Paper: Multiple Regression (crisis)

*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 19:16:06 +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/t1292786060r090y5g0vtuxn5k.htm/, Retrieved Sun, 19 Dec 2010 20:14:31 +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/t1292786060r090y5g0vtuxn5k.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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608 0 651 0 691 0 627 0 634 0 731 0 475 0 337 0 803 0 722 0 590 0 724 0 627 0 696 0 825 0 677 0 656 0 785 0 412 0 352 0 839 0 729 0 696 0 641 0 695 0 638 0 762 0 635 0 721 0 854 0 418 0 367 0 824 0 687 0 601 0 676 0 740 0 691 0 683 0 594 0 729 0 731 0 386 0 331 0 706 0 715 0 657 0 653 0 642 0 643 0 718 0 654 0 632 0 731 0 392 1 344 1 792 1 852 1 649 1 629 1 685 1 617 1 715 1 715 1 629 1 916 1 531 1 357 1 917 1 828 1 708 1 858 1 775 1 785 1 1006 1 789 1 734 1 906 1 532 1 387 1 991 1 841 1 892 1 782 1

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation faillissement[t] = + 648.925925925926 + 69.5407407407407crisis[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) 648.925925925926 20.403037 31.8054 0 0 crisis 69.5407407407407 34.140811 2.0369 0.044888 0.022444 Multiple Linear Regression - Regression Statistics Multiple R 0.219452565451463 R-squared 0.0481594284832285 Adjusted R-squared 0.036551616635463 F-TEST (value) 4.1488808670257 F-TEST (DF numerator) 1 F-TEST (DF denominator) 82 p-value 0.0448882839204829 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 149.931088657357 Sum Squared Residuals 1843305.17037037 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 608 648.925925925926 -40.9259259259263 2 651 648.925925925926 2.07407407407415 3 691 648.925925925926 42.0740740740741 4 627 648.925925925926 -21.9259259259259 5 634 648.925925925926 -14.9259259259259 6 731 648.925925925926 82.074074074074 7 475 648.925925925926 -173.925925925926 8 337 648.925925925926 -311.925925925926 9 803 648.925925925926 154.074074074074 10 722 648.925925925926 73.0740740740741 11 590 648.925925925926 -58.9259259259259 12 724 648.925925925926 75.0740740740741 13 627 648.925925925926 -21.9259259259259 14 696 648.925925925926 47.0740740740741 15 825 648.925925925926 176.074074074074 16 677 648.925925925926 28.0740740740741 17 656 648.925925925926 7.07407407407408 18 785 648.925925925926 136.074074074074 19 412 648.925925925926 -236.925925925926 20 352 648.925925925926 -296.925925925926 21 839 648.925925925926 190.074074074074 22 729 648.925925925926 80.0740740740741 23 696 648.925925925926 47.0740740740741 24 641 648.925925925926 -7.92592592592592 25 695 648.925925925926 46.0740740740741 26 638 648.925925925926 -10.9259259259259 27 762 648.925925925926 113.074074074074 28 635 648.925925925926 -13.9259259259259 29 721 648.925925925926 72.0740740740741 30 854 648.925925925926 205.074074074074 31 418 648.925925925926 -230.925925925926 32 367 648.925925925926 -281.925925925926 33 824 648.925925925926 175.074074074074 34 687 648.925925925926 38.0740740740741 35 601 648.925925925926 -47.9259259259259 36 676 648.925925925926 27.0740740740741 37 740 648.925925925926 91.0740740740741 38 691 648.925925925926 42.0740740740741 39 683 648.925925925926 34.0740740740741 40 594 648.925925925926 -54.9259259259259 41 729 648.925925925926 80.0740740740741 42 731 648.925925925926 82.074074074074 43 386 648.925925925926 -262.925925925926 44 331 648.925925925926 -317.925925925926 45 706 648.925925925926 57.0740740740741 46 715 648.925925925926 66.0740740740741 47 657 648.925925925926 8.07407407407408 48 653 648.925925925926 4.07407407407408 49 642 648.925925925926 -6.92592592592592 50 643 648.925925925926 -5.92592592592592 51 718 648.925925925926 69.0740740740741 52 654 648.925925925926 5.07407407407408 53 632 648.925925925926 -16.9259259259259 54 731 648.925925925926 82.074074074074 55 392 718.466666666667 -326.466666666667 56 344 718.466666666667 -374.466666666667 57 792 718.466666666667 73.5333333333333 58 852 718.466666666667 133.533333333333 59 649 718.466666666667 -69.4666666666667 60 629 718.466666666667 -89.4666666666667 61 685 718.466666666667 -33.4666666666667 62 617 718.466666666667 -101.466666666667 63 715 718.466666666667 -3.46666666666668 64 715 718.466666666667 -3.46666666666668 65 629 718.466666666667 -89.4666666666667 66 916 718.466666666667 197.533333333333 67 531 718.466666666667 -187.466666666667 68 357 718.466666666667 -361.466666666667 69 917 718.466666666667 198.533333333333 70 828 718.466666666667 109.533333333333 71 708 718.466666666667 -10.4666666666667 72 858 718.466666666667 139.533333333333 73 775 718.466666666667 56.5333333333333 74 785 718.466666666667 66.5333333333333 75 1006 718.466666666667 287.533333333333 76 789 718.466666666667 70.5333333333333 77 734 718.466666666667 15.5333333333333 78 906 718.466666666667 187.533333333333 79 532 718.466666666667 -186.466666666667 80 387 718.466666666667 -331.466666666667 81 991 718.466666666667 272.533333333333 82 841 718.466666666667 122.533333333333 83 892 718.466666666667 173.533333333333 84 782 718.466666666667 63.5333333333333 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0170121604355225 0.0340243208710449 0.982987839564478 6 0.0209138061682459 0.0418276123364919 0.979086193831754 7 0.102803936907832 0.205607873815663 0.897196063092168 8 0.449868881935515 0.89973776387103 0.550131118064485 9 0.527205060250917 0.945589879498167 0.472794939749083 10 0.459514457421349 0.919028914842699 0.540485542578651 11 0.361420815775097 0.722841631550193 0.638579184224903 12 0.305330008166042 0.610660016332085 0.694669991833958 13 0.223666380771086 0.447332761542173 0.776333619228914 14 0.168560072607048 0.337120145214096 0.831439927392952 15 0.209562217628146 0.419124435256291 0.790437782371854 16 0.152292573525794 0.304585147051589 0.847707426474206 17 0.105945008975025 0.211890017950049 0.894054991024975 18 0.101935612164554 0.203871224329109 0.898064387835446 19 0.189419000737823 0.378838001475646 0.810580999262177 20 0.378985534202379 0.757971068404759 0.621014465797621 21 0.433889268377559 0.867778536755118 0.566110731622441 22 0.383152394795285 0.76630478959057 0.616847605204715 23 0.321379301830676 0.642758603661352 0.678620698169324 24 0.258618225533429 0.517236451066858 0.741381774466571 25 0.208487317470968 0.416974634941935 0.791512682529032 26 0.160825897485356 0.321651794970712 0.839174102514644 27 0.143551722796178 0.287103445592356 0.856448277203822 28 0.107664206764371 0.215328413528742 0.892335793235629 29 0.0848265768184222 0.169653153636844 0.915173423181578 30 0.112327097276846 0.224654194553693 0.887672902723154 31 0.170178077167775 0.34035615433555 0.829821922832225 32 0.299319840377199 0.598639680754399 0.7006801596228 33 0.319528339077789 0.639056678155577 0.680471660922211 34 0.266505652399626 0.533011304799252 0.733494347600374 35 0.220382542736982 0.440765085473964 0.779617457263018 36 0.176426419186878 0.352852838373756 0.823573580813122 37 0.151140578336706 0.302281156673412 0.848859421663294 38 0.118931822578636 0.237863645157273 0.881068177421364 39 0.0913172231488308 0.182634446297662 0.90868277685117 40 0.0703648520521005 0.140729704104201 0.9296351479479 41 0.0565294381207438 0.113058876241488 0.943470561879256 42 0.0454681487827061 0.0909362975654123 0.954531851217294 43 0.0852520903971706 0.170504180794341 0.914747909602829 44 0.207514502911564 0.415029005823128 0.792485497088436 45 0.16923195264349 0.33846390528698 0.83076804735651 46 0.137307987677292 0.274615975354585 0.862692012322708 47 0.105303559971996 0.210607119943993 0.894696440028004 48 0.079075934770777 0.158151869541554 0.920924065229223 49 0.0583355177466632 0.116671035493326 0.941664482253337 50 0.0422086865543839 0.0844173731087678 0.957791313445616 51 0.0311973221297676 0.0623946442595353 0.968802677870232 52 0.0215076003199959 0.0430152006399919 0.978492399680004 53 0.0150265661489260 0.0300531322978519 0.984973433851074 54 0.0105135781452085 0.0210271562904170 0.989486421854791 55 0.0179607618322363 0.0359215236644726 0.982039238167764 56 0.049227394226957 0.098454788453914 0.950772605773043 57 0.078894774036783 0.157789548073566 0.921105225963217 58 0.102309000159893 0.204618000319787 0.897690999840107 59 0.0810764964189893 0.162152992837979 0.91892350358101 60 0.0652620920361321 0.130524184072264 0.934737907963868 61 0.0488591531996003 0.0977183063992006 0.9511408468004 62 0.0399141647479096 0.0798283294958192 0.96008583525209 63 0.0286595716003784 0.0573191432007568 0.971340428399622 64 0.0198923798982316 0.0397847597964631 0.980107620101768 65 0.0154341103877693 0.0308682207755386 0.98456588961223 66 0.0199942980424374 0.0399885960848749 0.980005701957563 67 0.0258417883225220 0.0516835766450441 0.974158211677478 68 0.180471945068283 0.360943890136566 0.819528054931717 69 0.193361135673338 0.386722271346677 0.806638864326662 70 0.155456032021735 0.31091206404347 0.844543967978265 71 0.117847882517779 0.235695765035558 0.88215211748222 72 0.0939064103329321 0.187812820665864 0.906093589667068 73 0.0625222832416775 0.125044566483355 0.937477716758323 74 0.0393439070578969 0.0786878141157938 0.960656092942103 75 0.0677308854689926 0.135461770937985 0.932269114531007 76 0.0402713880809344 0.0805427761618689 0.959728611919066 77 0.0212818721837811 0.0425637443675623 0.978718127816219 78 0.0172668626371928 0.0345337252743857 0.982733137362807 79 0.0208759401039273 0.0417518802078547 0.979124059896073 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 12 0.16 NOK 10% type I error level 22 0.293333333333333 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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