verband tussen invoer en transport

*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, 17 Dec 2008 16:40:07 -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/18/t1229557319b1ydsu679mbqvvm.htm/, Retrieved Thu, 18 Dec 2008 00:41:59 +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/18/t1229557319b1ydsu679mbqvvm.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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124.9 1487.6 132 1320.9 151.4 1514 108.9 1290.9 121.3 1392.5 123.4 1288.2 90.3 1304.4 79.3 1297.8 117.2 1211 116.9 1454 120.8 1405.7 96.1 1160.8 100.8 1492.1 105.3 1263 116.1 1376.3 112.8 1368.6 114.5 1427.6 117.2 1339.8 77.1 1248.3 80.1 1309.8 120.3 1424 133.4 1590.5 109.4 1423.1 93.2 1355.3 91.2 1515 99.2 1385.6 108.2 1430 101.5 1494.2 106.9 1580.9 104.4 1369.8 77.9 1407.5 60 1388.3 99.5 1478.5 95 1630.4 105.6 1413.5 102.5 1493.8 93.3 1641.3 97.3 1465 127 1725.1 111.7 1628.4 96.4 1679.8 133 1876 72.2 1669.4 95.8 1712.4 124.1 1768.8 127.6 1820.5 110.7 1776.2 104.6 1693.7 112.7 1799.1 115.3 1917.5 139.4 1887.2 119 1787.8 97.4 1803.8 154 2196.4 81.5 1759.5 88.8 2002.6 127.7 2056.8 105.1 1851.1 114.9 1984.3 106.4 1725.3 104.5 2096.6 121.6 1792.2 141.4 2029.9 99 1785.3 126.7 2026.5 134.1 1930.8 81.3 1845.5 88.6 1943.1 132.7 2066.8 132.9 2354.4 134.4 2190.7 103.7 1929.6

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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation transport[t] = + 12.4559752563566 + 0.0802653330259121Import[t] -15.0993762276999M1[t] + 4.86050178500652M2[t] + 13.5842789517794M3[t] + 0.812432578842404M4[t] -4.03685302338478M5[t] + 12.7811355727339M6[t] -23.7290083861327M7[t] -26.4189243286871M8[t] + 7.89414472530005M9[t] -2.29929218091119M10[t] + 2.84244365127035M11[t] -0.870630835956898t + 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) 12.4559752563566 10.557965 1.1798 0.242908 0.121454 Import 0.0802653330259121 0.009313 8.6182 0 0 M1 -15.0993762276999 5.266853 -2.8669 0.005769 0.002884 M2 4.86050178500652 4.808979 1.0107 0.316351 0.158176 M3 13.5842789517794 5.12356 2.6513 0.01032 0.00516 M4 0.812432578842404 4.818747 0.1686 0.866699 0.43335 M5 -4.03685302338478 5.008944 -0.8059 0.423576 0.211788 M6 12.7811355727339 5.015155 2.5485 0.013488 0.006744 M7 -23.7290083861327 4.74077 -5.0053 6e-06 3e-06 M8 -26.4189243286871 4.810629 -5.4918 1e-06 0 M9 7.89414472530005 4.909453 1.6079 0.113277 0.056639 M10 -2.29929218091119 5.255409 -0.4375 0.663367 0.331683 M11 2.84244365127035 4.9264 0.577 0.566185 0.283092 t -0.870630835956898 0.121532 -7.1638 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.920883307634184 R-squared 0.848026066279275 Adjusted R-squared 0.81396294320394 F-TEST (value) 24.8957226970574 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.17634311139641 Sum Squared Residuals 3877.45002716621 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 124.9 115.888677602047 9.01132239795325 2 132 121.597693763377 10.4023062366233 3 151.4 144.950075901496 6.44992409850368 4 108.9 113.400402894521 -4.5004028945214 5 121.3 115.83544429177 5.46455570823002 6 123.4 123.411127817329 -0.0111278173290963 7 90.3 87.3306514175254 2.96934858247461 8 79.3 83.2403534410431 -3.94035344104311 9 117.2 109.715760752424 7.48423924757582 10 116.9 118.156168935553 -1.25616893555268 11 120.8 118.550458346626 2.24954165337423 12 96.1 95.1804038013526 0.919596198647349 13 100.8 105.802301569181 -5.00230156918054 14 105.3 106.502760949694 -1.20276094969357 15 116.1 123.449969512345 -7.34996951234545 16 112.8 109.189449239152 3.61055076084801 17 114.5 108.205187449497 6.29481255050329 18 117.2 117.105248969983 0.0947510300166271 19 77.1 72.380196203289 4.71980379671107 20 80.1 73.7559674058713 6.34403259412873 21 120.3 116.364706655461 3.93529334453932 22 133.4 118.664816862107 14.7351831378931 23 109.4 109.499505109794 -0.09950510979384 24 93.2 100.344441043410 -7.14444104340977 25 91.2 97.1928076639911 -5.99280766399115 26 99.2 105.895720747188 -6.69572074718761 27 108.2 117.312647864354 -9.11264786435413 28 101.5 108.823205035724 -7.32320503572377 29 106.9 110.062292970886 -3.16229297088627 30 104.4 109.065638929278 -4.66563892927796 31 77.9 74.7108671895314 3.18913281046865 32 60 69.6092260169226 -9.60922601692258 33 99.5 110.29159727389 -10.7915972738901 34 95 111.419833618358 -16.4198336183580 35 105.6 98.2813878812623 7.31861211873768 36 102.5 101.013619636016 1.48638036398419 37 93.3 96.882749193681 -3.58274919368107 38 97.3 101.821218157962 -4.52121815796227 39 127 130.551377608818 -3.55137760881802 40 111.7 109.147242696318 2.5527573036816 41 96.4 107.552964375666 -11.1529643756662 42 133 139.248380475512 -6.24838047551189 43 72.2 85.284787877535 -13.0847878775350 44 95.8 85.175650419138 10.6243495808621 45 124.1 123.145053419830 0.954946580170384 46 127.6 116.230703395101 11.3692966048989 47 110.7 116.946054138278 -6.24605413827786 48 104.6 106.611089676413 -2.01108967641288 49 112.7 99.1010487136872 13.5989512863128 50 115.3 127.693711320705 -12.3937113207047 51 139.4 133.114818060836 6.2851819391644 52 119 111.493966749166 7.506033250834 53 97.4 107.058295639397 -9.6582956393965 54 154 154.517823145531 -0.517823145531363 55 81.5 82.0691243516869 -0.56912435168686 56 88.8 98.0210800317748 -9.22108003177483 57 127.7 135.813899299810 -8.11389929980953 58 105.1 108.239252554211 -3.13925255421125 59 114.9 123.201699909487 -8.30169990948737 60 106.4 98.6999041685489 7.7000958314511 61 104.5 112.532415257413 -8.03241525741329 62 121.6 107.188895061075 14.4111049389249 63 141.4 134.121111052150 7.27888894784952 64 99 100.845733385118 -1.84573338511844 65 126.7 114.485815272784 12.2141847272156 66 134.1 122.751780662366 11.3482193376337 67 81.3 78.5243729604325 2.77562703956749 68 88.6 82.7977226852503 5.80227731474972 69 132.7 126.168982598586 6.53101740141411 70 132.9 138.18922463467 -5.28922463467003 71 134.4 129.320894614553 5.07910538544716 72 103.7 104.65054167426 -0.950541674259964 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.198215742655946 0.396431485311891 0.801784257344054 18 0.0881852192798711 0.176370438559742 0.911814780720129 19 0.115049417747037 0.230098835494074 0.884950582252963 20 0.149142121274991 0.298284242549983 0.850857878725009 21 0.200261408605209 0.400522817210418 0.799738591394791 22 0.337284908982771 0.674569817965542 0.662715091017229 23 0.251872011910406 0.503744023820812 0.748127988089594 24 0.294872139459166 0.589744278918332 0.705127860540834 25 0.224745781010915 0.44949156202183 0.775254218989085 26 0.203682814672694 0.407365629345389 0.796317185327306 27 0.154881296419602 0.309762592839204 0.845118703580398 28 0.114074439631865 0.228148879263731 0.885925560368135 29 0.0928772117106972 0.185754423421394 0.907122788289303 30 0.0662810637103533 0.132562127420707 0.933718936289647 31 0.0570175529368594 0.114035105873719 0.94298244706314 32 0.0509528420566726 0.101905684113345 0.949047157943327 33 0.0746566871798922 0.149313374359784 0.925343312820108 34 0.180103774959826 0.360207549919651 0.819896225040174 35 0.221365843883746 0.442731687767491 0.778634156116254 36 0.212432109302505 0.42486421860501 0.787567890697495 37 0.169418903585912 0.338837807171824 0.830581096414088 38 0.134293078327065 0.268586156654129 0.865706921672935 39 0.108550029706634 0.217100059413268 0.891449970293366 40 0.100285389618478 0.200570779236955 0.899714610381522 41 0.103987670835930 0.207975341671859 0.89601232916407 42 0.0844140162402327 0.168828032480465 0.915585983759767 43 0.0957590314583677 0.191518062916735 0.904240968541632 44 0.165655396939288 0.331310793878576 0.834344603060712 45 0.117628828740031 0.235257657480063 0.882371171259969 46 0.245008948065715 0.490017896131429 0.754991051934286 47 0.190276384300394 0.380552768600787 0.809723615699606 48 0.134277489090623 0.268554978181246 0.865722510909377 49 0.370767473363641 0.741534946727283 0.629232526636359 50 0.458792585529672 0.917585171059345 0.541207414470328 51 0.400483325199537 0.800966650399073 0.599516674800463 52 0.59176705046913 0.81646589906174 0.40823294953087 53 0.760331113042224 0.479337773915553 0.239668886957776 54 0.655277531993918 0.689444936012164 0.344722468006082 55 0.524635072784494 0.950729854431012 0.475364927215506 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 = 12 ;

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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