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 16:33:00 -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/t1229556855uxhw5wmlu1w3ozr.htm/, Retrieved Thu, 18 Dec 2008 00:34:25 +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/t1229556855uxhw5wmlu1w3ozr.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:

» Textbox « » Textfile « » CSV «

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation transport[t] = + 68.4384844621544 + 0.025042547739914Import[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) 68.4384844621544 12.493067 5.4781 1e-06 0 Import 0.025042547739914 0.007544 3.3196 0.001434 0.000717 Multiple Linear Regression - Regression Statistics Multiple R 0.368797522645546 R-squared 0.136011612709492 Adjusted R-squared 0.123668921462484 F-TEST (value) 11.0196074735703 F-TEST (DF numerator) 1 F-TEST (DF denominator) 70 p-value 0.00143382764752187 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 17.7457142811268 Sum Squared Residuals 22043.7262743171 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 124.9 105.69177848005 19.20822151995 2 132 101.517185771807 30.4828142281932 3 151.4 106.352901740384 45.0470982596158 4 108.9 100.765909339609 8.13409066039064 5 121.3 103.310232189985 17.9897678100154 6 123.4 100.698294460712 22.7017055392884 7 90.3 101.103983734098 -10.8039837340982 8 79.3 100.938702919015 -21.6387029190148 9 117.2 98.7650097751902 18.4349902248098 10 116.9 104.850348875989 12.0496511240107 11 120.8 103.640793820151 17.1592061798485 12 96.1 97.5078738786465 -1.40787387864655 13 100.8 105.80446994488 -5.00446994488006 14 105.3 100.067222257666 5.23277774233424 15 116.1 102.904542916598 13.1954570834020 16 112.8 102.711715299001 10.0882847009993 17 114.5 104.189225615656 10.3107743843444 18 117.2 101.990489924091 15.2095100759088 19 77.1 99.699096805889 -22.5990968058890 20 80.1 101.239213491894 -21.1392134918937 21 120.3 104.099072443792 16.2009275562081 22 133.4 108.268656642488 25.1313433575124 23 109.4 104.076534150826 5.32346584917401 24 93.2 102.378649414060 -9.17864941405982 25 91.2 106.377944288124 -15.1779442881241 26 99.2 103.137438610579 -3.93743861057921 27 108.2 104.249327730231 3.9506722697686 28 101.5 105.857059295134 -4.35705929513388 29 106.9 108.028248184184 -1.12824818418443 30 104.4 102.741766356289 1.65823364371143 31 77.9 103.685870406083 -25.7858704060833 32 60 103.205053489477 -43.205053489477 33 99.5 105.463891295617 -5.96389129561723 34 95 109.267854297310 -14.2678542973102 35 105.6 103.836125692523 1.76387430747717 36 102.5 105.847042276038 -3.34704227603792 37 93.3 109.540818067675 -16.2408180676752 38 97.3 105.125816901128 -7.8258169011284 39 127 111.63938356828 15.3606164317200 40 111.7 109.217769201830 2.48223079816966 41 96.4 110.504956155662 -14.1049561556619 42 133 115.418304022233 17.5816959777669 43 72.2 110.244513659167 -38.0445136591668 44 95.8 111.321343211983 -15.5213432119831 45 124.1 112.733742904514 11.3662570954857 46 127.6 114.028442622668 13.5715573773322 47 110.7 112.919057757790 -2.21905775778963 48 104.6 110.853047569247 -6.25304756924674 49 112.7 113.492532101034 -0.792532101033663 50 115.3 116.457569753439 -1.15756975343949 51 139.4 115.69878055692 23.7012194430799 52 119 113.209551311573 5.79044868842736 53 97.4 113.610232075411 -16.2102320754113 54 154 123.441936318102 30.5580636818985 55 81.5 112.500847210533 -31.0008472105331 56 88.8 118.588690566106 -29.7886905661062 57 127.7 119.945996653610 7.75400334639049 58 105.1 114.794744583509 -9.6947445835092 59 114.9 118.130411942466 -3.23041194246574 60 106.4 111.644392077828 -5.24439207782801 61 104.5 120.942690053658 -16.4426900536581 62 121.6 113.319738521628 8.28026147837173 63 141.4 119.272352119406 22.1276478805942 64 99 113.146944942223 -14.1469449422229 65 126.7 119.187207457090 7.51279254290989 66 134.1 116.790635638380 17.3093643616197 67 81.3 114.654506316166 -33.3545063161657 68 88.6 117.098658975581 -28.4986589755813 69 132.7 120.196422131009 12.5035778689913 70 132.9 127.398658861008 5.50134113899208 71 134.4 123.299193795984 11.1008062040160 72 103.7 116.760584581092 -13.0605845810924 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.403870774257936 0.807741548515873 0.596129225742064 6 0.282855753088915 0.56571150617783 0.717144246911085 7 0.517190762070152 0.965618475859696 0.482809237929848 8 0.725743884645642 0.548512230708716 0.274256115354358 9 0.760534352773086 0.478931294453828 0.239465647226914 10 0.71236034752079 0.575279304958419 0.287639652479210 11 0.640408464279157 0.719183071441687 0.359591535720844 12 0.544586109008032 0.910827781983936 0.455413890991968 13 0.646712237806578 0.706575524386845 0.353287762193422 14 0.566771856664235 0.866456286671531 0.433228143335765 15 0.500606091768438 0.998787816463125 0.499393908231562 16 0.433846699179123 0.867693398358247 0.566153300820877 17 0.37661394499688 0.75322788999376 0.62338605500312 18 0.344189466617546 0.688378933235091 0.655810533382454 19 0.448202020114073 0.896404040228146 0.551797979885927 20 0.540374239656646 0.919251520686708 0.459625760343354 21 0.513097470148044 0.973805059703912 0.486902529851956 22 0.523820077412815 0.95235984517437 0.476179922587185 23 0.487712454370691 0.975424908741381 0.512287545629309 24 0.476270851455314 0.952541702910629 0.523729148544686 25 0.599828341138753 0.800343317722493 0.400171658861247 26 0.56050663755938 0.87898672488124 0.43949336244062 27 0.523231060422992 0.953537879154015 0.476768939577008 28 0.504630959237414 0.990738081525173 0.495369040762586 29 0.479789805447715 0.95957961089543 0.520210194552285 30 0.450401632050392 0.900803264100783 0.549598367949608 31 0.543489550453792 0.913020899092417 0.456510449546208 32 0.807629317601933 0.384741364796135 0.192370682398067 33 0.771753315269487 0.456493369461027 0.228246684730513 34 0.762650576472042 0.474698847055916 0.237349423527958 35 0.731608782318162 0.536782435363677 0.268391217681838 36 0.68827903837361 0.62344192325278 0.31172096162639 37 0.667262329512695 0.66547534097461 0.332737670487305 38 0.617861829887668 0.764276340224665 0.382138170112332 39 0.633481684644007 0.733036630711986 0.366518315355993 40 0.598593690328136 0.802812619343727 0.401406309671864 41 0.55713858693155 0.8857228261369 0.44286141306845 42 0.569004057508933 0.861991884982133 0.430995942491067 43 0.727324376159757 0.545351247680486 0.272675623840243 44 0.688180881788556 0.623638236422887 0.311819118211444 45 0.680286526012703 0.639426947974593 0.319713473987297 46 0.683251613095303 0.633496773809393 0.316748386904696 47 0.622702048286155 0.75459590342769 0.377297951713845 48 0.561518966487776 0.876962067024448 0.438481033512224 49 0.498462302333952 0.996924604667903 0.501537697666048 50 0.424762888924013 0.849525777848025 0.575237111075987 51 0.542838842483935 0.914322315032129 0.457161157516065 52 0.534633629833189 0.930732740333621 0.465366370166811 53 0.478883063381953 0.957766126763905 0.521116936618047 54 0.552182146406565 0.89563570718687 0.447817853593435 55 0.606459271606497 0.787081456787005 0.393540728393503 56 0.74248077966124 0.515038440677519 0.257519220338760 57 0.678046677470462 0.643906645059076 0.321953322529538 58 0.598428535235505 0.80314292952899 0.401571464764495 59 0.505769030308143 0.988461939383713 0.494230969691856 60 0.420439924873131 0.840879849746261 0.579560075126869 61 0.430552550176918 0.861105100353836 0.569447449823082 62 0.443801115470097 0.887602230940193 0.556198884529903 63 0.525175274288174 0.94964945142365 0.474824725711826 64 0.415485283853567 0.830970567707135 0.584514716146433 65 0.336462996251999 0.672925992503998 0.663537003748001 66 0.633451376770098 0.733097246459804 0.366548623229902 67 0.552258931840862 0.895482136318276 0.447741068159138 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 = 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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