Paper - Multiple Regression ECONOMISCHE SITUATIE 3 goed model

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R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 12 Dec 2008 14:45:14 -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/12/t1229118411wcwptyktes8fpka.htm/, Retrieved Fri, 12 Dec 2008 22:47:00 +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/2008/Dec/12/t1229118411wcwptyktes8fpka.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}, }

Original text written by user:

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Dataseries X:

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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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 44.5863157894737 -41.2736842105263D[t] -3.1393859649123M1[t] -0.713508771929829M2[t] + 0.512368421052628M3[t] + 2.33824561403509M4[t] + 1.16412280701754M5[t] -3.01000000000000M6[t] -3.78412280701754M7[t] + 1.49649122807017M8[t] + 3.12236842105263M9[t] + 1.14824561403508M10[t] + 1.17412280701754M11[t] -0.0258771929824561t + 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) 44.5863157894737 7.023227 6.3484 0 0 D -41.2736842105263 7.515307 -5.4919 2e-06 1e-06 M1 -3.1393859649123 8.582337 -0.3658 0.716194 0.358097 M2 -0.713508771929829 8.575479 -0.0832 0.934051 0.467025 M3 0.512368421052628 8.570141 0.0598 0.952586 0.476293 M4 2.33824561403509 8.566327 0.273 0.786107 0.393054 M5 1.16412280701754 8.564037 0.1359 0.892469 0.446234 M6 -3.01000000000000 8.563274 -0.3515 0.726817 0.363409 M7 -3.78412280701754 8.564037 -0.4419 0.660659 0.33033 M8 1.49649122807017 8.470555 0.1767 0.860543 0.430272 M9 3.12236842105263 8.465152 0.3688 0.713932 0.356966 M10 1.14824561403508 8.46129 0.1357 0.892646 0.446323 M11 1.17412280701754 8.458972 0.1388 0.890212 0.445106 t -0.0258771929824561 0.114342 -0.2263 0.821959 0.41098 Multiple Linear Regression - Regression Statistics Multiple R 0.698098851225719 R-squared 0.487342006082669 Adjusted R-squared 0.342460399106032 F-TEST (value) 3.36372584658904 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.00115547702335506 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 13.3735864541008 Sum Squared Residuals 8227.22947368421 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 34 41.421052631579 -7.421052631579 2 39 43.8210526315789 -4.82105263157894 3 40 45.0210526315789 -5.02105263157894 4 45 46.8210526315789 -1.82105263157895 5 43 45.6210526315789 -2.62105263157893 6 42 41.4210526315789 0.578947368421056 7 49 40.6210526315789 8.37894736842106 8 43 45.8757894736842 -2.87578947368420 9 50 47.4757894736842 2.52421052631579 10 44 45.4757894736842 -1.47578947368421 11 40 45.4757894736842 -5.47578947368421 12 41 44.2757894736842 -3.27578947368421 13 45 41.1105263157895 3.88947368421054 14 45 43.5105263157895 1.48947368421053 15 48 44.7105263157895 3.28947368421053 16 54 46.5105263157895 7.48947368421053 17 47 45.3105263157895 1.68947368421053 18 35 41.1105263157895 -6.11052631578947 19 28 40.3105263157895 -12.3105263157895 20 28 45.5652631578947 -17.5652631578947 21 34 47.1652631578947 -13.1652631578947 22 23 45.1652631578947 -22.1652631578947 23 33 45.1652631578947 -12.1652631578947 24 38 43.9652631578947 -5.96526315789474 25 41 40.8 0.200000000000014 26 47 43.2 3.80000000000000 27 46 44.4 1.6 28 45 46.2 -1.2 29 47 45 2.00000000000000 30 49 40.8 8.2 31 50 40 10 32 56 45.2547368421053 10.7452631578947 33 50 46.8547368421053 3.14526315789474 34 56 44.8547368421053 11.1452631578947 35 58 44.8547368421053 13.1452631578947 36 59 43.6547368421053 15.3452631578947 37 51 40.4894736842105 10.5105263157895 38 59 42.8894736842105 16.1105263157895 39 60 44.0894736842105 15.9105263157895 40 60 45.8894736842105 14.1105263157895 41 68 44.6894736842105 23.3105263157895 42 62 40.4894736842105 21.5105263157895 43 62 39.6894736842105 22.3105263157895 44 58 44.9442105263158 13.0557894736842 45 56 46.5442105263158 9.45578947368421 46 50 44.5442105263158 5.45578947368421 47 52 44.5442105263158 7.45578947368421 48 36 43.3442105263158 -7.3442105263158 49 33 40.178947368421 -7.17894736842104 50 26 42.5789473684211 -16.5789473684211 51 28 43.7789473684211 -15.7789473684211 52 27 45.5789473684211 -18.5789473684211 53 20 44.3789473684211 -24.3789473684211 54 16 40.1789473684211 -24.1789473684211 55 11 39.3789473684211 -28.3789473684211 56 0 3.36 -3.36 57 3 4.96 -1.96 58 10 2.96 7.04 59 0 2.96 -2.96 60 3 1.76000000000000 1.24000000000000 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00337679926164954 0.00675359852329908 0.99662320073835 18 0.0162969429053556 0.0325938858107113 0.983703057094644 19 0.0831081195222278 0.166216239044456 0.916891880477772 20 0.0821366799202358 0.164273359840472 0.917863320079764 21 0.0741728698273694 0.148345739654739 0.92582713017263 22 0.117600091765887 0.235200183531775 0.882399908234113 23 0.103008972048089 0.206017944096177 0.896991027951911 24 0.0838484708137524 0.167696941627505 0.916151529186248 25 0.0652473047272723 0.130494609454545 0.934752695272728 26 0.0517404585641453 0.103480917128291 0.948259541435855 27 0.0387795004911771 0.0775590009823541 0.961220499508823 28 0.0308546435814939 0.0617092871629878 0.969145356418506 29 0.0292885496657432 0.0585770993314865 0.970711450334257 30 0.0371348960506908 0.0742697921013815 0.96286510394931 31 0.0486216967045061 0.0972433934090123 0.951378303295494 32 0.0899548257494895 0.179909651498979 0.91004517425051 33 0.142221954545445 0.28444390909089 0.857778045454555 34 0.328925466664653 0.657850933329307 0.671074533335347 35 0.54884903822461 0.902301923550779 0.451150961775390 36 0.712918389681287 0.574163220637425 0.287081610318713 37 0.838588053889994 0.322823892220013 0.161411946110006 38 0.800304046755329 0.399391906489342 0.199695953244671 39 0.791802231611878 0.416395536776243 0.208197768388122 40 0.823230784775394 0.353538430449212 0.176769215224606 41 0.732037543449784 0.535924913100431 0.267962456550216 42 0.610541892244972 0.778916215510056 0.389458107755028 43 0.443063435333831 0.886126870667662 0.556936564666169 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0370370370370370 NOK 5% type I error level 2 0.0740740740740741 NOK 10% type I error level 7 0.259259259259259 NOK

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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