ws 7 regressie analyse laatste 4 maanden

*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, 18 Nov 2009 09:27:25 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/18/t1258561750aret92gsj1yc623.htm/, Retrieved Wed, 18 Nov 2009 17:29:22 +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/2009/Nov/18/t1258561750aret92gsj1yc623.htm/}, year = {2009}, } @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 = {2009}, 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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1751 9062 1643 1639 1395 1901 1797 8885 1751 1643 1639 1395 1373 9058 1797 1751 1643 1639 1558 9095 1373 1797 1751 1643 1555 9149 1558 1373 1797 1751 2061 9857 1555 1558 1373 1797 2010 9848 2061 1555 1558 1373 2119 10269 2010 2061 1555 1558 1985 10341 2119 2010 2061 1555 1963 9690 1985 2119 2010 2061 2017 10125 1963 1985 2119 2010 1975 9349 2017 1963 1985 2119 1589 9224 1975 2017 1963 1985 1679 9224 1589 1975 2017 1963 1392 9454 1679 1589 1975 2017 1511 9347 1392 1679 1589 1975 1449 9430 1511 1392 1679 1589 1767 9933 1449 1511 1392 1679 1899 10148 1767 1449 1511 1392 2179 10677 1899 1767 1449 1511 2217 10735 2179 1899 1767 1449 2049 9760 2217 2179 1899 1767 2343 10567 2049 2217 2179 1899 2175 9333 2343 2049 2217 2179 1607 9409 2175 2343 2049 2217 1702 9502 1607 2175 2343 2049 1764 9348 1702 1607 2175 2343 1766 9319 1764 1702 1607 2175 1615 9594 1766 1764 1702 1607 1953 10160 1615 1766 1764 1702 2091 10182 1953 1615 1766 1764 2411 10810 2091 1953 1615 1766 2550 11105 2411 2091 1 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation aanbod[t] = + 903.196828297846 -0.0300536354727465invoer[t] + 0.693384135006776`y(t-1)`[t] + 0.0290846274189062`y(t-2)`[t] -0.319846239397827`Y(t-3)`[t] + 0.257255528253368`Y(t-4)`[t] -231.481323073979M1[t] + 82.690332409393M2[t] -211.948225731399M3[t] -114.242382221827M4[t] -98.9220440105658M5[t] + 23.8776125317967M6[t] + 152.685639602411M7[t] + 275.426064938505M8[t] + 107.969432124962M9[t] -134.804093406645M10[t] + 451.038230443387M11[t] + 1.65970798276155t + 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) 903.196828297846 2534.165692 0.3564 0.723506 0.361753 invoer -0.0300536354727465 0.270351 -0.1112 0.912071 0.456035 `y(t-1)` 0.693384135006776 0.170614 4.064 0.000233 0.000117 `y(t-2)` 0.0290846274189062 0.201676 0.1442 0.886093 0.443047 `Y(t-3)` -0.319846239397827 0.225218 -1.4202 0.163712 0.081856 `Y(t-4)` 0.257255528253368 0.183185 1.4043 0.168336 0.084168 M1 -231.481323073979 173.995273 -1.3304 0.19132 0.09566 M2 82.690332409393 183.861322 0.4497 0.655451 0.327725 M3 -211.948225731399 150.850585 -1.405 0.168138 0.084069 M4 -114.242382221827 175.440654 -0.6512 0.518853 0.259426 M5 -98.9220440105658 163.508639 -0.605 0.548778 0.274389 M6 23.8776125317967 230.591342 0.1035 0.918071 0.459036 M7 152.685639602411 261.094796 0.5848 0.562145 0.281073 M8 275.426064938505 363.897294 0.7569 0.45379 0.226895 M9 107.969432124962 435.576005 0.2479 0.805564 0.402782 M10 -134.804093406645 205.967184 -0.6545 0.516736 0.258368 M11 451.038230443387 359.077004 1.2561 0.216746 0.108373 t 1.65970798276155 4.58814 0.3617 0.719551 0.359776 Multiple Linear Regression - Regression Statistics Multiple R 0.846111679499226 R-squared 0.715904974185 Adjusted R-squared 0.588809831057237 F-TEST (value) 5.63282716055745 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 4.80906334554554e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 207.083515112569 Sum Squared Residuals 1629576.12479236 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1751 1630.786261958 120.213738042000 2 1797 1818.72516428395 -21.7251642839474 3 1373 1617.07480909692 -244.074809096916 4 1558 1389.15702395320 168.842976046798 5 1555 1533.52902682140 21.4709731786024 6 2061 1787.45948090363 273.540519096372 7 2010 2100.71491883940 -90.7149188394047 8 2119 2240.36851365792 -121.368513657921 9 1985 1983.88931807042 1.11068192958421 10 1963 1819.08062301757 143.919376982426 11 2017 2326.37426034016 -309.374260340155 12 1975 2008.02048915246 -33.0204891524576 13 1589 1726.96839118647 -137.968391186471 14 1679 1751.00060563934 -72.000605639338 15 1392 1529.61266586988 -137.612665869879 16 1511 1548.46624229947 -37.4662422994723 17 1449 1509.03046529423 -60.0304652942333 18 1767 1693.79297371897 73.207026281025 19 1899 1924.59804608084 -25.5980460808352 20 2179 2184.31929827953 -5.31929827952983 21 2217 2097.10504433230 119.894955667696 22 2049 1959.37336856100 89.6266314390043 23 2343 2351.63958042612 -8.63958042611544 24 2175 2198.1933532383 -23.193353238301 25 1607 1921.65988592364 -314.659885923638 26 1702 1698.71413207105 3.28586792894569 27 1764 1589.08225975286 174.917740247143 28 1766 1873.52595788052 -107.525957880516 29 1615 1708.92473669881 -93.924736698813 30 1953 1716.33971675658 236.660283243418 31 2091 2091.42848099451 -0.428480994506065 32 2411 2351.28383914058 59.71616085942 33 2550 2255.56407994859 294.435920051408 34 2351 2199.94735071943 151.052649280573 35 2786 2554.08102833630 231.918971663697 36 2525 2487.89824313566 37.1017568643439 37 2474 2180.17706479593 293.822935204071 38 2332 2269.09915608013 62.9008439198704 39 1978 2059.96176273334 -81.961762733341 40 1789 1869.69703380967 -80.6970338096668 41 1904 1773.66257455228 130.337425447716 42 1997 2030.75673975296 -33.7567397529635 43 2207 2193.2972420938 13.7027579061983 44 2453 2367.5960775837 85.4039224162981 45 1948 2363.44155764869 -415.441557648688 46 1384 1768.59865770200 -384.598657702003 47 1989 1902.90513089743 86.0948691025735 48 2140 2120.88791447359 19.1120855264150 49 2100 2061.40839613596 38.5916038640392 50 2045 2017.46094192553 27.5390580744694 51 2083 1794.26850254701 288.731497452993 52 2022 1965.15374205714 56.8462579428565 53 1950 1947.85319663327 2.14680336672787 54 1422 1971.65108886785 -549.651088867852 55 1859 1755.96131199145 103.038688008548 56 2147 2165.43227133827 -18.4322713382674 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.00735191527431575 0.0147038305486315 0.992648084725684 22 0.0166100952895388 0.0332201905790775 0.983389904710461 23 0.00832031388868948 0.0166406277773790 0.99167968611131 24 0.0224755829477781 0.0449511658955561 0.977524417052222 25 0.0244727801589687 0.0489455603179374 0.975527219841031 26 0.0122496623748082 0.0244993247496163 0.987750337625192 27 0.0814829844455115 0.162965968891023 0.918517015554489 28 0.0464512707092153 0.0929025414184305 0.953548729290785 29 0.0503563828284695 0.100712765656939 0.94964361717153 30 0.0287142762529619 0.0574285525059239 0.971285723747038 31 0.125454483865877 0.250908967731755 0.874545516134122 32 0.0788969530640363 0.157793906128073 0.921103046935964 33 0.0595565863131308 0.119113172626262 0.94044341368687 34 0.0492452949871543 0.0984905899743086 0.950754705012846 35 0.0657270199265594 0.131454039853119 0.93427298007344 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 0.4 NOK 10% type I error level 9 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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