Sleep article - SWS Multiple Regression

*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: Tue, 14 Dec 2010 09:46:29 +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/14/t1292319924fpznamyq3ie0z4v.htm/, Retrieved Tue, 14 Dec 2010 10:45:34 +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/14/t1292319924fpznamyq3ie0z4v.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}, }

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Dataseries X:

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6654000 5712000 -999.0 38.6 645.0 3 5 3 1000 6600 6.3 4.5 42.0 3 1 3 3385 44500 -999.0 14.0 60.0 1 1 1 0.920 5700 -999.0 -999.0 25.0 5 2 3 2547000 4603000 2.1 69.0 624.0 3 5 4 10550 179500 9.1 27.0 180.0 4 4 4 0.023 0.300 15.8 19.0 35.0 1 1 1 160000 169000 5.2 30.4 392.0 4 5 4 3300 25600 10.9 28.0 63.0 1 2 1 52160 440000 8.3 50.0 230.0 1 1 1 0.425 6400 11.0 7.0 112.0 5 4 4 465000 423000 3.2 30.0 281.0 5 5 5 0.550 2400 7.6 -999.0 -999.0 2 1 2 187100 419000 -999.0 40.0 365.0 5 5 5 0.075 1200 6.3 3.5 42.0 1 1 1 3000 25000 8.6 50.0 28.0 2 2 2 0.785 3500 6.6 6.0 42.0 2 2 2 0.200 5000 9.5 10.4 120.0 2 2 2 1410 17500 4.8 34.0 -999.0 1 2 1 60000 81000 12.0 7.0 -999.0 1 1 1 529000 680000 -999.0 28.0 400.0 5 5 5 27660 115000 3.3 20.0 148.0 5 5 5 0.120 1000 11.0 3.9 16.0 3 1 2 207000 406000 -999.0 39.3 252.0 1 4 1 85000 325000 4.7 41.0 310.0 1 3 1 36330 119500 -999.0 16.2 63.0 1 1 1 0.101 4000 10.4 9.0 28.0 5 1 3 1040 5500 7.4 7.6 68.0 5 3 4 521000 655000 2.1 46.0 336.0 5 5 5 100000 157000 - 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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation SWS[t] = -154.896579262522 -0.000214879855393930Wbo[t] + 0.000190551747684777Wbr[t] + 0.190856174661067Lifeyears[t] -0.227222894392210Gestation[t] -46.3886594812592Predation[t] -138.680678623493Sleep_exposure[t] + 159.915106041459overall_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) -154.896579262522 123.516796 -1.2541 0.215224 0.107612 Wbo -0.000214879855393930 0.00017 -1.2641 0.211618 0.105809 Wbr 0.000190551747684777 0.000171 1.1156 0.26954 0.13477 Lifeyears 0.190856174661067 0.223989 0.8521 0.397935 0.198967 Gestation -0.227222894392210 0.200783 -1.1317 0.262767 0.131384 Predation -46.3886594812592 102.230655 -0.4538 0.651817 0.325908 Sleep_exposure -138.680678623493 64.537688 -2.1488 0.036148 0.018074 overall_danger 159.915106041459 130.671079 1.2238 0.226341 0.113171 Multiple Linear Regression - Regression Statistics Multiple R 0.408946732766345 R-squared 0.167237430240269 Adjusted R-squared 0.059286726752896 F-TEST (value) 1.54920185638096 F-TEST (DF numerator) 7 F-TEST (DF denominator) 54 p-value 0.170796471299805 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 411.987995727557 Sum Squared Residuals 9165641.86567492 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 -999 -988.291326256213 -10.7086737437870 2 6.3 39.3603346954103 -33.0603346954103 3 -999 -183.260014082628 -815.739985917372 4 -999 -379.715859365304 -619.284140634696 5 2.1 -146.612833802367 148.712833802367 6 9.1 -259.323455555434 268.423455555434 7 15.8 -184.377293087696 200.177293087696 8 5.2 -479.641064535542 484.841064535542 9 10.9 -323.533538187578 334.433538187578 10 8.3 -150.134632579016 158.434632579016 11 11 -324.795698085012 335.795698085012 12 3.2 -358.107431150887 361.307431150887 13 7.6 -29.7368057436822 37.3368057436822 14 -999 -316.332687709987 -682.667312290013 15 6.3 -188.697530297742 194.997530297742 16 8.6 -197.905321573101 206.505321573101 17 6.6 -212.936505469406 219.536505469406 18 9.5 -229.534170737247 239.034170737247 19 4.8 -82.2150335246377 87.0150335246377 20 12 50.8227536334598 -38.8227536334598 21 -999 -350.309179523105 -648.690820476895 22 3.3 -294.509730272263 297.809730272263 23 11 -115.613725513871 126.613725513871 24 -999 -612.968489425477 -386.031510574523 25 4.7 -476.361632384215 481.061632384215 26 -999 -176.309634941147 -822.690365058853 27 10.4 -49.6575873510936 60.0575873510936 28 7.4 -176.397578702052 183.797578702053 29 2.1 -335.376257987073 337.476257987073 30 -999 -190.069283605512 -808.930716394488 31 -999 -349.042823594339 -649.957176405661 32 7.7 -28.9298503224380 36.6298503224380 33 17.9 -186.831362364422 204.731362364422 34 6.1 16.5720492470536 -10.4720492470536 35 8.2 -423.349847097535 431.549847097535 36 8.4 -152.634885588007 161.034885588007 37 11.9 -3.09300164275009 14.9930016427501 38 10.8 -5.82149960127638 16.6214996012764 39 13.8 -227.376684410232 241.176684410232 40 14.3 -251.159773617727 265.459773617727 41 -999 -336.491214872504 -662.508785127496 42 15.2 -231.772525561303 246.972525561303 43 10 -270.521452404409 280.521452404409 44 11.9 -66.0818391418217 77.9818391418217 45 6.5 -283.448641307327 289.948641307327 46 7.5 -282.507761652749 290.007761652749 47 -999 -210.357132453648 -788.642867546352 48 10.6 43.4894131874954 -32.8894131874954 49 7.4 -181.302219426813 188.702219426813 50 8.4 -342.967867808858 351.367867808858 51 5.7 -252.650576068098 258.350576068098 52 4.9 -138.430591797229 143.330591797229 53 -999 -295.981105401431 -703.018894598569 54 3.2 -289.740549268520 292.940549268520 55 -999 -221.150165417705 -777.849834582295 56 8.1 114.941182717149 -106.841182717149 57 11 -78.8036444910635 89.8036444910635 58 4.9 4.90295101183433 -0.00295101183432789 59 13.2 -261.130629788983 274.330629788983 60 9.7 -149.817433751086 159.517433751086 61 12.8 -229.056950482491 241.856950482491 62 -999 -276.612353708348 -722.387646291652 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.765581012046011 0.468837975907978 0.234418987953989 12 0.64925638228077 0.70148723543846 0.35074361771923 13 0.547425988008875 0.90514802398225 0.452574011991125 14 0.841557991055439 0.316884017889122 0.158442008944561 15 0.77472477977884 0.450550440442319 0.225275220221160 16 0.68748490139415 0.6250301972117 0.31251509860585 17 0.596934988269757 0.806130023460486 0.403065011730243 18 0.517128130308994 0.965743739382011 0.482871869691006 19 0.519041266200281 0.961917467599437 0.480958733799719 20 0.43350231426201 0.86700462852402 0.56649768573799 21 0.564156836281008 0.871686327437983 0.435843163718992 22 0.503603905145944 0.992792189708112 0.496396094854056 23 0.441825417922268 0.883650835844537 0.558174582077732 24 0.450211334560398 0.900422669120796 0.549788665439602 25 0.477049995243553 0.954099990487105 0.522950004756447 26 0.67650704659464 0.646985906810719 0.323492953405359 27 0.601534809760799 0.796930380478402 0.398465190239201 28 0.526296457514178 0.947407084971643 0.473703542485822 29 0.543677736191602 0.912644527616796 0.456322263808398 30 0.679536900576038 0.640926198847924 0.320463099423962 31 0.774418703725307 0.451162592549385 0.225581296274693 32 0.709653090551136 0.580693818897727 0.290346909448864 33 0.65154242404958 0.696915151900839 0.348457575950420 34 0.597579976434251 0.804840047131498 0.402420023565749 35 0.60076278512435 0.7984744297513 0.39923721487565 36 0.531766954257099 0.936466091485802 0.468233045742901 37 0.447758807729985 0.89551761545997 0.552241192270015 38 0.36857245314813 0.73714490629626 0.63142754685187 39 0.312245611664553 0.624491223329106 0.687754388335447 40 0.272461762761249 0.544923525522498 0.727538237238751 41 0.366249409308454 0.732498818616908 0.633750590691546 42 0.317205776817975 0.634411553635949 0.682794223182025 43 0.260406027463952 0.520812054927903 0.739593972536048 44 0.195557609076649 0.391115218153298 0.804442390923351 45 0.153345663273985 0.30669132654797 0.846654336726015 46 0.297131956019747 0.594263912039493 0.702868043980253 47 0.40528331983098 0.81056663966196 0.59471668016902 48 0.314308691601503 0.628617383203005 0.685691308398497 49 0.218054130240811 0.436108260481622 0.781945869759189 50 0.135274559100689 0.270549118201378 0.864725440899311 51 0.101029838927594 0.202059677855188 0.898970161072406 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 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; 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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