Q3 Reeks 1, no trend season

*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: Mon, 24 Nov 2008 14:20:12 -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/24/t1227561691ye78dvx45vs0zro.htm/, Retrieved Mon, 24 Nov 2008 21:21:40 +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/24/t1227561691ye78dvx45vs0zro.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:

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User-defined keywords:

Dataseries X:

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577992 0 565464 0 547344 0 554788 0 562325 0 560854 0 555332 1 543599 1 536662 1 542722 1 593530 1 610763 1 612613 1 611324 1 594167 1 595454 1 590865 1 589379 1 584428 1 573100 1 567456 1 569028 1 620735 1 628884 1 628232 1 612117 1 595404 1 597141 1 593408 1 590072 1 579799 1 574205 1 572775 1 572942 1 619567 1 625809 1 619916 1 587625 1 565742 1 557274 1 560576 1 548854 1 531673 1 525919 1 511038 1 498662 1 555362 1 564591 1 541657 1 527070 1 509846 1 514258 1 516922 1 507561 1 492622 1 490243 1 469357 1 477580 1 528379 1 533590 1 517945 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 5 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Werkloosheid[t] = + 583322.096551724 + 9405.30344827585Aanslag[t] -8100.68275862071M1[t] -10126.3393103449M2[t] -28345.7393103448M3[t] -27063.3393103449M4[t] -26027.1393103449M5[t] -31502.3393103448M6[t] -43956.6M7[t] -51314.2M8[t] -61269.8M9[t] -60540.6M10[t] -9212.8M11[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) 583322.096551724 24702.939289 23.6135 0 0 Aanslag 9405.30344827585 17615.024541 0.5339 0.59585 0.297925 M1 -8100.68275862071 23633.035379 -0.3428 0.733268 0.366634 M2 -10126.3393103449 24744.773255 -0.4092 0.68419 0.342095 M3 -28345.7393103448 24744.773255 -1.1455 0.257671 0.128836 M4 -27063.3393103449 24744.773255 -1.0937 0.279545 0.139773 M5 -26027.1393103449 24744.773255 -1.0518 0.298147 0.149073 M6 -31502.3393103448 24744.773255 -1.2731 0.209117 0.104559 M7 -43956.6 24492.697684 -1.7947 0.079003 0.039501 M8 -51314.2 24492.697684 -2.0951 0.041465 0.020732 M9 -61269.8 24492.697684 -2.5016 0.015828 0.007914 M10 -60540.6 24492.697684 -2.4718 0.017042 0.008521 M11 -9212.8 24492.697684 -0.3761 0.708467 0.354233 Multiple Linear Regression - Regression Statistics Multiple R 0.500519309723004 R-squared 0.250519579405592 Adjusted R-squared 0.0631494742569906 F-TEST (value) 1.33703068163893 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.229759932151090 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 38726.3553617151 Sum Squared Residuals 71987068780.8883 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 577992 575221.413793103 2770.58620689655 2 565464 573195.757241379 -7731.75724137936 3 547344 554976.357241379 -7632.35724137926 4 554788 556258.757241379 -1470.75724137926 5 562325 557294.957241379 5030.04275862068 6 560854 551819.757241379 9034.24275862072 7 555332 548770.8 6561.20000000003 8 543599 541413.2 2185.80000000006 9 536662 531457.6 5204.39999999995 10 542722 532186.8 10535.2 11 593530 583514.6 10015.4000000000 12 610763 592727.4 18035.6 13 612613 584626.717241379 27986.2827586207 14 611324 582601.060689655 28722.9393103448 15 594167 564381.660689655 29785.3393103448 16 595454 565664.060689655 29789.9393103448 17 590865 566700.260689655 24164.7393103448 18 589379 561225.060689655 28153.9393103448 19 584428 548770.8 35657.2 20 573100 541413.2 31686.8 21 567456 531457.6 35998.4 22 569028 532186.8 36841.2 23 620735 583514.6 37220.4 24 628884 592727.4 36156.6 25 628232 584626.717241379 43605.2827586207 26 612117 582601.060689655 29515.9393103448 27 595404 564381.660689655 31022.3393103448 28 597141 565664.060689655 31476.9393103448 29 593408 566700.260689655 26707.7393103448 30 590072 561225.060689655 28846.9393103448 31 579799 548770.8 31028.2 32 574205 541413.2 32791.8 33 572775 531457.6 41317.4 34 572942 532186.8 40755.2 35 619567 583514.6 36052.4 36 625809 592727.4 33081.6 37 619916 584626.717241379 35289.2827586207 38 587625 582601.060689655 5023.93931034485 39 565742 564381.660689655 1360.33931034483 40 557274 565664.060689655 -8390.06068965517 41 560576 566700.260689655 -6124.26068965516 42 548854 561225.060689655 -12371.0606896552 43 531673 548770.8 -17097.8 44 525919 541413.2 -15494.2 45 511038 531457.6 -20419.6 46 498662 532186.8 -33524.8 47 555362 583514.6 -28152.6 48 564591 592727.4 -28136.4 49 541657 584626.717241379 -42969.7172413793 50 527070 582601.060689655 -55531.0606896551 51 509846 564381.660689655 -54535.6606896552 52 514258 565664.060689655 -51406.0606896552 53 516922 566700.260689655 -49778.2606896552 54 507561 561225.060689655 -53664.0606896552 55 492622 548770.8 -56148.8 56 490243 541413.2 -51170.2 57 469357 531457.6 -62100.6 58 477580 532186.8 -54606.8 59 528379 583514.6 -55135.6 60 533590 592727.4 -59137.4 61 517945 584626.717241379 -66681.7172413793 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.000919018484335658 0.00183803696867132 0.999080981515664 17 0.000412236506892618 0.000824473013785235 0.999587763493107 18 9.83958541168672e-05 0.000196791708233734 0.999901604145883 19 0.000456004613168797 0.000912009226337595 0.999543995386831 20 0.000569552939020591 0.00113910587804118 0.99943044706098 21 0.000593796447237273 0.00118759289447455 0.999406203552763 22 0.000415158252483439 0.000830316504966879 0.999584841747517 23 0.000302917141043744 0.000605834282087487 0.999697082858956 24 0.000148640651645903 0.000297281303291806 0.999851359348354 25 7.9279368984664e-05 0.000158558737969328 0.999920720631015 26 2.89685429720202e-05 5.79370859440405e-05 0.999971031457028 27 1.09618411119453e-05 2.19236822238907e-05 0.999989038158888 28 4.23847940276929e-06 8.47695880553857e-06 0.999995761520597 29 1.54698002606961e-06 3.09396005213922e-06 0.999998453019974 30 6.52191604593873e-07 1.30438320918775e-06 0.999999347808395 31 3.73840805054228e-07 7.47681610108455e-07 0.999999626159195 32 3.09536100504507e-07 6.19072201009015e-07 0.9999996904639 33 6.41553564862492e-07 1.28310712972498e-06 0.999999358446435 34 1.48381193799552e-06 2.96762387599105e-06 0.999998516188062 35 2.93125419987785e-06 5.8625083997557e-06 0.9999970687458 36 6.95119328717758e-06 1.39023865743552e-05 0.999993048806713 37 9.04273869720984e-05 0.000180854773944197 0.999909572613028 38 0.000354959297650974 0.000709918595301949 0.999645040702349 39 0.00160882410466552 0.00321764820933105 0.998391175895335 40 0.00706623440786658 0.0141324688157332 0.992933765592133 41 0.0193666251221730 0.0387332502443459 0.980633374877827 42 0.0553569363459565 0.110713872691913 0.944643063654043 43 0.111567503684847 0.223135007369694 0.888432496315153 44 0.16147517013318 0.32295034026636 0.83852482986682 45 0.306613053079370 0.613226106158741 0.69338694692063 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.8 NOK 5% type I error level 26 0.866666666666667 NOK 10% type I error level 26 0.866666666666667 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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