*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: Fri, 18 Dec 2009 04:17:42 -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/t1261135094gkw7kmpol416ssd.htm/, Retrieved Fri, 18 Dec 2009 12:18:27 +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/t1261135094gkw7kmpol416ssd.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkloosheidsgraad[t] = + 8.81968142713807 -0.032329859077164Bruto_index[t] + 1.43638244834049M1[t] + 1.56603495330607M2[t] + 1.39878884642556M3[t] + 1.29743004719855M4[t] + 1.02122293318781M5[t] + 1.29963924266591M6[t] + 1.49573623918489M7[t] + 1.63441962443005M8[t] + 1.36075205836195M9[t] + 1.11613685283547M10[t] + 1.8491789139581M11[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) 8.81968142713807 0.824406 10.6982 0 0 Bruto_index -0.032329859077164 0.015517 -2.0835 0.04255 0.021275 M1 1.43638244834049 0.77434 1.855 0.069747 0.034874 M2 1.56603495330607 0.982529 1.5939 0.117527 0.058763 M3 1.39878884642556 0.953527 1.467 0.148908 0.074454 M4 1.29743004719855 0.818321 1.5855 0.119425 0.059712 M5 1.02122293318781 0.585976 1.7428 0.087777 0.043889 M6 1.29963924266591 0.640737 2.0284 0.048093 0.024046 M7 1.49573623918489 0.745156 2.0073 0.050368 0.025184 M8 1.63441962443005 0.858452 1.9039 0.062925 0.031463 M9 1.36075205836195 0.836164 1.6274 0.110205 0.055103 M10 1.11613685283547 0.817791 1.3648 0.178674 0.089337 M11 1.8491789139581 0.966608 1.9131 0.061716 0.030858 Multiple Linear Regression - Regression Statistics Multiple R 0.423372626977428 R-squared 0.179244381273768 Adjusted R-squared -0.0259445234077893 F-TEST (value) 0.873557863920304 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.578201528447169 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.671486566251615 Sum Squared Residuals 21.6429220155064 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.1 7.25261996721003 0.847380032789968 2 7.7 6.90379055783358 0.796209442166424 3 7.5 6.87232985907716 0.627670140922835 4 7.6 7.17186131240699 0.428138687593012 5 7.8 7.26098160596819 0.539018394031807 6 7.8 7.7948038021559 0.00519619784410598 7 7.8 7.63527234882607 0.164727651173929 8 7.5 7.54118074871564 -0.0411807487156427 9 7.5 6.92481667642961 0.575183323570387 10 7.1 7.00350006167477 0.0964999383252329 11 7.5 7.15137167350073 0.348628326499271 12 7.5 7.39393464183514 0.106065358164858 13 7.6 7.22998906585601 0.370010934143988 14 7.7 6.91348951555673 0.786510484443275 15 7.7 7.09863887261731 0.601361127382688 16 7.9 7.09103666471408 0.808963335285923 17 8.1 7.36767014092284 0.732329859077163 18 8.2 7.63962047858551 0.560379521414493 19 8.2 7.59970950384119 0.600290496158809 20 8.2 7.11442660889708 1.08557339110292 21 7.9 7.31924095717101 0.580759042828986 22 7.3 6.7351622313343 0.564837768665695 23 6.9 7.2451282648245 -0.345128264824504 24 6.6 7.37453672638884 -0.774536726388844 25 6.7 7.21705712222515 -0.517057122225146 26 6.9 6.92318847327987 -0.0231884732798745 27 7 6.83030104227685 0.169698957723149 28 7.1 6.80330091892732 0.296699081072682 29 7.2 7.32887431003024 -0.128874310030239 30 7.1 7.36481667642961 -0.264816676429613 31 6.9 7.3637015325779 -0.463701532577892 32 7 7.01097105985015 -0.0109710598501535 33 6.8 7.19315450677007 -0.393154506770074 34 6.4 6.78365701995005 -0.383657019950051 35 6.7 7.20956541983962 -0.509565419839624 36 6.6 7.16762562829499 -0.567625628294995 37 6.4 7.06833977047019 -0.668339770470192 38 6.3 7.08160478275798 -0.781604782757979 39 6.2 6.52316738104379 -0.323167381043793 40 6.5 6.90352348206653 -0.403523482066526 41 6.8 7.49698957723149 -0.696989577231493 42 6.8 7.13527467698175 -0.335274676981749 43 6.4 7.10182967405286 -0.701829674052864 44 6.1 7.67696615683973 -1.57696615683973 45 5.8 6.64354690245829 -0.843546902458286 46 6.1 6.78042403404233 -0.680424034042335 47 7.2 7.2839240957171 -0.0839240957171013 48 7.3 6.98011244564744 0.319887554352557 49 6.9 7.45306509348844 -0.553065093488443 50 6.1 6.87792667057185 -0.777926670571846 51 5.8 6.87556284498488 -1.07556284498488 52 6.2 7.33027762188509 -1.13027762188509 53 7.1 7.54548436584724 -0.445484365847238 54 7.7 7.66548436584724 0.0345156341527624 55 7.9 7.49948694070198 0.400513059298018 56 7.7 7.15645542569739 0.543544574302608 57 7.4 7.31924095717101 0.0807590428289866 58 7.5 7.09725665299854 0.402743347001458 59 8 7.41001054611804 0.589989453881958 60 8.1 7.18379055783358 0.916209442166424 61 8 7.47892898075017 0.521071019249825 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0591394414005024 0.118278882801005 0.940860558599498 17 0.0240875655033081 0.0481751310066162 0.975912434496692 18 0.0191193558498127 0.0382387116996254 0.980880644150187 19 0.0124773258092974 0.0249546516185948 0.987522674190703 20 0.0100210132195465 0.0200420264390930 0.989978986780454 21 0.0167358843605584 0.0334717687211168 0.983264115639442 22 0.00821571314144245 0.0164314262828849 0.991784286858558 23 0.00748459527841556 0.0149691905568311 0.992515404721585 24 0.0207217802391430 0.0414435604782861 0.979278219760857 25 0.0779731433137553 0.155946286627511 0.922026856686245 26 0.0979998927328926 0.195999785465785 0.902000107267107 27 0.105767416657562 0.211534833315124 0.894232583342438 28 0.124432410375279 0.248864820750559 0.87556758962472 29 0.126675692349951 0.253351384699902 0.873324307650049 30 0.115908474334584 0.231816948669167 0.884091525665416 31 0.121137073832096 0.242274147664191 0.878862926167904 32 0.101009505109382 0.202019010218765 0.898990494890618 33 0.106029065190479 0.212058130380958 0.893970934809521 34 0.0867130601297637 0.173426120259527 0.913286939870236 35 0.0752247549838616 0.150449509967723 0.924775245016138 36 0.0870795677156309 0.174159135431262 0.912920432284369 37 0.0884621083808797 0.176924216761759 0.91153789161912 38 0.112724352160978 0.225448704321955 0.887275647839022 39 0.101906720200415 0.203813440400829 0.898093279799585 40 0.104381930921923 0.208763861843847 0.895618069078077 41 0.0929939903021904 0.185987980604381 0.90700600969781 42 0.0536741971203214 0.107348394240643 0.946325802879679 43 0.0455758288085948 0.0911516576171896 0.954424171191405 44 0.74315714778325 0.5136857044335 0.25684285221675 45 0.753700561600871 0.492598876798257 0.246299438399129 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 8 0.266666666666667 NOK 10% type I error level 9 0.3 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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