Multiple lineair regression aantal werklozen en nationale consumptieprijsindex

*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: Tue, 17 Nov 2009 10:02:38 -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/17/t1258477422nb9p9lfpan6hm0q.htm/, Retrieved Tue, 17 Nov 2009 18:03:53 +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/17/t1258477422nb9p9lfpan6hm0q.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:

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User-defined keywords:

Dataseries X:

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8.4 1.8 8.4 1.6 8.4 1.9 8.6 1.7 8.9 1.6 8.8 1.3 8.3 1.1 7.5 1.9 7.2 2.6 7.4 2.3 8.8 2.4 9.3 2.2 9.3 2 8.7 2.9 8.2 2.6 8.3 2.3 8.5 2.3 8.6 2.6 8.5 3.1 8.2 2.8 8.1 2.5 7.9 2.9 8.6 3.1 8.7 3.1 8.7 3.2 8.5 2.5 8.4 2.6 8.5 2.9 8.7 2.6 8.7 2.4 8.6 1.7 8.5 2 8.3 2.2 8 1.9 8.2 1.6 8.1 1.6 8.1 1.2 8 1.2 7.9 1.5 7.9 1.6 8 1.7 8 1.8 7.9 1.8 8 1.8 7.7 1.3 7.2 1.3 7.5 1.4 7.3 1.1 7 1.5 7 2.2 7 2.9 7.2 3.1 7.3 3.5 7.1 3.6 6.8 4.4 6.4 4.2 6.1 5.2 6.5 5.8 7.7 5.9 7.9 5.4 7.5 5.5

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 Wkz[t] = + 8.58467027907636 -0.234871558766587Ncp[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) 8.58467027907636 0.196948 43.5885 0 0 Ncp -0.234871558766587 0.071289 -3.2946 0.00167 0.000835 Multiple Linear Regression - Regression Statistics Multiple R 0.394193156871283 R-squared 0.155388244924148 Adjusted R-squared 0.141072791448286 F-TEST (value) 10.8545806939443 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.00167001030035618 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.650724001888195 Sum Squared Residuals 24.9830618713699 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.4 8.16190147329647 0.238098526703529 2 8.4 8.20887578504982 0.191124214950182 3 8.4 8.13841431741984 0.261585682580157 4 8.6 8.18538862917316 0.414611370826839 5 8.9 8.20887578504982 0.691124214950181 6 8.8 8.2793372526798 0.520662747320206 7 8.3 8.32631156443311 -0.0263115644331116 8 7.5 8.13841431741984 -0.638414317419843 9 7.2 7.97400422628323 -0.774004226283232 10 7.4 8.0444656939132 -0.644465693913208 11 8.8 8.02097853803655 0.779021461963451 12 9.3 8.06795284978987 1.23204715021013 13 9.3 8.11492716154318 1.18507283845682 14 8.7 7.90354275865326 0.796457241346743 15 8.2 7.97400422628323 0.225995773716767 16 8.3 8.0444656939132 0.255534306086792 17 8.5 8.0444656939132 0.455534306086792 18 8.6 7.97400422628323 0.625995773716767 19 8.5 7.85656844689994 0.643431553100061 20 8.2 7.92702991452992 0.272970085470084 21 8.1 7.99749138215989 0.102508617840109 22 7.9 7.90354275865326 -0.00354275865325595 23 8.6 7.85656844689994 0.743431553100061 24 8.7 7.85656844689994 0.84343155310006 25 8.7 7.83308129102328 0.866918708976719 26 8.5 7.99749138215989 0.502508617840109 27 8.4 7.97400422628323 0.425995773716768 28 8.5 7.90354275865326 0.596457241346744 29 8.7 7.97400422628323 0.725995773716767 30 8.7 8.02097853803655 0.67902146196345 31 8.6 8.18538862917316 0.414611370826839 32 8.5 8.11492716154318 0.385072838456816 33 8.3 8.06795284978987 0.232047150210134 34 8 8.13841431741984 -0.138414317419843 35 8.2 8.20887578504982 -0.00887578504981967 36 8.1 8.20887578504982 -0.108875785049819 37 8.1 8.30282440855645 -0.202824408556454 38 8 8.30282440855645 -0.302824408556454 39 7.9 8.23236294092648 -0.332362940926477 40 7.9 8.20887578504982 -0.308875785049819 41 8 8.18538862917316 -0.185388629173160 42 8 8.1619014732965 -0.161901473296502 43 7.9 8.1619014732965 -0.261901473296501 44 8 8.1619014732965 -0.161901473296502 45 7.7 8.2793372526798 -0.579337252679795 46 7.2 8.2793372526798 -1.07933725267979 47 7.5 8.25585009680314 -0.755850096803136 48 7.3 8.32631156443311 -1.02631156443311 49 7 8.23236294092648 -1.23236294092648 50 7 8.06795284978987 -1.06795284978987 51 7 7.90354275865326 -0.903542758653256 52 7.2 7.85656844689994 -0.656568446899939 53 7.3 7.76261982339330 -0.462619823393304 54 7.1 7.73913266751665 -0.639132667516646 55 6.8 7.55123542050338 -0.751235420503376 56 6.4 7.59820973225669 -1.19820973225669 57 6.1 7.3633381734901 -1.26333817349011 58 6.5 7.22241523823015 -0.722415238230155 59 7.7 7.1989280823535 0.501071917646504 60 7.9 7.31636386173679 0.583636138263211 61 7.5 7.29287670586013 0.207123294139869 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0394739395341962 0.0789478790683925 0.960526060465804 6 0.0108272733840216 0.0216545467680432 0.989172726615978 7 0.0174633722995655 0.034926744599131 0.982536627700434 8 0.121195660516483 0.242391321032967 0.878804339483517 9 0.0945788324709313 0.189157664941863 0.905421167529069 10 0.0629438224275462 0.125887644855092 0.937056177572454 11 0.225139074124868 0.450278148249737 0.774860925875132 12 0.492845817818871 0.985691635637742 0.507154182181129 13 0.638617261973673 0.722765476052655 0.361382738026327 14 0.642791055090013 0.714417889819975 0.357208944909987 15 0.559908122143191 0.880183755713619 0.440091877856809 16 0.477390556527811 0.954781113055623 0.522609443472189 17 0.411741204826039 0.823482409652078 0.588258795173961 18 0.372930284589857 0.745860569179714 0.627069715410143 19 0.334326447328995 0.668652894657991 0.665673552671005 20 0.272555981828313 0.545111963656626 0.727444018171687 21 0.21935663416516 0.43871326833032 0.78064336583484 22 0.177690055475781 0.355380110951563 0.822309944524219 23 0.175152789279385 0.350305578558769 0.824847210720615 24 0.190882650620015 0.381765301240031 0.809117349379985 25 0.215518518704149 0.431037037408297 0.784481481295851 26 0.196004180339066 0.392008360678133 0.803995819660934 27 0.173856948337622 0.347713896675243 0.826143051662378 28 0.174343745755977 0.348687491511954 0.825656254244023 29 0.211612417332106 0.423224834664211 0.788387582667894 30 0.262885044895188 0.525770089790376 0.737114955104812 31 0.279843156773846 0.559686313547692 0.720156843226154 32 0.302746828384383 0.605493656768767 0.697253171615617 33 0.309319782415104 0.618639564830208 0.690680217584896 34 0.292650828746143 0.585301657492286 0.707349171253857 35 0.279648448215031 0.559296896430062 0.720351551784969 36 0.263581695903248 0.527163391806495 0.736418304096752 37 0.241974365517346 0.483948731034692 0.758025634482654 38 0.218510365376641 0.437020730753282 0.781489634623359 39 0.200195021799693 0.400390043599387 0.799804978200307 40 0.185286453555532 0.370572907111064 0.814713546444468 41 0.183428467917080 0.366856935834160 0.81657153208292 42 0.193967272184459 0.387934544368918 0.806032727815541 43 0.204661404221285 0.409322808442571 0.795338595778715 44 0.254866244735241 0.509732489470482 0.745133755264759 45 0.264702402120151 0.529404804240302 0.735297597879849 46 0.273851315272699 0.547702630545399 0.7261486847273 47 0.266932786857020 0.533865573714041 0.73306721314298 48 0.248462627022887 0.496925254045774 0.751537372977113 49 0.247782112116358 0.495564224232716 0.752217887883642 50 0.257375173727176 0.514750347454352 0.742624826272824 51 0.26790782643795 0.5358156528759 0.73209217356205 52 0.249846343515269 0.499692687030538 0.750153656484731 53 0.245913381543604 0.491826763087208 0.754086618456396 54 0.261405589490701 0.522811178981402 0.738594410509299 55 0.206818152727043 0.413636305454085 0.793181847272957 56 0.145685395684859 0.291370791369719 0.85431460431514 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 2 0.0384615384615385 OK 10% type I error level 3 0.0576923076923077 OK

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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