regressiemodel zonder uitschieters

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

Title produced by software: Multiple Regression

Date of computation: Thu, 08 May 2008 10:13:08 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/08/t1210263259wmdifwtjjpmsssl.htm/, Retrieved Thu, 08 May 2008 18:14:20 +0200

User-defined keywords:

Dataseries X:

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56421 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972 58552 54955 51570 51145 46641 35704 33253 35193 41668 34865 21210 56126 49231 59723 48103 47472 50497 40059 34149 36860 46356 36577

Text written by user:

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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation [t] = + 49460.5 + 521.863888888879M1[t] -2159.85555555556M2[t] -7242.575M3[t] -10192.6277777778M4[t] -17879.0138888889M5[t] -18909.5666666667M6[t] -15860.4527777778M7[t] -15319.3388888889M8[t] -20173.4416666667M9[t] -20799.5611111111M10[t] -7096.28055555556M11[t] + 75.7194444444446t + 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) 49460.5 3587.511028 13.7869 0 0 M1 521.863888888879 4350.402154 0.12 0.904954 0.452477 M2 -2159.85555555556 4348.347223 -0.4967 0.621375 0.310688 M3 -7242.575 4346.748272 -1.6662 0.101359 0.050679 M4 -10192.6277777778 4345.605804 -2.3455 0.022636 0.011318 M5 -17879.0138888889 4344.920179 -4.1149 0.000131 6.5e-05 M6 -18909.5666666667 4344.691614 -4.3523 5.9e-05 3e-05 M7 -15860.4527777778 4344.920179 -3.6503 0.000584 0.000292 M8 -15319.3388888889 4345.605804 -3.5252 0.000861 0.000431 M9 -20173.4416666667 4539.851531 -4.4436 4.3e-05 2.2e-05 M10 -20799.5611111111 4538.75767 -4.5827 2.7e-05 1.3e-05 M11 -7096.28055555556 4538.101227 -1.5637 0.123621 0.061811 t 75.7194444444446 44.566214 1.699 0.094963 0.047482 Multiple Linear Regression - Regression Statistics Multiple R 0.762119677079126 R-squared 0.580826402191191 Adjusted R-squared 0.489370344487451 F-TEST (value) 6.35087950185544 F-TEST (DF numerator) 12 F-TEST (DF denominator) 55 p-value 6.80642322947733e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7175.02205575746 Sum Squared Residuals 2831451782.53333 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 56421 50058.0833333334 6362.91666666662 2 53536 47452.0833333333 6083.91666666667 3 52408 42445.0833333333 9962.91666666667 4 41454 39570.75 1883.25 5 38271 31960.0833333333 6310.91666666667 6 35306 31005.25 4300.75000000000 7 26414 34130.0833333333 -7716.08333333334 8 31917 34746.9166666667 -2829.91666666667 9 38030 29968.5333333333 8061.46666666668 10 27534 29418.1333333333 -1884.13333333333 11 18387 43197.1333333333 -24810.1333333333 12 50556 50369.1333333333 186.866666666671 13 43901 50966.7166666667 -7065.71666666666 14 43899 48360.7166666667 -4461.71666666666 15 37532 43353.7166666667 -5821.71666666666 16 40357 40479.3833333333 -122.383333333330 17 35489 32868.7166666667 2620.28333333334 18 29027 31913.8833333333 -2886.88333333333 19 34485 35038.7166666667 -553.716666666662 20 42598 35655.55 6942.45 21 30306 30877.1666666667 -571.166666666668 22 26451 30326.7666666667 -3875.76666666666 23 47460 44105.7666666667 3354.23333333334 24 50104 51277.7666666667 -1173.76666666667 25 61465 51875.35 9589.65000000001 26 53726 49269.35 4456.65 27 39477 44262.35 -4785.35 28 43895 41388.0166666667 2506.98333333333 29 31481 33777.35 -2296.35 30 29896 32822.5166666667 -2926.51666666667 31 33842 35947.35 -2105.35 32 39120 36564.1833333333 2555.81666666667 33 33702 31785.8 1916.2 34 25094 31235.4 -6141.4 35 51442 45014.4 6427.6 36 45594 52186.4 -6592.4 37 52518 52783.9833333333 -265.983333333322 38 48564 50177.9833333333 -1613.98333333333 39 41745 45170.9833333333 -3425.98333333333 40 49585 42296.65 7288.35 41 32747 34685.9833333333 -1938.98333333333 42 33379 33731.15 -352.150000000000 43 35645 36855.9833333333 -1210.98333333333 44 37034 37472.8166666667 -438.816666666667 45 35681 32694.4333333333 2986.56666666666 46 20972 32144.0333333333 -11172.0333333333 47 58552 45923.0333333333 12628.9666666667 48 54955 53095.0333333333 1859.96666666667 49 51570 53692.6166666667 -2122.61666666666 50 51145 51086.6166666667 58.3833333333317 51 46641 46079.6166666667 561.383333333333 52 35704 43205.2833333333 -7501.28333333333 53 33253 35594.6166666667 -2341.61666666667 54 35193 34639.7833333333 553.216666666665 55 41668 37764.6166666667 3903.38333333333 56 34865 38381.45 -3516.45 57 21210 33603.0666666667 -12393.0666666667 58 56126 33052.6666666667 23073.3333333333 59 49231 46831.6666666667 2399.33333333333 60 59723 54003.6666666667 5719.33333333332 61 48103 54601.25 -6498.24999999999 62 47472 51995.25 -4523.25 63 50497 46988.25 3508.75 64 40059 44113.9166666667 -4054.91666666667 65 34149 36503.25 -2354.25000000000 66 36860 35548.4166666667 1311.58333333333 67 46356 38673.25 7682.75 68 36577 39290.0833333333 -2713.08333333334 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.288217824021443 0.576435648042887 0.711782175978557 17 0.231570853189667 0.463141706379333 0.768429146810333 18 0.129243555346139 0.258487110692278 0.870756444653861 19 0.370679870870879 0.741359741741757 0.629320129129121 20 0.570468073782643 0.859063852434713 0.429531926217357 21 0.471527225684268 0.943054451368536 0.528472774315732 22 0.378995946728202 0.757991893456404 0.621004053271798 23 0.900142754716903 0.199714490566194 0.0998572452830969 24 0.849940382765607 0.300119234468786 0.150059617234393 25 0.884645179441797 0.230709641116405 0.115354820558203 26 0.853181275245208 0.293637449509584 0.146818724754792 27 0.819848093112053 0.360303813775894 0.180151906887947 28 0.7655479408863 0.468904118227399 0.234452059113699 29 0.711944135133773 0.576111729732454 0.288055864866227 30 0.636353852214157 0.727292295571686 0.363646147785843 31 0.566289034863429 0.867421930273142 0.433710965136571 32 0.49790239618833 0.99580479237666 0.50209760381167 33 0.442721711728702 0.885443423457404 0.557278288271298 34 0.422433741188463 0.844867482376927 0.577566258811536 35 0.507643226212759 0.984713547574481 0.492356773787241 36 0.495508542044031 0.991017084088061 0.504491457955969 37 0.422105966479642 0.844211932959283 0.577894033520358 38 0.341519513494819 0.683039026989637 0.658480486505181 39 0.278812759971301 0.557625519942602 0.721187240028699 40 0.331101891382822 0.662203782765644 0.668898108617178 41 0.259465677009688 0.518931354019377 0.740534322990312 42 0.189931480055555 0.379862960111111 0.810068519944445 43 0.146335536072138 0.292671072144276 0.853664463927862 44 0.103950857759234 0.207901715518469 0.896049142240766 45 0.144164160438295 0.288328320876590 0.855835839561705 46 0.976992720238055 0.0460145595238905 0.0230072797619453 47 0.998126963148955 0.00374607370208930 0.00187303685104465 48 0.996346530772372 0.00730693845525673 0.00365346922762836 49 0.996449928261158 0.00710014347768429 0.00355007173884215 50 0.99947817349125 0.00104365301750076 0.000521826508750382 51 0.997386552849851 0.00522689430029736 0.00261344715014868 52 0.991803045754725 0.0163939084905502 0.0081969542452751 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.135135135135135 NOK 5% type I error level 7 0.189189189189189 NOK 10% type I error level 7 0.189189189189189 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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