Model 2, rekening houdend met seizonaliteit

*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, 19 Nov 2009 09:44:31 -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/Nov/19/t1258650357osnxjjx07glrov4.htm/, Retrieved Thu, 19 Nov 2009 18:06:09 +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/Nov/19/t1258650357osnxjjx07glrov4.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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No (this computation is public)

User-defined keywords:

Dataseries X:

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96.8 9.3 114.1 9.3 110.3 8.7 103.9 8.2 101.6 8.3 94.6 8.5 95.9 8.6 104.7 8.5 102.8 8.2 98.1 8.1 113.9 7.9 80.9 8.6 95.7 8.7 113.2 8.7 105.9 8.5 108.8 8.4 102.3 8.5 99 8.7 100.7 8.7 115.5 8.6 100.7 8.5 109.9 8.3 114.6 8 85.4 8.2 100.5 8.1 114.8 8.1 116.5 8 112.9 7.9 102 7.9 106 8 105.3 8 118.8 7.9 106.1 8 109.3 7.7 117.2 7.2 92.5 7.5 104.2 7.3 112.5 7 122.4 7 113.3 7 100 7.2 110.7 7.3 112.8 7.1 109.8 6.8 117.3 6.4 109.1 6.1 115.9 6.5 96 7.7 99.8 7.9 116.8 7.5 115.7 6.9 99.4 6.6 94.3 6.9 91 7.7 93.2 8 103.1 8 94.1 7.7 91.8 7.3 102.7 7.4 82.6 8.1 89.1 8.3

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 tip[t] = + 109.456443765851 -2.74020495833550wrk[t] + 10.8792505563894M1[t] + 27.0740204958336M2[t] + 26.1319590083329M3[t] + 19.0839180166658M4[t] + 11.8475467108328M5[t] + 12.8348040991667M6[t] + 14.2644122975001M7[t] + 22.7355877024999M8[t] + 16.0075467108328M9[t] + 14.7350934216655M10[t] + 23.681072925832M11[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) 109.456443765851 10.200412 10.7306 0 0 wrk -2.74020495833550 1.223801 -2.2391 0.02982 0.01491 M1 10.8792505563894 3.773331 2.8832 0.005875 0.002938 M2 27.0740204958336 3.930389 6.8884 0 0 M3 26.1319590083329 3.936101 6.639 0 0 M4 19.0839180166658 3.958865 4.8206 1.5e-05 7e-06 M5 11.8475467108328 3.941348 3.006 0.004202 0.002101 M6 12.8348040991667 3.928559 3.2671 0.002011 0.001005 M7 14.2644122975001 3.929169 3.6304 0.000686 0.000343 M8 22.7355877024999 3.929169 5.7864 1e-06 0 M9 16.0075467108328 3.941348 4.0614 0.000179 9e-05 M10 14.7350934216655 3.979693 3.7026 0.00055 0.000275 M11 23.681072925832 4.001086 5.9187 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.815364744298947 R-squared 0.664819666245688 Adjusted R-squared 0.58102458280711 F-TEST (value) 7.93387438695019 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 6.91560221310894e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.21147729965435 Sum Squared Residuals 1851.95761171782 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 96.8 94.8517882097202 1.94821179027979 2 114.1 111.046558149164 3.05344185083592 3 110.3 111.748619636665 -1.44861963666477 4 103.9 106.070681124165 -2.17068112416541 5 101.6 98.5602893224988 3.03971067750115 6 94.6 98.9995057191657 -4.39950571916569 7 95.9 100.155093421666 -4.25509342166553 8 104.7 108.900289322499 -4.20028932249882 9 102.8 102.994309818332 -0.194309818332392 10 98.1 101.995877024999 -3.8958770249987 11 113.9 111.489897520832 2.41010247916776 12 80.9 85.8906811241654 -4.99068112416542 13 95.7 96.4959111847212 -0.79591118472123 14 113.2 112.690681124165 0.509318875834587 15 105.9 112.296660628332 -6.39666062833186 16 108.8 105.522640132498 3.27735986750169 17 102.3 98.0122483308317 4.28775166916827 18 99 98.4514647274986 0.54853527250143 19 100.7 99.881072925832 0.81892707416801 20 115.5 108.626268826665 6.87373117333472 21 100.7 102.172248330832 -1.47224833083172 22 109.9 101.447836033332 8.45216396666842 23 114.6 111.215877024999 3.38412297500129 24 85.4 86.9867631074996 -1.58676310749961 25 100.5 98.1400341597225 2.35996584027746 26 114.8 114.334804099167 0.465195900833286 27 116.5 113.666763107500 2.83323689250039 28 112.9 106.892742611666 6.00725738833395 29 102 99.656371305833 2.34362869416697 30 106 100.369608198333 5.63039180166659 31 105.3 101.799216396667 3.50078360333316 32 118.8 110.544412297500 8.25558770249987 33 106.1 103.542350809999 2.55764919000052 34 109.3 103.091959008333 6.2080409916671 35 117.2 113.408040991667 3.79195900833289 36 92.5 88.9049065783345 3.59509342166554 37 104.2 100.332198126391 3.86780187360906 38 112.5 117.349029553336 -4.84902955333577 39 122.4 116.406968065835 5.9930319341649 40 113.3 109.358927074168 3.94107292583199 41 100 101.574514776668 -1.57451477666788 42 110.7 102.287751669168 8.41224833083174 43 112.8 104.265400859169 8.53459914083121 44 109.8 113.558637751669 -3.75863775166919 45 117.3 107.926678743336 9.37332125666372 46 109.1 107.476286941670 1.62371305833029 47 115.9 115.326184462502 0.573815537498058 48 96 88.3568655866674 7.64313441333264 49 99.8 98.6880751513896 1.11192484861036 50 116.8 115.978927074168 0.821072925831983 51 115.7 116.680988561669 -0.980988561668662 52 99.4 110.455009057502 -11.0550090575022 53 94.3 102.396576264169 -8.09657626416853 54 91 101.191669685834 -10.1916696858341 55 93.2 101.799216396667 -8.59921639666684 56 103.1 110.270391801667 -7.17039180166658 57 94.1 104.364412297500 -10.2644122975001 58 91.8 104.188040991667 -12.3880409916671 59 102.7 112.86 -10.16 60 82.6 87.2607836033332 -4.66078360333317 61 89.1 97.5919931680554 -8.49199316805544 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0473854122356363 0.0947708244712727 0.952614587764364 17 0.0128495172990978 0.0256990345981957 0.987150482700902 18 0.0064261039050869 0.0128522078101738 0.993573896094913 19 0.00411954187317793 0.00823908374635587 0.995880458126822 20 0.0227108840191434 0.0454217680382867 0.977289115980857 21 0.0120827728163087 0.0241655456326174 0.987917227183691 22 0.0299798897050632 0.0599597794101265 0.970020110294937 23 0.0153272525891235 0.0306545051782469 0.984672747410877 24 0.0127755004035964 0.0255510008071929 0.987224499596404 25 0.0108830078958688 0.0217660157917376 0.989116992104131 26 0.00526860693612323 0.0105372138722465 0.994731393063877 27 0.0058025116056778 0.0116050232113556 0.994197488394322 28 0.00594423697339062 0.0118884739467812 0.99405576302661 29 0.00377947933750735 0.0075589586750147 0.996220520662493 30 0.0044188513678375 0.008837702735675 0.995581148632163 31 0.00287712321062843 0.00575424642125685 0.997122876789372 32 0.00511049587039251 0.0102209917407850 0.994889504129608 33 0.00367827047677008 0.00735654095354016 0.99632172952323 34 0.0131845701637472 0.0263691403274945 0.986815429836253 35 0.0144029965584889 0.0288059931169778 0.985597003441511 36 0.00912613167821009 0.0182522633564202 0.99087386832179 37 0.00474172294691329 0.00948344589382658 0.995258277053087 38 0.0127186093592520 0.0254372187185040 0.987281390640748 39 0.0121727072490438 0.0243454144980875 0.987827292750956 40 0.0739381684051446 0.147876336810289 0.926061831594855 41 0.116927701703108 0.233855403406216 0.883072298296892 42 0.318728945474407 0.637457890948815 0.681271054525592 43 0.323988678467838 0.647977356935676 0.676011321532162 44 0.75464316666661 0.490713666666779 0.245356833333389 45 0.614914766083575 0.770170467832851 0.385085233916426 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.2 NOK 5% type I error level 22 0.733333333333333 NOK 10% type I error level 24 0.8 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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