investeringen paper

*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: Mon, 01 Dec 2008 13:08:42 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/01/t1228162307gjfg8zzxy5y3fph.htm/, Retrieved Mon, 01 Dec 2008 20:11:56 +0000

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/2008/Dec/01/t1228162307gjfg8zzxy5y3fph.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1202455 0 1201423 0 1505916 0 1513378 0 1977605 0 1873830 0 1424049 0 1322740 0 1584826 0 1680460 0 1648574 0 3095469 1 1307983 0 1367589 0 1572718 0 1611603 0 1641196 0 1845262 0 1464238 0 1402386 0 2077100 0 1691130 0 1729013 0 3347792 1 1365088 0 1545460 0 1844355 0 1775550 0 1721779 0 2128726 0 1664320 0 1769471 0 1904578 0 1872042 0 1802181 0 3222199 1 1491414 0 1658519 0 2079207 0 1748767 0 2084447 0 2067182 0 1718123 0 1782337 0 1958118 0 2028681 0 2076128 0 3383873 1 1870369 0 1654853 0 2074338 0 1888654 0 1991138 0 2168238 0 1867424 0 1842360 0 1927476 0 2065555 0 2455609 0 3336171 1

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation x[t] = + 1755235.65454546 + 1521865.14545455y[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) 1755235.65454546 35172.347627 49.9039 0 0 y 1521865.14545455 121840.586222 12.4906 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.853810213286966 R-squared 0.728991880313135 Adjusted R-squared 0.72431932652543 F-TEST (value) 156.015727894116 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 260845.111256933 Sum Squared Residuals 3946329979865.23 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1202455 1755235.65454545 -552780.654545449 2 1201423 1755235.65454546 -553812.654545457 3 1505916 1755235.65454545 -249319.654545455 4 1513378 1755235.65454545 -241857.654545455 5 1977605 1755235.65454545 222369.345454545 6 1873830 1755235.65454545 118594.345454545 7 1424049 1755235.65454545 -331186.654545455 8 1322740 1755235.65454545 -432495.654545455 9 1584826 1755235.65454545 -170409.654545455 10 1680460 1755235.65454545 -74775.6545454546 11 1648574 1755235.65454545 -106661.654545455 12 3095469 3277100.8 -181631.8 13 1307983 1755235.65454545 -447252.654545455 14 1367589 1755235.65454545 -387646.654545455 15 1572718 1755235.65454545 -182517.654545455 16 1611603 1755235.65454545 -143632.654545455 17 1641196 1755235.65454545 -114039.654545455 18 1845262 1755235.65454545 90026.3454545454 19 1464238 1755235.65454545 -290997.654545455 20 1402386 1755235.65454545 -352849.654545455 21 2077100 1755235.65454545 321864.345454545 22 1691130 1755235.65454545 -64105.6545454546 23 1729013 1755235.65454545 -26222.6545454546 24 3347792 3277100.8 70691.2 25 1365088 1755235.65454545 -390147.654545455 26 1545460 1755235.65454545 -209775.654545455 27 1844355 1755235.65454545 89119.3454545454 28 1775550 1755235.65454545 20314.3454545454 29 1721779 1755235.65454545 -33456.6545454546 30 2128726 1755235.65454545 373490.345454545 31 1664320 1755235.65454545 -90915.6545454546 32 1769471 1755235.65454545 14235.3454545454 33 1904578 1755235.65454545 149342.345454545 34 1872042 1755235.65454545 116806.345454545 35 1802181 1755235.65454545 46945.3454545454 36 3222199 3277100.8 -54901.7999999999 37 1491414 1755235.65454545 -263821.654545455 38 1658519 1755235.65454545 -96716.6545454546 39 2079207 1755235.65454545 323971.345454545 40 1748767 1755235.65454545 -6468.65454545458 41 2084447 1755235.65454545 329211.345454545 42 2067182 1755235.65454545 311946.345454545 43 1718123 1755235.65454545 -37112.6545454546 44 1782337 1755235.65454545 27101.3454545454 45 1958118 1755235.65454545 202882.345454545 46 2028681 1755235.65454545 273445.345454545 47 2076128 1755235.65454545 320892.345454545 48 3383873 3277100.8 106772.2 49 1870369 1755235.65454545 115133.345454545 50 1654853 1755235.65454545 -100382.654545455 51 2074338 1755235.65454545 319102.345454545 52 1888654 1755235.65454545 133418.345454545 53 1991138 1755235.65454545 235902.345454545 54 2168238 1755235.65454545 413002.345454545 55 1867424 1755235.65454545 112188.345454545 56 1842360 1755235.65454545 87124.3454545454 57 1927476 1755235.65454545 172240.345454545 58 2065555 1755235.65454545 310319.345454545 59 2455609 1755235.65454545 700373.345454545 60 3336171 3277100.8 59070.2000000001 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.910406990967086 0.179186018065828 0.089593009032914 6 0.920876559825713 0.158246880348574 0.0791234401742872 7 0.882845206607366 0.234309586785268 0.117154793392634 8 0.872443636404148 0.255112727191704 0.127556363595852 9 0.81583476559231 0.368330468815381 0.184165234407691 10 0.763319511883878 0.473360976232243 0.236680488116122 11 0.695964956069053 0.608070087861894 0.304035043930947 12 0.61360438253771 0.77279123492458 0.38639561746229 13 0.660948883584649 0.678102232830703 0.339051116415351 14 0.673026131813749 0.653947736372503 0.326973868186251 15 0.618896575521353 0.762206848957294 0.381103424478647 16 0.565283002697023 0.869433994605953 0.434716997302977 17 0.514457867470193 0.971084265059614 0.485542132529807 18 0.543843379332183 0.912313241335635 0.456156620667817 19 0.54222568608609 0.91554862782782 0.45777431391391 20 0.599858834376596 0.800282331246807 0.400141165623404 21 0.798975155417437 0.402049689165126 0.201024844582563 22 0.766135098714189 0.467729802571622 0.233864901285811 23 0.73197708571979 0.53604582856042 0.26802291428021 24 0.68928039640297 0.621439207194061 0.310719603597031 25 0.812378556273752 0.375242887452497 0.187621443726248 26 0.831725637907858 0.336548724184283 0.168274362092142 27 0.823909851179339 0.352180297641322 0.176090148820661 28 0.803168212847432 0.393663574305136 0.196831787152568 29 0.782798122206269 0.434403755587463 0.217201877793731 30 0.882823720655448 0.234352558689104 0.117176279344552 31 0.876450845937144 0.247098308125711 0.123549154062856 32 0.855770695719104 0.288458608561792 0.144229304280896 33 0.838502849646675 0.322994300706650 0.161497150353325 34 0.811762806416707 0.376474387166587 0.188237193583293 35 0.779018807190934 0.441962385618132 0.220981192809066 36 0.727374614763734 0.545250770472532 0.272625385236266 37 0.850493154846581 0.299013690306837 0.149506845153419 38 0.875842331676624 0.248315336646753 0.124157668323376 39 0.88974747380451 0.220505052390978 0.110252526195489 40 0.886351493702128 0.227297012595744 0.113648506297872 41 0.891403504110622 0.217192991778755 0.108596495889378 42 0.886122114563612 0.227755770872775 0.113877885436388 43 0.892145242307173 0.215709515385654 0.107854757692827 44 0.883748834294014 0.232502331411972 0.116251165705986 45 0.847351074130728 0.305297851738544 0.152648925869272 46 0.809949203119972 0.380101593760057 0.190050796880028 47 0.777967692075565 0.444064615848871 0.222032307924435 48 0.699940730335174 0.600118539329652 0.300059269664826 49 0.630811230377151 0.738377539245697 0.369188769622849 50 0.747697899815845 0.50460420036831 0.252302100184155 51 0.673987668922488 0.652024662155024 0.326012331077512 52 0.603530141932139 0.792939716135722 0.396469858067861 53 0.48986634374836 0.97973268749672 0.51013365625164 54 0.409377216969393 0.818754433938785 0.590622783030607 55 0.323519379941045 0.64703875988209 0.676480620058955 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 0 0 OK 10% type I error level 0 0 OK

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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