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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: Thu, 11 Dec 2008 13:55:56 -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/11/t1229029052v52u0m57e7i9k5s.htm/, Retrieved Thu, 11 Dec 2008 20:57:32 +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/11/t1229029052v52u0m57e7i9k5s.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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Dataseries X:

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103.3 0 101.2 0 107.7 0 110.4 0 101.9 0 115.9 0 89.9 0 88.6 0 117.2 0 123.9 0 100 0 103.6 0 94.1 0 98.7 0 119.5 0 112.7 0 104.4 0 124.7 0 89.1 0 97 0 121.6 0 118.8 0 114 0 111.5 0 97.2 0 102.5 0 113.4 0 109.8 0 104.9 0 126.1 0 80 0 96.8 0 117.2 1 112.3 1 117.3 1 111.1 1 102.2 1 104.3 1 122.9 1 107.6 1 121.3 1 131.5 1 89 1 104.4 1 128.9 1 135.9 1 133.3 1 121.3 1 120.5 1 120.4 1 137.9 1 126.1 1 133.2 1 151.1 1 105 1 119 1 140.4 1 156.6 1 137.1 1 122.7 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 8 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation metaal[t] = + 105.323333333333 + 14.5277777777778conjunctuur[t] -7.67444444444447M1[t] -5.71444444444444M2[t] + 9.14555555555556M3[t] + 2.18555555555556M4[t] + 2.00555555555556M5[t] + 18.7255555555556M6[t] -20.5344444444444M7[t] -9.97444444444444M8[t] + 11.02M9[t] + 15.46M10[t] + 6.3M11[t] + 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) 105.323333333333 4.070443 25.8752 0 0 conjunctuur 14.5277777777778 2.261357 6.4244 0 0 M1 -7.67444444444447 5.446069 -1.4092 0.165367 0.082683 M2 -5.71444444444444 5.446069 -1.0493 0.299416 0.149708 M3 9.14555555555556 5.446069 1.6793 0.099732 0.049866 M4 2.18555555555556 5.446069 0.4013 0.690012 0.345006 M5 2.00555555555556 5.446069 0.3683 0.714335 0.357167 M6 18.7255555555556 5.446069 3.4384 0.001236 0.000618 M7 -20.5344444444444 5.446069 -3.7705 0.000455 0.000227 M8 -9.97444444444444 5.446069 -1.8315 0.073369 0.036684 M9 11.02 5.427257 2.0305 0.047986 0.023993 M10 15.46 5.427257 2.8486 0.006496 0.003248 M11 6.3 5.427257 1.1608 0.251582 0.125791 Multiple Linear Regression - Regression Statistics Multiple R 0.872146156682372 R-squared 0.760638918615832 Adjusted R-squared 0.699525451028385 F-TEST (value) 12.4463387309423 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 7.51571027635123e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.58124735376927 Sum Squared Residuals 3460.97688888889 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.3 97.648888888889 5.65111111111099 2 101.2 99.6088888888889 1.59111111111111 3 107.7 114.468888888889 -6.76888888888889 4 110.4 107.508888888889 2.89111111111112 5 101.9 107.328888888889 -5.42888888888889 6 115.9 124.048888888889 -8.14888888888888 7 89.9 84.7888888888889 5.11111111111112 8 88.6 95.3488888888889 -6.7488888888889 9 117.2 116.343333333333 0.856666666666672 10 123.9 120.783333333333 3.11666666666667 11 100 111.623333333333 -11.6233333333333 12 103.6 105.323333333333 -1.72333333333334 13 94.1 97.6488888888889 -3.54888888888886 14 98.7 99.6088888888889 -0.908888888888885 15 119.5 114.468888888889 5.03111111111111 16 112.7 107.508888888889 5.19111111111112 17 104.4 107.328888888889 -2.92888888888888 18 124.7 124.048888888889 0.651111111111117 19 89.1 84.7888888888889 4.31111111111111 20 97 95.3488888888889 1.65111111111111 21 121.6 116.343333333333 5.25666666666666 22 118.8 120.783333333333 -1.98333333333333 23 114 111.623333333333 2.37666666666667 24 111.5 105.323333333333 6.17666666666667 25 97.2 97.6488888888889 -0.448888888888854 26 102.5 99.6088888888889 2.89111111111111 27 113.4 114.468888888889 -1.06888888888889 28 109.8 107.508888888889 2.29111111111111 29 104.9 107.328888888889 -2.42888888888888 30 126.1 124.048888888889 2.05111111111111 31 80 84.7888888888889 -4.78888888888889 32 96.8 95.3488888888889 1.45111111111111 33 117.2 130.871111111111 -13.6711111111111 34 112.3 135.311111111111 -23.0111111111111 35 117.3 126.151111111111 -8.85111111111112 36 111.1 119.851111111111 -8.75111111111112 37 102.2 112.176666666667 -9.97666666666664 38 104.3 114.136666666667 -9.83666666666668 39 122.9 128.996666666667 -6.09666666666666 40 107.6 122.036666666667 -14.4366666666667 41 121.3 121.856666666667 -0.556666666666668 42 131.5 138.576666666667 -7.07666666666667 43 89 99.3166666666667 -10.3166666666667 44 104.4 109.876666666667 -5.47666666666666 45 128.9 130.871111111111 -1.97111111111111 46 135.9 135.311111111111 0.58888888888889 47 133.3 126.151111111111 7.1488888888889 48 121.3 119.851111111111 1.44888888888889 49 120.5 112.176666666667 8.32333333333336 50 120.4 114.136666666667 6.26333333333334 51 137.9 128.996666666667 8.90333333333333 52 126.1 122.036666666667 4.06333333333333 53 133.2 121.856666666667 11.3433333333333 54 151.1 138.576666666667 12.5233333333333 55 105 99.3166666666667 5.68333333333334 56 119 109.876666666667 9.12333333333333 57 140.4 130.871111111111 9.5288888888889 58 156.6 135.311111111111 21.2888888888889 59 137.1 126.151111111111 10.9488888888889 60 122.7 119.851111111111 2.84888888888889 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.261748226464826 0.523496452929652 0.738251773535174 17 0.136422554309615 0.272845108619231 0.863577445690385 18 0.106516807396376 0.213033614792753 0.893483192603624 19 0.0516181386336839 0.103236277267368 0.948381861366316 20 0.0388367700392382 0.0776735400784763 0.961163229960762 21 0.0207621335826464 0.0415242671652928 0.979237866417354 22 0.0110284471209898 0.0220568942419796 0.98897155287901 23 0.0186129538243360 0.0372259076486721 0.981387046175664 24 0.0132056202067624 0.0264112404135248 0.986794379793238 25 0.00612800858067308 0.0122560171613462 0.993871991419327 26 0.00289453795695278 0.00578907591390555 0.997105462043047 27 0.00119053500572680 0.00238107001145359 0.998809464994273 28 0.000538543400670596 0.00107708680134119 0.99946145659933 29 0.000217898233703407 0.000435796467406814 0.999782101766297 30 0.000115270228652841 0.000230540457305682 0.999884729771347 31 0.000110573887908111 0.000221147775816221 0.999889426112092 32 4.57660706174084e-05 9.15321412348168e-05 0.999954233929383 33 2.80995078445192e-05 5.61990156890383e-05 0.999971900492155 34 0.000215745174514155 0.000431490349028309 0.999784254825486 35 0.00100292316914477 0.00200584633828954 0.998997076830855 36 0.0006704178892923 0.0013408357785846 0.999329582110708 37 0.000731369429286471 0.00146273885857294 0.999268630570714 38 0.000676835903573398 0.00135367180714680 0.999323164096427 39 0.000880458825405475 0.00176091765081095 0.999119541174595 40 0.00169652576438964 0.00339305152877928 0.99830347423561 41 0.00455064870991978 0.00910129741983957 0.99544935129008 42 0.0113359031454521 0.0226718062909043 0.988664096854548 43 0.0176739221294544 0.0353478442589088 0.982326077870546 44 0.0281639073846167 0.0563278147692335 0.971836092615383 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 16 0.551724137931034 NOK 5% type I error level 23 0.793103448275862 NOK 10% type I error level 25 0.862068965517241 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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