WS7 Multiple Regression 4 (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 08:32:51 -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/t12587312699hq338qgw9s453p.htm/, Retrieved Fri, 20 Nov 2009 16:34:41 +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/t12587312699hq338qgw9s453p.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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101,6 79,8 103,9 110,3 114,1 96,8 94,6 71,9 101,6 103,9 110,3 114,1 95,9 82,9 94,6 101,6 103,9 110,3 104,7 90,1 95,9 94,6 101,6 103,9 102,8 100,7 104,7 95,9 94,6 101,6 98,1 90,7 102,8 104,7 95,9 94,6 113,9 108,8 98,1 102,8 104,7 95,9 80,9 44,1 113,9 98,1 102,8 104,7 95,7 93,6 80,9 113,9 98,1 102,8 113,2 107,4 95,7 80,9 113,9 98,1 105,9 96,5 113,2 95,7 80,9 113,9 108,8 93,6 105,9 113,2 95,7 80,9 102,3 76,5 108,8 105,9 113,2 95,7 99 76,7 102,3 108,8 105,9 113,2 100,7 84 99 102,3 108,8 105,9 115,5 103,3 100,7 99 102,3 108,8 100,7 88,5 115,5 100,7 99 102,3 109,9 99 100,7 115,5 100,7 99 114,6 105,9 109,9 100,7 115,5 100,7 85,4 44,7 114,6 109,9 100,7 115,5 100,5 94 85,4 114,6 109,9 100,7 114,8 107,1 100,5 85,4 114,6 109,9 116,5 104,8 114,8 100,5 85,4 114,6 112,9 102,5 116,5 114,8 100,5 85,4 102 77,7 112,9 116,5 114,8 100,5 106 85,2 102 112,9 116,5 114,8 105,3 91,3 106 102 112,9 116,5 118,8 106,5 105,3 106 102 112,9 106,1 92,4 118,8 105,3 106 102 109,3 97,5 106,1 118,8 105,3 106 117,2 1 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 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation Totind[t] = -29.5139603340959 + 0.665616707652597Bouw[t] + 0.284368980405653`Yt-1`[t] + 0.289338994260551`Yt-2`[t] + 0.157257661996291`Yt-3`[t] -0.0641304861653082`Yt-4`[t] + 5.1106498875945M1[t] + 7.13200327844603M2[t] + 5.96646531169032M3[t] + 9.41343049457463M4[t] + 0.972856350450679M5[t] + 0.391300760931872M6[t] + 3.03306035447898M7[t] + 14.0194673929411M8[t] + 0.117239138123227M9[t] + 8.83732777976529M10[t] + 8.1309443614198M11[t] -0.0421476113852508t + 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) -29.5139603340959 6.195053 -4.7641 2.8e-05 1.4e-05 Bouw 0.665616707652597 0.049005 13.5825 0 0 `Yt-1` 0.284368980405653 0.071642 3.9693 0.000309 0.000155 `Yt-2` 0.289338994260551 0.055434 5.2195 7e-06 3e-06 `Yt-3` 0.157257661996291 0.067752 2.3211 0.025746 0.012873 `Yt-4` -0.0641304861653082 0.07538 -0.8508 0.400233 0.200117 M1 5.1106498875945 2.576104 1.9839 0.054529 0.027264 M2 7.13200327844603 3.6609 1.9482 0.05881 0.029405 M3 5.96646531169032 3.435764 1.7366 0.090564 0.045282 M4 9.41343049457463 2.709243 3.4746 0.001295 0.000647 M5 0.972856350450679 1.87042 0.5201 0.605992 0.302996 M6 0.391300760931872 1.966985 0.1989 0.843375 0.421687 M7 3.03306035447898 2.397002 1.2654 0.213448 0.106724 M8 14.0194673929411 3.3133 4.2313 0.000141 7.1e-05 M9 0.117239138123227 3.37804 0.0347 0.972496 0.486248 M10 8.83732777976529 3.496589 2.5274 0.015771 0.007885 M11 8.1309443614198 2.851922 2.851 0.007006 0.003503 t -0.0421476113852508 0.016227 -2.5973 0.013292 0.006646 Multiple Linear Regression - Regression Statistics Multiple R 0.988348734440301 R-squared 0.976833220869745 Adjusted R-squared 0.966469135469368 F-TEST (value) 94.2517533514537 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.76382842703576 Sum Squared Residuals 118.221447360738 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.6 101.866051516852 -0.266051516851691 2 94.6 94.3740305614162 0.225969438583834 3 95.9 97.0693130284668 -1.16931302846682 4 104.7 103.659620098635 1.04037990136542 5 102.8 104.157719648558 -1.35771964855756 6 98.1 99.537079821602 -1.43707982160198 7 113.9 113.598573708827 0.301426291173327 8 80.9 83.7474309321176 -2.84743093211761 9 95.7 97.3211987629797 -1.62119876297968 10 113.2 112.631208802766 0.568791197233832 11 105.9 107.683365404488 -1.78336540448772 12 108.8 105.011243263089 3.78875673691121 13 102.3 99.2130731132015 3.08692688679845 14 99 98.0458225044514 0.954177495548632 15 100.7 99.8022175629381 0.89778243706188 16 115.5 114.373892964907 1.12610703509319 17 100.7 100.638479011873 0.0615209881274798 18 109.9 107.556276076112 2.34372392388758 19 114.6 115.301012416817 -0.701012416817162 20 85.4 86.2314376978671 -0.83143769786708 21 100.5 100.554186249729 -0.0541862497289154 22 114.8 113.946089660614 0.853910339386245 23 116.5 115.208798421149 1.29120157885144 24 112.9 114.372963797529 -1.47296379752900 25 102 103.682733910187 -1.68273391018725 26 106 105.863094804518 0.136905195481805 27 105.3 106.024202617573 -0.724202617573007 28 118.8 119.021453070585 -0.221453070585327 29 106.1 106.118032623855 -0.0180326238554691 30 109.3 108.816962695287 0.483037304713348 31 117.2 117.143178687603 0.0568213123970843 32 92.5 91.1889300131535 1.31106998684648 33 104.2 105.440893691775 -1.24089369177498 34 112.5 113.732616756133 -1.23261675613339 35 122.4 122.392681567200 0.0073184327998856 36 113.3 112.942604862390 0.357395137610363 37 100 100.937627930667 -0.937627930667136 38 110.7 110.705520053080 -0.00552005307985979 39 112.8 111.352316028745 1.44768397125529 40 109.8 107.956470663927 1.8435293360729 41 117.3 117.405838934343 -0.105838934343046 42 109.1 109.836653841622 -0.736653841622493 43 115.9 116.393914258810 -0.49391425880954 44 96 96.4546482973823 -0.45464829738235 45 99.8 96.8837212955164 2.91627870448357 46 116.8 116.990084780487 -0.190084780486683 47 115.7 115.215154607164 0.484845392836394 48 99.4 102.073188076993 -2.67318807699256 49 94.3 94.5005135290924 -0.200513529092374 50 91 92.3115320765344 -1.31153207653441 51 93.2 93.6519507622774 -0.451950762277349 52 103.1 106.888563201946 -3.78856320194618 53 94.1 92.6799297813714 1.42007021862860 54 91.8 92.4530275653764 -0.653027565376453 55 102.7 101.863320927944 0.836679072056288 56 82.6 79.7775530594794 2.82244694052056 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.267688366189689 0.535376732379378 0.732311633810311 22 0.161996528974833 0.323993057949666 0.838003471025167 23 0.108426320826288 0.216852641652575 0.891573679173713 24 0.151794370446729 0.303588740893459 0.84820562955327 25 0.527355837599889 0.945288324800223 0.472644162400111 26 0.608719073276088 0.782561853447824 0.391280926723912 27 0.484886574327489 0.969773148654979 0.515113425672511 28 0.384973013947591 0.769946027895182 0.615026986052409 29 0.295909658198540 0.591819316397079 0.70409034180146 30 0.261085076105282 0.522170152210563 0.738914923894718 31 0.179440991195457 0.358881982390914 0.820559008804543 32 0.132421283694576 0.264842567389152 0.867578716305424 33 0.144730076525154 0.289460153050309 0.855269923474846 34 0.175654879106201 0.351309758212402 0.824345120893799 35 0.103593080015877 0.207186160031753 0.896406919984123 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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