mr 2

*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: Wed, 15 Dec 2010 15:29:58 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/15/t1292426878a4yzqjia5lwz0zq.htm/, Retrieved Wed, 15 Dec 2010 16:28:08 +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/2010/Dec/15/t1292426878a4yzqjia5lwz0zq.htm/}, year = {2010}, } @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 = {2010}, 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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0,301029996 1,62324929 3 0,255272505 2,79518459 4 -0,15490196 2,255272505 4 0,591064607 1,544068044 1 0 2,593286067 4 0,556302501 1,799340549 1 0,146128036 2,361727836 1 0,176091259 2,049218023 4 -0,15490196 2,44870632 5 0,322219295 1,62324929 1 0,612783857 1,62324929 2 0,079181246 2,079181246 2 -0,301029996 2,170261715 5 0,531478917 1,204119983 2 0,176091259 2,491361694 1 0,531478917 1,447158031 3 -0,096910013 1,832508913 4 -0,096910013 2,526339277 5 0,146128036 1,33243846 4 0,301029996 1,698970004 1 0,278753601 2,426511261 1 0,113943352 1,278753601 3 0,301029996 1,477121255 3 0,748188027 1,079181246 1 0,491361694 2,079181246 1 -0,045757491 2,230448921 4 0,255272505 1,230448921 2 0,278753601 2,06069784 4 -0,045757491 1,491361694 5 0,414973348 1,322219295 3 0,380211242 1,716003344 1 0,079181246 2,214843848 2 -0,045757491 2,352182518 2 -0,301029996 2,352182518 3 -0,22184875 2,178976947 5 0,361727836 1,77815125 2 -0,301029996 2,301029996 3 0,414973348 1,662757832 2 -0,22184 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 13 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation logPS[t] = + 1.06545673391311 -0.298574713073021logTg[t] -0.111840159283892`D_(overall_danger)`[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) 1.06545673391311 0.122677 8.6851 0 0 logTg -0.298574713073021 0.065008 -4.5929 4.9e-05 2.5e-05 `D_(overall_danger)` -0.111840159283892 0.021393 -5.2279 7e-06 3e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.8091255697614 R-squared 0.654684187641711 Adjusted R-squared 0.636018468054776 F-TEST (value) 35.0741467315287 F-TEST (DF numerator) 2 F-TEST (DF denominator) 37 p-value 2.86420842599e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.179536482532290 Sum Squared Residuals 1.19263389672249 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.301029996 0.245275065053701 0.0557549309462992 2 0.255272505 -0.216475340167837 0.471747845167837 3 -0.15490196 -0.0552712443043056 -0.0996307156956944 4 0.591064607 0.492596901426696 0.0984677055733035 5 0 -0.156193546593246 0.156193546593246 6 0.556302501 0.41637898649089 0.139923514509110 7 0.146128036 0.248464363638951 -0.102336327638951 8 0.176091259 0.00625141353625408 0.169839845463746 9 -0.15490196 -0.224865849400442 0.0699638894004423 10 0.322219295 0.468955383621482 -0.146736088621482 11 0.612783857 0.357115224337591 0.255668632662409 12 0.079181246 0.220985471394069 -0.141804225394069 13 -0.301029996 -0.141729331355837 -0.159300664644163 14 0.531478917 0.48225663691561 0.0492222800843903 15 0.176091259 0.209758971682052 -0.0336677126820518 16 0.531478917 0.297851462184291 0.233627454815709 17 -0.096910013 0.0709552738748138 -0.167865286874814 18 -0.096910013 -0.248045087261727 0.151135074261727 19 0.146128036 0.220263665895584 -0.0741356298955844 20 0.301029996 0.446347093165248 -0.145317097165248 21 0.278753601 0.229121671107688 0.049631929892312 22 0.113943352 0.348132766551767 -0.234189414551767 23 0.301029996 0.288905201175748 0.0121247948242516 24 0.748188027 0.631400343750982 0.116787683249018 25 0.491361694 0.332825630677961 0.158536063322039 26 -0.045757491 -0.0478595498340618 0.0021020588340618 27 0.255272505 0.474395481806742 -0.219122976806742 28 0.278753601 0.00282383046934831 0.275929770530652 29 -0.045757491 0.0609730476195062 -0.106730538619506 30 0.414973348 0.335155009437197 0.0798183385628031 31 0.380211242 0.441261368562073 -0.0610501265620728 32 0.079181246 0.18048004892718 -0.10129880292718 33 -0.045757491 0.139474194938100 -0.185231685938100 34 -0.301029996 0.0276340356542080 -0.328664031654208 35 -0.22184875 -0.144331479249601 -0.0775172707503985 36 0.361727836 0.310865416076142 0.050862419923858 37 -0.301029996 0.0429068852333195 -0.343936881233320 38 0.414973348 0.345318972746007 0.0696543752539928 39 -0.22184875 -0.0752598629197156 -0.146588887080284 40 0.819543936 0.611411725135572 0.208132210864428 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.613262205557957 0.773475588884087 0.386737794442043 7 0.82040914462703 0.359181710745939 0.179590855372969 8 0.741655726459793 0.516688547080413 0.258344273540207 9 0.675702959644355 0.64859408071129 0.324297040355645 10 0.640975889672992 0.718048220654017 0.359024110327008 11 0.72127300746158 0.55745398507684 0.27872699253842 12 0.72370845854538 0.552583082909239 0.276291541454620 13 0.769566603229259 0.460866793541482 0.230433396770741 14 0.689597768749304 0.620804462501392 0.310402231250696 15 0.608931051574188 0.782137896851625 0.391068948425812 16 0.641745543610261 0.716508912779477 0.358254456389739 17 0.659351399133851 0.681297201732297 0.340648600866149 18 0.670404465777703 0.659191068444595 0.329595534222297 19 0.596764142497398 0.806471715005203 0.403235857502602 20 0.570959185437868 0.858081629124265 0.429040814562132 21 0.492103637236566 0.984207274473133 0.507896362763434 22 0.580137990143114 0.839724019713772 0.419862009856886 23 0.481395475728744 0.962790951457489 0.518604524271256 24 0.419332196688619 0.838664393377238 0.580667803311381 25 0.452099937442026 0.904199874884052 0.547900062557974 26 0.385296997622968 0.770593995245935 0.614703002377032 27 0.575658273655917 0.848683452688166 0.424341726344083 28 0.956399289943623 0.0872014201127545 0.0436007100563772 29 0.96749667104097 0.0650066579180591 0.0325033289590295 30 0.95840460859462 0.083190782810761 0.0415953914053805 31 0.927970722238634 0.144058555522733 0.0720292777613664 32 0.908566062334129 0.182867875331742 0.091433937665871 33 0.933224511459638 0.133550977080724 0.066775488540362 34 0.875801714774266 0.248396570451467 0.124198285225733 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 3 0.103448275862069 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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Software written by Ed van Stee & Patrick Wessa

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