MR4_werkloos

*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: Fri, 24 Dec 2010 10:57:59 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/24/t12931897185jdu1zu3ckb7sju.htm/, Retrieved Fri, 24 Dec 2010 12:22:09 +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/2010/Dec/24/t12931897185jdu1zu3ckb7sju.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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580 0 590 593 597 595 574 0 580 590 593 597 573 0 574 580 590 593 573 0 573 574 580 590 620 0 573 573 574 580 626 0 620 573 573 574 620 0 626 620 573 573 588 0 620 626 620 573 566 0 588 620 626 620 557 0 566 588 620 626 561 0 557 566 588 620 549 0 561 557 566 588 532 0 549 561 557 566 526 0 532 549 561 557 511 0 526 532 549 561 499 0 511 526 532 549 555 0 499 511 526 532 565 0 555 499 511 526 542 0 565 555 499 511 527 0 542 565 555 499 510 0 527 542 565 555 514 0 510 527 542 565 517 0 514 510 527 542 508 0 517 514 510 527 493 0 508 517 514 510 490 0 493 508 517 514 469 0 490 493 508 517 478 0 469 490 493 508 528 0 478 469 490 493 534 0 528 478 469 490 518 0 534 528 478 469 506 0 518 534 528 478 502 1 506 518 534 528 516 1 502 506 518 534 528 1 516 502 506 518 533 1 528 516 502 506 536 1 533 528 516 502 537 1 536 533 528 516 524 1 537 536 533 528 536 1 524 537 536 533 587 1 536 524 537 536 597 1 587 536 524 537 581 1 597 587 536 524 564 1 581 597 587 536 558 1 564 58 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation werkloosheid[t] = + 54.688868086339 + 15.4672034890724X[t] + 0.867182913866395Y1[t] + 0.0182351757154025Y2[t] + 0.0901575020601514Y3[t] -0.0792498762689881Y4[t] -6.32635130262516M1[t] -1.98379057484731M2[t] -9.38552483421278M3[t] + 6.24483290359042M4[t] + 55.5025039171427M5[t] + 18.4493878081356M6[t] -5.3793087605908M7[t] -15.4976086152822M8[t] -10.2896605094049M9[t] + 9.22862675771806M10[t] + 10.6463475101817M11[t] -0.326596864040714t + 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) 54.688868086339 19.801389 2.7619 0.008719 0.00436 X 15.4672034890724 5.117263 3.0226 0.004413 0.002207 Y1 0.867182913866395 0.163559 5.302 5e-06 2e-06 Y2 0.0182351757154025 0.210214 0.0867 0.931318 0.465659 Y3 0.0901575020601514 0.209349 0.4307 0.669089 0.334544 Y4 -0.0792498762689881 0.144881 -0.547 0.587496 0.293748 M1 -6.32635130262516 5.172696 -1.223 0.228658 0.114329 M2 -1.98379057484731 5.65065 -0.3511 0.727423 0.363712 M3 -9.38552483421278 5.221505 -1.7975 0.080006 0.040003 M4 6.24483290359042 5.407752 1.1548 0.255202 0.127601 M5 55.5025039171427 5.176836 10.7213 0 0 M6 18.4493878081356 8.624358 2.1392 0.038734 0.019367 M7 -5.3793087605908 8.72921 -0.6162 0.541315 0.270658 M8 -15.4976086152822 10.869989 -1.4257 0.161903 0.080952 M9 -10.2896605094049 7.227696 -1.4236 0.162501 0.081251 M10 9.22862675771806 6.585941 1.4013 0.169044 0.084522 M11 10.6463475101817 5.258996 2.0244 0.049815 0.024908 t -0.326596864040714 0.131138 -2.4905 0.017124 0.008562 Multiple Linear Regression - Regression Statistics Multiple R 0.990000066468989 R-squared 0.980100131608602 Adjusted R-squared 0.971425830002095 F-TEST (value) 112.988938599207 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.12271996026891 Sum Squared Residuals 1462.02028876314 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 580 577.157650649944 2.84234935005625 2 574 571.927950087091 2.07204991290907 3 573 558.860696722228 14.1393032777724 4 573 572.524038236037 0.475961763963054 5 620 621.688430960162 -1.68843096016204 6 626 625.451656694388 0.548343305611468 7 620 607.435763879713 12.5642361202872 8 588 596.134583328902 -8.13458332890183 9 566 569.97287110044 -3.9728711004398 10 557 568.486567505594 -11.4865675055936 11 561 558.962330495169 2.03766950483076 12 549 551.846532190258 -2.84653219025809 13 532 535.792409519433 -3.79240951943347 14 526 525.921320633519 0.0786793664814366 15 511 511.281004509954 -0.281004509954394 16 499 512.885931601634 -13.8859316016338 17 555 551.94358603323 3.05641396677045 18 565 562.030430854827 2.96956914517342 19 542 547.674994520099 -5.67499452009903 20 527 523.46706117019 3.53293882980978 21 510 511.384841612115 -1.38484161211476 22 514 512.694773533664 1.30522646633610 23 517 517.415015713675 -0.415015713675013 24 508 508.772631392926 -0.772631392925657 25 493 496.077620433422 -3.07762043342185 26 490 486.875197008829 3.12480299117106 27 469 475.222622360744 -6.22262236074419 28 478 471.621722871685 6.37827712831518 29 528 528.892780193825 -0.892780193824865 30 534 533.380771581079 0.619228418920864 31 518 517.815999337471 0.184000662529309 32 506 497.400213267755 8.59978673224463 33 502 503.629261419733 -1.62926141973265 34 516 517.215378768188 -1.21537876818814 35 528 530.560230743461 -2.56023074346098 36 533 530.839142302638 2.16085769736180 37 536 530.320135347807 5.67986465219281 38 537 537.001215588676 -0.00121558867650695 39 524 529.694561901356 -5.69456190135582 40 536 533.617403195406 2.38259680459390 41 587 592.570022900267 -5.57002290026737 42 597 598.38416323994 -1.38416323993952 43 581 585.94283132354 -4.94283132354058 44 564 565.45239382994 -1.45239382994006 45 558 552.159704055485 5.84029594451544 46 575 563.603280192554 11.3967198074457 47 580 579.062423047695 0.937576952305238 48 575 573.541694114178 1.45830588582193 49 563 564.652184049394 -1.65218404939374 50 552 557.274316681885 -5.27431668188508 51 537 538.941114505718 -1.94111450571803 52 545 540.350904095238 4.64909590476171 53 601 595.905179912516 5.09482008748383 54 604 606.752977629766 -2.75297762976624 55 586 588.130410939177 -2.13041093917693 56 564 566.545748403213 -2.54574840321251 57 549 547.853321812228 1.14667818777177 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.958437404485573 0.0831251910288544 0.0415625955144272 22 0.995133601511774 0.00973279697645296 0.00486639848822648 23 0.9894390889178 0.0211218221644008 0.0105609110822004 24 0.979387998807026 0.0412240023859472 0.0206120011929736 25 0.97760034509806 0.0447993098038802 0.0223996549019401 26 0.976110877515844 0.047778244968311 0.0238891224841555 27 0.976363648594834 0.0472727028103321 0.0236363514051661 28 0.984058213961216 0.0318835720775677 0.0159417860387838 29 0.971675086585397 0.0566498268292051 0.0283249134146026 30 0.954319686113465 0.0913606277730695 0.0456803138865347 31 0.923151445357877 0.153697109284246 0.0768485546421231 32 0.901811530573639 0.196376938852722 0.098188469426361 33 0.838750033797894 0.322499932404211 0.161249966202106 34 0.920795600211375 0.158408799577250 0.0792043997886252 35 0.843259445394139 0.313481109211723 0.156740554605861 36 0.706121654652964 0.587756690694072 0.293878345347036 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0625 NOK 5% type I error level 7 0.4375 NOK 10% type I error level 10 0.625 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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