autoregressie

*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: Sun, 19 Dec 2010 09:44:42 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/19/t1292751800kiy2gbkjf5yv7am.htm/, Retrieved Sun, 19 Dec 2010 10:43:31 +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/2010/Dec/19/t1292751800kiy2gbkjf5yv7am.htm/}, year = {2010}, } @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 = {2010}, 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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98,1 102,8 104,7 95,9 94,6 15607,4 -7,5 15172,6 113,9 98,1 102,8 104,7 95,9 17160,9 -7,8 16858,9 80,9 113,9 98,1 102,8 104,7 14915,8 -7,7 14143,5 95,7 80,9 113,9 98,1 102,8 13768 -6,6 14731,8 113,2 95,7 80,9 113,9 98,1 17487,5 -4,2 16471,6 105,9 113,2 95,7 80,9 113,9 16198,1 -2,0 15214 108,8 105,9 113,2 95,7 80,9 17535,2 -0,7 17637,4 102,3 108,8 105,9 113,2 95,7 16571,8 0,1 17972,4 99 102,3 108,8 105,9 113,2 16198,9 0,9 16896,2 100,7 99 102,3 108,8 105,9 16554,2 2,1 16698 115,5 100,7 99 102,3 108,8 19554,2 3,5 19691,6 100,7 115,5 100,7 99 102,3 15903,8 4,9 15930,7 109,9 100,7 115,5 100,7 99 18003,8 5,7 17444,6 114,6 109,9 100,7 115,5 100,7 18329,6 6,2 17699,4 85,4 114,6 109,9 100,7 115,5 16260,7 6,5 15189,8 100,5 85,4 114,6 109,9 100,7 14851,9 6,5 15672,7 114,8 100,5 85,4 114,6 109,9 18174,1 6,3 17180,8 116,5 114,8 100,5 85,4 114,6 18406,6 6,2 17664,9 112,9 116,5 114,8 100,5 85,4 18466,5 6,4 17862,9 102 112,9 116,5 114,8 100,5 16016,5 6,3 16162,3 106 102 112,9 116,5 114,8 17428,5 5,8 17463 etc...

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 29.3309960681547 + 0.0190513769829433y1[t] + 0.0543223455157287y2[t] + 0.178983788445719y3[t] -0.0339591841183791y4[t] + 0.00494920051812905uitvoer[t] -0.109468457659687ondernemersvertrouwen[t] -0.00165756844252513invoer[t] -2.68869089991944M1[t] + 0.792315193615192M2[t] -18.3121838438258M3[t] + 1.01821395587077M4[t] + 2.14089750440338M5[t] + 7.12195831693119M6[t] -0.0412927194513832M7[t] -4.42967383373736M8[t] -4.17140693402091M9[t] -2.3862059845378M10[t] + 3.62119270753337M11[t] -0.102508756541094t + 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) 29.3309960681547 9.598749 3.0557 0.003807 0.001904 y1 0.0190513769829433 0.100962 0.1887 0.851196 0.425598 y2 0.0543223455157287 0.083793 0.6483 0.520167 0.260084 y3 0.178983788445719 0.086166 2.0772 0.043654 0.021827 y4 -0.0339591841183791 0.090674 -0.3745 0.709816 0.354908 uitvoer 0.00494920051812905 0.00102 4.8538 1.6e-05 8e-06 ondernemersvertrouwen -0.109468457659687 0.067112 -1.6311 0.110002 0.055001 invoer -0.00165756844252513 0.000801 -2.0687 0.044484 0.022242 M1 -2.68869089991944 1.873314 -1.4353 0.158284 0.079142 M2 0.792315193615192 2.108389 0.3758 0.708878 0.354439 M3 -18.3121838438258 1.910392 -9.5856 0 0 M4 1.01821395587077 3.71713 0.2739 0.785424 0.392712 M5 2.14089750440338 3.115704 0.6871 0.495606 0.247803 M6 7.12195831693119 2.646913 2.6907 0.010041 0.005021 M7 -0.0412927194513832 2.252253 -0.0183 0.985455 0.492728 M8 -4.42967383373736 2.612258 -1.6957 0.097004 0.048502 M9 -4.17140693402091 3.36313 -1.2403 0.221425 0.110713 M10 -2.3862059845378 3.067236 -0.778 0.440752 0.220376 M11 3.62119270753337 2.40365 1.5065 0.139075 0.069538 t -0.102508756541094 0.025845 -3.9663 0.000265 0.000133 Multiple Linear Regression - Regression Statistics Multiple R 0.979407569564116 R-squared 0.959239187319488 Adjusted R-squared 0.941637927298357 F-TEST (value) 54.49832490219 F-TEST (DF numerator) 19 F-TEST (DF denominator) 44 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.45407124111589 Sum Squared Residuals 264.988488884771 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 98.1 101.053376683421 -2.95337668342122 2 113.9 110.696296368665 3.20370363133496 3 80.9 84.274639708616 -3.37463970861609 4 95.7 96.1791698417413 -0.479169841741336 5 113.2 113.938209086353 -0.738209086352653 6 105.9 108.973339143787 -3.07333914378726 7 108.8 108.747074144534 0.0529258554661365 8 102.3 101.133580544001 1.16641945599863 9 99 99.2729156795653 -0.272915679565312 10 100.7 103.262216973376 -2.56221697337623 11 115.5 117.490603074855 -1.99060307485530 12 100.7 101.785429915795 -1.08542991579462 13 109.9 107.728931798372 2.17106820162784 14 114.6 114.205327406793 0.394672593207415 15 85.4 86.3236629435323 -0.923662943532304 16 100.5 99.6269400905268 0.873059909473157 17 114.8 113.841726182395 0.958273817604575 18 116.5 114.786252641759 1.71374735824108 19 112.9 111.970317980252 0.929682019747777 20 102 100.254142103958 1.74585789604242 21 106 104.711347447797 1.28865255220274 22 105.3 105.105669734125 0.194330265875441 23 118.8 117.704643093038 1.09535690696214 24 106.1 107.056143045621 -0.95614304562059 25 109.3 107.756313730023 1.54368626997676 26 117.2 117.059218651778 0.140781348221566 27 92.5 90.9501424505017 1.54985754949833 28 104.2 103.906954916288 0.293045083711955 29 112.5 113.470401229774 -0.97040122977434 30 122.4 121.336349185140 1.06365081486016 31 113.3 111.261712057534 2.03828794246650 32 100 98.455034048103 1.54496595189709 33 110.7 107.035061756531 3.66493824346855 34 112.8 109.431741662475 3.36825833752521 35 109.8 112.936567011979 -3.13656701197929 36 117.3 116.335105235101 0.964894764898578 37 109.1 110.614333363003 -1.51433336300331 38 115.9 117.770046593989 -1.87004659398874 39 96 98.5561600206925 -2.55616002069252 40 99.8 100.112444377040 -0.312444377039719 41 116.8 117.809098790765 -1.00909879076508 42 115.7 118.305802811152 -2.60580281115219 43 99.4 99.2859780031238 0.114021996876163 44 94.3 93.9611795496069 0.338820450393129 45 91 91.272954312284 -0.272954312284033 46 93.2 93.0641278980282 0.135872101971792 47 103.1 101.442539716013 1.65746028398668 48 94.1 95.3574182556736 -1.25741825567361 49 91.8 90.7601338544058 1.03986614559418 50 102.7 101.816641862875 0.883358137125183 51 82.6 77.7925148037581 4.80748519624186 52 89.1 87.0227449088026 2.07725509119740 53 104.5 102.740564710713 1.7594352892875 54 105.1 102.198256218162 2.90174378183820 55 95.1 98.2349178145566 -3.13491781455658 56 88.7 93.4960637543313 -4.79606375433127 57 86.3 90.707720803822 -4.40772080382195 58 91.8 92.9362437319962 -1.13624373199622 59 111.5 109.125647104114 2.37435289588578 60 99.7 97.3659035478098 2.33409645219025 61 97.5 97.7869105707743 -0.286910570774256 62 111.7 114.452469115900 -2.75246911590038 63 86.2 85.7028800728993 0.497119927100712 64 95.4 97.8517458656015 -2.45174586560146 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 23 0.0681818823911909 0.136363764782382 0.93181811760881 24 0.0528686597648673 0.105737319529735 0.947131340235133 25 0.0273318793539638 0.0546637587079275 0.972668120646036 26 0.136890647037026 0.273781294074052 0.863109352962974 27 0.073505731076484 0.147011462152968 0.926494268923516 28 0.0542173896302575 0.108434779260515 0.945782610369743 29 0.034155302090372 0.068310604180744 0.965844697909628 30 0.0187148707648566 0.0374297415297132 0.981285129235143 31 0.0165884705489999 0.0331769410979999 0.983411529451 32 0.0095432758983876 0.0190865517967752 0.990456724101612 33 0.0155632604468650 0.0311265208937300 0.984436739553135 34 0.0632300424942235 0.126460084988447 0.936769957505777 35 0.052025863420219 0.104051726840438 0.94797413657978 36 0.115305052502418 0.230610105004835 0.884694947497582 37 0.076364377343717 0.152728754687434 0.923635622656283 38 0.126987214468363 0.253974428936727 0.873012785531637 39 0.105790400383884 0.211580800767767 0.894209599616116 40 0.0555215050375201 0.111043010075040 0.94447849496248 41 0.0278774387751858 0.0557548775503715 0.972122561224814 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 4 0.210526315789474 NOK 10% type I error level 7 0.368421052631579 NOK

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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