Paper - Multiple regression met dummy's

*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: Sat, 06 Dec 2008 04:29:09 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/06/t12285635399g1bu1eiag8vmys.htm/, Retrieved Sat, 06 Dec 2008 11:39:09 +0000

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/2008/Dec/06/t12285635399g1bu1eiag8vmys.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

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User-defined keywords:

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 1 15953689 0 1 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 0 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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation omzet[t] = + 16246717.3967962 -1413728.01969538D1[t] -1068775.45378151D2[t] -1711827.27958100M1[t] -1735673.65452264M2[t] + 429574.170535714M3[t] -921266.313649629M4[t] -992050.175408496M5[t] + 428662.049649861M6[t] -3256270.92529178M7[t] -3014493.90023343M8[t] -115806.675175070M9[t] + 225967.349883287M10[t] -702293.225058356M11[t] + 87127.7749416433t + 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) 16246717.3967962 469918.211464 34.5735 0 0 D1 -1413728.01969538 342938.327209 -4.1224 0.000159 8e-05 D2 -1068775.45378151 284106.776008 -3.7619 0.000485 0.000243 M1 -1711827.27958100 546665.917153 -3.1314 0.003055 0.001527 M2 -1735673.65452264 545757.714279 -3.1803 0.002664 0.001332 M3 429574.170535714 544930.294251 0.7883 0.434648 0.217324 M4 -921266.313649629 544184.025553 -1.6929 0.097382 0.048691 M5 -992050.175408496 538846.697754 -1.8411 0.072211 0.036105 M6 428662.049649861 538305.498786 0.7963 0.430029 0.215014 M7 -3256270.92529178 537847.135852 -6.0543 0 0 M8 -3014493.90023343 537471.820884 -5.6087 1e-06 1e-06 M9 -115806.675175070 537179.72795 -0.2156 0.830287 0.415144 M10 225967.349883287 536970.992863 0.4208 0.675891 0.337945 M11 -702293.225058356 536845.712853 -1.3082 0.197454 0.098727 t 87127.7749416433 6696.46093 13.011 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.944937868840558 R-squared 0.892907575968935 Adjusted R-squared 0.859589932937048 F-TEST (value) 26.7998422071566 F-TEST (DF numerator) 14 F-TEST (DF denominator) 45 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 848761.563721035 Sum Squared Residuals 32417828642258.0 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14929388 14622017.8921569 307370.107843138 2 14717825 14685299.2921569 32525.7078431433 3 15826281 16937674.8921569 -1111393.89215686 4 16301310 15673962.1829132 627347.817086832 5 15033017 15690306.0960959 -657289.096095943 6 16998461 17198146.0960959 -199685.096095938 7 14066463 13600340.8960959 466122.103904065 8 13328937 13929245.6960959 -600308.69609594 9 17319718 16915060.6960959 404657.303904062 10 17586427 17343962.4960959 242464.503904061 11 15887037 16502829.6960959 -615792.696095937 12 17935679 17292250.6960959 643428.303904062 13 15869489 15667551.1914566 201937.808543418 14 15892511 15730832.5914566 161678.408543415 15 17556558 17983208.1914566 -426650.191456582 16 16791643 15650720.0284314 1140922.97156863 17 15953689 15667063.9416141 286625.058385855 18 18144914 17174903.9416141 970010.058385854 19 14390881 13577098.7416141 813782.258385853 20 13885709 13906003.5416141 -20294.5416141452 21 17332572 16891818.5416141 440753.458385854 22 17152596 17320720.3416141 -168124.341614146 23 16003877 16479587.5416141 -475710.541614147 24 16841467 17269008.5416141 -427541.541614145 25 14783398 15644309.0369748 -860911.03697479 26 14667848 15707590.4369748 -1039742.43697479 27 17714362 17959966.0369748 -245604.036974790 28 16282088 16696253.3277311 -414165.327731092 29 15014866 16367644.675 -1352778.675 30 17722582 17875484.675 -152902.675000000 31 13876509 14277679.475 -401170.475000001 32 15495490 14606584.275 888905.725000001 33 17799521 17592399.275 207121.725 34 17920079 18021301.075 -101222.075000000 35 17248022 17180168.275 67853.7249999991 36 18813782 17969589.275 844192.725 37 16249688 17758617.790056 -1508929.79005602 38 17823359 17821899.1900560 1459.80994397594 39 20424438 20074274.7900560 350163.209943977 40 17814219 18810562.0808123 -996343.080812324 41 19699960 18826905.9939951 873054.006004903 42 19776328 20334745.9939951 -558417.993995098 43 15679833 16736940.7939951 -1057107.7939951 44 17119267 17065845.5939951 53421.406004902 45 20092613 20051660.5939951 40952.4060049018 46 20863688 20480562.3939951 383125.606004902 47 20925203 19639429.5939951 1285773.40600490 48 21032593 20428850.5939951 603742.406004903 49 20664684 18804151.0893557 1860532.91064426 50 19711511 18867432.4893557 844078.510644256 51 22553293 21119808.0893557 1433484.91064426 52 19498333 19856095.3801120 -357762.380112045 53 20722828 19872439.2932948 850388.706705183 54 21321275 21380279.2932948 -59004.2932948188 55 17960848 17782474.0932948 178373.906705181 56 17789655 18111378.8932948 -321723.893294818 57 20003709 21097193.8932948 -1093484.89329482 58 21169852 21526095.6932948 -356243.693294817 59 20422839 20684962.8932948 -262123.893294817 60 19810562 21474383.8932948 -1663821.89329482 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.0455920397342536 0.0911840794685072 0.954407960265746 19 0.0249334679988181 0.0498669359976363 0.975066532001182 20 0.00746501064287985 0.0149300212857597 0.99253498935712 21 0.00672221472588098 0.0134444294517620 0.993277785274119 22 0.0114423758571956 0.0228847517143911 0.988557624142804 23 0.00470468355781872 0.00940936711563743 0.995295316442181 24 0.0179513959703108 0.0359027919406217 0.98204860402969 25 0.0391196907771346 0.0782393815542691 0.960880309222865 26 0.0468932945243535 0.093786589048707 0.953106705475647 27 0.0353140085301502 0.0706280170603005 0.96468599146985 28 0.0333969718807157 0.0667939437614315 0.966603028119284 29 0.0468024266655740 0.0936048533311479 0.953197573334426 30 0.0289760234359550 0.0579520468719099 0.971023976564045 31 0.0159978579767823 0.0319957159535646 0.984002142023218 32 0.0431473491915852 0.0862946983831704 0.956852650808415 33 0.0247642928125394 0.0495285856250788 0.97523570718746 34 0.0137185091648361 0.0274370183296722 0.986281490835164 35 0.0141560664575595 0.028312132915119 0.98584393354244 36 0.00933392598822567 0.0186678519764513 0.990666074011774 37 0.0719008732266817 0.143801746453363 0.928099126773318 38 0.083567175746746 0.167134351493492 0.916432824253254 39 0.126813672564767 0.253627345129535 0.873186327435233 40 0.128277682847714 0.256555365695428 0.871722317152286 41 0.124488789619191 0.248977579238383 0.875511210380809 42 0.105179613437560 0.210359226875120 0.89482038656244 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.04 NOK 5% type I error level 11 0.44 NOK 10% type I error level 19 0.76 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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