Opdracht 6 : Q3

*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: Mon, 24 Nov 2008 15:21:37 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227565347wbtdkwhshnitu2u.htm/, Retrieved Mon, 24 Nov 2008 22:22:36 +0000

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/2008/Nov/24/t1227565347wbtdkwhshnitu2u.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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21 0 18 0 31 0 31 0 35 0 38 0 36 0 33 0 29 0 37 0 28 0 32 0 31 0 24 0 25 0 27 0 27 0 29 0 33 0 26 0 16 0 15 0 13 0 18 0 8 0 21 0 21 0 25 0 28 0 27 0 24 0 24 0 24 0 28 0 31 0 26 0 28 0 34 0 33 0 24 0 30 0 31 0 28 0 35 0 33 0 34 0 31 0 21 0 21 0 22 0 9 0 15 0 13 0 17 0 19 0 14 0 8 0 3 0 0 1 10 0

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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation FinSit[t] = + 29.3956521739130 -19.0869565217391OntslagYvesLeterme[t] -2.04311594202898M1[t] + 0.178985507246380M2[t] + 0.401086956521736M3[t] + 1.22318840579710M4[t] + 3.64528985507247M5[t] + 5.66739130434783M6[t] + 5.48949275362319M7[t] + 4.11159420289855M8[t] -0.0663043478260841M9[t] + 1.55579710144928M10[t] + 2.79528985507246M11[t] -0.222101449275362t + 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) 29.3956521739130 4.13274 7.1129 0 0 OntslagYvesLeterme -19.0869565217391 8.947644 -2.1332 0.038277 0.019138 M1 -2.04311594202898 5.000032 -0.4086 0.684714 0.342357 M2 0.178985507246380 4.992242 0.0359 0.971555 0.485777 M3 0.401086956521736 4.985184 0.0805 0.936224 0.468112 M4 1.22318840579710 4.97886 0.2457 0.807026 0.403513 M5 3.64528985507247 4.973274 0.733 0.467292 0.233646 M6 5.66739130434783 4.968427 1.1407 0.259907 0.129953 M7 5.48949275362319 4.964322 1.1058 0.274568 0.137284 M8 4.11159420289855 4.960961 0.8288 0.411503 0.205752 M9 -0.0663043478260841 4.958346 -0.0134 0.989389 0.494694 M10 1.55579710144928 4.956477 0.3139 0.755022 0.377511 M11 2.79528985507246 5.272801 0.5301 0.598569 0.299285 t -0.222101449275362 0.060881 -3.6481 0.000672 0.000336 Multiple Linear Regression - Regression Statistics Multiple R 0.61557955262221 R-squared 0.37893818560656 Adjusted R-squared 0.203420716321457 F-TEST (value) 2.15897703601816 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.0279487205040481 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.83451237289105 Sum Squared Residuals 2823.46086956522 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 21 27.1304347826087 -6.1304347826087 2 18 29.1304347826087 -11.1304347826087 3 31 29.1304347826087 1.8695652173913 4 31 29.7304347826087 1.2695652173913 5 35 31.9304347826087 3.06956521739131 6 38 33.7304347826087 4.26956521739131 7 36 33.3304347826087 2.66956521739131 8 33 31.7304347826087 1.26956521739131 9 29 27.3304347826087 1.66956521739131 10 37 28.7304347826087 8.2695652173913 11 28 29.7478260869565 -1.74782608695652 12 32 26.7304347826087 5.26956521739131 13 31 24.4652173913044 6.53478260869565 14 24 26.4652173913043 -2.46521739130434 15 25 26.4652173913043 -1.46521739130435 16 27 27.0652173913044 -0.0652173913043519 17 27 29.2652173913044 -2.26521739130435 18 29 31.0652173913043 -2.06521739130435 19 33 30.6652173913043 2.33478260869565 20 26 29.0652173913043 -3.06521739130435 21 16 24.6652173913043 -8.66521739130435 22 15 26.0652173913044 -11.0652173913044 23 13 27.0826086956522 -14.0826086956522 24 18 24.0652173913043 -6.06521739130434 25 8 21.8 -13.8 26 21 23.8 -2.8 27 21 23.8 -2.8 28 25 24.4 0.599999999999997 29 28 26.6 1.4 30 27 28.4 -1.4 31 24 28 -4 32 24 26.4 -2.4 33 24 22 2.00000000000000 34 28 23.4 4.6 35 31 24.4173913043478 6.58260869565218 36 26 21.4 4.60000000000001 37 28 19.1347826086957 8.86521739130435 38 34 21.1347826086957 12.8652173913043 39 33 21.1347826086957 11.8652173913043 40 24 21.7347826086957 2.26521739130435 41 30 23.9347826086957 6.06521739130435 42 31 25.7347826086957 5.26521739130435 43 28 25.3347826086957 2.66521739130435 44 35 23.7347826086957 11.2652173913043 45 33 19.3347826086957 13.6652173913043 46 34 20.7347826086957 13.2652173913043 47 31 21.7521739130435 9.24782608695652 48 21 18.7347826086956 2.26521739130435 49 21 16.4695652173913 4.5304347826087 50 22 18.4695652173913 3.53043478260869 51 9 18.4695652173913 -9.4695652173913 52 15 19.0695652173913 -4.06956521739131 53 13 21.2695652173913 -8.2695652173913 54 17 23.0695652173913 -6.0695652173913 55 19 22.6695652173913 -3.6695652173913 56 14 21.0695652173913 -7.0695652173913 57 8 16.6695652173913 -8.6695652173913 58 3 18.0695652173913 -15.0695652173913 59 0 8.88178419700125e-16 -8.88178419700125e-16 60 10 16.0695652173913 -6.0695652173913 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.325094668329926 0.650189336659851 0.674905331670074 18 0.239073718941733 0.478147437883466 0.760926281058267 19 0.130814582797957 0.261629165595913 0.869185417202043 20 0.0752190035132875 0.150438007026575 0.924780996486713 21 0.0734645364542896 0.146929072908579 0.92653546354571 22 0.16475159480535 0.3295031896107 0.83524840519465 23 0.203549446697727 0.407098893395454 0.796450553302273 24 0.169879453377102 0.339758906754205 0.830120546622898 25 0.251189839030248 0.502379678060495 0.748810160969752 26 0.351076920034554 0.702153840069109 0.648923079965446 27 0.305366195079938 0.610732390159876 0.694633804920062 28 0.250567961803274 0.501135923606548 0.749432038196726 29 0.202250917417821 0.404501834835641 0.79774908258218 30 0.163911439487805 0.327822878975609 0.836088560512195 31 0.161112073123576 0.322224146247152 0.838887926876424 32 0.206486469603522 0.412972939207044 0.793513530396478 33 0.305427487367722 0.610854974735444 0.694572512632278 34 0.347936523420542 0.695873046841085 0.652063476579458 35 0.568981013865013 0.862037972269975 0.431018986134987 36 0.679749176403037 0.640501647193927 0.320250823596963 37 0.76257806371754 0.47484387256492 0.23742193628246 38 0.790492986918472 0.419014026163055 0.209507013081528 39 0.760153956548557 0.479692086902886 0.239846043451443 40 0.733805289532496 0.532389420935009 0.266194710467504 41 0.60610995894019 0.787780082119619 0.393890041059810 42 0.48594227423787 0.97188454847574 0.51405772576213 43 0.533746717244425 0.93250656551115 0.466253282755575 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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