Reeks 1 Werkloosheid Multiple regression

*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, 19 Nov 2008 09:28:26 -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/19/t1227112331zgk9xjyuyny1zzd.htm/, Retrieved Wed, 19 Nov 2008 16:32:27 +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/19/t1227112331zgk9xjyuyny1zzd.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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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 0 549 0 532 0 526 0 511 0 499 0 555 0 565 0 542 0 527 0 510 0 514 0 517 0 508 0 493 1 490 1 469 1 478 1 528 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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation werkloosheid_in_duizenden[t] = + 566.687128712872 -47.1485148514851dummy[t] + 43.7426292629265M1[t] + 53.4654565456546M2[t] + 48.1559405940593M3[t] + 33.2464246424642M4[t] + 15.7369086908691M5[t] + 17.6273927392739M6[t] + 19.5178767876787M7[t] + 14.8083608360836M8[t] + 14.3285478547854M9[t] + 7.6190319031903M10[t] -1.69048404840486M11[t] -0.690484048404842t + 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) 566.687128712872 14.74035 38.4446 0 0 dummy -47.1485148514851 15.898554 -2.9656 0.004735 0.002368 M1 43.7426292629265 17.168566 2.5478 0.014169 0.007085 M2 53.4654565456546 18.140856 2.9472 0.004978 0.002489 M3 48.1559405940593 18.130899 2.656 0.010764 0.005382 M4 33.2464246424642 18.124001 1.8344 0.072931 0.036466 M5 15.7369086908691 18.120165 0.8685 0.389548 0.194774 M6 17.6273927392739 18.119392 0.9728 0.33561 0.167805 M7 19.5178767876787 18.121684 1.077 0.286957 0.143479 M8 14.8083608360836 18.127039 0.8169 0.418095 0.209048 M9 14.3285478547854 17.912726 0.7999 0.427788 0.213894 M10 7.6190319031903 17.904974 0.4255 0.672395 0.336198 M11 -1.69048404840486 17.900322 -0.0944 0.925162 0.462581 t -0.690484048404842 0.235642 -2.9302 0.005214 0.002607 Multiple Linear Regression - Regression Statistics Multiple R 0.772445428045574 R-squared 0.59667193930851 Adjusted R-squared 0.485113114010864 F-TEST (value) 5.34849607564934 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 9.02126592139396e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 28.3004415499957 Sum Squared Residuals 37643.004620462 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 569 609.739273927392 -40.7392739273918 2 580 618.771617161716 -38.7716171617163 3 578 612.771617161716 -34.7716171617163 4 565 597.171617161716 -32.1716171617163 5 547 578.971617161716 -31.9716171617161 6 555 580.171617161716 -25.1716171617162 7 562 581.371617161716 -19.3716171617162 8 561 575.971617161716 -14.9716171617162 9 555 574.801320132013 -19.8013201320132 10 544 567.401320132013 -23.4013201320132 11 537 557.401320132013 -20.4013201320132 12 543 558.401320132013 -15.4013201320133 13 594 601.453465346535 -7.45346534653489 14 611 610.485808580858 0.51419141914192 15 613 604.485808580858 8.51419141914189 16 611 588.885808580858 22.1141914191419 17 594 570.685808580858 23.3141914191419 18 595 571.885808580858 23.1141914191419 19 591 573.085808580858 17.9141914191419 20 589 567.685808580858 21.3141914191419 21 584 566.515511551155 17.4844884488449 22 573 559.115511551155 13.8844884488449 23 567 549.115511551155 17.8844884488449 24 569 550.115511551155 18.8844884488448 25 621 593.167656765677 27.8323432343232 26 629 602.2 26.8000000000000 27 628 596.2 31.8 28 612 580.6 31.4000000000000 29 595 562.4 32.6 30 597 563.6 33.4 31 593 564.8 28.2 32 590 559.4 30.6 33 580 558.229702970297 21.7702970297030 34 574 550.829702970297 23.1702970297030 35 573 540.829702970297 32.170297029703 36 573 541.829702970297 31.1702970297029 37 620 584.881848184819 35.1181518151813 38 626 593.914191419142 32.0858085808581 39 620 587.914191419142 32.0858085808581 40 588 572.314191419142 15.6858085808582 41 566 554.114191419142 11.8858085808581 42 557 555.314191419142 1.68580858085812 43 561 556.514191419142 4.4858085808581 44 549 551.114191419142 -2.11419141914190 45 532 549.943894389439 -17.9438943894389 46 526 542.543894389439 -16.5438943894389 47 511 532.543894389439 -21.5438943894389 48 499 533.543894389439 -34.5438943894390 49 555 576.59603960396 -21.5960396039606 50 565 585.628382838284 -20.6283828382837 51 542 579.628382838284 -37.6283828382838 52 527 564.028382838284 -37.0283828382837 53 510 545.828382838284 -35.8283828382838 54 514 547.028382838284 -33.0283828382838 55 517 548.228382838284 -31.2283828382838 56 508 542.828382838284 -34.8283828382838 57 493 494.509570957096 -1.50957095709567 58 490 487.109570957096 2.89042904290434 59 469 477.109570957096 -8.10957095709567 60 478 478.109570957096 -0.109570957095683 61 528 521.161716171617 6.8382838283827 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.125131008341601 0.250262016683202 0.874868991658399 18 0.0532848802573608 0.106569760514722 0.94671511974264 19 0.0320590283852285 0.064118056770457 0.967940971614772 20 0.0203248812122931 0.0406497624245862 0.979675118787707 21 0.0110133722311301 0.0220267444622602 0.98898662776887 22 0.00750864495267639 0.0150172899053528 0.992491355047324 23 0.00484164523533906 0.00968329047067812 0.99515835476466 24 0.00458386559867016 0.00916773119734033 0.99541613440133 25 0.00807695457215038 0.0161539091443008 0.99192304542785 26 0.0303602387543657 0.0607204775087314 0.969639761245634 27 0.0543100420941383 0.108620084188277 0.945689957905862 28 0.134557066133515 0.269114132267030 0.865442933866485 29 0.203699224538986 0.407398449077971 0.796300775461015 30 0.272866984099599 0.545733968199198 0.727133015900401 31 0.548499181339544 0.903001637320911 0.451500818660456 32 0.777483012739821 0.445033974520357 0.222516987260179 33 0.823964564409996 0.352070871180008 0.176035435590004 34 0.829116169466738 0.341767661066524 0.170883830533262 35 0.794411810432464 0.411176379135072 0.205588189567536 36 0.792821485571719 0.414357028856563 0.207178514428281 37 0.756847079511984 0.486305840976032 0.243152920488016 38 0.729492867355977 0.541014265288046 0.270507132644023 39 0.947476189392334 0.105047621215331 0.0525238106076655 40 0.98324292416078 0.0335141516784388 0.0167570758392194 41 0.99170507503121 0.0165898499375783 0.00829492496878915 42 0.987275537379944 0.0254489252401122 0.0127244626200561 43 0.97138694738591 0.0572261052281783 0.0286130526140892 44 0.93224036559679 0.135519268806418 0.067759634403209 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0714285714285714 NOK 5% type I error level 9 0.321428571428571 NOK 10% type I error level 12 0.428571428571429 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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