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: Sat, 22 Nov 2008 09:26:17 -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/22/t1227372319sk8miek3j4nbnhz.htm/, Retrieved Sat, 22 Nov 2008 16:45:29 +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/22/t1227372319sk8miek3j4nbnhz.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:

IsPrivate?

No (this computation is public)

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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Woongebouwen[t] = + 13.4520547945205 + 2.34425253126862Conjunctuur[t] -10.7323903116935M1[t] -20.9140956918801M2[t] -33.8958010720667M3[t] -23.0775064522533M4[t] -16.5280623386937M5[t] + 4.6902322811197M6[t] + 2.10852690093308M7[t] -8.47317847925353M8[t] -2.65488385944015M9[t] -36.2988882271193M10[t] + 1.78170538018661M11[t] -0.0182946198133809t + 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) 13.4520547945205 5.183467 2.5952 0.012645 0.006322 Conjunctuur 2.34425253126862 2.535822 0.9245 0.360074 0.180037 M1 -10.7323903116935 6.070974 -1.7678 0.083723 0.041862 M2 -20.9140956918801 6.062104 -3.45 0.001211 0.000606 M3 -33.8958010720667 6.054082 -5.5988 1e-06 1e-06 M4 -23.0775064522533 6.04691 -3.8164 0.000403 0.000201 M5 -16.5280623386937 6.020303 -2.7454 0.008594 0.004297 M6 4.6902322811197 6.014676 0.7798 0.439504 0.219752 M7 2.10852690093308 6.00991 0.3508 0.727309 0.363654 M8 -8.47317847925353 6.006008 -1.4108 0.165036 0.082518 M9 -2.65488385944015 6.002971 -0.4423 0.660372 0.330186 M10 -36.2988882271193 6.085337 -5.965 0 0 M11 1.78170538018661 5.999498 0.297 0.767822 0.383911 t -0.0182946198133809 0.072179 -0.2535 0.801041 0.40052 Multiple Linear Regression - Regression Statistics Multiple R 0.857459474391303 R-squared 0.73523675022341 Adjusted R-squared 0.660412353547417 F-TEST (value) 9.82616342911732 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 2.34161934287158e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.48535314482555 Sum Squared Residuals 4138.70851697439 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8 2.70136986301371 5.29863013698629 2 -10 -7.49863013698628 -2.50136986301372 3 -24 -20.4986301369863 -3.50136986301369 4 -19 -9.69863013698634 -9.30136986301366 5 8 -0.823228111971414 8.82322811197141 6 24 20.3767718880286 3.62322811197138 7 14 17.7767718880286 -3.77677188802860 8 7 7.17677188802858 -0.176771888028577 9 9 12.9767718880286 -3.97677188802859 10 -26 -23.0297796307326 -2.97022036926743 11 19 15.0325193567600 3.96748064324002 12 15 13.23251935676 1.76748064324000 13 -1 2.48183442525312 -3.48183442525312 14 -10 -7.7181655747469 -2.28183442525311 15 -21 -20.7181655747469 -0.281834425253125 16 -14 -9.91816557474686 -4.08183442525314 17 -27 -3.38701608100060 -23.6129839189994 18 26 17.8129839189994 8.18701608100061 19 23 15.2129839189994 7.7870160810006 20 5 4.61298391899940 0.387016081000596 21 19 10.4129839189994 8.5870160810006 22 -19 -23.2493150684932 4.24931506849316 23 24 17.157236450268 6.842763549732 24 17 15.357236450268 1.64276354973198 25 1 4.60655151876116 -3.60655151876116 26 -9 -5.59344848123884 -3.40655151876116 27 -16 -18.5934484812388 2.59344848123883 28 -21 -7.79344848123882 -13.2065515187612 29 -14 -1.26229898749255 -12.7377010125075 30 31 19.9377010125074 11.0622989874926 31 27 17.3377010125074 9.66229898749256 32 10 6.73770101250745 3.26229898749255 33 12 12.5377010125074 -0.537701012507439 34 -23 -21.1245979749851 -1.87540202501488 35 13 16.9377010125074 -3.93770101250744 36 26 15.1377010125075 10.8622989874925 37 -1 4.38701608100059 -5.38701608100059 38 4 -5.81298391899942 9.81298391899942 39 -16 -18.8129839189994 2.81298391899940 40 -5 -8.0129839189994 3.01298391899939 41 9 -1.48183442525313 10.4818344252531 42 23 19.7181655747469 3.28183442525314 43 9 17.1181655747469 -8.11816557474687 44 2 6.51816557474688 -4.51816557474688 45 10 12.3181655747469 -2.31816557474687 46 -29 -23.6883859440143 -5.31161405598571 47 17 14.3739130434783 2.62608695652173 48 9 12.5739130434783 -3.57391304347827 49 9 1.82322811197141 7.17677188802859 50 -10 -8.3767718880286 -1.62322811197140 51 -23 -21.3767718880286 -1.62322811197141 52 13 -10.5767718880286 23.5767718880286 53 13 -4.04562239428231 17.0456223942823 54 -9 17.1543776057177 -26.1543776057177 55 9 14.5543776057177 -5.55437760571769 56 5 3.95437760571769 1.04562239428231 57 8 9.7543776057177 -1.75437760571769 58 -18 -23.9079213817749 5.90792138177487 59 7 16.4986301369863 -9.4986301369863 60 4 14.6986301369863 -10.6986301369863 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.102363055907575 0.204726111815151 0.897636944092425 18 0.575933919838464 0.848132160323072 0.424066080161536 19 0.660808855740121 0.678382288519757 0.339191144259878 20 0.546642456410654 0.906715087178693 0.453357543589346 21 0.517862955749248 0.964274088501504 0.482137044250752 22 0.413043698513587 0.826087397027175 0.586956301486413 23 0.312074691459318 0.624149382918637 0.687925308540682 24 0.219793143498371 0.439586286996742 0.78020685650163 25 0.158144184630015 0.316288369260031 0.841855815369985 26 0.106052943770004 0.212105887540007 0.893947056229996 27 0.0677643912243087 0.135528782448617 0.932235608775691 28 0.103292601632949 0.206585203265898 0.896707398367051 29 0.225713861907378 0.451427723814756 0.774286138092622 30 0.246568786860428 0.493137573720856 0.753431213139572 31 0.245190551443711 0.490381102887423 0.754809448556289 32 0.175269798948312 0.350539597896625 0.824730201051688 33 0.120807208902536 0.241614417805071 0.879192791097464 34 0.0805833516422541 0.161166703284508 0.919416648357746 35 0.0649744502025661 0.129948900405132 0.935025549797434 36 0.0793465483629744 0.158693096725949 0.920653451637026 37 0.0671684353462591 0.134336870692518 0.93283156465374 38 0.0777206004151469 0.155441200830294 0.922279399584853 39 0.0485744450334065 0.097148890066813 0.951425554966594 40 0.0948277283344863 0.189655456668973 0.905172271665514 41 0.105429676894032 0.210859353788064 0.894570323105968 42 0.758435970131763 0.483128059736475 0.241564029868237 43 0.646539086371763 0.706921827256474 0.353460913628237 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 0.0370370370370370 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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