Paper H4 Vrouwen Multiple Regression (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 14:32:40 -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/t12294632372nj4fu2m2m36lke.htm/, Retrieved Tue, 16 Dec 2008 22:33:57 +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/t12294632372nj4fu2m2m36lke.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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Vrouwen[t] = + 349150.813333333 + 9773.3444444444Dummy[t] -12342.5461111112M1[t] -21066.9566666667M2[t] -29802.5338888889M3[t] -29253.3155555555M4[t] -28363.7261111111M5[t] -31151.5366666666M6[t] -35647.3472222222M7[t] -39108.1577777778M8[t] -42675.1683333333M9[t] -37988.5788888889M10[t] -7103.18944444443M11[t] -1044.58944444444t + 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) 349150.813333333 8539.665595 40.8858 0 0 Dummy 9773.3444444444 8290.341127 1.1789 0.244138 0.122069 M1 -12342.5461111112 9789.730415 -1.2608 0.213364 0.106682 M2 -21066.9566666667 9782.799741 -2.1535 0.036229 0.018115 M3 -29802.5338888889 9781.104829 -3.0469 0.003718 0.001859 M4 -29253.3155555555 10366.271094 -2.822 0.006876 0.003438 M5 -28363.7261111111 10329.12815 -2.746 0.008413 0.004207 M6 -31151.5366666666 10296.829222 -3.0254 0.003948 0.001974 M7 -35647.3472222222 10269.420015 -3.4712 0.001091 0.000546 M8 -39108.1577777778 10246.939768 -3.8166 0.00038 0.00019 M9 -42675.1683333333 10229.420977 -4.1718 0.000123 6.2e-05 M10 -37988.5788888889 10216.889163 -3.7182 0.000516 0.000258 M11 -7103.18944444443 10209.362691 -0.6958 0.489871 0.244935 t -1044.58944444444 226.375508 -4.6144 2.9e-05 1.4e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.800835531194454 R-squared 0.641337548023504 Adjusted R-squared 0.546182203621576 F-TEST (value) 6.73990044442015 F-TEST (DF numerator) 13 F-TEST (DF denominator) 49 p-value 3.61344651977902e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 16138.4510315766 Sum Squared Residuals 12762030483.2311 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 308347 335763.677777778 -27416.6777777783 2 298427 325994.677777778 -27567.6777777777 3 289231 316214.511111111 -26983.5111111111 4 291975 315719.14 -23744.14 5 294912 315564.14 -20652.1400000000 6 293488 311731.74 -18243.7400000000 7 290555 306191.34 -15636.34 8 284736 301685.94 -16949.94 9 281818 297074.34 -15256.3400000000 10 287854 300716.34 -12862.3400000000 11 316263 330557.14 -14294.1400000000 12 325412 336615.74 -11203.7400000000 13 326011 323228.604444444 2782.39555555569 14 328282 313459.604444444 14822.3955555556 15 317480 303679.437777778 13800.5622222222 16 317539 303184.066666667 14354.9333333333 17 313737 303029.066666667 10707.9333333333 18 312276 299196.666666667 13079.3333333333 19 309391 293656.266666667 15734.7333333333 20 302950 289150.866666667 13799.1333333333 21 300316 284539.266666667 15776.7333333333 22 304035 288181.266666667 15853.7333333333 23 333476 318022.066666667 15453.9333333333 24 337698 324080.666666667 13617.3333333333 25 335932 310693.531111111 25238.468888889 26 323931 300924.531111111 23006.4688888889 27 313927 291144.364444444 22782.6355555555 28 314485 300422.337777778 14062.6622222222 29 313218 300267.337777778 12950.6622222222 30 309664 296434.937777778 13229.0622222222 31 302963 290894.537777778 12068.4622222222 32 298989 286389.137777778 12599.8622222222 33 298423 281777.537777778 16645.4622222222 34 301631 285419.537777778 16211.4622222222 35 329765 315260.337777778 14504.6622222222 36 335083 321318.937777778 13764.0622222223 37 327616 307931.802222222 19684.1977777779 38 309119 298162.802222222 10956.1977777778 39 295916 288382.635555556 7533.36444444446 40 291413 287887.264444444 3525.73555555555 41 291542 287732.264444444 3809.73555555555 42 284678 283899.864444444 778.135555555549 43 276475 278359.464444444 -1884.46444444445 44 272566 273854.064444444 -1288.06444444445 45 264981 269242.464444444 -4261.46444444446 46 263290 272884.464444444 -9594.46444444446 47 296806 302725.264444444 -5919.26444444445 48 303598 308783.864444444 -5185.86444444445 49 286994 295396.728888889 -8402.7288888888 50 276427 285627.728888889 -9200.7288888889 51 266424 275847.562222222 -9423.56222222223 52 267153 275352.191111111 -8199.19111111114 53 268381 275197.191111111 -6816.19111111114 54 262522 271364.791111111 -8842.79111111115 55 255542 265824.391111111 -10282.3911111111 56 253158 261318.991111111 -8160.99111111115 57 243803 256707.391111111 -12904.3911111111 58 250741 260349.391111111 -9608.39111111115 59 280445 290190.191111111 -9745.19111111115 60 285257 296248.791111111 -10991.7911111111 61 270976 282861.655555555 -11885.6555555555 62 261076 273092.655555556 -12016.6555555556 63 255603 263312.488888889 -7709.48888888892 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.528432673960422 0.943134652079156 0.471567326039578 18 0.454415431489883 0.908830862979766 0.545584568510117 19 0.357870775876647 0.715741551753295 0.642129224123353 20 0.299227911607242 0.598455823214484 0.700772088392758 21 0.227178223962344 0.454356447924688 0.772821776037656 22 0.201075986902617 0.402151973805234 0.798924013097383 23 0.166504141328105 0.333008282656210 0.833495858671895 24 0.268895185568965 0.537790371137931 0.731104814431035 25 0.421169954945475 0.842339909890949 0.578830045054525 26 0.742016780620259 0.515966438759483 0.257983219379741 27 0.82771027294384 0.344579454112319 0.172289727056159 28 0.758041735502415 0.483916528995169 0.241958264497585 29 0.685171535543621 0.629656928912758 0.314828464456379 30 0.598385070353003 0.803229859293994 0.401614929646997 31 0.525995855954825 0.94800828809035 0.474004144045175 32 0.432314992874452 0.864629985748904 0.567685007125548 33 0.397998862714729 0.795997725429458 0.602001137285271 34 0.397293763247507 0.794587526495013 0.602706236752493 35 0.356168956055009 0.712337912110019 0.643831043944991 36 0.328841325330828 0.657682650661657 0.671158674669172 37 0.7768964314818 0.4462071370364 0.2231035685182 38 0.972502607056126 0.0549947858877471 0.0274973929438735 39 0.992944028583825 0.0141119428323501 0.00705597141617505 40 0.998605043194867 0.00278991361026564 0.00139495680513282 41 0.999214269460697 0.00157146107860560 0.000785730539302801 42 0.999385165328312 0.00122966934337515 0.000614834671687576 43 0.999251514614324 0.00149697077135188 0.00074848538567594 44 0.998283034884205 0.00343393023159028 0.00171696511579514 45 0.99824520282549 0.00350959434901887 0.00175479717450944 46 0.993529300723218 0.0129413985535633 0.00647069927678166 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.2 NOK 5% type I error level 8 0.266666666666667 NOK 10% type I error level 9 0.3 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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