paper multiple intercept = deposito's 2 jaar

*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, 26 Dec 2010 15:00:13 +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/26/t1293375567xxzqqaun42rqomf.htm/, Retrieved Sun, 26 Dec 2010 15:59:37 +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/26/t1293375567xxzqqaun42rqomf.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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No (this computation is public)

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Dataseries X:

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61,2 2,08 83,9 10554,27 62 2,09 85,6 10532,54 65,1 2,07 87,5 10324,31 63,2 2,04 88,5 10695,25 66,3 2,35 91 10827,81 61,9 2,33 90,6 10872,48 62,1 2,37 91,2 10971,19 66,3 2,59 93,2 11145,65 72 2,62 90,1 11234,68 65,3 2,6 95 11333,88 67,6 2,83 95,4 10997,97 70,5 2,78 93,7 11036,89 74,2 3,01 93,9 11257,35 77,8 3,06 92,5 11533,59 78,5 3,33 89,2 11963,12 77,8 3,32 93,3 12185,15 81,4 3,6 93 12377,62 84,5 3,57 96,1 12512,89 88 3,57 96,7 12631,48 93,9 3,83 97,6 12268,53 98,9 3,84 102,6 12754,8 96,7 3,8 107,6 13407,75 98,9 4,07 103,5 13480,21 102,2 4,05 100,8 13673,28 105,4 4,272 94,5 13239,71 105,1 3,858 100,1 13557,69 116,6 4,067 97,4 13901,28 112 3,964 103 13200,58 108,8 3,782 100,2 13406,97 106,9 4,114 100,2 12538,12 109,5 4,009 99 12419,57 106,7 4,025 102,4 12193,88 118,9 4,082 99 12656,63 117,5 4,044 103,7 12812,48 113,7 3,916 103,4 12056,67 119,6 4,289 95,3 11322,38 120,6 4,296 93,6 11530,75 117,5 4,193 102,4 11114,08 120,3 3,48 110,5 9181,73 119,8 2,934 109,1 8614,55 108 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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation 2JAAR[t] = + 11.6109108530227 + 23.9376081304436Eonia[t] + 1.06465328450808deposits[t] -0.00867124946976638DowJones[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) 11.6109108530227 20.80869 0.558 0.579041 0.28952 Eonia 23.9376081304436 1.533361 15.6112 0 0 deposits 1.06465328450808 0.170415 6.2474 0 0 DowJones -0.00867124946976638 0.001197 -7.2428 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.914476528233309 R-squared 0.836267320689645 Adjusted R-squared 0.827649811252258 F-TEST (value) 97.0428088029121 F-TEST (DF numerator) 3 F-TEST (DF denominator) 57 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.0618089935600 Sum Squared Residuals 5770.68001270445 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 61.2 59.206838193302 1.99316180669800 2 62 61.4445511092479 0.555448890752112 3 65.1 64.7942544642938 0.30574553570624 4 63.2 61.9242662265735 1.27573377342653 5 66.3 70.8570971285689 -4.5570971285689 6 61.9 69.5651389383423 -7.66513893834233 7 62.1 70.3054961991043 -8.20549619910427 8 66.3 76.1882903743226 -9.88829037432258 9 72 72.8339920959675 -0.83399209596754 10 65.3 76.7118530800474 -11.4118530800474 11 67.6 85.5561236732419 -17.9561236732419 12 70.5 82.2118476536927 -11.7118476536927 13 74.2 86.0187645224916 -11.8187645224916 14 77.8 83.3297843771742 -5.52978437717424 15 78.5 82.5550209487686 -4.05502094876860 16 77.8 84.755445814175 -6.95544581417505 17 81.4 89.4696247199009 -8.06962471990089 18 84.5 90.8789617421873 -6.37896174218732 19 88 90.4894302382726 -2.48943023827258 20 93.9 100.818626303297 -6.91862630329687 21 98.9 102.164700327478 -3.2647003274784 22 96.7 100.868570083517 -4.16857008351707 23 98.9 102.338327075674 -3.43832707567448 24 102.2 97.310852909766 4.88914709023401 25 105.4 99.6772798549302 5.72272014506978 26 105.1 92.9718845757755 12.1281154242245 27 116.6 92.1209262015494 24.4790737984506 28 112 101.693355460824 10.3066445391758 29 108.8 92.5660224063958 16.2339775936042 30 106.9 108.047323407510 -1.14732340750953 31 109.5 105.284267237044 4.21573276295591 32 106.7 111.244104427290 -4.54410442729023 33 118.9 104.976106231264 13.9238937687364 34 117.5 107.718933329632 9.78106667036834 35 113.7 110.889340565327 2.81065943467342 36 119.6 117.561588566621 2.03841143337862 37 120.6 114.112412987856 6.48758701214446 38 117.5 124.628837770658 -7.12883777065846 39 120.3 132.940903691071 -12.6409036910707 40 119.8 123.298614327799 -3.49861432779925 41 108 97.6656098252576 10.3343901747424 42 98.8 82.8828295562603 15.9171704437396 43 94.6 87.3534000861 7.24659991389993 44 84.6 90.5592904798884 -5.9592904798884 45 84.4 70.8575832595695 13.5424167404305 46 79.1 72.8758741673779 6.2241258326221 47 73.3 66.7038757901134 6.59612420988661 48 74.3 59.8245310647252 14.4754689352748 49 67.8 55.7475738330756 12.0524261669244 50 64.8 55.2307063216614 9.56929367833862 51 66.5 48.4372201561194 18.0627798438806 52 57.7 52.5389386037386 5.16106139626141 53 53.8 50.4602179346836 3.33978206531639 54 51.8 50.3750122331428 1.42498776685721 55 50.9 52.7769524460857 -1.87695244608566 56 49 52.2193507720482 -3.21935077204824 57 48.1 48.134848484057 -0.0348484840569988 58 42.6 59.1760402955841 -16.5760402955841 59 40.9 65.2144948502598 -24.3144948502598 60 43.3 54.9575510356737 -11.6575510356737 61 43.7 56.8783395636238 -13.1783395636238 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.0053174920420485 0.010634984084097 0.994682507957952 8 0.00150109020981988 0.00300218041963976 0.99849890979018 9 0.0050088476851756 0.0100176953703512 0.994991152314824 10 0.00140058192420542 0.00280116384841084 0.998599418075795 11 0.000633519383897079 0.00126703876779416 0.999366480616103 12 0.000224050896460446 0.000448101792920893 0.99977594910354 13 8.5561780103095e-05 0.00017112356020619 0.999914438219897 14 4.15573216643668e-05 8.31146433287336e-05 0.999958442678336 15 2.89186196098268e-05 5.78372392196536e-05 0.99997108138039 16 1.47929578640985e-05 2.95859157281969e-05 0.999985207042136 17 1.28788621370312e-05 2.57577242740624e-05 0.999987121137863 18 3.49659105217438e-05 6.99318210434875e-05 0.999965034089478 19 0.000212121797719233 0.000424243595438465 0.99978787820228 20 0.00274720392698551 0.00549440785397101 0.997252796073014 21 0.0169085671918246 0.0338171343836492 0.983091432808175 22 0.0106973229626601 0.0213946459253202 0.98930267703734 23 0.00628228655533414 0.0125645731106683 0.993717713444666 24 0.00461909438653162 0.00923818877306323 0.995380905613468 25 0.0107139624324245 0.0214279248648491 0.989286037567575 26 0.0143660383847868 0.0287320767695735 0.985633961615213 27 0.0611034176618914 0.122206835323783 0.938896582338109 28 0.207487690571553 0.414975381143106 0.792512309428447 29 0.272824832694333 0.545649665388665 0.727175167305667 30 0.372528241159759 0.745056482319517 0.627471758840241 31 0.488483002880721 0.976966005761442 0.511516997119279 32 0.503075584759317 0.993848830481366 0.496924415240683 33 0.693899600581178 0.612200798837643 0.306100399418822 34 0.903057652131056 0.193884695737887 0.0969423478689436 35 0.949872792092302 0.100254415815395 0.0501272079076976 36 0.946631043198835 0.106737913602329 0.0533689568011647 37 0.947252267232371 0.105495465535258 0.0527477327676289 38 0.93902061500199 0.121958769996020 0.0609793849980098 39 0.930893452740537 0.138213094518925 0.0691065472594625 40 0.973270007399793 0.0534599852004139 0.0267299926002069 41 0.984494676877385 0.0310106462452289 0.0155053231226145 42 0.99931560549113 0.00136878901774008 0.000684394508870038 43 0.998965617090373 0.00206876581925490 0.00103438290962745 44 0.99778723566702 0.00442552866596025 0.00221276433298013 45 0.996053816507514 0.00789236698497185 0.00394618349248593 46 0.99878574062184 0.00242851875632043 0.00121425937816022 47 0.99787045854675 0.00425908290650161 0.00212954145325081 48 0.994821704053616 0.0103565918927676 0.00517829594638379 49 0.988298350181829 0.0234032996363427 0.0117016498181713 50 0.983789388683356 0.0324212226332876 0.0162106113166438 51 0.976492679396969 0.0470146412060616 0.0235073206030308 52 0.98923857383121 0.0215228523375784 0.0107614261687892 53 0.984475148134572 0.0310497037308569 0.0155248518654284 54 0.960682090022055 0.0786358199558895 0.0393179099779447 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 19 0.395833333333333 NOK 5% type I error level 33 0.6875 NOK 10% type I error level 35 0.729166666666667 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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