Paper - Multiple Regression ECONOMISCHE SITUATIE 1

*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, 05 Dec 2008 10:15:56 -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/05/t1228497423soprcfoxnvlqnx9.htm/, Retrieved Fri, 05 Dec 2008 17:17:17 +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/05/t1228497423soprcfoxnvlqnx9.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

34 0 39 0 40 0 45 0 43 0 42 0 49 0 43 0 50 0 44 0 40 0 41 0 45 0 45 0 48 0 54 0 47 0 35 0 28 0 28 0 34 0 23 0 33 0 38 0 41 0 47 0 46 0 45 0 47 0 49 0 50 0 56 0 50 0 56 0 58 0 59 0 51 0 59 0 60 0 60 0 68 0 62 0 62 0 58 0 56 0 50 0 52 0 36 0 33 0 26 0 28 0 27 0 20 0 16 0 11 0 0 1 3 1 10 1 0 1 3 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 Eco[t] = + 43.7636363636364 -40.5636363636364Val[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) 43.7636363636364 1.632999 26.7995 0 0 Val -40.5636363636364 5.656874 -7.1707 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.685511372404466 R-squared 0.469925841695855 Adjusted R-squared 0.460786632069922 F-TEST (value) 51.4186522609557 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 1.51452894670001e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 12.1106445575265 Sum Squared Residuals 8506.72727272727 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 34 43.7636363636364 -9.76363636363643 2 39 43.7636363636364 -4.76363636363636 3 40 43.7636363636364 -3.76363636363636 4 45 43.7636363636364 1.23636363636364 5 43 43.7636363636364 -0.763636363636361 6 42 43.7636363636364 -1.76363636363636 7 49 43.7636363636364 5.23636363636364 8 43 43.7636363636364 -0.763636363636361 9 50 43.7636363636364 6.23636363636364 10 44 43.7636363636364 0.236363636363639 11 40 43.7636363636364 -3.76363636363636 12 41 43.7636363636364 -2.76363636363636 13 45 43.7636363636364 1.23636363636364 14 45 43.7636363636364 1.23636363636364 15 48 43.7636363636364 4.23636363636364 16 54 43.7636363636364 10.2363636363636 17 47 43.7636363636364 3.23636363636364 18 35 43.7636363636364 -8.76363636363636 19 28 43.7636363636364 -15.7636363636364 20 28 43.7636363636364 -15.7636363636364 21 34 43.7636363636364 -9.76363636363636 22 23 43.7636363636364 -20.7636363636364 23 33 43.7636363636364 -10.7636363636364 24 38 43.7636363636364 -5.76363636363636 25 41 43.7636363636364 -2.76363636363636 26 47 43.7636363636364 3.23636363636364 27 46 43.7636363636364 2.23636363636364 28 45 43.7636363636364 1.23636363636364 29 47 43.7636363636364 3.23636363636364 30 49 43.7636363636364 5.23636363636364 31 50 43.7636363636364 6.23636363636364 32 56 43.7636363636364 12.2363636363636 33 50 43.7636363636364 6.23636363636364 34 56 43.7636363636364 12.2363636363636 35 58 43.7636363636364 14.2363636363636 36 59 43.7636363636364 15.2363636363636 37 51 43.7636363636364 7.23636363636364 38 59 43.7636363636364 15.2363636363636 39 60 43.7636363636364 16.2363636363636 40 60 43.7636363636364 16.2363636363636 41 68 43.7636363636364 24.2363636363636 42 62 43.7636363636364 18.2363636363636 43 62 43.7636363636364 18.2363636363636 44 58 43.7636363636364 14.2363636363636 45 56 43.7636363636364 12.2363636363636 46 50 43.7636363636364 6.23636363636364 47 52 43.7636363636364 8.23636363636364 48 36 43.7636363636364 -7.76363636363636 49 33 43.7636363636364 -10.7636363636364 50 26 43.7636363636364 -17.7636363636364 51 28 43.7636363636364 -15.7636363636364 52 27 43.7636363636364 -16.7636363636364 53 20 43.7636363636364 -23.7636363636364 54 16 43.7636363636364 -27.7636363636364 55 11 43.7636363636364 -32.7636363636364 56 0 3.2 -3.2 57 3 3.2 -0.199999999999999 58 10 3.2 6.8 59 0 3.2 -3.2 60 3 3.2 -0.199999999999999 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.07044386023606 0.14088772047212 0.92955613976394 6 0.0230683948631441 0.0461367897262882 0.976931605136856 7 0.0259665160861918 0.0519330321723836 0.974033483913808 8 0.00922809298500613 0.0184561859700123 0.990771907014994 9 0.00903286542633998 0.0180657308526800 0.99096713457366 10 0.00330257494140675 0.00660514988281351 0.996697425058593 11 0.00130146035242087 0.00260292070484175 0.99869853964758 12 0.000445964028413591 0.000891928056827183 0.999554035971586 13 0.00015735923143017 0.00031471846286034 0.99984264076857 14 5.28567962384128e-05 0.000105713592476826 0.999947143203762 15 2.86165582542145e-05 5.7233116508429e-05 0.999971383441746 16 8.82362059391642e-05 0.000176472411878328 0.99991176379406 17 3.49760110564259e-05 6.99520221128517e-05 0.999965023988943 18 4.56315571581809e-05 9.12631143163617e-05 0.999954368442842 19 0.000358341204837246 0.000716682409674491 0.999641658795163 20 0.00115292543945914 0.00230585087891827 0.99884707456054 21 0.00093191164807725 0.0018638232961545 0.999068088351923 22 0.00522839529150056 0.0104567905830011 0.9947716047085 23 0.00434482027738169 0.00868964055476337 0.995655179722618 24 0.00253222065111217 0.00506444130222434 0.997467779348888 25 0.00134635120321636 0.00269270240643272 0.998653648796784 26 0.000852433924866432 0.00170486784973286 0.999147566075134 27 0.000489278526762217 0.000978557053524435 0.999510721473238 28 0.000258556875008087 0.000517113750016173 0.999741443124992 29 0.000148800157299023 0.000297600314598046 0.9998511998427 30 9.82878401256585e-05 0.000196575680251317 0.999901712159874 31 6.92534373298353e-05 0.000138506874659671 0.99993074656267 32 0.000110462656129479 0.000220925312258958 0.99988953734387 33 7.10020724512795e-05 0.000142004144902559 0.99992899792755 34 9.50014235285131e-05 0.000190002847057026 0.999904998576471 35 0.000159549201736492 0.000319098403472984 0.999840450798263 36 0.000282747792301214 0.000565495584602429 0.999717252207699 37 0.000180665543579064 0.000361331087158128 0.999819334456421 38 0.000295440807281831 0.000590881614563663 0.999704559192718 39 0.000544124322685815 0.00108824864537163 0.999455875677314 40 0.000994192275479975 0.00198838455095995 0.99900580772452 41 0.00724823241544332 0.0144964648308866 0.992751767584557 42 0.0190630614546892 0.0381261229093784 0.98093693854531 43 0.0574352220158451 0.114870444031690 0.942564777984155 44 0.127985105585908 0.255970211171815 0.872014894414092 45 0.284322115547954 0.568644231095907 0.715677884452046 46 0.458259271795338 0.916518543590675 0.541740728204662 47 0.883781640721647 0.232436718556705 0.116218359278353 48 0.93174203201907 0.136515935961859 0.0682579679809296 49 0.961553362052485 0.0768932758950311 0.0384466379475155 50 0.955883368831573 0.0882332623368543 0.0441166311684272 51 0.967391476876795 0.0652170462464092 0.0326085231232046 52 0.987818583529194 0.0243628329416128 0.0121814164708064 53 0.98640184390215 0.0271963121957005 0.0135981560978503 54 0.975452470581794 0.0490950588364121 0.0245475294182061 55 0.935715909679633 0.128568180640734 0.0642840903203671 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 30 0.588235294117647 NOK 5% type I error level 39 0.764705882352941 NOK 10% type I error level 43 0.843137254901961 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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