Multiple Lineair Regression Totaal # niet-werkende werkzoekende vrouwen in het Vlaams gewest

*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: Tue, 16 Dec 2008 14:55:43 -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/Dec/16/t1229464873cdf59olwhk1bmv3.htm/, Retrieved Tue, 16 Dec 2008 23:01:25 +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/2008/Dec/16/t1229464873cdf59olwhk1bmv3.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}, }

Original text written by user:

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No (this computation is public)

User-defined keywords:

Multiple Lineair Regression Totaal niet-werkende werkzoekende vrouwen Vlaams gewest

Dataseries X:

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121148 1 114624 1 109822 1 112081 1 113534 1 112110 1 109826 1 107423 1 105540 1 108573 1 128591 1 139145 1 129700 1 132828 1 126868 1 128390 1 126830 1 124105 1 122323 1 119296 1 116822 1 119224 1 139357 1 144322 1 133676 1 128283 1 121640 1 122877 0 117284 0 116463 0 112685 0 113235 0 111692 0 113152 0 129889 0 131153 0 123770 0 112516 0 105940 0 104320 0 103582 0 99064 0 94989 0 92241 0 89752 0 90610 0 109456 0 110213 0 97694 0 91844 0 87572 0 89812 0 89050 0 85990 0 85070 0 83277 0 79586 0 84215 0 99708 0 100698 0 90861 0 86700 0

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 werkl.vrouwen[t] = + 124894.424539170 + 4421.27050264550Wetswijziging[t] -517.044354838710t + 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) 124894.424539170 7691.226151 16.2386 0 0 Wetswijziging 4421.27050264550 5953.963167 0.7426 0.460685 0.230342 t -517.044354838710 164.962713 -3.1343 0.002683 0.001342 Multiple Linear Regression - Regression Statistics Multiple R 0.693931270817882 R-squared 0.481540608618921 Adjusted R-squared 0.463965713995833 F-TEST (value) 27.3993454268761 F-TEST (DF numerator) 2 F-TEST (DF denominator) 59 p-value 3.83782350343864e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11904.7773391412 Sum Squared Residuals 8361699686.17732 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 121148 128798.650686977 -7650.65068697747 2 114624 128281.606332139 -13657.6063321386 3 109822 127764.5619773 -17942.5619772999 4 112081 127247.517622461 -15166.5176224612 5 113534 126730.473267622 -13196.4732676225 6 112110 126213.428912784 -14103.4289127837 7 109826 125696.384557945 -15870.3845579450 8 107423 125179.340203106 -17756.3402031063 9 105540 124662.295848268 -19122.2958482676 10 108573 124145.251493429 -15572.2514934289 11 128591 123628.207138590 4962.79286140981 12 139145 123111.162783751 16033.8372162485 13 129700 122594.118428913 7105.88157108723 14 132828 122077.074074074 10750.9259259259 15 126868 121560.029719235 5307.97028076464 16 128390 121042.985364397 7347.01463560335 17 126830 120525.941009558 6304.05899044206 18 124105 120008.896654719 4096.10334528077 19 122323 119491.852299881 2831.14770011948 20 119296 118974.807945042 321.192054958192 21 116822 118457.763590203 -1635.76359020310 22 119224 117940.719235364 1283.28076463561 23 139357 117423.674880526 21933.3251194743 24 144322 116906.630525687 27415.3694743130 25 133676 116389.586170848 17286.4138291517 26 128283 115872.541816010 12410.4581839904 27 121640 115355.497461171 6284.50253882916 28 122877 110417.182603687 12459.8173963134 29 117284 109900.138248848 7383.86175115207 30 116463 109383.093894009 7079.90610599078 31 112685 108866.049539171 3818.95046082949 32 113235 108349.005184332 4885.9948156682 33 111692 107831.960829493 3860.03917050691 34 113152 107314.916474654 5837.08352534562 35 129889 106797.872119816 23091.1278801843 36 131153 106280.827764977 24872.1722350230 37 123770 105763.783410138 18006.2165898618 38 112516 105246.739055300 7269.26094470046 39 105940 104729.694700461 1210.30529953917 40 104320 104212.650345622 107.349654377878 41 103582 103695.605990783 -113.605990783412 42 99064 103178.561635945 -4114.5616359447 43 94989 102661.517281106 -7672.517281106 44 92241 102144.472926267 -9903.47292626728 45 89752 101627.428571429 -11875.4285714286 46 90610 101110.384216590 -10500.3842165899 47 109456 100593.339861751 8862.66013824884 48 110213 100076.295506912 10136.7044930876 49 97694 99559.2511520737 -1865.25115207374 50 91844 99042.206797235 -7198.20679723503 51 87572 98525.1624423963 -10953.1624423963 52 89812 98008.1180875576 -8196.11808755761 53 89050 97491.073732719 -8441.0737327189 54 85990 96974.0293778802 -10984.0293778802 55 85070 96456.9850230415 -11386.9850230415 56 83277 95939.9406682028 -12662.9406682028 57 79586 95422.896313364 -15836.8963133641 58 84215 94905.8519585254 -10690.8519585253 59 99708 94388.8076036866 5319.19239631336 60 100698 93871.763248848 6826.23675115207 61 90861 93354.7188940092 -2493.71889400922 62 86700 92837.6745391705 -6137.67453917051 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.0536831835781306 0.107366367156261 0.94631681642187 7 0.0175517039094053 0.0351034078188105 0.982448296090595 8 0.00623256101552895 0.0124651220310579 0.99376743898447 9 0.00271881634154785 0.00543763268309569 0.997281183658452 10 0.00231830805160955 0.00463661610321911 0.99768169194839 11 0.328482425888572 0.656964851777145 0.671517574111428 12 0.76561519847135 0.468769603057302 0.234384801528651 13 0.72630766153862 0.547384676922758 0.273692338461379 14 0.677689928804647 0.644620142390705 0.322310071195353 15 0.600102830994428 0.799794338011145 0.399897169005572 16 0.514411217459538 0.971177565080924 0.485588782540462 17 0.440577995706178 0.881155991412356 0.559422004293822 18 0.400440244095686 0.800880488191372 0.599559755904314 19 0.38614952398026 0.77229904796052 0.61385047601974 20 0.424736876820877 0.849473753641755 0.575263123179123 21 0.520570215614952 0.958859568770096 0.479429784385048 22 0.571640161495789 0.856719677008422 0.428359838504211 23 0.58549761536228 0.82900476927544 0.41450238463772 24 0.673487114837218 0.653025770325563 0.326512885162782 25 0.613535356104572 0.772929287790857 0.386464643895428 26 0.559286100834726 0.881427798330548 0.440713899165274 27 0.555453384144977 0.889093231710046 0.444546615855023 28 0.481106797913082 0.962213595826164 0.518893202086918 29 0.417528742479229 0.835057484958459 0.582471257520771 30 0.353506301159445 0.70701260231889 0.646493698840555 31 0.31543575642083 0.63087151284166 0.68456424357917 32 0.268358478659255 0.536716957318509 0.731641521340745 33 0.232817357002142 0.465634714004284 0.767182642997858 34 0.188221184659571 0.376442369319142 0.811778815340429 35 0.266695343663437 0.533390687326875 0.733304656336563 36 0.476395917423193 0.952791834846385 0.523604082576807 37 0.621699396698502 0.756601206602995 0.378300603301498 38 0.66082380551505 0.678352388969901 0.339176194484950 39 0.700167120418807 0.599665759162386 0.299832879581193 40 0.730906626141495 0.538186747717009 0.269093373858505 41 0.752835419777832 0.494329160444336 0.247164580222168 42 0.773734218471674 0.452531563056651 0.226265781528326 43 0.79755433698798 0.404891326024041 0.202445663012020 44 0.820932449397784 0.358135101204431 0.179067550602216 45 0.851475254631919 0.297049490736163 0.148524745368081 46 0.861951939198318 0.276096121603363 0.138048060801682 47 0.881009464978175 0.237981070043650 0.118990535021825 48 0.962800708268224 0.0743985834635515 0.0371992917317757 49 0.96822137883597 0.0635572423280585 0.0317786211640293 50 0.960192563858114 0.0796148722837726 0.0398074361418863 51 0.939464906055772 0.121070187888457 0.0605350939442283 52 0.914694769198997 0.170610461602007 0.0853052308010035 53 0.88102586414636 0.237948271707280 0.118974135853640 54 0.813347316972967 0.373305366054066 0.186652683027033 55 0.704283192470007 0.591433615059987 0.295716807529993 56 0.548060587068018 0.903878825863964 0.451939412931982 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0392156862745098 NOK 5% type I error level 4 0.0784313725490196 NOK 10% type I error level 7 0.137254901960784 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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