656 624.284972623223 31.7150273767775 6 785 703.831976869419 81.1680231305815 7 412 472.292803913649 -60.2928039136494 8 352 365.76312274882 -13.7631227488197 9 839 795.938332034768 43.0616679652324 10 729 731.774857626753 -2.77485762675332 11 696 620.97499615664 75.02500384336 12 641 704.55954947926 -63.5595494792602 13 695 612.460398364585 82.5396016354146 14 638 681.86515667834 -43.86515667834 15 762 808.283243242017 -46.2832432420173 16 635 664.468583770398 -29.4685837703984 17 721 651.285457521341 69.7145424786591 18 854 759.667997115537 94.3320028844635 19 418 415.561108450601 2.43889154939859 20 367 372.792966309634 -5.79296630963431 21 824 819.52139546007 4.4786045399307 22 687 735.61333713935 -48.6133371393502 23 601 719.318216038807 -118.318216038807 24 676 634.382669523146 41.6173304768536 25 740 680.467938648196 59.5320613518039 26 691 635.922318355684 55.0776816443163 27 683 746.562975156992 -63.5629751569915 28 594 622.532999283228 -28.5329992832278 29 729 708.513294139564 20.4867058604357 30 731 829.646853761366 -98.6468537613659 31 386 433.041223703366 -47.0412237033658 32 331 391.854367208974 -60.8543672089737 33 706 819.565012805232 -113.565012805232 34 715 710.399811071624 4.6001889283759 35 657 638.035445160221 18.9645548397787 36 653 675.800529999639 -22.8005299996388 37 642 722.882822805624 -80.8828228056244 38 643 683.534725385952 -40.5347253859522 39 718 678.7450882239 39.2549117761002 40 654 594.480471726391 59.5195282736086 41 632 720.142602369862 -88.1426023698623 42 731 717.470047717896 13.5299522821041 43 392 443.554678744105 -51.5546787441054 44 344 409.983642712329 -65.9836427123293 45 792 757.767985853137 34.2320141468632 46 852 775.790293872783 76.2097061272167 47 649 724.170862585362 -75.1708625853621 48 629 687.242836233866 -58.2428362338664 49 685 662.342157442895 22.6578425571052 50 617 678.479707871134 -61.4797078711336 51 715 758.022292546142 -43.0222925461423 52 715 691.700468430393 23.2995315696065 53 629 673.473025466088 -44.4730254660883 54 916 761.604095419201 154.395904580799 55 531 435.068547711106 95.9314522888938 56 357 409.122038470214 -52.1220384702138 57 917 815.392117364984 101.607882635016 58 828 876.555584219967 -48.5555842199668 59 708 708.735863983664 -0.735863983663852 60 858 650.751570193512 207.248429806488 61 775 688.097303610541 86.902696389459 62 785 639.768039339306 145.231960660694 63 1.006 721.571921610401 -720.565921610401 64 789 714.079141185658 74.9208588143419 65 734 640.876174018532 93.1238259814677 66 906 892.0848944205 13.9151055794995 67 532 544.027063923525 -12.0270639235247 68 387 408.832869721819 -21.8328697218192 69 991 926.58303892649 64.4169610735098 70 841 850.553502373705 -9.55350237370484 71 892 757.732297079978 134.267702920022 72 782 845.04198466866 -63.0419846686606 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0735032413788997 0.147006482757799 0.9264967586211 11 0.0300134881251002 0.0600269762502005 0.9699865118749 12 0.116164291069673 0.232328582139346 0.883835708930327 13 0.0594405479873565 0.118881095974713 0.940559452012643 14 0.061781418168086 0.123562836336172 0.938218581831914 15 0.0836375822439005 0.167275164487801 0.9163624177561 16 0.0517078027605255 0.103415605521051 0.948292197239474 17 0.0302978161432875 0.0605956322865751 0.969702183856712 18 0.0222747730335727 0.0445495460671455 0.977725226966427 19 0.0113948758864185 0.0227897517728371 0.988605124113581 20 0.00562439309361093 0.0112487861872219 0.99437560690639 21 0.00277323234555857 0.00554646469111714 0.997226767654441 22 0.00167982423316816 0.00335964846633632 0.998320175766832 23 0.00314918380938055 0.00629836761876109 0.99685081619062 24 0.00167336066015782 0.00334672132031564 0.998326639339842 25 0.000890082999782387 0.00178016599956477 0.999109917000218 26 0.000493854972232076 0.000987709944464152 0.999506145027768 27 0.000436222572160719 0.000872445144321437 0.99956377742784 28 0.000247587813353395 0.00049517562670679 0.999752412186647 29 0.000112123412927019 0.000224246825854037 0.999887876587073 30 0.000146857602631442 0.000293715205262885 0.999853142397369 31 8.10546365716003e-05 0.000162109273143201 0.999918945363428 32 4.88671675022848e-05 9.77343350045696e-05 0.999951132832498 33 5.13410388845333e-05 0.000102682077769067 0.999948658961116 34 2.59982105363725e-05 5.1996421072745e-05 0.999974001789464 35 1.32282700189324e-05 2.64565400378648e-05 0.999986771729981 36 5.5881533832024e-06 1.11763067664048e-05 0.999994411846617 37 4.56830539755925e-06 9.1366107951185e-06 0.999995431694602 38 2.12282296752964e-06 4.24564593505928e-06 0.999997877177032 39 9.54186569136833e-07 1.90837313827367e-06 0.99999904581343 40 5.11358073745533e-07 1.02271614749107e-06 0.999999488641926 41 3.85524200773394e-07 7.71048401546788e-07 0.9999996144758 42 1.41904558297529e-07 2.83809116595058e-07 0.999999858095442 43 5.13892606234756e-08 1.02778521246951e-07 0.99999994861074 44 2.08468776397029e-08 4.16937552794059e-08 0.999999979153122 45 1.41998099645042e-08 2.83996199290084e-08 0.99999998580019 46 9.21827861699168e-09 1.84365572339834e-08 0.999999990781721 47 4.81727578795535e-09 9.6345515759107e-09 0.999999995182724 48 2.01021050551950e-09 4.02042101103901e-09 0.99999999798979 49 6.48708924847079e-10 1.29741784969416e-09 0.999999999351291 50 2.58621392567656e-10 5.17242785135312e-10 0.999999999741379 51 8.44509385941946e-11 1.68901877188389e-10 0.99999999991555 52 2.53545879979093e-11 5.07091759958186e-11 0.999999999974645 53 7.89397181016572e-12 1.57879436203314e-11 0.999999999992106 54 4.08100733455101e-11 8.16201466910201e-11 0.99999999995919 55 2.11987135234445e-11 4.23974270468889e-11 0.999999999978801 56 6.8646037482636e-12 1.37292074965272e-11 0.999999999993135 57 3.87204843060043e-12 7.74409686120087e-12 0.999999999996128 58 1.25022179468475e-12 2.50044358936951e-12 0.99999999999875 59 3.90589806061609e-13 7.81179612123219e-13 0.99999999999961 60 3.09795412917365e-11 6.1959082583473e-11 0.99999999996902 61 1.08243215578310e-11 2.16486431156619e-11 0.999999999989176 62 7.6719700408112e-12 1.53439400816224e-11 0.999999999992328 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 42 0.79245283018868 NOK 5% type I error level 45 0.849056603773585 NOK 10% type I error level 47 0.886792452830189 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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