Multiple lineair regression aantal werklozen(onder 25jaar) - Rente op basis-herfinancieringstransacties (include trend)

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 20 Nov 2009 03:01:53 -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/20/t1258711367pyvow9vcfstgyj3.htm/, Retrieved Fri, 20 Nov 2009 11:02:59 +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/20/t1258711367pyvow9vcfstgyj3.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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Dataseries X:

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127 2.75 123 2.75 118 2.55 114 2.5 108 2.5 111 2.1 151 2 159 2 158 2 148 2 138 2 137 2 136 2 133 2 126 2 120 2 114 2 116 2 153 2 162 2 161 2 149 2 139 2 135 2 130 2 127 2 122 2 117 2 112 2 113 2 149 2 157 2 157 2 147 2 137 2 132 2.21 125 2.25 123 2.25 117 2.45 114 2.5 111 2.5 112 2.64 144 2.75 150 2.93 149 3 134 3.17 123 3.25 116 3.39 117 3.5 111 3.5 105 3.65 102 3.75 95 3.75 93 3.9 124 4 130 4 124 4 115 4 106 4 105 4 105 4 101 4 95 4 93 4 84 4 87 4 116 4.18 120 4.25 117 4.25 109 3.97 105 3.42 107 2.75

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 Werkloosheid[t] = + 160.409211785205 -11.7887483839392Rente[t] -0.0179859767984057M1[t] -3.53501282348974M2[t] -8.9239876272491M3[t] -12.4112020008746M4[t] -18.2615621808991M5[t] -16.9947160812959M6[t] + 17.8913799105700M7[t] + 25.3655509132096M8[t] + 23.6527261309978M9[t] + 12.9195722306010M10[t] + 3.14576009383461M11[t] -0.149639819975488t + 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) 160.409211785205 2.274144 70.5361 0 0 Rente -11.7887483839392 1.009939 -11.6727 0 0 M1 -0.0179859767984057 2.326654 -0.0077 0.993859 0.496929 M2 -3.53501282348974 2.318495 -1.5247 0.132768 0.066384 M3 -8.9239876272491 2.314878 -3.8551 0.000292 0.000146 M4 -12.4112020008746 2.310244 -5.3722 1e-06 1e-06 M5 -18.2615621808991 2.303634 -7.9273 0 0 M6 -16.9947160812959 2.295606 -7.4032 0 0 M7 17.8913799105700 2.295994 7.7924 0 0 M8 25.3655509132096 2.295865 11.0484 0 0 M9 23.6527261309978 2.292406 10.3179 0 0 M10 12.9195722306010 2.286515 5.6503 1e-06 0 M11 3.14576009383461 2.278919 1.3804 0.172769 0.086384 t -0.149639819975488 0.041489 -3.6068 0.000646 0.000323 Multiple Linear Regression - Regression Statistics Multiple R 0.982661562704323 R-squared 0.965623746816503 Adjusted R-squared 0.957918724551236 F-TEST (value) 125.323939837193 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.94402337980184 Sum Squared Residuals 902.208584384567 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 127 127.822527932597 -0.822527932597231 2 123 124.155861265931 -1.15586126593133 3 118 120.974996318984 -2.97499631898430 4 114 117.927579544580 -3.92757954458025 5 108 111.927579544580 -3.92757954458025 6 111 117.760285177784 -6.76028517778374 7 151 153.675616188068 -2.67561618806805 8 159 161.000147370732 -2.00014737073211 9 158 159.137682768545 -1.13768276854481 10 148 148.254889048173 -0.254889048172563 11 138 138.331437091431 -0.331437091430672 12 137 135.036037177621 1.96396282237942 13 136 134.868411380847 1.13158861915331 14 133 131.20174471418 1.79825528582013 15 126 125.663130090445 0.336869909554977 16 120 122.026275896844 -2.02627589684401 17 114 116.026275896844 -2.02627589684401 18 116 117.143482176472 -1.14348217647179 19 153 151.879938348362 1.12006165163781 20 162 159.204469531026 2.79553046897367 21 161 157.342004928839 3.65799507116105 22 149 146.459211208467 2.54078879153327 23 139 136.535759251725 2.46424074827518 24 135 133.240359337915 1.75964066208527 25 130 133.072733541141 -3.07273354114084 26 127 129.406066874474 -2.40606687447402 27 122 123.867452250739 -1.86745225073917 28 117 120.230598057138 -3.23059805713816 29 112 114.230598057138 -2.23059805713816 30 113 115.347804336766 -2.34780433676594 31 149 150.084260508656 -1.08426050865633 32 157 157.408791691320 -0.408791691320483 33 157 155.546327089133 1.45367291086690 34 147 144.663533368761 2.33646663123912 35 137 134.740081412019 2.25991858798103 36 132 128.969044337582 3.03095566241836 37 125 128.329868605450 -3.32986860545017 38 123 124.663201938783 -1.66320193878335 39 117 116.766837638261 0.233162361739342 40 114 112.540546025463 1.45945397453731 41 111 106.540546025463 4.45945397453731 42 112 106.007327531339 5.99267246866103 43 144 139.447021380996 4.55297861900395 44 150 144.649577854551 5.35042214544886 45 149 141.961900865488 7.03809913451201 46 134 129.075019919846 4.92498008015388 47 123 118.208468092389 4.79153190761094 48 116 113.262643404827 2.73735659517252 49 117 111.798255285820 5.20174471417973 50 111 108.131588619153 2.86841138084655 51 105 100.824661737828 4.17533826217228 52 102 96.0089327058328 5.99106729416722 53 95 90.0089327058328 4.99106729416722 54 93 89.3578267278697 3.64217327213033 55 124 122.915408061366 1.08459193863385 56 130 130.239939244030 -0.239939244030294 57 124 128.377474641843 -4.37747464184291 58 115 117.494680921471 -2.49468092147069 59 106 107.571228964729 -1.57122896472878 60 105 104.275829050919 0.724170949081313 61 105 104.108203254145 0.891796745855202 62 101 100.441536587478 0.558463412522023 63 95 94.9029219637431 0.0970780362568695 64 93 91.2660677701421 1.73393222985788 65 84 85.2660677701421 -1.26606777014212 66 87 86.3832740497699 0.616725950230104 67 116 118.997755512551 -2.99775551255123 68 120 125.497074308340 -5.49707430833964 69 117 123.634609706152 -6.63460970615224 70 109 116.052665533283 -7.05266553328302 71 105 112.613025187708 -7.6130251877077 72 107 117.216086691137 -10.2160866911369 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00458051224916398 0.00916102449832796 0.995419487750836 18 0.00405334554042543 0.00810669108085087 0.995946654459575 19 0.00127406303352974 0.00254812606705948 0.99872593696647 20 0.000237739378784199 0.000475478757568397 0.999762260621216 21 4.04608553297374e-05 8.09217106594748e-05 0.99995953914467 22 2.92142280683855e-05 5.8428456136771e-05 0.999970785771932 23 1.22513576037394e-05 2.45027152074789e-05 0.999987748642396 24 0.000169159835690466 0.000338319671380931 0.99983084016431 25 0.0195359423553242 0.0390718847106484 0.980464057644676 26 0.0469896452755508 0.0939792905511015 0.95301035472445 27 0.0434973116861776 0.0869946233723552 0.956502688313822 28 0.0549617813834345 0.109923562766869 0.945038218616566 29 0.0632319760409688 0.126463952081938 0.936768023959031 30 0.0982016329928429 0.196403265985686 0.901798367007157 31 0.099165142275505 0.19833028455101 0.900834857724495 32 0.0869024140530434 0.173804828106087 0.913097585946957 33 0.0575442822489599 0.115088564497920 0.94245571775104 34 0.0363101821976398 0.0726203643952796 0.96368981780236 35 0.0219060917237227 0.0438121834474454 0.978093908276277 36 0.0128155761954910 0.0256311523909821 0.98718442380451 37 0.0525450471871782 0.105090094374356 0.947454952812822 38 0.0885071430809797 0.177014286161959 0.91149285691902 39 0.152885649603662 0.305771299207323 0.847114350396338 40 0.542020885886872 0.915958228226255 0.457979114113128 41 0.747171000194172 0.505657999611656 0.252828999805828 42 0.870194452987206 0.259611094025588 0.129805547012794 43 0.845043584598198 0.309912830803605 0.154956415401803 44 0.782531037507081 0.434937924985838 0.217468962492919 45 0.956583302428758 0.0868333951424842 0.0434166975712421 46 0.989190443111978 0.021619113776043 0.0108095568880215 47 0.99831399556975 0.0033720088605003 0.00168600443025015 48 0.997083224688889 0.00583355062222271 0.00291677531111136 49 0.995234586838589 0.00953082632282293 0.00476541316141146 50 0.98931514636788 0.0213697072642403 0.0106848536321201 51 0.975781570324523 0.0484368593509534 0.0242184296754767 52 0.949667782035139 0.100664435929722 0.0503322179648611 53 0.97219822948248 0.0556035410350386 0.0278017705175193 54 0.945062497340706 0.109875005318589 0.0549375026592944 55 0.880709654355832 0.238580691288335 0.119290345644167 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 11 0.282051282051282 NOK 5% type I error level 17 0.435897435897436 NOK 10% type I error level 22 0.564102564102564 NOK

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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