Seatbelt law Q3 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 08:34:51 -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/t1227627396ncdol549tqnt2bo.htm/, Retrieved Tue, 25 Nov 2008 15:36:36 +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/t1227627396ncdol549tqnt2bo.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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 20.9644444444444 -3.62069444444444x[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) 20.9644444444444 0.322281 65.0501 0 0 x -3.62069444444444 0.629275 -5.7538 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.599526359057155 R-squared 0.359431855204328 Adjusted R-squared 0.348574768004402 F-TEST (value) 33.1057353216024 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 3.30099532930284e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.16192979593723 Sum Squared Residuals 275.762486111111 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 20.9644444444444 4.03555555555558 2 23.6 20.9644444444444 2.63555555555556 3 22.3 20.9644444444444 1.33555555555556 4 21.8 20.9644444444444 0.835555555555556 5 20.8 20.9644444444444 -0.164444444444444 6 19.7 20.9644444444444 -1.26444444444445 7 18.3 20.9644444444444 -2.66444444444444 8 17.4 20.9644444444444 -3.56444444444445 9 17 20.9644444444444 -3.96444444444444 10 18.1 20.9644444444444 -2.86444444444444 11 23.9 20.9644444444444 2.93555555555555 12 25.6 20.9644444444444 4.63555555555556 13 25.3 20.9644444444444 4.33555555555556 14 23.6 20.9644444444444 2.63555555555556 15 21.9 20.9644444444444 0.935555555555554 16 21.4 20.9644444444444 0.435555555555554 17 20.6 20.9644444444444 -0.364444444444444 18 20.5 20.9644444444444 -0.464444444444445 19 20.2 20.9644444444444 -0.764444444444446 20 20.6 20.9644444444444 -0.364444444444444 21 19.7 20.9644444444444 -1.26444444444445 22 19.3 20.9644444444444 -1.66444444444444 23 22.8 20.9644444444444 1.83555555555556 24 23.5 20.9644444444444 2.53555555555555 25 23.8 20.9644444444444 2.83555555555556 26 22.6 20.9644444444444 1.63555555555556 27 22 20.9644444444444 1.03555555555556 28 21.7 20.9644444444444 0.735555555555554 29 20.7 20.9644444444444 -0.264444444444446 30 20.2 20.9644444444444 -0.764444444444446 31 19.1 20.9644444444444 -1.86444444444444 32 19.5 20.9644444444444 -1.46444444444445 33 18.7 20.9644444444444 -2.26444444444445 34 18.6 20.9644444444444 -2.36444444444444 35 22.2 20.9644444444444 1.23555555555555 36 23.2 20.9644444444444 2.23555555555555 37 23.5 20.9644444444444 2.53555555555555 38 21.3 20.9644444444444 0.335555555555556 39 20 20.9644444444444 -0.964444444444445 40 18.7 20.9644444444444 -2.26444444444445 41 18.9 20.9644444444444 -2.06444444444445 42 18.3 20.9644444444444 -2.66444444444444 43 18.4 20.9644444444444 -2.56444444444445 44 19.9 20.9644444444444 -1.06444444444445 45 19.2 20.9644444444444 -1.76444444444445 46 18.5 17.34375 1.15625 47 20.9 17.34375 3.55625 48 20.5 17.34375 3.15625 49 19.4 17.34375 2.05625 50 18.1 17.34375 0.756250000000001 51 17 17.34375 -0.34375 52 17 17.34375 -0.34375 53 17.3 17.34375 -0.0437499999999995 54 16.7 17.34375 -0.643750000000001 55 15.5 17.34375 -1.84375 56 15.3 17.34375 -2.04375 57 13.7 17.34375 -3.64375 58 14.1 17.34375 -3.24375 59 17.3 17.34375 -0.0437499999999995 60 18.1 17.34375 0.756250000000001 61 18.1 17.34375 0.756250000000001 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.486786873981084 0.973573747962168 0.513213126018916 6 0.571037741959698 0.857924516080604 0.428962258040302 7 0.741102712034093 0.517794575931815 0.258897287965907 8 0.870813040674503 0.258373918650994 0.129186959325497 9 0.937224296716217 0.125551406567566 0.0627757032837831 10 0.939193745710445 0.121612508579111 0.0608062542895554 11 0.957186310847905 0.085627378304191 0.0428136891520955 12 0.989834602868935 0.020330794262131 0.0101653971310655 13 0.997066283185215 0.00586743362956914 0.00293371681478457 14 0.997171909242876 0.00565618151424724 0.00282809075712362 15 0.995105318112022 0.0097893637759558 0.0048946818879779 16 0.991472951759122 0.0170540964817554 0.0085270482408777 17 0.986069418168663 0.0278611636626746 0.0139305818313373 18 0.97817200562673 0.0436559887465384 0.0218279943732692 19 0.967976958148518 0.0640460837029635 0.0320230418514818 20 0.95210841256795 0.0957831748640986 0.0478915874320493 21 0.938161881913089 0.123676236173823 0.0618381180869114 22 0.927344574323394 0.145310851353212 0.072655425676606 23 0.918355640464994 0.163288719070011 0.0816443595350056 24 0.928265157989571 0.143469684020858 0.0717348420104288 25 0.947716625503652 0.104566748992695 0.0522833744963477 26 0.942874166501653 0.114251666996694 0.0571258334983468 27 0.92971351927602 0.140572961447958 0.0702864807239791 28 0.911382970392268 0.177234059215463 0.0886170296077317 29 0.881637361627372 0.236725276745255 0.118362638372628 30 0.84694484199536 0.306110316009279 0.153055158004640 31 0.82809979054463 0.343800418910738 0.171900209455369 32 0.794216338563201 0.411567322873597 0.205783661436799 33 0.785100418353723 0.429799163292555 0.214899581646277 34 0.780177493624342 0.439645012751317 0.219822506375659 35 0.757094497915329 0.485811004169342 0.242905502084671 36 0.803401045946839 0.393197908106323 0.196598954053161 37 0.88956954367128 0.220860912657439 0.110430456328719 38 0.881610149190731 0.236779701618537 0.118389850809269 39 0.851007373117937 0.297985253764126 0.148992626882063 40 0.821219717833864 0.357560564332273 0.178780282166136 41 0.781134352191935 0.437731295616131 0.218865647808065 42 0.751432034623312 0.497135930753376 0.248567965376688 43 0.717391991391967 0.565216017216066 0.282608008608033 44 0.647566368658492 0.704867262683016 0.352433631341508 45 0.575289137928713 0.849421724142574 0.424710862071287 46 0.505805526415318 0.988388947169364 0.494194473584682 47 0.646450664555457 0.707098670889086 0.353549335444543 48 0.785524479920549 0.428951040158903 0.214475520079451 49 0.843640282521566 0.312719434956869 0.156359717478434 50 0.82773398234551 0.344532035308979 0.172266017654489 51 0.765672389933903 0.468655220132194 0.234327610066097 52 0.686029093724548 0.627941812550903 0.313970906275452 53 0.605884613461527 0.788230773076946 0.394115386538473 54 0.490156259675632 0.980312519351265 0.509843740324368 55 0.370763455277574 0.741526910555148 0.629236544722426 56 0.257705398642962 0.515410797285924 0.742294601357038 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.0576923076923077 NOK 5% type I error level 7 0.134615384615385 NOK 10% type I error level 10 0.192307692307692 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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