Paper Regressie analyse (met Seasonal Dummies)

*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, 19 Dec 2009 02:31:23 -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/Dec/19/t1261215244xcr1356m3jjnqyz.htm/, Retrieved Sat, 19 Dec 2009 10:34:17 +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/Dec/19/t1261215244xcr1356m3jjnqyz.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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84 0 78 0 74 0 75 0 79 0 79 0 82 0 88 0 81 0 69 1 62 1 62 1 68 1 57 1 67 1 72 0 75 0 81 0 80 0 79 0 81 0 83 0 84 0 90 0 84 0 90 0 92 0 93 0 85 0 93 0 94 0 94 0 102 0 96 0 96 0 92 0 90 0 84 0 86 0 70 0 67 1 60 1 62 1 61 1 54 1 50 1 45 1 34 1 37 1 44 1 34 1 37 1 31 1 31 1 28 1 31 1 33 1 36 1 39 1 42 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Consumentenvertrouwen[t] = + 86.9885714285714 -38.3142857142857Dummy[t] + 0.937142857142851M1[t] -1.06285714285715M2[t] -1.06285714285713M3[t] -9.92571428571427M4[t] -4.26285714285714M5[t] -2.86285714285714M6[t] -2.46285714285714M7[t] -1.06285714285714M8[t] -1.46285714285714M9[t] + 2.8M10[t] + 1.2M11[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) 86.9885714285714 5.54458 15.6889 0 0 Dummy -38.3142857142857 3.11907 -12.2839 0 0 M1 0.937142857142851 7.407381 0.1265 0.899864 0.449932 M2 -1.06285714285715 7.407381 -0.1435 0.88652 0.44326 M3 -1.06285714285713 7.407381 -0.1435 0.88652 0.44326 M4 -9.92571428571427 7.485768 -1.3259 0.191266 0.095633 M5 -4.26285714285714 7.407381 -0.5755 0.567707 0.283853 M6 -2.86285714285714 7.407381 -0.3865 0.70088 0.35044 M7 -2.46285714285714 7.407381 -0.3325 0.741 0.3705 M8 -1.06285714285714 7.407381 -0.1435 0.88652 0.44326 M9 -1.46285714285714 7.407381 -0.1975 0.844299 0.422149 M10 2.8 7.381067 0.3793 0.706137 0.353069 M11 1.2 7.381067 0.1626 0.871548 0.435774 Multiple Linear Regression - Regression Statistics Multiple R 0.874918892822606 R-squared 0.765483069017934 Adjusted R-squared 0.705606405788471 F-TEST (value) 12.7843307848401 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 4.78992401298228e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.6704911953885 Sum Squared Residuals 6401.41714285715 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 84 87.9257142857143 -3.92571428571433 2 78 85.9257142857143 -7.92571428571435 3 74 85.9257142857143 -11.9257142857143 4 75 77.0628571428572 -2.06285714285715 5 79 82.7257142857143 -3.72571428571428 6 79 84.1257142857143 -5.12571428571429 7 82 84.5257142857143 -2.52571428571428 8 88 85.9257142857143 2.07428571428572 9 81 85.5257142857143 -4.52571428571428 10 69 51.4742857142857 17.5257142857143 11 62 49.8742857142857 12.1257142857143 12 62 48.6742857142857 13.3257142857143 13 68 49.6114285714286 18.3885714285714 14 57 47.6114285714286 9.38857142857144 15 67 47.6114285714286 19.3885714285714 16 72 77.0628571428571 -5.06285714285714 17 75 82.7257142857143 -7.72571428571428 18 81 84.1257142857143 -3.12571428571428 19 80 84.5257142857143 -4.52571428571428 20 79 85.9257142857143 -6.92571428571428 21 81 85.5257142857143 -4.52571428571428 22 83 89.7885714285714 -6.78857142857142 23 84 88.1885714285714 -4.18857142857142 24 90 86.9885714285714 3.01142857142858 25 84 87.9257142857143 -3.92571428571427 26 90 85.9257142857143 4.07428571428573 27 92 85.9257142857143 6.07428571428571 28 93 77.0628571428571 15.9371428571429 29 85 82.7257142857143 2.27428571428572 30 93 84.1257142857143 8.87428571428572 31 94 84.5257142857143 9.47428571428572 32 94 85.9257142857143 8.07428571428572 33 102 85.5257142857143 16.4742857142857 34 96 89.7885714285714 6.21142857142858 35 96 88.1885714285714 7.81142857142858 36 92 86.9885714285714 5.01142857142858 37 90 87.9257142857143 2.07428571428573 38 84 85.9257142857143 -1.92571428571427 39 86 85.9257142857143 0.0742857142857098 40 70 77.0628571428571 -7.06285714285714 41 67 44.4114285714286 22.5885714285714 42 60 45.8114285714286 14.1885714285714 43 62 46.2114285714286 15.7885714285714 44 61 47.6114285714286 13.3885714285714 45 54 47.2114285714286 6.78857142857142 46 50 51.4742857142857 -1.47428571428571 47 45 49.8742857142857 -4.87428571428572 48 34 48.6742857142857 -14.6742857142857 49 37 49.6114285714286 -12.6114285714286 50 44 47.6114285714286 -3.61142857142856 51 34 47.6114285714286 -13.6114285714286 52 37 38.7485714285714 -1.74857142857143 53 31 44.4114285714286 -13.4114285714286 54 31 45.8114285714286 -14.8114285714286 55 28 46.2114285714286 -18.2114285714286 56 31 47.6114285714286 -16.6114285714286 57 33 47.2114285714286 -14.2114285714286 58 36 51.4742857142857 -15.4742857142857 59 39 49.8742857142857 -10.8742857142857 60 42 48.6742857142857 -6.67428571428571 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0680090233851259 0.136018046770252 0.931990976614874 17 0.0285585574093204 0.0571171148186407 0.97144144259068 18 0.009470871682521 0.018941743365042 0.990529128317479 19 0.00306281149525672 0.00612562299051345 0.996937188504743 20 0.00411222615813483 0.00822445231626965 0.995887773841865 21 0.00147751092654899 0.00295502185309797 0.998522489073451 22 0.000476889716191045 0.00095377943238209 0.999523110283809 23 0.000334268896945277 0.000668537793890555 0.999665731103055 24 0.000590785252297 0.001181570504594 0.999409214747703 25 0.000197799288300039 0.000395598576600078 0.9998022007117 26 0.000799624852329818 0.00159924970465964 0.99920037514767 27 0.00125828008506035 0.00251656017012069 0.99874171991494 28 0.00893013446513733 0.0178602689302747 0.991069865534863 29 0.0072915042357765 0.014583008471553 0.992708495764223 30 0.00775851148646276 0.0155170229729255 0.992241488513537 31 0.0076124374115742 0.0152248748231484 0.992387562588426 32 0.00571252351748148 0.0114250470349630 0.994287476482518 33 0.0126885531447921 0.0253771062895842 0.987311446855208 34 0.0085392803314788 0.0170785606629576 0.991460719668521 35 0.00662093976206782 0.0132418795241356 0.993379060237932 36 0.00372371539125918 0.00744743078251835 0.99627628460874 37 0.00198138819291043 0.00396277638582087 0.99801861180709 38 0.000851847652512999 0.00170369530502600 0.999148152347487 39 0.000434628516133646 0.000869257032267293 0.999565371483866 40 0.000231578056050741 0.000463156112101483 0.99976842194395 41 0.000989616465318267 0.00197923293063653 0.999010383534682 42 0.00201450004714807 0.00402900009429613 0.997985499952852 43 0.0131467576062889 0.0262935152125779 0.986853242393711 44 0.0933231650504135 0.186646330100827 0.906676834949586 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 16 0.551724137931034 NOK 5% type I error level 26 0.896551724137931 NOK 10% type I error level 27 0.93103448275862 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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