Multiple Regression Lineaire trend werkloosheid inflatie

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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 07:07:10 -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/t1261058903bgkil45jk108ut9.htm/, Retrieved Thu, 17 Dec 2009 15:08:35 +0100

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@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/t1261058903bgkil45jk108ut9.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:

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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] = + 9.65369544559226 -0.140310005125642inflatie[t] + 0.00724839024648894M1[t] -0.109041281500898M2[t] -0.379718553043269M3[t] -0.575651625508257M4[t] -0.409135097153141M5[t] -0.113843369208077M6[t] -0.0361020404429104M7[t] -0.143616512600359M8[t] -0.319906184347756M9[t] -0.559002056197666M10[t] -0.629679327740038M11[t] -0.0293227284576283t + 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) 9.65369544559226 0.271248 35.59 0 0 inflatie -0.140310005125642 0.039035 -3.5945 0.000789 0.000395 M1 0.00724839024648894 0.270519 0.0268 0.97874 0.48937 M2 -0.109041281500898 0.269961 -0.4039 0.688147 0.344074 M3 -0.379718553043269 0.269588 -1.4085 0.165703 0.082851 M4 -0.575651625508257 0.26871 -2.1423 0.037497 0.018749 M5 -0.409135097153141 0.268366 -1.5245 0.13422 0.06711 M6 -0.113843369208077 0.267901 -0.4249 0.672857 0.336429 M7 -0.0361020404429104 0.267801 -0.1348 0.893351 0.446676 M8 -0.143616512600359 0.267409 -0.5371 0.59381 0.296905 M9 -0.319906184347756 0.267218 -1.1972 0.237373 0.118686 M10 -0.559002056197666 0.267058 -2.0932 0.041875 0.020938 M11 -0.629679327740038 0.266998 -2.3584 0.022661 0.011331 t -0.0293227284576283 0.003212 -9.1278 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.850310348823393 R-squared 0.72302768931616 Adjusted R-squared 0.644752905862031 F-TEST (value) 9.23704490016092 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 6.05654348895257e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.422038240916151 Sum Squared Residuals 8.19334873259757 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9.3 9.07038108687861 0.229618913121392 2 9.3 8.95283068769867 0.34716931230133 3 8.7 8.5265516830856 0.173448316914407 4 8.2 8.35741988421323 -0.157419884213233 5 8.3 8.55073768616098 -0.250737686160978 6 8.5 8.80267568513585 -0.302675685135848 7 8.6 8.8090012839057 -0.209001283905695 8 8.5 8.6020090807278 -0.102009080727797 9 8.2 8.45252068257303 -0.252520682573029 10 8.1 8.19813308277805 -0.098133082778054 11 7.9 8.0420090807278 -0.142009080727796 12 8.6 8.6423656800102 -0.0423656800102068 13 8.7 8.59222934077394 0.107770659226060 14 8.7 8.43258594005636 0.267414059943641 15 8.5 8.24483394415687 0.255166055843126 16 8.4 8.0055471427217 0.394452857278307 17 8.5 8.07258594005636 0.42741405994364 18 8.7 8.3385549395438 0.361445060456203 19 8.7 8.38697353985133 0.313026460148665 20 8.6 8.33432234231164 0.265677657688357 21 8.5 8.07258594005636 0.42741405994364 22 8.3 7.77610533872369 0.523894661276307 23 8 7.71819834026139 0.281801659738614 24 8.2 8.33258594005636 -0.132585940056360 25 8.1 8.32454260235778 -0.224542602357785 26 8.1 8.23505420420303 -0.135054204203027 27 8 7.96311620522815 0.0368837947718451 28 7.9 7.69576740276785 0.204232597232153 29 7.9 7.81893020215277 0.0810697978472305 30 8 8.14102320369046 -0.141023203690462 31 8 8.17541080348544 -0.175410803485436 32 7.9 8.03857360287036 -0.138573602870359 33 8 7.83296120266533 0.167038797334666 34 7.7 7.63469760492062 0.0653023950793838 35 7.2 7.53469760492062 -0.334697604920617 36 7.5 8.13505420420303 -0.635054204203026 37 7.3 8.12701086650445 -0.827010866504452 38 7 7.9533364652743 -0.953336465274308 39 7 7.5410884611738 -0.541088461173794 40 7 7.21761565666323 -0.217615656663229 41 7.2 7.32674745553559 -0.126747455535588 42 7.3 7.53659245297277 -0.236592452972767 43 7.1 7.57098005276774 -0.470980052767741 44 6.8 7.32189484805215 -0.52189484805215 45 6.4 7.15837544938482 -0.758375449384817 46 6.1 6.74964684395164 -0.649646843951637 47 6.5 6.55142984036369 -0.0514298403636871 48 7.7 7.13775543913353 0.562244560866467 49 7.9 7.18583610348522 0.714163896514785 50 7.5 7.02619270276764 0.473807297232364 51 6.9 6.82440970635558 0.0755902936444153 52 6.6 6.823649913634 -0.223649913633997 53 6.9 7.0309987160943 -0.130998716094305 54 7.7 7.38115371865713 0.318846281342874 55 8 7.45763431998979 0.542365680010207 56 8 7.50320012603805 0.496799873961950 57 7.7 7.28355672532046 0.416443274679540 58 7.3 7.141417129626 0.158582870374000 59 7.4 7.15366513372651 0.246334866273486 60 8.1 7.85223873659687 0.247761263403126 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.227403661232766 0.454807322465533 0.772596338767234 18 0.171675837938098 0.343351675876197 0.828324162061902 19 0.0968816139087476 0.193763227817495 0.903118386091252 20 0.0468034574599534 0.0936069149199068 0.953196542540047 21 0.0326774885976317 0.0653549771952634 0.967322511402368 22 0.0242273787053083 0.0484547574106167 0.975772621294692 23 0.01297844283267 0.02595688566534 0.98702155716733 24 0.012837667473058 0.025675334946116 0.987162332526942 25 0.0448065292803413 0.0896130585606825 0.955193470719659 26 0.0526045473330719 0.105209094666144 0.947395452666928 27 0.0364750320799456 0.0729500641598913 0.963524967920054 28 0.0298548142732299 0.0597096285464597 0.97014518572677 29 0.0223875836432134 0.0447751672864267 0.977612416356787 30 0.0130665510526925 0.0261331021053849 0.986933448947308 31 0.00751142563825143 0.0150228512765029 0.99248857436175 32 0.00465468219650521 0.00930936439301041 0.995345317803495 33 0.00850406109851262 0.0170081221970252 0.991495938901487 34 0.0389635904001886 0.0779271808003772 0.961036409599811 35 0.0524732894246101 0.104946578849220 0.94752671057539 36 0.0365919703958257 0.0731839407916514 0.963408029604174 37 0.0601556566217611 0.120311313243522 0.939844343378239 38 0.170210909274567 0.340421818549133 0.829789090725433 39 0.166654106593175 0.33330821318635 0.833345893406825 40 0.222426430962984 0.444852861925967 0.777573569037016 41 0.538895348910003 0.922209302179995 0.461104651089997 42 0.761235258845263 0.477529482309475 0.238764741154737 43 0.910014557553378 0.179970884893245 0.0899854424466224 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0370370370370370 NOK 5% type I error level 8 0.296296296296296 NOK 10% type I error level 15 0.555555555555556 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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