Paper - Regression Analyse - Met trend en seizonaliteit

*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: Fri, 05 Dec 2008 08:26:04 -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/05/t1228490822x01jlghwavevpwv.htm/, Retrieved Fri, 05 Dec 2008 15:27:12 +0000

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/05/t1228490822x01jlghwavevpwv.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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95.2 0 95.00 0 94.00 0 92.2 0 91.00 0 91.2 0 103.4 1 105.00 0 104.6 0 103.8 0 101.8 0 102.4 0 103.8 0 103.4 0 102.00 0 101.8 0 100.2 0 101.4 0 113.8 0 116.00 0 115.6 0 113.00 0 109.4 0 111.00 0 112.4 0 112.2 0 111.00 0 108.8 0 107.4 0 108.6 0 118.8 0 122.2 1 122.6 0 122.2 0 118.8 0 119.00 0 118.2 0 117.8 0 116.8 0 114.6 0 113.4 0 113.8 0 124.2 0 125.8 0 125.6 0 122.4 0 119.00 0 119.4 0 118.6 0 118.00 0 116.00 0 114.8 0 114.6 0 114.6 0 124.00 0 125.2 0 124.00 0 117.6 1 113.2 0 111.4 0 112.2 0 109.8 0 106.4 0 105.2 0 102.2 0 99.8 0 111.00 0 113.00 0 108.4 0 105.4 0 102.00 0 102.8 0

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 Werkloosheid[t] = + 103.498852223816 -0.554088952654242Dumivariabele[t] + 1.03125298900049M1[t] + 0.152654232424681M2[t] -1.69261119081780M3[t] -3.33787661406025M4[t] -4.94980870396939M5[t] -5.02840746054521M6[t] + 5.85200860832138M7[t] + 7.67340985174558M8[t] + 6.3357962697274M9[t] + 3.51621233859398M10[t] -0.121401243424195M11[t] + 0.178598756575801t + 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) 103.498852223816 3.600988 28.7418 0 0 Dumivariabele -0.554088952654242 4.808957 -0.1152 0.908669 0.454334 M1 1.03125298900049 4.406866 0.234 0.815801 0.4079 M2 0.152654232424681 4.402309 0.0347 0.972457 0.486229 M3 -1.69261119081780 4.398181 -0.3848 0.701761 0.35088 M4 -3.33787661406025 4.394484 -0.7596 0.450594 0.225297 M5 -4.94980870396939 4.39122 -1.1272 0.264297 0.132149 M6 -5.02840746054521 4.388389 -1.1458 0.256566 0.128283 M7 5.85200860832138 4.45605 1.3133 0.194263 0.097131 M8 7.67340985174558 4.454633 1.7226 0.090295 0.045148 M9 6.3357962697274 4.382504 1.4457 0.153643 0.076821 M10 3.51621233859398 4.453088 0.7896 0.432971 0.216485 M11 -0.121401243424195 4.380758 -0.0277 0.977987 0.488993 t 0.178598756575801 0.043725 4.0846 0.000137 6.9e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.640784343492286 R-squared 0.410604574864839 Adjusted R-squared 0.278498703713855 F-TEST (value) 3.10814781574362 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0.00149136738186972 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.58731818362793 Sum Squared Residuals 3338.90903873744 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.2 104.708703969393 -9.50870396939259 2 95 104.008703969393 -9.00870396939262 3 94 102.342037302726 -8.34203730272597 4 92.2 100.875370636059 -8.67537063605931 5 91 99.442037302726 -8.44203730272597 6 91.2 99.542037302726 -8.34203730272596 7 103.4 110.046963175514 -6.64696317551412 8 105 112.601052128168 -7.60105212816832 9 104.6 111.442037302726 -6.84203730272598 10 103.8 108.801052128168 -5.00105212816834 11 101.8 105.342037302726 -3.54203730272597 12 102.4 105.642037302726 -3.24203730272596 13 103.8 106.851889048302 -3.05188904830226 14 103.4 106.151889048302 -2.75188904830223 15 102 104.485222381636 -2.48522238163558 16 101.8 103.018555714969 -1.21855571496892 17 100.2 101.585222381636 -1.38522238163558 18 101.4 101.685222381636 -0.285222381635574 19 113.8 112.744237207078 1.05576279292204 20 116 114.744237207078 1.25576279292204 21 115.6 113.585222381636 2.01477761836441 22 113 110.944237207078 2.05576279292204 23 109.4 107.485222381636 1.91477761836442 24 111 107.785222381636 3.21477761836442 25 112.4 108.995074127212 3.40492587278813 26 112.2 108.295074127212 3.90492587278814 27 111 106.628407460545 4.37159253945481 28 108.8 105.161740793879 3.63825920612147 29 107.4 103.728407460545 3.67159253945481 30 108.6 103.828407460545 4.7715925394548 31 118.8 114.887422285988 3.91257771401243 32 122.2 116.333333333333 5.86666666666665 33 122.6 115.728407460545 6.8715925394548 34 122.2 113.087422285988 9.11257771401244 35 118.8 109.628407460545 9.1715925394548 36 119 109.928407460545 9.07159253945481 37 118.2 111.138259206121 7.06174079387852 38 117.8 110.438259206121 7.36174079387852 39 116.8 108.771592539455 8.02840746054519 40 114.6 107.304925872788 7.29507412721185 41 113.4 105.871592539455 7.5284074605452 42 113.8 105.971592539455 7.8284074605452 43 124.2 117.030607364897 7.16939263510282 44 125.8 119.030607364897 6.7693926351028 45 125.6 117.871592539455 7.7284074605452 46 122.4 115.230607364897 7.16939263510283 47 119 111.771592539455 7.2284074605452 48 119.4 112.071592539455 7.3284074605452 49 118.6 113.281444285031 5.3185557149689 50 118 112.581444285031 5.41855571496891 51 116 110.914777618364 5.08522238163559 52 114.8 109.448110951698 5.35188904830225 53 114.6 108.014777618364 6.58522238163558 54 114.6 108.114777618364 6.48522238163558 55 124 119.173792443807 4.82620755619321 56 125.2 121.173792443807 4.02620755619320 57 124 120.014777618364 3.98522238163559 58 117.6 116.819703491153 0.78029650884743 59 113.2 113.914777618364 -0.714777618364414 60 111.4 114.214777618364 -2.81477761836441 61 112.2 115.424629363941 -3.22462936394070 62 109.8 114.724629363941 -4.9246293639407 63 106.4 113.057962697274 -6.65796269727402 64 105.2 111.591296030607 -6.39129603060736 65 102.2 110.157962697274 -7.95796269727402 66 99.8 110.257962697274 -10.4579626972740 67 111 121.316977522716 -10.3169775227164 68 113 123.316977522716 -10.3169775227164 69 108.4 122.157962697274 -13.7579626972740 70 105.4 119.516977522716 -14.1169775227164 71 102 116.057962697274 -14.0579626972740 72 102.8 116.357962697274 -13.5579626972740 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.000928152205296276 0.00185630441059255 0.999071847794704 18 0.000309247113416212 0.000618494226832425 0.999690752886584 19 3.23567820170955e-05 6.47135640341909e-05 0.999967643217983 20 2.63287329633982e-05 5.26574659267964e-05 0.999973671267037 21 1.11294142787016e-05 2.22588285574032e-05 0.999988870585721 22 1.87000273854808e-06 3.74000547709617e-06 0.999998129997261 23 1.13387395547069e-06 2.26774791094139e-06 0.999998866126045 24 2.52555021935058e-07 5.05110043870116e-07 0.999999747444978 25 7.58710922260604e-08 1.51742184452121e-07 0.999999924128908 26 1.99854627580138e-08 3.99709255160276e-08 0.999999980014537 27 5.17699671165076e-09 1.03539934233015e-08 0.999999994823003 28 5.59091398559214e-09 1.11818279711843e-08 0.999999994409086 29 5.79748195802338e-09 1.15949639160468e-08 0.999999994202518 30 3.25917723480674e-09 6.51835446961349e-09 0.999999996740823 31 1.02810985201841e-07 2.05621970403681e-07 0.999999897189015 32 1.15146406786644e-07 2.30292813573287e-07 0.999999884853593 33 8.6333596503733e-08 1.72667193007466e-07 0.999999913666404 34 3.7742201394031e-08 7.5484402788062e-08 0.999999962257799 35 1.54123613434915e-08 3.08247226869830e-08 0.999999984587639 36 6.85435007286094e-09 1.37087001457219e-08 0.99999999314565 37 5.25496176270613e-08 1.05099235254123e-07 0.999999947450382 38 2.28603290733624e-07 4.57206581467248e-07 0.99999977139671 39 3.96015106869575e-07 7.9203021373915e-07 0.999999603984893 40 2.29280955736129e-06 4.58561911472257e-06 0.999997707190443 41 1.07099269519224e-05 2.14198539038449e-05 0.999989290073048 42 4.34355453913659e-05 8.68710907827318e-05 0.99995656445461 43 0.000561941092659683 0.00112388218531937 0.99943805890734 44 0.0112211227691090 0.0224422455382179 0.98877887723089 45 0.0489881969526702 0.0979763939053405 0.95101180304733 46 0.120592083158643 0.241184166317286 0.879407916841357 47 0.28629463744151 0.57258927488302 0.71370536255849 48 0.488876276995072 0.977752553990143 0.511123723004928 49 0.750841758424806 0.498316483150389 0.249158241575194 50 0.844685789593943 0.310628420812115 0.155314210406057 51 0.86772062180286 0.264558756394279 0.132279378197139 52 0.88142713799627 0.237145724007461 0.118572862003730 53 0.807249471021032 0.385501057957936 0.192750528978968 54 0.774366729879871 0.451266540240259 0.225633270120129 55 0.663785585996179 0.672428828007642 0.336214414003821 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 27 0.692307692307692 NOK 5% type I error level 28 0.717948717948718 NOK 10% type I error level 29 0.743589743589744 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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