Finaal model - vertraagde loonkostindex

*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: Wed, 26 Jan 2011 14:15:00 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/26/t1296051400oexe56v5qx3smxq.htm/, Retrieved Wed, 26 Jan 2011 15:17:00 +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/2011/Jan/26/t1296051400oexe56v5qx3smxq.htm/}, year = {2011}, } @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 = {2011}, 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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90,09 85,61 87,703 81,71 100,639 85,52 90,09 87,703 83,042 86,51 100,639 90,09 89,956 86,66 83,042 100,639 89,561 87,27 89,956 83,042 105,38 87,62 89,561 89,956 86,554 88,17 105,38 89,561 93,131 87,99 86,554 105,38 92,812 88,83 93,131 86,554 102,195 88,75 92,812 93,131 88,925 88,81 102,195 92,812 94,184 89,43 88,925 102,195 94,196 89,5 94,184 88,925 108,932 89,34 94,196 94,184 91,134 89,75 108,932 94,196 97,149 90,26 91,134 108,932 96,415 90,32 97,149 91,134 112,432 90,76 96,415 97,149 92,47 91,53 112,432 96,415 98,61410515 92,35 92,47 112,432 97,80117197 93,04 98,61410515 92,47 111,8560178 93,35 97,80117197 98,61410515 95,63981455 93,54 111,8560178 97,80117197 104,1120262 95,07 95,63981455 111,8560178 104,0148224 95,39 104,1120262 95,63981455 118,1743476 95,43 104,0148224 104,1120262 102,033431 96,09 118,1743476 104,0148224 109,3138852 96,35 102,033431 118,1743476 108,1523649 96,6 109,3138852 102,033431 121,30381 96,62 108,1523649 109,3138852 103,8725146 97,6 121,30381 108,15236 etc...

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' @ www.wessa.org Multiple Linear Regression - Estimated Regression Equation LKI[t] = -17.2457869176623 + 0.508784678881672CPI[t] + 0.307209058050048LKI_1[t] + 0.380198032535317LKI_2[t] + 2.62067959823466Q1[t] + 15.0228547971945Q2[t] -6.65102587567938Q3[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) -17.2457869176623 6.345783 -2.7177 0.009176 0.004588 CPI 0.508784678881672 0.205988 2.47 0.017199 0.008599 LKI_1 0.307209058050048 0.139895 2.196 0.033062 0.016531 LKI_2 0.380198032535317 0.142802 2.6624 0.010588 0.005294 Q1 2.62067959823466 3.214801 0.8152 0.419074 0.209537 Q2 15.0228547971945 2.123296 7.0753 0 0 Q3 -6.65102587567938 3.999931 -1.6628 0.103011 0.051506 Multiple Linear Regression - Regression Statistics Multiple R 0.994087973665726 R-squared 0.98821089938683 Adjusted R-squared 0.98670590781919 F-TEST (value) 656.622216785721 F-TEST (DF numerator) 6 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.6184093348068 Sum Squared Residuals 123.10469242452 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 90.09 86.9410862962569 3.1489137037431 2 100.639 102.309305704667 -1.67030570466656 3 83.042 85.2874029209173 -2.24540292091734 4 89.956 90.6194977491373 -0.663497749137338 5 89.561 88.9842346503239 0.576765349676142 6 105.38 104.071826105912 1.30817389408831 7 86.554 87.387338872865 -0.833338872865004 8 93.131 94.1776184561717 -1.04661845617166 9 92.812 92.0885829989522 0.723417001047783 10 102.195 106.852618194068 -4.65761819406831 11 88.925 87.9705240212322 0.954475978767807 12 94.184 94.427730336773 -0.243730336772957 13 94.196 93.6544094070709 0.541590592929128 14 108.932 107.978327019209 0.95367298079056 15 91.134 91.044643120493 0.0893568795069851 16 97.149 98.0900405746677 -0.941040574667734 17 96.415 95.8223451547427 0.59265484525726 18 112.432 110.509785329502 1.9222146704983 19 92.47 93.8691709862734 -1.39917098627343 20 98.61410515 100.894524968959 -2.2804198189589 21 97.80117197 98.1642776258439 -0.363105655843864 22 111.8560178 112.810412328492 -0.954394528491658 23 95.63981455 95.2419010974596 0.397913452540391 24 104.1120262 103.033227738401 1.07879846159948 25 104.0148224 102.254090023632 1.76073237636836 26 118.1743476 117.867872922463 0.306474677537374 27 102.033431 100.842767843264 1.19066315673635 28 109.3138852 108.050865573376 1.26301962662388 29 108.1523649 106.898618083653 1.25374681634693 30 121.30381 121.722153781725 -0.418343781724991 31 103.8725146 104.145517422513 -0.273002822513262 32 112.7185207 110.477259937304 2.24126076269553 33 109.0381253 109.473087941577 -0.434962641576914 34 122.4434864 124.138373532199 -1.69488713219932 35 106.6325686 105.488732932974 1.14383566702581 36 113.8153852 112.882890392147 0.932494807852829 37 111.1071252 111.973660198673 -0.86653499867255 38 130.039536 126.473152158224 3.56638384177639 39 109.6121057 109.936865878669 -0.324760178668566 40 116.8592117 118.065040770793 -1.20582907079335 41 113.8982545 115.649324999157 -1.7510704991574 42 128.9375926 129.841236453877 -0.903643853876615 43 111.8120023 111.814461974203 -0.00245967420316595 44 119.9689463 119.370008658938 0.598937641062172 45 117.018539 118.224588400988 -1.20604940098795 46 132.4743387 132.745308110919 -0.270969410919278 47 116.3369106 115.008208708773 1.32870189122736 48 124.6405636 122.878118096241 1.76244550375922 49 121.025249 122.092411334788 -1.06716233478832 50 137.2054829 137.227820990874 -0.0223380908737981 51 120.0187687 120.045580270364 -0.0268115703639352 52 127.0443429 128.540163697091 -1.49582079709117 53 124.349043 127.257978154342 -2.9089351543417 54 143.6114438 141.07586316787 2.53558063212959 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.933384986035624 0.133230027928751 0.0666150139643757 11 0.921937795008702 0.156124409982596 0.0780622049912979 12 0.8652175594991 0.269564881001798 0.134782440500899 13 0.80898062662899 0.38203874674202 0.19101937337101 14 0.89955214543752 0.200895709124959 0.10044785456248 15 0.888602584123432 0.222794831753135 0.111397415876568 16 0.847095521581233 0.305808956837533 0.152904478418767 17 0.789026682397122 0.421946635205755 0.210973317602878 18 0.830802905760954 0.338394188478092 0.169197094239046 19 0.812034140704234 0.375931718591532 0.187965859295766 20 0.860568455967124 0.278863088065753 0.139431544032876 21 0.841697032723562 0.316605934552876 0.158302967276438 22 0.837078481417407 0.325843037165186 0.162921518582593 23 0.79618005485147 0.407639890297058 0.203819945148529 24 0.768775960212639 0.462448079574723 0.231224039787361 25 0.735631566160567 0.528736867678866 0.264368433839433 26 0.693519233698767 0.612961532602466 0.306480766301233 27 0.645035118551283 0.709929762897434 0.354964881448717 28 0.601016217143676 0.797967565712648 0.398983782856324 29 0.607052526231926 0.785894947536148 0.392947473768074 30 0.581889595697985 0.83622080860403 0.418110404302015 31 0.495628456069441 0.991256912138883 0.504371543930559 32 0.531717608047371 0.936564783905259 0.468282391952629 33 0.491987577255809 0.983975154511618 0.508012422744191 34 0.631981623668348 0.736036752663304 0.368018376331652 35 0.575913418973918 0.848173162052164 0.424086581026082 36 0.475195813374315 0.95039162674863 0.524804186625685 37 0.440413487552873 0.880826975105745 0.559586512447127 38 0.726716810300376 0.546566379399249 0.273283189699624 39 0.79119097596576 0.417618048068481 0.20880902403424 40 0.729987685219669 0.540024629560663 0.270012314780331 41 0.70402412332244 0.591951753355121 0.295975876677561 42 0.702013328816525 0.595973342366951 0.297986671183475 43 0.554485838748145 0.89102832250371 0.445514161251855 44 0.427818457613053 0.855636915226106 0.572181542386947 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 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Quarterly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Quarterly 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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