Multiple Regression werkloosheid ecogr

*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: Thu, 17 Dec 2009 06:41:03 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/17/t1261057377k024ufs1q5ais0x.htm/, Retrieved Thu, 17 Dec 2009 14:43:09 +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/2009/Dec/17/t1261057377k024ufs1q5ais0x.htm/}, year = {2009}, } @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 = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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Dataseries X:

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9,3 96,8 9,3 114,1 8,7 110,3 8,2 103,9 8,3 101,6 8,5 94,6 8,6 95,9 8,5 104,7 8,2 102,8 8,1 98,1 7,9 113,9 8,6 80,9 8,7 95,7 8,7 113,2 8,5 105,9 8,4 108,8 8,5 102,3 8,7 99 8,7 100,7 8,6 115,5 8,5 100,7 8,3 109,9 8 114,6 8,2 85,4 8,1 100,5 8,1 114,8 8 116,5 7,9 112,9 7,9 102 8 106 8 105,3 7,9 118,8 8 106,1 7,7 109,3 7,2 117,2 7,5 92,5 7,3 104,2 7 112,5 7 122,4 7 113,3 7,2 100 7,3 110,7 7,1 112,8 6,8 109,8 6,4 117,3 6,1 109,1 6,5 115,9 7,7 96 7,9 99,8 7,5 116,8 6,9 115,7 6,6 99,4 6,9 94,3 7,7 91 8 93,2 8 103,1 7,7 94,1 7,3 91,8 7,4 102,7 8,1 82,6

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 werklh[t] = + 9.96948812558808 -0.0201393836545193ecogr[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) 9.96948812558808 0.993981 10.0299 0 0 ecogr -0.0201393836545193 0.009459 -2.1291 0.037503 0.018752 Multiple Linear Regression - Regression Statistics Multiple R 0.269240771992664 R-squared 0.0724905933032056 Adjusted R-squared 0.0564990518084334 F-TEST (value) 4.53305851264576 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.0375032893091131 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.687792930496844 Sum Squared Residuals 27.4374286840033 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9.3 8.01999578783066 1.28000421216934 2 9.3 7.67158445060743 1.62841554939257 3 8.7 7.7481141084946 0.951885891505398 4 8.2 7.87700616388352 0.322993836116475 5 8.3 7.92332674628892 0.376673253711081 6 8.5 8.06430243187055 0.435697568129445 7 8.6 8.03812123311968 0.56187876688032 8 8.5 7.8608946569599 0.639105343040091 9 8.2 7.8991594859035 0.300840514096503 10 8.1 7.99381458907974 0.106185410920263 11 7.9 7.67561232733833 0.224387672661669 12 8.6 8.34021198793747 0.25978801206253 13 8.7 8.04214910985058 0.657850890149416 14 8.7 7.6897098958965 1.01029010410350 15 8.5 7.83672739657449 0.663272603425514 16 8.4 7.77832318397638 0.62167681602362 17 8.5 7.90922917773076 0.590770822269244 18 8.7 7.97568914379067 0.72431085620933 19 8.7 7.94145219157799 0.758547808422013 20 8.6 7.6433893134911 0.9566106865089 21 8.5 7.94145219157799 0.558547808422013 22 8.3 7.75616986195641 0.543830138043592 23 8 7.66151475878017 0.338485241219832 24 8.2 8.24958476149213 -0.0495847614921333 25 8.1 7.94548006830889 0.154519931691109 26 8.1 7.65748688204926 0.442513117950736 27 8 7.62324992983658 0.376750070163419 28 7.9 7.69575171099285 0.20424828900715 29 7.9 7.91527099282711 -0.0152709928271111 30 8 7.83471345820903 0.165286541790966 31 8 7.8488110267672 0.151188973232802 32 7.9 7.57692934743119 0.323070652568814 33 8 7.83269951984358 0.167300480156418 34 7.7 7.76825349214912 -0.0682534921491201 35 7.2 7.60915236127842 -0.409152361278417 36 7.5 8.10659513754505 -0.606595137545045 37 7.3 7.87096434878717 -0.570964348787169 38 7 7.70380746445466 -0.703807464454658 39 7 7.50442756627492 -0.504427566274916 40 7 7.68769595753104 -0.687695957531043 41 7.2 7.95554976013615 -0.75554976013615 42 7.3 7.7400583550328 -0.440058355032793 43 7.1 7.6977656493583 -0.597765649358303 44 6.8 7.75818380032186 -0.95818380032186 45 6.4 7.60713842291297 -1.20713842291296 46 6.1 7.77228136888002 -1.67228136888002 47 6.5 7.63533356002929 -1.13533356002929 48 7.7 8.03610729475423 -0.336107294754227 49 7.9 7.95957763686705 -0.0595776368670538 50 7.5 7.61720811474023 -0.117208114740225 51 6.9 7.6393614367602 -0.739361436760196 52 6.6 7.96763339032886 -1.36763339032886 53 6.9 8.07034424696691 -1.17034424696691 54 7.7 8.13680421302682 -0.436804213026824 55 8 8.09249756898688 -0.0924975689868818 56 8 7.89311767080714 0.106882329192860 57 7.7 8.07437212369781 -0.374372123697814 58 7.3 8.12069270610321 -0.820692706103209 59 7.4 7.90117342426895 -0.501173424268948 60 8.1 8.30597503572479 -0.205975035724787 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.545528105638287 0.908943788723427 0.454471894361713 6 0.381033502204633 0.762067004409266 0.618966497795367 7 0.249613192264833 0.499226384529665 0.750386807735167 8 0.170657665924100 0.341315331848201 0.8293423340759 9 0.145550658975742 0.291101317951485 0.854449341024258 10 0.117320231263177 0.234640462526354 0.882679768736823 11 0.162890997287671 0.325781994575343 0.837109002712329 12 0.106939522794744 0.213879045589489 0.893060477205256 13 0.076765225673159 0.153530451346318 0.923234774326841 14 0.0630899906591629 0.126179981318326 0.936910009340837 15 0.0443609454795889 0.0887218909591778 0.95563905452041 16 0.0317740563958036 0.0635481127916072 0.968225943604196 17 0.0221960467878829 0.0443920935757658 0.977803953212117 18 0.0183109010136444 0.0366218020272888 0.981689098986356 19 0.0164544101881882 0.0329088203763765 0.983545589811812 20 0.0177581029501140 0.0355162059002281 0.982241897049886 21 0.0152219500478522 0.0304439000957045 0.984778049952148 22 0.0152008144150634 0.0304016288301268 0.984799185584937 23 0.0202130682479649 0.0404261364959298 0.979786931752035 24 0.0182038671308683 0.0364077342617366 0.981796132869132 25 0.0189097068135910 0.0378194136271820 0.98109029318641 26 0.0235094117128963 0.0470188234257925 0.976490588287104 27 0.0319614267400515 0.063922853480103 0.968038573259949 28 0.0434341373215162 0.0868682746430323 0.956565862678484 29 0.0529997127830285 0.105999425566057 0.947000287216971 30 0.0627488165471811 0.125497633094362 0.937251183452819 31 0.0754531112868472 0.150906222573694 0.924546888713153 32 0.127669730799682 0.255339461599364 0.872330269200318 33 0.173496291189407 0.346992582378813 0.826503708810593 34 0.237250109348874 0.474500218697749 0.762749890651126 35 0.36119682889689 0.72239365779378 0.63880317110311 36 0.448758499524152 0.897516999048304 0.551241500475848 37 0.514334783370788 0.971330433258423 0.485665216629212 38 0.598267072231332 0.803465855537335 0.401732927768668 39 0.637380567577753 0.725238864844494 0.362619432422247 40 0.655779559163065 0.688440881673871 0.344220440836935 41 0.674128238657755 0.651743522684489 0.325871761342245 42 0.655203549636609 0.689592900726783 0.344796450363391 43 0.633737060952578 0.732525878094844 0.366262939047422 44 0.643163006680332 0.713673986639335 0.356836993319668 45 0.677739293265436 0.644521413469127 0.322260706734564 46 0.893950680187967 0.212098639624065 0.106049319812033 47 0.914772726571678 0.170454546856644 0.0852272734283222 48 0.874339202618679 0.251321594762643 0.125660797381321 49 0.845645960231083 0.308708079537834 0.154354039768917 50 0.817232042428698 0.365535915142604 0.182767957571302 51 0.737339461700033 0.525321076599933 0.262660538299967 52 0.876932348186234 0.246135303627533 0.123067651813766 53 0.957134844709529 0.0857303105809427 0.0428651552904713 54 0.9027064609065 0.194587078186999 0.0972935390934994 55 0.819381671558883 0.361236656882234 0.180618328441117 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 10 0.196078431372549 NOK 10% type I error level 15 0.294117647058824 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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