*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: Fri, 20 Nov 2009 06:30:42 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258723943qeqc4t1hblhb0kn.htm/, Retrieved Fri, 20 Nov 2009 14:32:35 +0100

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/2009/Nov/20/t1258723943qeqc4t1hblhb0kn.htm/}, year = {2009}, } @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 = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

ws73lags

Dataseries X:

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7,50 103,90 7,70 8,10 8,00 7,60 101,60 7,50 7,70 8,10 7,80 94,60 7,60 7,50 7,70 7,80 95,90 7,80 7,60 7,50 7,80 104,70 7,80 7,80 7,60 7,50 102,80 7,80 7,80 7,80 7,50 98,10 7,50 7,80 7,80 7,10 113,90 7,50 7,50 7,80 7,50 80,90 7,10 7,50 7,50 7,50 95,70 7,50 7,10 7,50 7,60 113,20 7,50 7,50 7,10 7,70 105,90 7,60 7,50 7,50 7,70 108,80 7,70 7,60 7,50 7,90 102,30 7,70 7,70 7,60 8,10 99,00 7,90 7,70 7,70 8,20 100,70 8,10 7,90 7,70 8,20 115,50 8,20 8,10 7,90 8,20 100,70 8,20 8,20 8,10 7,90 109,90 8,20 8,20 8,20 7,30 114,60 7,90 8,20 8,20 6,90 85,40 7,30 7,90 8,20 6,60 100,50 6,90 7,30 7,90 6,70 114,80 6,60 6,90 7,30 6,90 116,50 6,70 6,60 6,90 7,00 112,90 6,90 6,70 6,60 7,10 102,00 7,00 6,90 6,70 7,20 106,00 7,10 7,00 6,90 7,10 105,30 7,20 7,10 7,00 6,90 118,80 7,10 7,20 7,10 7,00 106,10 6,90 7,10 7,20 6,80 109,30 7,00 6,90 7,10 6,40 117,20 6,80 7,00 6,90 6,70 92,50 6,40 6,80 7,00 6,60 104,20 6,70 6,40 6,80 6,40 112,50 6,60 6,70 6,40 6,30 122,40 6,40 6,60 6,70 6,20 113,30 6,30 6,40 6, etc...

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 2.98518401342828 -0.0145944931655954X[t] + 1.60214515152688Y1[t] -1.14767852541949Y2[t] + 0.354459259946489Y3[t] + 0.0193598686132426M1[t] + 0.082891000338969M2[t] + 0.0325486589288215M3[t] -0.0821859560428094M4[t] + 0.0890126310675888M5[t] + 0.00699035407687789M6[t] -0.128436830127242M7[t] + 0.0290728814144387M8[t] + 0.159023499959213M9[t] -0.5450041439469M10[t] + 0.185451716720582M11[t] -0.00279480398198670t + 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) 2.98518401342828 1.032594 2.891 0.00618 0.00309 X -0.0145944931655954 0.005253 -2.7784 0.00828 0.00414 Y1 1.60214515152688 0.134769 11.8881 0 0 Y2 -1.14767852541949 0.215066 -5.3364 4e-06 2e-06 Y3 0.354459259946489 0.141146 2.5113 0.016169 0.008085 M1 0.0193598686132426 0.143425 0.135 0.893303 0.446651 M2 0.082891000338969 0.159809 0.5187 0.606836 0.303418 M3 0.0325486589288215 0.161876 0.2011 0.841662 0.420831 M4 -0.0821859560428094 0.158924 -0.5171 0.607907 0.303954 M5 0.0890126310675888 0.144348 0.6167 0.540958 0.270479 M6 0.00699035407687789 0.146545 0.0477 0.962192 0.481096 M7 -0.128436830127242 0.146643 -0.8758 0.386341 0.193171 M8 0.0290728814144387 0.138753 0.2095 0.835098 0.417549 M9 0.159023499959213 0.195947 0.8116 0.421846 0.210923 M10 -0.5450041439469 0.176414 -3.0894 0.003641 0.00182 M11 0.185451716720582 0.154617 1.1994 0.23742 0.11871 t -0.00279480398198670 0.002487 -1.1237 0.267846 0.133923 Multiple Linear Regression - Regression Statistics Multiple R 0.96434445443667 R-squared 0.929960226802759 Adjusted R-squared 0.901944317523863 F-TEST (value) 33.1940047901022 F-TEST (DF numerator) 16 F-TEST (DF denominator) 40 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.203295340925834 Sum Squared Residuals 1.65315982568604 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.5 7.36137692858522 0.138623071414778 2 7.6 7.62976889646691 -0.0297688964669144 3 7.8 7.92675971949194 -0.126759719491939 4 7.8 7.92502678519718 -0.125026785197176 5 7.8 7.7709092493791 0.0290907506209001 6 7.5 7.78471355741033 -0.284713557410331 7 7.5 7.23444214164446 0.265557858355541 8 7.1 7.50286761481359 -0.402867614813591 9 7.5 7.36444586524633 0.135554134753674 10 7.5 7.54155438928596 -0.0415543892859626 11 7.6 7.41295670142715 0.187043298572851 12 7.7 7.63324819996471 0.0667518000352907 13 7.7 7.65293589702648 0.0470641029735206 14 7.9 7.72921450379929 0.170785496200712 15 8.1 8.08011414215365 0.0198858578463546 16 8.2 8.02866741004 0.171332589960006 17 8.2 7.98264335637568 0.217356643624318 18 8.2 8.06994877370115 0.130051226298854 19 7.9 7.83290337438621 0.0670966256137905 20 7.3 7.43838061860954 -0.138380618609543 21 6.9 7.37471210031743 -0.47471210031743 22 6.6 6.38892408228583 0.211075917714166 23 6.7 6.67363619544515 0.0263638045548499 24 6.9 6.82331340516101 0.076686594838991 25 7 6.99174204496789 0.00825795503211118 26 7.1 7.17768308428006 -0.0776830842800585 27 7.2 7.18250648082558 0.0174935191744210 28 7.1 7.15608579569327 -0.0560857956932686 29 6.9 6.88792747938615 0.0120725206138481 30 7 6.81824520984774 0.181754790152260 31 6.8 6.98762513777366 -0.187625137773663 32 6.4 6.52095481448853 -0.120954814488530 33 6.7 6.63271818070932 0.067281819290682 34 6.6 6.62396326642031 -0.0239632664203125 35 6.4 6.58418825307424 -0.184188253074237 36 6.3 6.15213285025279 0.147867149747206 37 6.2 6.33538306662753 -0.135383066627526 38 6.5 6.47388763887365 0.0261123611263514 39 6.8 6.824554888615 -0.0245548886150067 40 6.8 6.77727109585121 0.0227289041487908 41 6.4 6.75149257883451 -0.351492578834507 42 6.1 6.02269651649304 0.0773034835069607 43 5.8 5.98257723697454 -0.182577236974543 44 6.1 5.75992589919738 0.340074100802625 45 7.2 6.89612145285547 0.303878547144526 46 7.3 7.44555826200789 -0.145558262007891 47 6.9 6.92921885005346 -0.0292188500534638 48 6.1 6.39130554462149 -0.291305544621488 49 5.8 5.85856206279288 -0.0585620627928845 50 6.2 6.28944587658009 -0.0894458765800902 51 7.1 6.98606476891383 0.113935231086171 52 7.7 7.71294891321835 -0.0129489132183525 53 7.9 7.80702733602456 0.0929726639754414 54 7.7 7.80439594254774 -0.104395942547744 55 7.4 7.36245210922113 0.0375478907788737 56 7.5 7.17787105289096 0.322128947109039 57 8 8.03200240087145 -0.0320024008714517 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.179066267953271 0.358132535906543 0.820933732046729 21 0.751363782560165 0.49727243487967 0.248636217439835 22 0.760638426543275 0.478723146913449 0.239361573456725 23 0.680189858298589 0.639620283402822 0.319810141701411 24 0.559970981735697 0.880058036528605 0.440029018264303 25 0.505986556492342 0.988026887015317 0.494013443507658 26 0.54370681189388 0.91258637621224 0.45629318810612 27 0.429376768240673 0.858753536481347 0.570623231759327 28 0.322372016770568 0.644744033541135 0.677627983229433 29 0.263526061230964 0.527052122461928 0.736473938769036 30 0.32289344163802 0.64578688327604 0.67710655836198 31 0.247648632738999 0.495297265477999 0.752351367261 32 0.306028149297254 0.612056298594509 0.693971850702746 33 0.276913520656727 0.553827041313454 0.723086479343273 34 0.253222519161681 0.506445038323362 0.746777480838319 35 0.222104283076366 0.444208566152732 0.777895716923634 36 0.73942236201172 0.521155275976559 0.260577637988280 37 0.662683933712723 0.674632132574553 0.337316066287277 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

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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