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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 18 Dec 2009 04:10:49 -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/18/t1261134680e0lqkj9x1bcj0mz.htm/, Retrieved Fri, 18 Dec 2009 12:11:32 +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/18/t1261134680e0lqkj9x1bcj0mz.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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8.1 92.9 7.7 107.7 7.5 103.5 7.6 91.1 7.8 79.8 7.8 71.9 7.8 82.9 7.5 90.1 7.5 100.7 7.1 90.7 7.5 108.8 7.5 44.1 7.6 93.6 7.7 107.4 7.7 96.5 7.9 93.6 8.1 76.5 8.2 76.7 8.2 84 8.2 103.3 7.9 88.5 7.3 99 6.9 105.9 6.6 44.7 6.7 94 6.9 107.1 7 104.8 7.1 102.5 7.2 77.7 7.1 85.2 6.9 91.3 7 106.5 6.8 92.4 6.4 97.5 6.7 107 6.6 51.1 6.4 98.6 6.3 102.2 6.2 114.3 6.5 99.4 6.8 72.5 6.8 92.3 6.4 99.4 6.1 85.9 5.8 109.4 6.1 97.6 7.2 104.7 7.3 56.9 6.9 86.7 6.1 108.5 5.8 103.4 6.2 86.2 7.1 71 7.7 75.9 7.9 87.1 7.7 102 7.4 88.5 7.5 87.8 8 100.8 8.1 50.6 8 85.9

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 Werkloosheidsgraad[t] = + 9.269949293332 -0.0310552406551667Bruto_index[t] + 1.31095273927571M1[t] + 1.35066091204492M2[t] + 1.20032534441868M3[t] + 1.12589558524283M4[t] + 0.888242031291867M5[t] + 1.17467204343869M6[t] + 1.37414313157033M7[t] + 1.51609863895437M8[t] + 1.25880627240331M9[t] + 1.03020937323569M10[t] + 1.76359193412662M11[t] -0.0142593329365101t + 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) 9.269949293332 0.771489 12.0157 0 0 Bruto_index -0.0310552406551667 0.014272 -2.176 0.034615 0.017307 M1 1.31095273927571 0.713043 1.8385 0.072307 0.036154 M2 1.35066091204492 0.905939 1.4909 0.14267 0.071335 M3 1.20032534441868 0.878948 1.3656 0.178553 0.089276 M4 1.12589558524283 0.754345 1.4925 0.142239 0.071119 M5 0.888242031291867 0.54041 1.6436 0.106924 0.053462 M6 1.17467204343869 0.590435 1.9895 0.052483 0.026241 M7 1.37414313157033 0.686184 2.0026 0.051009 0.025505 M8 1.51609863895437 0.790151 1.9187 0.061101 0.030551 M9 1.25880627240331 0.769445 1.636 0.108521 0.054261 M10 1.03020937323569 0.752364 1.3693 0.177414 0.088707 M11 1.76359193412662 0.889103 1.9836 0.053163 0.026582 t -0.0142593329365101 0.004558 -3.1284 0.003016 0.001508 Multiple Linear Regression - Regression Statistics Multiple R 0.566302299484839 R-squared 0.320698294401816 Adjusted R-squared 0.132806333278914 F-TEST (value) 1.70682285971801 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0.0907637807319794 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.617352823253533 Sum Squared Residuals 17.9128518938181 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.1 7.68161084280623 0.418389157193768 2 7.7 7.24744212094245 0.452557879057546 3 7.5 7.21327923113141 0.286720768868591 4 7.6 7.50967512314312 0.0903248768568812 5 7.8 7.60868645565902 0.191313544340977 6 7.8 8.12619353604516 -0.326193536045158 7 7.8 7.96979764403345 -0.169797644033449 8 7.5 7.87389608576378 -0.373896085763784 9 7.5 7.27315883533144 0.226841164668557 10 7.1 7.34085500977898 -0.240855009778979 11 7.5 7.49787838187488 0.00212161812511804 12 7.5 7.72930118520104 -0.229301185201038 13 7.6 7.48876017910949 0.111239820890511 14 7.7 7.08564669790088 0.614353302099116 15 7.7 7.25955392047945 0.440446079520546 16 7.9 7.26092502626708 0.63907497373292 17 8.1 7.54005675458295 0.559943245417045 18 8.2 7.80601638566224 0.393983614337762 19 8.2 7.76452488407464 0.435475115925355 20 8.2 7.29285491387746 0.907145086122535 21 7.9 7.48092077608635 0.419079223913646 22 7.3 6.91198451710297 0.388015482897026 23 6.9 7.41682658453674 -0.516826584536744 24 6.6 7.53955604556982 -0.939556045569818 25 6.7 7.3052260876093 -0.605226087609301 26 6.9 6.92385127485931 -0.0238512748593132 27 7 6.83068342780345 0.16931657219655 28 7.1 6.81342138919798 0.286578610802023 29 7.2 7.33167847055863 -0.131678470558633 30 7.1 7.3709348448552 -0.2709348448552 31 6.9 7.3667096320538 -0.466709632053806 32 7 7.02236614854281 -0.0223661485428098 33 6.8 7.18869334229308 -0.388693342293083 34 6.4 6.7874553828476 -0.387455382847603 35 6.7 7.21155382457794 -0.51155382457794 36 6.6 7.16969051013863 -0.56969051013863 37 6.4 6.99125998535741 -0.591259985357413 38 6.3 6.90490995883151 -0.60490995883151 39 6.2 6.36454664634125 -0.164546646341246 40 6.5 6.73858063999087 -0.238580639990872 41 6.8 7.32205372672738 -0.52205372672738 42 6.8 6.9793306409654 -0.179330640965396 43 6.4 6.94405018750884 -0.544050187508835 44 6.1 7.49099211080112 -1.39099211080112 45 5.8 6.48964225591713 -0.689642255917129 46 6.1 6.61323786354397 -0.513237863543966 47 7.2 7.1118688828467 0.0881311171532975 48 7.3 6.81845811910054 0.481541880899457 49 6.9 7.18970535391578 -0.289705353915776 50 6.1 6.53814994746584 -0.438149947465839 51 5.8 6.53193677424444 -0.731936774244441 52 6.2 6.97739782140095 -0.777397821400951 53 7.1 7.19752459247201 -0.0975245924720088 54 7.7 7.31752459247201 0.382475407527992 55 7.9 7.15491765232927 0.745082347670735 56 7.7 6.81989074101482 0.880109258985182 57 7.4 6.96758479037199 0.432415209628008 58 7.5 6.74646722672648 0.753532773273522 59 8 7.06187232616373 0.938127673836268 60 8.1 6.84299413998997 1.25700586001003 61 8 7.04343755120179 0.956562448798212 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0709288898627885 0.141857779725577 0.929071110137212 18 0.0382294835709125 0.076458967141825 0.961770516429088 19 0.0173607608128697 0.0347215216257393 0.98263923918713 20 0.0103748207961262 0.0207496415922524 0.989625179203874 21 0.00949292849061106 0.0189858569812221 0.990507071509389 22 0.00482768840532423 0.00965537681064846 0.995172311594676 23 0.0109955389716141 0.0219910779432281 0.989004461028386 24 0.0362883689485373 0.0725767378970745 0.963711631051463 25 0.106858897688785 0.213717795377569 0.893141102311215 26 0.115936918803268 0.231873837606535 0.884063081196732 27 0.136395972389791 0.272791944779582 0.86360402761021 28 0.182011576805928 0.364023153611856 0.817988423194072 29 0.184128255881976 0.368256511763952 0.815871744118024 30 0.166284327463767 0.332568654927533 0.833715672536233 31 0.156458220277214 0.312916440554427 0.843541779722786 32 0.177120868678232 0.354241737356465 0.822879131321768 33 0.230626402237039 0.461252804474077 0.769373597762961 34 0.211609078482184 0.423218156964367 0.788390921517816 35 0.149096160842321 0.298192321684642 0.850903839157679 36 0.0981325870973486 0.196265174194697 0.901867412902651 37 0.0650612522995597 0.130122504599119 0.93493874770044 38 0.092943626318501 0.185887252637002 0.907056373681499 39 0.205841100142562 0.411682200285124 0.794158899857438 40 0.557627917987896 0.884744164024208 0.442372082012104 41 0.76304621629302 0.47390756741396 0.23695378370698 42 0.698575404005471 0.602849191989058 0.301424595994529 43 0.600515540173493 0.798968919653014 0.399484459826507 44 0.85285583237471 0.294288335250578 0.147144167625289 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0357142857142857 NOK 5% type I error level 5 0.178571428571429 NOK 10% type I error level 7 0.25 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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