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 12:41:50 -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/t125857351218e0rf5ajsih91c.htm/, Retrieved Wed, 18 Nov 2009 20:45:24 +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/18/t125857351218e0rf5ajsih91c.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 Januari 2004 - Januari 2009 Basisjaar 2000=100 Quarterly dummies

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Energieprijsindex[t] = -74.6161237649833 + 2.83539086868026totindusprodindex[t] -16.1680758262366Q1[t] -26.4898484416942Q2[t] -1.08872420201358Q3[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) -74.6161237649833 110.717431 -0.6739 0.503126 0.251563 totindusprodindex 2.83539086868026 1.072798 2.643 0.010637 0.005319 Q1 -16.1680758262366 25.684884 -0.6295 0.531596 0.265798 Q2 -26.4898484416942 27.334113 -0.9691 0.336656 0.168328 Q3 -1.08872420201358 25.765151 -0.0423 0.966445 0.483223 Multiple Linear Regression - Regression Statistics Multiple R 0.334720114098809 R-squared 0.112037554782320 Adjusted R-squared 0.0486116658381996 F-TEST (value) 1.76643255061081 F-TEST (DF numerator) 4 F-TEST (DF denominator) 56 p-value 0.148504525221584 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 70.4995807399476 Sum Squared Residuals 278330.68953247 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 117.1 178.861472020272 -61.7614720202719 2 118.7 173.926942055307 -55.2269420553073 3 126.5 243.843702933268 -117.343702933268 4 127.5 217.145596622215 -89.645596622215 5 134.6 185.382871018237 -50.7828710182369 6 131.8 214.756570564303 -82.956570564303 7 135.9 172.108313955657 -36.2083139556574 8 142.7 199.849712323265 -57.1497123232654 9 141.7 232.733898525197 -91.0338985251972 10 153.4 211.637640608755 -58.2376406087546 11 145 218.892263288882 -73.8922632888816 12 137.7 213.459588492931 -75.7595884929306 13 148.3 177.443776585932 -29.1437765859322 14 152.2 170.808012099759 -18.608012099759 15 169.4 221.160575983826 -51.7605759838258 16 168.6 216.862057535347 -48.2620575353469 17 161.1 187.367644626313 -26.2676446263131 18 174.1 221.845047736004 -47.7450477360036 19 179 153.678273309236 25.3217266907642 20 190.6 196.730782367717 -6.13078236771712 21 190 230.182046743385 -40.1820467433850 22 181.6 199.161920786562 -17.5619207865615 23 174.8 232.785678545415 -57.9856785454149 24 180.5 215.444362101007 -34.9443621010068 25 196.8 189.919496408125 6.8805035918747 26 193.8 184.417888269424 9.38211173057581 27 197 251.782797365573 -54.7827973655726 28 216.3 210.907736711118 5.39226328888162 29 221.4 220.82525687674 0.574743123259888 30 217.9 223.829821344080 -5.92982134407972 31 229.7 166.437532218297 63.2624677817031 32 227.4 210.340658537382 17.0593414626177 33 204.2 234.718672133273 -30.5186721332734 34 196.6 229.217063994572 -32.6170639945722 35 198.8 244.410781107004 -45.6107811070039 36 207.5 214.593744840403 -7.09374484040271 37 190.7 209.767232488887 -19.0672324888871 38 201.6 197.460686265353 4.13931373464664 39 210.5 261.139587232217 -50.6395872322174 40 223.5 226.218847401992 -2.71884740199175 41 223.8 219.124022355532 4.67597764446807 42 231.2 231.201837602648 -0.00183760264842636 43 244 186.568807385927 57.4311926140733 44 234.7 220.831604751499 13.8683952485007 45 250.2 228.197273135309 22.0027268646912 46 265.7 245.945870119786 19.7541298802142 47 287.6 245.544937454476 42.055062545524 48 283.3 208.922963103042 74.3770368969578 49 295.4 223.093569571684 72.3064304283157 50 312.3 218.726117780455 93.5738822195447 51 333.8 235.621069414095 98.1789305859049 52 347.7 257.975225131211 89.7247748687894 53 383.2 218.556944181796 164.643055818204 54 407.1 227.515829473364 179.584170526636 55 413.6 196.492675426308 217.107324573692 56 362.7 208.355884929306 154.344115070694 57 321.9 240.389453870634 81.5105461293661 58 239.4 226.948751299628 12.4512487003720 59 191 206.133004379820 -15.1330043798205 60 159.7 192.761235151565 -33.0612351515647 61 163.4 167.236369458683 -3.83636945868326 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.00621832887146033 0.0124366577429207 0.99378167112854 9 0.00166265762584049 0.00332531525168098 0.99833734237416 10 0.00113943472565917 0.00227886945131835 0.99886056527434 11 0.000299031221628023 0.000598062443256046 0.999700968778372 12 6.06539261425395e-05 0.000121307852285079 0.999939346073857 13 2.6413558196087e-05 5.2827116392174e-05 0.999973586441804 14 1.07237765282257e-05 2.14475530564513e-05 0.999989276223472 15 1.51494157300699e-05 3.02988314601398e-05 0.99998485058427 16 1.49087128230088e-05 2.98174256460176e-05 0.999985091287177 17 9.05513292013106e-06 1.81102658402621e-05 0.99999094486708 18 8.04975749495783e-06 1.60995149899157e-05 0.999991950242505 19 8.74979848601027e-06 1.74995969720205e-05 0.999991250201514 20 1.36313585953729e-05 2.72627171907458e-05 0.999986368641405 21 2.66475231953851e-05 5.32950463907703e-05 0.999973352476805 22 2.09163338594476e-05 4.18326677188952e-05 0.99997908366614 23 1.25865042482255e-05 2.51730084964510e-05 0.999987413495752 24 7.85877709463213e-06 1.57175541892643e-05 0.999992141222905 25 1.06312153695202e-05 2.12624307390404e-05 0.99998936878463 26 1.01339666096004e-05 2.02679332192008e-05 0.99998986603339 27 1.04447915540703e-05 2.08895831081406e-05 0.999989555208446 28 1.73517363018377e-05 3.47034726036754e-05 0.999982648263698 29 2.89774286908723e-05 5.79548573817447e-05 0.999971022571309 30 3.24368570309026e-05 6.48737140618051e-05 0.999967563142969 31 7.83207899082903e-05 0.000156641579816581 0.999921679210092 32 8.78524002553905e-05 0.000175704800510781 0.999912147599745 33 6.80792741481706e-05 0.000136158548296341 0.999931920725852 34 5.17544887777433e-05 0.000103508977555487 0.999948245511222 35 4.72887257894054e-05 9.45774515788108e-05 0.99995271127421 36 3.23824042864875e-05 6.4764808572975e-05 0.999967617595714 37 2.32393361852589e-05 4.64786723705177e-05 0.999976760663815 38 1.73348069238069e-05 3.46696138476138e-05 0.999982665193076 39 3.31010550943395e-05 6.62021101886791e-05 0.999966898944906 40 2.99920272115804e-05 5.99840544231609e-05 0.999970007972788 41 3.11204498859463e-05 6.22408997718925e-05 0.999968879550114 42 3.72596331570583e-05 7.45192663141167e-05 0.999962740366843 43 5.30961980570826e-05 0.000106192396114165 0.999946903801943 44 4.77900279251915e-05 9.5580055850383e-05 0.999952209972075 45 6.1548395650174e-05 0.000123096791300348 0.99993845160435 46 0.000110237041702418 0.000220474083404835 0.999889762958298 47 0.000247876947713140 0.000495753895426279 0.999752123052287 48 0.000311044296037877 0.000622088592075755 0.999688955703962 49 0.000380047693320003 0.000760095386640006 0.99961995230668 50 0.00049118977488305 0.0009823795497661 0.999508810225117 51 0.000633550418625825 0.00126710083725165 0.999366449581374 52 0.000564324814354569 0.00112864962870914 0.999435675185645 53 0.00181567045023681 0.00363134090047363 0.998184329549763 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 45 0.978260869565217 NOK 5% type I error level 46 1 NOK 10% type I error level 46 1 NOK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

par1 = 1 ; par2 = Include Quarterly 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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