*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: Fri, 20 Nov 2009 05:32:59 -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/Nov/20/t1258720452nlzvlpo8wbg1gcp.htm/, Retrieved Fri, 20 Nov 2009 13:34:24 +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/Nov/20/t1258720452nlzvlpo8wbg1gcp.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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1.4 2 1.2 2 1 2 1.7 2 2.4 2 2 2 2.1 2 2 2 1.8 2 2.7 2 2.3 2 1.9 2 2 2 2.3 2 2.8 2 2.4 2 2.3 2 2.7 2 2.7 2 2.9 2 3 2 2.2 2 2.3 2 2.8 2.21 2.8 2.25 2.8 2.25 2.2 2.45 2.6 2.5 2.8 2.5 2.5 2.64 2.4 2.75 2.3 2.93 1.9 3 1.7 3.17 2 3.25 2.1 3.39 1.7 3.5 1.8 3.5 1.8 3.65 1.8 3.75 1.3 3.75 1.3 3.9 1.3 4 1.2 4 1.4 4 2.2 4 2.9 4 3.1 4 3.5 4 3.6 4 4.4 4 4.1 4 5.1 4 5.8 4 5.9 4.18 5.4 4.25 5.5 4.25 4.8 3.97 3.2 3.42 2.7 2.75

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 Inflatie[t] = + 0.94880597817748 + 0.547454363004362rente[t] -0.174305476439478M1[t] -0.114305476439477M2[t] -0.0526272818497814M3[t] + 0.0109490872600876M4[t] + 0.270949087260088M5[t] + 0.319196734205835M6[t] + 0.296495293891495M7[t] + 0.149122575741277M8[t] + 0.101458214659215M9[t] + 0.113502210645311M10[t] -0.0150370792322786M11[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) 0.94880597817748 0.72387 1.3107 0.196314 0.098157 rente 0.547454363004362 0.173988 3.1465 0.002866 0.001433 M1 -0.174305476439478 0.74143 -0.2351 0.815157 0.407579 M2 -0.114305476439477 0.74143 -0.1542 0.878137 0.439068 M3 -0.0526272818497814 0.741187 -0.071 0.943696 0.471848 M4 0.0109490872600876 0.741144 0.0148 0.988276 0.494138 M5 0.270949087260088 0.741144 0.3656 0.716317 0.358158 M6 0.319196734205835 0.741165 0.4307 0.668678 0.334339 M7 0.296495293891495 0.74141 0.3999 0.691037 0.345518 M8 0.149122575741277 0.741698 0.2011 0.841523 0.420761 M9 0.101458214659215 0.741797 0.1368 0.891794 0.445897 M10 0.113502210645311 0.741645 0.153 0.879021 0.439511 M11 -0.0150370792322786 0.741219 -0.0203 0.9839 0.49195 Multiple Linear Regression - Regression Statistics Multiple R 0.443564739811477 R-squared 0.196749678404024 Adjusted R-squared -0.00833551008856603 F-TEST (value) 0.959355864995257 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.499354669494684 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.17183823442489 Sum Squared Residuals 64.5406278400223 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.4 1.86940922774674 -0.469409227746737 2 1.2 1.92940922774673 -0.729409227746731 3 1 1.99108742233642 -0.991087422336423 4 1.7 2.05466379144629 -0.354663791446293 5 2.4 2.31466379144629 0.085336208553708 6 2 2.36291143839204 -0.36291143839204 7 2.1 2.3402099980777 -0.2402099980777 8 2 2.19283727992748 -0.192837279927482 9 1.8 2.14517291884542 -0.34517291884542 10 2.7 2.15721691483152 0.542783085168484 11 2.3 2.02867762495393 0.271322375046073 12 1.9 2.04371470418620 -0.143714704186205 13 2 1.86940922774673 0.130590772253273 14 2.3 1.92940922774673 0.370590772253272 15 2.8 1.99108742233642 0.808912577663576 16 2.4 2.05466379144629 0.345336208553707 17 2.3 2.31466379144629 -0.0146637914462926 18 2.7 2.36291143839204 0.33708856160796 19 2.7 2.3402099980777 0.3597900019223 20 2.9 2.19283727992748 0.707162720072518 21 3 2.14517291884542 0.85482708115458 22 2.2 2.15721691483152 0.0427830851684838 23 2.3 2.02867762495393 0.271322375046073 24 2.8 2.15868012041712 0.641319879582879 25 2.8 2.00627281849782 0.793727181502182 26 2.8 2.06627281849782 0.733727181502181 27 2.2 2.23744188568839 -0.0374418856883864 28 2.6 2.32839097294847 0.271609027051527 29 2.8 2.58839097294847 0.211609027051527 30 2.5 2.71328223071483 -0.213282230714831 31 2.4 2.75080077033097 -0.350800770330971 32 2.3 2.70196983752154 -0.401969837521538 33 1.9 2.69262728184978 -0.792627281849782 34 1.7 2.79773851954662 -1.09773851954662 35 2 2.71299557870938 -0.712995578709378 36 2.1 2.80467626876227 -0.704676268762268 37 1.7 2.69059077225327 -0.99059077225327 38 1.8 2.75059077225327 -0.95059077225327 39 1.8 2.89438712129362 -1.09438712129362 40 1.8 3.01270892670393 -1.21270892670393 41 1.3 3.27270892670392 -1.97270892670392 42 1.3 3.40307472810033 -2.10307472810033 43 1.3 3.43511872408642 -2.13511872408642 44 1.2 3.28774600593620 -2.08774600593620 45 1.4 3.24008164485414 -1.84008164485414 46 2.2 3.25212564084024 -1.05212564084024 47 2.9 3.12358635096265 -0.223586350962649 48 3.1 3.13862343019493 -0.0386234301949278 49 3.5 2.96431795375545 0.53568204624455 50 3.6 3.02431795375545 0.575682046244549 51 4.4 3.08599614834515 1.31400385165485 52 4.1 3.14957251745502 0.950427482544984 53 5.1 3.40957251745502 1.69042748254498 54 5.8 3.45782016440076 2.34217983559924 55 5.9 3.53366050942721 2.36633949057279 56 5.4 3.42460959668729 1.97539040331271 57 5.5 3.37694523560523 2.12305476439477 58 4.8 3.23570200995011 1.56429799004989 59 3.2 2.80606282042012 0.393937179579881 60 2.7 2.45430547643948 0.245694523560524 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.281987355283330 0.563974710566661 0.71801264471667 17 0.14332944793089 0.28665889586178 0.85667055206911 18 0.0783636646758306 0.156727329351661 0.92163633532417 19 0.0396360311480216 0.0792720622960432 0.960363968851978 20 0.0238664254168793 0.0477328508337586 0.97613357458312 21 0.0186720637229132 0.0373441274458264 0.981327936277087 22 0.00875301045083862 0.0175060209016772 0.991246989549161 23 0.00356757805837451 0.00713515611674902 0.996432421941626 24 0.00142544316878395 0.00285088633756789 0.998574556831216 25 0.000575130477490016 0.00115026095498003 0.99942486952251 26 0.000229836935056387 0.000459673870112774 0.999770163064944 27 0.000200396096535288 0.000400792193070577 0.999799603903465 28 8.88327004843554e-05 0.000177665400968711 0.999911167299516 29 3.86730824985778e-05 7.73461649971555e-05 0.999961326917501 30 1.95028617443509e-05 3.90057234887018e-05 0.999980497138256 31 1.01399014324411e-05 2.02798028648822e-05 0.999989860098567 32 5.7716199531706e-06 1.15432399063412e-05 0.999994228380047 33 3.46090948963644e-06 6.92181897927289e-06 0.99999653909051 34 1.79815219201476e-06 3.59630438402952e-06 0.999998201847808 35 5.24234058123672e-07 1.04846811624734e-06 0.999999475765942 36 1.52038077527634e-07 3.04076155055268e-07 0.999999847961923 37 3.93388972215717e-08 7.86777944431433e-08 0.999999960661103 38 9.23729786479997e-09 1.84745957295999e-08 0.999999990762702 39 2.75422225580247e-09 5.50844451160495e-09 0.999999997245778 40 8.18741184863495e-10 1.63748236972699e-09 0.999999999181259 41 1.62840713312882e-09 3.25681426625765e-09 0.999999998371593 42 1.10011936209979e-08 2.20023872419958e-08 0.999999988998806 43 1.98048392775034e-07 3.96096785550067e-07 0.999999801951607 44 7.71802307836185e-06 1.54360461567237e-05 0.999992281976922 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 22 0.758620689655172 NOK 5% type I error level 25 0.862068965517241 NOK 10% type I error level 26 0.896551724137931 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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