multiple regression with monthly dummies and linear trend, 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 08:27:59 -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/t125864466433g9plaenpn1bpf.htm/, Retrieved Thu, 19 Nov 2009 16:31:17 +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/Nov/19/t125864466433g9plaenpn1bpf.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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95.1 117.1 97 118.7 112.7 126.5 102.9 127.5 97.4 134.6 111.4 131.8 87.4 135.9 96.8 142.7 114.1 141.7 110.3 153.4 103.9 145 101.6 137.7 94.6 148.3 95.9 152.2 104.7 169.4 102.8 168.6 98.1 161.1 113.9 174.1 80.9 179 95.7 190.6 113.2 190 105.9 181.6 108.8 174.8 102.3 180.5 99 196.8 100.7 193.8 115.5 197 100.7 216.3 109.9 221.4 114.6 217.9 85.4 229.7 100.5 227.4 114.8 204.2 116.5 196.6 112.9 198.8 102 207.5 106 190.7 105.3 201.6 118.8 210.5 106.1 223.5 109.3 223.8 117.2 231.2 92.5 244 104.2 234.7 112.5 250.2 122.4 265.7 113.3 287.6 100 283.3 110.7 295.4 112.8 312.3 109.8 333.8 117.3 347.7 109.1 383.2 115.9 407.1 96 413.6 99.8 362.7 116.8 321.9 115.7 239.4 99.4 191 94.3 159.7 91 163.4

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 tot.ind.prod.index[t] = + 91.8225099826307 + 0.0465801300311876prijsindex.grondst.incl.energie[t] -0.358162974657512M1[t] + 1.98362012729574M2[t] + 11.4201161248545M3[t] + 4.6702676396893M4[t] + 3.11538370796093M5[t] + 12.6237898412482M6[t] -13.8873676800777M7[t] -2.49411581167839M8[t] + 12.8750322127584M9[t] + 13.4416799885274M10[t] + 7.33207813729798M11[t] -0.0224151215242509t + 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) 91.8225099826307 2.602587 35.2813 0 0 prijsindex.grondst.incl.energie 0.0465801300311876 0.014497 3.213 0.002374 0.001187 M1 -0.358162974657512 2.755462 -0.13 0.897135 0.448567 M2 1.98362012729574 2.933325 0.6762 0.502205 0.251103 M3 11.4201161248545 2.953214 3.867 0.000338 0.000169 M4 4.6702676396893 2.969676 1.5727 0.122508 0.061254 M5 3.11538370796093 2.984416 1.0439 0.301879 0.150939 M6 12.6237898412482 2.999031 4.2093 0.000115 5.7e-05 M7 -13.8873676800777 3.017088 -4.6029 3.2e-05 1.6e-05 M8 -2.49411581167839 2.966896 -0.8406 0.404802 0.202401 M9 12.8750322127584 2.923458 4.404 6.1e-05 3.1e-05 M10 13.4416799885274 2.885767 4.6579 2.6e-05 1.3e-05 M11 7.33207813729798 2.873289 2.5518 0.014028 0.007014 t -0.0224151215242509 0.058184 -0.3852 0.701795 0.350898 Multiple Linear Regression - Regression Statistics Multiple R 0.89764089211575 R-squared 0.80575917119836 Adjusted R-squared 0.752032984508545 F-TEST (value) 14.9975127743638 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 1.48236978247951e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.53809224582419 Sum Squared Residuals 967.931217885652 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.1 96.896465113101 -1.79646511310108 2 97 99.29036130158 -2.29036130157994 3 112.7 109.067767191858 3.63223280814230 4 102.9 102.342083715199 0.557916284800547 5 97.4 101.095503585168 -3.69550358516828 6 111.4 110.451070232844 0.948929767156081 7 87.4 84.1084761231217 3.29152387687832 8 96.8 95.7960577542088 1.00394224579119 9 114.1 111.096210527090 3.00378947290986 10 110.3 112.185430702700 -1.88543070269976 11 103.9 105.662140637684 -1.76214063768416 12 101.6 97.9676124296343 3.63238757036573 13 94.6 98.0807837117831 -3.4807837117831 14 95.9 100.581814199334 -4.68181419933372 15 104.7 110.797073311905 -6.09707331190463 16 102.8 103.987545601190 -1.18754560119027 17 98.1 102.060895572704 -3.96089557270374 18 113.9 112.152428274872 1.74757172512785 19 80.9 85.8470982691749 -4.94709826917484 20 95.7 97.7582645244117 -2.05826452441169 21 113.2 113.077049349305 0.122950650694521 22 105.9 113.230008911288 -7.33000891128824 23 108.8 106.781247054323 2.01875294567745 24 102.3 99.692260536678 2.60773946332191 25 99 100.070938560005 -1.07093856000468 26 100.7 102.25056615034 -1.55056615034012 27 115.5 111.813703442474 3.6862965575256 28 100.7 105.940436345387 -5.2404363453869 29 109.9 104.600695955293 5.29930404470667 30 114.6 113.923656511947 0.676343488052836 31 85.4 87.939729403465 -2.53972940346504 32 100.5 99.2034318512684 1.29656814873161 33 114.8 113.469505737457 1.33049426254266 34 116.5 113.659729403465 2.84027059653495 35 112.9 107.63018871678 5.26981128321996 36 102 100.680942589229 1.31905741077086 37 106 99.5178183085234 6.48218169147658 38 105.3 102.344909706292 2.95509029370762 39 118.8 112.173553739604 6.62644626039557 40 106.1 106.006831823320 0.0931681766795536 41 109.3 104.443506809077 4.85649319092282 42 117.2 114.274190783071 2.92580921692906 43 92.5 88.33684380462 4.16315619537998 44 104.2 99.274485342205 4.92551465779495 45 112.5 115.343210260601 -2.84321026060095 46 122.4 116.609434930329 5.79056506967091 47 113.3 111.497522805258 1.80247719474150 48 100 103.942734987302 -3.94273498730215 49 110.7 104.125776464498 6.57422353550225 50 112.8 107.232348642454 5.56765135754617 51 109.8 117.647902314159 -7.84790231415885 52 117.3 111.523102514903 5.77689748509707 53 109.1 111.599398077757 -2.49939807775748 54 115.9 122.198654197266 -6.29865419726583 55 96 95.9678523996184 0.032147600381574 56 99.8 104.967760527906 -5.16776052790605 57 116.8 118.414024125546 -1.61402412554610 58 115.7 115.115396052218 0.584603947782148 59 99.4 106.728900785955 -7.32890078595475 60 94.3 97.9164494571563 -3.61644945715635 61 91 97.70821784209 -6.70821784208998 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0937793426544245 0.187558685308849 0.906220657345576 18 0.119196181718474 0.238392363436948 0.880803818281526 19 0.0859624197077843 0.171924839415569 0.914037580292216 20 0.051786956021849 0.103573912043698 0.948213043978151 21 0.0264964387803404 0.0529928775606807 0.97350356121966 22 0.0324122536172082 0.0648245072344164 0.967587746382792 23 0.039132906764254 0.078265813528508 0.960867093235746 24 0.0228412759325923 0.0456825518651846 0.977158724067408 25 0.0396784634026749 0.0793569268053499 0.960321536597325 26 0.0521797153227162 0.104359430645432 0.947820284677284 27 0.0542468890927848 0.108493778185570 0.945753110907215 28 0.0815167401301334 0.163033480260267 0.918483259869867 29 0.261177651181226 0.522355302362451 0.738822348818774 30 0.189553424083017 0.379106848166035 0.810446575916983 31 0.228605724257815 0.457211448515630 0.771394275742185 32 0.190718882997110 0.381437765994219 0.80928111700289 33 0.136547545179578 0.273095090359157 0.863452454820422 34 0.187566632382688 0.375133264765376 0.812433367617312 35 0.135958840439562 0.271917680879125 0.864041159560438 36 0.102518571185457 0.205037142370913 0.897481428814543 37 0.07120307327596 0.14240614655192 0.92879692672404 38 0.0748953249621022 0.149790649924204 0.925104675037898 39 0.106583459598786 0.213166919197571 0.893416540401214 40 0.270713646970908 0.541427293941817 0.729286353029092 41 0.184233109916253 0.368466219832507 0.815766890083747 42 0.144590232197692 0.289180464395384 0.855409767802308 43 0.0847002858923725 0.169400571784745 0.915299714107628 44 0.153318351718373 0.306636703436745 0.846681648281627 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 1 0.0357142857142857 OK 10% type I error level 5 0.178571428571429 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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