Stefan Temmerman

*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 26 Nov 2008 11:40:54 -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/26/t1227725521kqouhmmd7cn1qdo.htm/, Retrieved Wed, 26 Nov 2008 18:52:10 +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/26/t1227725521kqouhmmd7cn1qdo.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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8 0 -10 0 -24 0 -19 0 8 1 24 1 14 1 7 1 9 1 -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 1 17 1 1 1 -9 1 -16 1 -21 1 -14 1 31 1 27 1 10 1 12 1 -23 1 13 1 26 1 -1 1 4 1 -16 1 -5 1 9 1 23 1 9 1 2 1 10 1 -29 0 17 0 9 0 9 0 -10 0 -23 0 13 0 13 0 -9 0 9 0 5 0 8 0 -18 0 7 1 4 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Woongebouwen[t] = + 12.8028571428571 + 2.32857142857144Conjunctuur[t] -10.5342857142857M1[t] -20.7342857142858M2[t] -33.7342857142857M3[t] -22.9342857142857M4[t] -16.4M5[t] + 4.79999999999998M6[t] + 2.19999999999999M7[t] -8.4M8[t] -2.60000000000001M9[t] -36.2685714285714M10[t] + 1.79999999999999M11[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) 12.8028571428571 4.461348 2.8697 0.006138 0.003069 Conjunctuur 2.32857142857144 2.509704 0.9278 0.358238 0.179119 M1 -10.5342857142857 5.960217 -1.7674 0.083648 0.041824 M2 -20.7342857142858 5.960217 -3.4788 0.001097 0.000548 M3 -33.7342857142857 5.960217 -5.6599 1e-06 0 M4 -22.9342857142857 5.960217 -3.8479 0.000358 0.000179 M5 -16.4 5.939044 -2.7614 0.008185 0.004092 M6 4.79999999999998 5.939044 0.8082 0.423041 0.211521 M7 2.19999999999999 5.939044 0.3704 0.712726 0.356363 M8 -8.4 5.939044 -1.4144 0.163844 0.081922 M9 -2.60000000000001 5.939044 -0.4378 0.66355 0.331775 M10 -36.2685714285714 6.02329 -6.0214 0 0 M11 1.79999999999999 5.939044 0.3031 0.763167 0.381584 Multiple Linear Regression - Regression Statistics Multiple R 0.85724383117176 R-squared 0.734866986082036 Adjusted R-squared 0.66717345061362 F-TEST (value) 10.8557926690784 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 7.0631644977226e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.3904530190367 Sum Squared Residuals 4144.48857142857 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8 2.26857142857144 5.73142857142856 2 -10 -7.93142857142855 -2.06857142857145 3 -24 -20.9314285714286 -3.06857142857143 4 -19 -10.1314285714286 -8.8685714285714 5 8 -1.26857142857143 9.26857142857143 6 24 19.9314285714286 4.06857142857139 7 14 17.3314285714286 -3.33142857142859 8 7 6.73142857142857 0.268571428571433 9 9 12.5314285714286 -3.53142857142858 10 -26 -23.4657142857143 -2.53428571428572 11 19 14.6028571428572 4.39714285714285 12 15 12.8028571428572 2.19714285714283 13 -1 2.26857142857143 -3.26857142857143 14 -10 -7.93142857142858 -2.06857142857142 15 -21 -20.9314285714286 -0.06857142857143 16 -14 -10.1314285714286 -3.86857142857144 17 -27 -3.59714285714286 -23.4028571428571 18 26 17.6028571428571 8.39714285714287 19 23 15.0028571428571 7.99714285714286 20 5 4.40285714285714 0.597142857142855 21 19 10.2028571428571 8.79714285714286 22 -19 -23.4657142857143 4.46571428571429 23 24 16.9314285714286 7.06857142857143 24 17 15.1314285714286 1.86857142857143 25 1 4.59714285714285 -3.59714285714285 26 -9 -5.60285714285716 -3.39714285714284 27 -16 -18.6028571428571 2.60285714285714 28 -21 -7.80285714285713 -13.1971428571429 29 -14 -1.26857142857143 -12.7314285714286 30 31 19.9314285714286 11.0685714285714 31 27 17.3314285714286 9.66857142857143 32 10 6.73142857142857 3.26857142857143 33 12 12.5314285714286 -0.531428571428566 34 -23 -21.1371428571429 -1.86285714285714 35 13 16.9314285714286 -3.93142857142857 36 26 15.1314285714286 10.8685714285714 37 -1 4.59714285714285 -5.59714285714285 38 4 -5.60285714285716 9.60285714285716 39 -16 -18.6028571428571 2.60285714285714 40 -5 -7.80285714285714 2.80285714285714 41 9 -1.26857142857143 10.2685714285714 42 23 19.9314285714286 3.06857142857144 43 9 17.3314285714286 -8.33142857142856 44 2 6.73142857142857 -4.73142857142857 45 10 12.5314285714286 -2.53142857142857 46 -29 -23.4657142857143 -5.53428571428571 47 17 14.6028571428571 2.39714285714285 48 9 12.8028571428572 -3.80285714285715 49 9 2.26857142857142 6.73142857142858 50 -10 -7.93142857142858 -2.06857142857142 51 -23 -20.9314285714286 -2.06857142857143 52 13 -10.1314285714286 23.1314285714286 53 13 -3.59714285714286 16.5971428571429 54 -9 17.6028571428571 -26.6028571428571 55 9 15.0028571428571 -6.00285714285713 56 5 4.40285714285714 0.597142857142855 57 8 10.2028571428571 -2.20285714285714 58 -18 -23.4657142857143 5.46571428571429 59 7 16.9314285714286 -9.93142857142857 60 4 15.1314285714286 -11.1314285714286 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0774943192331073 0.154988638466215 0.922505680766893 17 0.034163639784915 0.06832727956983 0.965836360215085 18 0.42635170827499 0.85270341654998 0.57364829172501 19 0.544511249263739 0.910977501472523 0.455488750736261 20 0.428283979246306 0.856567958492612 0.571716020753694 21 0.423791831385584 0.847583662771169 0.576208168614416 22 0.336067794681464 0.672135589362929 0.663932205318536 23 0.258185307916637 0.516370615833275 0.741814692083363 24 0.178742304517687 0.357484609035373 0.821257695482313 25 0.125996655622458 0.251993311244917 0.874003344377542 26 0.0819422308972438 0.163884461794488 0.918057769102756 27 0.0517681974987007 0.103536394997401 0.9482318025013 28 0.0699078211238654 0.139815642247731 0.930092178876135 29 0.108916825929347 0.217833651858693 0.891083174070653 30 0.151737690420734 0.303475380841468 0.848262309579266 31 0.18149498912931 0.36298997825862 0.81850501087069 32 0.133008818344752 0.266017636689505 0.866991181655248 33 0.089871849439573 0.179743698879146 0.910128150560427 34 0.0569592758870676 0.113918551774135 0.943040724112932 35 0.0438840723301910 0.0877681446603821 0.95611592766981 36 0.079006540382527 0.158013080765054 0.920993459617473 37 0.0652688437725746 0.130537687545149 0.934731156227425 38 0.0833544836508262 0.166708967301652 0.916645516349174 39 0.0563814217330752 0.112762843466150 0.943618578266925 40 0.0993134984217687 0.198626996843537 0.900686501578231 41 0.116927099393635 0.233854198787269 0.883072900606365 42 0.851995844934515 0.296008310130970 0.148004155065485 43 0.782683592541895 0.43463281491621 0.217316407458105 44 0.630118100280394 0.739763799439212 0.369881899719606 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 0.0689655172413793 OK

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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