textiel

*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: Sat, 20 Dec 2008 02:10:22 -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/20/t122976441070ythazwq8v847z.htm/, Retrieved Sat, 20 Dec 2008 10:13:40 +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/20/t122976441070ythazwq8v847z.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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101.3 11554.5 102 13182.1 109.2 14800.1 88.6 12150.7 94.3 14478.2 98.3 13253.9 86.4 12036.8 80.6 12653.2 104.1 14035.4 108.2 14571.4 93.4 15400.9 71.9 14283.2 94.1 14485.3 94.9 14196.3 96.4 15559.1 91.1 13767.4 84.4 14634 86.4 14381.1 88 12509.9 75.1 12122.3 109.7 13122.3 103 13908.7 82.1 13456.5 68 12441.6 96.4 12953 94.3 13057.2 90 14350.1 88 13830.2 76.1 13755.5 82.5 13574.4 81.4 12802.6 66.5 11737.3 97.2 13850.2 94.1 15081.8 80.7 13653.3 70.5 14019.1 87.8 13962 89.5 13768.7 99.6 14747.1 84.2 13858.1 75.1 13188 92 13693.1 80.8 12970 73.1 11392.8 99.8 13985.2 90 14994.7 83.1 13584.7 72.4 14257.8 78.8 13553.4 87.3 14007.3 91 16535.8 80.1 14721.4 73.6 13664.6 86.4 16405.9 74.5 13829.4 71.2 13735.6 92.4 15870.5 81.5 15962.4 85.3 15744.1 69.9 16083.7 84.2 14863.9 90.7 15533.1 100.3 17473.1 79.4 15925.5 84.8 15573.7 92.9 17495 81.6 14155.8 76 14913.9 98.7 17250.4 89.1 15879.8 88.7 17647.8 67.1 17749.9

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 11 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation textiel[t] = + 48.4889749918958 + 0.00216522109184291Invoer[t] + 20.3888770273164M1[t] + 22.4679221288493M2[t] + 23.8452931332386M3[t] + 14.9048749448654M4[t] + 10.9312297084359M5[t] + 18.2833709204343M6[t] + 14.6906899025766M7[t] + 7.20724189420556M8[t] + 29.8545585764057M9[t] + 23.2819547465826M10[t] + 15.0961336127357M11[t] -0.251912361950662t + 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) 48.4889749918958 8.947831 5.4191 1e-06 1e-06 Invoer 0.00216522109184291 0.000663 3.2672 0.001827 0.000914 M1 20.3888770273164 2.806518 7.2648 0 0 M2 22.4679221288493 2.769609 8.1123 0 0 M3 23.8452931332386 2.854587 8.3533 0 0 M4 14.9048749448654 2.764624 5.3913 1e-06 1e-06 M5 10.9312297084359 2.754897 3.9679 0.000202 0.000101 M6 18.2833709204343 2.750649 6.6469 0 0 M7 14.6906899025766 2.929941 5.014 5e-06 3e-06 M8 7.20724189420556 3.01319 2.3919 0.020024 0.010012 M9 29.8545585764057 2.742263 10.8868 0 0 M10 23.2819547465826 2.75101 8.4631 0 0 M11 15.0961336127357 2.742978 5.5036 1e-06 0 t -0.251912361950662 0.038703 -6.5088 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.913762753336958 R-squared 0.834962369385939 Adjusted R-squared 0.79797117631727 F-TEST (value) 22.5719232098286 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.74761747954602 Sum Squared Residuals 1307.31256046127 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.3 93.6439867629602 7.6560132370398 2 102 98.995233351626 3.00476664837388 3 109.2 103.624019720667 5.5759802793334 4 88.6 88.6951524096141 -0.0951524096141227 5 94.3 89.5091469024983 4.79085309750167 6 98.3 93.9584955698028 4.34150443019717 7 86.4 87.4786115991124 -1.07861159911242 8 80.6 81.0778935098027 -0.477893509802712 9 104.1 106.466066423197 -2.36606642319747 10 108.2 100.802108736651 7.39789126334853 11 93.4 94.1604261365377 -0.760426136537657 12 71.9 76.3923125474984 -4.49231254749843 13 94.1 96.9668683955257 -2.86686839552566 14 94.9 98.1682522395653 -3.26825223956525 15 96.4 102.244474185967 -5.84447418596741 16 91.1 89.1727170053886 1.92728299461137 17 84.4 86.8235400051995 -2.42354000519952 18 86.4 93.3761844411202 -6.9761844411202 19 88 85.4800293542553 2.51997064574466 20 75.1 76.9054292887354 -1.80542928873537 21 109.7 101.466054700828 8.23394529917224 22 103 96.3442683756793 6.65573162432074 23 82.1 86.9274219021504 -4.82742190215037 24 68 69.3818930413526 -1.38189304135259 25 96.4 90.6261517730868 5.77384822691321 26 94.3 92.678900550439 1.62109944956093 27 90 96.6037735425214 -6.60377354252139 28 88 86.2857445465484 1.71425545345159 29 76.1 81.8984449326076 -5.7984449326076 30 82.5 88.6065522429226 -6.10655224292259 31 81.4 83.0908412244298 -1.69084122442982 32 66.5 73.0488708249679 -6.54887082496789 33 97.2 100.019170790172 -2.81917079017228 34 94.1 95.8613408951122 -1.76134089511224 35 80.7 84.3305890696171 -3.63058906961710 36 70.5 69.7745809703268 0.725419029673165 37 87.8 89.7879115113484 -1.98791151134835 38 89.5 91.1965070138774 -1.69650701387735 39 99.6 94.440417972575 5.15958202742491 40 84.2 83.3232058716029 0.876794128397117 41 75.1 77.6467336195788 -2.54673361957881 42 92 85.8406156431164 6.1593843568836 43 80.8 80.4303508917964 0.369649108203621 44 73.1 69.28000381542 3.81999618457993 45 99.8 97.2885272941631 2.51147270583687 46 90 92.6498017946048 -2.64980179460477 47 83.1 81.1591065593087 1.94089344069126 48 72.4 67.2684709015418 5.13152909845821 49 78.8 85.8802538298134 -7.0802538298134 50 87.3 88.6901804229831 -1.39018042298312 51 91 95.2904005961466 -4.29040059614655 52 80.1 82.169492896783 -2.06949289678293 53 73.6 75.6557296485432 -2.05572964854319 54 86.4 88.69147907766 -2.29147907765990 55 74.5 79.2681935547182 -4.76819355471823 56 71.2 71.3297354459817 -0.129735445981702 57 92.4 98.3476702752066 -5.94767027520663 58 81.5 91.7221379017732 -10.2221379017732 59 85.3 82.8117366416264 2.48826335837363 60 69.9 68.1989997497298 1.70100025027019 61 84.2 85.6948277272656 -1.49482772726558 62 90.7 88.9709264215091 1.72907357849091 63 100.3 94.296913982123 6.00308601787703 64 79.4 81.753687270063 -2.35368727006303 65 84.8 76.7664048915725 8.03359510842746 66 92.9 88.0266730253781 4.87332697462193 67 81.6 76.9519733756878 4.64802662431218 68 76 70.8580671150923 5.14193288490775 69 98.7 98.3125105164327 0.38748948356728 70 89.1 88.520342296179 0.579657703820955 71 88.7 83.9107196907598 4.78928030924023 72 67.1 68.7837427895505 -1.68374278955055 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.500358574803002 0.999282850393997 0.499641425196998 18 0.405718657351007 0.811437314702013 0.594281342648993 19 0.543105255114378 0.913789489771243 0.456894744885622 20 0.412855792010725 0.825711584021449 0.587144207989275 21 0.585632104582742 0.828735790834517 0.414367895417258 22 0.600450901106029 0.799098197787943 0.399549098893971 23 0.621494316393516 0.757011367212967 0.378505683606484 24 0.52053948648257 0.958921027034859 0.479460513517429 25 0.645841536591484 0.708316926817033 0.354158463408516 26 0.590767964541229 0.818464070917542 0.409232035458771 27 0.633503056591939 0.732993886816122 0.366496943408061 28 0.653229025586545 0.69354194882691 0.346770974413455 29 0.648270866378087 0.703458267243826 0.351729133621913 30 0.641948188741046 0.716103622517908 0.358051811258954 31 0.56536768022313 0.869264639553739 0.434632319776869 32 0.581968397418705 0.83606320516259 0.418031602581295 33 0.503014153301304 0.993971693397393 0.496985846698696 34 0.520894025678483 0.958211948643033 0.479105974321517 35 0.475441421800072 0.950882843600145 0.524558578199928 36 0.509814364499742 0.980371271000516 0.490185635500258 37 0.51585661517215 0.96828676965570 0.48414338482785 38 0.447258838936356 0.894517677872711 0.552741161063644 39 0.590832058120965 0.81833588375807 0.409167941879035 40 0.60869885080552 0.78260229838896 0.39130114919448 41 0.528049481039156 0.943901037921688 0.471950518960844 42 0.621719427535874 0.756561144928252 0.378280572464126 43 0.623670456188344 0.752659087623311 0.376329543811656 44 0.583466534229493 0.833066931541015 0.416533465770507 45 0.613106706006268 0.773786587987463 0.386893293993732 46 0.864455119082045 0.27108976183591 0.135544880917955 47 0.827355640787074 0.345288718425852 0.172644359212926 48 0.9429428544064 0.114114291187199 0.0570571455935994 49 0.918596106749527 0.162807786500947 0.0814038932504733 50 0.86528236990611 0.269435260187779 0.134717630093889 51 0.825106363704942 0.349787272590116 0.174893636295058 52 0.83370831645101 0.332583367097980 0.166291683548990 53 0.94572380897013 0.108552382059738 0.0542761910298691 54 0.897860326688492 0.204279346623016 0.102139673311508 55 0.780794522569253 0.438410954861494 0.219205477430747 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

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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