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 16:36:56 -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/t1229557091n8mn5owsv84wt7i.htm/, Retrieved Thu, 18 Dec 2008 00:38:20 +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/t1229557091n8mn5owsv84wt7i.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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation transport[t] = + 71.8518914312245 + 0.0187411071659618Import[t] + 1.3805811093125M1[t] + 11.3693698776109M2[t] + 27.6133952119599M3[t] + 7.74364094227462M4[t] + 7.72394403001493M5[t] + 24.5931397743116M6[t] -20.6463294703562M7[t] -19.9063328612569M8[t] + 17.1445012034594M9[t] + 13.2069896234022M10[t] + 12.2751959194037M11[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) 71.8518914312245 8.89768 8.0754 0 0 Import 0.0187411071659618 0.004905 3.8211 0.000322 0.000161 M1 1.3805811093125 6.449238 0.2141 0.831231 0.415616 M2 11.3693698776109 6.428105 1.7687 0.082114 0.041057 M3 27.6133952119599 6.444658 4.2847 6.8e-05 3.4e-05 M4 7.74364094227462 6.425718 1.2051 0.232976 0.116488 M5 7.72394403001493 6.441575 1.1991 0.235292 0.117646 M6 24.5931397743116 6.447146 3.8146 0.000329 0.000164 M7 -20.6463294703562 6.426515 -3.2127 0.002132 0.001066 M8 -19.9063328612569 6.430256 -3.0957 0.003002 0.001501 M9 17.1445012034594 6.447473 2.6591 0.01007 0.005035 M10 13.2069896234022 6.518742 2.026 0.047294 0.023647 M11 12.2751959194037 6.461868 1.8996 0.062372 0.031186 Multiple Linear Regression - Regression Statistics Multiple R 0.844722581779279 R-squared 0.713556240167851 Adjusted R-squared 0.65529649240538 F-TEST (value) 12.2478429374097 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 5.71576119767769e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.1296685048460 Sum Squared Residuals 7308.30174063787 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 124.9 101.111743560621 23.7882564393787 2 132 107.976389764354 24.0236102356457 3 151.4 127.839322892450 23.5606771075496 4 108.9 103.788427614039 5.11157238596088 5 121.3 105.672827189841 15.6271728101588 6 123.4 120.587325456728 2.81267454327200 7 90.3 75.6514621481488 14.6485378518512 8 79.3 76.2677674499527 3.03223255004734 9 117.2 111.691873412664 5.50812658733642 10 116.9 112.308450873935 4.59154912606494 11 120.8 110.471461693821 10.3285383061794 12 96.1 93.6065686294729 2.49343137052709 13 100.8 101.196078542869 -0.396078542868528 14 105.3 106.891279659445 -1.59127965944512 15 116.1 125.258672435697 -9.1586724356975 16 112.8 105.244611640834 7.55538835916564 17 114.5 106.330640051366 8.16935994863359 18 117.2 121.554366586492 -4.35436658649164 19 77.1 74.6000860361383 2.49991396386167 20 80.1 76.4926607359442 3.60733926405575 21 120.3 115.683729239013 4.61627076098659 22 133.4 114.866612002089 18.5333879979112 23 109.4 110.797556958508 -1.39755695850831 24 93.2 97.2517139732524 -4.05171397325245 25 91.2 101.625249896969 -10.4252498969690 26 99.2 109.188939397992 -9.98893939799202 27 108.2 126.265069890510 -18.0650698905096 28 101.5 107.598494700879 -6.09849470087915 29 106.9 109.203651779908 -2.30365177990835 30 104.4 122.116599801470 -17.7165998014705 31 77.9 77.5836702969594 0.316329703040578 32 60 77.9638376484722 -17.9638376484723 33 99.5 116.705119579558 -17.2051195795583 34 95 115.614382178011 -20.6143821780107 35 105.6 110.617642329715 -5.01764232971509 36 102.5 99.8473573157382 2.65264268426185 37 93.3 103.99225173203 -10.6922517320300 38 97.3 110.676983306969 -13.3769833069694 39 127 131.795570615185 -4.79557061518496 40 111.7 110.113551282551 1.58644871744878 41 96.4 111.057147278622 -14.6571472786220 42 133 131.603348248880 1.39665175111965 43 72.2 82.4919662637248 -10.2919662637248 44 95.8 84.0378304809605 11.7621695190395 45 124.1 122.145662989837 1.95433701016297 46 127.6 119.17706665026 8.42293334973998 47 110.7 117.415041898809 -6.71504189880941 48 104.6 103.593704638214 1.00629536178609 49 112.7 106.949598442819 5.75040155718123 50 115.3 119.157334299567 -3.85733429956709 51 139.4 134.833504086787 4.56649591321264 52 119 113.100883764806 5.89911623519447 53 97.4 113.381044567201 -15.9810445672012 54 154 137.607998984855 16.3920010151455 55 81.5 84.180540019378 -2.68054001937798 56 88.8 89.4764997805225 -0.676499780522547 57 127.7 127.543101853634 0.156898146365985 58 105.1 119.750544529538 -14.6505445295385 59 114.9 121.315066300046 -6.41506630004606 60 106.4 104.185923624658 2.21407637534171 61 104.5 112.525077824692 -8.0250778246924 62 121.6 116.809073571672 4.79092642832791 63 141.4 137.50786007937 3.8921399206299 64 99 113.054030996891 -14.0540309968906 65 126.7 117.554689133061 9.1453108669391 66 134.1 132.630360921575 1.46963907842495 67 81.3 85.7922752356507 -4.49227523565069 68 88.6 88.3614039041478 0.238596095852162 69 132.7 127.730512925294 4.96948707470636 70 132.9 129.182943766167 3.71705623383301 71 134.4 125.183230819101 9.21676918089944 72 103.7 108.014731818664 -4.31473181866428 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.857455831967243 0.285088336065513 0.142544168032757 17 0.85752584717496 0.284948305650080 0.142474152825040 18 0.853177010126764 0.293645979746472 0.146822989873236 19 0.78915439176437 0.42169121647126 0.21084560823563 20 0.715526795869017 0.568946408261966 0.284473204130983 21 0.849206095472045 0.301587809055911 0.150793904527955 22 0.910600005487374 0.178799989025252 0.0893999945126261 23 0.908023854648087 0.183952290703826 0.091976145351913 24 0.917448282000197 0.165103435999606 0.0825517179998032 25 0.954724856405003 0.090550287189994 0.045275143594997 26 0.973784275560499 0.0524314488790022 0.0262157244395011 27 0.986320094958842 0.0273598100823163 0.0136799050411581 28 0.982919937238182 0.0341601255236367 0.0170800627618184 29 0.982120230560543 0.0357595388789134 0.0178797694394567 30 0.9829971949023 0.0340056101953990 0.0170028050976995 31 0.981707600307623 0.0365847993847538 0.0182923996923769 32 0.985449510624147 0.0291009787517055 0.0145504893758528 33 0.986437371841405 0.0271252563171891 0.0135626281585946 34 0.993950671598678 0.0120986568026442 0.0060493284013221 35 0.990650558123164 0.0186988837536717 0.00934944187683587 36 0.988751628709152 0.0224967425816960 0.0112483712908480 37 0.982805790737687 0.0343884185246263 0.0171942092623131 38 0.977624029562694 0.0447519408746112 0.0223759704373056 39 0.968646580969897 0.0627068380602068 0.0313534190301034 40 0.95821411237163 0.083571775256742 0.041785887628371 41 0.949801407536094 0.100397184927812 0.0501985924639060 42 0.950969005145861 0.0980619897082775 0.0490309948541387 43 0.929749404878594 0.140501190242812 0.070250595121406 44 0.948904227550827 0.102191544898345 0.0510957724491726 45 0.924113020222181 0.151773959555637 0.0758869797778187 46 0.953182867669162 0.0936342646616755 0.0468171323308377 47 0.922698866788158 0.154602266423683 0.0773011332118417 48 0.88550837174672 0.228983256506561 0.114491628253280 49 0.940099236973273 0.119801526053455 0.0599007630267273 50 0.935818654020126 0.128362691959748 0.0641813459798738 51 0.903147673046398 0.193704653907204 0.0968523269536022 52 0.951548126566981 0.0969037468660379 0.0484518734330189 53 0.977081153162241 0.0458376936755173 0.0229188468377586 54 0.961746916723652 0.0765061665526966 0.0382530832763483 55 0.917096154182657 0.165807691634687 0.0829038458173435 56 0.816978854774102 0.366042290451797 0.183021145225898 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 13 0.317073170731707 NOK 10% type I error level 21 0.51219512195122 NOK

Charts produced by software:

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Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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