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: Sat, 20 Dec 2008 01:42:11 -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/t1229762619kfbtpe3gq0ur4h6.htm/, Retrieved Sat, 20 Dec 2008 09:43:48 +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/t1229762619kfbtpe3gq0ur4h6.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 11554,5 132 13182,1 151,4 14800,1 108,9 12150,7 121,3 14478,2 123,4 13253,9 90,3 12036,8 79,3 12653,2 117,2 14035,4 116,9 14571,4 120,8 15400,9 96,1 14283,2 100,8 14485,3 105,3 14196,3 116,1 15559,1 112,8 13767,4 114,5 14634 117,2 14381,1 77,1 12509,9 80,1 12122,3 120,3 13122,3 133,4 13908,7 109,4 13456,5 93,2 12441,6 91,2 12953 99,2 13057,2 108,2 14350,1 101,5 13830,2 106,9 13755,5 104,4 13574,4 77,9 12802,6 60 11737,3 99,5 13850,2 95 15081,8 105,6 13653,3 102,5 14019,1 93,3 13962 97,3 13768,7 127 14747,1 111,7 13858,1 96,4 13188 133 13693,1 72,2 12970 95,8 11392,8 124,1 13985,2 127,6 14994,7 110,7 13584,7 104,6 14257,8 112,7 13553,4 115,3 14007,3 139,4 16535,8 119 14721,4 97,4 13664,6 154 16405,9 81,5 13829,4 88,8 13735,6 127,7 15870,5 105,1 15962,4 114,9 15744,1 106,4 16083,7 104,5 14863,9 121,6 15533,1 141,4 17473,1 99 15925,5 126,7 15573,7 134,1 17495 81,3 14155,8 88,6 14913,9 132,7 17250,4 132,9 15879,8 134,4 17647,8 103,7 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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation transport[t] = + 45.6868318715026 + 0.00393335216032763Invoer[t] + 7.63202351997289M1[t] + 13.3609366719667M2[t] + 25.8561378782793M3[t] + 10.1961029363617M4[t] + 11.2981547120789M5[t] + 26.2151620747627M6[t] -14.4679010513006M7[t] -11.2034416318284M8[t] + 19.4366460284292M9[t] + 16.2397839003692M10[t] + 14.388284023985M11[t] -0.0676250412593975t + 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) 45.6868318715026 22.202055 2.0578 0.044116 0.022058 Invoer 0.00393335216032763 0.001644 2.392 0.020018 0.010009 M1 7.63202351997289 6.963752 1.096 0.277624 0.138812 M2 13.3609366719667 6.872169 1.9442 0.056726 0.028363 M3 25.8561378782793 7.083025 3.6504 0.000563 0.000282 M4 10.1961029363617 6.859801 1.4864 0.142601 0.071301 M5 11.2981547120789 6.835666 1.6528 0.10377 0.051885 M6 26.2151620747627 6.825125 3.841 0.000306 0.000153 M7 -14.4679010513006 7.269998 -1.9901 0.051302 0.025651 M8 -11.2034416318284 7.476562 -1.4985 0.139433 0.069717 M9 19.4366460284292 6.804317 2.8565 0.005936 0.002968 M10 16.2397839003692 6.82602 2.3791 0.020667 0.010333 M11 14.388284023985 6.80609 2.114 0.038823 0.019412 t -0.0676250412593975 0.096034 -0.7042 0.484139 0.242069 Multiple Linear Regression - Regression Statistics Multiple R 0.827365424448612 R-squared 0.684533545573033 Adjusted R-squared 0.613825547166988 F-TEST (value) 9.68113312502586 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 2.73402855910376e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.7801588769225 Sum Squared Residuals 8048.78430360103 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 124.9 98.6991478867212 26.2008521132788 2 132 110.762359973605 21.2376400263948 3 151.4 129.554099934069 21.8459000659315 4 108.9 103.405416737320 5.49458326268046 5 121.3 113.59472062494 7.70527937506008 6 123.4 123.628499896475 -0.228499896475197 7 90.3 78.0905288148177 12.2094711851823 8 79.3 83.7118814646565 -4.41188146465651 9 117.2 119.721023439660 -2.52102343965957 10 116.9 118.564813028276 -1.66481302827571 11 120.8 119.908403727624 0.891596272376054 12 96.1 101.056186952781 -4.95618695278136 13 100.8 109.415515903097 -8.61551590309705 14 105.3 113.940065239497 -8.64006523949674 15 116.1 131.728013728644 -15.6280137286445 16 112.8 108.952966679808 3.84703332019154 17 114.5 113.396036396406 1.10396360359378 18 117.2 127.250673956484 -10.0506739564837 19 77.1 79.139897226756 -2.03989722675597 20 80.1 80.8121643076258 -0.712164307625836 21 120.3 115.317979086952 4.98202091304839 22 133.4 115.146680056514 18.2533199434862 23 109.4 111.448893291970 -2.04889329197012 24 93.2 93.0010251192092 0.198974880790798 25 91.2 102.576939892714 -11.3769398927143 26 99.2 108.648083298555 -9.44808329855477 27 108.2 126.161090471696 -17.9610904716956 28 101.5 108.388480700364 -6.88848070036426 29 106.9 109.129086028446 -2.22908602844562 30 104.4 123.266138273635 -18.8661382736347 31 77.9 79.479688908971 -1.57968890897109 32 60 78.4863232307869 -18.4863232307869 33 99.5 117.369565629341 -17.8695656293413 34 95 118.949394980681 -23.9493949806814 35 105.6 111.411476502010 -5.81147650200984 36 102.5 98.3943876570133 4.10561234298673 37 93.3 105.734191727372 -12.4341917273721 38 97.3 110.635162865515 -13.3351628655151 39 127 126.911130784233 0.088869215767128 40 111.7 107.686720730525 4.01327926947538 41 96.4 106.085408182347 -9.68540818234692 42 133 122.921526679953 10.0784733200472 43 72.2 79.3266315654972 -7.12663156549716 44 95.8 76.3197829164413 19.4802170835587 45 124.1 117.089067675873 7.01093232412722 46 127.6 117.795299512404 9.80470048759589 47 110.7 110.330148048699 0.369851951301411 48 104.6 98.5217783225707 6.07822167742929 49 112.7 103.315523539549 9.38447646045059 50 115.3 110.762160195857 4.53783980414349 51 139.4 133.135217298298 6.26478270170188 52 119 110.270883155423 8.7291168445773 53 97.4 107.148543326846 -9.7485433268463 54 154 132.780423925377 21.2195760746232 55 81.5 81.89545391697 -0.395453916969955 56 88.8 84.723339862544 4.07666013745591 57 127.7 123.693116008626 4.00688399137431 58 105.1 120.790103902840 -15.6901039028404 59 114.9 118.012328208597 -3.11232820859729 60 106.4 104.892185537000 1.50781446299986 61 104.5 107.658681050546 -3.158681050546 62 121.6 115.952168426972 5.64783157302836 63 141.4 136.010447783060 5.38955221693957 64 99 114.195531996560 -15.1955319965604 65 126.7 113.846205441015 12.853794558985 66 134.1 136.252737268077 -2.15273726807685 67 81.3 82.3677995669881 -1.06779956698812 68 88.6 88.5465082179453 0.0534917820546443 69 132.7 128.309248159549 4.39075184045098 70 132.9 119.653708519285 13.2462914807155 71 134.4 124.688750221100 9.71124977889979 72 103.7 110.634436411425 -6.93443641142527 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.747821620732441 0.504356758535118 0.252178379267559 18 0.652688788339916 0.694622423320168 0.347311211660084 19 0.515902189943737 0.968195620112526 0.484097810056263 20 0.439418392895213 0.878836785790426 0.560581607104787 21 0.35306108198118 0.70612216396236 0.64693891801882 22 0.513936340591831 0.972127318816338 0.486063659408169 23 0.539894013684875 0.92021197263025 0.460105986315125 24 0.443278234692812 0.886556469385624 0.556721765307188 25 0.385281904471423 0.770563808942846 0.614718095528577 26 0.318662652059427 0.637325304118853 0.681337347940573 27 0.32837855510631 0.65675711021262 0.67162144489369 28 0.286490318519829 0.572980637039659 0.71350968148017 29 0.249933505062661 0.499867010125322 0.750066494937339 30 0.264753895756698 0.529507791513396 0.735246104243302 31 0.285362508800925 0.57072501760185 0.714637491199075 32 0.284009447076926 0.568018894153852 0.715990552923074 33 0.276676234546581 0.553352469093163 0.723323765453419 34 0.304898359161843 0.609796718323687 0.695101640838157 35 0.246296188620397 0.492592377240793 0.753703811379603 36 0.385858484805812 0.771716969611625 0.614141515194188 37 0.34672259822305 0.6934451964461 0.65327740177695 38 0.34815304736039 0.69630609472078 0.65184695263961 39 0.395121065727239 0.790242131454477 0.604878934272761 40 0.443987990945275 0.88797598189055 0.556012009054725 41 0.413619632057287 0.827239264114574 0.586380367942713 42 0.566758315175953 0.866483369648095 0.433241684824047 43 0.500601765055474 0.998796469889051 0.499398234944526 44 0.645527695436216 0.708944609127567 0.354472304563784 45 0.622744757876507 0.754510484246987 0.377255242123493 46 0.622899481870455 0.75420103625909 0.377100518129545 47 0.553073944594407 0.893852110811186 0.446926055405593 48 0.484472146894474 0.968944293788947 0.515527853105526 49 0.456310292200105 0.91262058440021 0.543689707799895 50 0.369737476704501 0.739474953409002 0.630262523295499 51 0.303976918383628 0.607953836767255 0.696023081616372 52 0.386152084858203 0.772304169716406 0.613847915141797 53 0.484589823004678 0.969179646009356 0.515410176995322 54 0.72081793967157 0.55836412065686 0.27918206032843 55 0.693997522110557 0.612004955778885 0.306002477889443 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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