Paper H4 Vrouwen Multiple Regression (No seasonal, 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 14:25:55 -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/t12294629763vgg3lwl45wrtl7.htm/, Retrieved Tue, 16 Dec 2008 22:29:45 +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/t12294629763vgg3lwl45wrtl7.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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Vrouwen[t] = + 321046.305590762 + 3652.16906069565Dummy[t] -868.389552779286t + 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) 321046.305590762 5243.929306 61.2225 0 0 Dummy 3652.16906069565 9627.822483 0.3793 0.705778 0.352889 t -868.389552779286 262.014574 -3.3143 0.001562 0.000781 Multiple Linear Regression - Regression Statistics Multiple R 0.600535714783968 R-squared 0.360643144731091 Adjusted R-squared 0.339331249555461 F-TEST (value) 16.9221527113872 F-TEST (DF numerator) 2 F-TEST (DF denominator) 60 p-value 1.48696170199081e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 19472.1080189223 Sum Squared Residuals 22749779442.0346 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 308347 320177.916037983 -11830.9160379828 2 298427 319309.526485203 -20882.5264852033 3 289231 318441.136932424 -29210.136932424 4 291975 317572.747379645 -25597.7473796447 5 294912 316704.357826865 -21792.3578268654 6 293488 315835.968274086 -22347.9682740861 7 290555 314967.578721307 -24412.5787213068 8 284736 314099.189168528 -29363.1891685276 9 281818 313230.799615748 -31412.7996157483 10 287854 312362.410062969 -24508.410062969 11 316263 311494.020510190 4768.9794898103 12 325412 310625.630957410 14786.3690425896 13 326011 309757.241404631 16253.7585953689 14 328282 308888.851851852 19393.1481481482 15 317480 308020.462299073 9459.53770092744 16 317539 307152.072746293 10386.9272537067 17 313737 306283.683193514 7453.31680648601 18 312276 305415.293640735 6860.7063592653 19 309391 304546.904087955 4844.09591204458 20 302950 303678.514535176 -728.514535176134 21 300316 302810.124982397 -2494.12498239685 22 304035 301941.735429618 2093.26457038244 23 333476 301073.345876838 32402.6541231617 24 337698 300204.956324059 37493.043675941 25 335932 299336.566771280 36595.4332287203 26 323931 298468.177218500 25462.8227814996 27 313927 297599.787665721 16327.2123342789 28 314485 300383.567173638 14101.4328263625 29 313218 299515.177620858 13702.8223791418 30 309664 298646.788068079 11017.2119319211 31 302963 297778.3985153 5184.60148470036 32 298989 296910.008962520 2078.99103747965 33 298423 296041.619409741 2381.38059025893 34 301631 295173.229856962 6457.77014303822 35 329765 294304.840304182 35460.1596958175 36 335083 293436.450751403 41646.5492485968 37 327616 292568.061198624 35047.9388013761 38 309119 291699.671645845 17419.3283541554 39 295916 290831.282093065 5084.71790693464 40 291413 289962.892540286 1450.10745971393 41 291542 289094.502987507 2447.49701249322 42 284678 288226.113434727 -3548.1134347275 43 276475 287357.723881948 -10882.7238819482 44 272566 286489.334329169 -13923.3343291689 45 264981 285620.944776390 -20639.9447763896 46 263290 284752.555223610 -21462.5552236104 47 296806 283884.165670831 12921.8343291689 48 303598 283015.776118052 20582.2238819482 49 286994 282147.386565273 4846.6134347275 50 276427 281278.997012493 -4851.99701249322 51 266424 280410.607459714 -13986.6074597139 52 267153 279542.217906935 -12389.2179069346 53 268381 278673.828354155 -10292.8283541554 54 262522 277805.438801376 -15283.4388013761 55 255542 276937.049248597 -21395.0492485968 56 253158 276068.659695818 -22910.6596958175 57 243803 275200.270143038 -31397.2701430382 58 250741 274331.880590259 -23590.8805902589 59 280445 273463.491037480 6981.50896252035 60 285257 272595.101484700 12661.8985152996 61 270976 271726.711931921 -750.711931921075 62 261076 270858.322379142 -9782.32237914179 63 255603 269989.932826362 -14386.9328263625 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.0581783094557606 0.116356618911521 0.94182169054424 7 0.0200698658066299 0.0401397316132597 0.97993013419337 8 0.00748783518793323 0.0149756703758665 0.992512164812067 9 0.00329432700044276 0.00658865400088552 0.996705672999557 10 0.00293396610566584 0.00586793221133169 0.997066033894334 11 0.214218361927432 0.428436723854865 0.785781638072568 12 0.474081617474035 0.94816323494807 0.525918382525965 13 0.524088464804248 0.951823070391504 0.475911535195752 14 0.504643171742010 0.990713656515979 0.495356828257990 15 0.416760225077796 0.833520450155593 0.583239774922204 16 0.334924675872461 0.669849351744922 0.665075324127539 17 0.278629556027276 0.557259112054553 0.721370443972724 18 0.237683515551333 0.475367031102666 0.762316484448667 19 0.219466532464582 0.438933064929165 0.780533467535418 20 0.259838313021378 0.519676626042756 0.740161686978622 21 0.336754039193804 0.673508078387608 0.663245960806196 22 0.38303831078344 0.76607662156688 0.61696168921656 23 0.379827746519073 0.759655493038145 0.620172253480927 24 0.382970679529329 0.765941359058658 0.617029320470671 25 0.356291890781325 0.712583781562651 0.643708109218675 26 0.291978604479081 0.583957208958163 0.708021395520919 27 0.262508076416758 0.525016152833517 0.737491923583242 28 0.203921484597570 0.407842969195139 0.79607851540243 29 0.154498338385676 0.308996676771351 0.845501661614324 30 0.117311111805948 0.234622223611897 0.882688888194052 31 0.100187357098321 0.200374714196642 0.89981264290168 32 0.0947851177482016 0.189570235496403 0.905214882251798 33 0.0883777608038819 0.176755521607764 0.911622239196118 34 0.0713891674605169 0.142778334921034 0.928610832539483 35 0.0961606544890981 0.192321308978196 0.903839345510902 36 0.202708075581646 0.405416151163291 0.797291924418354 37 0.325320254217269 0.650640508434538 0.674679745782731 38 0.349526557692925 0.69905311538585 0.650473442307075 39 0.385093923346305 0.770187846692611 0.614906076653695 40 0.427066096936283 0.854132193872566 0.572933903063717 41 0.455267055686381 0.910534111372762 0.544732944313619 42 0.493005093122613 0.986010186245226 0.506994906877387 43 0.553287975504187 0.893424048991627 0.446712024495813 44 0.606717536185227 0.786564927629547 0.393282463814773 45 0.706451767316996 0.587096465366008 0.293548232683004 46 0.798792296321261 0.402415407357477 0.201207703678739 47 0.773565680845827 0.452868638308347 0.226434319154173 48 0.869541991732436 0.260916016535129 0.130458008267565 49 0.887300243098982 0.225399513802037 0.112699756901018 50 0.878676946573587 0.242646106852827 0.121323053426413 51 0.845867984740501 0.308264030518998 0.154132015259499 52 0.80450356715871 0.390992865682580 0.195496432841290 53 0.76858823824187 0.462823523516260 0.231411761758130 54 0.703900966337819 0.592198067324362 0.296099033662181 55 0.601756334329801 0.796487331340398 0.398243665670199 56 0.478950616287454 0.957901232574908 0.521049383712546 57 0.514787260224767 0.970425479550466 0.485212739775233 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0384615384615385 NOK 5% type I error level 4 0.0769230769230769 NOK 10% type I error level 4 0.0769230769230769 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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