Multiple lineair regression

*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: Wed, 26 Nov 2008 08:55:29 -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/26/t1227714959a0x0n3nogpsd4b2.htm/, Retrieved Wed, 26 Nov 2008 15:56:09 +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/26/t1227714959a0x0n3nogpsd4b2.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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IsPrivate?

No (this computation is public)

User-defined keywords:

Multiple lineair regression

Dataseries X:

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309365 159129 308347 157928 298427 147768 289231 137507 291975 136919 294912 136151 293488 133001 290555 125554 284736 119647 281818 114158 287854 116193 316263 152803 325412 161761 326011 160942 328282 149470 317480 139208 317539 134588 313737 130322 312276 126611 309391 122401 302950 117352 300316 112135 304035 112879 333476 148729 337698 157230 335932 157221 323931 146681 313927 136524 314485 132111 313218 125326 309664 122716 302963 116615 298989 113719 298423 110737 301631 112093 329765 143565 335083 149946 327616 149147 309119 134339 295916 122683 291413 115614 291542 116566 284678 111272 276475 104609 272566 101802 264981 94542 263290 93051 296806 124129 303598 130374 286994 123946 276427 114971 266424 105531 267153 104919 268381 104782 262522 101281 255542 94545 253158 93248 243803 84031 250741 87486 280445 115867 285257 120327

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation vrouwen[t] = + 170903.751487260 + 1.01004381176518jonger_dan_25[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) 170903.751487260 9386.174337 18.208 0 0 jonger_dan_25 1.01004381176518 0.074147 13.6222 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.871066021088032 R-squared 0.758756013094136 Adjusted R-squared 0.754667131960138 F-TEST (value) 185.565681228865 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11478.7064714329 Sum Squared Residuals 7773881433.18165 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 309365 331631.013209642 -22266.0132096425 2 308347 330417.950591712 -22070.9505917117 3 298427 320155.905464177 -21728.9054641775 4 289231 309791.845911655 -20560.8459116549 5 291975 309197.940150337 -17222.940150337 6 294912 308422.226502901 -13510.2265029014 7 293488 305240.588495841 -11752.5884958410 8 290555 297718.792229626 -7163.7922296257 9 284736 291752.463433529 -7016.46343352876 10 281818 286208.332950750 -4390.33295074966 11 287854 288263.772107692 -409.77210769181 12 316263 325241.476056415 -8978.47605641521 13 325412 334289.448522208 -8877.44852220773 14 326011 333462.222640372 -7451.22264037205 15 328282 321875.000031802 6406.99996819815 16 317480 311509.930435468 5970.06956453247 17 317539 306843.528025112 10695.4719748876 18 313737 302534.681124122 11202.3188758779 19 312276 298786.408538661 13489.5914613385 20 309391 294534.12409113 14856.8759088699 21 302950 289434.412885528 13515.5871144723 22 300316 284165.014319549 16150.9856804513 23 304035 284916.486915502 19118.513084498 24 333476 321126.557567284 12349.4424327162 25 337698 329712.9400111 7985.05998890032 26 335932 329703.849616794 6228.15038320621 27 323931 319057.987840789 4873.01215921125 28 313927 308798.97284469 5128.02715531023 29 314485 304341.64950337 10143.35049663 30 313218 297488.502240543 15729.4977594568 31 309664 294852.287891836 14811.7121081639 32 302963 288690.010596257 14272.9894037433 33 298989 285764.923717385 13224.0762826153 34 298423 282752.973070701 15670.0269292990 35 301631 284122.592479455 17508.4075205455 36 329765 315910.691323328 13854.3086766716 37 335083 322355.780886202 12727.2191137979 38 327616 321548.755880602 6067.24411939831 39 309119 306592.027115983 2526.97288401716 40 295916 294818.956446048 1097.04355395214 41 291413 287678.95674068 3734.04325932023 42 291542 288640.51844948 2901.48155051978 43 284678 283293.346509995 1384.65349000466 44 276475 276563.424592204 -88.4245922039113 45 272566 273728.231612579 -1162.23161257904 46 264981 266395.313539164 -1414.31353916380 47 263290 264889.338215822 -1599.33821582191 48 296806 296279.479797860 526.520202139689 49 303598 302587.203402334 1010.79659766611 50 286994 296094.641780307 -9100.64178030728 51 276427 287029.498569715 -10602.4985697148 52 266424 277494.684986651 -11070.6849866514 53 267153 276876.538173851 -9723.53817385112 54 268381 276738.162171639 -8357.16217163929 55 262522 273201.998786649 -10679.9987866494 56 255542 266398.343670599 -10856.3436705991 57 253158 265088.316846740 -11930.3168467397 58 243803 255778.7430337 -11975.7430336999 59 250741 259268.444403349 -8527.44440334866 60 280445 287934.497825056 -7489.49782505636 61 285257 292439.293225529 -7182.29322552908 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00475743783858105 0.0095148756771621 0.995242562161419 6 0.00989651949821277 0.0197930389964255 0.990103480501787 7 0.00709870486005772 0.0141974097201154 0.992901295139942 8 0.00537178140216092 0.0107435628043218 0.99462821859784 9 0.00173053898542180 0.00346107797084361 0.998269461014578 10 0.000511216329791728 0.00102243265958346 0.999488783670208 11 0.000515051205709276 0.00103010241141855 0.99948494879429 12 0.0126086675307208 0.0252173350614417 0.98739133246928 13 0.0657121537901505 0.131424307580301 0.93428784620985 14 0.14719336698337 0.29438673396674 0.85280663301663 15 0.484306206377 0.968612412754 0.515693793623 16 0.630440031353295 0.739119937293411 0.369559968646705 17 0.779167863900014 0.441664272199973 0.220832136099986 18 0.846003048498565 0.30799390300287 0.153996951501435 19 0.893936946766959 0.212126106466083 0.106063053233041 20 0.923332892029567 0.153334215940866 0.0766671079704328 21 0.92893353564311 0.142132928713779 0.0710664643568897 22 0.94590371908179 0.108192561836419 0.0540962809182097 23 0.973570118679147 0.0528597626417052 0.0264298813208526 24 0.984621921689135 0.0307561566217303 0.0153780783108651 25 0.98848905970304 0.0230218805939215 0.0115109402969608 26 0.989524145628429 0.0209517087431421 0.0104758543715711 27 0.986840756929457 0.0263184861410861 0.0131592430705430 28 0.980484554223343 0.0390308915533147 0.0195154457766573 29 0.974006509412178 0.0519869811756434 0.0259934905878217 30 0.978251939240145 0.0434961215197106 0.0217480607598553 31 0.981419842371643 0.0371603152567145 0.0185801576283572 32 0.986172092469015 0.0276558150619705 0.0138279075309852 33 0.990626451285576 0.0187470974288478 0.0093735487144239 34 0.997522749882497 0.00495450023500647 0.00247725011750323 35 0.99990487868596 0.000190242628079146 9.51213140395732e-05 36 0.999947362246628 0.000105275506745124 5.26377533725620e-05 37 0.999963970744934 7.20585101322224e-05 3.60292550661112e-05 38 0.999927163714262 0.000145672571475526 7.2836285737763e-05 39 0.999837675147715 0.000324649704569372 0.000162324852284686 40 0.999698141597887 0.000603716804225833 0.000301858402112916 41 0.999724316803024 0.000551366393951926 0.000275683196975963 42 0.999741027944573 0.000517944110854099 0.000258972055427049 43 0.999766743472084 0.000466513055832429 0.000233256527916215 44 0.999800512089844 0.000398975820311999 0.000199487910156000 45 0.99982507276825 0.000349854463499768 0.000174927231749884 46 0.999916559488185 0.000166881023630776 8.34405118153879e-05 47 0.999988388755554 2.32224888925781e-05 1.16112444462891e-05 48 0.999994238671331 1.15226573385717e-05 5.76132866928584e-06 49 0.999999953490864 9.30182721054105e-08 4.65091360527052e-08 50 0.999999724725299 5.50549402316168e-07 2.75274701158084e-07 51 0.999999282700625 1.43459874910467e-06 7.17299374552337e-07 52 0.999997883442866 4.23311426836843e-06 2.11655713418422e-06 53 0.999984181162064 3.16376758721794e-05 1.58188379360897e-05 54 0.999888720019817 0.000222559960365589 0.000111279980182794 55 0.999339322025746 0.00132135594850773 0.000660677974253863 56 0.99538391035747 0.0092321792850596 0.0046160896425298 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 27 0.519230769230769 NOK 5% type I error level 40 0.769230769230769 NOK 10% type I error level 42 0.807692307692308 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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