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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: Thu, 19 Nov 2009 11:19:09 -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/19/t1258654987gd7mvq5uzweomyq.htm/, Retrieved Thu, 19 Nov 2009 19:23:19 +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/19/t1258654987gd7mvq5uzweomyq.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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8.9 1.4 8.8 1.2 8.3 1 7.5 1.7 7.2 2.4 7.4 2 8.8 2.1 9.3 2 9.3 1.8 8.7 2.7 8.2 2.3 8.3 1.9 8.5 2 8.6 2.3 8.5 2.8 8.2 2.4 8.1 2.3 7.9 2.7 8.6 2.7 8.7 2.9 8.7 3 8.5 2.2 8.4 2.3 8.5 2.8 8.7 2.8 8.7 2.8 8.6 2.2 8.5 2.6 8.3 2.8 8 2.5 8.2 2.4 8.1 2.3 8.1 1.9 8 1.7 7.9 2 7.9 2.1 8 1.7 8 1.8 7.9 1.8 8 1.8 7.7 1.3 7.2 1.3 7.5 1.3 7.3 1.2 7 1.4 7 2.2 7 2.9 7.2 3.1 7.3 3.5 7.1 3.6 6.8 4.4 6.4 4.1 6.1 5.1 6.5 5.8 7.7 5.9 7.9 5.4 7.5 5.5 6.9 4.8 6.6 3.2 6.9 2.7

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 Y[t] = + 8.89484092155787 + 0.000137136588041943X[t] + 0.173170369354539M1[t] + 0.164695099652587M2[t] -0.0237856555128910M3[t] -0.292263667946609M4[t] -0.500766364966173M5[t] -0.54924437739989M6[t] + 0.242285838361675M7[t] + 0.373835253245565M8[t] + 0.265373697202413M9[t] -0.00309334430426069M10[t] -0.171535701225087M11[t] -0.031532958493326t + 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) 8.89484092155787 0.255544 34.8074 0 0 X 0.000137136588041943 0.063784 0.0022 0.998294 0.499147 M1 0.173170369354539 0.297778 0.5815 0.563715 0.281857 M2 0.164695099652587 0.297391 0.5538 0.582398 0.291199 M3 -0.0237856555128910 0.297183 -0.08 0.936555 0.468278 M4 -0.292263667946609 0.296986 -0.9841 0.330214 0.165107 M5 -0.500766364966173 0.297925 -1.6808 0.099571 0.049786 M6 -0.54924437739989 0.297965 -1.8433 0.07173 0.035865 M7 0.242285838361675 0.297596 0.8141 0.419758 0.209879 M8 0.373835253245565 0.29639 1.2613 0.213562 0.106781 M9 0.265373697202413 0.295865 0.8969 0.37442 0.18721 M10 -0.00309334430426069 0.295605 -0.0105 0.991696 0.495848 M11 -0.171535701225087 0.295041 -0.5814 0.563812 0.281906 t -0.031532958493326 0.004289 -7.3519 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.832460976610311 R-squared 0.692991277578994 Adjusted R-squared 0.606227942981753 F-TEST (value) 7.98714434842653 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 5.19511160756991e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.466431076529146 Sum Squared Residuals 10.0076656609984 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.9 9.03667032364237 -0.136670323642367 2 8.8 8.99663466812946 -0.196634668129456 3 8.3 8.77659352715304 -0.476593527153044 4 7.5 8.47667855183763 -0.97667855183763 5 7.2 8.23673889193637 -1.03673889193637 6 7.4 8.1566730663741 -0.756673066374107 7 8.8 8.91668403730115 -0.116684037301150 8 9.3 9.01668678003291 0.283313219967088 9 9.3 8.87666483817883 0.423335161821176 10 8.7 8.57678826110806 0.123211738891937 11 8.2 8.3767580910587 -0.176758091058695 12 8.3 8.51670597915524 -0.216705979155237 13 8.5 8.65835710367526 -0.158357103675255 14 8.6 8.61839001645639 -0.0183900164563883 15 8.5 8.3984448710916 0.101555128908393 16 8.2 8.09837904552935 0.101620954470652 17 8.1 7.85832967635765 0.241670323642348 18 7.9 7.77837356006583 0.121626439934175 19 8.6 8.53837081733406 0.0616291826659352 20 8.7 8.63841470104224 0.0615852989577617 21 8.7 8.49843390016456 0.201566099835436 22 8.5 8.19832419089413 0.30167580910587 23 8.4 7.99836258913878 0.401637410861218 24 8.5 8.13843390016456 0.361566099835436 25 8.7 8.28007131102578 0.419928688974223 26 8.7 8.2400630828305 0.4599369171695 27 8.6 8.01996708721887 0.580032912781129 28 8.5 7.72001097092704 0.779989029072957 29 8.3 7.48000274273176 0.81999725726824 30 8 7.3999506308283 0.600049369171695 31 8.2 8.15993417443774 0.0400658255622591 32 8.1 8.2599369171695 -0.159936917169501 33 8.1 8.1198875479978 -0.0198875479978061 34 8 7.8198601206802 0.180139879319803 35 7.9 7.61992594624246 0.280074053757543 36 7.9 7.75994240263302 0.140057597366978 37 8 7.90152495885902 0.0984750411409812 38 8 7.86153044432255 0.138469555677454 39 7.9 7.64151673066374 0.258483269336259 40 8 7.3415057597367 0.658494240263302 41 7.7 7.10140153592979 0.598598464070213 42 7.2 7.02139056500274 0.178609434997257 43 7.5 7.78138782227098 -0.281387822270982 44 7.3 7.88139056500274 -0.581390565002743 45 7 7.74142347778387 -0.741423477783873 46 7 7.44153318705431 -0.441533187054307 47 7 7.24165386725178 -0.241653867251783 48 7.2 7.38168403730115 -0.181684037301152 49 7.3 7.52337630279758 -0.223376302797582 50 7.1 7.48338178826111 -0.383381788261109 51 6.8 7.26347778387274 -0.463477783872738 52 6.4 6.96342567196928 -0.563425671969282 53 6.1 6.72352715304443 -0.623527153044434 54 6.5 6.64361217772902 -0.143612177729019 55 7.7 7.40362314865606 0.296376851343938 56 7.9 7.5035710367526 0.396428963247394 57 7.5 7.36359023587493 0.136409764125068 58 6.9 7.0634942402633 -0.163494240263303 59 6.6 6.86329950630828 -0.263299506308284 60 6.9 7.00323368074602 -0.103233680746024 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.688070133470162 0.623859733059676 0.311929866529838 18 0.572405922469946 0.855188155060108 0.427594077530054 19 0.562495098404988 0.875009803190023 0.437504901595012 20 0.641104269302008 0.717791461395985 0.358895730697992 21 0.607277888991688 0.785444222016623 0.392722111008312 22 0.59650306443683 0.806993871126339 0.403496935563170 23 0.484423181635139 0.968846363270277 0.515576818364861 24 0.398487535553692 0.796975071107385 0.601512464446308 25 0.297267957390287 0.594535914780574 0.702732042609713 26 0.210529815800016 0.421059631600031 0.789470184199984 27 0.145906089205061 0.291812178410122 0.854093910794939 28 0.139210889518738 0.278421779037477 0.860789110481262 29 0.124816748630588 0.249633497261175 0.875183251369412 30 0.0832124738590364 0.166424947718073 0.916787526140964 31 0.135522197618633 0.271044395237266 0.864477802381367 32 0.260700427397851 0.521400854795701 0.73929957260215 33 0.276333078225325 0.55266615645065 0.723666921774675 34 0.209755043877191 0.419510087754383 0.790244956122809 35 0.146045670086540 0.292091340173081 0.85395432991346 36 0.100267645005011 0.200535290010023 0.899732354994989 37 0.0662616551663278 0.132523310332656 0.933738344833672 38 0.0437303559548941 0.0874607119097882 0.956269644045106 39 0.0336901280726572 0.0673802561453143 0.966309871927343 40 0.0824418524866806 0.164883704973361 0.91755814751332 41 0.54053215349516 0.91893569300968 0.45946784650484 42 0.944440499604316 0.111119000791368 0.0555595003956839 43 0.934142539843172 0.131714920313657 0.0658574601568284 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 2 0.0740740740740741 OK

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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