Paper - Regressie analyse - Enkel dummy variabele

*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: Wed, 10 Dec 2008 13:26:13 -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/10/t1228941019h7pwzyjjurvlft6.htm/, Retrieved Wed, 10 Dec 2008 20:30:41 +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/10/t1228941019h7pwzyjjurvlft6.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:

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User-defined keywords:

Dataseries X:

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108,00 0 99,00 0 108,00 0 104,00 0 111,00 0 110,00 0 106,00 0 101,00 0 102,00 0 99,00 0 100,00 0 98,00 0 92,00 1 87,00 1 79,00 1 87,00 1 87,00 1 88,00 1 83,00 1 85,00 1 92,00 1 84,00 1 92,00 1 98,00 1 103,00 0 104,00 0 109,00 0 107,00 0 106,00 0 113,00 0 107,00 0 114,00 0 108,00 0 104,00 0 105,00 0 109,00 0 109,00 0 112,00 0 118,00 0 111,00 0 99,00 1 92,00 1 92,00 1 98,00 1 87,00 1 97,00 1 102,00 0 105,00 0 111,00 0 110,00 0 109,00 0 111,00 0 113,00 0 114,00 0 120,00 0 114,00 0 120,00 0 122,00 0 123,00 0 115,00 0 123,00 0 124,00 0 124,00 0 132,00 0 126,00 0 126,00 0 122,00 0 120,00 0 114,00 0 116,00 0 100,00 0 97,00 0

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 Consumentenvertrouwen[t] = + 111.074074074074 -21.1296296296296Dummy[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) 111.074074074074 1.060679 104.7198 0 0 Dummy -21.1296296296296 2.121357 -9.9604 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.765710939773387 R-squared 0.586313243288644 Adjusted R-squared 0.580403432478482 F-TEST (value) 99.2101544571356 F-TEST (DF numerator) 1 F-TEST (DF denominator) 70 p-value 4.66293670342566e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.79436440013658 Sum Squared Residuals 4252.64814814815 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 108 111.074074074074 -3.07407407407365 2 99 111.074074074074 -12.0740740740742 3 108 111.074074074074 -3.07407407407408 4 104 111.074074074074 -7.07407407407408 5 111 111.074074074074 -0.0740740740740797 6 110 111.074074074074 -1.07407407407408 7 106 111.074074074074 -5.07407407407408 8 101 111.074074074074 -10.0740740740741 9 102 111.074074074074 -9.07407407407408 10 99 111.074074074074 -12.0740740740741 11 100 111.074074074074 -11.0740740740741 12 98 111.074074074074 -13.0740740740741 13 92 89.9444444444444 2.05555555555555 14 87 89.9444444444444 -2.94444444444445 15 79 89.9444444444444 -10.9444444444444 16 87 89.9444444444444 -2.94444444444445 17 87 89.9444444444444 -2.94444444444445 18 88 89.9444444444444 -1.94444444444445 19 83 89.9444444444444 -6.94444444444445 20 85 89.9444444444444 -4.94444444444445 21 92 89.9444444444444 2.05555555555555 22 84 89.9444444444444 -5.94444444444445 23 92 89.9444444444444 2.05555555555555 24 98 89.9444444444444 8.05555555555555 25 103 111.074074074074 -8.07407407407408 26 104 111.074074074074 -7.07407407407408 27 109 111.074074074074 -2.07407407407408 28 107 111.074074074074 -4.07407407407408 29 106 111.074074074074 -5.07407407407408 30 113 111.074074074074 1.92592592592592 31 107 111.074074074074 -4.07407407407408 32 114 111.074074074074 2.92592592592592 33 108 111.074074074074 -3.07407407407408 34 104 111.074074074074 -7.07407407407408 35 105 111.074074074074 -6.07407407407408 36 109 111.074074074074 -2.07407407407408 37 109 111.074074074074 -2.07407407407408 38 112 111.074074074074 0.92592592592592 39 118 111.074074074074 6.92592592592592 40 111 111.074074074074 -0.0740740740740797 41 99 89.9444444444444 9.05555555555555 42 92 89.9444444444444 2.05555555555555 43 92 89.9444444444444 2.05555555555555 44 98 89.9444444444444 8.05555555555555 45 87 89.9444444444444 -2.94444444444445 46 97 89.9444444444444 7.05555555555555 47 102 111.074074074074 -9.07407407407408 48 105 111.074074074074 -6.07407407407408 49 111 111.074074074074 -0.0740740740740797 50 110 111.074074074074 -1.07407407407408 51 109 111.074074074074 -2.07407407407408 52 111 111.074074074074 -0.0740740740740797 53 113 111.074074074074 1.92592592592592 54 114 111.074074074074 2.92592592592592 55 120 111.074074074074 8.92592592592592 56 114 111.074074074074 2.92592592592592 57 120 111.074074074074 8.92592592592592 58 122 111.074074074074 10.9259259259259 59 123 111.074074074074 11.9259259259259 60 115 111.074074074074 3.92592592592592 61 123 111.074074074074 11.9259259259259 62 124 111.074074074074 12.9259259259259 63 124 111.074074074074 12.9259259259259 64 132 111.074074074074 20.9259259259259 65 126 111.074074074074 14.9259259259259 66 126 111.074074074074 14.9259259259259 67 122 111.074074074074 10.9259259259259 68 120 111.074074074074 8.92592592592592 69 114 111.074074074074 2.92592592592592 70 116 111.074074074074 4.92592592592592 71 100 111.074074074074 -11.0740740740741 72 97 111.074074074074 -14.0740740740741 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.290886754298317 0.581773508596634 0.709113245701683 6 0.188607897139438 0.377215794278876 0.811392102860562 7 0.0977543346945003 0.195508669389001 0.9022456653055 8 0.086155172814742 0.172310345629484 0.913844827185258 9 0.0598001297792977 0.119600259558595 0.940199870220702 10 0.0680440786003055 0.136088157200611 0.931955921399694 11 0.0594455884320059 0.118891176864012 0.940554411567994 12 0.071889624242719 0.143779248485438 0.928110375757281 13 0.0417454839360989 0.0834909678721979 0.958254516063901 14 0.0287392839156515 0.057478567831303 0.971260716084348 15 0.0545732452872916 0.109146490574583 0.945426754712708 16 0.033727142142175 0.06745428428435 0.966272857857825 17 0.0201839056178297 0.0403678112356593 0.97981609438217 18 0.0119276234810040 0.0238552469620080 0.988072376518996 19 0.00912587006045215 0.0182517401209043 0.990874129939548 20 0.00567056036110966 0.0113411207222193 0.99432943963889 21 0.00527469995162996 0.0105493999032599 0.99472530004837 22 0.00391354682446992 0.00782709364893983 0.99608645317553 23 0.00344851720430606 0.00689703440861213 0.996551482795694 24 0.00980813465708063 0.0196162693141613 0.99019186534292 25 0.00741042720184144 0.0148208544036829 0.992589572798159 26 0.00540105595786691 0.0108021119157338 0.994598944042133 27 0.00459211257406406 0.00918422514812812 0.995407887425936 28 0.00330742496821655 0.0066148499364331 0.996692575031783 29 0.00234606395863053 0.00469212791726107 0.99765393604137 30 0.00332707427518605 0.0066541485503721 0.996672925724814 31 0.00236756555197643 0.00473513110395286 0.997632434448024 32 0.00340142220488332 0.00680284440976664 0.996598577795117 33 0.00242070300900563 0.00484140601801126 0.997579296990994 34 0.00215781666847740 0.00431563333695479 0.997842183331523 35 0.00182484522739411 0.00364969045478822 0.998175154772606 36 0.00140108396512042 0.00280216793024083 0.99859891603488 37 0.00107550775818040 0.00215101551636080 0.99892449224182 38 0.000999518981300081 0.00199903796260016 0.9990004810187 39 0.00254659017431202 0.00509318034862404 0.997453409825688 40 0.00196847147371695 0.00393694294743391 0.998031528526283 41 0.00358462408976365 0.00716924817952729 0.996415375910236 42 0.00230160090254899 0.00460320180509798 0.99769839909745 43 0.00143865369312538 0.00287730738625075 0.998561346306875 44 0.00169532384248639 0.00339064768497277 0.998304676157514 45 0.00128976389493788 0.00257952778987576 0.998710236105062 46 0.00110214250077499 0.00220428500154997 0.998897857499225 47 0.00206534833513455 0.00413069667026911 0.997934651664866 48 0.00255562473637469 0.00511124947274938 0.997444375263625 49 0.00209597986055727 0.00419195972111453 0.997904020139443 50 0.00178292218042142 0.00356584436084284 0.998217077819579 51 0.00167921400467411 0.00335842800934823 0.998320785995326 52 0.00147540862713327 0.00295081725426654 0.998524591372867 53 0.00127766948684567 0.00255533897369134 0.998722330513154 54 0.00111088901340006 0.00222177802680012 0.9988891109866 55 0.00164849193332294 0.00329698386664587 0.998351508066677 56 0.00130531442047431 0.00261062884094862 0.998694685579526 57 0.00153362570019993 0.00306725140039985 0.9984663742998 58 0.00212614593569359 0.00425229187138718 0.997873854064306 59 0.00296835699321475 0.0059367139864295 0.997031643006785 60 0.00190148631215023 0.00380297262430047 0.99809851368785 61 0.00217303578684728 0.00434607157369456 0.997826964213153 62 0.00263024289297798 0.00526048578595595 0.997369757107022 63 0.00293209512668572 0.00586419025337145 0.997067904873314 64 0.0187989488548523 0.0375978977097045 0.981201051145148 65 0.0305156748490222 0.0610313496980444 0.969484325150978 66 0.0603901885262018 0.120780377052404 0.939609811473798 67 0.077767762332227 0.155535524664454 0.922232237667773 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 39 0.619047619047619 NOK 5% type I error level 48 0.761904761904762 NOK 10% type I error level 52 0.825396825396825 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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