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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: Fri, 18 Dec 2009 05:20:07 -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/Dec/18/t1261138871z71a1e52j7p966i.htm/, Retrieved Fri, 18 Dec 2009 13:21:23 +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/Dec/18/t1261138871z71a1e52j7p966i.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 0 8,8 0 8,3 0 7,5 0 7,2 0 7,4 0 8,8 0 9,3 0 9,3 0 8,7 0 8,2 0 8,3 0 8,5 0 8,6 0 8,5 0 8,2 0 8,1 0 7,9 0 8,6 0 8,7 0 8,7 0 8,5 0 8,4 0 8,5 0 8,7 0 8,7 0 8,6 0 8,5 0 8,3 0 8 0 8,2 0 8,1 0 8,1 0 8 0 7,9 0 7,9 0 8 0 8 0 7,9 0 8 0 7,7 0 7,2 0 7,5 0 7,3 0 7 0 7 0 7 0 7,2 0 7,3 1 7,1 1 6,8 1 6,4 1 6,1 1 6,5 1 7,7 1 7,9 1 7,5 1 6,9 1 6,6 1 6,9 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 7.99291666666666 -1.16458333333333X[t] + 0.519999999999995M1[t] + 0.48M2[t] + 0.26M3[t] -0.0400000000000002M4[t] -0.280000000000000M5[t] -0.36M6[t] + 0.4M7[t] + 0.5M8[t] + 0.36M9[t] + 0.0599999999999997M10[t] -0.140000000000000M11[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) 7.99291666666666 0.248048 32.2233 0 0 X -1.16458333333333 0.177177 -6.573 0 0 M1 0.519999999999995 0.347195 1.4977 0.140893 0.070447 M2 0.48 0.347195 1.3825 0.17335 0.086675 M3 0.26 0.347195 0.7489 0.457674 0.228837 M4 -0.0400000000000002 0.347195 -0.1152 0.90877 0.454385 M5 -0.280000000000000 0.347195 -0.8065 0.424038 0.212019 M6 -0.36 0.347195 -1.0369 0.305097 0.152548 M7 0.4 0.347195 1.1521 0.25511 0.127555 M8 0.5 0.347195 1.4401 0.156464 0.078232 M9 0.36 0.347195 1.0369 0.305097 0.152548 M10 0.0599999999999997 0.347195 0.1728 0.86354 0.43177 M11 -0.140000000000000 0.347195 -0.4032 0.688606 0.344303 Multiple Linear Regression - Regression Statistics Multiple R 0.751988834719333 R-squared 0.56548720754254 Adjusted R-squared 0.454547771170422 F-TEST (value) 5.09726050568492 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 2.29121731929460e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.54896340096844 Sum Squared Residuals 14.1639583333333 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.9 8.51291666666669 0.387083333333313 2 8.8 8.47291666666666 0.327083333333336 3 8.3 8.25291666666667 0.0470833333333337 4 7.5 7.95291666666667 -0.452916666666666 5 7.2 7.71291666666667 -0.512916666666667 6 7.4 7.63291666666667 -0.232916666666666 7 8.8 8.39291666666667 0.407083333333334 8 9.3 8.49291666666667 0.807083333333335 9 9.3 8.35291666666667 0.947083333333334 10 8.7 8.05291666666667 0.647083333333333 11 8.2 7.85291666666667 0.347083333333333 12 8.3 7.99291666666667 0.307083333333334 13 8.5 8.51291666666666 -0.0129166666666613 14 8.6 8.47291666666667 0.127083333333333 15 8.5 8.25291666666667 0.247083333333333 16 8.2 7.95291666666667 0.247083333333333 17 8.1 7.71291666666667 0.387083333333333 18 7.9 7.63291666666667 0.267083333333334 19 8.6 8.39291666666667 0.207083333333333 20 8.7 8.49291666666667 0.207083333333333 21 8.7 8.35291666666667 0.347083333333333 22 8.5 8.05291666666667 0.447083333333333 23 8.4 7.85291666666667 0.547083333333334 24 8.5 7.99291666666667 0.507083333333333 25 8.7 8.51291666666666 0.187083333333338 26 8.7 8.47291666666667 0.227083333333333 27 8.6 8.25291666666667 0.347083333333333 28 8.5 7.95291666666667 0.547083333333334 29 8.3 7.71291666666667 0.587083333333334 30 8 7.63291666666667 0.367083333333333 31 8.2 8.39291666666667 -0.192916666666667 32 8.1 8.49291666666667 -0.392916666666667 33 8.1 8.35291666666667 -0.252916666666667 34 8 8.05291666666667 -0.0529166666666665 35 7.9 7.85291666666667 0.0470833333333337 36 7.9 7.99291666666667 -0.0929166666666665 37 8 8.51291666666666 -0.512916666666661 38 8 8.47291666666667 -0.472916666666667 39 7.9 8.25291666666667 -0.352916666666667 40 8 7.95291666666667 0.0470833333333335 41 7.7 7.71291666666667 -0.0129166666666668 42 7.2 7.63291666666667 -0.432916666666667 43 7.5 8.39291666666667 -0.892916666666666 44 7.3 8.49291666666667 -1.19291666666667 45 7 8.35291666666667 -1.35291666666667 46 7 8.05291666666667 -1.05291666666667 47 7 7.85291666666667 -0.852916666666666 48 7.2 7.99291666666667 -0.792916666666666 49 7.3 7.34833333333333 -0.0483333333333285 50 7.1 7.30833333333333 -0.208333333333334 51 6.8 7.08833333333333 -0.288333333333334 52 6.4 6.78833333333333 -0.388333333333333 53 6.1 6.54833333333333 -0.448333333333335 54 6.5 6.46833333333333 0.0316666666666660 55 7.7 7.22833333333333 0.471666666666667 56 7.9 7.32833333333333 0.571666666666667 57 7.5 7.18833333333333 0.311666666666666 58 6.9 6.88833333333333 0.0116666666666667 59 6.6 6.68833333333333 -0.0883333333333341 60 6.9 6.82833333333333 0.0716666666666664 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.230988724045684 0.461977448091367 0.769011275954316 17 0.325025200894954 0.650050401789909 0.674974799105046 18 0.249225644861856 0.498451289723711 0.750774355138145 19 0.157171758108160 0.314343516216321 0.84282824189184 20 0.139926599970315 0.279853199940630 0.860073400029685 21 0.133932157631975 0.267864315263950 0.866067842368025 22 0.0979036391648705 0.195807278329741 0.902096360835130 23 0.0744963580812362 0.148992716162472 0.925503641918764 24 0.0566035062528214 0.113207012505643 0.943396493747179 25 0.0354671147063244 0.0709342294126488 0.964532885293676 26 0.0232124172399919 0.0464248344799838 0.976787582760008 27 0.0181100395082765 0.036220079016553 0.981889960491724 28 0.0327250022780279 0.0654500045560558 0.967274997721972 29 0.062646715297093 0.125293430594186 0.937353284702907 30 0.064622274252162 0.129244548504324 0.935377725747838 31 0.0561295674839927 0.112259134967985 0.943870432516007 32 0.0831251563230906 0.166250312646181 0.91687484367691 33 0.120140430505943 0.240280861011886 0.879859569494057 34 0.139250761343917 0.278501522687833 0.860749238656083 35 0.155506450434933 0.311012900869866 0.844493549565067 36 0.151214194342225 0.30242838868445 0.848785805657775 37 0.136302278470396 0.272604556940792 0.863697721529604 38 0.127289371558763 0.254578743117527 0.872710628441237 39 0.124084819112004 0.248169638224008 0.875915180887996 40 0.228946839015692 0.457893678031384 0.771053160984308 41 0.665067584503159 0.669864830993683 0.334932415496841 42 0.77155028031209 0.456899439375821 0.228449719687910 43 0.700391920659583 0.599216158680834 0.299608079340417 44 0.792206664233966 0.415586671532068 0.207793335766034 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 2 0.0689655172413793 NOK 10% type I error level 4 0.137931034482759 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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