Paper - Regressi analyse - geen seizoenaliteit en 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: Sun, 07 Dec 2008 06:21:59 -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/07/t1228656270yg3y31er14iyb26.htm/, Retrieved Sun, 07 Dec 2008 13:24:40 +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/07/t1228656270yg3y31er14iyb26.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)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

95.2 0 95.00 0 94.00 0 92.2 0 91.00 0 91.2 0 103.4 1 105.00 1 104.6 1 103.8 0 101.8 0 102.4 0 103.8 0 103.4 0 102.00 0 101.8 0 100.2 0 101.4 0 113.8 1 116.00 1 115.6 1 113.00 0 109.4 0 111.00 0 112.4 0 112.2 0 111.00 0 108.8 0 107.4 0 108.6 0 118.8 1 122.2 1 122.6 1 122.2 0 118.8 0 119.00 0 118.2 0 117.8 0 116.8 0 114.6 0 113.4 0 113.8 0 124.2 1 125.8 1 125.6 1 122.4 0 119.00 0 119.4 0 118.6 0 118.00 0 116.00 0 114.8 0 114.6 0 114.6 0 124.00 1 125.2 1 124.00 1 117.6 0 113.2 0 111.4 0 112.2 0 109.8 0 106.4 0 105.2 0 102.2 0 99.8 0 111.00 1 113.00 1 108.4 1 105.4 0 102.00 0 102.8 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 Werkloosheid[t] = + 108.759259259259 + 8.08518518518518dummy[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) 108.759259259259 1.124813 96.6909 0 0 dummy 8.08518518518518 2.249627 3.594 0.000602 0.000301 Multiple Linear Regression - Regression Statistics Multiple R 0.394691653181559 R-squared 0.155781501091192 Adjusted R-squared 0.143721236821067 F-TEST (value) 12.9169226811285 F-TEST (DF numerator) 1 F-TEST (DF denominator) 70 p-value 0.00060163810795455 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.26565598020319 Sum Squared Residuals 4782.47481481481 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.2 108.759259259259 -13.5592592592592 2 95 108.759259259259 -13.7592592592592 3 94 108.759259259259 -14.7592592592593 4 92.2 108.759259259259 -16.5592592592593 5 91 108.759259259259 -17.7592592592593 6 91.2 108.759259259259 -17.5592592592593 7 103.4 116.844444444444 -13.4444444444444 8 105 116.844444444444 -11.8444444444444 9 104.6 116.844444444444 -12.2444444444445 10 103.8 108.759259259259 -4.95925925925926 11 101.8 108.759259259259 -6.95925925925926 12 102.4 108.759259259259 -6.35925925925926 13 103.8 108.759259259259 -4.95925925925926 14 103.4 108.759259259259 -5.35925925925926 15 102 108.759259259259 -6.75925925925926 16 101.8 108.759259259259 -6.95925925925926 17 100.2 108.759259259259 -8.55925925925926 18 101.4 108.759259259259 -7.35925925925926 19 113.8 116.844444444444 -3.04444444444445 20 116 116.844444444444 -0.844444444444448 21 115.6 116.844444444444 -1.24444444444445 22 113 108.759259259259 4.24074074074074 23 109.4 108.759259259259 0.640740740740745 24 111 108.759259259259 2.24074074074074 25 112.4 108.759259259259 3.64074074074074 26 112.2 108.759259259259 3.44074074074074 27 111 108.759259259259 2.24074074074074 28 108.8 108.759259259259 0.0407407407407361 29 107.4 108.759259259259 -1.35925925925926 30 108.6 108.759259259259 -0.159259259259267 31 118.8 116.844444444444 1.95555555555555 32 122.2 116.844444444444 5.35555555555555 33 122.6 116.844444444444 5.75555555555555 34 122.2 108.759259259259 13.4407407407407 35 118.8 108.759259259259 10.0407407407407 36 119 108.759259259259 10.2407407407407 37 118.2 108.759259259259 9.44074074074074 38 117.8 108.759259259259 9.04074074074074 39 116.8 108.759259259259 8.04074074074074 40 114.6 108.759259259259 5.84074074074073 41 113.4 108.759259259259 4.64074074074074 42 113.8 108.759259259259 5.04074074074074 43 124.2 116.844444444444 7.35555555555555 44 125.8 116.844444444444 8.95555555555555 45 125.6 116.844444444444 8.75555555555555 46 122.4 108.759259259259 13.6407407407407 47 119 108.759259259259 10.2407407407407 48 119.4 108.759259259259 10.6407407407407 49 118.6 108.759259259259 9.84074074074073 50 118 108.759259259259 9.24074074074074 51 116 108.759259259259 7.24074074074074 52 114.8 108.759259259259 6.04074074074074 53 114.6 108.759259259259 5.84074074074073 54 114.6 108.759259259259 5.84074074074073 55 124 116.844444444444 7.15555555555555 56 125.2 116.844444444444 8.35555555555555 57 124 116.844444444444 7.15555555555555 58 117.6 108.759259259259 8.84074074074073 59 113.2 108.759259259259 4.44074074074074 60 111.4 108.759259259259 2.64074074074074 61 112.2 108.759259259259 3.44074074074074 62 109.8 108.759259259259 1.04074074074074 63 106.4 108.759259259259 -2.35925925925926 64 105.2 108.759259259259 -3.55925925925926 65 102.2 108.759259259259 -6.55925925925926 66 99.8 108.759259259259 -8.95925925925926 67 111 116.844444444444 -5.84444444444445 68 113 116.844444444444 -3.84444444444445 69 108.4 116.844444444444 -8.44444444444444 70 105.4 108.759259259259 -3.35925925925926 71 102 108.759259259259 -6.75925925925926 72 102.8 108.759259259259 -5.95925925925926 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.030889114886891 0.061778229773782 0.96911088511311 6 0.0149920628737452 0.0299841257474903 0.985007937126255 7 0.00437454358457617 0.00874908716915235 0.995625456415424 8 0.00149974835256799 0.00299949670513598 0.998500251647432 9 0.000461434357101922 0.000922868714203844 0.999538565642898 10 0.0588203660378667 0.117640732075733 0.941179633962133 11 0.0927639161179116 0.185527832235823 0.907236083882088 12 0.121832591573295 0.243665183146591 0.878167408426705 13 0.162807021965711 0.325614043931421 0.83719297803429 14 0.179822039913946 0.359644079827892 0.820177960086054 15 0.171253793451386 0.342507586902772 0.828746206548614 16 0.161652111358812 0.323304222717625 0.838347888641188 17 0.151678301896509 0.303356603793019 0.84832169810349 18 0.149011841334418 0.298023682668837 0.850988158665582 19 0.21534175768826 0.43068351537652 0.78465824231174 20 0.277351227317244 0.554702454634488 0.722648772682756 21 0.290587013097902 0.581174026195803 0.709412986902098 22 0.531959106789684 0.936081786420632 0.468040893210316 23 0.592902980485182 0.814194039029635 0.407097019514818 24 0.659993998099312 0.680012003801375 0.340006001900688 25 0.725170744110103 0.549658511779793 0.274829255889897 26 0.759994175264224 0.480011649471552 0.240005824735776 27 0.764800683933992 0.470398632132016 0.235199316066008 28 0.747045799150154 0.505908401699691 0.252954200849846 29 0.723908396523397 0.552183206953205 0.276091603476603 30 0.701207448801188 0.597585102397624 0.298792551198812 31 0.693739663556647 0.612520672886706 0.306260336443353 32 0.710345049813305 0.579309900373391 0.289654950186695 33 0.712821129842614 0.574357740314772 0.287178870157386 34 0.867923763042465 0.264152473915070 0.132076236957535 35 0.905269949556803 0.189460100886394 0.0947300504431968 36 0.929987547882594 0.140024904234812 0.0700124521174059 37 0.940973589842009 0.118052820315983 0.0590264101579913 38 0.94628079527078 0.107438409458440 0.0537192047292198 39 0.944991786026667 0.110016427946666 0.0550082139733329 40 0.93354081295073 0.132918374098539 0.0664591870492696 41 0.91530356335337 0.169392873293261 0.0846964366466304 42 0.894313168003063 0.211373663993874 0.105686831996937 43 0.885008725623064 0.229982548753871 0.114991274376936 44 0.886607702005224 0.226784595989552 0.113392297994776 45 0.888586061658204 0.222827876683592 0.111413938341796 46 0.931611870817381 0.136776258365237 0.0683881291826186 47 0.939378145396026 0.121243709207949 0.0606218546039744 48 0.950337404738863 0.0993251905222737 0.0496625952611369 49 0.957235339281826 0.0855293214363484 0.0427646607181742 50 0.962453624862524 0.0750927502749519 0.0375463751374760 51 0.960153408926845 0.0796931821463109 0.0398465910731554 52 0.953914763215637 0.092170473568727 0.0460852367843635 53 0.947726549735138 0.104546900529723 0.0522734502648616 54 0.943565176068022 0.112869647863957 0.0564348239319783 55 0.940894543466303 0.118210913067393 0.0591054565336966 56 0.959324921361694 0.0813501572766129 0.0406750786383064 57 0.983214064680867 0.0335718706382652 0.0167859353191326 58 0.995228179205654 0.0095436415886912 0.0047718207943456 59 0.996682073585106 0.00663585282978859 0.00331792641489429 60 0.997032898862802 0.00593420227439646 0.00296710113719823 61 0.999096702092716 0.00180659581456775 0.000903297907283873 62 0.99969175264607 0.000616494707859872 0.000308247353929936 63 0.999525847904128 0.00094830419174381 0.000474152095871905 64 0.99895143152188 0.00209713695624008 0.00104856847812004 65 0.99573172350066 0.00853655299868039 0.00426827649934019 66 0.993233855124927 0.0135322897501455 0.00676614487507275 67 0.97075863826134 0.0584827234773182 0.0292413617386591 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 11 0.174603174603175 NOK 5% type I error level 14 0.222222222222222 NOK 10% type I error level 22 0.349206349206349 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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