multiple regression with monthly dummies, index van totale industriële productie & prijsindex van grondstoffen, incl. enerige

*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: Thu, 19 Nov 2009 08:22:43 -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/19/t1258644293cay9t5ytbk851kl.htm/, Retrieved Thu, 19 Nov 2009 16:25:06 +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/19/t1258644293cay9t5ytbk851kl.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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95.1 117.1 97 118.7 112.7 126.5 102.9 127.5 97.4 134.6 111.4 131.8 87.4 135.9 96.8 142.7 114.1 141.7 110.3 153.4 103.9 145 101.6 137.7 94.6 148.3 95.9 152.2 104.7 169.4 102.8 168.6 98.1 161.1 113.9 174.1 80.9 179 95.7 190.6 113.2 190 105.9 181.6 108.8 174.8 102.3 180.5 99 196.8 100.7 193.8 115.5 197 100.7 216.3 109.9 221.4 114.6 217.9 85.4 229.7 100.5 227.4 114.8 204.2 116.5 196.6 112.9 198.8 102 207.5 106 190.7 105.3 201.6 118.8 210.5 106.1 223.5 109.3 223.8 117.2 231.2 92.5 244 104.2 234.7 112.5 250.2 122.4 265.7 113.3 287.6 100 283.3 110.7 295.4 112.8 312.3 109.8 333.8 117.3 347.7 109.1 383.2 115.9 407.1 96 413.6 99.8 362.7 116.8 321.9 115.7 239.4 99.4 191 94.3 159.7 91 163.4

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 tot.ind.prod.index[t] = + 91.9003613736778 + 0.0420132064949011prijsindex.grondst.incl.energie[t] -0.284708317074785M1[t] + 2.2168138511401M2[t] + 11.6844190710199M3[t] + 4.95453651474717M4[t] + 3.41422954213848M5[t] + 12.9349291727772M6[t] -13.5620167433119M7[t] -2.23146026202685M8[t] + 13.0695120670521M9[t] + 13.5486203916694M10[t] + 7.38052472297907M11[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) 91.9003613736778 2.571609 35.7365 0 0 prijsindex.grondst.incl.energie 0.0420132064949011 0.00827 5.0799 6e-06 3e-06 M1 -0.284708317074785 2.724364 -0.1045 0.917204 0.458602 M2 2.2168138511401 2.844615 0.7793 0.439627 0.219814 M3 11.6844190710199 2.846823 4.1044 0.000156 7.8e-05 M4 4.95453651474717 2.850909 1.7379 0.088645 0.044322 M5 3.41422954213848 2.856157 1.1954 0.237806 0.118903 M6 12.9349291727772 2.862499 4.5188 4.1e-05 2e-05 M7 -13.5620167433119 2.870668 -4.7243 2e-05 1e-05 M8 -2.23146026202685 2.861767 -0.7797 0.439367 0.219683 M9 13.0695120670521 2.853884 4.5796 3.3e-05 1.7e-05 M10 13.5486203916694 2.84679 4.7593 1.8e-05 9e-06 M11 7.38052472297907 2.844958 2.5942 0.012534 0.006267 Multiple Linear Regression - Regression Statistics Multiple R 0.89729917874334 R-squared 0.805145816173473 Adjusted R-squared 0.756432270216841 F-TEST (value) 16.5281709709712 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 3.78808096002103e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.49765600544344 Sum Squared Residuals 970.987658078468 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.1 96.535399537156 -1.43539953715601 2 97 99.1041428357627 -2.10414283576271 3 112.7 108.899451066303 3.8005489336973 4 102.9 102.211581716525 0.688418283475089 5 97.4 100.96956851003 -3.56956851003002 6 111.4 110.372631162483 1.02736883751696 7 87.4 84.047939393023 3.35206060697696 8 96.8 95.6641856784734 1.13581432152662 9 114.1 110.923144801057 3.17685519894260 10 110.3 111.893807641665 -1.59380764166503 11 103.9 105.372801038418 -1.47280103841758 12 101.6 97.6855799080257 3.91442009197425 13 94.6 97.8462115797969 -3.24621157979691 14 95.9 100.511585253342 -4.6115852533419 15 104.7 110.701817624934 -6.00181762493396 16 102.8 103.938324503465 -1.13832450346536 17 98.1 102.082918482145 -3.9829184821449 18 113.9 112.149789797217 1.75021020278264 19 80.9 85.8587085929533 -4.95870859295327 20 95.7 97.6766182695792 -1.97661826957915 21 113.2 112.952382674761 0.24761732523888 22 105.9 113.078580064821 -7.17858006482124 23 108.8 106.624794591966 2.17520540803436 24 102.3 99.4837451460075 2.81625485399249 25 99 99.8838520947996 -0.883852094799607 26 100.7 102.259334643530 -1.55933464352979 27 115.5 111.861382124193 3.63861787580677 28 100.7 105.942354453272 -5.24235445327214 29 109.9 104.616314833787 5.28368516621257 30 114.6 113.989968241694 0.610031758305956 31 85.4 87.9887781622448 -2.58877816224476 32 100.5 99.2227042685915 1.27729573140848 33 114.8 113.548970206989 1.25102979301128 34 116.5 113.708778162245 2.79122183775523 35 112.9 107.633111547843 5.26688845215674 36 102 100.618101721370 1.38189827863016 37 106 99.6275715351807 6.37242846481929 38 105.3 102.58703765419 2.71296234580998 39 118.8 112.428560411874 6.3714395881256 40 106.1 106.244849540035 -0.144849540035436 41 109.3 104.717146529375 4.5828534706248 42 117.2 114.548743888076 2.65125611192378 43 92.5 88.5895670151218 3.91043298487815 44 104.2 99.5294006760043 4.6705993239957 45 112.5 115.481577705754 -2.98157770575417 46 122.4 116.611890731042 5.78810926895758 47 113.3 111.363884284590 1.93611571540951 48 100 103.802702773683 -3.80270277368334 49 110.7 104.026354255197 6.67364574480314 50 112.8 107.237899613176 5.56210038682442 51 109.8 117.608788772696 -7.80878877269571 52 117.3 111.462889786702 5.83711021329785 53 109.1 111.414051644662 -2.31405164466245 54 115.9 121.938866910529 -6.03886691052933 55 96 95.715006836657 0.284993163342916 56 99.8 104.907091107352 -5.10709110735165 57 116.8 118.493924611439 -1.69392461143858 58 115.7 115.506943400227 0.193056599773469 59 99.4 107.305408537183 -7.90540853718303 60 94.3 98.6098704509136 -4.30987045091357 61 91 98.4806109978699 -7.48061099786991 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.140058506450219 0.280117012900439 0.85994149354978 17 0.0757406705509501 0.151481341101900 0.92425932944905 18 0.0645880294779395 0.129176058955879 0.93541197052206 19 0.0585002604918368 0.117000520983674 0.941499739508163 20 0.0286398166777092 0.0572796333554184 0.97136018332229 21 0.0129714366354464 0.0259428732708927 0.987028563364554 22 0.0117209519827252 0.0234419039654505 0.988279048017275 23 0.0177914165478884 0.0355828330957767 0.982208583452112 24 0.0105042347542599 0.0210084695085197 0.98949576524574 25 0.0144555510392413 0.0289111020784826 0.98554444896076 26 0.0154076084732892 0.0308152169465784 0.98459239152671 27 0.0223192718164748 0.0446385436329497 0.977680728183525 28 0.0223825902642352 0.0447651805284705 0.977617409735765 29 0.0785229953038979 0.157045990607796 0.921477004696102 30 0.0482601649745072 0.0965203299490145 0.951739835025493 31 0.0356490392624704 0.0712980785249409 0.96435096073753 32 0.0217194656613200 0.0434389313226399 0.97828053433868 33 0.0121900291652416 0.0243800583304833 0.987809970834758 34 0.0144988050793576 0.0289976101587152 0.985501194920642 35 0.0167333894459201 0.0334667788918402 0.98326661055408 36 0.0116802211146264 0.0233604422292528 0.988319778885374 37 0.0208223761479193 0.0416447522958385 0.97917762385208 38 0.0167832596256781 0.0335665192513562 0.983216740374322 39 0.0398077114702466 0.0796154229404932 0.960192288529753 40 0.0314232235915867 0.0628464471831735 0.968576776408413 41 0.0267043194765463 0.0534086389530926 0.973295680523454 42 0.0321086770431088 0.0642173540862177 0.96789132295689 43 0.0305565025995837 0.0611130051991673 0.969443497400416 44 0.312596494649785 0.625192989299569 0.687403505350215 45 0.250821773416507 0.501643546833013 0.749178226583493 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 15 0.5 NOK 10% type I error level 23 0.766666666666667 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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