Paper H4 Vrouwen Multiple Regression (Monthly dummies, No trend)

*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: Tue, 16 Dec 2008 14:17:12 -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/16/t1229462271trfgp4wvc06nugq.htm/, Retrieved Tue, 16 Dec 2008 22:18:00 +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/16/t1229462271trfgp4wvc06nugq.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:

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308347 0 298427 0 289231 0 291975 0 294912 0 293488 0 290555 0 284736 0 281818 0 287854 0 316263 0 325412 0 326011 0 328282 0 317480 0 317539 0 313737 0 312276 0 309391 0 302950 0 300316 0 304035 0 333476 0 337698 0 335932 0 323931 0 313927 0 314485 1 313218 1 309664 1 302963 1 298989 1 298423 1 301631 1 329765 1 335083 1 327616 1 309119 1 295916 1 291413 1 291542 1 284678 1 276475 1 272566 1 264981 1 263290 1 296806 1 303598 1 286994 1 276427 1 266424 1 267153 1 268381 1 262522 1 255542 1 253158 1 243803 1 250741 1 280445 1 285257 1 270976 1 261076 1 255603 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Vrouwen[t] = + 331454.239215686 -23407.7320261438Dummy[t] -10437.7065359477M1[t] -20206.7065359477M2[t] -29986.8732026144M3[t] -20896.6000000000M4[t] -21051.5999999999M5[t] -24884.0000000000M6[t] -30424.4000000000M7[t] -34929.8M8[t] -39541.4M9[t] -35899.4M10[t] -6058.59999999998M11[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) 331454.239215686 9046.89495 36.6373 0 0 Dummy -23407.7320261438 4892.000519 -4.7849 1.6e-05 8e-06 M1 -10437.7065359477 11597.240197 -0.9 0.372426 0.186213 M2 -20206.7065359477 11597.240197 -1.7424 0.087592 0.043796 M3 -29986.8732026144 11597.240197 -2.5857 0.01268 0.00634 M4 -20896.6000000000 12102.140915 -1.7267 0.090398 0.045199 M5 -21051.5999999999 12102.140915 -1.7395 0.088101 0.044051 M6 -24884.0000000000 12102.140915 -2.0562 0.045005 0.022503 M7 -30424.4000000000 12102.140915 -2.514 0.015203 0.007602 M8 -34929.8 12102.140915 -2.8862 0.005743 0.002871 M9 -39541.4 12102.140915 -3.2673 0.001966 0.000983 M10 -35899.4 12102.140915 -2.9664 0.004611 0.002306 M11 -6058.59999999998 12102.140915 -0.5006 0.618834 0.309417 Multiple Linear Regression - Regression Statistics Multiple R 0.696765395071021 R-squared 0.485482015768476 Adjusted R-squared 0.36199769955291 F-TEST (value) 3.93152774900557 F-TEST (DF numerator) 12 F-TEST (DF denominator) 50 p-value 0.000290426128867538 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 19135.1649279895 Sum Squared Residuals 18307726841.0680 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 308347 321016.532679739 -12669.5326797387 2 298427 311247.532679739 -12820.5326797385 3 289231 301467.366013072 -12236.3660130719 4 291975 310557.639215686 -18582.6392156863 5 294912 310402.639215686 -15490.6392156862 6 293488 306570.239215686 -13082.2392156863 7 290555 301029.839215686 -10474.8392156863 8 284736 296524.439215686 -11788.4392156863 9 281818 291912.839215686 -10094.8392156863 10 287854 295554.839215686 -7700.83921568627 11 316263 325395.639215686 -9132.63921568626 12 325412 331454.239215686 -6042.23921568625 13 326011 321016.532679739 4994.46732026147 14 328282 311247.532679739 17034.4673202614 15 317480 301467.366013072 16012.6339869281 16 317539 310557.639215686 6981.36078431373 17 313737 310402.639215686 3334.36078431372 18 312276 306570.239215686 5705.76078431372 19 309391 301029.839215686 8361.16078431374 20 302950 296524.439215686 6425.56078431373 21 300316 291912.839215686 8403.16078431374 22 304035 295554.839215686 8480.16078431372 23 333476 325395.639215686 8080.36078431374 24 337698 331454.239215686 6243.76078431375 25 335932 321016.532679739 14915.4673202615 26 323931 311247.532679739 12683.4673202614 27 313927 301467.366013072 12459.6339869281 28 314485 287149.907189542 27335.0928104575 29 313218 286994.907189542 26223.0928104575 30 309664 283162.507189542 26501.4928104575 31 302963 277622.107189542 25340.8928104575 32 298989 273116.707189542 25872.2928104575 33 298423 268505.107189542 29917.8928104575 34 301631 272147.107189542 29483.8928104575 35 329765 301987.907189542 27777.0928104575 36 335083 308046.507189542 27036.4928104575 37 327616 297608.800653595 30007.1993464053 38 309119 287839.800653595 21279.1993464052 39 295916 278059.633986928 17856.3660130719 40 291413 287149.907189542 4263.09281045751 41 291542 286994.907189542 4547.0928104575 42 284678 283162.507189542 1515.49281045751 43 276475 277622.107189542 -1147.10718954247 44 272566 273116.707189542 -550.707189542478 45 264981 268505.107189542 -3524.10718954247 46 263290 272147.107189542 -8857.10718954249 47 296806 301987.907189542 -5181.90718954248 48 303598 308046.507189542 -4448.50718954247 49 286994 297608.800653595 -10614.8006535947 50 276427 287839.800653595 -11412.8006535948 51 266424 278059.633986928 -11635.6339869281 52 267153 287149.907189542 -19996.9071895425 53 268381 286994.907189542 -18613.9071895425 54 262522 283162.507189542 -20640.5071895425 55 255542 277622.107189542 -22080.1071895425 56 253158 273116.707189542 -19958.7071895425 57 243803 268505.107189542 -24702.1071895425 58 250741 272147.107189542 -21406.1071895425 59 280445 301987.907189542 -21542.9071895425 60 285257 308046.507189542 -22789.5071895425 61 270976 297608.800653595 -26632.8006535947 62 261076 287839.800653595 -26763.8006535948 63 255603 278059.633986928 -22456.6339869281 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.597912332447587 0.804175335104825 0.402087667552413 17 0.486815803070351 0.973631606140702 0.513184196929649 18 0.390275863782931 0.780551727565862 0.609724136217069 19 0.308236645578904 0.616473291157809 0.691763354421096 20 0.238419723300348 0.476839446600697 0.761580276699652 21 0.182196049081841 0.364392098163681 0.81780395091816 22 0.131278285916206 0.262556571832412 0.868721714083794 23 0.0948605119707088 0.189721023941418 0.90513948802929 24 0.0620324082343845 0.124064816468769 0.937967591765616 25 0.0479396142521541 0.0958792285043082 0.952060385747846 26 0.0294543389329427 0.0589086778658854 0.970545661067057 27 0.0175223687006167 0.0350447374012335 0.982477631299383 28 0.0118085152066419 0.0236170304132838 0.988191484793358 29 0.00779690697720825 0.0155938139544165 0.992203093022792 30 0.00553401522509116 0.0110680304501823 0.994465984774909 31 0.00423765591816599 0.00847531183633199 0.995762344081834 32 0.00323939434248237 0.00647878868496473 0.996760605657518 33 0.00340351815660854 0.00680703631321709 0.996596481843391 34 0.00423205080740839 0.00846410161481677 0.995767949192592 35 0.00532148753846566 0.0106429750769313 0.994678512461534 36 0.0077924972880942 0.0155849945761884 0.992207502711906 37 0.0247914429029719 0.0495828858059437 0.975208557097028 38 0.0724064322838574 0.144812864567715 0.927593567716143 39 0.175439722032366 0.350879444064732 0.824560277967634 40 0.228459453433864 0.456918906867727 0.771540546566136 41 0.276738100565641 0.553476201131281 0.72326189943436 42 0.343383498948965 0.68676699789793 0.656616501051035 43 0.417359134930807 0.834718269861613 0.582640865069193 44 0.459293428829598 0.918586857659196 0.540706571170402 45 0.544804082881854 0.910391834236292 0.455195917118146 46 0.521236066244368 0.957527867511263 0.478763933755632 47 0.49584395766994 0.99168791533988 0.50415604233006 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.125 NOK 5% type I error level 11 0.34375 NOK 10% type I error level 13 0.40625 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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