investeringen paper 2

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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: Mon, 01 Dec 2008 13:19:24 -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/t1228163122ym8h6emtx4dxpgr.htm/, Retrieved Mon, 01 Dec 2008 20:25:22 +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/t1228163122ym8h6emtx4dxpgr.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)

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

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User-defined keywords:

Dataseries X:

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

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation x[t] = + 2946058.15 -1728487.07916667M1[t] -1699575.70833333M2[t] -1379033.3375M3[t] -1495945.36666667M4[t] -1329498.39583333M5[t] -1205279.425M6[t] -1603491.85416667M7[t] -1616459.48333333M8[t] -1359094.3125M9[t] -1391135.94166667M10[t] -1325604.17083333M11[t] + 9195.62916666667t + 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) 2946058.15 63896.007907 46.1071 0 0 M1 -1728487.07916667 77733.069599 -22.2362 0 0 M2 -1699575.70833333 77616.930339 -21.897 0 0 M3 -1379033.3375 77511.702014 -17.7913 0 0 M4 -1495945.36666667 77417.429117 -19.3231 0 0 M5 -1329498.39583333 77334.151712 -17.1916 0 0 M6 -1205279.425 77261.905354 -15.5999 0 0 M7 -1603491.85416667 77200.721013 -20.7704 0 0 M8 -1616459.48333333 77150.625007 -20.952 0 0 M9 -1359094.3125 77111.638946 -17.625 0 0 M10 -1391135.94166667 77083.779687 -18.0471 0 0 M11 -1325604.17083333 77067.059298 -17.2007 0 0 t 9195.62916666667 926.905607 9.9208 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.975746732983841 R-squared 0.95208168692864 Adjusted R-squared 0.939847224016803 F-TEST (value) 77.8196553285163 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 121844.906282912 Sum Squared Residuals 697770515793.3 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1202455 1226766.70000000 -24311.7000000018 2 1201423 1264873.7 -63450.6999999993 3 1505916 1594611.7 -88695.6999999998 4 1513378 1486895.3 26482.6999999998 5 1977605 1662537.9 315067.100000000 6 1873830 1795952.5 77877.5000000001 7 1424049 1406935.7 17113.3000000002 8 1322740 1403163.7 -80423.6999999995 9 1584826 1669724.5 -84898.5000000005 10 1680460 1646878.5 33581.5000000000 11 1648574 1721605.9 -73031.8999999998 12 3095469 3056405.7 39063.2999999999 13 1307983 1337114.25 -29131.2499999995 14 1367589 1375221.25 -7632.25000000013 15 1572718 1704959.25 -132241.25 16 1611603 1597242.85 14360.1500000001 17 1641196 1772885.45 -131689.45 18 1845262 1906300.05 -61038.05 19 1464238 1517283.25 -53045.25 20 1402386 1513511.25 -111125.25 21 2077100 1780072.05 297027.95 22 1691130 1757226.05 -66096.0499999999 23 1729013 1831953.45 -102940.45 24 3347792 3166753.25 181038.75 25 1365088 1447461.8 -82373.7999999996 26 1545460 1485568.8 59891.1999999999 27 1844355 1815306.8 29048.2 28 1775550 1707590.4 67959.6 29 1721779 1883233 -161454 30 2128726 2016647.6 112078.4 31 1664320 1627630.8 36689.2 32 1769471 1623858.8 145612.200000000 33 1904578 1890419.6 14158.4000000001 34 1872042 1867573.6 4468.4 35 1802181 1942301 -140120 36 3222199 3277100.8 -54901.7999999999 37 1491414 1557809.35 -66395.3499999995 38 1658519 1595916.35 62602.6499999998 39 2079207 1925654.35 153552.65 40 1748767 1817937.95 -69170.95 41 2084447 1993580.55 90866.4499999999 42 2067182 2126995.15 -59813.15 43 1718123 1737978.35 -19855.3500000001 44 1782337 1734206.35 48130.6499999999 45 1958118 2000767.15 -42649.1499999999 46 2028681 1977921.15 50759.85 47 2076128 2052648.55 23479.4500000000 48 3383873 3387448.35 -3575.35000000004 49 1870369 1668156.9 202212.100000000 50 1654853 1706263.9 -51410.9000000002 51 2074338 2036001.9 38336.0999999999 52 1888654 1928285.5 -39631.5 53 1991138 2103928.1 -112790.100000000 54 2168238 2237342.7 -69104.7 55 1867424 1848325.9 19098.1 56 1842360 1844553.9 -2193.90000000018 57 1927476 2111114.7 -183638.7 58 2065555 2088268.7 -22713.7000000000 59 2455609 2162996.1 292612.9 60 3336171 3497795.9 -161624.9 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0172609973219868 0.0345219946439736 0.982739002678013 17 0.698464535015938 0.603070929968125 0.301535464984062 18 0.567921032276098 0.864157935447804 0.432078967723902 19 0.437241137302249 0.874482274604499 0.56275886269775 20 0.36199471124752 0.72398942249504 0.63800528875248 21 0.849056127656002 0.301887744687996 0.150943872343998 22 0.789391356616517 0.421217286766967 0.210608643383483 23 0.753298634404754 0.493402731190492 0.246701365595246 24 0.797298812687623 0.405402374624755 0.202701187312377 25 0.759288350261437 0.481423299477127 0.240711649738563 26 0.710965570674967 0.578068858650066 0.289034429325033 27 0.681904770878705 0.636190458242591 0.318095229121295 28 0.614233509810952 0.771532980378096 0.385766490189048 29 0.70731147083125 0.5853770583375 0.29268852916875 30 0.695523488002111 0.608953023995778 0.304476511997889 31 0.61146434485073 0.777071310298541 0.388535655149271 32 0.643430587722623 0.713138824554754 0.356569412277377 33 0.614779266508008 0.770441466983984 0.385220733491992 34 0.515155888148918 0.969688223702165 0.484844111851082 35 0.698920665675672 0.602158668648657 0.301079334324328 36 0.639297208783688 0.721405582432624 0.360702791216312 37 0.801436041634648 0.397127916730704 0.198563958365352 38 0.733356015610672 0.533287968778655 0.266643984389328 39 0.701500946469584 0.596998107060832 0.298499053530416 40 0.619239056224446 0.761521887551108 0.380760943775554 41 0.622055876840537 0.755888246318927 0.377944123159463 42 0.4963103491084 0.9926206982168 0.5036896508916 43 0.365316066550486 0.730632133100973 0.634683933449514 44 0.226612541710027 0.453225083420053 0.773387458289973 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 0.0344827586206897 OK 10% type I error level 1 0.0344827586206897 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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