*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 09:17:24 -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/t1258734039ovbrseggxn03obv.htm/, Retrieved Fri, 20 Nov 2009 17:20:51 +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/t1258734039ovbrseggxn03obv.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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111.4 0 87.4 0 96.8 0 114.1 0 110.3 0 103.9 0 101.6 0 94.6 0 95.9 0 104.7 0 102.8 0 98.1 0 113.9 0 80.9 0 95.7 0 113.2 0 105.9 0 108.8 0 102.3 0 99 0 100.7 0 115.5 0 100.7 0 109.9 0 114.6 0 85.4 0 100.5 0 114.8 0 116.5 0 112.9 0 102 0 106 0 105.3 0 118.8 0 106.1 0 109.3 0 117.2 0 92.5 0 104.2 0 112.5 0 122.4 0 113.3 0 100 0 110.7 0 112.8 0 109.8 0 117.3 0 109.1 0 115.9 0 96 0 99.8 0 116.8 1 115.7 1 99.4 1 94.3 1 91 1 93.2 1 103.1 1 94.1 1 91.8 1 102.7 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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 105.760784313725 -5.55078431372549X[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) 105.760784313725 1.274012 83.0139 0 0 X -5.55078431372549 3.146578 -1.7641 0.082897 0.041448 Multiple Linear Regression - Regression Statistics Multiple R 0.223835121573278 R-squared 0.0501021616497242 Adjusted R-squared 0.0340021982878552 F-TEST (value) 3.11194258791827 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.082896958868956 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.09826819862025 Sum Squared Residuals 4883.93056862745 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 111.4 105.760784313726 5.63921568627445 2 87.4 105.760784313725 -18.3607843137255 3 96.8 105.760784313725 -8.9607843137255 4 114.1 105.760784313725 8.3392156862745 5 110.3 105.760784313725 4.53921568627451 6 103.9 105.760784313725 -1.86078431372548 7 101.6 105.760784313725 -4.16078431372549 8 94.6 105.760784313725 -11.1607843137255 9 95.9 105.760784313725 -9.86078431372549 10 104.7 105.760784313725 -1.06078431372549 11 102.8 105.760784313725 -2.96078431372549 12 98.1 105.760784313725 -7.6607843137255 13 113.9 105.760784313725 8.13921568627451 14 80.9 105.760784313725 -24.8607843137255 15 95.7 105.760784313725 -10.0607843137255 16 113.2 105.760784313725 7.43921568627451 17 105.9 105.760784313725 0.139215686274516 18 108.8 105.760784313725 3.03921568627451 19 102.3 105.760784313725 -3.46078431372549 20 99 105.760784313725 -6.76078431372549 21 100.7 105.760784313725 -5.06078431372549 22 115.5 105.760784313725 9.7392156862745 23 100.7 105.760784313725 -5.06078431372549 24 109.9 105.760784313725 4.13921568627452 25 114.6 105.760784313725 8.8392156862745 26 85.4 105.760784313725 -20.3607843137255 27 100.5 105.760784313725 -5.26078431372549 28 114.8 105.760784313725 9.0392156862745 29 116.5 105.760784313725 10.7392156862745 30 112.9 105.760784313725 7.13921568627452 31 102 105.760784313725 -3.76078431372549 32 106 105.760784313725 0.239215686274511 33 105.3 105.760784313725 -0.460784313725492 34 118.8 105.760784313725 13.0392156862745 35 106.1 105.760784313725 0.339215686274505 36 109.3 105.760784313725 3.53921568627451 37 117.2 105.760784313725 11.4392156862745 38 92.5 105.760784313725 -13.2607843137255 39 104.2 105.760784313725 -1.56078431372549 40 112.5 105.760784313725 6.73921568627451 41 122.4 105.760784313725 16.6392156862745 42 113.3 105.760784313725 7.5392156862745 43 100 105.760784313725 -5.76078431372549 44 110.7 105.760784313725 4.93921568627451 45 112.8 105.760784313725 7.0392156862745 46 109.8 105.760784313725 4.03921568627451 47 117.3 105.760784313725 11.5392156862745 48 109.1 105.760784313725 3.33921568627451 49 115.9 105.760784313725 10.1392156862745 50 96 105.760784313725 -9.7607843137255 51 99.8 105.760784313725 -5.96078431372549 52 116.8 100.21 16.59 53 115.7 100.21 15.49 54 99.4 100.21 -0.809999999999993 55 94.3 100.21 -5.91 56 91 100.21 -9.21 57 93.2 100.21 -7.01 58 103.1 100.21 2.89000000000000 59 94.1 100.21 -6.11 60 91.8 100.21 -8.41 61 102.7 100.21 2.49000000000000 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.897985916817082 0.204028166365837 0.102014083182919 6 0.812032224770843 0.375935550458315 0.187967775229157 7 0.71046956695774 0.579060866084521 0.289530433042260 8 0.688308414583284 0.623383170833433 0.311691585416716 9 0.635145011639991 0.729709976720017 0.364854988360008 10 0.532774340528160 0.934451318943681 0.467225659471840 11 0.426787178947596 0.853574357895192 0.573212821052404 12 0.355354847599449 0.710709695198897 0.644645152400551 13 0.406374785845953 0.812749571691906 0.593625214154047 14 0.814679088304675 0.370641823390649 0.185320911695325 15 0.795905674279264 0.408188651441473 0.204094325720736 16 0.812210626987503 0.375578746024993 0.187789373012497 17 0.759283173630326 0.481433652739348 0.240716826369674 18 0.715894415357842 0.568211169284315 0.284105584642158 19 0.650561080785194 0.698877838429611 0.349438919214806 20 0.604508008339214 0.790983983321571 0.395491991660786 21 0.545381748384415 0.90923650323117 0.454618251615585 22 0.59440575504533 0.81118848990934 0.40559424495467 23 0.539226515043885 0.921546969912229 0.460773484956115 24 0.493320361954427 0.986640723908854 0.506679638045573 25 0.507592019411658 0.984815961176684 0.492407980588342 26 0.788881036464537 0.422237927070926 0.211118963535463 27 0.760886549579255 0.47822690084149 0.239113450420745 28 0.76683473940439 0.466330521191219 0.233165260595609 29 0.789687788514404 0.420624422971193 0.210312211485596 30 0.766737921126365 0.466524157747269 0.233262078873635 31 0.726253378622552 0.547493242754896 0.273746621377448 32 0.665815099453407 0.668369801093186 0.334184900546593 33 0.602658233856291 0.794683532287419 0.397341766143709 34 0.659565906503109 0.680868186993783 0.340434093496891 35 0.591789663760477 0.816420672479046 0.408210336239523 36 0.524341186979242 0.951317626041516 0.475658813020758 37 0.544376131919863 0.911247736160274 0.455623868080137 38 0.674717801637967 0.650564396724066 0.325282198362033 39 0.619589557635581 0.760820884728837 0.380410442364419 40 0.564942966298566 0.87011406740287 0.435057033701434 41 0.688510570894359 0.622978858211282 0.311489429105641 42 0.645858148712254 0.708283702575492 0.354141851287746 43 0.623056804190788 0.753886391618424 0.376943195809212 44 0.548872788269006 0.902254423461988 0.451127211730994 45 0.490039785805799 0.980079571611598 0.509960214194201 46 0.408688850683805 0.817377701367609 0.591311149316196 47 0.440487810966049 0.880975621932098 0.559512189033951 48 0.367041712276813 0.734083424553626 0.632958287723187 49 0.480290669037475 0.960581338074949 0.519709330962525 50 0.404672681818399 0.809345363636798 0.595327318181601 51 0.31135091002244 0.62270182004488 0.68864908997756 52 0.52993364509276 0.94013270981448 0.47006635490724 53 0.91192361667177 0.176152766656460 0.0880763833282299 54 0.866836544616279 0.266326910767443 0.133163455383721 55 0.776845441772916 0.446309116454169 0.223154558227084 56 0.71003141398658 0.579937172026841 0.289968586013421 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 0 0 OK 10% type I error level 0 0 OK

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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