WS7 Multiple Regression 5 (significante autocorrelatie filteren)

*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: Fri, 20 Nov 2009 08:50:53 -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/20/t1258732381iojhbr6lbi48pr1.htm/, Retrieved Fri, 20 Nov 2009 16:53:13 +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/20/t1258732381iojhbr6lbi48pr1.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:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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103,9 91,1 110,3 114,1 96,8 101,6 79,8 103,9 110,3 114,1 94,6 71,9 101,6 103,9 110,3 95,9 82,9 94,6 101,6 103,9 104,7 90,1 95,9 94,6 101,6 102,8 100,7 104,7 95,9 94,6 98,1 90,7 102,8 104,7 95,9 113,9 108,8 98,1 102,8 104,7 80,9 44,1 113,9 98,1 102,8 95,7 93,6 80,9 113,9 98,1 113,2 107,4 95,7 80,9 113,9 105,9 96,5 113,2 95,7 80,9 108,8 93,6 105,9 113,2 95,7 102,3 76,5 108,8 105,9 113,2 99 76,7 102,3 108,8 105,9 100,7 84 99 102,3 108,8 115,5 103,3 100,7 99 102,3 100,7 88,5 115,5 100,7 99 109,9 99 100,7 115,5 100,7 114,6 105,9 109,9 100,7 115,5 85,4 44,7 114,6 109,9 100,7 100,5 94 85,4 114,6 109,9 114,8 107,1 100,5 85,4 114,6 116,5 104,8 114,8 100,5 85,4 112,9 102,5 116,5 114,8 100,5 102 77,7 112,9 116,5 114,8 106 85,2 102 112,9 116,5 105,3 91,3 106 102 112,9 118,8 106,5 105,3 106 102 106,1 92,4 118,8 105,3 106 109,3 97,5 106,1 118,8 105,3 117,2 107 109,3 106,1 118,8 92,5 51,1 117,2 109,3 106,1 104,2 98,6 92,5 117,2 109,3 112,5 102,2 104,2 92,5 117,2 122,4 114,3 112,5 104,2 92, 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Totind[t] = -24.0516684867312 + 0.670388000769807Bouw[t] + 0.253998840317328`Yt-1`[t] + 0.269978457642583`Yt-2`[t] + 0.160638800436104`Yt-3`[t] -6.37661479692486M1[t] -1.88110503246155M2[t] -1.19156849898619M3[t] -2.50634377705874M4[t] + 1.38913552902864M5[t] -6.26009234136988M6[t] -6.86826776767659M7[t] -4.52699001781147M8[t] + 6.45481886381635M9[t] -7.94932174721686M10[t] + 0.517101623635753M11[t] -0.0448299433002486t + 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) -24.0516684867312 6.175792 -3.8945 0.000365 0.000182 Bouw 0.670388000769807 0.048239 13.8973 0 0 `Yt-1` 0.253998840317328 0.056669 4.4821 6.1e-05 3e-05 `Yt-2` 0.269978457642583 0.051346 5.2581 5e-06 3e-06 `Yt-3` 0.160638800436104 0.066553 2.4137 0.020462 0.010231 M1 -6.37661479692486 1.715957 -3.7161 0.000619 0.000309 M2 -1.88110503246155 3.210205 -0.586 0.561183 0.280592 M3 -1.19156849898619 3.243081 -0.3674 0.715244 0.357622 M4 -2.50634377705874 2.561296 -0.9785 0.333686 0.166843 M5 1.38913552902864 1.891241 0.7345 0.466922 0.233461 M6 -6.26009234136988 1.661245 -3.7683 0.000531 0.000265 M7 -6.86826776767659 2.043213 -3.3615 0.001716 0.000858 M8 -4.52699001781147 2.173725 -2.0826 0.043727 0.021863 M9 6.45481886381635 3.533982 1.8265 0.075245 0.037622 M10 -7.94932174721686 3.093976 -2.5693 0.014025 0.007012 M11 0.517101623635753 2.663718 0.1941 0.847058 0.423529 t -0.0448299433002486 0.014545 -3.0821 0.003713 0.001856 Multiple Linear Regression - Regression Statistics Multiple R 0.987973486143355 R-squared 0.976091609322253 Adjusted R-squared 0.966528253051154 F-TEST (value) 102.065800086533 F-TEST (DF numerator) 16 F-TEST (DF denominator) 40 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.74653764901953 Sum Squared Residuals 122.015750377706 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.9 104.969683629408 -1.06968362940815 2 101.6 101.972519572344 -0.372519572344110 3 94.6 94.3986740531382 0.201325946861819 4 95.9 96.986306182643 -1.08630618264294 5 104.7 103.734629198884 0.965370801115925 6 102.8 104.608374380020 -1.80837438002040 7 98.1 99.353532073934 -1.25353207393411 8 113.9 113.490870519258 0.40912948074217 9 80.9 83.492815013044 -2.59281501304397 10 95.7 97.3567460350472 -1.65674603504723 11 113.2 112.417680654605 0.78231934539542 12 105.9 107.688100343550 -1.78810034354973 13 108.8 104.570416121975 4.22958387802476 14 102.3 99.1343940337358 3.16560596626418 15 99 97.8724600459822 1.12753995401782 16 100.7 99.2794836037697 1.4205163962303 17 115.5 114.565338296898 0.934661703101635 18 100.7 100.637576245056 0.062423754943834 19 109.9 107.533229180687 2.36677081931268 20 114.6 115.173916596827 -0.573916596827391 21 85.4 86.3832920013917 -0.983292001391662 22 100.5 100.314459462676 0.185540537324012 23 114.8 114.225149587991 0.574850412009274 24 116.5 115.139530773491 1.36046922650927 25 112.9 113.894329490909 -0.994329490908626 26 102 103.561089292067 -1.56108929206679 27 106 105.766282041785 0.233717958215348 28 105.3 105.990974116503 -0.690974116502855 29 118.8 119.182672808586 -0.38267280858572 30 106.1 105.918698809711 0.181301190288773 31 109.3 108.991148989870 0.308851010130198 32 117.2 117.20897648659 -0.00897648658987273 33 92.5 91.50167531931 0.99832468069009 34 104.2 105.269237422476 -1.06923742247619 35 112.5 113.676592704186 -1.17659270418602 36 122.4 122.525515904845 -0.125515904844945 37 113.3 112.750173635827 0.549826364172864 38 100 100.862115563676 -0.862115563675945 39 110.7 110.535840152643 0.164159847357327 40 112.8 111.601250757516 1.19874924248398 41 109.8 107.687333125553 2.11266687444738 42 117.3 117.271186734708 0.0288132652919417 43 109.1 110.140000366385 -1.04000036638540 44 115.9 116.656334518825 -0.756334518824865 45 96 96.2669267851151 -0.26692678511512 46 99.8 97.2595570798006 2.54044292019941 47 116.8 116.980577053219 -0.180577053218678 48 115.7 115.146852978115 0.553147021885413 49 99.4 102.115397121881 -2.71539712188085 50 94.3 94.6698815381773 -0.369881538177339 51 91 92.7267437064523 -1.72674370645231 52 93.2 94.0419853395685 -0.841985339568484 53 103.1 106.730026570079 -3.63002657007922 54 94.1 92.5641638305041 1.53583616949585 55 91.8 92.1820893891234 -0.382089389123366 56 102.7 101.7699018785 0.930098121499961 57 82.6 79.7552908811393 2.84470911886066 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.225732003534464 0.451464007068928 0.774267996465536 21 0.16156478242614 0.32312956485228 0.83843521757386 22 0.0900387423119481 0.180077484623896 0.909961257688052 23 0.0944393695090182 0.188878739018036 0.905560630490982 24 0.075368432000861 0.150736864001722 0.924631567999139 25 0.155656093567007 0.311312187134015 0.844343906432993 26 0.446153673789121 0.892307347578243 0.553846326210879 27 0.518101584485397 0.963796831029206 0.481898415514603 28 0.399447180629779 0.798894361259558 0.600552819370221 29 0.303414385124131 0.606828770248263 0.696585614875868 30 0.225974704429022 0.451949408858043 0.774025295570978 31 0.197237740853324 0.394475481706648 0.802762259146676 32 0.146591868117160 0.293183736234320 0.85340813188284 33 0.100506742259601 0.201013484519202 0.8994932577404 34 0.0828119743171122 0.165623948634224 0.917188025682888 35 0.114784655396428 0.229569310792856 0.885215344603572 36 0.111391143474654 0.222782286949308 0.888608856525346 37 0.0558066614142812 0.111613322828562 0.94419333858572 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 = 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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