Paper Regressie analyse (Seasonal Dummies + Linear Trend)

*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: Sat, 19 Dec 2009 03:57:36 -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/Dec/19/t1261220352b7hn9jdls169af4.htm/, Retrieved Sat, 19 Dec 2009 11:59:24 +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/Dec/19/t1261220352b7hn9jdls169af4.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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84 0 78 0 74 0 75 0 79 0 79 0 82 0 88 0 81 0 69 1 62 1 62 1 68 1 57 1 67 1 72 0 75 0 81 0 80 0 79 0 81 0 83 0 84 0 90 0 84 0 90 0 92 0 93 0 85 0 93 0 94 0 94 0 102 0 96 0 96 0 92 0 90 0 84 0 86 0 70 0 67 1 60 1 62 1 61 1 54 1 50 1 45 1 34 1 37 1 44 1 34 1 37 1 31 1 31 1 28 1 31 1 33 1 36 1 39 1 42 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 Consumentenvertrouwen[t] = + 93.1815812337098 -33.2632493483927Dummy[t] -0.870981754995648M1[t] -2.61476976542136M2[t] -2.35855777584706M3[t] -9.95499565595133M4[t] -5.04613379669851M5[t] -3.38992180712423M6[t] -2.73370981754994M7[t] -1.07749782797566M8[t] -1.22128583840137M9[t] + 2.28757602085144M10[t] + 0.943788010425726M11[t] -0.256211989574283t + 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) 93.1815812337098 5.799247 16.0679 0 0 Dummy -33.2632493483927 3.570317 -9.3166 0 0 M1 -0.870981754995648 7.054806 -0.1235 0.902281 0.451141 M2 -2.61476976542136 7.045201 -0.3711 0.712236 0.356118 M3 -2.35855777584706 7.03705 -0.3352 0.739026 0.369513 M4 -9.95499565595133 7.092537 -1.4036 0.167157 0.083578 M5 -5.04613379669851 7.025131 -0.7183 0.476207 0.238103 M6 -3.38992180712423 7.021371 -0.4828 0.631527 0.315764 M7 -2.73370981754994 7.01908 -0.3895 0.698727 0.349364 M8 -1.07749782797566 7.01826 -0.1535 0.878654 0.439327 M9 -1.22128583840137 7.018912 -0.174 0.86263 0.431315 M10 2.28757602085144 6.996279 0.327 0.745174 0.372587 M11 0.943788010425726 6.994065 0.1349 0.893247 0.446624 t -0.256211989574283 0.101625 -2.5212 0.015226 0.007613 Multiple Linear Regression - Regression Statistics Multiple R 0.89104115125093 R-squared 0.793954333222582 Adjusted R-squared 0.735724036089833 F-TEST (value) 13.6347292099951 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.0915823800417e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.0574195977528 Sum Squared Residuals 5624.26029539531 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 84 92.05438748914 -8.05438748913993 2 78 90.05438748914 -12.0543874891399 3 74 90.0543874891399 -16.0543874891399 4 75 82.2017376194613 -7.20173761946134 5 79 86.8543874891399 -7.85438748913987 6 79 88.2543874891399 -9.25438748913988 7 82 88.6543874891399 -6.65438748913987 8 88 90.0543874891399 -2.05438748913987 9 81 89.6543874891399 -8.65438748913987 10 69 59.6437880104257 9.35621198957428 11 62 58.0437880104257 3.95621198957428 12 62 56.8437880104257 5.15621198957431 13 68 55.7165942658558 12.2834057341442 14 57 53.7165942658558 3.28340573414423 15 67 53.7165942658558 13.2834057341442 16 72 79.12719374457 -7.12719374456993 17 75 83.7798436142485 -8.77984361424848 18 81 85.1798436142485 -4.17984361424847 19 80 85.5798436142485 -5.57984361424847 20 79 86.9798436142485 -7.97984361424848 21 81 86.5798436142485 -5.57984361424848 22 83 89.832493483927 -6.83249348392702 23 84 88.232493483927 -4.23249348392701 24 90 87.032493483927 2.96750651607299 25 84 85.905299739357 -1.90529973935707 26 90 83.905299739357 6.09470026064293 27 92 83.9052997393571 8.0947002606429 28 93 76.0526498696785 16.9473501303215 29 85 80.705299739357 4.29470026064292 30 93 82.105299739357 10.8947002606429 31 94 82.505299739357 11.4947002606429 32 94 83.905299739357 10.0947002606429 33 102 83.505299739357 18.4947002606429 34 96 86.7579496090356 9.24205039096438 35 96 85.1579496090356 10.8420503909644 36 92 83.9579496090356 8.0420503909644 37 90 82.8307558644657 7.16924413553433 38 84 80.8307558644657 3.16924413553433 39 86 80.8307558644657 5.1692441355343 40 70 72.9781059947871 -2.97810599478714 41 67 44.367506516073 22.632493483927 42 60 45.767506516073 14.232493483927 43 62 46.167506516073 15.832493483927 44 61 47.567506516073 13.4324934839270 45 54 47.167506516073 6.83249348392702 46 50 50.4201563857515 -0.420156385751522 47 45 48.8201563857515 -3.82015638575152 48 34 47.6201563857515 -13.6201563857515 49 37 46.4929626411816 -9.49296264118157 50 44 44.4929626411816 -0.492962641181577 51 34 44.4929626411816 -10.4929626411816 52 37 36.6403127715030 0.359687228496953 53 31 41.2929626411816 -10.2929626411816 54 31 42.6929626411816 -11.6929626411816 55 28 43.0929626411816 -15.0929626411816 56 31 44.4929626411816 -13.4929626411816 57 33 44.0929626411816 -11.0929626411816 58 36 47.3456125108601 -11.3456125108601 59 39 45.7456125108601 -6.74561251086012 60 42 44.5456125108601 -2.54561251086011 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0659047241063968 0.131809448212794 0.934095275893603 18 0.0297111611494699 0.0594223222989398 0.97028883885053 19 0.0103672635080771 0.0207345270161542 0.989632736491923 20 0.00880957773685352 0.0176191554737070 0.991190422263146 21 0.00505576632501252 0.0101115326500250 0.994944233674987 22 0.00324847979850001 0.00649695959700002 0.9967515202015 23 0.00727057772828894 0.0145411554565779 0.992729422271711 24 0.0182470701931241 0.0364941403862483 0.981752929806876 25 0.0142795002942529 0.0285590005885059 0.985720499705747 26 0.0457051771763883 0.0914103543527767 0.954294822823612 27 0.0535149119489017 0.107029823897803 0.946485088051098 28 0.109117737587914 0.218235475175828 0.890882262412086 29 0.115343280496795 0.230686560993591 0.884656719503204 30 0.0953312565992573 0.190662513198515 0.904668743400743 31 0.0731028301970874 0.146205660394175 0.926897169802913 32 0.0508556791375938 0.101711358275188 0.949144320862406 33 0.0648502731343017 0.129700546268603 0.935149726865698 34 0.0390403328589231 0.0780806657178462 0.960959667141077 35 0.0241211488264090 0.0482422976528179 0.97587885117359 36 0.0128894357483336 0.0257788714966673 0.987110564251666 37 0.0103214246652685 0.0206428493305370 0.989678575334731 38 0.00691351553868716 0.0138270310773743 0.993086484461313 39 0.0074876189100448 0.0149752378200896 0.992512381089955 40 0.0141397620704736 0.0282795241409473 0.985860237929526 41 0.0154773560506687 0.0309547121013374 0.984522643949331 42 0.0157374191002465 0.031474838200493 0.984262580899753 43 0.0322384415687917 0.0644768831375834 0.967761558431208 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 15 0.555555555555556 NOK 10% type I error level 19 0.703703703703704 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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