Multiple Lineair Regression q3

*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 13:42:13 -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/t1227559651po80z6kq8wai37k.htm/, Retrieved Mon, 24 Nov 2008 20:47:40 +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/t1227559651po80z6kq8wai37k.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?

No (this computation is public)

User-defined keywords:

Multiple Lineair Regression

Dataseries X:

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8.4 0 8.4 0 8.4 0 8.6 0 8.9 0 8.8 0 8.3 0 7.5 0 7.2 0 7.5 0 8.8 0 9.3 0 9.3 0 8.7 0 8.2 0 8.3 0 8.5 0 8.6 0 8.6 0 8.2 0 8.1 0 8 1 8.6 1 8.7 1 8.8 1 8.5 1 8.4 1 8.5 1 8.7 1 8.7 1 8.6 1 8.5 1 8.3 1 8.1 1 8.2 1 8.1 1 8.1 1 7.9 1 7.9 1 7.9 1 8 1 8 1 7.9 1 8 1 7.7 1 7.2 1 7.5 1 7.3 1 7 1 7 1 7 1 7.2 1 7.3 1 7.1 1 6.8 1 6.6 1 6.2 1 6.2 1 6.8 1 6.9 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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Totaal%werkzoekenden[t] = + 9.19236363636363 + 0.894545454545455stockmarketcrashfollowedbyeconomicdepression[t] -0.125757575757581M1[t] -0.294424242424242M2[t] -0.363090909090908M3[t] -0.191757575757574M4[t] + 0.0395757575757589M5[t] + 0.0509090909090923M6[t] -0.0977575757575742M7[t] -0.326424242424242M8[t] -0.535090909090908M9[t] -0.762666666666665M10[t] -0.131333333333332M11[t] -0.0513333333333333t + 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) 9.19236363636363 0.214208 42.9132 0 0 stockmarketcrashfollowedbyeconomicdepression 0.894545454545455 0.201066 4.449 5.4e-05 2.7e-05 M1 -0.125757575757581 0.260735 -0.4823 0.631867 0.315933 M2 -0.294424242424242 0.260202 -1.1315 0.263699 0.13185 M3 -0.363090909090908 0.259786 -1.3977 0.168921 0.084461 M4 -0.191757575757574 0.259489 -0.739 0.463672 0.231836 M5 0.0395757575757589 0.25931 0.1526 0.879366 0.439683 M6 0.0509090909090923 0.25925 0.1964 0.845185 0.422593 M7 -0.0977575757575742 0.25931 -0.377 0.707914 0.353957 M8 -0.326424242424242 0.259489 -1.258 0.214757 0.107379 M9 -0.535090909090908 0.259786 -2.0597 0.045108 0.022554 M10 -0.762666666666665 0.258513 -2.9502 0.004981 0.00249 M11 -0.131333333333332 0.258334 -0.5084 0.613612 0.306806 t -0.0513333333333333 0.005557 -9.2373 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.872093262063936 R-squared 0.760546657737317 Adjusted R-squared 0.692875061010907 F-TEST (value) 11.2387869435405 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 2.76699552159698e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.408367036333293 Sum Squared Residuals 7.67112727272732 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.4 9.01527272727275 -0.615272727272753 2 8.4 8.79527272727273 -0.395272727272731 3 8.4 8.67527272727273 -0.275272727272727 4 8.6 8.79527272727273 -0.195272727272726 5 8.9 8.97527272727273 -0.0752727272727255 6 8.8 8.93527272727273 -0.135272727272725 7 8.3 8.73527272727273 -0.435272727272726 8 7.5 8.45527272727272 -0.955272727272725 9 7.2 8.19527272727273 -0.995272727272727 10 7.5 7.91636363636363 -0.416363636363634 11 8.8 8.49636363636363 0.303636363636366 12 9.3 8.57636363636363 0.723636363636367 13 9.3 8.39927272727272 0.90072727272728 14 8.7 8.17927272727272 0.520727272727274 15 8.2 8.05927272727273 0.140727272727273 16 8.3 8.17927272727273 0.120727272727274 17 8.5 8.35927272727273 0.140727272727273 18 8.6 8.31927272727273 0.280727272727273 19 8.6 8.11927272727273 0.480727272727273 20 8.2 7.83927272727273 0.360727272727273 21 8.1 7.57927272727273 0.520727272727273 22 8 8.1949090909091 -0.194909090909090 23 8.6 8.77490909090909 -0.17490909090909 24 8.7 8.85490909090909 -0.15490909090909 25 8.8 8.67781818181817 0.122181818181826 26 8.5 8.45781818181818 0.0421818181818194 27 8.4 8.33781818181818 0.0621818181818188 28 8.5 8.45781818181818 0.0421818181818181 29 8.7 8.63781818181818 0.0621818181818174 30 8.7 8.59781818181818 0.102181818181817 31 8.6 8.39781818181818 0.202181818181818 32 8.5 8.11781818181818 0.382181818181818 33 8.3 7.85781818181818 0.442181818181819 34 8.1 7.57890909090909 0.521090909090909 35 8.2 8.15890909090909 0.041090909090909 36 8.1 8.23890909090909 -0.13890909090909 37 8.1 8.06181818181818 0.038181818181824 38 7.9 7.84181818181818 0.0581818181818191 39 7.9 7.72181818181818 0.178181818181818 40 7.9 7.84181818181818 0.0581818181818178 41 8 8.02181818181818 -0.0218181818181824 42 8 7.98181818181818 0.0181818181818173 43 7.9 7.78181818181818 0.118181818181818 44 8 7.50181818181818 0.498181818181818 45 7.7 7.24181818181818 0.458181818181817 46 7.2 6.96290909090909 0.237090909090908 47 7.5 7.54290909090909 -0.0429090909090911 48 7.3 7.62290909090909 -0.322909090909091 49 7 7.44581818181818 -0.445818181818176 50 7 7.22581818181818 -0.225818181818182 51 7 7.10581818181818 -0.105818181818183 52 7.2 7.22581818181818 -0.0258181818181832 53 7.3 7.40581818181818 -0.105818181818184 54 7.1 7.36581818181818 -0.265818181818184 55 6.8 7.16581818181818 -0.365818181818184 56 6.6 6.88581818181818 -0.285818181818183 57 6.2 6.62581818181818 -0.425818181818183 58 6.2 6.34690909090909 -0.146909090909092 59 6.8 6.92690909090909 -0.126909090909092 60 6.9 7.00690909090909 -0.106909090909091 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.981959688441397 0.0360806231172068 0.0180403115586034 18 0.96408574013091 0.0718285197381804 0.0359142598690902 19 0.94313532732763 0.113729345344740 0.0568646726723701 20 0.956699614607823 0.0866007707843546 0.0433003853921773 21 0.972190128147901 0.0556197437041977 0.0278098718520988 22 0.98350007737318 0.0329998452536408 0.0164999226268204 23 0.990730737193708 0.0185385256125843 0.00926926280629217 24 0.994444174985299 0.0111116500294025 0.00555582501470126 25 0.988740856902454 0.0225182861950914 0.0112591430975457 26 0.98035286735897 0.0392942652820608 0.0196471326410304 27 0.973437665758802 0.0531246684823953 0.0265623342411976 28 0.96625328503873 0.0674934299225407 0.0337467149612703 29 0.951178246679055 0.0976435066418905 0.0488217533209452 30 0.923761976887401 0.152476046225198 0.0762380231125988 31 0.882970581188893 0.234058837622213 0.117029418811107 32 0.891262402705244 0.217475194589512 0.108737597294756 33 0.879544256480426 0.240911487039149 0.120455743519574 34 0.823555738359407 0.352888523281187 0.176444261640593 35 0.859162542221701 0.281674915556598 0.140837457778299 36 0.935598251834033 0.128803496331933 0.0644017481659666 37 0.931618047810787 0.136763904378425 0.0683819521892127 38 0.900264203862807 0.199471592274386 0.0997357961371932 39 0.837946741421896 0.324106517156207 0.162053258578104 40 0.779762898218268 0.440474203563465 0.220237101781732 41 0.716783958085626 0.566432083828748 0.283216041914374 42 0.592178447671983 0.815643104656034 0.407821552328017 43 0.428714320744957 0.857428641489914 0.571285679255043 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 6 0.222222222222222 NOK 10% type I error level 12 0.444444444444444 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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