multiple regression met 4 maanden minder, index van totale industriële productie & prijsindex van grondstoffen, incl. enerige

*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: Thu, 19 Nov 2009 08:39:29 -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/19/t1258645508q2r8f18kfrkbz3f.htm/, Retrieved Thu, 19 Nov 2009 16:45:23 +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/19/t1258645508q2r8f18kfrkbz3f.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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97.4 134.6 102.9 112.7 97 95.1 111.4 131.8 97.4 102.9 112.7 97 87.4 135.9 111.4 97.4 102.9 112.7 96.8 142.7 87.4 111.4 97.4 102.9 114.1 141.7 96.8 87.4 111.4 97.4 110.3 153.4 114.1 96.8 87.4 111.4 103.9 145 110.3 114.1 96.8 87.4 101.6 137.7 103.9 110.3 114.1 96.8 94.6 148.3 101.6 103.9 110.3 114.1 95.9 152.2 94.6 101.6 103.9 110.3 104.7 169.4 95.9 94.6 101.6 103.9 102.8 168.6 104.7 95.9 94.6 101.6 98.1 161.1 102.8 104.7 95.9 94.6 113.9 174.1 98.1 102.8 104.7 95.9 80.9 179 113.9 98.1 102.8 104.7 95.7 190.6 80.9 113.9 98.1 102.8 113.2 190 95.7 80.9 113.9 98.1 105.9 181.6 113.2 95.7 80.9 113.9 108.8 174.8 105.9 113.2 95.7 80.9 102.3 180.5 108.8 105.9 113.2 95.7 99 196.8 102.3 108.8 105.9 113.2 100.7 193.8 99 102.3 108.8 105.9 115.5 197 100.7 99 102.3 108.8 100.7 216.3 115.5 100.7 99 102.3 109.9 221.4 100.7 115.5 100.7 99 114.6 217.9 109.9 100.7 115.5 100.7 85.4 229.7 114.6 109.9 100.7 115.5 100.5 227.4 85.4 114.6 109.9 100.7 114.8 204.2 100.5 85.4 114.6 109.9 116.5 196.6 114.8 100.5 etc...

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 tot.ind.prod.index[t] = + 181.261496740705 + 0.0723003449900399prijsindex.grondst.incl.energie[t] -0.0344610887961219`y(t-1)`[t] -0.405354806386297`y(t-2)`[t] -0.112859202625963`y(t-3)`[t] -0.31403889358322`y(t-4)`[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) 181.261496740705 33.248005 5.4518 1e-06 1e-06 prijsindex.grondst.incl.energie 0.0723003449900399 0.020901 3.4592 0.001103 0.000552 `y(t-1)` -0.0344610887961219 0.13934 -0.2473 0.805656 0.402828 `y(t-2)` -0.405354806386297 0.139292 -2.9101 0.005343 0.002672 `y(t-3)` -0.112859202625963 0.139774 -0.8074 0.423163 0.211581 `y(t-4)` -0.31403889358322 0.142256 -2.2076 0.0318 0.0159 Multiple Linear Regression - Regression Statistics Multiple R 0.491238995726365 R-squared 0.241315750922248 Adjusted R-squared 0.166934942189135 F-TEST (value) 3.24432814098751 F-TEST (DF numerator) 5 F-TEST (DF denominator) 51 p-value 0.0128063031585952 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.40592598582137 Sum Squared Residuals 3603.63917563446 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.4 100.951149025025 -3.55114902502536 2 111.4 102.542157770982 8.8578422290183 3 87.4 100.761194933898 -13.3611949338977 4 96.8 100.103242893087 -3.30324289308704 5 114.1 109.582708744629 4.51729125537117 6 110.3 104.334187117666 5.96581288233378 7 103.9 103.321235148005 0.57876485199455 8 101.6 99.6499120570299 1.95008794297015 9 94.6 98.0858190900166 -3.4858190900166 10 95.9 101.456980804161 -5.55698080416148 11 104.7 107.762656052232 -3.06265605223161 12 102.8 108.386900820155 -5.58690082015467 13 98.1 106.394557296911 -8.29455729691138 14 113.9 106.865191486491 7.03480851350903 15 80.9 106.031035785436 -25.1310357854360 16 95.7 102.729441926839 -7.02944192683917 17 113.2 115.245553614761 -2.04555361476126 18 105.9 106.798449696437 -0.898449696437474 19 108.8 108.157631476339 0.642368523661264 20 102.3 104.806084700907 -2.50608470090717 21 99 100.361240004363 -1.36124000436252 22 100.7 104.858059039473 -4.15805903947275 23 115.5 106.191379179240 9.30862082076033 24 100.7 108.801336729465 -8.10133672946474 25 109.9 104.525309172940 5.37469082706016 26 114.6 107.750284765112 6.84971523488814 27 85.4 101.734738073731 -16.3347380737312 28 100.5 104.279014443958 -3.77901444395809 29 114.8 110.498048272540 4.30195172746007 30 116.5 105.154420421235 11.3455795787650 31 112.9 106.924085330914 5.97591466908639 32 102 100.632181190478 1.36781880952160 33 106 96.56982174281 9.43017825719006 34 105.3 101.510845547990 3.78915445201048 35 118.8 102.917727480536 15.8822725194644 36 106.1 106.647742760682 -0.547742760682093 37 109.3 100.457644673180 8.84235532681986 38 117.2 104.726625773123 12.4733742268774 39 92.5 101.276479017046 -8.77647901704582 40 104.2 101.880116231555 2.31988376844527 41 112.5 110.713328397516 1.78667160248416 42 122.4 107.112020518688 15.2879794813122 43 113.3 111.426096402664 1.87390359733640 44 100 102.804801807308 -2.80480180730762 45 110.7 104.102868278053 6.59713172194693 46 112.8 108.265263080626 4.53473691937363 47 109.8 109.768837109640 0.0311628903603979 48 117.3 112.995073894537 4.30492610546267 49 109.1 112.922121908017 -3.82212190801674 50 115.9 111.571615964863 4.32838403513721 51 96 115.226814876907 -19.226814876907 52 99.8 108.046244060189 -8.24624406018872 53 116.8 114.839674843783 1.96032515621701 54 115.7 106.859143264193 8.84085673580655 55 99.4 102.327191068112 -2.92719106811164 56 94.3 97.9598420640675 -3.65984206406751 57 91 99.7958721694613 -8.79587216946133 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.53346611711588 0.933067765768241 0.466533882884121 10 0.431299387242889 0.862598774485777 0.568700612757111 11 0.362446418482482 0.724892836964963 0.637553581517518 12 0.284660654154233 0.569321308308466 0.715339345845767 13 0.256133241316617 0.512266482633233 0.743866758683383 14 0.252202661877389 0.504405323754779 0.74779733812261 15 0.680491926739614 0.639016146520772 0.319508073260386 16 0.608799605173275 0.78240078965345 0.391200394826725 17 0.517635444655832 0.964729110688336 0.482364555344168 18 0.551499332854422 0.897001334291155 0.448500667145578 19 0.469007607702257 0.938015215404514 0.530992392297743 20 0.429727155367801 0.859454310735602 0.570272844632199 21 0.43933826736017 0.87867653472034 0.56066173263983 22 0.382540297884216 0.765080595768431 0.617459702115784 23 0.471145612477271 0.942291224954543 0.528854387522729 24 0.474245189069636 0.948490378139273 0.525754810930364 25 0.443041928916165 0.88608385783233 0.556958071083835 26 0.421098240991004 0.842196481982008 0.578901759008996 27 0.648106696194557 0.703786607610887 0.351893303805443 28 0.610982732723435 0.77803453455313 0.389017267276565 29 0.547581988507213 0.904836022985575 0.452418011492787 30 0.633956891034685 0.73208621793063 0.366043108965315 31 0.57301010571631 0.853979788567381 0.426989894283691 32 0.497996901502567 0.995993803005134 0.502003098497433 33 0.545699855049547 0.908600289900905 0.454300144950453 34 0.472467518080049 0.944935036160097 0.527532481919951 35 0.584227659846452 0.831544680307096 0.415772340153548 36 0.503155061335456 0.993689877329088 0.496844938664544 37 0.481835235066548 0.963670470133096 0.518164764933452 38 0.637620692602485 0.72475861479503 0.362379307397515 39 0.643107863314867 0.713784273370266 0.356892136685133 40 0.550840307783422 0.898319384433156 0.449159692216578 41 0.45423649265208 0.90847298530416 0.54576350734792 42 0.47853608588757 0.95707217177514 0.52146391411243 43 0.378423475767937 0.756846951535873 0.621576524232063 44 0.287123754753799 0.574247509507599 0.7128762452462 45 0.405400573274817 0.810801146549635 0.594599426725183 46 0.445712783269265 0.89142556653853 0.554287216730735 47 0.323004618765948 0.646009237531896 0.676995381234052 48 0.218364660504086 0.436729321008172 0.781635339495914 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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