Multiple Regression werkloosheid inflatie

*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: Thu, 17 Dec 2009 06:47:34 -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/Dec/17/t1261057716g7oj9wcqdumbd5f.htm/, Retrieved Thu, 17 Dec 2009 14:48:48 +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/Dec/17/t1261057716g7oj9wcqdumbd5f.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?

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Dataseries X:

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9,3 4 9,3 3,8 8,7 4,7 8,2 4,3 8,3 3,9 8,5 4 8,6 4,3 8,5 4,8 8,2 4,4 8,1 4,3 7,9 4,7 8,6 4,7 8,7 4,9 8,7 5 8,5 4,2 8,4 4,3 8,5 4,8 8,7 4,8 8,7 4,8 8,6 4,2 8,5 4,6 8,3 4,8 8 4,5 8,2 4,4 8,1 4,3 8,1 3,9 8 3,7 7,9 4 7,9 4,1 8 3,7 8 3,8 7,9 3,8 8 3,8 7,7 3,3 7,2 3,3 7,5 3,3 7,3 3,2 7 3,4 7 4,2 7 4,9 7,2 5,1 7,3 5,5 7,1 5,6 6,8 6,4 6,4 6,1 6,1 7,1 6,5 7,8 7,7 7,9 7,9 7,4 7,5 7,5 6,9 6,8 6,6 5,2 6,9 4,7 7,7 4,1 8 3,9 8 2,6 7,7 2,7 7,3 1,8 7,4 1 8,1 0,3

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation werklh[t] = + 8.47966411761748 -0.138668089218583inflatie[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) 8.47966411761748 0.29349 28.8926 0 0 inflatie -0.138668089218583 0.062785 -2.2086 0.031167 0.015584 Multiple Linear Regression - Regression Statistics Multiple R 0.278528953951772 R-squared 0.0775783781894685 Adjusted R-squared 0.0616745571237698 F-TEST (value) 4.87797101520393 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.0311670609145538 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.685903917563281 Sum Squared Residuals 27.2869226794620 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9.3 7.9249917607432 1.37500823925680 2 9.3 7.95272537858687 1.34727462141313 3 8.7 7.82792409829014 0.872075901709855 4 8.2 7.88339133397758 0.316608666022422 5 8.3 7.93885856966501 0.36114143033499 6 8.5 7.92499176074315 0.575008239256848 7 8.6 7.88339133397758 0.716608666022422 8 8.5 7.81405728936829 0.685942710631714 9 8.2 7.86952452505572 0.330475474944280 10 8.1 7.88339133397758 0.216608666022422 11 7.9 7.82792409829014 0.0720759017098564 12 8.6 7.82792409829014 0.772075901709856 13 8.7 7.80019048044643 0.899809519553572 14 8.7 7.78632367152457 0.91367632847543 15 8.5 7.89725814289944 0.602741857100564 16 8.4 7.88339133397758 0.516608666022423 17 8.5 7.81405728936829 0.685942710631714 18 8.7 7.81405728936829 0.885942710631714 19 8.7 7.81405728936829 0.885942710631714 20 8.6 7.89725814289944 0.702741857100564 21 8.5 7.841790907212 0.658209092787998 22 8.3 7.81405728936829 0.485942710631715 23 8 7.85565771613386 0.144342283866139 24 8.2 7.86952452505572 0.330475474944280 25 8.1 7.88339133397758 0.216608666022422 26 8.1 7.93885856966501 0.161141430334989 27 8 7.96659218750873 0.0334078124912729 28 7.9 7.92499176074315 -0.0249917607431518 29 7.9 7.9111249518213 -0.0111249518212935 30 8 7.96659218750873 0.0334078124912729 31 8 7.95272537858687 0.0472746214131312 32 7.9 7.95272537858687 -0.0527253785868685 33 8 7.95272537858687 0.0472746214131312 34 7.7 8.02205942319616 -0.32205942319616 35 7.2 8.02205942319616 -0.82205942319616 36 7.5 8.02205942319616 -0.52205942319616 37 7.3 8.03592623211802 -0.735926232118019 38 7 8.0081926142743 -1.00819261427430 39 7 7.89725814289944 -0.897258142899436 40 7 7.80019048044643 -0.800190480446427 41 7.2 7.77245686260271 -0.57245686260271 42 7.3 7.71698962691528 -0.416989626915278 43 7.1 7.70312281799342 -0.60312281799342 44 6.8 7.59218834661855 -0.792188346618553 45 6.4 7.63378877338413 -1.23378877338413 46 6.1 7.49512068416554 -1.39512068416554 47 6.5 7.39805302171254 -0.898053021712536 48 7.7 7.38418621279068 0.315813787209322 49 7.9 7.45352025739997 0.446479742600031 50 7.5 7.43965344847811 0.060346551521889 51 6.9 7.53672111093112 -0.636721110931119 52 6.6 7.75859005368085 -1.15859005368085 53 6.9 7.82792409829014 -0.927924098290144 54 7.7 7.9111249518213 -0.211124951821294 55 8 7.93885856966501 0.0611414303349895 56 8 8.11912708564917 -0.119127085649169 57 7.7 8.10526027672731 -0.40526027672731 58 7.3 8.23006155702403 -0.930061557024036 59 7.4 8.3409960283989 -0.940996028398901 60 8.1 8.43806369085191 -0.33806369085191 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.485759258889777 0.971518517779554 0.514240741110223 6 0.359127784370548 0.718255568741096 0.640872215629452 7 0.235045267437659 0.470090534875318 0.764954732562341 8 0.147447124229219 0.294894248458438 0.852552875770781 9 0.113342992258041 0.226685984516082 0.886657007741959 10 0.100421067465155 0.200842134930311 0.899578932534845 11 0.0779309792540824 0.155861958508165 0.922069020745918 12 0.0618078408575336 0.123615681715067 0.938192159142466 13 0.0618409912998893 0.123681982599779 0.93815900870011 14 0.0589000734925011 0.117800146985002 0.941099926507499 15 0.0413474379295297 0.0826948758590594 0.95865256207047 16 0.0292289735736949 0.0584579471473898 0.970771026426305 17 0.0217389043813737 0.0434778087627474 0.978261095618626 18 0.0223008153360601 0.0446016306721201 0.97769918466394 19 0.0248011491672760 0.0496022983345521 0.975198850832724 20 0.0233158429280902 0.0466316858561805 0.97668415707191 21 0.0230802053973736 0.0461604107947471 0.976919794602626 22 0.0227834017065860 0.0455668034131721 0.977216598293414 23 0.0307670668069358 0.0615341336138716 0.969232933193064 24 0.0336732531315486 0.0673465062630972 0.966326746868451 25 0.0402159380168549 0.0804318760337098 0.959784061983145 26 0.0481772022298766 0.0963544044597532 0.951822797770123 27 0.0557252207218135 0.111450441443627 0.944274779278186 28 0.0658075437872568 0.131615087574514 0.934192456212743 29 0.0749077285544582 0.149815457108916 0.925092271445542 30 0.0735247916175015 0.147049583235003 0.926475208382499 31 0.0743483547859806 0.148696709571961 0.92565164521402 32 0.0751118875619367 0.150223775123873 0.924888112438063 33 0.0793237348895843 0.158647469779169 0.920676265110416 34 0.0690921264372827 0.138184252874565 0.930907873562717 35 0.0916060418443307 0.183212083688661 0.90839395815567 36 0.073500167866601 0.147000335733202 0.926499832133399 37 0.0624958789560139 0.124991757912028 0.937504121043986 38 0.0886837275033339 0.177367455006668 0.911316272496666 39 0.188749201387963 0.377498402775926 0.811250798612037 40 0.383317266244393 0.766634532488785 0.616682733755607 41 0.468328775825939 0.936657551651878 0.531671224174061 42 0.504818299384851 0.990363401230297 0.495181700615149 43 0.526941343159022 0.946117313681957 0.473058656840978 44 0.561387888702741 0.877224222594517 0.438612111297259 45 0.681512948082881 0.636974103834238 0.318487051917119 46 0.846501969464057 0.306996061071887 0.153498030535943 47 0.879039273035944 0.241921453928112 0.120960726964056 48 0.858496162482561 0.283007675034878 0.141503837517439 49 0.894027215510847 0.211945568978306 0.105972784489153 50 0.895484952620254 0.209030094759493 0.104515047379746 51 0.830931370546218 0.338137258907565 0.169068629453782 52 0.879639389823297 0.240721220353407 0.120360610176703 53 0.942079456857742 0.115841086284516 0.057920543142258 54 0.877561490809406 0.244877018381187 0.122438509190593 55 0.778762261174682 0.442475477650636 0.221237738825318 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 0.117647058823529 NOK 10% type I error level 12 0.235294117647059 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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