Werkloosheid - Jongeren < 25 jaar - Regression model

*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, 20 Dec 2008 08:56:21 -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/Dec/20/t12297886606u8f6ijidjcj0ol.htm/, Retrieved Sat, 20 Dec 2008 16:57:49 +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/2008/Dec/20/t12297886606u8f6ijidjcj0ol.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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21.1 0 21 0 20.4 0 19.5 0 18.6 0 18.8 0 23.7 0 24.8 0 25 0 23.6 0 22.3 0 21.8 0 20.8 0 19.7 0 18.3 0 17.4 0 17 0 18.1 0 23.9 0 25.6 0 25.3 0 23.6 0 21.9 0 21.4 0 20.6 0 20.5 0 20.2 0 20.6 0 19.7 0 19.3 0 22.8 0 23.5 0 23.8 0 22.6 0 22 0 21.7 0 20.7 0 20.2 0 19.1 0 19.5 0 18.7 0 18.6 0 22.2 0 23.2 0 23.5 0 21.3 0 20 0 18.7 0 18.9 1 18.3 1 18.4 1 19.9 1 19.2 1 18.5 1 20.9 1 20.5 1 19.4 1 18.1 1 17 1 17 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 21.4291666666666 -1.49583333333334X[t] -0.0086111111111364M1[t] -0.460555555555551M2[t] -1.09249999999999M3[t] -0.96444444444444M4[t] -1.67638888888889M5[t] -1.62833333333333M6[t] + 2.43972222222222M7[t] + 3.28777777777778M8[t] + 3.19583333333334M9[t] + 1.66388888888889M10[t] + 0.491944444444446M11[t] -0.0280555555555553t + 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) 21.4291666666666 0.663035 32.3198 0 0 X -1.49583333333334 0.545011 -2.7446 0.008612 0.004306 M1 -0.0086111111111364 0.768296 -0.0112 0.991106 0.495553 M2 -0.460555555555551 0.766038 -0.6012 0.550646 0.275323 M3 -1.09249999999999 0.763988 -1.43 0.159476 0.079738 M4 -0.96444444444444 0.76215 -1.2654 0.212091 0.106046 M5 -1.67638888888889 0.760525 -2.2043 0.032549 0.016274 M6 -1.62833333333333 0.759113 -2.145 0.037263 0.018631 M7 2.43972222222222 0.757916 3.219 0.002361 0.00118 M8 3.28777777777778 0.756936 4.3435 7.6e-05 3.8e-05 M9 3.19583333333334 0.756172 4.2263 0.000111 5.6e-05 M10 1.66388888888889 0.755627 2.202 0.032718 0.016359 M11 0.491944444444446 0.755299 0.6513 0.518078 0.259039 t -0.0280555555555553 0.012846 -2.184 0.034099 0.01705 Multiple Linear Regression - Regression Statistics Multiple R 0.881146077902452 R-squared 0.776418410602874 Adjusted R-squared 0.713232309251513 F-TEST (value) 12.2878037099553 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 6.36077857052442e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.19405987517681 Sum Squared Residuals 65.5858333333334 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 21.1 21.3925000000001 -0.292500000000114 2 21 20.9125 0.0875000000000067 3 20.4 20.2525 0.147500000000005 4 19.5 20.3525 -0.852499999999993 5 18.6 19.6125 -1.01250000000000 6 18.8 19.6325 -0.832499999999994 7 23.7 23.6725 0.0275000000000042 8 24.8 24.4925 0.307500000000008 9 25 24.3725 0.627500000000007 10 23.6 22.8125 0.787500000000006 11 22.3 21.6125 0.687500000000008 12 21.8 21.0925 0.707500000000008 13 20.8 21.0558333333333 -0.2558333333333 14 19.7 20.5758333333333 -0.875833333333331 15 18.3 19.9158333333333 -1.61583333333333 16 17.4 20.0158333333333 -2.61583333333333 17 17 19.2758333333333 -2.27583333333333 18 18.1 19.2958333333333 -1.19583333333333 19 23.9 23.3358333333333 0.564166666666669 20 25.6 24.1558333333333 1.44416666666667 21 25.3 24.0358333333333 1.26416666666667 22 23.6 22.4758333333333 1.12416666666667 23 21.9 21.2758333333333 0.624166666666668 24 21.4 20.7558333333333 0.64416666666667 25 20.6 20.7191666666666 -0.119166666666637 26 20.5 20.2391666666667 0.260833333333332 27 20.2 19.5791666666667 0.620833333333331 28 20.6 19.6791666666667 0.920833333333333 29 19.7 18.9391666666667 0.760833333333332 30 19.3 18.9591666666667 0.340833333333332 31 22.8 22.9991666666667 -0.199166666666666 32 23.5 23.8191666666667 -0.319166666666669 33 23.8 23.6991666666667 0.100833333333332 34 22.6 22.1391666666667 0.460833333333332 35 22 20.9391666666667 1.06083333333333 36 21.7 20.4191666666667 1.28083333333333 37 20.7 20.3825000000000 0.317500000000024 38 20.2 19.9025 0.297499999999994 39 19.1 19.2425 -0.142500000000004 40 19.5 19.3425 0.157499999999995 41 18.7 18.6025 0.0974999999999943 42 18.6 18.6225 -0.0225000000000043 43 22.2 22.6625 -0.462500000000004 44 23.2 23.4825 -0.282500000000007 45 23.5 23.3625 0.137499999999995 46 21.3 21.8025 -0.502500000000005 47 20 20.6025 -0.602500000000005 48 18.7 20.0825 -1.38250000000000 49 18.9 18.5500000000000 0.350000000000026 50 18.3 18.07 0.229999999999999 51 18.4 17.41 0.989999999999997 52 19.9 17.51 2.39000000000000 53 19.2 16.77 2.43 54 18.5 16.79 1.71000000000000 55 20.9 20.83 0.0699999999999988 56 20.5 21.65 -1.15000000000000 57 19.4 21.53 -2.13000000000000 58 18.1 19.97 -1.87 59 17 18.77 -1.77000000000000 60 17 18.25 -1.25000000000000 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.225154974514504 0.450309949029009 0.774845025485496 18 0.214137489603368 0.428274979206736 0.785862510396632 19 0.291538539535776 0.583077079071552 0.708461460464224 20 0.42828252293142 0.85656504586284 0.57171747706858 21 0.394167460119152 0.788334920238304 0.605832539880848 22 0.318098973121627 0.636197946243254 0.681901026878373 23 0.222065104805544 0.444130209611087 0.777934895194456 24 0.146823745221628 0.293647490443256 0.853176254778372 25 0.111961280646939 0.223922561293878 0.888038719353061 26 0.0964846747426109 0.192969349485222 0.903515325257389 27 0.117383957641968 0.234767915283935 0.882616042358032 28 0.298366200262921 0.596732400525841 0.70163379973708 29 0.403947911753213 0.807895823506427 0.596052088246787 30 0.413113663742481 0.826227327484962 0.586886336257519 31 0.43326118614343 0.86652237228686 0.56673881385657 32 0.497255540989818 0.994511081979636 0.502744459010182 33 0.474526368169131 0.949052736338261 0.525473631830869 34 0.405864788852552 0.811729577705103 0.594135211147448 35 0.309713773059433 0.619427546118865 0.690286226940567 36 0.223668604598941 0.447337209197882 0.776331395401059 37 0.151202963532622 0.302405927065243 0.848797036467378 38 0.0958526458421968 0.191705291684394 0.904147354157803 39 0.0643564357915376 0.128712871583075 0.935643564208462 40 0.0871037344622274 0.174207468924455 0.912896265537773 41 0.195196909999971 0.390393819999943 0.804803090000029 42 0.425850283364688 0.851700566729377 0.574149716635312 43 0.528181036505459 0.943637926989081 0.471818963494541 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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