paper: regression: samenwerking

*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 08:39:35 -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/t1229442050hsxqd5r1ev4zopu.htm/, Retrieved Tue, 16 Dec 2008 16:41:00 +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/t1229442050hsxqd5r1ev4zopu.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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User-defined keywords:

paper: regression: samenwerking

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 1 21.3 1 20 1 18.7 1 18.9 1 18.3 1 18.4 1 19.9 1 19.2 1 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werklozen[t] = + 24.9764743589744 -1.15608974358974Samenwerking[t] + 0.128103632478631M1[t] -0.988344017094017M2[t] -2.12350961538462M3[t] -2.57867521367522M4[t] -2.97384081196581M5[t] -3.48900641025642M6[t] -4.20417200854701M7[t] -3.89933760683761M8[t] -4.71450320512821M9[t] -4.58966880341881M10[t] -0.824834401709404M11[t] -0.0648344017094017t + 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) 24.9764743589744 0.808742 30.8831 0 0 Samenwerking -1.15608974358974 0.730442 -1.5827 0.12019 0.060095 M1 0.128103632478631 0.864396 0.1482 0.882819 0.441409 M2 -0.988344017094017 0.908894 -1.0874 0.282399 0.1412 M3 -2.12350961538462 0.904418 -2.3479 0.023139 0.011569 M4 -2.57867521367522 0.900394 -2.8639 0.006235 0.003117 M5 -2.97384081196581 0.896829 -3.316 0.001767 0.000883 M6 -3.48900641025642 0.893727 -3.9039 0.000301 0.000151 M7 -4.20417200854701 0.891094 -4.718 2.2e-05 1.1e-05 M8 -3.89933760683761 0.888935 -4.3865 6.5e-05 3.2e-05 M9 -4.71450320512821 0.887251 -5.3136 3e-06 1e-06 M10 -4.58966880341881 0.886047 -5.1799 5e-06 2e-06 M11 -0.824834401709404 0.885323 -0.9317 0.356265 0.178133 t -0.0648344017094017 0.020668 -3.1369 0.002945 0.001472 Multiple Linear Regression - Regression Statistics Multiple R 0.886671674815299 R-squared 0.786186658919767 Adjusted R-squared 0.72704679862098 F-TEST (value) 13.2936847491316 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 1.24500409981465e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.39943713843066 Sum Squared Residuals 92.0459423076923 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 25 25.0397435897436 -0.0397435897435853 2 23.6 23.8584615384615 -0.258461538461536 3 22.3 22.6584615384615 -0.358461538461538 4 21.8 22.1384615384615 -0.338461538461541 5 20.8 21.6784615384615 -0.878461538461533 6 19.7 21.0984615384615 -1.39846153846154 7 18.3 20.3184615384615 -2.01846153846154 8 17.4 20.5584615384615 -3.15846153846154 9 17 19.6784615384615 -2.67846153846154 10 18.1 19.7384615384615 -1.63846153846154 11 23.9 23.4384615384615 0.46153846153846 12 25.6 24.1984615384615 1.40153846153847 13 25.3 24.2617307692308 1.03826923076923 14 23.6 23.0804487179487 0.51955128205128 15 21.9 21.8804487179487 0.0195512820512812 16 21.4 21.3604487179487 0.0395512820512814 17 20.6 20.9004487179487 -0.300448717948719 18 20.5 20.3204487179487 0.179551282051283 19 20.2 19.5404487179487 0.659551282051284 20 20.6 19.7804487179487 0.819551282051282 21 19.7 18.9004487179487 0.79955128205128 22 19.3 18.9604487179487 0.339551282051282 23 22.8 22.6604487179487 0.139551282051282 24 23.5 23.4204487179487 0.0795512820512797 25 23.8 23.4837179487179 0.316282051282051 26 22.6 22.3024358974359 0.297564102564103 27 22 21.1024358974359 0.897564102564104 28 21.7 20.5824358974359 1.11756410256410 29 20.7 20.1224358974359 0.5775641025641 30 20.2 19.5424358974359 0.657564102564103 31 19.1 18.7624358974359 0.337564102564107 32 19.5 19.0024358974359 0.497564102564102 33 18.7 18.1224358974359 0.577564102564102 34 18.6 18.1824358974359 0.417564102564103 35 22.2 21.8824358974359 0.317564102564102 36 23.2 22.6424358974359 0.5575641025641 37 23.5 21.5496153846154 1.95038461538461 38 21.3 20.3683333333333 0.931666666666665 39 20 19.1683333333333 0.831666666666667 40 18.7 18.6483333333333 0.0516666666666665 41 18.9 18.1883333333333 0.711666666666663 42 18.3 17.6083333333333 0.69166666666667 43 18.4 16.8283333333333 1.57166666666667 44 19.9 17.0683333333333 2.83166666666666 45 19.2 16.1883333333333 3.01166666666667 46 18.5 16.2483333333333 2.25166666666667 47 20.9 19.9483333333333 0.951666666666666 48 20.5 20.7083333333333 -0.208333333333335 49 19.4 20.7716025641026 -1.37160256410257 50 18.1 19.5903205128205 -1.49032051282051 51 17 18.3903205128205 -1.39032051282051 52 17 17.8703205128205 -0.870320512820512 53 17.3 17.4103205128205 -0.110320512820514 54 16.7 16.8303205128205 -0.130320512820511 55 15.5 16.0503205128205 -0.55032051282051 56 15.3 16.2903205128205 -0.990320512820512 57 13.7 15.4103205128205 -1.71032051282051 58 14.1 15.4703205128205 -1.37032051282051 59 17.3 19.1703205128205 -1.87032051282051 60 18.1 19.9303205128205 -1.83032051282051 61 18.1 19.9935897435897 -1.89358974358974 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0199615881162668 0.0399231762325335 0.980038411883733 18 0.0368347128948875 0.0736694257897751 0.963165287105112 19 0.190768383636686 0.381536767273373 0.809231616363314 20 0.609953649519773 0.780092700960453 0.390046350480227 21 0.712251051341115 0.575497897317771 0.287748948658885 22 0.707082404063395 0.58583519187321 0.292917595936605 23 0.820351956376997 0.359296087246006 0.179648043623003 24 0.944064708182545 0.111870583634910 0.0559352918174549 25 0.957587760926206 0.0848244781475879 0.0424122390737940 26 0.943619876989606 0.112760246020788 0.056380123010394 27 0.916882756814551 0.166234486370897 0.0831172431854486 28 0.899027157598723 0.201945684802554 0.100972842401277 29 0.846892285392148 0.306215429215704 0.153107714607852 30 0.779743208473474 0.440513583053051 0.220256791526526 31 0.708450772019596 0.583098455960808 0.291549227980404 32 0.65503164524968 0.68993670950064 0.34496835475032 33 0.584156173072339 0.831687653855322 0.415843826927661 34 0.530273191125653 0.939453617748694 0.469726808874347 35 0.485395697687712 0.970791395375424 0.514604302312288 36 0.428078876371996 0.856157752743992 0.571921123628004 37 0.328491566536202 0.656983133072404 0.671508433463798 38 0.243987045914223 0.487974091828445 0.756012954085777 39 0.167277371905262 0.334554743810525 0.832722628094738 40 0.154641397625088 0.309282795250177 0.845358602374912 41 0.144723719797867 0.289447439595733 0.855276280202133 42 0.158724529967218 0.317449059934435 0.841275470032782 43 0.109817537014458 0.219635074028917 0.890182462985542 44 0.113512224965811 0.227024449931623 0.886487775034189 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 1 0.0357142857142857 OK 10% type I error level 3 0.107142857142857 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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