Q3 goud

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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: Mon, 24 Nov 2008 12:10:25 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227553889tmxq3dfwd3co1sp.htm/, Retrieved Mon, 24 Nov 2008 19:11:38 +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/24/t1227553889tmxq3dfwd3co1sp.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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User-defined keywords:

Dataseries X:

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10511 0 10812 0 10738 0 10171 0 9721 0 9897 0 9828 0 9924 0 10371 0 10846 0 10413 0 10709 0 10662 0 10570 0 10297 0 10635 0 10872 0 10296 0 10383 0 10431 0 10574 0 10653 0 10805 0 10872 0 10625 0 10407 0 10463 0 10556 0 10646 0 10702 0 11353 0 11346 0 11451 0 11964 0 12574 0 13031 0 13812 0 14544 1 14931 1 14886 1 16005 1 17064 1 15168 1 16050 1 15839 1 15137 1 14954 1 15648 1 15305 1 15579 1 16348 1 15928 1 16171 1 15937 1 15713 1 15594 1 15683 1 16438 1 17032 1 17696 1 17745 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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Yt[t] = + 10291.2347107438 + 3480.52376033058D[t] + 15.8009986225896M1[t] -678.867837465564M2[t] -558.861053719007M3[t] -732.05426997245M4[t] -537.247486225894M5[t] -494.040702479338M6[t] -837.233918732781M7[t] -710.227134986226M8[t] -648.620351239668M9[t] -477.613567493112M10[t] -382.606783746556M11[t] + 52.9932162534436t + 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) 10291.2347107438 369.626715 27.8422 0 0 D 3480.52376033058 330.785842 10.522 0 0 M1 15.8009986225896 391.392102 0.0404 0.967968 0.483984 M2 -678.867837465564 418.099298 -1.6237 0.111129 0.055564 M3 -558.861053719007 416.12662 -1.343 0.185719 0.09286 M4 -732.05426997245 414.353631 -1.7667 0.083766 0.041883 M5 -537.247486225894 412.782905 -1.3015 0.199422 0.099711 M6 -494.040702479338 411.416758 -1.2008 0.235835 0.117918 M7 -837.233918732781 410.257235 -2.0408 0.046914 0.023457 M8 -710.227134986226 409.306091 -1.7352 0.089259 0.04463 M9 -648.620351239668 408.564781 -1.5876 0.119092 0.059546 M10 -477.613567493112 408.034449 -1.1705 0.247692 0.123846 M11 -382.606783746556 407.715919 -0.9384 0.352829 0.176414 t 52.9932162534436 9.306646 5.6941 1e-06 0 Multiple Linear Regression - Regression Statistics Multiple R 0.976366334071566 R-squared 0.95329121830835 Adjusted R-squared 0.940371768053213 F-TEST (value) 73.7872896665464 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 644.487504184479 Sum Squared Residuals 19522114.7233471 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10511 10360.0289256198 150.971074380158 2 10812 9718.35330578513 1093.64669421487 3 10738 9891.35330578512 846.646694214877 4 10171 9771.15330578512 399.846694214879 5 9721 10018.9533057851 -297.953305785124 6 9897 10115.1533057851 -218.153305785124 7 9828 9824.95330578512 3.04669421487689 8 9924 10004.9533057851 -80.9533057851238 9 10371 10119.5533057851 251.446694214876 10 10846 10343.5533057851 502.446694214877 11 10413 10491.5533057851 -78.5533057851243 12 10709 10927.1533057851 -218.153305785122 13 10662 10995.9475206612 -333.947520661156 14 10570 10354.2719008264 215.728099173555 15 10297 10527.2719008264 -230.271900826445 16 10635 10407.0719008264 227.928099173554 17 10872 10654.8719008264 217.128099173554 18 10296 10751.0719008264 -455.071900826446 19 10383 10460.8719008264 -77.8719008264461 20 10431 10640.8719008264 -209.871900826446 21 10574 10755.4719008264 -181.471900826446 22 10653 10979.4719008264 -326.471900826447 23 10805 11127.4719008264 -322.471900826446 24 10872 11563.0719008264 -691.071900826445 25 10625 11631.8661157025 -1006.86611570248 26 10407 10990.1904958678 -583.190495867769 27 10463 11163.1904958678 -700.190495867768 28 10556 11042.9904958678 -486.990495867769 29 10646 11290.7904958678 -644.790495867769 30 10702 11386.9904958678 -684.990495867769 31 11353 11096.7904958678 256.209504132231 32 11346 11276.7904958678 69.2095041322312 33 11451 11391.3904958678 59.6095041322312 34 11964 11615.3904958678 348.609504132231 35 12574 11763.3904958678 810.609504132231 36 13031 12198.9904958678 832.009504132232 37 13812 12267.7847107438 1544.2152892562 38 14544 15106.6328512397 -562.63285123967 39 14931 15279.6328512397 -348.632851239669 40 14886 15159.4328512397 -273.43285123967 41 16005 15407.2328512397 597.767148760331 42 17064 15503.4328512397 1560.56714876033 43 15168 15213.2328512397 -45.2328512396695 44 16050 15393.2328512397 656.767148760331 45 15839 15507.8328512397 331.167148760331 46 15137 15731.8328512397 -594.83285123967 47 14954 15879.8328512397 -925.83285123967 48 15648 16315.4328512397 -667.432851239668 49 15305 16384.2270661157 -1079.22706611570 50 15579 15742.551446281 -163.551446280992 51 16348 15915.551446281 432.448553719008 52 15928 15795.351446281 132.648553719008 53 16171 16043.151446281 127.848553719008 54 15937 16139.351446281 -202.351446280992 55 15713 15849.151446281 -136.151446280992 56 15594 16029.151446281 -435.151446280992 57 15683 16143.751446281 -460.751446280992 58 16438 16367.751446281 70.2485537190071 59 17032 16515.751446281 516.248553719008 60 17696 16951.351446281 744.648553719009 61 17745 17020.145661157 724.854338842976 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.360872597767115 0.72174519553423 0.639127402232885 18 0.208953044857539 0.417906089715078 0.791046955142461 19 0.118466834880343 0.236933669760685 0.881533165119657 20 0.0602495005310285 0.120499001062057 0.939750499468971 21 0.0277744062097939 0.0555488124195878 0.972225593790206 22 0.0171008969278800 0.0342017938557600 0.98289910307212 23 0.00726496280671998 0.0145299256134400 0.99273503719328 24 0.00310757174662859 0.00621514349325719 0.996892428253371 25 0.00211606202894106 0.00423212405788212 0.997883937971059 26 0.00184014953391682 0.00368029906783364 0.998159850466083 27 0.00102385008362358 0.00204770016724717 0.998976149916376 28 0.000428174728882764 0.000856349457765527 0.999571825271117 29 0.000308325777814765 0.000616651555629531 0.999691674222185 30 0.000820624679045268 0.00164124935809054 0.999179375320955 31 0.00287646316137178 0.00575292632274355 0.997123536838628 32 0.00521628802840894 0.0104325760568179 0.994783711971591 33 0.00537946588518623 0.0107589317703725 0.994620534114814 34 0.0059737338504121 0.0119474677008242 0.994026266149588 35 0.0203361147399709 0.0406722294799419 0.97966388526003 36 0.0577925203129344 0.115585040625869 0.942207479687066 37 0.170437068110018 0.340874136220037 0.829562931889982 38 0.111371859545391 0.222743719090781 0.88862814045461 39 0.076733721946828 0.153467443893656 0.923266278053172 40 0.0448228278081524 0.0896456556163047 0.955177172191848 41 0.0393740703703052 0.0787481407406103 0.960625929629695 42 0.176319732602350 0.352639465204700 0.82368026739765 43 0.115318948033337 0.230637896066675 0.884681051966663 44 0.218847081077963 0.437694162155926 0.781152918922037 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 8 0.285714285714286 NOK 5% type I error level 14 0.5 NOK 10% type I error level 17 0.607142857142857 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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