paper multiple alles

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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: Sun, 26 Dec 2010 17:24:50 +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/t1293384610u38s79ejity3qtc.htm/, Retrieved Sun, 26 Dec 2010 18:30:20 +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/t1293384610u38s79ejity3qtc.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}, }

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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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation 2JAAR[t] = + 111.020989459042 + 23.3612140925946Eonia[t] -0.272891438563962deposits[t] -0.00776632084898145DowJones[t] -0.0946750391652894M1[t] + 4.74945252117933M2[t] + 7.35576735626189M3[t] + 6.81072177491929M4[t] + 5.60982904331188M5[t] + 4.6853631855139M6[t] + 2.63886426724786M7[t] + 0.275054900138095M8[t] + 8.58264908164894M9[t] + 5.56042748620996M10[t] + 0.692937437920097M11[t] + 0.801501000137598t + 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) 111.020989459042 38.525963 2.8817 0.006041 0.003021 Eonia 23.3612140925946 1.456574 16.0385 0 0 deposits -0.272891438563962 0.451644 -0.6042 0.548733 0.274366 DowJones -0.00776632084898145 0.001141 -6.8044 0 0 M1 -0.0946750391652894 5.605833 -0.0169 0.9866 0.4933 M2 4.74945252117933 5.864748 0.8098 0.422299 0.21115 M3 7.35576735626189 5.852008 1.257 0.215252 0.107626 M4 6.81072177491929 5.990779 1.1369 0.261612 0.130806 M5 5.60982904331188 5.842139 0.9602 0.342068 0.171034 M6 4.6853631855139 5.90962 0.7928 0.432033 0.216017 M7 2.63886426724786 5.855147 0.4507 0.654376 0.327188 M8 0.275054900138095 6.093598 0.0451 0.964197 0.482098 M9 8.58264908164894 5.907376 1.4529 0.153198 0.076599 M10 5.56042748620996 6.418455 0.8663 0.390911 0.195456 M11 0.692937437920097 6.320002 0.1096 0.913181 0.45659 t 0.801501000137598 0.226036 3.5459 0.000927 0.000464 Multiple Linear Regression - Regression Statistics Multiple R 0.944529868531104 R-squared 0.892136672547384 Adjusted R-squared 0.856182230063178 F-TEST (value) 24.8129747232013 F-TEST (DF numerator) 15 F-TEST (DF denominator) 45 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.19128985490603 Sum Squared Residuals 3801.59141386043 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 61.2 55.4557018903147 5.74429810968529 2 62 61.0397892982126 0.96021070178737 3 65.1 65.0790681086928 0.0209318913072214 4 63.2 61.4809566104248 1.71904338957517 5 66.3 66.6118091595084 -0.31180915950841 6 61.9 65.7838550430977 -3.88385504309774 7 62.1 64.5429572945317 -2.44295729453171 8 66.3 66.2194208154891 0.0805791845108795 9 72 76.1838803342789 -4.18388033427887 10 65.3 71.3883483799432 -6.08834837994323 11 67.6 75.1950668340435 -7.59506683404349 12 70.5 74.2972199297476 -3.79721992974763 13 74.2 78.6103837499374 -4.41038374993744 14 77.8 83.6607525577163 -5.86075255771633 15 78.5 90.940770150935 -12.4407701509351 16 77.8 88.1204023125925 -10.3204023125925 17 81.4 92.849234184815 -11.4492341848149 18 84.5 90.1289192235867 -5.62891922358671 19 88 87.7991784528392 0.200821547160819 20 93.9 94.8839696073719 -0.983969607371844 21 98.9 99.0856908978922 -0.185690897892223 22 96.7 89.4950453477248 7.2049546522752 23 98.9 92.2926913939681 6.60730860603187 24 102.2 91.1713939921436 11.0286060078564 25 105.4 102.150869275118 3.24913072488226 26 105.1 94.1272284417485 10.9727715582515 27 116.6 100.485914725942 16.1140852740579 28 112 102.249834056123 9.75016594387706 29 108.8 96.7599064277587 12.0400935722413 30 106.9 111.140632518477 -4.24063251847727 31 109.5 108.69087418355 0.80912581645007 32 106.7 108.327295303348 -1.62729530334843 33 118.9 116.101945606526 2.79805439347395 34 117.5 110.500528010142 6.99947198985831 35 113.7 109.396033950575 4.30396604942482 36 119.6 126.131482757897 -6.53148275789715 37 120.6 125.847484387774 -5.2474843877741 38 117.5 129.921456145501 -12.4214561455013 39 120.3 129.469555772863 -9.16955577286273 40 119.8 121.757738170216 -1.95773817021594 41 108 107.086993019873 0.913006980127153 42 98.8 82.9526772954843 15.8473227045157 43 94.6 89.6462592324194 4.95374076758056 44 84.6 82.3684769810633 2.23152301893673 45 84.4 75.4008098868643 8.99919011313569 46 79.1 74.1206770434154 4.97932295658456 47 73.3 59.5751124996921 13.7248875003079 48 74.3 60.6394405001166 13.6605594998834 49 67.8 55.0961988394533 12.7038011605467 50 64.8 58.4507735568213 6.34922644317872 51 66.5 61.0246912415673 5.47530875843267 52 57.7 56.8910688506438 0.808931149356247 53 53.8 54.9920572080451 -1.19205720804508 54 51.8 53.8939159193539 -2.09391591935394 55 50.9 54.4207308366597 -3.52073083665975 56 49 48.7008372927273 0.299162707272664 57 48.1 55.5276732744385 -7.42767327443854 58 42.6 55.6954012187748 -13.0954012187748 59 40.9 57.9410953217211 -17.0410953217211 60 43.3 57.660462820095 -14.360462820095 61 43.7 55.7393618574027 -12.0393618574027 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.00739933740407924 0.0147986748081585 0.99260066259592 20 0.414430785202321 0.828861570404641 0.585569214797679 21 0.357628889292741 0.715257778585483 0.642371110707258 22 0.271353500234123 0.542707000468247 0.728646499765877 23 0.23395055747251 0.46790111494502 0.76604944252749 24 0.152931427783962 0.305862855567925 0.847068572216038 25 0.400169822684402 0.800339645368803 0.599830177315598 26 0.327622218437265 0.65524443687453 0.672377781562735 27 0.338061996203751 0.676123992407502 0.661938003796249 28 0.376768743916999 0.753537487833998 0.623231256083001 29 0.284345499597869 0.568690999195738 0.715654500402131 30 0.580097412906 0.839805174187999 0.419902587094000 31 0.659746575288325 0.68050684942335 0.340253424711675 32 0.849039390186714 0.301921219626572 0.150960609813286 33 0.817977585329623 0.364044829340753 0.182022414670377 34 0.815348991437487 0.369302017125026 0.184651008562513 35 0.737067120580609 0.525865758838783 0.262932879419391 36 0.745586642336419 0.508826715327162 0.254413357663581 37 0.676076424266419 0.647847151467162 0.323923575733581 38 0.761779684733804 0.476440630532392 0.238220315266196 39 0.813812271490952 0.372375457018096 0.186187728509048 40 0.701838244681438 0.596323510637124 0.298161755318562 41 0.640707602487516 0.718584795024969 0.359292397512484 42 0.733139247641918 0.533721504716163 0.266860752358082 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 0.0416666666666667 OK 10% type I error level 1 0.0416666666666667 OK

Charts produced by software:

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Parameters (Session):

par1 = 12 ; par2 = 0.3 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 1 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 1 ; par9 = 0 ; par10 = FALSE ;

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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