uitbreiding model met trendbreuk

*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, 22 Dec 2010 18:00:44 +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/22/t12930408026uzqvg9zldhp006.htm/, Retrieved Wed, 22 Dec 2010 19:00:02 +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/22/t12930408026uzqvg9zldhp006.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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14544.5 94.6 -3.0 14097.8 0 1 0 15116.3 95.9 -3.7 14776.8 0 2 0 17413.2 104.7 -4.7 16833.3 0 3 0 16181.5 102.8 -6.4 15385.5 0 4 0 15607.4 98.1 -7.5 15172.6 0 5 0 17160.9 113.9 -7.8 16858.9 0 6 0 14915.8 80.9 -7.7 14143.5 0 7 0 13768 95.7 -6.6 14731.8 0 8 0 17487.5 113.2 -4.2 16471.6 0 9 0 16198.1 105.9 -2.0 15214 0 10 0 17535.2 108.8 -0.7 17637.4 0 11 0 16571.8 102.3 0.1 17972.4 0 12 0 16198.9 99 0.9 16896.2 0 13 0 16554.2 100.7 2.1 16698 0 14 0 19554.2 115.5 3.5 19691.6 0 15 0 15903.8 100.7 4.9 15930.7 0 16 0 18003.8 109.9 5.7 17444.6 0 17 0 18329.6 114.6 6.2 17699.4 0 18 0 16260.7 85.4 6.5 15189.8 0 19 0 14851.9 100.5 6.5 15672.7 0 20 0 18174.1 114.8 6.3 17180.8 0 21 0 18406.6 116.5 6.2 17664.9 0 22 0 18466.5 112.9 6.4 17862.9 0 23 0 16016.5 102 6.3 16162.3 0 24 0 17428.5 106 5.8 17463.6 0 25 0 17167.2 105.3 5.1 16772.1 0 26 0 19630 118.8 5.1 19106.9 0 27 0 17183.6 106.1 5.8 16721.3 0 28 0 18344.7 109.3 6.7 18161.3 0 29 0 19301.4 117.2 7.1 18509.9 0 30 0 18147.5 92.5 6.7 17802. 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation productie[t] = + 36.4727038520854 + 0.00549235243275046uitvoer[t] + 0.0597164546218206ondernemersvertrouwen[t] -0.00144467436394928invoer[t] + 35.0197206427131d[t] -0.0776395306949473t -0.576686462681621dt[t] -0.728263870202597M1[t] -0.676881229364584M2[t] + 2.07421799874795M3[t] + 1.24778117172163M4[t] -0.135633454856029M5[t] + 3.83630637755584M6[t] -15.440128343158M7[t] + 5.40312515228908M8[t] + 4.46738807176625M9[t] + 5.50014087544772M10[t] + 1.00152774905909M11[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) 36.4727038520854 6.384065 5.7131 1e-06 0 uitvoer 0.00549235243275046 0.000875 6.2758 0 0 ondernemersvertrouwen 0.0597164546218206 0.066237 0.9016 0.371614 0.185807 invoer -0.00144467436394928 0.000715 -2.0195 0.048807 0.024404 d 35.0197206427131 8.831995 3.9651 0.000234 0.000117 t -0.0776395306949473 0.049978 -1.5535 0.12662 0.06331 dt -0.576686462681621 0.127626 -4.5186 3.8e-05 1.9e-05 M1 -0.728263870202597 1.437442 -0.5066 0.614635 0.307318 M2 -0.676881229364584 1.633577 -0.4144 0.680386 0.340193 M3 2.07421799874795 1.936893 1.0709 0.289357 0.144678 M4 1.24778117172163 1.639962 0.7609 0.450314 0.225157 M5 -0.135633454856029 1.717342 -0.079 0.937365 0.468682 M6 3.83630637755584 2.052374 1.8692 0.067457 0.033728 M7 -15.440128343158 1.908858 -8.0887 0 0 M8 5.40312515228908 1.61112 3.3536 0.001527 0.000764 M9 4.46738807176625 2.003307 2.23 0.030266 0.015133 M10 5.50014087544772 1.938259 2.8377 0.006549 0.003274 M11 1.00152774905909 1.718007 0.583 0.562541 0.281271 Multiple Linear Regression - Regression Statistics Multiple R 0.979844173627738 R-squared 0.960094604592224 Adjusted R-squared 0.94652677015358 F-TEST (value) 70.7625530760965 F-TEST (DF numerator) 17 F-TEST (DF denominator) 50 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.30087511123178 Sum Squared Residuals 264.701313874292 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 94.6 95.0044407973773 -0.404440797377269 2 95.9 97.0959756172102 -1.19597561721023 3 104.7 109.354130333329 -4.65413033332882 4 102.8 103.675205055457 -0.875205055457485 5 98.1 99.3028744385436 -1.20287443854362 6 113.9 109.275474928224 4.62452507177583 7 80.9 81.5193606433774 -0.619360643377413 8 95.7 95.1966386575912 0.503361342408794 9 113.2 112.241941952682 0.95805804731784 10 105.9 108.063414679151 -2.16341467915087 11 108.8 107.407593997312 1.3924060026884 12 102.3 100.600901635620 1.69909836437978 13 99 99.3494317267297 -0.349431726729702 14 100.7 101.63260186071 -0.932601860709944 15 115.5 116.541944716931 -1.04194471693088 16 100.7 101.105463890545 -0.405463890544733 17 109.9 109.039030486163 0.86096951383728 18 114.6 114.384494409846 0.215505590153624 19 85.4 87.3107619304739 -1.91076193047386 20 100.5 99.641116537616 0.858883462383976 21 114.8 114.683776479286 0.116223520714464 22 116.5 116.210523187837 0.289476812163499 23 112.9 111.689160208337 1.21083979166292 24 102 99.6045710462144 2.39542895378559 25 106 104.644056303242 1.35594369675761 26 105.3 104.139838527143 1.16016147285657 27 118.8 116.96683809099 1.83316190900995 28 106.1 106.114487422661 -0.0144874226607434 29 109.3 109.004017400127 0.295982599872628 30 117.2 117.673124372833 -0.473124372832654 31 92.5 92.9792117776093 -0.479211777609335 32 104.2 104.949956385870 -0.749956385869784 33 112.5 113.590001491529 -1.09000149152858 34 122.4 122.881427724439 -0.481427724439092 35 113.3 110.78281131434 2.51718868565995 36 100 98.2286198327026 1.77138016729742 37 110.7 106.769112042874 3.93088795712564 38 112.8 109.839414881514 2.96058511848628 39 109.8 111.876236795875 -2.07623679587475 40 117.3 116.472074440892 0.827925559107628 41 109.1 110.822263907833 -1.72226390783314 42 115.9 119.704281701539 -3.80428170153892 43 96 98.5744635754251 -2.57446357542509 44 99.8 100.552920559872 -0.752920559871924 45 116.8 118.017468658232 -1.21746865823248 46 115.7 116.286543575894 -0.586543575894364 47 99.4 101.541289384131 -2.14128938413117 48 94.3 94.656908854431 -0.356908854430943 49 91 91.2844617628334 -0.284461762833364 50 93.2 93.8679422014329 -0.667942201432886 51 103.1 99.6958288178929 3.40417118210713 52 94.1 95.447612986957 -1.34761298695698 53 91.8 90.6886414423245 1.11135855767547 54 102.7 102.349544457698 0.350455542302467 55 82.6 79.1102359045874 3.48976409541258 56 89.1 88.292288158801 0.807711841198931 57 104.5 103.266811418271 1.23318858172876 58 105.1 102.158090832679 2.94190916732082 59 95.1 98.07914509588 -2.9791450958801 60 88.7 94.2089986310319 -5.50899863103185 61 86.3 90.548497366943 -4.24849736694291 62 91.8 93.1242269119898 -1.32422691198979 63 111.5 108.965021244983 2.53497875501736 64 99.7 97.8851562034877 1.81484379651231 65 97.5 96.8431723250086 0.656827674991383 66 111.7 112.613080129860 -0.913080129860346 67 86.2 84.1059661685269 2.09403383147313 68 95.4 96.06707970025 -0.667079700249992 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.413175849512748 0.826351699025496 0.586824150487252 22 0.309222211610669 0.618444423221337 0.690777788389331 23 0.272539568050076 0.545079136100153 0.727460431949924 24 0.238216818722745 0.47643363744549 0.761783181277255 25 0.145952564659941 0.291905129319882 0.85404743534006 26 0.0921778836050123 0.184355767210025 0.907822116394988 27 0.100395135325852 0.200790270651704 0.899604864674148 28 0.074676827146317 0.149353654292634 0.925323172853683 29 0.0561366210490275 0.112273242098055 0.943863378950972 30 0.123614295505005 0.24722859101001 0.876385704494995 31 0.119688745043404 0.239377490086808 0.880311254956596 32 0.110760892499452 0.221521784998904 0.889239107500548 33 0.131008278673150 0.262016557346300 0.86899172132685 34 0.263170471722854 0.526340943445709 0.736829528277146 35 0.189374855961685 0.378749711923369 0.810625144038315 36 0.139650690741572 0.279301381483143 0.860349309258428 37 0.178504236597858 0.357008473195715 0.821495763402142 38 0.436281495364135 0.87256299072827 0.563718504635865 39 0.515922660058415 0.96815467988317 0.484077339941585 40 0.570930715087971 0.858138569824058 0.429069284912029 41 0.637414220235361 0.725171559529279 0.362585779764639 42 0.755523665951354 0.488952668097292 0.244476334048646 43 0.726864337559694 0.546271324880611 0.273135662440306 44 0.610648232569155 0.77870353486169 0.389351767430845 45 0.472073395135487 0.944146790270974 0.527926604864513 46 0.333863483497376 0.667726966994752 0.666136516502624 47 0.789954025376408 0.420091949247183 0.210045974623592 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 = 2 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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