vraag 3

*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: Sun, 23 Nov 2008 13:14:32 -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/Nov/23/t1227471697k7bn6h2epj4ida0.htm/, Retrieved Sun, 23 Nov 2008 20:21:47 +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/Nov/23/t1227471697k7bn6h2epj4ida0.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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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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519 0 517 0 510 0 509 0 501 0 507 0 569 0 580 0 578 0 565 0 547 0 555 0 562 0 561 0 555 0 544 0 537 0 543 0 594 0 611 0 613 0 611 0 594 0 595 0 591 0 589 0 584 0 573 0 567 0 569 0 621 0 629 0 628 0 612 0 595 0 597 0 593 0 590 0 580 0 574 0 573 0 573 0 620 0 626 0 620 0 588 0 566 0 557 0 561 1 549 1 532 1 526 1 511 1 499 1 555 1 565 1 542 1 527 1 510 1 514 1 517 1 508 1 493 1 490 1 469 1 478 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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Aantal_werklozen[t] = + 574.833333333333 -55.6111111111111Dummyvariabele[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) 574.833333333333 4.69457 122.4464 0 0 Dummyvariabele -55.6111111111111 8.989418 -6.1863 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.611724101294281 R-squared 0.374206376104296 Adjusted R-squared 0.364428350730925 F-TEST (value) 38.2701375600247 F-TEST (DF numerator) 1 F-TEST (DF denominator) 64 p-value 4.85282544149257e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 32.5249370142016 Sum Squared Residuals 67703.7777777778 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 519 574.833333333334 -55.8333333333337 2 517 574.833333333333 -57.8333333333333 3 510 574.833333333333 -64.8333333333333 4 509 574.833333333333 -65.8333333333333 5 501 574.833333333333 -73.8333333333333 6 507 574.833333333333 -67.8333333333333 7 569 574.833333333333 -5.83333333333333 8 580 574.833333333333 5.16666666666667 9 578 574.833333333333 3.16666666666667 10 565 574.833333333333 -9.83333333333333 11 547 574.833333333333 -27.8333333333333 12 555 574.833333333333 -19.8333333333333 13 562 574.833333333333 -12.8333333333333 14 561 574.833333333333 -13.8333333333333 15 555 574.833333333333 -19.8333333333333 16 544 574.833333333333 -30.8333333333333 17 537 574.833333333333 -37.8333333333333 18 543 574.833333333333 -31.8333333333333 19 594 574.833333333333 19.1666666666667 20 611 574.833333333333 36.1666666666667 21 613 574.833333333333 38.1666666666667 22 611 574.833333333333 36.1666666666667 23 594 574.833333333333 19.1666666666667 24 595 574.833333333333 20.1666666666667 25 591 574.833333333333 16.1666666666667 26 589 574.833333333333 14.1666666666667 27 584 574.833333333333 9.16666666666667 28 573 574.833333333333 -1.83333333333333 29 567 574.833333333333 -7.83333333333333 30 569 574.833333333333 -5.83333333333333 31 621 574.833333333333 46.1666666666667 32 629 574.833333333333 54.1666666666667 33 628 574.833333333333 53.1666666666667 34 612 574.833333333333 37.1666666666667 35 595 574.833333333333 20.1666666666667 36 597 574.833333333333 22.1666666666667 37 593 574.833333333333 18.1666666666667 38 590 574.833333333333 15.1666666666667 39 580 574.833333333333 5.16666666666667 40 574 574.833333333333 -0.833333333333325 41 573 574.833333333333 -1.83333333333333 42 573 574.833333333333 -1.83333333333333 43 620 574.833333333333 45.1666666666667 44 626 574.833333333333 51.1666666666667 45 620 574.833333333333 45.1666666666667 46 588 574.833333333333 13.1666666666667 47 566 574.833333333333 -8.83333333333333 48 557 574.833333333333 -17.8333333333333 49 561 519.222222222222 41.7777777777778 50 549 519.222222222222 29.7777777777778 51 532 519.222222222222 12.7777777777778 52 526 519.222222222222 6.77777777777778 53 511 519.222222222222 -8.22222222222222 54 499 519.222222222222 -20.2222222222222 55 555 519.222222222222 35.7777777777778 56 565 519.222222222222 45.7777777777778 57 542 519.222222222222 22.7777777777778 58 527 519.222222222222 7.77777777777778 59 510 519.222222222222 -9.22222222222222 60 514 519.222222222222 -5.22222222222222 61 517 519.222222222222 -2.22222222222222 62 508 519.222222222222 -11.2222222222222 63 493 519.222222222222 -26.2222222222222 64 490 519.222222222222 -29.2222222222222 65 469 519.222222222222 -50.2222222222222 66 478 519.222222222222 -41.2222222222222 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0345708517926192 0.0691417035852384 0.96542914820738 6 0.0122181177406341 0.0244362354812682 0.987781882259366 7 0.528133095010136 0.943733809979727 0.471866904989864 8 0.81882392050513 0.36235215898974 0.18117607949487 9 0.88961495577638 0.220770088447241 0.110385044223620 10 0.8835520627541 0.232895874491799 0.116447937245900 11 0.852847174380243 0.294305651239514 0.147152825619757 12 0.82414656072946 0.35170687854108 0.17585343927054 13 0.801763055231628 0.396473889536744 0.198236944768372 14 0.77431369512883 0.451372609742339 0.225686304871169 15 0.740612381903566 0.518775236192868 0.259387618096434 16 0.72090206564992 0.558195868700161 0.279097934350080 17 0.734009509948376 0.531980980103248 0.265990490051624 18 0.743224733847472 0.513550532305057 0.256775266152528 19 0.833089861407649 0.333820277184702 0.166910138592351 20 0.931328231988191 0.137343536023618 0.0686717680118092 21 0.969419237731417 0.0611615245371656 0.0305807622685828 22 0.982578550846118 0.0348428983077637 0.0174214491538818 23 0.981362359803395 0.0372752803932096 0.0186376401966048 24 0.979503201528844 0.0409935969423117 0.0204967984711559 25 0.97509161311112 0.0498167737777611 0.0249083868888806 26 0.968518624564194 0.0629627508716117 0.0314813754358059 27 0.958585954431177 0.082828091137646 0.041414045568823 28 0.946432715525703 0.107134568948594 0.0535672844742971 29 0.935694954914555 0.128610090170890 0.0643050450854452 30 0.923559600020719 0.152880799958562 0.0764403999792812 31 0.94602324623441 0.107953507531179 0.0539767537655894 32 0.970283819820856 0.0594323603582874 0.0297161801791437 33 0.9830819918633 0.033836016273402 0.016918008136701 34 0.982991876079881 0.0340162478402384 0.0170081239201192 35 0.976046829197827 0.047906341604347 0.0239531708021735 36 0.967387447223048 0.0652251055539045 0.0326125527769523 37 0.954310364686652 0.0913792706266954 0.0456896353133477 38 0.93580489443171 0.128390211136580 0.0641951055682899 39 0.910572653894689 0.178854692210623 0.0894273461053114 40 0.882377506502711 0.235244986994577 0.117622493497289 41 0.851549643112876 0.296900713774248 0.148450356887124 42 0.819770636244892 0.360458727510217 0.180229363755108 43 0.825296668343897 0.349406663312207 0.174703331656103 44 0.86332307670741 0.27335384658518 0.13667692329259 45 0.900558257432567 0.198883485134867 0.0994417425674333 46 0.877884521162799 0.244230957674402 0.122115478837201 47 0.83258642395594 0.334827152088121 0.167413576044061 48 0.777626902329738 0.444746195340523 0.222373097670262 49 0.810387453006901 0.379225093986198 0.189612546993099 50 0.80935884765626 0.381282304687481 0.190641152343741 51 0.765238303648939 0.469523392702122 0.234761696351061 52 0.703014602237754 0.593970795524493 0.296985397762246 53 0.624897173199997 0.750205653600007 0.375102826800003 54 0.559499334468362 0.881001331063275 0.440500665531638 55 0.620540970229615 0.75891805954077 0.379459029770385 56 0.836433118290311 0.327133763419377 0.163566881709689 57 0.89924668111359 0.201506637772821 0.100753318886411 58 0.908002887776661 0.183994224446678 0.091997112223339 59 0.856621497085062 0.286757005829876 0.143378502914938 60 0.814151962643785 0.371696074712429 0.185848037356215 61 0.831015425857572 0.337969148284856 0.168984574142428 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 8 0.140350877192982 NOK 10% type I error level 15 0.263157894736842 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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