Ws 7.3

*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, 20 Nov 2009 08:45:46 -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/Nov/20/t1258731993ldv87z1sirhuqny.htm/, Retrieved Fri, 20 Nov 2009 16:46:45 +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/Nov/20/t1258731993ldv87z1sirhuqny.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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100 100 96,21064363 97,82226485 96,31280765 94,04971502 107,1793443 91,12460521 114,9066592 93,13202153 92,56060184 93,88342812 114,9995356 92,55349954 107,1236185 94,43494835 117,7765394 96,25017563 107,3650971 100,4355715 106,2970187 101,5036685 114,5072908 99,39789728 98,0031578 99,68990733 103,0649206 101,6895041 100,2879168 103,6652759 104,6066685 103,0532766 111,1544534 100,9500712 104,9874617 102,345366 109,9284852 101,6472299 111,5352466 99,56809393 132,4974459 95,67727392 100,3436426 96,58494865 123,0983561 96,32604937 114,2379493 95,37109101 104,569518 96,00056203 109,0833101 96,88367859 106,9843039 94,85280372 133,6769759 92,46943974 124,8537197 93,99180173 122,5132349 93,45262168 116,8013374 92,26698759 116,0118882 90,39653498 129,7575926 90,43001228 125,1973623 91,04995327 143,7912139 89,07845784 127,9465032 89,69314509 130,2962757 87,92459054 108,4424631 85,8789319 129,3675118 83,20612366 143,6797622 83,85722053 131,8844618 83,01393462 117,6186496 82,8450 etc...

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 Import[t] = + 159.23583988678 -0.527705277557674Wisselkoers[t] -1.42952943199583M1[t] -9.62959659104806M2[t] -1.74482004101209M3[t] + 4.7166932453793M4[t] + 2.2752518187206M5[t] -4.09312791143662M6[t] -8.21383428477751M7[t] -12.0086173119050M8[t] + 4.34543457019099M9[t] -8.35340229011195M10[t] -1.39536111330011M11[t] + 0.355466572662176t + 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) 159.23583988678 33.816236 4.7089 2.3e-05 1.2e-05 Wisselkoers -0.527705277557674 0.333419 -1.5827 0.12034 0.06017 M1 -1.42952943199583 8.631223 -0.1656 0.869179 0.43459 M2 -9.62959659104806 8.641211 -1.1144 0.270905 0.135452 M3 -1.74482004101209 8.624537 -0.2023 0.840567 0.420284 M4 4.7166932453793 8.5931 0.5489 0.585733 0.292867 M5 2.2752518187206 8.586352 0.265 0.792205 0.396103 M6 -4.09312791143662 8.597037 -0.4761 0.63625 0.318125 M7 -8.21383428477751 8.569283 -0.9585 0.342811 0.171406 M8 -12.0086173119050 8.564508 -1.4021 0.167587 0.083793 M9 4.34543457019099 8.56554 0.5073 0.614357 0.307178 M10 -8.35340229011195 8.55609 -0.9763 0.334017 0.167009 M11 -1.39536111330011 8.555046 -0.1631 0.871151 0.435576 t 0.355466572662176 0.131429 2.7046 0.009555 0.004777 Multiple Linear Regression - Regression Statistics Multiple R 0.660933492374028 R-squared 0.436833081341729 Adjusted R-squared 0.277677213025261 F-TEST (value) 2.74468724252834 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.00585073172241857 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13.5244071167880 Sum Squared Residuals 8413.84104158875 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100 105.391249271679 -5.39124927167932 2 96.21064363 98.695851017067 -2.48520738706693 3 96.31280765 108.926888594905 -12.6140809449054 4 107.1793443 117.287464338132 -10.1081200381317 5 114.9066592 114.142165297816 0.764493902184287 6 92.56060184 107.732730917186 -15.1721290771860 7 114.9995356 104.669301446948 10.3302341530519 8 107.1236185 100.237134525991 6.88648397400883 9 117.7765394 115.988747965127 1.78779143487328 10 107.3650971 101.436722188219 5.92837491178112 11 106.2970187 108.186589513849 -1.88957081384937 12 114.5072908 111.048643785935 3.45864701406529 13 98.0031578 109.820485682116 -11.8173278821162 14 103.0649206 100.920687327210 2.14423327279016 15 100.2879168 108.118305243798 -7.83038844379835 16 104.6066685 115.258240363324 -10.6515718633235 17 111.1544534 114.282138098695 -3.12768469869481 18 104.9874617 107.532920511491 -2.54545881149098 19 109.9284852 104.136090815236 5.79239438476421 20 111.5352466 101.793945384899 9.74130121510055 21 132.4974459 120.556670092962 11.9407758070384 22 100.3436426 107.734315059994 -7.39067245999414 23 123.0983561 115.18444532588 7.91391077411996 24 114.2379493 117.439209578262 -3.20126027826215 25 104.569518 116.032971539605 -11.4634535396049 26 109.0833101 107.722345683804 1.36096441619577 27 106.9843039 117.034292193461 -10.0499882934606 28 133.6769759 125.108985803101 8.56799009689892 29 124.8537197 122.219652492628 2.63406720737165 30 122.5132349 116.491267493072 6.02196740692788 31 116.8013374 113.351693058939 3.44964434106131 32 116.0118882 110.899424318192 5.11246388180813 33 129.7575926 127.591276625062 2.16631597493833 34 125.1973623 114.920760205224 10.2766020947764 35 143.7912139 123.274636497789 20.5165774022106 36 127.9465032 124.701090477879 3.24541272212068 37 130.2962757 124.560303188229 5.7359725117707 38 108.4424631 117.795207462249 -9.35274436224869 39 129.3675118 127.445905599094 1.92160620090552 40 143.6797622 133.919298203648 9.76046399635223 41 131.8844618 132.278329774848 -0.393867974848265 42 117.6186496 126.354521062442 -8.73587146244193 43 118.9560695 124.782656158174 -5.82658665817375 44 104.8202842 121.933866189015 -17.1135819890153 45 134.624315 138.132936099242 -3.50862109924163 46 140.401226 125.778862967040 14.6223630329598 47 143.8005015 133.662845477793 10.1376560222074 48 153.4317823 133.243122417698 20.1886598823023 49 153.2924677 130.356409518370 22.9360581816297 50 127.3149438 118.982189739670 8.3327540603297 51 153.5525216 124.979670118741 28.5728514812588 52 136.9276493 134.496411491796 2.43123780820405 53 131.7730101 131.650018536013 0.122991563987134 54 144.3391845 123.907692555809 20.4314919441911 55 107.4208229 121.166509120704 -13.7456862207037 56 113.6249652 118.251632281902 -4.62666708190224 57 124.2221603 136.608422417608 -12.3862621176083 58 102.0618557 125.498523279523 -23.4366675795232 59 96.36853348 133.047106864689 -36.6785733846885 60 111.6838488 135.375308140226 -23.6914593402261 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0210476302330990 0.0420952604661981 0.978952369766901 18 0.0228611839239628 0.0457223678479255 0.977138816076037 19 0.0103557561510918 0.0207115123021836 0.989644243848908 20 0.0031783499544957 0.0063566999089914 0.996821650045504 21 0.00219219527024911 0.00438439054049821 0.99780780472975 22 0.00245921309234862 0.00491842618469725 0.997540786907651 23 0.00193897764818260 0.00387795529636520 0.998061022351817 24 0.000854946923354262 0.00170989384670852 0.999145053076646 25 0.000489220374722175 0.00097844074944435 0.999510779625278 26 0.000168036321892331 0.000336072643784661 0.999831963678108 27 0.000128592126157 0.000257184252314 0.999871407873843 28 0.000658942463577554 0.00131788492715511 0.999341057536422 29 0.000265480168157079 0.000530960336314157 0.999734519831843 30 0.000257099552178888 0.000514199104357777 0.999742900447821 31 0.000148410576408577 0.000296821152817154 0.999851589423591 32 6.57310452964148e-05 0.000131462090592830 0.999934268954704 33 3.1334055849358e-05 6.2668111698716e-05 0.99996866594415 34 1.68022111593111e-05 3.36044223186222e-05 0.99998319778884 35 2.41866322675995e-05 4.8373264535199e-05 0.999975813367732 36 8.37845168406375e-06 1.67569033681275e-05 0.999991621548316 37 4.75287384330502e-05 9.50574768661004e-05 0.999952471261567 38 0.00124820020034400 0.00249640040068799 0.998751799799656 39 0.00186708288373385 0.0037341657674677 0.998132917116266 40 0.00261170328189449 0.00522340656378898 0.997388296718106 41 0.00403366390922693 0.00806732781845385 0.995966336090773 42 0.109207857153101 0.218415714306202 0.890792142846899 43 0.106338076925775 0.212676153851551 0.893661923074225 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 22 0.814814814814815 NOK 5% type I error level 25 0.925925925925926 NOK 10% type I error level 25 0.925925925925926 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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