deterministische 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: Wed, 01 Dec 2010 21:57:34 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/01/t1291240583d7x0l2ih118qc5n.htm/, Retrieved Wed, 01 Dec 2010 22:56:33 +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/2010/Dec/01/t1291240583d7x0l2ih118qc5n.htm/}, year = {2010}, } @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 = {2010}, 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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11 0 8 17 2 6 10 -2 3 23 3 7 9 -4 3 24 1 4 8 -4 7 27 1 3 7 -7 4 31 0 0 6 -9 -4 40 1 6 5 -13 -6 47 -1 3 4 -8 8 43 2 1 3 -13 2 60 2 6 2 -15 -1 64 0 5 1 -15 -2 65 1 7 12 -15 0 65 1 4 11 -10 10 55 3 3 10 -12 3 57 3 6 9 -11 6 57 1 6 8 -11 7 57 1 5 7 -17 -4 65 -2 2 6 -18 -5 69 1 3 5 -19 -7 70 1 -2 4 -22 -10 71 -1 -4 3 -24 -21 71 -4 0 2 -24 -22 73 -2 1 1 -20 -16 68 -1 4 12 -25 -25 65 -5 -3 11 -22 -22 57 -4 -3 10 -17 -22 41 -5 0 9 -9 -19 21 0 6 8 -11 -21 21 -2 -1 7 -13 -31 17 -4 0 6 -11 -28 9 -6 -1 5 -9 -23 11 -2 1 4 -7 -17 6 -2 -4 3 -3 -12 -2 -2 -1 2 -3 -14 0 1 -1 1 -6 -18 5 -2 0 12 -4 -16 3 0 3 11 -8 -22 7 -1 0 10 -1 -9 4 2 8 9 -2 -10 8 3 8 8 -2 -10 9 2 8 7 -1 0 14 3 8 6 1 3 12 4 11 5 2 2 12 5 13 4 2 4 7 5 5 3 -1 -3 15 4 12 2 1 0 14 5 13 1 -1 -1 19 6 9 12 -8 -7 39 4 11 11 1 2 12 6 7 10 2 3 11 6 12 9 -2 -3 17 3 11 8 -2 -5 16 5 10 7 -2 0 25 5 13 6 -2 -3 24 5 14 5 -6 -7 28 3 10 4 -4 -7 25 5 13 3 -5 -7 31 5 12 2 -2 -4 24 6 13 1 -1 -3 24 6 17 12 -5 -6 33 5 15

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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation werkloosheid[t] = + 1.85423823704046 -0.114537989510701maand[t] -3.92322970510058indicator[t] + 0.973210530445734economie[t] + 1.09728386413799`financiën`[t] + 0.908015384045378spaarvermogen[t] -0.0221617445973184t + 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) 1.85423823704046 0.620938 2.9862 0.004269 0.002135 maand -0.114537989510701 0.044347 -2.5828 0.012598 0.006299 indicator -3.92322970510058 0.030814 -127.3206 0 0 economie 0.973210530445734 0.03735 26.0563 0 0 `financiën` 1.09728386413799 0.155836 7.0413 0 0 spaarvermogen 0.908015384045378 0.057907 15.6805 0 0 t -0.0221617445973184 0.019223 -1.1529 0.254136 0.127068 Multiple Linear Regression - Regression Statistics Multiple R 0.998851623219125 R-squared 0.99770456520748 Adjusted R-squared 0.99744470466493 F-TEST (value) 3839.38459998337 F-TEST (DF numerator) 6 F-TEST (DF denominator) 53 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.16791092469633 Sum Squared Residuals 72.2928441853268 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 17 16.0005028839395 0.999497116060498 2 23 21.0785851350088 1.92141486499121 3 24 24.0988069097113 -0.0988069097112732 4 27 27.1760098923622 -0.176009892362197 5 31 32.2971136449659 -1.29711364496594 6 40 38.9956412249249 1.00435877507512 7 47 47.915901348937 -0.915901348936988 8 43 43.492897318911 -0.492897318910983 9 60 61.9022358268797 -1.90223582687975 10 64 63.8188567783357 0.181143221664279 11 65 65.8513371250321 -0.851337125032118 12 65 63.7916324045724 1.20836759542759 13 55 55.2865177726709 -0.286517772670855 14 57 59.1369258668014 -2.13692586680139 15 57 56.0311362696754 0.968863730324596 16 57 56.1887076609892 0.81129233901085 17 65 63.0992485570528 1.90075144294720 18 69 70.3415109530804 -1.34151095308039 19 70 67.870618921976 2.12938107802400 20 71 72.8024541944872 -1.80245419448717 21 71 70.3761839584662 0.623816041533841 22 73 72.5979327852552 0.402067214744819 23 68 66.6579834087148 1.34201659128521 24 65 65.4879143861214 -0.487914386121406 25 57 57.8275169712083 -0.827516971208253 26 41 39.9305069786169 1.06949302138312 27 21 22.4911887990251 -1.49118879902508 28 21 19.9329279766545 1.06707202334548 29 17 16.8531059830811 0.146894016918893 30 9 8.91607129680916 0.0839287031908366 31 11 12.2332070083928 -1.23320700839280 32 6 5.77831010555254 0.221689894447462 33 -2 -2.23213366557159 0.232133665571593 34 0 -0.79432688913569 0.79432688913569 35 5 4.79106014092789 0.208939859072115 36 3 2.52755604281528 0.472443957184719 37 7 8.65225790918245 -1.65225790918244 38 4 4.48973777896333 -0.489737778963332 39 8 8.62941706266955 -0.629417062669553 40 9 7.62450944344495 1.37549055655505 41 14 14.6230451518531 -0.623045151853085 42 12 13.6099235941766 -1.60992359417664 43 12 11.7191742357725 0.280825764227542 44 7 6.4938484692143 0.506151530785706 45 15 16.8022639404889 -1.80226394048892 46 14 13.9731116147217 0.026888385278277 47 19 18.4039590673470 0.596040932652981 48 39 38.3666872309764 0.633312769023607 49 12 10.4713970960906 1.52860290390936 50 11 12.1538310865761 -1.15383108657607 51 17 17.899995992758 -0.899995992758005 52 16 17.3325035210105 -1.33250352101054 53 25 25.0149785702887 -0.0149785702887253 54 24 23.0957386079103 0.904261392089716 55 28 29.1615622869855 -1.16156228698554 56 25 26.3260930021099 -1.32609300210989 57 31 29.4336835680785 1.56631643192152 58 24 22.6813015372107 1.31869846278930 59 24 23.4557201436508 0.544279856349244 60 33 32.0336131112721 0.966386888727928 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.32327220229585 0.6465444045917 0.67672779770415 11 0.380006792593185 0.76001358518637 0.619993207406815 12 0.254404327279232 0.508808654558463 0.745595672720768 13 0.30661902010617 0.61323804021234 0.69338097989383 14 0.629059702566752 0.741880594866495 0.370940297433248 15 0.615922165350405 0.76815566929919 0.384077834649595 16 0.535209096065173 0.929581807869653 0.464790903934827 17 0.593962737103193 0.812074525793615 0.406037262896807 18 0.536659292798307 0.926681414403386 0.463340707201693 19 0.82753150243192 0.344936995136159 0.172468497568080 20 0.913591031550603 0.172817936898793 0.0864089684493967 21 0.882051270552776 0.235897458894449 0.117948729447224 22 0.834932217117616 0.330135565764768 0.165067782882384 23 0.807446163643747 0.385107672712507 0.192553836356253 24 0.830957366224274 0.338085267551451 0.169042633775726 25 0.860957663933353 0.278084672133293 0.139042336066647 26 0.847177977473803 0.305644045052394 0.152822022526197 27 0.90231194359172 0.19537611281656 0.09768805640828 28 0.896524234978885 0.20695153004223 0.103475765021115 29 0.860246355168403 0.279507289663195 0.139753644831597 30 0.838327838541057 0.323344322917886 0.161672161458943 31 0.8164013266059 0.367197346788199 0.183598673394100 32 0.763425690522437 0.473148618955125 0.236574309477563 33 0.719052505385213 0.561894989229575 0.280947494614787 34 0.673283211176698 0.653433577646604 0.326716788823302 35 0.654159067049983 0.691681865900035 0.345840932950017 36 0.640024117798433 0.719951764403134 0.359975882201567 37 0.64481205042535 0.710375899149299 0.355187949574650 38 0.561033848369394 0.877932303261212 0.438966151630606 39 0.523491474917227 0.953017050165545 0.476508525082773 40 0.781278860269605 0.437442279460789 0.218721139730395 41 0.738362873940004 0.523274252119992 0.261637126059996 42 0.725862808902707 0.548274382194585 0.274137191097293 43 0.708915917921986 0.582168164156027 0.291084082078014 44 0.62716373174987 0.74567253650026 0.37283626825013 45 0.553057366593667 0.893885266812665 0.446942633406333 46 0.530381441244163 0.939237117511674 0.469618558755837 47 0.421578206892999 0.843156413785999 0.578421793107001 48 0.373213224640305 0.74642644928061 0.626786775359695 49 0.386105985024137 0.772211970048273 0.613894014975863 50 0.298835307952802 0.597670615905603 0.701164692047198 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 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal 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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