Multiple lineair regression aantal werklozen(onder 25jaar) - Rente op basis-herfinancieringstransacties (seasonal dummies)

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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 02:57:39 -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/t1258711271sa9syydth8qhpct.htm/, Retrieved Fri, 20 Nov 2009 11:01:24 +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/t1258711271sa9syydth8qhpct.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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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] = + 162.436002337051 -14.8388999402021Rente[t] + 1.70430583183854M1[t] -1.96236083482829M2[t] -7.42472166965657M3[t] -11.0107400039865M4[t] -17.0107400039865M5[t] -15.9494531695569M6[t] + 18.9344269942195M7[t] + 26.3860478250613M8[t] + 24.5591683243636M9[t] + 13.6204551587933M10[t] + 3.45807466347745M11[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) 162.436002337051 2.417503 67.1916 0 0 Rente -14.8388999402021 0.605681 -24.4995 0 0 M1 1.70430583183854 2.498139 0.6822 0.497763 0.248882 M2 -1.96236083482829 2.498139 -0.7855 0.435287 0.217643 M3 -7.42472166965657 2.498277 -2.9719 0.004278 0.002139 M4 -11.0107400039865 2.49842 -4.4071 4.5e-05 2.2e-05 M5 -17.0107400039865 2.49842 -6.8086 0 0 M6 -15.9494531695569 2.498265 -6.3842 0 0 M7 18.9344269942195 2.49878 7.5775 0 0 M8 26.3860478250613 2.499498 10.5565 0 0 M9 24.5591683243636 2.499745 9.8247 0 0 M10 13.6204551587933 2.499366 5.4496 1e-06 1e-06 M11 3.45807466347745 2.498302 1.3842 0.17152 0.08576 Multiple Linear Regression - Regression Statistics Multiple R 0.978730583058003 R-squared 0.957913554213058 Adjusted R-squared 0.949353599137748 F-TEST (value) 111.906376351904 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.32682497197846 Sum Squared Residuals 1104.56344595005 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 127 123.333333333333 3.66666666666746 2 123 119.666666666667 3.33333333333329 3 118 117.172085819879 0.827914180121201 4 114 114.328012482559 -0.328012482558943 5 108 108.328012482559 -0.328012482558939 6 111 115.324859293069 -4.32485929306941 7 151 151.692629450866 -0.69262945086605 8 159 159.144250281708 -0.144250281707726 9 158 157.31737078101 0.682629218989846 10 148 146.378657615440 1.62134238456025 11 138 136.216277120124 1.78372287987606 12 137 132.758202456647 4.2417975433535 13 136 134.462508288485 1.53749171151496 14 133 130.795841621818 2.20415837818179 15 126 125.33348078699 0.666519213010061 16 120 121.74746245266 -1.74746245265997 17 114 115.74746245266 -1.74746245265997 18 116 116.808749287090 -0.8087492870896 19 153 151.692629450866 1.30737054913397 20 162 159.144250281708 2.8557497182922 21 161 157.31737078101 3.68262921898985 22 149 146.378657615440 2.62134238456022 23 139 136.216277120124 2.78372287987606 24 135 132.758202456647 2.2417975433535 25 130 134.462508288485 -4.46250828848505 26 127 130.795841621818 -3.79584162181821 27 122 125.33348078699 -3.33348078698994 28 117 121.74746245266 -4.74746245265997 29 112 115.74746245266 -3.74746245265997 30 113 116.808749287090 -3.8087492870896 31 149 151.692629450866 -2.69262945086603 32 157 159.144250281708 -2.1442502817078 33 157 157.31737078101 -0.317370781010147 34 147 146.378657615440 0.621342384560223 35 137 136.216277120124 0.783722879876056 36 132 129.642033469204 2.35796653079593 37 125 130.752783303435 -5.75278330343453 38 123 127.086116636768 -4.08611663676769 39 117 118.655975813899 -1.65597581389901 40 114 114.328012482559 -0.328012482558939 41 111 108.328012482559 2.67198751744106 42 112 107.311853325360 4.68814667463973 43 144 140.563454495714 3.43654550428552 44 150 145.34407333732 4.65592666268013 45 149 142.478470840808 6.52152915919193 46 134 129.017144685403 4.98285531459664 47 123 117.667652194871 5.33234780512864 48 116 112.132131539766 3.86786846023438 49 117 112.204158378182 4.79584162181806 50 111 108.537491711515 2.46250828848490 51 105 100.849295885657 4.15070411434348 52 102 95.7793875573064 6.22061244269365 53 95 89.7793875573064 5.22061244269365 54 93 88.6148394007057 4.38516059929434 55 124 122.014829570462 1.98517042953811 56 130 129.466450401304 0.533549598696344 57 124 127.639570900606 -3.639570900606 58 115 116.700857735036 -1.70085773503563 59 106 106.538477239720 -0.538477239719803 60 105 103.080402576242 1.91959742375764 61 105 104.784708408081 0.215291591919096 62 101 101.118041741414 -0.118041741414070 63 95 95.6556809065858 -0.655680906585797 64 93 92.0696625722558 0.93033742774417 65 84 86.0696625722558 -2.06966257225583 66 87 87.1309494066855 -0.130949406685456 67 116 119.343827581226 -3.34382758122552 68 120 125.756725416253 -5.75672541625314 69 117 123.929845915555 -6.92984591555548 70 109 117.146024733242 -8.1460247332417 71 105 115.145039205037 -10.145039205037 72 107 121.629027501495 -14.6290275014949 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.00168269827871803 0.00336539655743606 0.998317301721282 17 0.000178403148110627 0.000356806296221254 0.99982159685189 18 0.00298682623456448 0.00597365246912896 0.997013173765436 19 0.00124909252365801 0.00249818504731602 0.998750907476342 20 0.00100724662817263 0.00201449325634527 0.998992753371827 21 0.000756804398522882 0.00151360879704576 0.999243195601477 22 0.000244200604353932 0.000488401208707864 0.999755799395646 23 7.78177029534565e-05 0.000155635405906913 0.999922182297047 24 3.50021285233935e-05 7.00042570467871e-05 0.999964997871477 25 0.000521360409146856 0.00104272081829371 0.999478639590853 26 0.00101896326018427 0.00203792652036854 0.998981036739816 27 0.000642870083987755 0.00128574016797551 0.999357129916012 28 0.000431402984301285 0.000862805968602571 0.9995685970157 29 0.000220104757587952 0.000440209515175904 0.999779895242412 30 0.000119309590413415 0.000238619180826829 0.999880690409587 31 8.58238534206005e-05 0.000171647706841201 0.99991417614658 32 6.97669924176976e-05 0.000139533984835395 0.999930233007582 33 3.72318104866142e-05 7.44636209732284e-05 0.999962768189513 34 1.56430849891774e-05 3.12861699783548e-05 0.99998435691501 35 6.47329539389757e-06 1.29465907877951e-05 0.999993526704606 36 3.51307333232687e-06 7.02614666465374e-06 0.999996486926668 37 2.19872489131853e-05 4.39744978263707e-05 0.999978012751087 38 3.93654353720136e-05 7.87308707440273e-05 0.999960634564628 39 2.85334442375619e-05 5.70668884751237e-05 0.999971466555762 40 1.97656204238692e-05 3.95312408477384e-05 0.999980234379576 41 1.28908414385940e-05 2.57816828771881e-05 0.999987109158561 42 1.10407334047671e-05 2.20814668095343e-05 0.999988959266595 43 4.28243105963752e-06 8.56486211927504e-06 0.99999571756894 44 1.77212350519045e-06 3.54424701038089e-06 0.999998227876495 45 1.89638032290184e-06 3.79276064580369e-06 0.999998103619677 46 5.28133276168864e-06 1.05626655233773e-05 0.999994718667238 47 3.61474127178305e-05 7.2294825435661e-05 0.999963852587282 48 0.000254726031630581 0.000509452063261163 0.99974527396837 49 0.000273080576272791 0.000546161152545582 0.999726919423727 50 0.00024839518340256 0.00049679036680512 0.999751604816597 51 0.000316529799403856 0.000633059598807713 0.999683470200596 52 0.000501418565730974 0.00100283713146195 0.999498581434269 53 0.00213721926231875 0.00427443852463749 0.997862780737681 54 0.00217199098655101 0.00434398197310203 0.99782800901345 55 0.0076438521397298 0.0152877042794596 0.99235614786027 56 0.0901826901361003 0.180365380272201 0.9098173098639 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 39 0.951219512195122 NOK 5% type I error level 40 0.97560975609756 NOK 10% type I error level 40 0.97560975609756 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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