Paper: Zonder seizoenaliteit en met lineaire 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, 13 Dec 2009 05:04:40 -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/13/t1260705947bydl4t02z7cn6e5.htm/, Retrieved Sun, 13 Dec 2009 13:05:59 +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/13/t1260705947bydl4t02z7cn6e5.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:

Zonder seizoenaliteit en met lineaire trend

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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0.7461 0.527 0.7775 0.472 0.7790 0 0.7744 0.052 0.7905 0.313 0.7719 0.364 0.7811 0.363 0.7557 -0.155 0.7637 0.052 0.7595 0.568 0.7471 0.668 0.7615 1.378 0.7487 0.252 0.7389 -0.402 0.7337 -0.05 0.7510 0.555 0.7382 0.05 0.7159 0.15 0.7542 0.45 0.7636 0.299 0.7433 0.199 0.7658 0.496 0.7627 0.444 0.7480 -0.393 0.7692 -0.444 0.7850 0.198 0.7913 0.494 0.7720 0.133 0.7880 0.388 0.8070 0.484 0.8268 0.278 0.8244 0.369 0.8487 0.165 0.8572 0.155 0.8214 0.087 0.8827 0.414 0.9216 0.36 0.8865 0.975 0.8816 0.27 0.8884 0.359 0.9466 0.169 0.9180 0.381 0.9337 0.154 0.9559 0.486 0.9626 0.925 0.9434 0.728 0.8639 -0.014 0.7996 0.046 0.6680 -0.819 0.6572 -1.674 0.6928 -0.788 0.6438 0.279 0.6454 0.396 0.6873 -0.141 0.7265 -0.019 0.7912 0.099 0.8114 0.742 0.8281 0.005 0.8393 0.448

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 USDOLLAR[t] = + 0.73519855173591 + 0.0825943778864721Amerikaanse_inflatie[t] + 0.00136131812051283t + 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) 0.73519855173591 0.019125 38.4426 0 0 Amerikaanse_inflatie 0.0825943778864721 0.019896 4.1513 0.000114 5.7e-05 t 0.00136131812051283 0.000523 2.6011 0.011863 0.005932 Multiple Linear Regression - Regression Statistics Multiple R 0.520729865010518 R-squared 0.271159592313872 Adjusted R-squared 0.245129577753653 F-TEST (value) 10.4171894213336 F-TEST (DF numerator) 2 F-TEST (DF denominator) 56 p-value 0.000142465066987896 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0673810400075746 Sum Squared Residuals 0.254251454940132 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.7461 0.78008710700259 -0.0339871070025906 2 0.7775 0.77690573433935 0.000594265660650347 3 0.779 0.739282506097448 0.0397174939025523 4 0.7744 0.744938731868057 0.0294612681319429 5 0.7905 0.767857182616939 0.0226428173830608 6 0.7719 0.773430814009662 -0.00153081400966201 7 0.7811 0.774709537752288 0.00639046224771163 8 0.7557 0.733286968127609 0.0224130318723914 9 0.7637 0.751745322470621 0.0119546775293788 10 0.7595 0.795725339580554 -0.0362253395805537 11 0.7471 0.805346095489714 -0.0582460954897137 12 0.7615 0.865349421909622 -0.103849421909622 13 0.7487 0.773709470529967 -0.0250094705299669 14 0.7389 0.721054065512727 0.017845934487273 15 0.7337 0.751488604649278 -0.017788604649278 16 0.751 0.802819521391106 -0.0518195213911065 17 0.7382 0.762470678678951 -0.0242706786789509 18 0.7159 0.772091434588111 -0.056191434588111 19 0.7542 0.798231066074565 -0.0440310660745654 20 0.7636 0.787120633134221 -0.0235206331342210 21 0.7433 0.780222513466087 -0.0369225134660866 22 0.7658 0.806114361818882 -0.0403143618188815 23 0.7627 0.803180772289298 -0.0404807722892978 24 0.748 0.735410596118834 0.0125894038811665 25 0.7692 0.732559600967136 0.0366403990328637 26 0.785 0.786946509690764 -0.00194650969076417 27 0.7913 0.812755763665673 -0.0214557636656728 28 0.772 0.784300511369169 -0.0123005113691691 29 0.788 0.806723395850732 -0.0187233958507323 30 0.807 0.816013774248347 -0.00901377424834646 31 0.8268 0.800360650524246 0.0264393494757539 32 0.8244 0.809238057032428 0.0151619429675721 33 0.8487 0.7937501220641 0.0549498779358996 34 0.8572 0.794285496405749 0.0629145035942515 35 0.8214 0.790030396829981 0.0313696031700188 36 0.8827 0.81840007651937 0.0642999234806296 37 0.9216 0.815301298234014 0.106298701765986 38 0.8865 0.867458158754707 0.0190418412452930 39 0.8816 0.810590440465257 0.0710095595347431 40 0.8884 0.819302658217666 0.0690973417823342 41 0.9466 0.804971044539749 0.141628955460251 42 0.918 0.823842370772194 0.0941576292278062 43 0.9337 0.806454765112477 0.127245234887522 44 0.9559 0.8352374166913 0.120662583308701 45 0.9626 0.872857666703973 0.0897423332960269 46 0.9434 0.85794789238085 0.085452107619149 47 0.8639 0.798024182109601 0.0658758178903985 48 0.7996 0.804341162903303 -0.00474116290330264 49 0.668 0.734258344152017 -0.0662583441520171 50 0.6572 0.665001469179596 -0.0078014691795963 51 0.6928 0.739541406107523 -0.0467414061075234 52 0.6438 0.829030925432902 -0.185230925432902 53 0.6454 0.840055785766132 -0.194655785766132 54 0.6873 0.79706392296161 -0.109763922961609 55 0.7265 0.808501755184272 -0.0820017551842717 56 0.7912 0.819609209895388 -0.0284092098953882 57 0.8114 0.874078712996903 -0.0626787129969026 58 0.8281 0.814567974615086 0.0135320253849144 59 0.8393 0.852518602139306 -0.0132186021393054 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.0112561925884675 0.0225123851769350 0.988743807411532 7 0.00187864610064451 0.00375729220128901 0.998121353899355 8 0.00192330556487978 0.00384661112975957 0.99807669443512 9 0.000470559354112788 0.000941118708225577 0.999529440645887 10 0.000113445670160821 0.000226891340321642 0.99988655432984 11 3.19012077812098e-05 6.38024155624197e-05 0.999968098792219 12 9.1659266711945e-06 1.8331853342389e-05 0.999990834073329 13 2.14544409821765e-06 4.2908881964353e-06 0.999997854555902 14 5.75016070173572e-07 1.15003214034714e-06 0.99999942498393 15 1.39596006816896e-07 2.79192013633791e-07 0.999999860403993 16 3.04273871867666e-08 6.08547743735332e-08 0.999999969572613 17 5.26010318655923e-09 1.05202063731185e-08 0.999999994739897 18 3.18241273030716e-09 6.36482546061432e-09 0.999999996817587 19 1.76204553860701e-09 3.52409107721402e-09 0.999999998237954 20 2.01403204877270e-09 4.02806409754541e-09 0.999999997985968 21 5.16492348743025e-10 1.03298469748605e-09 0.999999999483508 22 5.4595341287835e-10 1.0919068257567e-09 0.999999999454047 23 3.81698545046685e-10 7.6339709009337e-10 0.999999999618301 24 1.04339420891356e-10 2.08678841782713e-10 0.99999999989566 25 9.70772999086574e-11 1.94154599817315e-10 0.999999999902923 26 2.28630121975507e-10 4.57260243951013e-10 0.99999999977137 27 5.45065724579488e-10 1.09013144915898e-09 0.999999999454934 28 2.88334709169426e-10 5.76669418338851e-10 0.999999999711665 29 3.81564707581058e-10 7.63129415162116e-10 0.999999999618435 30 1.44863815768873e-09 2.89727631537746e-09 0.999999998551362 31 1.10390692842310e-08 2.20781385684621e-08 0.99999998896093 32 3.37380789579229e-08 6.74761579158459e-08 0.999999966261921 33 2.02265922970327e-07 4.04531845940654e-07 0.999999797734077 34 7.06410413042676e-07 1.41282082608535e-06 0.999999293589587 35 6.07190627933956e-07 1.21438125586791e-06 0.999999392809372 36 2.67094607662653e-06 5.34189215325305e-06 0.999997329053923 37 2.45351208124863e-05 4.90702416249726e-05 0.999975464879188 38 4.89655028191778e-05 9.79310056383556e-05 0.99995103449718 39 4.28792476847373e-05 8.57584953694745e-05 0.999957120752315 40 3.59110748686737e-05 7.18221497373473e-05 0.999964088925131 41 0.000117376416778554 0.000234752833557108 0.999882623583221 42 8.1067559388506e-05 0.000162135118777012 0.999918932440611 43 9.99924346771229e-05 0.000199984869354246 0.999900007565323 44 0.000156543540395108 0.000313087080790216 0.999843456459605 45 0.00016667472023652 0.00033334944047304 0.999833325279764 46 0.000543688507653075 0.00108737701530615 0.999456311492347 47 0.0118118038172708 0.0236236076345415 0.98818819618273 48 0.744104109856292 0.511791780287417 0.255895890143708 49 0.934600714809191 0.130798570381617 0.0653992851908086 50 0.89187830419828 0.216243391603441 0.108121695801721 51 0.970283909789696 0.0594321804206087 0.0297160902103043 52 0.966751479120626 0.0664970417587479 0.0332485208793740 53 0.956620244403278 0.086759511193444 0.043379755596722 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 40 0.833333333333333 NOK 5% type I error level 42 0.875 NOK 10% type I error level 45 0.9375 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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