ws 8

*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, 12 Dec 2010 19:24:41 +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/12/t1292181761x7p1qeeojsz8g6u.htm/, Retrieved Sun, 12 Dec 2010 20:22:44 +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/12/t1292181761x7p1qeeojsz8g6u.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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1.3031 1.3241 1.2961 1.2865 1.2305 1.2101 1.2125 1.2350 1.2014 1.1992 1.1791 1.1832 1.2159 1.1922 1.2114 1.2614 1.2812 1.2786 1.2772 1.2815 1.2679 1.2765 1.3247 1.3191 1.3029 1.3234 1.3354 1.3651 1.3453 1.3534 1.3706 1.3638 1.4268 1.4485 1.4635 1.4587 1.4876 1.5189 1.5783 1.5633 1.5554 1.5757 1.5593 1.4660 1.4065 1.2759 1.2705 1.3954 1.2793 1.2694 1.3282 1.3230 1.4135 1.4042 1.4253 1.4322 1.4632 1.4713 1.5016 1.4318

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Y[t] = + 1.2019 + 0.00770722222222199M1[t] + 0.0112211111111111M2[t] + 0.031175M3[t] + 0.0368288888888889M4[t] + 0.0378227777777777M5[t] + 0.0327166666666666M6[t] + 0.0329705555555555M7[t] + 0.0153644444444444M8[t] + 0.0084983333333334M9[t] -0.0147077777777778M10[t] -0.00543388888888887M11[t] + 0.00432611111111111t + 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) 1.2019 0.047738 25.1772 0 0 M1 0.00770722222222199 0.058076 0.1327 0.894989 0.447495 M2 0.0112211111111111 0.057989 0.1935 0.847398 0.423699 M3 0.031175 0.05791 0.5383 0.592887 0.296444 M4 0.0368288888888889 0.05784 0.6367 0.527384 0.263692 M5 0.0378227777777777 0.057778 0.6546 0.515899 0.257949 M6 0.0327166666666666 0.057724 0.5668 0.57356 0.28678 M7 0.0329705555555555 0.057678 0.5716 0.570295 0.285147 M8 0.0153644444444444 0.05764 0.2666 0.790977 0.395488 M9 0.0084983333333334 0.057611 0.1475 0.883359 0.44168 M10 -0.0147077777777778 0.057591 -0.2554 0.79954 0.39977 M11 -0.00543388888888887 0.057578 -0.0944 0.925213 0.462606 t 0.00432611111111111 0.000693 6.247 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.681525635374022 R-squared 0.464477191671965 Adjusted R-squared 0.327747964013743 F-TEST (value) 3.39705854868869 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.00126934927493771 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0910322443068723 Sum Squared Residuals 0.389482866666666 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.3031 1.21393333333333 0.0891666666666656 2 1.3241 1.22177333333333 0.102326666666667 3 1.2961 1.24605333333333 0.0500466666666667 4 1.2865 1.25603333333333 0.0304666666666667 5 1.2305 1.26135333333333 -0.0308533333333333 6 1.2101 1.26057333333333 -0.0504733333333333 7 1.2125 1.26515333333333 -0.0526533333333333 8 1.235 1.25187333333333 -0.0168733333333332 9 1.2014 1.24933333333333 -0.0479333333333333 10 1.1992 1.23045333333333 -0.0312533333333332 11 1.1791 1.24405333333333 -0.0649533333333333 12 1.1832 1.25381333333333 -0.0706133333333333 13 1.2159 1.26584666666667 -0.0499466666666664 14 1.1922 1.27368666666667 -0.0814866666666667 15 1.2114 1.29796666666667 -0.0865666666666666 16 1.2614 1.30794666666667 -0.0465466666666665 17 1.2812 1.31326666666667 -0.0320666666666667 18 1.2786 1.31248666666667 -0.0338866666666666 19 1.2772 1.31706666666667 -0.0398666666666667 20 1.2815 1.30378666666667 -0.0222866666666666 21 1.2679 1.30124666666667 -0.0333466666666667 22 1.2765 1.28236666666667 -0.00586666666666668 23 1.3247 1.29596666666667 0.0287333333333333 24 1.3191 1.30572666666667 0.0133733333333333 25 1.3029 1.31776 -0.0148599999999998 26 1.3234 1.3256 -0.00220000000000004 27 1.3354 1.34988 -0.0144800000000001 28 1.3651 1.35986 0.00523999999999999 29 1.3453 1.36518 -0.01988 30 1.3534 1.3644 -0.0110000000000001 31 1.3706 1.36898 0.0016200000000001 32 1.3638 1.3557 0.00809999999999989 33 1.4268 1.35316 0.07364 34 1.4485 1.33428 0.11422 35 1.4635 1.34788 0.11562 36 1.4587 1.35764 0.10106 37 1.4876 1.36967333333333 0.117926666666667 38 1.5189 1.37751333333333 0.141386666666667 39 1.5783 1.40179333333333 0.176506666666667 40 1.5633 1.41177333333333 0.151526666666667 41 1.5554 1.41709333333333 0.138306666666667 42 1.5757 1.41631333333333 0.159386666666667 43 1.5593 1.42089333333333 0.138406666666667 44 1.466 1.40761333333333 0.0583866666666667 45 1.4065 1.40507333333333 0.00142666666666669 46 1.2759 1.38619333333333 -0.110293333333333 47 1.2705 1.39979333333333 -0.129293333333333 48 1.3954 1.40955333333333 -0.0141533333333333 49 1.2793 1.42158666666667 -0.142286666666666 50 1.2694 1.42942666666667 -0.160026666666667 51 1.3282 1.45370666666667 -0.125506666666667 52 1.323 1.46368666666667 -0.140686666666667 53 1.4135 1.46900666666667 -0.0555066666666666 54 1.4042 1.46822666666667 -0.0640266666666668 55 1.4253 1.47280666666667 -0.0475066666666666 56 1.4322 1.45952666666667 -0.0273266666666668 57 1.4632 1.45698666666667 0.00621333333333326 58 1.4713 1.43810666666667 0.0331933333333333 59 1.5016 1.45170666666667 0.0498933333333333 60 1.4318 1.46146666666667 -0.0296666666666668 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0373825339631509 0.0747650679263018 0.96261746603685 17 0.0866816353472062 0.173363270694412 0.913318364652794 18 0.098713943587917 0.197427887175834 0.901286056412083 19 0.0830642263914149 0.16612845278283 0.916935773608585 20 0.0532067012451282 0.106413402490256 0.946793298754872 21 0.0392999116390735 0.078599823278147 0.960700088360926 22 0.0283717832729178 0.0567435665458357 0.971628216727082 23 0.0365369138178142 0.0730738276356284 0.963463086182186 24 0.0357363039152121 0.0714726078304242 0.964263696084788 25 0.019392408173793 0.038784816347586 0.980607591826207 26 0.0103010090782988 0.0206020181565975 0.989698990921701 27 0.00626205667615103 0.0125241133523021 0.99373794332385 28 0.00353334773214608 0.00706669546429216 0.996466652267854 29 0.00250299595292182 0.00500599190584363 0.997497004047078 30 0.00219734346862916 0.00439468693725833 0.99780265653137 31 0.00232439392493385 0.0046487878498677 0.997675606075066 32 0.00196125346480653 0.00392250692961307 0.998038746535193 33 0.0028450463350273 0.00569009267005461 0.997154953664973 34 0.00341598285779934 0.00683196571559868 0.9965840171422 35 0.00332314529648582 0.00664629059297164 0.996676854703514 36 0.00288846851899937 0.00577693703799875 0.997111531481 37 0.00244063032136608 0.00488126064273217 0.997559369678634 38 0.00357725208776978 0.00715450417553956 0.99642274791223 39 0.010356785200282 0.020713570400564 0.989643214799718 40 0.0254790935104373 0.0509581870208747 0.974520906489563 41 0.0322931685449801 0.0645863370899602 0.96770683145502 42 0.0882071096986423 0.176414219397285 0.911792890301358 43 0.251731904273715 0.503463808547429 0.748268095726285 44 0.358377883037085 0.71675576607417 0.641622116962915 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 11 0.379310344827586 NOK 5% type I error level 15 0.517241379310345 NOK 10% type I error level 22 0.758620689655172 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 1 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 1 ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; par4 = 1 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 1 ;

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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