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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, 19 Nov 2009 12:02:36 -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/19/t1258657457qnf0pxqxf56cnzy.htm/, Retrieved Thu, 19 Nov 2009 20:04:29 +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/19/t1258657457qnf0pxqxf56cnzy.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:

Dataseries X:

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19 24,4 19 18 19 23 22 22,5 19 19 18 19 23 19,4 22 19 19 18 20 18,1 23 22 19 19 14 18,1 20 23 22 19 14 20,7 14 20 23 22 14 19,1 14 14 20 23 15 18,3 14 14 14 20 11 16,9 15 14 14 14 17 17,9 11 15 14 14 16 20,2 17 11 15 14 20 21,2 16 17 11 15 24 23,8 20 16 17 11 23 24 24 20 16 17 20 26,6 23 24 20 16 21 25,3 20 23 24 20 19 27,6 21 20 23 24 23 24,7 19 21 20 23 23 26,6 23 19 21 20 23 24,4 23 23 19 21 23 24,6 23 23 23 19 27 26 23 23 23 23 26 24,8 27 23 23 23 17 24 26 27 23 23 24 22,7 17 26 27 23 26 23 24 17 26 27 24 24,1 26 24 17 26 27 24 24 26 24 17 27 22,7 27 24 26 24 26 22,6 27 27 24 26 24 23,1 26 27 27 24 23 24,4 24 26 27 27 23 23 23 24 26 27 24 22 23 23 24 26 17 21,3 24 23 23 24 21 21,5 17 24 23 23 19 21,3 21 17 24 23 22 23,2 19 21 17 24 22 21,8 22 19 21 17 18 23,3 22 22 19 21 16 21 18 22 22 19 14 22,4 16 18 22 22 12 20,4 14 16 18 22 14 19,9 12 14 16 18 16 21,3 14 12 14 16 8 18,9 16 14 12 14 3 15,6 8 16 14 12 0 12,5 3 8 16 14 5 7,8 0 3 8 16 1 5,5 5 0 3 8 1 4 1 5 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 0.62534313143448 + 0.134177451152066X[t] + 0.763994640040319`Y(t-1)`[t] + 0.0704456425436845`Y(t-2)`[t] + 0.0782248700521776`Y(t-3)`[t] -0.146998416229665`Y(t-4)`[t] + 3.86274414161116M1[t] + 2.64053282326136M2[t] + 0.873677019898664M3[t] + 1.00749157087014M4[t] + 0.226587076443826M5[t] + 1.87144092960793M6[t] + 0.964855849929924M7[t] + 3.12046893188267M8[t] + 0.988941013633353M9[t] + 2.26002196920389M10[t] -1.84545590981347M11[t] -0.0211274789115458t + 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) 0.62534313143448 3.092271 0.2022 0.84079 0.420395 X 0.134177451152066 0.180865 0.7419 0.462614 0.231307 `Y(t-1)` 0.763994640040319 0.169359 4.5111 5.8e-05 2.9e-05 `Y(t-2)` 0.0704456425436845 0.206742 0.3407 0.735127 0.367563 `Y(t-3)` 0.0782248700521776 0.20344 0.3845 0.702689 0.351344 `Y(t-4)` -0.146998416229665 0.16191 -0.9079 0.369505 0.184753 M1 3.86274414161116 2.442532 1.5815 0.121852 0.060926 M2 2.64053282326136 2.55431 1.0338 0.307618 0.153809 M3 0.873677019898664 2.457133 0.3556 0.72408 0.36204 M4 1.00749157087014 2.443923 0.4122 0.682418 0.341209 M5 0.226587076443826 2.423242 0.0935 0.925981 0.46299 M6 1.87144092960793 2.368799 0.79 0.434283 0.217142 M7 0.964855849929924 2.426073 0.3977 0.693018 0.346509 M8 3.12046893188267 2.380822 1.3107 0.197636 0.098818 M9 0.988941013633353 2.489186 0.3973 0.693316 0.346658 M10 2.26002196920389 2.505296 0.9021 0.372543 0.186271 M11 -1.84545590981347 2.554184 -0.7225 0.474284 0.237142 t -0.0211274789115458 0.034949 -0.6045 0.548997 0.274499 Multiple Linear Regression - Regression Statistics Multiple R 0.919899890899325 R-squared 0.84621580927659 Adjusted R-squared 0.779181674858694 F-TEST (value) 12.6236553455171 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 6.12756512197166e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.47962494480970 Sum Squared Residuals 472.203800505133 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 19 21.630118286506 -2.63011828650599 2 22 20.7120567694659 1.28794323053411 3 23 21.0253305950230 1.97466940497697 4 20 21.791920132027 -1.79192013202699 5 14 19.0030244912684 -5.00302449126839 6 14 15.8175370920065 -1.81753709200653 7 14 13.8707937299254 0.129206270074637 8 15 15.8695834004208 -0.869583400420844 9 11 15.1750647090654 -4.17506470906540 10 17 13.5736627192589 3.42633728074114 11 16 14.1360756390991 1.86392436090094 12 20 15.2933628399365 4.70663716006354 13 24 23.5267166784808 0.473283321519236 14 23 24.6877591343557 -1.68775913435569 15 20 23.2263230516496 -3.22632305164961 16 21 20.5270556898373 0.472944310162739 17 19 19.9200710315876 -0.920071031587584 18 23 19.6094629660353 3.39053703396467 19 23 22.3709949584498 0.629005041550219 20 23 24.1886245827972 -1.18862458279716 21 23 22.6697009885347 0.330299011465254 22 27 23.5195092318880 3.48049076811203 23 26 22.2878694927379 3.71213050726213 24 17 23.5226438928525 -6.52264389285255 25 24 20.5563319463566 3.44366805364337 26 26 23.4009795468591 2.59902045314085 27 24 23.2246748244987 0.775325175501328 28 27 23.8074059928824 3.19259400711764 29 27 24.1094967945771 2.89050320542290 30 26 25.4806957787818 0.519304221218178 31 24 24.3847487483438 -0.384748748343841 32 23 24.6542348665694 -1.65423486656941 33 23 21.3306202426158 1.66937975738421 34 24 22.3664993017043 1.63350069829566 35 17 19.1257363304165 -2.12573633041646 36 21 15.8463818300399 5.15361816996009 37 19 22.3022469349168 -3.30224693491677 38 22 19.3730660783435 2.62693392165645 39 22 20.8902153933064 1.10978460669364 40 18 20.6710621647024 -2.67106216470244 41 16 17.0331149361694 -1.03311493616941 42 14 16.5939226430905 -2.59392264309049 43 12 13.4160751368201 -1.41607513682008 44 14 14.2461353739316 -0.246135373931552 45 16 13.8059734957318 2.19402650426818 46 8 16.5403287471488 -8.54032874714883 47 3 6.45031853774661 -3.45031853774661 48 0 3.33761143717108 -3.33761143717108 49 5 2.98458615373985 2.01541384626015 50 1 5.82613847097573 -4.82613847097573 51 1 1.63345613552232 -0.633456135522325 52 3 2.20255602055096 0.797443979449044 53 6 1.93429274639753 4.06570725360247 54 7 6.49838152008584 0.501618479914164 55 8 6.95738742646093 1.04261257353907 56 14 10.0414217762810 3.95857822371897 57 14 14.0186405640523 -0.0186405640522542 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.373070549844811 0.746141099689622 0.626929450155189 22 0.349474674790675 0.698949349581351 0.650525325209325 23 0.272016363830697 0.544032727661394 0.727983636169303 24 0.729319665539629 0.541360668920743 0.270680334460371 25 0.695398224588654 0.609203550822693 0.304601775411346 26 0.621722670211397 0.756554659577205 0.378277329788603 27 0.529954654909137 0.940090690181725 0.470045345090863 28 0.439054755848634 0.878109511697268 0.560945244151366 29 0.383031002312029 0.766062004624058 0.616968997687971 30 0.272605390944969 0.545210781889939 0.72739460905503 31 0.178907154429273 0.357814308858546 0.821092845570727 32 0.151589693533477 0.303179387066954 0.848410306466523 33 0.198508483621600 0.397016967243199 0.8014915163784 34 0.192881983911404 0.385763967822808 0.807118016088596 35 0.158903622051204 0.317807244102407 0.841096377948797 36 0.121153536403580 0.242307072807159 0.87884646359642 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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