Hypothese 1 en 2 Paper : multiple regression

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R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Wed, 03 Dec 2008 08:49:48 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/03/t12283195615q5fsohn0wsy64d.htm/, Retrieved Wed, 03 Dec 2008 15:52:51 +0000

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@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/03/t12283195615q5fsohn0wsy64d.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}, }

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Hypothese 1 en 2 Paper: multiple regression

Dataseries X:

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14929388 0 0 14717825 0 0 15826281 0 0 16301310 0 0 15033017 0 0 16998461 0 0 14066463 0 0 13328937 0 0 17319718 0 0 17586427 0 0 15887037 0 0 17935679 0 0 15869489 0 0 15892511 0 0 17556558 0 0 16791643 0 0 15953689 0 0 18144914 0 1 14390881 0 1 13885709 0 1 17332572 0 1 17152596 0 1 16003877 0 1 16841467 0 1 14783398 0 1 14667848 0 1 17714362 0 1 16282088 0 1 15014866 1 0 17722582 1 0 13876509 1 0 15495490 1 0 17799521 1 0 17920079 1 0 17248022 1 0 18813782 1 0 16249688 1 0 17823359 0 0 20424438 0 0 17814219 0 0 19699960 0 0 19776328 0 0 15679833 0 0 17119267 0 0 20092613 0 0 20863688 0 0 20925203 0 0 21032593 0 0 20664684 0 0 19711511 0 0 22553293 0 0 19498333 0 0 20722828 0 0 21321275 0 0 17960848 0 0 17789655 0 0 20003709 0 0 21169852 0 0 20422839 0 0 19810562 0 0

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Omzet_Industriële_Sector[t] = + 16230758.1876265 -1476066.76604186Dummy_1_tijdenscrisis[t] -1233878.07618445Dummy_2_voorcrisis[t] -1410306.05586093M1[t] -1731072.65853649M2[t] + 432468.291996321M3[t] -1133834.15747087M4[t] -1226877.66896657M5[t] + 438903.296803129M6[t] -3247736.55266406M7[t] -3007666.40213125M8[t] -110686.051598434M9[t] + 229381.098934378M10[t] -700586.35053281M11[t] + 88834.649467188t + 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) 16230758.1876265 433828.074267 37.4129 0 0 Dummy_1_tijdenscrisis -1476066.76604186 301162.440975 -4.9012 1.3e-05 6e-06 Dummy_2_voorcrisis -1233878.07618445 278799.166525 -4.4257 6.1e-05 3e-05 M1 -1410306.05586093 505209.318392 -2.7915 0.007672 0.003836 M2 -1731072.65853649 508072.68847 -3.4071 0.001393 0.000696 M3 432468.291996321 507354.021452 0.8524 0.398506 0.199253 M4 -1133834.15747087 506709.391175 -2.2376 0.03024 0.01512 M5 -1226877.66896657 506589.691049 -2.4218 0.019534 0.009767 M6 438903.296803129 502000.002823 0.8743 0.386592 0.193296 M7 -3247736.55266406 501583.178989 -6.475 0 0 M8 -3007666.40213125 501241.883487 -6.0004 0 0 M9 -110686.051598434 500976.270682 -0.2209 0.826138 0.413069 M10 229381.098934378 500786.460998 0.458 0.649127 0.324563 M11 -700586.35053281 500672.540647 -1.3993 0.168582 0.084291 t 88834.649467188 6166.753895 14.4054 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.952288281719405 R-squared 0.906852971500098 Adjusted R-squared 0.877873895966795 F-TEST (value) 31.2933713312537 F-TEST (DF numerator) 14 F-TEST (DF denominator) 45 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 791572.744768455 Sum Squared Residuals 28196433461711.9 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14929388 14909286.7812328 20101.2187672456 2 14717825 14677354.8280244 40470.1719756243 3 15826281 16929730.4280244 -1103449.42802438 4 16301310 15452262.6280244 849047.371975625 5 15033017 15448053.7659959 -415036.765995863 6 16998461 17202669.3812327 -204208.38123275 7 14066463 13604864.1812328 461598.81876725 8 13328937 13933768.9812328 -604831.981232751 9 17319718 16919583.9812328 400134.018767249 10 17586427 17348485.7812327 237941.218767251 11 15887037 16507352.9812328 -620315.981232752 12 17935679 17296773.9812328 638905.018767249 13 15869489 15975302.574839 -105813.574839006 14 15892511 15743370.6216306 149140.378369364 15 17556558 17995746.2216306 -439188.221630632 16 16791643 16518278.4216306 273364.578369364 17 15953689 16514069.5596021 -560380.559602116 18 18144914 17034807.0986546 1110106.90134545 19 14390881 13437001.8986546 953879.101345446 20 13885709 13765906.6986546 119802.301345446 21 17332572 16751721.6986546 580850.301345446 22 17152596 17180623.4986546 -28027.4986545544 23 16003877 16339490.6986546 -335613.698654554 24 16841467 17128911.6986546 -287444.698654552 25 14783398 15807440.2922608 -1024042.29226081 26 14667848 15575508.3390524 -907660.339052439 27 17714362 17827883.9390524 -113521.939052438 28 16282088 16350416.1390524 -68328.1390524391 29 15014866 16104018.5871665 -1089152.58716651 30 17722582 17858634.2024034 -136052.202403404 31 13876509 14260829.0024034 -384320.002403405 32 15495490 14589733.8024034 905756.197596597 33 17799521 17575548.8024034 223972.197596596 34 17920079 18004450.6024034 -84371.6024034042 35 17248022 17163317.8024034 84704.1975965965 36 18813782 17952738.8024034 861043.197596598 37 16249688 16631267.3960097 -381579.396009660 38 17823359 17875402.2088431 -52043.2088431474 39 20424438 20127777.8088431 296660.191156854 40 17814219 18650310.0088431 -836091.008843148 41 19699960 18646101.1468146 1053858.85318537 42 19776328 20400716.7620515 -624388.762051518 43 15679833 16802911.5620515 -1123078.56205152 44 17119267 17131816.3620515 -12549.3620515181 45 20092613 20117631.3620515 -25018.3620515182 46 20863688 20546533.1620515 317154.837948482 47 20925203 19705400.3620515 1219802.63794848 48 21032593 20494821.3620515 537771.637948483 49 20664684 19173349.9556578 1491334.04434223 50 19711511 18941418.0024494 770092.997550597 51 22553293 21193793.6024494 1359499.39755060 52 19498333 19716325.8024494 -217992.802449403 53 20722828 19712116.9404209 1010711.05957912 54 21321275 21466732.5556578 -145457.555657774 55 17960848 17868927.3556578 91920.6443422264 56 17789655 18197832.1556578 -408177.155657773 57 20003709 21183647.1556578 -1179938.15565777 58 21169852 21612548.9556578 -442696.955657774 59 20422839 20771416.1556578 -348577.155657773 60 19810562 21560837.1556578 -1750275.15565777 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.0987255859727375 0.197451171945475 0.901274414027262 19 0.0726590136750557 0.145318027350111 0.927340986324944 20 0.0284042969985016 0.0568085939970031 0.971595703001498 21 0.0221047257414601 0.0442094514829201 0.97789527425854 22 0.025724343329638 0.051448686659276 0.974275656670362 23 0.0110708682978200 0.0221417365956399 0.98892913170218 24 0.0290045231048702 0.0580090462097404 0.97099547689513 25 0.0509155067412262 0.101831013482452 0.949084493258774 26 0.0554443470985472 0.110888694197094 0.944555652901453 27 0.0523778061205962 0.104755612241192 0.947622193879404 28 0.0346213273738681 0.0692426547477362 0.965378672626132 29 0.0535982010977174 0.107196402195435 0.946401798902283 30 0.0299936164654402 0.0599872329308804 0.97000638353456 31 0.0175486772757903 0.0350973545515806 0.98245132272421 32 0.0584872605257927 0.116974521051585 0.941512739474207 33 0.0394876320854282 0.0789752641708564 0.960512367914572 34 0.0215379312229624 0.0430758624459247 0.978462068777038 35 0.0156513816211030 0.0313027632422059 0.984348618378897 36 0.0535729819486214 0.107145963897243 0.946427018051379 37 0.0292771010246753 0.0585542020493506 0.970722898975325 38 0.0226662071600408 0.0453324143200816 0.97733379283996 39 0.0297698973749998 0.0595397947499995 0.970230102625 40 0.0449536448163463 0.0899072896326925 0.955046355183654 41 0.0502423702547739 0.100484740509548 0.949757629745226 42 0.0546883593063928 0.109376718612786 0.945311640693607 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 6 0.24 NOK 10% type I error level 15 0.6 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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