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: Sat, 22 Nov 2008 10:39:57 -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/22/t1227375721sp6cfzr93tslnrh.htm/, Retrieved Sat, 22 Nov 2008 17:42:01 +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/22/t1227375721sp6cfzr93tslnrh.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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IsPrivate?

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User-defined keywords:

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 0 613,7 0 759,2 0 816,4 0 736,8 0 680,1 0 736,5 0 637,2 0 801,9 0 772,3 0 897,3 0 792,1 0 826,8 0 666,8 0 906,6 0 871,4 0 891 0 739,2 0 833,6 0 715,6 0 871,6 0 751,6 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 1 982,3 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation UitvoerBEVS[t] = + 766.191836734694 -0.783503401360561Dummy[t] + 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) 766.191836734694 16.437419 46.6127 0 0 Dummy -0.783503401360561 37.060214 -0.0211 0.983204 0.491602 Multiple Linear Regression - Regression Statistics Multiple R 0.00275236051100763 R-squared 7.57548838255417e-06 Adjusted R-squared -0.0169414486558821 F-TEST (value) 0.000446957200489776 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.983204227297773 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 115.061932174009 Sum Squared Residuals 781115.64590136 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 604.4 766.191836734693 -161.791836734693 2 883.9 766.191836734694 117.708163265306 3 527.9 766.191836734694 -238.291836734694 4 756.2 766.191836734694 -9.99183673469385 5 812.9 766.191836734694 46.7081632653061 6 655.6 766.191836734694 -110.591836734694 7 707.6 766.191836734694 -58.5918367346939 8 612.6 766.191836734694 -153.591836734694 9 659.2 766.191836734694 -106.991836734694 10 833.4 766.191836734694 67.2081632653061 11 727.8 766.191836734694 -38.3918367346939 12 797.2 766.191836734694 31.0081632653061 13 753 766.191836734694 -13.1918367346939 14 762 766.191836734694 -4.1918367346939 15 613.7 766.191836734694 -152.491836734694 16 759.2 766.191836734694 -6.99183673469385 17 816.4 766.191836734694 50.2081632653061 18 736.8 766.191836734694 -29.3918367346939 19 680.1 766.191836734694 -86.0918367346939 20 736.5 766.191836734694 -29.6918367346939 21 637.2 766.191836734694 -128.991836734694 22 801.9 766.191836734694 35.7081632653061 23 772.3 766.191836734694 6.10816326530606 24 897.3 766.191836734694 131.108163265306 25 792.1 766.191836734694 25.9081632653061 26 826.8 766.191836734694 60.6081632653061 27 666.8 766.191836734694 -99.391836734694 28 906.6 766.191836734694 140.408163265306 29 871.4 766.191836734694 105.208163265306 30 891 766.191836734694 124.808163265306 31 739.2 766.191836734694 -26.9918367346939 32 833.6 766.191836734694 67.4081632653061 33 715.6 766.191836734694 -50.5918367346939 34 871.6 766.191836734694 105.408163265306 35 751.6 766.191836734694 -14.5918367346939 36 1005.5 766.191836734694 239.308163265306 37 681.2 766.191836734694 -84.9918367346938 38 837.3 766.191836734694 71.108163265306 39 674.7 766.191836734694 -91.4918367346938 40 806.3 766.191836734694 40.1081632653061 41 860.2 766.191836734694 94.0081632653062 42 689.8 766.191836734694 -76.391836734694 43 691.6 766.191836734694 -74.5918367346939 44 682.6 766.191836734694 -83.5918367346939 45 800.1 766.191836734694 33.9081632653061 46 1023.7 766.191836734694 257.508163265306 47 733.5 766.191836734694 -32.6918367346939 48 875.3 766.191836734694 109.108163265306 49 770.2 766.191836734694 4.00816326530615 50 1005.7 765.408333333333 240.291666666667 51 982.3 765.408333333333 216.891666666667 52 742.9 765.408333333333 -22.5083333333334 53 974.2 765.408333333333 208.791666666667 54 822.3 765.408333333333 56.8916666666666 55 773.2 765.408333333333 7.79166666666668 56 750.9 765.408333333333 -14.5083333333334 57 708 765.408333333333 -57.4083333333334 58 690 765.408333333333 -75.4083333333334 59 652.8 765.408333333333 -112.608333333333 60 620.7 765.408333333333 -144.708333333333 61 461.9 765.408333333333 -303.508333333333 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.91253604032093 0.174927919358141 0.0874639596790706 6 0.855771225472745 0.28845754905451 0.144228774527255 7 0.766055254343783 0.467889491312435 0.233944745656217 8 0.730941228272343 0.538117543455314 0.269058771727657 9 0.647286767483537 0.705426465032927 0.352713232516463 10 0.660385082868212 0.679229834263576 0.339614917131788 11 0.563935207019582 0.872129585960837 0.436064792980418 12 0.508565043765482 0.982869912469036 0.491434956234518 13 0.418714673374168 0.837429346748337 0.581285326625832 14 0.337658728013767 0.675317456027534 0.662341271986233 15 0.35089369323444 0.70178738646888 0.64910630676556 16 0.28079952390701 0.56159904781402 0.71920047609299 17 0.253625331851525 0.50725066370305 0.746374668148475 18 0.192007002836340 0.384014005672679 0.80799299716366 19 0.155778339125686 0.311556678251372 0.844221660874314 20 0.113394466004620 0.226788932009241 0.88660553399538 21 0.113468951202381 0.226937902404763 0.886531048797619 22 0.0936346526797233 0.187269305359447 0.906365347320277 23 0.0687884344478189 0.137576868895638 0.931211565552181 24 0.102906863088328 0.205813726176655 0.897093136911672 25 0.0777645570594068 0.155529114118814 0.922235442940593 26 0.0650375550436892 0.130075110087378 0.93496244495631 27 0.0587378559542476 0.117475711908495 0.941262144045752 28 0.0824722098361474 0.164944419672295 0.917527790163853 29 0.0829921522527577 0.165984304505515 0.917007847747242 30 0.091790280576035 0.18358056115207 0.908209719423965 31 0.0662691825498054 0.132538365099611 0.933730817450195 32 0.0522400709205631 0.104480141841126 0.947759929079437 33 0.0385461827186206 0.0770923654372411 0.96145381728138 34 0.0359017599572873 0.0718035199145746 0.964098240042713 35 0.0237904378574743 0.0475808757149486 0.976209562142526 36 0.0808159742980142 0.161631948596028 0.919184025701986 37 0.0694742461748772 0.138948492349754 0.930525753825123 38 0.0533784515013556 0.106756903002711 0.946621548498644 39 0.0473507292437814 0.0947014584875628 0.952649270756219 40 0.032120206609805 0.06424041321961 0.967879793390195 41 0.0257851561664174 0.0515703123328348 0.974214843833583 42 0.0205499544202560 0.0410999088405121 0.979450045579744 43 0.0169153889328812 0.0338307778657625 0.983084611067119 44 0.0163228973626322 0.0326457947252645 0.983677102637368 45 0.0102605166679692 0.0205210333359385 0.98973948333203 46 0.0340635921345973 0.0681271842691945 0.965936407865403 47 0.0231822878229612 0.0463645756459224 0.976817712177039 48 0.0175848085072277 0.0351696170144554 0.982415191492772 49 0.009822067332692 0.019644134665384 0.990177932667308 50 0.023528131173242 0.047056262346484 0.976471868826758 51 0.0660531805258154 0.132106361051631 0.933946819474185 52 0.0558966334102543 0.111793266820509 0.944103366589746 53 0.247523813846732 0.495047627693465 0.752476186153268 54 0.307565847530346 0.615131695060693 0.692434152469654 55 0.31777942282995 0.6355588456599 0.68222057717005 56 0.318777246084451 0.637554492168902 0.681222753915549 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 9 0.173076923076923 NOK 10% type I error level 15 0.288461538461538 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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