Paper - Multiple Regression SPAREN 4

*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: Sun, 07 Dec 2008 15:00:11 -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/Dec/07/t1228687522vuz1hnjh3ujsiys.htm/, Retrieved Sun, 07 Dec 2008 22:05:32 +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/Dec/07/t1228687522vuz1hnjh3ujsiys.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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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

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Dataseries X:

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0 0 9 0 1 0 4 0 6 0 21 0 24 0 23 0 22 0 21 0 20 0 16 0 18 0 18 0 24 0 16 0 15 0 24 0 18 0 15 0 4 0 3 0 6 0 5 0 12 0 12 0 12 0 14 0 12 0 17 0 12 0 20 0 21 0 15 0 22 0 19 0 19 0 26 0 25 0 19 0 20 0 30 0 31 0 35 0 33 0 26 0 25 0 17 0 14 0 8 0 12 0 7 0 4 0 10 0 8 0 16 1 14 1 20 1 9 1 10 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 Val[t] = + 0.0399112517118016 -0.0077177040095967Spa[t] -0.125658446480324M1[t] -0.117542649072708M2[t] -0.123318718882366M3[t] -0.152247900720814M4[t] -0.16419813373815M5[t] -0.102058408263357M6[t] -0.123269886092209M7[t] + 0.0941071561269228M8[t] + 0.0636344334865551M9[t] + 0.0424229556577034M10[t] + 0.0304727226403677M11[t] + 0.00731961061157762t + 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) 0.0399112517118016 0.143572 0.278 0.782267 0.391134 Spa -0.0077177040095967 0.004542 -1.6992 0.096033 0.048017 M1 -0.125658446480324 0.162373 -0.7739 0.442956 0.221478 M2 -0.117542649072708 0.162307 -0.7242 0.472609 0.236305 M3 -0.123318718882366 0.162121 -0.7607 0.450743 0.225371 M4 -0.152247900720814 0.161774 -0.9411 0.351563 0.175782 M5 -0.16419813373815 0.161711 -1.0154 0.315236 0.157618 M6 -0.102058408263357 0.164747 -0.6195 0.538654 0.269327 M7 -0.123269886092209 0.16314 -0.7556 0.453738 0.226869 M8 0.0941071561269228 0.165812 0.5676 0.573098 0.286549 M9 0.0636344334865551 0.163028 0.3903 0.698096 0.349048 M10 0.0424229556577034 0.161885 0.2621 0.794449 0.397224 M11 0.0304727226403677 0.161572 0.1886 0.851234 0.425617 t 0.00731961061157762 0.001949 3.7562 0.000484 0.000242 Multiple Linear Regression - Regression Statistics Multiple R 0.591520511071267 R-squared 0.349896515018013 Adjusted R-squared 0.166171617088321 F-TEST (value) 1.90445888913713 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.054827258663043 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.254508946320681 Sum Squared Residuals 2.97964097283411 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0 -0.0784275841569441 0.0784275841569441 2 0 -0.132451512224121 0.132451512224121 3 0 -0.0691663393454283 0.0691663393454283 4 0 -0.113929022601089 0.113929022601089 5 0 -0.133995053026041 0.133995053026041 6 0 -0.180301277083621 0.180301277083621 7 0 -0.217346256329685 0.217346256329685 8 0 0.0150681005106211 -0.0150681005106211 9 0 -0.000367307508572454 0.000367307508572454 10 0 -0.00654147071624967 0.00654147071624967 11 0 -0.00345438911241079 0.00345438911241079 12 0 0.00426331489718572 -0.00426331489718572 13 0 -0.129510928990754 0.129510928990754 14 0 -0.114075520971561 0.114075520971561 15 0 -0.158838204227221 0.158838204227221 16 0 -0.118706143377318 0.118706143377318 17 0 -0.115619061773480 0.115619061773480 18 0 -0.115619061773479 0.115619061773479 19 0 -0.0832047049331733 0.0832047049331733 20 0 0.164645059926326 -0.164645059926326 21 0 0.2263866920031 -0.2263866920031 22 0 0.220212528795422 -0.220212528795422 23 0 0.192428794360874 -0.192428794360874 24 0 0.176993386341681 -0.176993386341681 25 0 0.00463062240575796 -0.00463062240575796 26 0 0.0200660304249515 -0.0200660304249515 27 0 0.0216095712268708 -0.0216095712268708 28 0 -0.0154354080191933 0.0154354080191933 29 0 -0.00463062240575811 0.00463062240575811 30 0 0.0262401936326288 -0.0262401936326288 31 0 0.0509368464633383 -0.0509368464633383 32 0 0.213891867217274 -0.213891867217274 33 0 0.183021051178887 -0.183021051178887 34 0 0.215435408019193 -0.215435408019193 35 0 0.156780857546258 -0.156780857546258 36 0 0.156780857546258 -0.156780857546258 37 0 0.0384420216775124 -0.0384420216775124 38 0 -0.000146498370470996 0.000146498370470996 39 0 0.00911474644104501 -0.00911474644104501 40 0 0.0338113992717546 -0.0338113992717546 41 0 0.0214630728563997 -0.0214630728563997 42 0 0.0137453688468031 -0.0137453688468031 43 0 -0.0078642023800677 0.0078642023800677 44 0 0.185961634412255 -0.185961634412255 45 0 0.178243930402658 -0.178243930402658 46 0 0.218375991252561 -0.218375991252561 47 0 0.221463072856400 -0.221463072856400 48 0 0.260051592904383 -0.260051592904383 49 0 0.164865869064427 -0.164865869064427 50 0 0.226607501141201 -0.226607501141201 51 0 0.197280225904734 -0.197280225904734 52 0 0.214259174725847 -0.214259174725847 53 0 0.232781664348878 -0.232781664348878 54 0 0.255934776377669 -0.255934776377669 55 0 0.257478317179588 -0.257478317179588 56 1 0.420433337933523 0.579566662066477 57 1 0.412715633923927 0.587284366076073 58 1 0.352517542649073 0.647482457350927 59 1 0.432781664348878 0.567218335651122 60 1 0.401910848310492 0.598089151689508 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0 0 1 18 0 0 1 19 0 0 1 20 0 0 1 21 0 0 1 22 0 0 1 23 0 0 1 24 0 0 1 25 0 0 1 26 0 0 1 27 0 0 1 28 0 0 1 29 0 0 1 30 0 0 1 31 0 0 1 32 0 0 1 33 0 0 1 34 0 0 1 35 0 0 1 36 0 0 1 37 0 0 1 38 0 0 1 39 0 0 1 40 0 0 1 41 0 0 1 42 0 0 1 43 0 0 1 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 27 1 NOK 5% type I error level 27 1 NOK 10% type I error level 27 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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Software written by Ed van Stee & Patrick Wessa

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