Paper 'interactie effecten'

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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: Tue, 28 Dec 2010 18:44:08 +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/28/t12935617171xpfcdl8s9b84rt.htm/, Retrieved Tue, 28 Dec 2010 19:42:08 +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/28/t12935617171xpfcdl8s9b84rt.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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141 9.3 16 6 7 4 136 14.2 20 20 0 5 246 17.3 7 12 0 6 309 23 8 15 0 7 95 16.3 21 25 0 8 161 18.4 7 4 0 9 108 14.2 17 6 0 10 79 9.1 20 2 0 11 40 5.9 18 1 1 12 35 7.2 26 4 2 1 49 6.8 18 4 2 2 145 8 20 8 2 3 284 14.3 0 3 0 4 164 14.6 22 14 0 5 130 17.5 19 17 0 6 178 17.2 18 14 0 7 150 17.2 13 10 0 8 104 14.1 16 7 0 9 111 10.4 11 4 0 10 51 6.8 22 1 1 11 70 4.1 19 6 0 12 42 6.5 23 2 1 1 126 6.1 11 2 0 2 68 6.3 24 8 7 3 135 9.3 14 10 0 4 231 16.4 11 13 0 5 185 16.1 17 10 0 6 181 18 20 14 0 7 138 17.6 19 13 0 8 158 14 12 6 0 9 122 10.5 19 6 2 10 40 6.9 26 9 3 11 62 2.8 13 2 5 12 89 0.7 12 4 5 1 33 3.6 20 3 7 2 150 6.7 15 4 2 3 196 12.5 15 10 0 4 196 14.4 17 15 0 5 225 16.5 11 14 0 6 213 18.7 20 18 0 7 258 19.4 9 10 0 8 156 15.8 10 5 0 9 90 11.3 17 5 0 10 48 9.7 25 7 0 11 46 2.9 19 2 7 12 49 0.1 18 0 14 1 29 2.5 24 4 10 2 118 6.7 13 7 2 3 223 10.3 6 8 0 4 172 11.2 14 6 0 5 259 17.4 9 3 0 6 252 20.5 13 12 0 7 136 17 23 15 0 8 143 14.2 18 8 0 9 119 10.6 16 6 0 10 2 etc...

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 11 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation GemiddeldeTemperatuur[t] = -1.68681067708564 + 0.0516575621816613UrenZonneschijn[t] + 0.152185240873801Neerslagdagen[t] + 0.279003835025269Onweersdagen[t] -0.391768728279492Sneeuwdagen[t] + 0.330848013568777Maand[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) -1.68681067708564 2.733139 -0.6172 0.539923 0.269962 UrenZonneschijn 0.0516575621816613 0.009481 5.4487 2e-06 1e-06 Neerslagdagen 0.152185240873801 0.106599 1.4276 0.159609 0.079805 Onweersdagen 0.279003835025269 0.089398 3.1209 0.002993 0.001496 Sneeuwdagen -0.391768728279492 0.145934 -2.6846 0.009825 0.004913 Maand 0.330848013568777 0.107591 3.0751 0.003407 0.001703 Multiple Linear Regression - Regression Statistics Multiple R 0.911599239034732 R-squared 0.831013172608702 Adjusted R-squared 0.814114489869572 F-TEST (value) 49.1762100891121 F-TEST (DF numerator) 5 F-TEST (DF denominator) 50 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.41751035472080 Sum Squared Residuals 292.217815759115 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9.3 8.28690341097967 1.01309658902033 2 14.2 15.6166393654456 -1.41663936544557 3 17.3 17.4193804074355 -0.119380407435531 4 23 21.9938515843986 1.00614841560142 5 16.3 16.0384277727039 0.261572227296067 6 18.4 11.7890009824985 6.6109990175015 7 14.2 11.4618582792278 2.73814172077223 8 9.1 9.6351773720487 -0.535177372048699 9 5.9 6.97623741548032 -1.07623741548032 10 7.2 4.74134615910219 2.45865384089781 11 6.8 4.57791811622382 2.22208188377618 12 8 11.2882779210808 -3.28827792108076 13 14.3 15.1443405418571 -0.844340541857082 14 14.6 15.6933985781281 -1.09339857812807 15 17.5 14.6483452599748 2.85165474002523 16 17.2 16.4695595123137 0.730440487686317 17 17.2 13.4770542403259 3.72294575967413 18 14.1 11.0511986110838 3.04880138891618 19 10.4 10.1457118504794 0.254288149520585 20 6.8 7.82236354940502 -1.02236354940502 21 4.1 10.4649374252098 -6.3649374252098 22 6.5 4.48015442998137 2.01984557001863 23 6.1 7.71578350460358 -1.61578350460358 24 6.3 5.96054295519058 0.339457044809423 25 9.3 11.5309839941996 -2.23098399419964 26 16.4 17.2014137596623 -0.801413759662306 27 16.1 15.2321138530417 0.867886146958343 28 18 16.9289026806063 1.07109731939373 29 17.6 14.6072864444645 2.99271355553546 30 14 12.9529621703731 1.04703782962694 31 10.5 11.7058971749596 -1.20589717495965 32 6.9 9.31136455254512 -2.41136455254512 33 2.8 6.06370650101517 -3.26370650101517 34 0.7 4.22495495984021 -3.52495495984021 35 3.6 1.81792012664211 1.78207987335789 36 6.7 9.66962418751898 -2.96962418751898 37 12.5 14.8342805281548 -2.33428052815478 38 14.4 16.8645181985975 -2.4645181985975 39 16.5 17.5013202351664 -1.00132023516638 40 18.7 19.6979600105205 -0.997960010520504 41 19.4 18.4473299924501 0.952670007549917 42 15.8 12.2662727292369 3.53372727076314 43 11.3 10.2530183249326 1.0469816750674 44 9.7 10.1897383239125 -0.489738323912547 45 2.9 5.3667594947924 -2.46675949479241 46 0.1 -1.57016997679994 1.67016997679994 47 2.5 1.32372849159746 1.17627150840254 48 6.7 8.54922322103403 -1.84922322103403 49 10.3 14.3013598691449 -4.00135986914489 50 11.2 12.6571464683888 -1.45714646838881 51 17.4 15.8842646823173 1.51573531768269 52 20.5 18.9732852393371 1.52671476066292 53 17 15.6707199536470 1.32928004635304 54 14.2 13.6492178529415 0.55078214705852 55 10.6 11.8779062223522 -1.27790622235225 56 6.1 4.31658048822891 1.78341951177109 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.76738155768784 0.465236884624321 0.232618442312160 10 0.696936115787152 0.606127768425696 0.303063884212848 11 0.638546962504322 0.722906074991356 0.361453037495678 12 0.695322696738217 0.609354606523567 0.304677303261783 13 0.783469350351724 0.433061299296552 0.216530649648276 14 0.705402836065687 0.589194327868625 0.294597163934313 15 0.713470133485839 0.573059733028322 0.286529866514161 16 0.63855456307156 0.72289087385688 0.36144543692844 17 0.694279979315768 0.611440041368464 0.305720020684232 18 0.71100425218626 0.57799149562748 0.28899574781374 19 0.720693813896626 0.558612372206747 0.279306186103374 20 0.663372516173082 0.673254967653836 0.336627483826918 21 0.95771327270705 0.0845734545858993 0.0422867272929496 22 0.943847760634557 0.112304478730885 0.0561522393654427 23 0.951664472396928 0.0966710552061447 0.0483355276030724 24 0.925456651455265 0.149086697089471 0.0745433485447353 25 0.921459784432 0.157080431136001 0.0785402155680003 26 0.887814336028626 0.224371327942749 0.112185663971374 27 0.850332079772058 0.299335840455883 0.149667920227942 28 0.810400070218452 0.379199859563097 0.189599929781548 29 0.8734355769424 0.253128846115199 0.126564423057600 30 0.846293663655263 0.307412672689474 0.153706336344737 31 0.811260779512372 0.377478440975257 0.188739220487628 32 0.810060428125811 0.379879143748378 0.189939571874189 33 0.842056006767026 0.315887986465947 0.157943993232974 34 0.84437116385941 0.311257672281179 0.155628836140590 35 0.85767885344453 0.284642293110939 0.142321146555470 36 0.87153626970734 0.256927460585320 0.128463730292660 37 0.8600808315283 0.279838336943400 0.139919168471700 38 0.840711251086718 0.318577497826564 0.159288748913282 39 0.772885839712118 0.454228320575763 0.227114160287882 40 0.714282635351795 0.571434729296409 0.285717364648205 41 0.622967964971835 0.75406407005633 0.377032035028165 42 0.92331369926365 0.153372601472701 0.0766863007363505 43 0.952542243308912 0.0949155133821753 0.0474577566910876 44 0.920989416618548 0.158021166762905 0.0790105833814523 45 0.98185686244306 0.0362862751138805 0.0181431375569403 46 0.951089879690266 0.097820240619467 0.0489101203097335 47 0.950315251803516 0.0993694963929678 0.0496847481964839 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 1 0.0256410256410256 OK 10% type I error level 6 0.153846153846154 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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