WS7-1Werkloosheid

*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: Thu, 19 Nov 2009 08:40:05 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/19/t1258645261p0fdpewj6q2qunt.htm/, Retrieved Thu, 19 Nov 2009 16:41:14 +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/2009/Nov/19/t1258645261p0fdpewj6q2qunt.htm/}, year = {2009}, } @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 = {2009}, 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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10.9 8.1 10 7.7 9.2 7.5 9.2 7.6 9.5 7.8 9.6 7.8 9.5 7.8 9.1 7.5 8.9 7.5 9 7.1 10.1 7.5 10.3 7.5 10.2 7.6 9.6 7.7 9.2 7.7 9.3 7.9 9.4 8.1 9.4 8.2 9.2 8.2 9 8.2 9 7.9 9 7.3 9.8 6.9 10 6.6 9.8 6.7 9.3 6.9 9 7 9 7.1 9.1 7.2 9.1 7.1 9.1 6.9 9.2 7 8.8 6.8 8.3 6.4 8.4 6.7 8.1 6.6 7.7 6.4 7.9 6.3 7.9 6.2 8 6.5 7.9 6.8 7.6 6.8 7.1 6.4 6.8 6.1 6.5 5.8 6.9 6.1 8.2 7.2 8.7 7.3 8.3 6.9 7.9 6.1 7.5 5.8 7.8 6.2 8.3 7.1 8.4 7.7 8.2 7.9 7.7 7.7 7.2 7.4 7.3 7.5 8.1 8 8.5 8.1

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 2.70950552586520 + 0.835106106989052X[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) 2.70950552586520 1.111025 2.4387 0.017821 0.00891 X 0.835106106989052 0.154242 5.4143 1e-06 1e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.579423898585697 R-squared 0.335732054252248 Adjusted R-squared 0.324279158635908 F-TEST (value) 29.3141634656339 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 1.2302241262363e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.78189229948904 Sum Squared Residuals 35.458622944015 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10.9 9.47386499247651 1.42613500752349 2 10 9.1398225496809 0.860177450319103 3 9.2 8.9728013282831 0.227198671716909 4 9.2 9.056311938982 0.143688061018004 5 9.5 9.2233331603798 0.276666839620194 6 9.6 9.2233331603798 0.376666839620194 7 9.5 9.2233331603798 0.276666839620194 8 9.1 8.9728013282831 0.127198671716909 9 8.9 8.9728013282831 -0.0728013282830901 10 9 8.63875888548747 0.361241114512530 11 10.1 8.9728013282831 1.12719867171691 12 10.3 8.9728013282831 1.32719867171691 13 10.2 9.056311938982 1.14368806101800 14 9.6 9.1398225496809 0.460177450319099 15 9.2 9.1398225496809 0.0601774503190984 16 9.3 9.30684377107871 -0.00684377107871056 17 9.4 9.47386499247652 -0.0738649924765206 18 9.4 9.55737560317543 -0.157375603175426 19 9.2 9.55737560317543 -0.357375603175427 20 9 9.55737560317543 -0.557375603175426 21 9 9.30684377107871 -0.306843771078711 22 9 8.80578010688528 0.19421989311472 23 9.8 8.47173766408966 1.32826233591034 24 10 8.22120583199294 1.77879416800706 25 9.8 8.30471644269185 1.49528355730815 26 9.3 8.47173766408966 0.82826233591034 27 9 8.55524827478856 0.444751725211435 28 9 8.63875888548747 0.361241114512530 29 9.1 8.72226949618637 0.377730503813624 30 9.1 8.63875888548747 0.46124111451253 31 9.1 8.47173766408966 0.62826233591034 32 9.2 8.55524827478856 0.644751725211434 33 8.8 8.38822705339075 0.411772946609246 34 8.3 8.05418461059513 0.245815389404866 35 8.4 8.30471644269185 0.095283557308151 36 8.1 8.22120583199294 -0.121205831992944 37 7.7 8.05418461059513 -0.354184610595134 38 7.9 7.97067399989623 -0.0706739998962283 39 7.9 7.88716338919732 0.0128366108026765 40 8 8.13769522129404 -0.137695221294039 41 7.9 8.38822705339075 -0.488227053390754 42 7.6 8.38822705339075 -0.788227053390755 43 7.1 8.05418461059513 -0.954184610595134 44 6.8 7.80365277849842 -1.00365277849842 45 6.5 7.5531209464017 -1.05312094640170 46 6.9 7.80365277849842 -0.903652778498418 47 8.2 8.72226949618637 -0.522269496186376 48 8.7 8.80578010688528 -0.105780106885281 49 8.3 8.47173766408966 -0.171737664089659 50 7.9 7.80365277849842 0.0963472215015821 51 7.5 7.5531209464017 -0.0531209464017029 52 7.8 7.88716338919732 -0.087163389197324 53 8.3 8.63875888548747 -0.338758885487469 54 8.4 9.1398225496809 -0.7398225496809 55 8.2 9.30684377107871 -1.10684377107871 56 7.7 9.1398225496809 -1.4398225496809 57 7.2 8.88929071758418 -1.68929071758419 58 7.3 8.9728013282831 -1.67280132828309 59 8.1 9.39035438177762 -1.29035438177762 60 8.5 9.47386499247652 -0.973864992476521 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.104453868982327 0.208907737964653 0.895546131017674 6 0.0548345934899461 0.109669186979892 0.945165406510054 7 0.0323977796641757 0.0647955593283514 0.967602220335824 8 0.0120958623795675 0.0241917247591351 0.987904137620432 9 0.00442328104088511 0.00884656208177023 0.995576718959115 10 0.0122910969844129 0.0245821939688257 0.987708903015587 11 0.0312676415579527 0.0625352831159054 0.968732358442047 12 0.0767267249632572 0.153453449926514 0.923273275036743 13 0.0876632881889357 0.175326576377871 0.912336711811064 14 0.0598821975986328 0.119764395197266 0.940117802401367 15 0.0522854030560193 0.104570806112039 0.94771459694398 16 0.0517373693149608 0.103474738629922 0.94826263068504 17 0.049172188253989 0.098344376507978 0.95082781174601 18 0.0416156659527625 0.083231331905525 0.958384334047238 19 0.0364391453270226 0.0728782906540453 0.963560854672977 20 0.0339880883602210 0.0679761767204421 0.96601191163978 21 0.0276073531653358 0.0552147063306716 0.972392646834664 22 0.0211224962790403 0.0422449925580806 0.97887750372096 23 0.0267074959602235 0.0534149919204469 0.973292504039777 24 0.0544330453003503 0.108866090600701 0.94556695469965 25 0.0905072289922121 0.181014457984424 0.909492771007788 26 0.106162089882550 0.212324179765101 0.89383791011745 27 0.119971439440128 0.239942878880255 0.880028560559872 28 0.130899041217287 0.261798082434575 0.869100958782713 29 0.143357981814524 0.286715963629048 0.856642018185476 30 0.170040151414001 0.340080302828003 0.829959848585999 31 0.229494056295517 0.458988112591034 0.770505943704483 32 0.345706127101862 0.691412254203724 0.654293872898138 33 0.456183345363332 0.912366690726663 0.543816654636668 34 0.558792485265538 0.882415029468925 0.441207514734462 35 0.630737703160812 0.738524593678377 0.369262296839188 36 0.68169315636134 0.636613687277321 0.318306843638661 37 0.724673824909788 0.550652350180425 0.275326175090212 38 0.72567215141497 0.54865569717006 0.27432784858503 39 0.721926149710535 0.556147700578929 0.278073850289465 40 0.718505186659742 0.562989626680516 0.281494813340258 41 0.70973101726039 0.580537965479219 0.290268982739609 42 0.715625377659837 0.568749244680326 0.284374622340163 43 0.747078426913322 0.505843146173356 0.252921573086678 44 0.790403559376853 0.419192881246294 0.209596440623147 45 0.881377309649361 0.237245380701277 0.118622690350639 46 0.927048471758179 0.145903056483643 0.0729515282418215 47 0.89901315567151 0.201973688656981 0.100986844328491 48 0.923941148084055 0.152117703831891 0.0760588519159453 49 0.908580492500835 0.18283901499833 0.091419507499165 50 0.865036882287067 0.269926235425865 0.134963117712933 51 0.785618631104973 0.428762737790054 0.214381368895027 52 0.720473585687382 0.559052828625237 0.279526414312618 53 0.95060924996371 0.098781500072578 0.049390750036289 54 0.998363194940028 0.00327361011994483 0.00163680505997241 55 0.99578547144192 0.00842905711615963 0.00421452855807982 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.0588235294117647 NOK 5% type I error level 6 0.117647058823529 NOK 10% type I error level 15 0.294117647058824 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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