Eigen tijdreeksen

*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: Mon, 24 Nov 2008 03:30:04 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227522739r0vjgwcm0ur5x8j.htm/, Retrieved Mon, 24 Nov 2008 10:32:30 +0000

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/2008/Nov/24/t1227522739r0vjgwcm0ur5x8j.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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604,4 0 883,9 0 527,9 0 756,2 0 812,9 0 655,6 0 707,6 0 612,6 0 659,2 0 833,4 0 727,8 0 797,2 0 753 0 762 1 613,7 0 759,2 0 816,4 0 736,8 0 680,1 1 736,5 0 637,2 0 801,9 1 772,3 1 897,3 1 792,1 1 826,8 0 666,8 0 906,6 1 871,4 1 891 1 739,2 0 833,6 1 715,6 1 871,6 1 751,6 0 1005,5 0 681,2 0 837,3 0 674,7 0 806,3 0 860,2 0 689,8 0 691,6 0 682,6 0 800,1 0 1023,7 0 733,5 0 875,3 0 770,2 0 1005,7 0 982,3 1 742,9 1 974,2 1 822,3 1 773,2 1 750,9 1 708 1 690 1 652,8 1 620,7 1 461,9 1

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation UitvoerBEVS[t] = + 802.183529411765 + 4.93372093023258Dummy[t] -156.870671074632M1[t] + 34.6609059127527M2[t] -136.372510259918M3[t] -37.1726706186350M4[t] + 34.6339132086943M5[t] -74.2595029639763M6[t] -115.992919136647M7[t] -112.066335309317M8[t] -132.259751481988M9[t] + 5.88008815929469M10[t] -110.626583827329M11[t] + 0.97341617267062t + 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) 802.183529411765 52.603841 15.2495 0 0 Dummy 4.93372093023258 29.863755 0.1652 0.869489 0.434745 M1 -156.870671074632 61.349352 -2.557 0.013846 0.006923 M2 34.6609059127527 64.446388 0.5378 0.593235 0.296618 M3 -136.372510259918 64.378768 -2.1183 0.039467 0.019733 M4 -37.1726706186350 64.290629 -0.5782 0.565891 0.282946 M5 34.6339132086943 64.212759 0.5394 0.592183 0.296092 M6 -74.2595029639763 64.145196 -1.1577 0.252845 0.126422 M7 -115.992919136647 64.087971 -1.8099 0.076708 0.038354 M8 -112.066335309317 64.041112 -1.7499 0.08666 0.04333 M9 -132.259751481988 64.004643 -2.0664 0.044325 0.022162 M10 5.88008815929469 64.318428 0.0914 0.927546 0.463773 M11 -110.626583827329 63.962939 -1.7295 0.090276 0.045138 t 0.97341617267062 0.816763 1.1918 0.239324 0.119662 Multiple Linear Regression - Regression Statistics Multiple R 0.620220957202846 R-squared 0.384674035753614 Adjusted R-squared 0.214477492451423 F-TEST (value) 2.26017537307211 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0.0209299169179100 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 101.126040916517 Sum Squared Residuals 480644.379118103 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 604.4 646.286274509805 -41.8862745098046 2 883.9 838.791267669859 45.1087323301413 3 527.9 668.731267669858 -140.831267669859 4 756.2 768.904523483812 -12.7045234838121 5 812.9 841.684523483812 -28.7845234838121 6 655.6 733.764523483812 -78.1645234838121 7 707.6 693.004523483812 14.5954765161879 8 612.6 697.904523483812 -85.304523483812 9 659.2 678.684523483812 -19.4845234838120 10 833.4 817.797779297766 15.6022207022342 11 727.8 702.264523483812 25.535476516188 12 797.2 813.864523483812 -16.6645234838120 13 753 657.967268581851 95.0327314181488 14 762 855.405982672138 -93.4059826721384 15 613.7 680.412261741906 -66.712261741906 16 759.2 780.58551755586 -21.3855175558595 17 816.4 853.36551755586 -36.9655175558595 18 736.8 745.44551755586 -8.64551755585953 19 680.1 709.619238486092 -29.5192384860921 20 736.5 709.58551755586 26.9144824441405 21 637.2 690.36551755586 -53.1655175558595 22 801.9 834.412494300046 -32.5124943000455 23 772.3 718.879238486092 53.4207615139079 24 897.3 830.479238486092 66.8207615139079 25 792.1 674.581983584131 117.518016415869 26 826.8 862.153255813953 -35.3532558139535 27 666.8 692.093255813954 -25.2932558139536 28 906.6 797.20023255814 109.399767441860 29 871.4 869.98023255814 1.41976744186046 30 891 762.06023255814 128.939767441860 31 739.2 716.366511627907 22.8334883720930 32 833.6 726.20023255814 107.399767441860 33 715.6 706.98023255814 8.61976744186045 34 871.6 846.093488372093 25.5065116279071 35 751.6 725.626511627907 25.9734883720931 36 1005.5 837.226511627907 168.273488372093 37 681.2 681.329256725946 -0.129256725946058 38 837.3 873.834249886 -36.534249886001 39 674.7 703.774249886001 -29.0742498860009 40 806.3 803.947505699954 2.35249430004549 41 860.2 876.727505699954 -16.5275056999544 42 689.8 768.807505699954 -79.0075056999545 43 691.6 728.047505699955 -36.4475056999544 44 682.6 732.947505699954 -50.3475056999544 45 800.1 713.727505699954 86.3724943000455 46 1023.7 852.840761513908 170.859238486092 47 733.5 737.307505699954 -3.80750569995441 48 875.3 848.907505699954 26.3924943000455 49 770.2 693.010250797994 77.1897492020065 50 1005.7 885.515243958048 120.184756041952 51 982.3 720.388964888281 261.911035111719 52 742.9 820.562220702234 -77.6622207022344 53 974.2 893.342220702234 80.8577792977656 54 822.3 785.422220702234 36.8777792977656 55 773.2 744.662220702234 28.5377792977656 56 750.9 749.562220702234 1.33777929776554 57 708 730.342220702234 -22.3422207022345 58 690 869.455476516188 -179.455476516188 59 652.8 753.922220702234 -101.122220702234 60 620.7 865.522220702234 -244.822220702234 61 461.9 709.624965800273 -247.724965800274 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.106128478499095 0.212256956998190 0.893871521500905 18 0.0397152345757967 0.0794304691515934 0.960284765424203 19 0.0231673812133698 0.0463347624267395 0.97683261878663 20 0.0112068326251813 0.0224136652503626 0.988793167374819 21 0.0104348490616564 0.0208696981233128 0.989565150938344 22 0.00468737279918741 0.00937474559837482 0.995312627200813 23 0.00383545445220379 0.00767090890440759 0.996164545547796 24 0.00479645832832240 0.00959291665664479 0.995203541671678 25 0.00383335289168756 0.00766670578337512 0.996166647108312 26 0.00387443765223990 0.00774887530447981 0.99612556234776 27 0.00286919316773983 0.00573838633547966 0.99713080683226 28 0.00273719946593314 0.00547439893186628 0.997262800534067 29 0.00127963153439633 0.00255926306879266 0.998720368465604 30 0.00187814936713865 0.00375629873427731 0.998121850632861 31 0.000869886733842248 0.00173977346768450 0.999130113266158 32 0.00059281243755561 0.00118562487511122 0.999407187562444 33 0.000256176605197438 0.000512353210394876 0.999743823394803 34 0.000103070085772183 0.000206140171544366 0.999896929914228 35 4.87538117277617e-05 9.75076234555235e-05 0.999951246188272 36 0.000101955518786858 0.000203911037573717 0.999898044481213 37 0.000180520655726174 0.000361041311452348 0.999819479344274 38 8.03965800890145e-05 0.000160793160178029 0.99991960341991 39 0.000516097353653215 0.00103219470730643 0.999483902646347 40 0.000242519169669656 0.000485038339339312 0.99975748083033 41 0.000276365767860227 0.000552731535720454 0.99972363423214 42 0.00153566293483689 0.00307132586967377 0.998464337065163 43 0.00487234430946833 0.00974468861893667 0.995127655690532 44 0.052811418848742 0.105622837697484 0.947188581151258 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 22 0.785714285714286 NOK 5% type I error level 25 0.892857142857143 NOK 10% type I error level 26 0.928571428571429 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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