Dow Jones and Dummy

*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 13 Dec 2008 06:10:09 -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/13/t1229173954be0z55qx6tu96s6.htm/, Retrieved Sat, 13 Dec 2008 14:12:43 +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/2008/Dec/13/t1229173954be0z55qx6tu96s6.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

10540.05 0 10601.61 0 10323.73 0 10418.4 0 10092.96 0 10364.91 0 10152.09 0 10032.8 0 10204.59 0 10001.6 0 10411.75 0 10673.38 0 10539.51 0 10723.78 0 10682.06 0 10283.19 0 10377.18 0 10486.64 0 10545.38 0 10554.27 0 10532.54 0 10324.31 0 10695.25 0 10827.81 0 10872.48 0 10971.19 0 11145.65 0 11234.68 0 11333.88 0 10997.97 0 11036.89 0 11257.35 0 11533.59 0 11963.12 0 12185.15 0 12377.62 0 12512.89 0 12631.48 0 12268.53 0 12754.8 1 13407.75 1 13480.21 1 13673.28 1 13239.71 1 13557.69 1 13901.28 1 13200.58 1 13406.97 1 12538.12 1 12419.57 1 12193.88 1 12656.63 1 12812.48 1 12056.67 1 11322.38 1 11530.75 1 11114.08 1 9181.73 1 8614.55 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 DowJones[t] = + 10890.0579487179 + 1463.09755128205Dummy[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) 10890.0579487179 161.908667 67.2605 0 0 Dummy 1463.09755128205 278.087267 5.2613 2e-06 1e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.571740250962192 R-squared 0.32688691457031 Adjusted R-squared 0.315077913071544 F-TEST (value) 27.6811646272087 F-TEST (DF numerator) 1 F-TEST (DF denominator) 57 p-value 2.24571108931038e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1011.11929930318 Sum Squared Residuals 58274647.533131 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10540.05 10890.0579487180 -350.00794871798 2 10601.61 10890.0579487179 -288.447948717946 3 10323.73 10890.0579487179 -566.327948717948 4 10418.4 10890.0579487179 -471.657948717948 5 10092.96 10890.0579487179 -797.097948717949 6 10364.91 10890.0579487179 -525.147948717948 7 10152.09 10890.0579487179 -737.967948717948 8 10032.8 10890.0579487179 -857.257948717949 9 10204.59 10890.0579487179 -685.467948717948 10 10001.6 10890.0579487179 -888.457948717947 11 10411.75 10890.0579487179 -478.307948717948 12 10673.38 10890.0579487179 -216.677948717949 13 10539.51 10890.0579487179 -350.547948717948 14 10723.78 10890.0579487179 -166.277948717947 15 10682.06 10890.0579487179 -207.997948717948 16 10283.19 10890.0579487179 -606.867948717947 17 10377.18 10890.0579487179 -512.877948717948 18 10486.64 10890.0579487179 -403.417948717949 19 10545.38 10890.0579487179 -344.677948717949 20 10554.27 10890.0579487179 -335.787948717948 21 10532.54 10890.0579487179 -357.517948717947 22 10324.31 10890.0579487179 -565.747948717948 23 10695.25 10890.0579487179 -194.807948717948 24 10827.81 10890.0579487179 -62.2479487179484 25 10872.48 10890.0579487179 -17.5779487179484 26 10971.19 10890.0579487179 81.1320512820526 27 11145.65 10890.0579487179 255.592051282052 28 11234.68 10890.0579487179 344.622051282052 29 11333.88 10890.0579487179 443.822051282051 30 10997.97 10890.0579487179 107.912051282051 31 11036.89 10890.0579487179 146.832051282052 32 11257.35 10890.0579487179 367.292051282052 33 11533.59 10890.0579487179 643.532051282052 34 11963.12 10890.0579487179 1073.06205128205 35 12185.15 10890.0579487179 1295.09205128205 36 12377.62 10890.0579487179 1487.56205128205 37 12512.89 10890.0579487179 1622.83205128205 38 12631.48 10890.0579487179 1741.42205128205 39 12268.53 10890.0579487179 1378.47205128205 40 12754.8 12353.1555 401.644500000000 41 13407.75 12353.1555 1054.5945 42 13480.21 12353.1555 1127.0545 43 13673.28 12353.1555 1320.12450000000 44 13239.71 12353.1555 886.5545 45 13557.69 12353.1555 1204.53450000000 46 13901.28 12353.1555 1548.1245 47 13200.58 12353.1555 847.4245 48 13406.97 12353.1555 1053.8145 49 12538.12 12353.1555 184.964500000001 50 12419.57 12353.1555 66.4145 51 12193.88 12353.1555 -159.275500000000 52 12656.63 12353.1555 303.474499999999 53 12812.48 12353.1555 459.3245 54 12056.67 12353.1555 -296.485500000000 55 11322.38 12353.1555 -1030.7755 56 11530.75 12353.1555 -822.4055 57 11114.08 12353.1555 -1239.0755 58 9181.73 12353.1555 -3171.4255 59 8614.55 12353.1555 -3738.6055 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.014550503313173 0.029101006626346 0.985449496686827 6 0.00262994023713794 0.00525988047427588 0.997370059762862 7 0.000822383901253337 0.00164476780250667 0.999177616098747 8 0.000413784279142333 0.000827568558284666 0.999586215720858 9 9.08088839263032e-05 0.000181617767852606 0.999909191116074 10 4.30325519873216e-05 8.60651039746431e-05 0.999956967448013 11 1.01830139057641e-05 2.03660278115281e-05 0.999989816986094 12 7.52890169790515e-06 1.50578033958103e-05 0.999992471098302 13 2.35769367273524e-06 4.71538734547048e-06 0.999997642306327 14 1.58892632118695e-06 3.1778526423739e-06 0.999998411073679 15 7.22344542320889e-07 1.44468908464178e-06 0.999999277655458 16 1.85407309810371e-07 3.70814619620741e-07 0.99999981459269 17 4.26226166692469e-08 8.52452333384937e-08 0.999999957377383 18 1.03568074083745e-08 2.07136148167491e-08 0.999999989643193 19 2.79347160061773e-09 5.58694320123546e-09 0.999999997206528 20 7.57653735379483e-10 1.51530747075897e-09 0.999999999242346 21 1.93075822257269e-10 3.86151644514538e-10 0.999999999806924 22 4.94766628602966e-11 9.89533257205932e-11 0.999999999950523 23 2.40274930023819e-11 4.80549860047639e-11 0.999999999975973 24 2.36333324752883e-11 4.72666649505766e-11 0.999999999976367 25 2.53000537183595e-11 5.0600107436719e-11 0.9999999999747 26 4.07260902119855e-11 8.1452180423971e-11 0.999999999959274 27 1.47202728490201e-10 2.94405456980402e-10 0.999999999852797 28 5.26921170980392e-10 1.05384234196078e-09 0.999999999473079 29 1.91359074158454e-09 3.82718148316908e-09 0.99999999808641 30 1.32677740558366e-09 2.65355481116731e-09 0.999999998673223 31 1.02720415637502e-09 2.05440831275004e-09 0.999999998972796 32 1.54805175074853e-09 3.09610350149706e-09 0.999999998451948 33 5.73160843242451e-09 1.14632168648490e-08 0.999999994268392 34 8.07961049660301e-08 1.61592209932060e-07 0.999999919203895 35 9.36959090249285e-07 1.87391818049857e-06 0.99999906304091 36 7.52565377728621e-06 1.50513075545724e-05 0.999992474346223 37 3.79930939865708e-05 7.59861879731415e-05 0.999962006906013 38 0.000134757981128406 0.000269515962256812 0.999865242018872 39 0.000174330523777128 0.000348661047554256 0.999825669476223 40 8.37680216125402e-05 0.000167536043225080 0.999916231978387 41 5.82374578981138e-05 0.000116474915796228 0.999941762542102 42 4.19684203060543e-05 8.39368406121085e-05 0.999958031579694 43 3.98181536850997e-05 7.96363073701993e-05 0.999960181846315 44 2.62775639557538e-05 5.25551279115075e-05 0.999973722436044 45 2.67441631463034e-05 5.34883262926069e-05 0.999973255836854 46 6.41827149232175e-05 0.000128365429846435 0.999935817285077 47 6.90508739984713e-05 0.000138101747996943 0.999930949126002 48 0.000134130580885443 0.000268261161770886 0.999865869419114 49 0.000134484577973739 0.000268969155947478 0.999865515422026 50 0.000134136160802559 0.000268272321605118 0.999865863839198 51 0.000126836983338825 0.000253673966677651 0.999873163016661 52 0.000221359600752883 0.000442719201505765 0.999778640399247 53 0.00117158598224193 0.00234317196448386 0.998828414017758 54 0.00320661650120749 0.00641323300241498 0.996793383498793 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 49 0.98 NOK 5% type I error level 50 1 NOK 10% type I error level 50 1 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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