Multiple Regression Monthly Dummies Werkloosheid Inflatie

*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, 17 Dec 2009 07:03:58 -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/17/t1261058705c8kxk2cmzjohkel.htm/, Retrieved Thu, 17 Dec 2009 15:05:17 +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/17/t1261058705c8kxk2cmzjohkel.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:

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Dataseries X:

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9.3 4 9.3 3.8 8.7 4.7 8.2 4.3 8.3 3.9 8.5 4 8.6 4.3 8.5 4.8 8.2 4.4 8.1 4.3 7.9 4.7 8.6 4.7 8.7 4.9 8.7 5 8.5 4.2 8.4 4.3 8.5 4.8 8.7 4.8 8.7 4.8 8.6 4.2 8.5 4.6 8.3 4.8 8 4.5 8.2 4.4 8.1 4.3 8.1 3.9 8 3.7 7.9 4 7.9 4.1 8 3.7 8 3.8 7.9 3.8 8 3.8 7.7 3.3 7.2 3.3 7.5 3.3 7.3 3.2 7 3.4 7 4.2 7 4.9 7.2 5.1 7.3 5.5 7.1 5.6 6.8 6.4 6.4 6.1 6.1 7.1 6.5 7.8 7.7 7.9 7.9 7.4 7.5 7.5 6.9 6.8 6.6 5.2 6.9 4.7 7.7 4.1 8 3.9 8 2.6 7.7 2.7 7.3 1.8 7.4 1 8.1 0.3

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 werklh[t] = + 8.64886359752554 -0.152636795515909inflatie[t] + 0.337687549130172M1[t] + 0.191582077309546M2[t] -0.108417922690454M3[t] -0.335892545883318M4[t] -0.198945281793636M5[t] + 0.065791038654773M6[t] + 0.114949246385727M7[t] -0.0233671690761815M8[t] -0.229472640896818M9[t] -0.498630848627772M10[t] -0.598630848627772M11[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) 8.64886359752554 0.411208 21.0328 0 0 inflatie -0.152636795515909 0.06471 -2.3588 0.022544 0.011272 M1 0.337687549130172 0.444683 0.7594 0.451412 0.225706 M2 0.191582077309546 0.44445 0.4311 0.668399 0.3342 M3 -0.108417922690454 0.44445 -0.2439 0.808341 0.40417 M4 -0.335892545883318 0.443584 -0.7572 0.452695 0.226348 M5 -0.198945281793636 0.443507 -0.4486 0.655801 0.3279 M6 0.065791038654773 0.443176 0.1485 0.88262 0.44131 M7 0.114949246385727 0.443363 0.2593 0.796562 0.398281 M8 -0.0233671690761815 0.443023 -0.0527 0.958159 0.479079 M9 -0.229472640896818 0.44294 -0.5181 0.606841 0.303421 M10 -0.498630848627772 0.442843 -1.126 0.265892 0.132946 M11 -0.598630848627772 0.442843 -1.3518 0.182913 0.091456 Multiple Linear Regression - Regression Statistics Multiple R 0.470499971547118 R-squared 0.221370223225839 Adjusted R-squared 0.0225711312835001 F-TEST (value) 1.11353739628774 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.372158752790684 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.700050093722839 Sum Squared Residuals 23.0332962849037 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9.3 8.37600396459213 0.923996035407869 2 9.3 8.26042585187464 1.03957414812536 3 8.7 7.82305273591032 0.876947264089681 4 8.2 7.65663283092382 0.543367169076181 5 8.3 7.85463481321986 0.445365186780136 6 8.5 8.10410745411668 0.395892545883319 7 8.6 8.10747462319286 0.492525376807137 8 8.5 7.892839809973 0.607160190027 9 8.2 7.74778905635873 0.452210943641272 10 8.1 7.49389452817936 0.606105471820636 11 7.9 7.332839809973 0.567160190027 12 8.6 7.93147065860077 0.668529341399227 13 8.7 8.23863084862776 0.461369151372237 14 8.7 8.07726169725555 0.622738302744454 15 8.5 7.89937113366827 0.600628866331727 16 8.4 7.65663283092382 0.743367169076182 17 8.5 7.71726169725555 0.782738302744454 18 8.7 7.98199801770395 0.718001982296045 19 8.7 8.03115622543491 0.66884377456509 20 8.6 7.98442188728255 0.615578112717454 21 8.5 7.71726169725555 0.782738302744455 22 8.3 7.41757613042141 0.882423869578592 23 8 7.36336716907618 0.636632830923818 24 8.2 7.97726169725555 0.222738302744454 25 8.1 8.3302129259373 -0.230212925937309 26 8.1 8.24516217232305 -0.145162172323046 27 8 7.97568953142623 0.0243104685737725 28 7.9 7.70242386957859 0.197576130421409 29 7.9 7.82410745411668 0.075892545883318 30 8 8.14989849277145 -0.149898492771455 31 8 8.18379302095082 -0.183793020950818 32 7.9 8.04547660548891 -0.145476605488909 33 8 7.83937113366827 0.160628866331727 34 7.7 7.64653132369527 0.0534686763047275 35 7.2 7.54653132369527 -0.346531323695273 36 7.5 8.14516217232305 -0.645162172323045 37 7.3 8.49811340100481 -1.19811340100481 38 7 8.321480570081 -1.321480570081 39 7 7.89937113366827 -0.899371133668273 40 7 7.56505075361427 -0.565050753614273 41 7.2 7.67147065860077 -0.471470658600773 42 7.3 7.87515226084282 -0.575152260842818 43 7.1 7.90904678902218 -0.809046789022182 44 6.8 7.64862093714754 -0.848620937147545 45 6.4 7.48830650398168 -1.08830650398168 46 6.1 7.06651150073482 -0.966511500734817 47 6.5 6.85966574387368 -0.359665743873681 48 7.7 7.44303291294986 0.256967087050138 49 7.9 7.85703885983799 0.0429611401620114 50 7.5 7.69566970846577 -0.195669708465772 51 6.9 7.5025154653269 -0.602515465326908 52 6.6 7.5192597149595 -0.9192597149595 53 6.9 7.73252537680714 -0.832525376807136 54 7.7 8.08884377456509 -0.388843774565091 55 8 8.16852934139923 -0.168529341399227 56 8 8.228640760108 -0.228640760108001 57 7.7 8.00727160873577 -0.307271608735773 58 7.3 7.87548651696914 -0.575486516969137 59 7.4 7.89759595338186 -0.497595953381864 60 8.1 8.60307255887077 -0.503072558870774 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0441601440123017 0.0883202880246034 0.955839855987698 17 0.0512893989796171 0.102578797959234 0.948710601020383 18 0.0362467586697153 0.0724935173394306 0.963753241330285 19 0.0186309316381073 0.0372618632762146 0.981369068361893 20 0.00852684587697217 0.0170536917539443 0.991473154123028 21 0.0071582124452837 0.0143164248905674 0.992841787554716 22 0.0072333048616348 0.0144666097232696 0.992766695138365 23 0.00479343701728209 0.00958687403456418 0.995206562982718 24 0.00483508283569228 0.00967016567138457 0.995164917164308 25 0.0376194783186476 0.0752389566372952 0.962380521681352 26 0.102622640575444 0.205245281150887 0.897377359424556 27 0.120070094293479 0.240140188586958 0.879929905706521 28 0.137705397027821 0.275410794055643 0.862294602972179 29 0.151290465820174 0.302580931640348 0.848709534179826 30 0.133111577593264 0.266223155186529 0.866888422406736 31 0.113621767553190 0.227243535106380 0.88637823244681 32 0.0974169105147965 0.194833821029593 0.902583089485203 33 0.108678047956071 0.217356095912142 0.891321952043929 34 0.129651880404803 0.259303760809606 0.870348119595197 35 0.090058539515817 0.180117079031634 0.909941460484183 36 0.0803103024760515 0.160620604952103 0.919689697523949 37 0.221560129211651 0.443120258423301 0.77843987078835 38 0.592415909877044 0.815168180245912 0.407584090122956 39 0.693213942783929 0.613572114432142 0.306786057216071 40 0.758141573250394 0.483716853499211 0.241858426749606 41 0.760092408003112 0.479815183993777 0.239907591996888 42 0.725688795815237 0.548622408369526 0.274311204184763 43 0.733290378803413 0.533419242393173 0.266709621196587 44 0.714811494783157 0.570377010433687 0.285188505216843 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0689655172413793 NOK 5% type I error level 6 0.206896551724138 NOK 10% type I error level 9 0.310344827586207 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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