Q3 Seatbelt law- werkloosheid

*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, 25 Nov 2008 08:56:16 -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/25/t1227628718b275lpoqaftf0qj.htm/, Retrieved Tue, 25 Nov 2008 15:58:47 +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/25/t1227628718b275lpoqaftf0qj.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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IsPrivate?

No (this computation is public)

User-defined keywords:

multiple regression

Dataseries X:

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25 0 23.6 0 22.3 0 21.8 0 20.8 0 19.7 0 18.3 0 17.4 0 17 0 18.1 0 23.9 0 25.6 0 25.3 0 23.6 0 21.9 0 21.4 0 20.6 0 20.5 0 20.2 0 20.6 0 19.7 0 19.3 0 22.8 0 23.5 0 23.8 0 22.6 0 22 0 21.7 0 20.7 0 20.2 0 19.1 0 19.5 0 18.7 0 18.6 0 22.2 0 23.2 0 23.5 0 21.3 0 20 0 18.7 0 18.9 0 18.3 0 18.4 0 19.9 0 19.2 0 18.5 1 20.9 1 20.5 1 19.4 1 18.1 1 17 1 17 1 17.3 1 16.7 1 15.5 1 15.3 1 13.7 1 14.1 1 17.3 1 18.1 1 18.1 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 24.7241059602649 -2.86879139072848x[t] -0.0485568432671088M1[t] -1.30169977924945M2[t] -2.46290562913908M3[t] -2.94411147902870M4[t] -3.36531732891832M5[t] -3.90652317880795M6[t] -4.64772902869757M7[t] -4.36893487858720M8[t] -5.21014072847682M9[t] -4.53758830022075M10[t] -0.798794150110375M11[t] -0.0387941501103753t + 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) 24.7241059602649 0.595372 41.5272 0 0 x -2.86879139072848 0.510233 -5.6225 1e-06 0 M1 -0.0485568432671088 0.673862 -0.0721 0.942862 0.471431 M2 -1.30169977924945 0.707149 -1.8408 0.071973 0.035986 M3 -2.46290562913908 0.706385 -3.4866 0.001072 0.000536 M4 -2.94411147902870 0.705849 -4.171 0.000129 6.5e-05 M5 -3.36531732891832 0.705539 -4.7699 1.8e-05 9e-06 M6 -3.90652317880795 0.705457 -5.5376 1e-06 1e-06 M7 -4.64772902869757 0.705603 -6.5869 0 0 M8 -4.36893487858720 0.705977 -6.1885 0 0 M9 -5.21014072847682 0.706578 -7.3738 0 0 M10 -4.53758830022075 0.702821 -6.4563 0 0 M11 -0.798794150110375 0.702478 -1.1371 0.261257 0.130628 t -0.0387941501103753 0.012677 -3.0602 0.003648 0.001824 Multiple Linear Regression - Regression Statistics Multiple R 0.930244373511343 R-squared 0.865354594449512 Adjusted R-squared 0.82811224823342 F-TEST (value) 23.2357700943017 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 4.44089209850063e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.11053375732208 Sum Squared Residuals 57.9644056291391 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 24.6367549668874 0.363245033112585 2 23.6 23.3448178807947 0.255182119205299 3 22.3 22.1448178807947 0.155182119205298 4 21.8 21.6248178807947 0.175182119205297 5 20.8 21.1648178807947 -0.364817880794695 6 19.7 20.5848178807947 -0.884817880794708 7 18.3 19.8048178807947 -1.5048178807947 8 17.4 20.0448178807947 -2.64481788079470 9 17 19.1648178807947 -2.16481788079470 10 18.1 19.7985761589404 -1.6985761589404 11 23.9 23.4985761589404 0.401423841059604 12 25.6 24.2585761589404 1.34142384105960 13 25.3 24.1712251655629 1.12877483443709 14 23.6 22.8792880794702 0.7207119205298 15 21.9 21.6792880794702 0.2207119205298 16 21.4 21.1592880794702 0.2407119205298 17 20.6 20.6992880794702 -0.0992880794701991 18 20.5 20.1192880794702 0.380711920529803 19 20.2 19.3392880794702 0.8607119205298 20 20.6 19.5792880794702 1.02071192052980 21 19.7 18.6992880794702 1.00071192052980 22 19.3 19.3330463576159 -0.0330463576158951 23 22.8 23.0330463576159 -0.233046357615894 24 23.5 23.7930463576159 -0.293046357615894 25 23.8 23.7056953642384 0.0943046357615896 26 22.6 22.4137582781457 0.186241721854305 27 22 21.2137582781457 0.786241721854305 28 21.7 20.6937582781457 1.00624172185430 29 20.7 20.2337582781457 0.466241721854302 30 20.2 19.6537582781457 0.546241721854306 31 19.1 18.8737582781457 0.226241721854306 32 19.5 19.1137582781457 0.386241721854304 33 18.7 18.2337582781457 0.466241721854305 34 18.6 18.8675165562914 -0.267516556291390 35 22.2 22.5675165562914 -0.367516556291392 36 23.2 23.3275165562914 -0.127516556291391 37 23.5 23.2401655629139 0.259834437086093 38 21.3 21.9482284768212 -0.648228476821192 39 20 20.7482284768212 -0.748228476821191 40 18.7 20.2282284768212 -1.52822847682119 41 18.9 19.7682284768212 -0.868228476821195 42 18.3 19.1882284768212 -0.888228476821188 43 18.4 18.4082284768212 -0.00822847682119302 44 19.9 18.6482284768212 1.25177152317881 45 19.2 17.7682284768212 1.43177152317881 46 18.5 15.5331953642384 2.96680463576159 47 20.9 19.2331953642384 1.66680463576159 48 20.5 19.9931953642384 0.506804635761589 49 19.4 19.9058443708609 -0.505844370860929 50 18.1 18.6139072847682 -0.513907284768211 51 17 17.4139072847682 -0.413907284768212 52 17 16.8939072847682 0.106092715231789 53 17.3 16.4339072847682 0.866092715231787 54 16.7 15.8539072847682 0.846092715231788 55 15.5 15.0739072847682 0.426092715231787 56 15.3 15.3139072847682 -0.0139072847682126 57 13.7 14.4339072847682 -0.733907284768213 58 14.1 15.0676655629139 -0.967665562913907 59 17.3 18.7676655629139 -1.46766556291391 60 18.1 19.5276655629139 -1.42766556291391 61 18.1 19.4403145695364 -1.34031456953642 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0271217249336567 0.0542434498673134 0.972878275066343 18 0.0490262104360771 0.0980524208721542 0.950973789563923 19 0.231515511209996 0.463031022419993 0.768484488790004 20 0.642655830488052 0.714688339023896 0.357344169511948 21 0.702466291250064 0.595067417499872 0.297533708749936 22 0.64617127806993 0.707657443860139 0.353828721930070 23 0.715735409245886 0.568529181508228 0.284264590754114 24 0.842070803419601 0.315858393160797 0.157929196580399 25 0.862013313600476 0.275973372799048 0.137986686399524 26 0.82968092740672 0.340638145186559 0.170319072593280 27 0.760397150004077 0.479205699991846 0.239602849995923 28 0.689956258451679 0.620087483096642 0.310043741548321 29 0.6022385621022 0.7955228757956 0.3977614378978 30 0.508091466733603 0.983817066532794 0.491908533266397 31 0.445923468545736 0.891846937091472 0.554076531454264 32 0.433121791567757 0.866243583135513 0.566878208432243 33 0.420097812435343 0.840195624870687 0.579902187564657 34 0.457994743539913 0.915989487079826 0.542005256460087 35 0.469536173741602 0.939072347483205 0.530463826258398 36 0.42883516528146 0.85767033056292 0.57116483471854 37 0.358104458447593 0.716208916895187 0.641895541552407 38 0.325162069722516 0.650324139445032 0.674837930277484 39 0.278353314699664 0.556706629399328 0.721646685300336 40 0.330217289654497 0.660434579308994 0.669782710345503 41 0.354196461012464 0.708392922024928 0.645803538987536 42 0.512073406629049 0.975853186741903 0.487926593370951 43 0.569920091708281 0.860159816583438 0.430079908291719 44 0.453319439645937 0.906638879291874 0.546680560354063 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 0 0 OK 10% type I error level 2 0.0714285714285714 OK

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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