Grondstofprijsindex & Totale productieindex

*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: Wed, 18 Nov 2009 12:47:38 -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/18/t125857379798etzi9m4ifizlt.htm/, Retrieved Wed, 18 Nov 2009 20:50:10 +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/18/t125857379798etzi9m4ifizlt.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:

Tijdsperiode 2004 - 2009 Basisjaar 2000 = 100 Quarterly dummies Linear trend

Dataseries X:

» Textbox « » Textfile « » CSV «

117.1 95.1 118.7 97 126.5 112.7 127.5 102.9 134.6 97.4 131.8 111.4 135.9 87.4 142.7 96.8 141.7 114.1 153.4 110.3 145 103.9 137.7 101.6 148.3 94.6 152.2 95.9 169.4 104.7 168.6 102.8 161.1 98.1 174.1 113.9 179 80.9 190.6 95.7 190 113.2 181.6 105.9 174.8 108.8 180.5 102.3 196.8 99 193.8 100.7 197 115.5 216.3 100.7 221.4 109.9 217.9 114.6 229.7 85.4 227.4 100.5 204.2 114.8 196.6 116.5 198.8 112.9 207.5 102 190.7 106 201.6 105.3 210.5 118.8 223.5 106.1 223.8 109.3 231.2 117.2 244 92.5 234.7 104.2 250.2 112.5 265.7 122.4 287.6 113.3 283.3 100 295.4 110.7 312.3 112.8 333.8 109.8 347.7 117.3 383.2 109.1 407.1 115.9 413.6 96 362.7 99.8 321.9 116.8 239.4 115.7 191 99.4 159.7 94.3 163.4 91

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 Energieprijsindex[t] = + 8.00420722973749 + 1.07246415184596totindusprodindex[t] -6.22216318831792Q1[t] -5.33459235212556Q2[t] + 3.70062778916478Q3[t] + 3.02642527434408t + 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) 8.00420722973749 73.627296 0.1087 0.913826 0.456913 totindusprodindex 1.07246415184596 0.73646 1.4562 0.151011 0.075505 Q1 -6.22216318831792 16.973724 -0.3666 0.715342 0.357671 Q2 -5.33459235212556 18.188964 -0.2933 0.770406 0.385203 Q3 3.70062778916478 16.996272 0.2177 0.828444 0.414222 t 3.02642527434408 0.352222 8.5924 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.787977569766432 R-squared 0.620908650455013 Adjusted R-squared 0.586445800496378 F-TEST (value) 18.0167528570699 F-TEST (DF numerator) 5 F-TEST (DF denominator) 55 p-value 1.52458712321391e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 46.4808264055017 Sum Squared Residuals 118825.697283611 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 117.1 106.799810156314 10.3001898436863 2 118.7 112.751488155358 5.94851184464198 3 126.5 141.650820754974 -15.1508207549741 4 127.5 130.466469552063 -2.96646955206286 5 134.6 121.372178802936 13.2278211970637 6 131.8 140.300673039316 -8.50067303931608 7 135.9 126.623178810648 9.27682118935242 8 142.7 136.030139323179 6.66986067682111 9 141.7 151.38803123614 -9.6880312361401 10 153.4 151.226663569662 2.17333643033807 11 145 156.424538413482 -11.4245384134822 12 137.7 153.283668349416 -15.5836683494158 13 148.3 142.580681372520 5.71931862747976 14 152.2 147.888880880456 4.31111911954351 15 169.4 169.388210832335 0.0117891676646906 16 168.6 166.676326429007 1.92367357099271 17 161.1 158.440007001357 2.65999299864257 18 174.1 179.29893671106 -5.19893671106007 19 179 155.969265115778 23.0307348842221 20 190.6 171.167532048277 19.4324679517227 21 190 186.739916791608 3.26008320839226 22 181.6 182.824924593669 -1.22492459366874 23 174.8 197.996716049656 -23.1967160496564 24 180.5 190.351496547837 -9.85149654783698 25 196.8 183.616626932771 13.1833730672285 26 193.8 189.353812101446 4.44618789855394 27 197 217.287926964401 -20.2879269644007 28 216.3 200.741255002260 15.5587449977402 29 221.4 207.412187285269 13.9878127147313 30 217.9 216.366764909481 1.53323509051879 31 229.7 197.112457091214 32.5875429087863 32 227.4 212.632463269267 14.7675367307331 33 204.2 224.772962726690 -20.5729627266903 34 196.6 230.510147895365 -33.9101478953649 35 198.8 238.710922364354 -39.9109223643538 36 207.5 226.346860594412 -18.8468605944122 37 190.7 227.440979287822 -36.7409792878222 38 201.6 230.604250492066 -29.0042504920665 39 210.5 257.144161957621 -46.6441619576213 40 223.5 242.849664714357 -19.3496647143569 41 223.8 243.08581208629 -19.2858120862901 42 231.2 255.472274996410 -24.2722749964097 43 244 241.044055861449 2.95594413855106 44 234.7 252.917683923226 -18.2176839232260 45 250.2 258.623398469574 -8.42339846957358 46 265.7 273.154789683385 -7.45478968338505 47 287.6 275.457011317221 12.1429886827788 48 283.3 260.519035582849 22.7809644171508 49 295.4 268.798664093627 26.6013359063728 50 312.3 274.96483492304 37.3351650769598 51 333.8 283.809087883137 49.9909121168633 52 347.7 291.178366507161 56.5216334928393 53 383.2 279.18842254805 104.01157745195 54 407.1 290.395174891139 116.704825108861 55 413.6 281.114783685039 132.485216314961 56 362.7 284.515944947233 78.1840550527672 57 321.9 299.55209761464 22.3479023853598 58 239.4 302.286383158146 -62.8863831581461 59 191 296.866862898691 -105.866862898691 60 159.7 290.723093209456 -131.023093209456 61 163.4 283.988223594391 -120.588223594391 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.000285511164038148 0.000571022328076296 0.999714488835962 10 8.9179686443723e-05 0.000178359372887446 0.999910820313556 11 1.49298498015162e-05 2.98596996030325e-05 0.999985070150198 12 1.85590972052239e-05 3.71181944104479e-05 0.999981440902795 13 2.23495716773956e-06 4.46991433547912e-06 0.999997765042832 14 2.36015983991667e-07 4.72031967983334e-07 0.999999763984016 15 1.00456449493701e-07 2.00912898987401e-07 0.99999989954355 16 2.30364935936087e-08 4.60729871872175e-08 0.999999976963506 17 2.81795211215379e-09 5.63590422430759e-09 0.999999997182048 18 3.36279369894091e-10 6.72558739788181e-10 0.99999999966372 19 6.81301711292285e-11 1.36260342258457e-10 0.99999999993187 20 6.04554157164597e-11 1.20910831432919e-10 0.999999999939545 21 1.16556418056542e-11 2.33112836113085e-11 0.999999999988344 22 1.61839197425718e-12 3.23678394851436e-12 0.999999999998382 23 1.62087272589024e-12 3.24174545178048e-12 0.999999999998379 24 4.26688036127809e-13 8.53376072255619e-13 0.999999999999573 25 6.27478712202247e-14 1.25495742440449e-13 0.999999999999937 26 7.62401354806323e-15 1.52480270961265e-14 0.999999999999992 27 9.49491367910636e-16 1.89898273582127e-15 1 28 5.29711701993917e-16 1.05942340398783e-15 1 29 2.39160882865998e-16 4.78321765731995e-16 1 30 3.65246498128505e-17 7.3049299625701e-17 1 31 3.02031153725308e-17 6.04062307450616e-17 1 32 5.41522820528595e-18 1.08304564105719e-17 1 33 7.5307202208982e-18 1.50614404417964e-17 1 34 3.53781628782863e-17 7.07563257565727e-17 1 35 8.74412788208518e-17 1.74882557641704e-16 1 36 6.89445448731108e-17 1.37889089746222e-16 1 37 6.47700700892697e-16 1.29540140178539e-15 1 38 4.75382369793854e-16 9.50764739587707e-16 1 39 5.77400140217404e-16 1.15480028043481e-15 1 40 1.27456509313913e-16 2.54913018627826e-16 1 41 2.68094047377385e-17 5.3618809475477e-17 1 42 7.77913076342767e-18 1.55582615268553e-17 1 43 1.20233984156447e-18 2.40467968312894e-18 1 44 3.51660902134046e-19 7.03321804268093e-19 1 45 2.24990170534993e-19 4.49980341069986e-19 1 46 1.82683186993496e-18 3.65366373986992e-18 1 47 1.58883086139002e-16 3.17766172278003e-16 1 48 3.69722051334623e-16 7.39444102669246e-16 1 49 3.47583543916558e-14 6.95167087833117e-14 0.999999999999965 50 2.31199336018357e-10 4.62398672036713e-10 0.9999999997688 51 1.74159116745418e-06 3.48318233490835e-06 0.999998258408832 52 0.000491806614042217 0.000983613228084434 0.999508193385958 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 44 1 NOK 5% type I error level 44 1 NOK 10% type I error level 44 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Quarterly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Quarterly 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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