mammels

*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: Mon, 06 Dec 2010 19:47:58 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/06/t12916649697ejdmqa613i5d2i.htm/, Retrieved Mon, 06 Dec 2010 20:49:39 +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/2010/Dec/06/t12916649697ejdmqa613i5d2i.htm/}, year = {2010}, } @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 = {2010}, 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:

Dataseries X:

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1 6.6 6.3 2 8.3 4.5 42 3 1 3 2547 4603 2.1 1.8 3.9 69 624 3 5 4 10.55 179.5 9.1 0.7 9.8 27 180 4 4 4 0.023 0.3 15.8 3.9 19.7 19 35 1 1 1 160 169 5.2 1 6.2 30.4 392 4 5 4 3.3 25.6 10.9 3.6 14.5 28 63 1 2 1 52.16 440 8.3 1.4 9.7 50 230 1 1 1 0.425 6.4 11 1.5 12.5 7 112 5 4 4 465 423 3.2 0.7 3.9 30 281 5 5 5 0.075 1.2 6.3 2.1 8.4 3.5 42 1 1 1 3 25 8.6 0 8.6 50 28 2 2 2 0.785 3.5 6.6 4.1 10.7 6 42 2 2 2 0.2 5 9.5 1.2 10.7 10.4 120 2 2 2 27.66 115 3.3 0.5 3.8 20 148 5 5 5 0.12 1 11 3.4 14.4 3.9 16 3 1 2 85 325 4.7 1.5 6.2 41 310 1 3 1 0.101 4 10.4 3.4 13.8 9 28 5 1 3 1.04 5.5 7.4 0.8 8.2 7.6 68 5 3 4 521 655 2.1 0.8 2.9 46 336 5 5 5 0.005 0.14 7.7 1.4 9.1 2.6 21.5 5 2 4 0.01 0.25 17.9 2 19.9 24 50 1 1 1 62 1320 6.1 1.9 8 100 267 1 1 1 0.023 0.4 11.9 1.3 13.2 3.2 19 4 1 3 0.048 0.33 10.8 2 12.8 2 30 4 1 3 1.7 6.3 13.8 5.6 19.4 5 12 2 1 1 3.5 10.8 14. 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 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation SWS[t] = + 3.90251060291830e-15 -2.60766319228936e-18BodyW[t] + 3.73591105584469e-19BrainW[t] -0.999999999999999PS[t] + 1TS[t] -6.5599409757104e-18LifeSpan[t] -1.18067716440613e-18GT[t] -1.80651147672450e-15PI[t] -1.41855482167557e-15SEI[t] + 3.09735631561724e-15ODI[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) 3.90251060291830e-15 0 0.9507 0.346311 0.173156 BodyW -2.60766319228936e-18 0 -0.3513 0.726844 0.363422 BrainW 3.73591105584469e-19 0 0.0855 0.93224 0.46612 PS -0.999999999999999 0 -1345466643607859 0 0 TS 1 0 4352397546464108 0 0 LifeSpan -6.5599409757104e-18 0 -0.1158 0.908298 0.454149 GT -1.18067716440613e-18 0 -0.1233 0.902388 0.451194 PI -1.80651147672450e-15 0 -1.2384 0.221335 0.110668 SEI -1.41855482167557e-15 0 -1.5628 0.124414 0.062207 ODI 3.09735631561724e-15 0 1.4641 0.149418 0.074709 Multiple Linear Regression - Regression Statistics Multiple R 1 R-squared 1 Adjusted R-squared 1 F-TEST (value) 4.51833201861869e+30 F-TEST (DF numerator) 9 F-TEST (DF denominator) 50 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.48660196962828e-15 Sum Squared Residuals 1.00647986169362e-27 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.3 6.29999999999997 2.82984272371989e-14 2 2.1 2.1 -1.55057448124169e-15 3 9.1 9.1 -6.74002398415465e-16 4 15.8 15.8 3.78604810682705e-15 5 5.2 5.2 -8.71674959388824e-16 6 10.9 10.9 -1.07496909021451e-15 7 8.3 8.3 9.1097574417062e-16 8 11 11 2.612964737267e-15 9 3.2 3.2 -1.3106652950192e-17 10 6.3 6.3 -2.41050600199826e-15 11 8.6 8.6 3.59745374515703e-16 12 6.6 6.6 -2.9170739510406e-15 13 9.5 9.5 2.85417236666445e-16 14 3.3 3.3 -1.50251045196857e-16 15 11 11 -1.63236646445596e-15 16 4.7 4.7 1.93624121990118e-15 17 10.4 10.4 -1.83067179595234e-15 18 7.4 7.4 1.08509994120049e-15 19 2.1 2.1 -9.89600837025628e-16 20 7.7 7.7 -1.36165324727408e-15 21 17.9 17.9 -7.1910182012252e-16 22 6.1 6.1 -1.11743333014729e-15 23 11.9 11.9 -5.04616756415198e-16 24 10.8 10.8 -1.26573067885998e-15 25 13.8 13.8 2.1235389234113e-15 26 14.3 14.3 3.23214756066576e-15 27 15.2 15.2 -1.36179893330729e-15 28 10 10 -6.80158153322428e-16 29 11.9 11.9 -3.97863046295061e-16 30 6.5 6.5 -1.05719883892986e-15 31 7.5 7.5 -8.1623669131203e-17 32 10.6 10.6 -3.48939743051969e-15 33 7.4 7.4 -2.11976525850569e-15 34 8.4 8.4 1.58302997856186e-15 35 5.7 5.7 -2.28555979761372e-16 36 4.9 4.9 -2.22485258119647e-15 37 3.2 3.2 -2.86132929834189e-16 38 11 11 -3.62311786501690e-15 39 4.9 4.9 -3.64065293609689e-15 40 13.2 13.2 9.11009610508859e-17 41 9.7 9.7 -2.65600488809830e-15 42 12.8 12.8 9.984541986002e-16 43 6.3 6.3 -5.38475534204902e-15 44 2.1 2.1 1.67252468663414e-15 45 9.1 9.1 -1.03060624012443e-15 46 15.8 15.8 -3.47248712996384e-16 47 5.2 5.2 1.55585115730031e-15 48 10.9 10.9 -1.07496909021452e-15 49 8.3 8.3 9.10975744170619e-16 50 11 11 2.61296473726701e-15 51 3.2 3.2 -1.31066529501912e-17 52 6.3 6.3 -2.41050600199826e-15 53 8.6 8.6 3.59745374515703e-16 54 6.6 6.6 -2.9170739510406e-15 55 9.5 9.5 2.85417236666445e-16 56 3.3 3.3 -1.50251045196857e-16 57 11 11 -1.63236646445596e-15 58 4.7 4.7 1.93624121990118e-15 59 10.4 10.4 -1.83067179595234e-15 60 7.4 7.4 1.08509994120049e-15 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.417457130629511 0.834914261259022 0.582542869370489 14 0.0235697516980491 0.0471395033960982 0.97643024830195 15 0.939848449898536 0.120303100202927 0.0601515501014637 16 7.38772163032634e-05 0.000147754432606527 0.999926122783697 17 0.0165709313512618 0.0331418627025237 0.983429068648738 18 0.686230927561171 0.627538144877658 0.313769072438829 19 9.78609864952819e-06 1.95721972990564e-05 0.99999021390135 20 0.132675064274820 0.265350128549641 0.86732493572518 21 0.999967105434647 6.57891307069267e-05 3.28945653534633e-05 22 0.0516680688068073 0.103336137613615 0.948331931193193 23 0.468852483002698 0.937704966005395 0.531147516997302 24 4.39279151787076e-05 8.78558303574153e-05 0.99995607208482 25 0.999998873752882 2.25249423583883e-06 1.12624711791941e-06 26 2.04884776505975e-08 4.0976955301195e-08 0.999999979511522 27 0.149334097384373 0.298668194768746 0.850665902615627 28 0.373569026934274 0.747138053868548 0.626430973065726 29 0.998562069802646 0.00287586039470803 0.00143793019735401 30 0.58555566185728 0.828888676285439 0.414444338142719 31 0.999934750136783 0.000130499726433702 6.52498632168508e-05 32 0.00039221986705892 0.00078443973411784 0.99960778013294 33 0.535228857037842 0.929542285924317 0.464771142962158 34 0.000226827331795163 0.000453654663590326 0.999773172668205 35 0.488970191702752 0.977940383405505 0.511029808297248 36 0.14655207902159 0.29310415804318 0.85344792097841 37 0.948044656754758 0.103910686490484 0.0519553432452419 38 0.79461706488114 0.410765870237719 0.205382935118860 39 0.00722014751430422 0.0144402950286084 0.992779852485696 40 0.0450060830375399 0.0900121660750798 0.95499391696246 41 0.388847585253040 0.777695170506081 0.61115241474696 42 0.00914019272735561 0.0182803854547112 0.990859807272644 43 0.952976358148224 0.0940472837035527 0.0470236418517763 44 0.732423791352084 0.535152417295832 0.267576208647916 45 0.545631652714176 0.908736694571648 0.454368347285824 46 0.246389704679345 0.492779409358691 0.753610295320654 47 0.295892855278387 0.591785710556774 0.704107144721613 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.285714285714286 NOK 5% type I error level 14 0.4 NOK 10% type I error level 16 0.457142857142857 NOK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; par2 = Do not include Seasonal 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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