Multiple Regression eigen dataset + dummie

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Tue, 25 Nov 2008 09:06:35 -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/Nov/25/t122762933679jvtaifg5rklzg.htm/, Retrieved Tue, 25 Nov 2008 16:09:11 +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/Nov/25/t122762933679jvtaifg5rklzg.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}, }

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Natalie De Wilde

Dataseries X:

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6.06 106.8 5.983 114.3 6.11 105.7 6.143 90.1 6.093 91.6 6.148 97.7 6.464 100.8 6.532 104.6 6.321 95.9 6.23 102.7 6.176 104 6.338 107.9 6.462 113.8 6.401 113.8 6.46 123.1 6.519 125.1 6.542 137.6 6.637 134 7.114 140.3 7.579 152.1 7.408 150.6 8.243 167.3 8.243 153.2 8.434 142 8.576 154.4 8.58 158.5 8.645 180.9 8.66 181.3 8.72 172.4 8.787 192 9.162 199.3 9.144 215.4 8.806 214.3 8.778 201.5 8.66 190.5 8.826 196 8.609 215.7 8.628 209.4 8.619 214.1 8.775 237.8 8.84 239 8.745 237.8 9.092 251.5 8.934 248.8 8.749 215.4 8.298 201.2 8.067 203.1 7.969 214.2 7.999 188.9 7.865 203 7.746 213.3 7.633 228.5 7.458 228.2 7.391 240.9 7.856 258.8 7.72 248.5 7.297 269.2 7.123 289.6 7.004 323.4 7.151 317.2

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation werkloosheid_textielsector[t] = + 5.81197085338971 + 0.0089425481890016energieprijzen[t] + 0.207324617989468M1[t] + 0.117724234416474M2[t] + 0.0690787206166146M3[t] + 0.0480107263254788M4[t] + 0.0167763718990092M5[t] -0.0374208485307496M6[t] + 0.267090839363828M7[t] + 0.272742412537294M8[t] + 0.0449633472448334M9[t] + 0.0278342377663408M10[t] -0.102952323523151M11[t] + 0.00510329659966777t + 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) 5.81197085338971 0.71066 8.1783 0 0 energieprijzen 0.0089425481890016 0.006354 1.4073 0.166053 0.083027 M1 0.207324617989468 0.603098 0.3438 0.732589 0.366294 M2 0.117724234416474 0.602017 0.1955 0.845824 0.422912 M3 0.0690787206166146 0.600776 0.115 0.908959 0.45448 M4 0.0480107263254788 0.600272 0.08 0.936599 0.468299 M5 0.0167763718990092 0.599396 0.028 0.977792 0.488896 M6 -0.0374208485307496 0.599422 -0.0624 0.950492 0.475246 M7 0.267090839363828 0.602186 0.4435 0.659458 0.329729 M8 0.272742412537294 0.602196 0.4529 0.652741 0.32637 M9 0.0449633472448334 0.598006 0.0752 0.940391 0.470195 M10 0.0278342377663408 0.59783 0.0466 0.963066 0.481533 M11 -0.102952323523151 0.597535 -0.1723 0.863961 0.431981 t 0.00510329659966777 0.021573 0.2366 0.814052 0.407026 Multiple Linear Regression - Regression Statistics Multiple R 0.598938556194584 R-squared 0.358727394096452 Adjusted R-squared 0.177498179384580 F-TEST (value) 1.97941261659593 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.0450107465049226 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.944360703491922 Sum Squared Residuals 41.0235883617888 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.06 6.97946291456422 -0.919462914564217 2 5.983 6.9620349390084 -0.979034939008404 3 6.11 6.8415868073828 -0.731586807382796 4 6.143 6.6861183579429 -0.543118357942903 5 6.093 6.6734011223996 -0.580401122399603 6 6.148 6.67885674252242 -0.530856742522422 7 6.464 7.01619362640257 -0.552193626402571 8 6.532 7.06093017929391 -0.528930179293911 9 6.321 6.7604542413568 -0.439454241356806 10 6.23 6.80923775616319 -0.579237756163191 11 6.176 6.69517980411907 -0.519179804119069 12 6.338 6.838111362179 -0.500111362178994 13 6.462 7.10330031108324 -0.64130031108324 14 6.401 7.01880322410991 -0.617803224109913 15 6.46 7.05842670506744 -0.598426705067436 16 6.519 7.06034710375397 -0.541347103753971 17 6.542 7.14599789828969 -0.60399789828969 18 6.637 7.0647108009792 -0.427710800979193 19 7.114 7.43066383906415 -0.316663839064148 20 7.579 7.5469407774675 0.0320592225324994 21 7.408 7.3108511864912 0.097148813508795 22 8.243 7.4481659283687 0.794834071631293 23 8.243 7.19639273421396 1.04660726578604 24 8.434 7.20429181461996 1.22970818538004 25 8.576 7.52760732675272 1.04839267324728 26 8.58 7.4797746873543 1.10022531264570 27 8.645 7.63654554958774 1.00845445041226 28 8.66 7.62415787117187 1.03584212882813 29 8.72 7.51843813446296 1.20156186553704 30 8.787 7.6446181551373 1.14238184486270 31 9.162 8.01951374141126 1.14248625858875 32 9.144 8.17424363702732 0.969756362972686 33 8.806 7.94173106532662 0.864268934673379 34 8.778 7.81524063562857 0.962759364371426 35 8.66 7.59118934085973 1.06881065914027 36 8.826 7.74842897602206 1.07757102397794 37 8.609 8.13702508993453 0.471974910065472 38 8.628 7.99618994937049 0.631810050629509 39 8.619 7.9946777086586 0.624322291341392 40 8.775 8.19065140304648 0.584348596953523 41 8.84 8.17525140304648 0.664748596953523 42 8.745 8.11542642138958 0.629573578610415 43 9.092 8.54755431607315 0.544445683926849 44 8.934 8.53416430573598 0.399835694264019 45 8.749 8.01280742753053 0.736192572469466 46 8.298 7.87379743036789 0.424202569632112 47 8.067 7.76510500723717 0.301894992762834 48 7.969 7.9724229122579 -0.00342291225790253 49 7.999 7.9586043576653 0.0403956423347012 50 7.865 8.0001972001569 -0.135197200156894 51 7.746 8.04876322930342 -0.302763229303419 52 7.633 8.16872526408478 -0.535725264084775 53 7.458 8.13991144180127 -0.681911441801273 54 7.391 8.2043878799715 -0.813387879971502 55 7.856 8.67407447704888 -0.818074477048876 56 7.72 8.5927211004753 -0.872721100475294 57 7.297 8.55515607929483 -1.25815607929483 58 7.123 8.72555824947164 -1.60255824947164 59 7.004 8.90213311357007 -1.89813311357007 60 7.151 8.95474493492108 -1.80374493492108 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.000103650033812628 0.000207300067625256 0.999896349966187 18 1.99787746941637e-05 3.99575493883274e-05 0.999980021225306 19 8.03442605757157e-05 0.000160688521151431 0.999919655739424 20 0.00270442067918692 0.00540884135837385 0.997295579320813 21 0.00764982270363962 0.0152996454072792 0.99235017729636 22 0.137571899004514 0.275143798009027 0.862428100995486 23 0.421420894606539 0.842841789213078 0.578579105393461 24 0.76849289872678 0.463014202546439 0.231507101273220 25 0.895588014763647 0.208823970472706 0.104411985236353 26 0.943707169697445 0.112585660605110 0.0562928303025548 27 0.944691636137366 0.110616727725269 0.0553083638626344 28 0.94965000846009 0.100699983079820 0.0503499915399102 29 0.959496159327333 0.0810076813453333 0.0405038406726666 30 0.955713059772126 0.0885738804557471 0.0442869402278736 31 0.962686992899654 0.0746260142006923 0.0373130071003461 32 0.969830128714422 0.0603397425711568 0.0301698712855784 33 0.987216005952317 0.0255679880953666 0.0127839940476833 34 0.989106859601872 0.0217862807962551 0.0108931403981276 35 0.991093913881526 0.0178121722369473 0.00890608611847366 36 0.991775470308462 0.0164490593830751 0.00822452969153757 37 0.997632376809854 0.00473524638029267 0.00236762319014633 38 0.998893178829437 0.00221364234112564 0.00110682117056282 39 0.999510539000436 0.000978921999127265 0.000489460999563632 40 0.999117185062888 0.00176562987422379 0.000882814937111896 41 0.996622770974776 0.00675445805044762 0.00337722902522381 42 0.987756314641744 0.0244873707165116 0.0122436853582558 43 0.958453006894422 0.0830939862111564 0.0415469931055782 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 9 0.333333333333333 NOK 5% type I error level 15 0.555555555555556 NOK 10% type I error level 20 0.740740740740741 NOK

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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