Model 3, seizonaliteit + lineair verband

*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 10:09:33 -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/t1258653210fvc0u7pz2wm3eit.htm/, Retrieved Thu, 19 Nov 2009 18:53:43 +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/t1258653210fvc0u7pz2wm3eit.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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96.8 9.3 114.1 9.3 110.3 8.7 103.9 8.2 101.6 8.3 94.6 8.5 95.9 8.6 104.7 8.5 102.8 8.2 98.1 8.1 113.9 7.9 80.9 8.6 95.7 8.7 113.2 8.7 105.9 8.5 108.8 8.4 102.3 8.5 99 8.7 100.7 8.7 115.5 8.6 100.7 8.5 109.9 8.3 114.6 8 85.4 8.2 100.5 8.1 114.8 8.1 116.5 8 112.9 7.9 102 7.9 106 8 105.3 8 118.8 7.9 106.1 8 109.3 7.7 117.2 7.2 92.5 7.5 104.2 7.3 112.5 7 122.4 7 113.3 7 100 7.2 110.7 7.3 112.8 7.1 109.8 6.8 117.3 6.4 109.1 6.1 115.9 6.5 96 7.7 99.8 7.9 116.8 7.5 115.7 6.9 99.4 6.6 94.3 6.9 91 7.7 93.2 8 103.1 8 94.1 7.7 91.8 7.3 102.7 7.4 82.6 8.1 89.1 8.3

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 tip[t] = + 148.709722845724 -6.73344601992774wrk[t] + 10.8604325507622M1[t] + 25.4657096670195M2[t] + 23.5264393545385M3[t] + 15.8805136440503M4[t] + 9.40395958033748M5[t] + 11.7100879594146M6[t] + 13.5001892937090M7[t] + 21.692939264815M8[t] + 14.3670135543268M9[t] + 12.2570810826429M10[t] + 21.0044999741475M11[t] -0.200763493497329t + 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) 148.709722845724 15.459616 9.6192 0 0 wrk -6.73344601992774 1.681322 -4.0049 0.000219 0.00011 M1 10.8604325507622 3.457746 3.1409 0.002912 0.001456 M2 25.4657096670195 3.636829 7.0022 0 0 M3 23.5264393545385 3.698346 6.3613 0 0 M4 15.8805136440503 3.764367 4.2186 0.000111 5.6e-05 M5 9.40395958033748 3.692156 2.547 0.014198 0.007099 M6 11.7100879594146 3.617235 3.2373 0.002215 0.001107 M7 13.5001892937090 3.608518 3.7412 0.000498 0.000249 M8 21.692939264815 3.615371 6.0002 0 0 M9 14.3670135543268 3.648186 3.9381 0.000271 0.000135 M10 12.2570810826429 3.728772 3.2872 0.00192 0.00096 M11 21.0044999741475 3.76136 5.5843 1e-06 1e-06 t -0.200763493497329 0.062979 -3.1878 0.002551 0.001275 Multiple Linear Regression - Regression Statistics Multiple R 0.85112026922121 R-squared 0.724405712679186 Adjusted R-squared 0.648177505547897 F-TEST (value) 9.50311885771538 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 3.17124770887744e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.69196778054146 Sum Squared Residuals 1522.72936909194 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 96.8 96.7483439176615 0.0516560823385169 2 114.1 111.152857540421 2.94714245957885 3 110.3 113.052891346400 -2.7528913463995 4 103.9 108.572925152378 -4.67292515237781 5 101.6 101.222262993175 0.377737006825067 6 94.6 101.980938674769 -7.38093867476915 7 95.9 102.896931913573 -6.99693191357347 8 104.7 111.562262993175 -6.86226299317491 9 102.8 106.055607595168 -3.25560759516771 10 98.1 104.418256231979 -6.31825623197926 11 113.9 114.311600833972 -0.411600833972023 12 80.9 88.3929251523778 -7.49292515237782 13 95.7 98.3792496076499 -2.67924960764985 14 113.2 112.783763230410 0.416236769590139 15 105.9 111.990418628417 -6.09041862841709 16 108.8 104.817074026424 3.98292597357569 17 102.3 97.4664118672214 4.83358813277858 18 99 98.2250875488157 0.774912451184354 19 100.7 99.8144253896128 0.885574610387246 20 115.5 108.479756469214 7.0202435307858 21 100.7 101.626411867221 -0.926411867221417 22 109.9 100.662405106026 9.23759489397426 23 114.6 111.229094310011 3.37090568998868 24 85.4 88.677141638381 -3.27714163838096 25 100.5 100.010155297639 0.489844702361455 26 114.8 114.414668920399 0.385331079601439 27 116.5 112.947979716413 3.55202028358699 28 112.9 105.774635114420 7.12536488557977 29 102 99.0973175572101 2.90268244278989 30 106 100.529337840797 5.4706621592029 31 105.3 102.118675681594 3.18132431840578 32 118.8 110.784006761196 8.01599323880433 33 106.1 102.583972955217 3.51602704478266 34 109.3 102.293310796014 7.00668920398555 35 117.2 114.206689203986 2.99331079601445 36 92.5 90.9813919303624 1.51860806963758 37 104.2 102.987750191613 1.21224980838722 38 112.5 119.412297620351 -6.91229762035112 39 122.4 117.272263814373 5.12773618562722 40 113.3 109.425574610387 3.87442538961275 41 100 101.401567849192 -1.40156784919158 42 110.7 102.833588132779 7.86641186722143 43 112.8 105.769615177561 7.03038482243877 44 109.8 115.781635461148 -5.98163546114823 45 117.3 110.948324665134 6.35167533486623 46 109.1 110.657662505931 -1.55766250593089 47 115.9 116.510939495967 -0.610939495967005 48 96 87.225540804409 8.77445919559107 49 99.8 96.5385206576882 3.26147934231181 50 116.8 113.636412688419 3.16358731158070 51 115.7 115.536446494398 0.163553505602383 52 99.4 109.709791096390 -10.3097910963904 53 94.3 101.012439733202 -6.71243973320195 54 91 97.7310478028395 -6.73104780283953 55 93.2 97.3003518376583 -4.10035183765832 56 103.1 105.292338315267 -2.19233831526699 57 94.1 99.7856829172598 -5.68568291725976 58 91.8 100.168365360050 -8.36836536004965 59 102.7 108.041676156064 -5.3416761560641 60 82.6 82.1230004744699 0.47699952553011 61 89.1 91.4359803277491 -2.33598032774915 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.103644711302395 0.207289422604789 0.896355288697605 18 0.0493284138367071 0.0986568276734143 0.950671586163293 19 0.0260896876526105 0.052179375305221 0.97391031234739 20 0.0735792231557039 0.147158446311408 0.926420776844296 21 0.103961921022482 0.207923842044964 0.896038078977518 22 0.146757177135812 0.293514354271624 0.853242822864188 23 0.0963903534003695 0.192780706800739 0.90360964659963 24 0.129339944778401 0.258679889556801 0.8706600552216 25 0.121948349830986 0.243896699661971 0.878051650169015 26 0.0807158429044832 0.161431685808966 0.919284157095517 27 0.0902857951590934 0.180571590318187 0.909714204840907 28 0.0611501288616575 0.122300257723315 0.938849871138343 29 0.0467465613825124 0.0934931227650248 0.953253438617488 30 0.0438284966418503 0.0876569932837006 0.95617150335815 31 0.0343480422445660 0.0686960844891319 0.965651957755434 32 0.0296406039680056 0.0592812079360112 0.970359396031994 33 0.0197696235977607 0.0395392471955215 0.98023037640224 34 0.0119030350749487 0.0238060701498974 0.988096964925051 35 0.00621844985537458 0.0124368997107492 0.993781550144625 36 0.0135963146089699 0.0271926292179397 0.98640368539103 37 0.0135084778538605 0.0270169557077210 0.98649152214614 38 0.213632244812531 0.427264489625061 0.78636775518747 39 0.239767571237016 0.479535142474033 0.760232428762984 40 0.197696609767324 0.395393219534649 0.802303390232675 41 0.237947597161131 0.475895194322261 0.76205240283887 42 0.270467894535583 0.540935789071166 0.729532105464417 43 0.275592063116883 0.551184126233766 0.724407936883117 44 0.813516799760314 0.372966400479371 0.186483200239686 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 5 0.178571428571429 NOK 10% type I error level 11 0.392857142857143 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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