Multiple Regression werklh inflatie lineaire trend

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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 06:47:18 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/19/t1261230557b5opl8bwbe0dhqz.htm/, Retrieved Sat, 19 Dec 2009 14:49:29 +0100

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@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/t1261230557b5opl8bwbe0dhqz.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}, }

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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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation werklh[t] = + 9.3799763651523 -0.136316098563579inflatie[t] -0.0298621077340095t + 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) 9.3799763651523 0.214633 43.7025 0 0 inflatie -0.136316098563579 0.04065 -3.3534 0.001424 0.000712 t -0.0298621077340095 0.00331 -9.0205 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.787410954804067 R-squared 0.620016011745452 Adjusted R-squared 0.606683240227748 F-TEST (value) 46.503160346083 F-TEST (DF numerator) 2 F-TEST (DF denominator) 57 p-value 1.05515596260375e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.444076471403359 Sum Squared Residuals 11.2406230098813 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9.3 8.80484986316403 0.49515013683597 2 9.3 8.80225097514269 0.497749024857314 3 8.7 8.64970437870146 0.0502956212985438 4 8.2 8.67436871039288 -0.474368710392879 5 8.3 8.6990330420843 -0.399033042084299 6 8.5 8.65553932449393 -0.155539324493933 7 8.6 8.58478238719085 0.0152176128091501 8 8.5 8.48676223017505 0.0132377698249493 9 8.2 8.51142656186647 -0.311426561866473 10 8.1 8.49519606398882 -0.395196063988821 11 7.9 8.41080751682938 -0.51080751682938 12 8.6 8.38094540909537 0.219054590904629 13 8.7 8.32382008164864 0.376179918351354 14 8.7 8.28032636405828 0.419673635941721 15 8.5 8.35951713517513 0.140482864824869 16 8.4 8.31602341758476 0.0839765824152362 17 8.5 8.21800326056897 0.281996739431035 18 8.7 8.18814115283496 0.511858847165043 19 8.7 8.15827904510095 0.541720954899053 20 8.6 8.21020659650508 0.389793403494916 21 8.5 8.12581804934564 0.374181950654357 22 8.3 8.06869272189892 0.231307278101083 23 8 8.07972544373398 -0.0797254437339819 24 8.2 8.06349494585633 0.136505054143669 25 8.1 8.04726444797868 0.0527355520213210 26 8.1 8.0719287796701 0.0280712203298990 27 8 8.0693298916488 -0.069329891648807 28 7.9 7.99857295434572 -0.0985729543457235 29 7.9 7.95507923675536 -0.0550792367553561 30 8 7.97974356844678 0.0202564315532216 31 8 7.93624985085641 0.0637501491435889 32 7.9 7.9063877431224 -0.0063877431224013 33 8 7.87652563538839 0.123474364611608 34 7.7 7.91482157693617 -0.214821576936172 35 7.2 7.88495946920216 -0.684959469202162 36 7.5 7.85509736146815 -0.355097361468153 37 7.3 7.8388668635905 -0.538866863590502 38 7 7.78174153614378 -0.781741536143776 39 7 7.6428265495589 -0.642826549558904 40 7 7.51754317283039 -0.517543172830389 41 7.2 7.46041784538366 -0.260417845383664 42 7.3 7.37602929822422 -0.076029298224223 43 7.1 7.33253558063386 -0.232535580633856 44 6.8 7.19362059404898 -0.393620594048983 45 6.4 7.20465331588405 -0.804653315884047 46 6.1 7.03847510958646 -0.93847510958646 47 6.5 6.91319173285794 -0.413191732857944 48 7.7 6.86969801526758 0.830301984732423 49 7.9 6.90799395681536 0.992006043184644 50 7.5 6.86450023922499 0.635499760775011 51 6.9 6.93005940048548 -0.0300594004854847 52 6.6 7.1183030504532 -0.518303050453202 53 6.9 7.15659899200098 -0.256598992000981 54 7.7 7.20852654340512 0.491473456594881 55 8 7.20592765538383 0.794072344616175 56 8 7.35327647578247 0.646723524217532 57 7.7 7.3097827581921 0.390217241807899 58 7.3 7.40260513916531 -0.102605139165313 59 7.4 7.48179591028217 -0.0817959102821655 60 8.1 7.54735507154266 0.552644928457338 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.252699732077804 0.505399464155609 0.747300267922196 7 0.354410630869459 0.708821261738917 0.645589369130541 8 0.321013452963197 0.642026905926394 0.678986547036803 9 0.208375655073657 0.416751310147314 0.791624344926343 10 0.130036972455627 0.260073944911253 0.869963027544373 11 0.0814644681833977 0.162928936366795 0.918535531816602 12 0.177450509680815 0.354901019361630 0.822549490319185 13 0.253474179133553 0.506948358267105 0.746525820866447 14 0.269090220773834 0.538180441547667 0.730909779226166 15 0.221387905241176 0.442775810482352 0.778612094758824 16 0.160039695858498 0.320079391716996 0.839960304141502 17 0.122956559490838 0.245913118981676 0.877043440509162 18 0.121376304079656 0.242752608159313 0.878623695920344 19 0.117816491602204 0.235632983204407 0.882183508397796 20 0.0956004546341306 0.191200909268261 0.90439954536587 21 0.0767434432737855 0.153486886547571 0.923256556726215 22 0.0595615781977245 0.119123156395449 0.940438421802275 23 0.0537111650008602 0.107422330001720 0.94628883499914 24 0.0404559505838818 0.0809119011677637 0.959544049416118 25 0.0303190478311158 0.0606380956622316 0.969680952168884 26 0.0217099180687512 0.0434198361375025 0.978290081931249 27 0.0149619175754831 0.0299238351509662 0.985038082424517 28 0.0106333494405851 0.0212666988811701 0.989366650559415 29 0.00751865651315282 0.0150373130263056 0.992481343486847 30 0.00554866316896436 0.0110973263379287 0.994451336831036 31 0.00464173833319929 0.00928347666639857 0.9953582616668 32 0.00391148260262405 0.0078229652052481 0.996088517397376 33 0.00506096899905105 0.0101219379981021 0.99493903100095 34 0.00458467896482767 0.00916935792965534 0.995415321035172 35 0.0059790534660718 0.0119581069321436 0.994020946533928 36 0.00476576799518619 0.00953153599037237 0.995234232004814 37 0.00372634439108308 0.00745268878216615 0.996273655608917 38 0.00427981085495392 0.00855962170990784 0.995720189145046 39 0.00581832758032314 0.0116366551606463 0.994181672419677 40 0.00676968063024455 0.0135393612604891 0.993230319369755 41 0.00539094776154518 0.0107818955230904 0.994609052238455 42 0.00630238830041335 0.0126047766008267 0.993697611699587 43 0.0102093589207433 0.0204187178414866 0.989790641079257 44 0.0150111406711467 0.0300222813422935 0.984988859328853 45 0.0235895434134676 0.0471790868269352 0.976410456586532 46 0.0241539368201932 0.0483078736403864 0.975846063179807 47 0.0274243049671751 0.0548486099343502 0.972575695032825 48 0.0693806591055883 0.138761318211177 0.930619340894412 49 0.258903032775634 0.517806065551269 0.741096967224366 50 0.271887959536745 0.543775919073489 0.728112040463256 51 0.195766680903277 0.391533361806555 0.804233319096723 52 0.248089061805868 0.496178123611737 0.751910938194132 53 0.488521493746299 0.977042987492598 0.511478506253701 54 0.420149457545678 0.840298915091356 0.579850542454322 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.122448979591837 NOK 5% type I error level 21 0.428571428571429 NOK 10% type I error level 24 0.489795918367347 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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