Q3 Multiple Regression met dummies en lineaire trend

*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: Sun, 30 Nov 2008 10:13:28 -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/Nov/30/t122806583256494evwcf2jzfl.htm/, Retrieved Sun, 30 Nov 2008 17:24:03 +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/Nov/30/t122806583256494evwcf2jzfl.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

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

512927 0 502831 0 470984 0 471067 0 476049 0 474605 0 470439 0 461251 0 454724 0 455626 0 516847 0 525192 0 522975 0 518585 0 509239 0 512238 0 519164 0 517009 0 509933 0 509127 0 500857 0 506971 0 569323 0 579714 0 577992 0 565464 0 547344 0 554788 0 562325 0 560854 0 555332 0 543599 0 536662 0 542722 0 593530 0 610763 1 612613 1 611324 1 594167 1 595454 1 590865 1 589379 1 584428 1 573100 1 567456 1 569028 1 620735 1 628884 1 628232 1 612117 1 595404 1 597141 1 593408 1 590072 1 579799 1 574205 1 572775 1 572942 1 619567 1 625809 1 619916 1

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 5 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation X[t] = + 506330.123076923 -539.189102564112Y[t] -2785.79246794871M1[t] -7653.31826923078M2[t] -28736.190224359M3[t] -28472.4621794872M4[t] -28694.1341346154M5[t] -33118.8060897435M6[t] -41962.6780448717M7[t] -52138.75M8[t] -60346.6219551282M9[t] -59829.8939102564M10[t] -7733.5658653846M11[t] + 2446.27195512821t + 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) 506330.123076923 8252.816225 61.3524 0 0 Y -539.189102564112 7967.355909 -0.0677 0.946332 0.473166 M1 -2785.79246794871 9261.991751 -0.3008 0.764911 0.382456 M2 -7653.31826923078 9726.250482 -0.7869 0.435306 0.217653 M3 -28736.190224359 9708.585055 -2.9599 0.00481 0.002405 M4 -28472.4621794872 9696.130573 -2.9365 0.005126 0.002563 M5 -28694.1341346154 9688.907132 -2.9615 0.004788 0.002394 M6 -33118.8060897435 9686.926434 -3.4189 0.001308 0.000654 M7 -41962.6780448717 9690.191693 -4.3304 7.8e-05 3.9e-05 M8 -52138.75 9698.697611 -5.3759 2e-06 1e-06 M9 -60346.6219551282 9712.43042 -6.2133 0 0 M10 -59829.8939102564 9731.36799 -6.1481 0 0 M11 -7733.5658653846 9755.480011 -0.7927 0.431912 0.215956 t 2446.27195512821 225.442892 10.851 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.96220883818894 R-squared 0.92584584828891 Adjusted R-squared 0.905335125475204 F-TEST (value) 45.1396012075322 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 15264.4813318957 Sum Squared Residuals 10951206345.5942 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 512927 505990.602564103 6936.39743589748 2 502831 503569.348717949 -738.348717948746 3 470984 484932.748717949 -13948.7487179486 4 471067 487642.748717949 -16575.7487179487 5 476049 489867.348717949 -13818.3487179487 6 474605 487888.948717949 -13283.9487179487 7 470439 481491.348717949 -11052.3487179487 8 461251 473761.548717949 -12510.5487179489 9 454724 467999.948717949 -13275.9487179488 10 455626 470962.948717949 -15336.9487179488 11 516847 525505.548717949 -8658.5487179487 12 525192 535685.386538462 -10493.3865384615 13 522975 535345.866025641 -12370.8660256411 14 518585 532924.612179487 -14339.6121794872 15 509239 514288.012179487 -5049.01217948718 16 512238 516998.012179487 -4760.01217948718 17 519164 519222.612179487 -58.612179487193 18 517009 517244.212179487 -235.212179487179 19 509933 510846.612179487 -913.612179487188 20 509127 503116.812179487 6010.18782051285 21 500857 497355.212179487 3501.78782051284 22 506971 500318.212179487 6652.78782051283 23 569323 554860.812179487 14462.1878205128 24 579714 565040.65 14673.35 25 577992 564701.12948718 13290.8705128205 26 565464 562279.875641026 3184.12435897437 27 547344 543643.275641026 3700.72435897435 28 554788 546353.275641026 8434.72435897435 29 562325 548577.875641026 13747.1243589743 30 560854 546599.475641026 14254.5243589744 31 555332 540201.875641026 15130.1243589744 32 543599 532472.075641026 11126.9243589744 33 536662 526710.475641026 9951.52435897438 34 542722 529673.475641026 13048.5243589744 35 593530 584216.075641026 9313.92435897436 36 610763 593856.724358974 16906.2756410256 37 612613 593517.203846154 19095.7961538461 38 611324 591095.95 20228.05 39 594167 572459.35 21707.65 40 595454 575169.35 20284.65 41 590865 577393.95 13471.0500000000 42 589379 575415.55 13963.45 43 584428 569017.95 15410.05 44 573100 561288.15 11811.8500000000 45 567456 555526.55 11929.45 46 569028 558489.55 10538.45 47 620735 613032.15 7702.85 48 628884 623211.987820513 5672.01217948718 49 628232 622872.467307692 5359.53269230767 50 612117 620451.213461538 -8334.21346153846 51 595404 601814.613461538 -6410.61346153846 52 597141 604524.613461538 -7383.61346153847 53 593408 606749.213461538 -13341.2134615385 54 590072 604770.813461539 -14698.8134615385 55 579799 598373.213461538 -18574.2134615385 56 574205 590643.413461538 -16438.4134615384 57 572775 584881.813461539 -12106.8134615385 58 572942 587844.813461538 -14902.8134615385 59 619567 642387.413461538 -22820.4134615385 60 625809 652567.251282051 -26758.2512820513 61 619916 652227.730769231 -32311.7307692308 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.768048162736369 0.463903674527262 0.231951837263631 18 0.763223060197584 0.473553879604833 0.236776939802416 19 0.778382997278535 0.443234005442929 0.221617002721465 20 0.829080961312227 0.341838077375545 0.170919038687773 21 0.913910821526596 0.172178356946809 0.0860891784734045 22 0.984501173681207 0.0309976526375854 0.0154988263187927 23 0.993637909755195 0.0127241804896097 0.00636209024480483 24 0.99404203212173 0.0119159357565396 0.00595796787826979 25 0.99049102929753 0.0190179414049414 0.00950897070247071 26 0.993685177519932 0.0126296449601353 0.00631482248006764 27 0.998446807420826 0.00310638515834707 0.00155319257917354 28 0.999380628037983 0.00123874392403399 0.000619371962016994 29 0.998650033423367 0.00269993315326503 0.00134996657663251 30 0.99714573429181 0.00570853141638214 0.00285426570819107 31 0.994605811775662 0.0107883764486760 0.00539418822433801 32 0.989085925158889 0.0218281496822227 0.0109140748411113 33 0.983584193723456 0.0328316125530884 0.0164158062765442 34 0.969222420465378 0.061555159069244 0.030777579534622 35 0.954523898204204 0.0909522035915916 0.0454761017957958 36 0.989502566450354 0.0209948670992922 0.0104974335496461 37 0.99809967667263 0.00380064665473808 0.00190032332736904 38 0.99519925551448 0.00960148897104015 0.00480074448552007 39 0.98891941288808 0.0221611742238384 0.0110805871119192 40 0.97533380825275 0.0493323834944994 0.0246661917472497 41 0.956439701680684 0.0871205966386312 0.0435602983193156 42 0.912122396864775 0.175755206270450 0.0878776031352249 43 0.853290187966184 0.293419624067632 0.146709812033816 44 0.730974982510017 0.538050034979966 0.269025017489983 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.214285714285714 NOK 5% type I error level 17 0.607142857142857 NOK 10% type I error level 20 0.714285714285714 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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