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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: Sun, 23 Nov 2008 12:02:03 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t1227467159gbcx67lzqyzq0on.htm/, Retrieved Sun, 23 Nov 2008 19:06:16 +0000

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/2008/Nov/23/t1227467159gbcx67lzqyzq0on.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

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User-defined keywords:

Dataseries X:

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16 0 8 0 -10 0 -24 0 -19 0 8 0 24 0 14 0 7 0 9 0 -26 0 19 0 15 0 -1 0 -10 0 -21 0 -14 0 -27 0 26 0 23 0 5 0 19 0 -19 0 24 0 17 0 1 0 -9 0 -16 0 -21 0 -14 0 31 0 27 0 10 0 12 0 -23 0 13 0 26 0 -1 0 4 0 -16 0 -5 0 9 0 23 0 9 0 2 0 10 1 -29 1 17 1 9 1 9 1 -10 1 -23 1 13 1 13 1 -9 1 9 1 5 1 8 1 -18 1 7 1 4 0

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation x[t] = + 16.1343151693667 -2.39911634756995y[t] -1.94516445753562M1[t] -13.0505645557192M2[t] -23.2734904270987M3[t] -36.2964162984782M4[t] -25.5193421698576M5[t] -18.5422680412371M6[t] + 2.63480608738341M7[t] + 0.0118802160039215M8[t] -10.6110456553755M9[t] -4.35414825724105M10[t] -38.9770741286205M11[t] + 0.0229258713794794t + 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) 16.1343151693667 4.993567 3.231 0.002255 0.001128 y -2.39911634756995 4.089544 -0.5866 0.560249 0.280124 M1 -1.94516445753562 5.756622 -0.3379 0.736943 0.368471 M2 -13.0505645557192 6.010267 -2.1714 0.034984 0.017492 M3 -23.2734904270987 6.004305 -3.8761 0.000328 0.000164 M4 -36.2964162984782 5.999982 -6.0494 0 0 M5 -25.5193421698576 5.997302 -4.2551 9.9e-05 4.9e-05 M6 -18.5422680412371 5.996266 -3.0923 0.003337 0.001668 M7 2.63480608738341 5.996877 0.4394 0.662412 0.331206 M8 0.0118802160039215 5.999132 0.002 0.998428 0.499214 M9 -10.6110456553755 6.00303 -1.7676 0.083617 0.041808 M10 -4.35414825724105 5.972073 -0.7291 0.469568 0.234784 M11 -38.9770741286205 5.969594 -6.5293 0 0 t 0.0229258713794794 0.099339 0.2308 0.818484 0.409242 Multiple Linear Regression - Regression Statistics Multiple R 0.857577001083252 R-squared 0.735438312786945 Adjusted R-squared 0.662261675898227 F-TEST (value) 10.0501791836287 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 1.31296329364261e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.4374504900065 Sum Squared Residuals 4186.07717231222 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 16 14.2120765832106 1.78792341678938 2 8 3.12960235640649 4.87039764359351 3 -10 -7.07039764359356 -2.92960235640644 4 -24 -20.0703976435936 -3.92960235640644 5 -19 -9.27039764359358 -9.72960235640642 6 8 -2.27039764359355 10.2703976435935 7 24 18.9296023564065 5.07039764359349 8 14 16.3296023564065 -2.32960235640648 9 7 5.7296023564065 1.27039764359350 10 9 12.0094256259205 -3.00942562592048 11 -26 -22.5905743740795 -3.40942562592051 12 19 16.4094256259205 2.59057437407953 13 15 14.4871870397644 0.512812960235637 14 -1 3.40471281296024 -4.40471281296024 15 -10 -6.79528718703976 -3.20471281296024 16 -21 -19.7952871870398 -1.20471281296025 17 -14 -8.99528718703975 -5.00471281296025 18 -27 -1.99528718703975 -25.0047128129603 19 26 19.2047128129602 6.79528718703977 20 23 16.6047128129602 6.39528718703976 21 5 6.00471281296023 -1.00471281296023 22 19 12.2845360824742 6.71546391752577 23 -19 -22.3154639175258 3.31546391752578 24 24 16.6845360824742 7.31546391752576 25 17 14.7622974963181 2.23770250368189 26 1 3.67982326951399 -2.67982326951399 27 -9 -6.520176730486 -2.479823269514 28 -16 -19.520176730486 3.520176730486 29 -21 -8.720176730486 -12.279823269514 30 -14 -1.720176730486 -12.279823269514 31 31 19.479823269514 11.5201767304860 32 27 16.879823269514 10.120176730486 33 10 6.27982326951399 3.72017673048601 34 12 12.5596465390280 -0.559646539027982 35 -23 -22.0403534609720 -0.95964653902797 36 13 16.959646539028 -3.95964653902798 37 26 15.0374079528719 10.9625920471281 38 -1 3.95493372606774 -4.95493372606774 39 4 -6.24506627393225 10.2450662739322 40 -16 -19.2450662739322 3.24506627393225 41 -5 -8.44506627393225 3.44506627393225 42 9 -1.44506627393225 10.4450662739322 43 23 19.7549337260677 3.24506627393226 44 9 17.1549337260677 -8.15493372606774 45 2 6.55493372606774 -4.55493372606774 46 10 10.4356406480118 -0.435640648011781 47 -29 -24.1643593519882 -4.83564064801177 48 17 14.8356406480118 2.16435935198821 49 9 12.9134020618557 -3.91340206185567 50 9 1.83092783505154 7.16907216494846 51 -10 -8.36907216494845 -1.63092783505155 52 -23 -21.3690721649484 -1.63092783505155 53 13 -10.5690721649484 23.5690721649484 54 13 -3.56907216494844 16.5690721649484 55 -9 17.6309278350515 -26.6309278350515 56 9 15.0309278350515 -6.03092783505154 57 5 4.43092783505154 0.569072164948459 58 8 10.7107511045655 -2.71075110456553 59 -18 -23.8892488954345 5.88924889543447 60 7 15.1107511045655 -8.11075110456554 61 4 15.5876288659794 -11.5876288659794 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0758849313996962 0.151769862799392 0.924115068600304 18 0.746937833124886 0.506124333750228 0.253062166875114 19 0.648715275469716 0.702569449060568 0.351284724530284 20 0.59949137494477 0.80101725011046 0.40050862505523 21 0.475412409797655 0.95082481959531 0.524587590202345 22 0.427647375234184 0.855294750468369 0.572352624765816 23 0.343722022943414 0.687444045886828 0.656277977056586 24 0.267548930336484 0.535097860672968 0.732451069663516 25 0.185573429099363 0.371146858198726 0.814426570900637 26 0.124437083810806 0.248874167621612 0.875562916189194 27 0.0825597608136426 0.165119521627285 0.917440239186357 28 0.0556335026536212 0.111267005307242 0.944366497346379 29 0.0844227445972256 0.168845489194451 0.915577255402774 30 0.203116702674950 0.406233405349901 0.79688329732505 31 0.222872889673234 0.445745779346467 0.777127110326766 32 0.223131369729428 0.446262739458857 0.776868630270572 33 0.158806194647698 0.317612389295397 0.841193805352302 34 0.107532021816061 0.215064043632122 0.892467978183939 35 0.0705144199790839 0.141028839958168 0.929485580020916 36 0.0550787889937179 0.110157577987436 0.944921211006282 37 0.0709877731767223 0.141975546353445 0.929012226823278 38 0.0622293456389841 0.124458691277968 0.937770654361016 39 0.0698272238708103 0.139654447741621 0.93017277612919 40 0.0426694948269023 0.0853389896538046 0.957330505173098 41 0.0939731034656298 0.187946206931260 0.90602689653437 42 0.111184416211984 0.222368832423968 0.888815583788016 43 0.699687098982222 0.600625802035556 0.300312901017778 44 0.582960702447857 0.834078595104286 0.417039297552143 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 1 0.0357142857142857 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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