Multiple Lineair Regression 2 Bouwproductie

*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, 11 Dec 2008 14:57:38 -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/Dec/11/t1229033201yb32skvd49oz50j.htm/, Retrieved Thu, 11 Dec 2008 22:06:41 +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/Dec/11/t1229033201yb32skvd49oz50j.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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Dataseries X:

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82.7 0 88.9 0 105.9 0 100.8 0 94 0 105 0 58.5 0 87.6 0 113.1 0 112.5 0 89.6 0 74.5 0 82.7 0 90.1 0 109.4 0 96 0 89.2 0 109.1 0 49.1 0 92.9 0 107.7 0 103.5 0 91.1 0 79.8 0 71.9 0 82.9 0 90.1 0 100.7 0 90.7 0 108.8 0 44.1 0 93.6 0 107.4 0 96.5 0 93.6 0 76.5 0 76.7 1 84 1 103.3 1 88.5 1 99 1 105.9 1 44.7 1 94 1 107.1 1 104.8 1 102.5 1 77.7 1 85.2 1 91.3 1 106.5 1 92.4 1 97.5 1 107 1 51.1 1 98.6 1 102.2 1 114.3 1 99.4 1 72.5 1 92.3 1 99.4 1 85.9 1 109.4 1 97.6 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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Bouwproductie[t] = + 75.5011320754717 + 1.74716981132075d[t] + 5.54194968553461M1[t] + 13.0586163522013M2[t] + 23.8086163522013M3[t] + 21.5919496855346M4[t] + 18.2919496855346M5[t] + 30.96M6[t] -26.7M7[t] + 17.14M8[t] + 31.3M9[t] + 30.12M10[t] + 19.04M11[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) 75.5011320754717 2.719976 27.758 0 0 d 1.74716981132075 1.488305 1.1739 0.245771 0.122885 M1 5.54194968553461 3.596651 1.5409 0.129414 0.064707 M2 13.0586163522013 3.596651 3.6308 0.000646 0.000323 M3 23.8086163522013 3.596651 6.6197 0 0 M4 21.5919496855346 3.596651 6.0033 0 0 M5 18.2919496855346 3.596651 5.0858 5e-06 3e-06 M6 30.96 3.753362 8.2486 0 0 M7 -26.7 3.753362 -7.1136 0 0 M8 17.14 3.753362 4.5666 3.1e-05 1.5e-05 M9 31.3 3.753362 8.3392 0 0 M10 30.12 3.753362 8.0248 0 0 M11 19.04 3.753362 5.0728 5e-06 3e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.944259102235573 R-squared 0.89162525215473 Adjusted R-squared 0.866615694959667 F-TEST (value) 35.6513809980914 F-TEST (DF numerator) 12 F-TEST (DF denominator) 52 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.93458619079094 Sum Squared Residuals 1831.40428930818 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 82.7 81.0430817610062 1.65691823899380 2 88.9 88.559748427673 0.340251572327051 3 105.9 99.309748427673 6.59025157232705 4 100.8 97.0930817610063 3.70691823899371 5 94 93.7930817610063 0.206918238993713 6 105 106.461132075472 -1.46113207547170 7 58.5 48.8011320754717 9.6988679245283 8 87.6 92.6411320754717 -5.04113207547171 9 113.1 106.801132075472 6.2988679245283 10 112.5 105.621132075472 6.8788679245283 11 89.6 94.5411320754717 -4.94113207547169 12 74.5 75.5011320754717 -1.0011320754717 13 82.7 81.0430817610063 1.65691823899370 14 90.1 88.559748427673 1.54025157232704 15 109.4 99.309748427673 10.0902515723270 16 96 97.0930817610063 -1.09308176100629 17 89.2 93.7930817610063 -4.59308176100629 18 109.1 106.461132075472 2.63886792452830 19 49.1 48.8011320754717 0.298867924528297 20 92.9 92.6411320754717 0.258867924528309 21 107.7 106.801132075472 0.898867924528302 22 103.5 105.621132075472 -2.12113207547170 23 91.1 94.5411320754717 -3.44113207547171 24 79.8 75.5011320754717 4.2988679245283 25 71.9 81.0430817610063 -9.1430817610063 26 82.9 88.559748427673 -5.65974842767295 27 90.1 99.309748427673 -9.20974842767296 28 100.7 97.0930817610063 3.60691823899371 29 90.7 93.7930817610063 -3.09308176100629 30 108.8 106.461132075472 2.3388679245283 31 44.1 48.8011320754717 -4.7011320754717 32 93.6 92.6411320754717 0.958867924528297 33 107.4 106.801132075472 0.598867924528305 34 96.5 105.621132075472 -9.1211320754717 35 93.6 94.5411320754717 -0.941132075471707 36 76.5 75.5011320754717 0.998867924528305 37 76.7 82.790251572327 -6.09025157232706 38 84 90.3069182389937 -6.30691823899371 39 103.3 101.056918238994 2.24308176100629 40 88.5 98.840251572327 -10.3402515723270 41 99 95.540251572327 3.45974842767296 42 105.9 108.208301886792 -2.30830188679244 43 44.7 50.5483018867925 -5.84830188679245 44 94 94.3883018867924 -0.388301886792447 45 107.1 108.548301886792 -1.44830188679245 46 104.8 107.368301886792 -2.56830188679245 47 102.5 96.2883018867925 6.21169811320755 48 77.7 77.2483018867924 0.45169811320755 49 85.2 82.790251572327 2.40974842767294 50 91.3 90.3069182389937 0.993081761006285 51 106.5 101.056918238994 5.44308176100629 52 92.4 98.840251572327 -6.44025157232704 53 97.5 95.540251572327 1.95974842767296 54 107 108.208301886792 -1.20830188679245 55 51.1 50.5483018867925 0.55169811320755 56 98.6 94.3883018867924 4.21169811320755 57 102.2 108.548301886792 -6.34830188679245 58 114.3 107.368301886792 6.93169811320754 59 99.4 96.2883018867925 3.11169811320756 60 72.5 77.2483018867925 -4.74830188679246 61 92.3 82.790251572327 9.50974842767294 62 99.4 90.3069182389937 9.0930817610063 63 85.9 101.056918238994 -15.1569182389937 64 109.4 98.840251572327 10.5597484276730 65 97.6 95.540251572327 2.05974842767295 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.088670233153953 0.177340466307906 0.911329766846047 17 0.0701591272576212 0.140318254515242 0.929840872742379 18 0.0457680917566344 0.0915361835132687 0.954231908243366 19 0.112727881195541 0.225455762391081 0.88727211880446 20 0.0861033709819932 0.172206741963986 0.913896629018007 21 0.0689666777029096 0.137933355405819 0.93103332229709 22 0.091170916058817 0.182341832117634 0.908829083941183 23 0.0550434837688582 0.110086967537716 0.944956516231142 24 0.0457695524309481 0.0915391048618962 0.954230447569052 25 0.113508019709086 0.227016039418171 0.886491980290914 26 0.109899083554496 0.219798167108993 0.890100916445504 27 0.369960565337148 0.739921130674296 0.630039434662852 28 0.314166507861500 0.628333015722999 0.6858334921385 29 0.243668602731765 0.48733720546353 0.756331397268235 30 0.190442769264738 0.380885538529476 0.809557230735262 31 0.196569032038210 0.393138064076420 0.80343096796179 32 0.145418202235754 0.290836404471509 0.854581797764246 33 0.120794338941021 0.241588677882043 0.879205661058979 34 0.164094931760788 0.328189863521575 0.835905068239212 35 0.131081558756844 0.262163117513689 0.868918441243156 36 0.0880610290709607 0.176122058141921 0.91193897092904 37 0.093273823008344 0.186547646016688 0.906726176991656 38 0.0985739507673088 0.197147901534618 0.901426049232691 39 0.0831914390302399 0.166382878060480 0.91680856096976 40 0.136870020571936 0.273740041143872 0.863129979428064 41 0.131699594001546 0.263399188003092 0.868300405998454 42 0.0855904611108962 0.171180922221792 0.914409538889104 43 0.0651778194524875 0.130355638904975 0.934822180547513 44 0.0447192183053619 0.0894384366107237 0.955280781694638 45 0.0272884770247049 0.0545769540494097 0.972711522975295 46 0.0224065784701107 0.0448131569402214 0.97759342152989 47 0.0197184742282080 0.0394369484564159 0.980281525771792 48 0.0100951362407994 0.0201902724815989 0.9899048637592 49 0.00624447659327353 0.0124889531865471 0.993755523406726 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 4 0.117647058823529 NOK 10% type I error level 8 0.235294117647059 NOK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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