multiple regression

*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: Wed, 22 Dec 2010 20:01:00 +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/22/t1293048284l9j4wk2ixxbbvb4.htm/, Retrieved Wed, 22 Dec 2010 21:04:47 +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/22/t1293048284l9j4wk2ixxbbvb4.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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-999,00 -999,00 38,60 6654,00 5712,00 645,00 3,00 5,00 3,00 6,30 2,00 4,50 1,00 6600,00 42,00 3,00 1,00 3,00 -999,00 -999,00 14,00 3,39 44,50 60,00 1,00 1,00 1,00 -999,00 -999,00 -999,00 0,92 5,70 25,00 5,00 2,00 3,00 2,10 1,80 69,00 2547,00 4603,00 624,00 3,00 5,00 4,00 9,10 0,70 27,00 10,55 179,50 180,00 4,00 4,00 4,00 15,80 3,90 19,00 0,02 0,30 35,00 1,00 1,00 1,00 5,20 1,00 30,40 160,00 169,00 392,00 4,00 5,00 4,00 10,90 3,60 28,00 3,30 25,60 63,00 1,00 2,00 1,00 8,30 1,40 50,00 52,16 440,00 230,00 1,00 1,00 1,00 11,00 1,50 7,00 0,43 6,40 112,00 5,00 4,00 4,00 3,20 0,70 30,00 465,00 423,00 281,00 5,00 5,00 5,00 7,60 2,70 -999,00 0,55 2,40 -999,00 2,00 1,00 2,00 -999,00 -999,00 40,00 187,10 419,00 365,00 5,00 5,00 5,00 6,30 2,10 3,50 0,08 1,20 42,00 1,00 1,00 1,00 8,60 0,00 50,00 3,00 25,00 28,00 2,00 2,00 2,00 6,60 4,10 6,00 0,79 3500,00 42,00 2,00 2,00 2,00 9,50 1,20 10,40 0,20 5,00 120,00 2,00 2,00 2,00 4,80 1,30 34,00 1,41 17,50 -999,00 1,00 2,00 1,00 12,00 6,10 7,00 60,00 81,00 -999 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 5 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation D [t] = -0.101608832209852 -6.09551076358242e-05SWS[t] + 0.000261740059678429PS[t] + 7.3273090252969e-06L[t] -0.000138734472492483Wb[t] + 0.00010510687851621Wbr[t] + 1.26344683983161e-05Tg[t] + 0.660225760372188P[t] + 0.34557106541433S[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) -0.101608832209852 0.128875 -0.7884 0.433959 0.21698 SWS -6.09551076358242e-05 0.000316 -0.1927 0.847948 0.423974 PS 0.000261740059678429 0.000333 0.7868 0.434886 0.217443 L 7.3273090252969e-06 0.000227 0.0323 0.974378 0.487189 Wb -0.000138734472492483 8.4e-05 -1.6455 0.105786 0.052893 Wbr 0.00010510687851621 5.5e-05 1.9142 0.061005 0.030503 Tg 1.26344683983161e-05 2e-04 0.0631 0.949934 0.474967 P 0.660225760372188 0.048881 13.5067 0 0 S 0.34557106541433 0.050219 6.8813 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.963410634069038 R-squared 0.928160049837306 Adjusted R-squared 0.917316283775013 F-TEST (value) 85.5938835737854 F-TEST (DF numerator) 8 F-TEST (DF denominator) 53 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.41442883884995 Sum Squared Residuals 9.10281691093745 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3 3.0920029852527 -0.0920029852527001 2 3 2.91890926156013 0.0810907384398717 3 1 0.708671423148579 0.291328576851421 4 3 3.68354528687572 -0.68354528687572 5 4 3.7461066553348 0.253893344665197 6 4 3.94108207516275 0.0589179248372471 7 1 0.904855871748293 0.0951441282517073 8 4 4.26783531852748 -0.267835318527475 9 1 1.2532709610252 -0.253270961025201 10 1 0.94633143191164 0.0536685680883593 11 4 4.58360571503705 -0.583605715037052 12 5 4.91108224321412 0.0889177567858839 13 2 1.54489133019433 0.455108669805667 14 5 4.74977836525352 0.250221634746478 15 1 0.905024953274623 0.0949750467253773 16 2 1.91239220454936 0.0876077954506383 17 2 2.27899473599782 -0.278994735997816 18 2 1.911809961632 0.0881900383679984 19 1 1.23907778589669 -0.239077785896688 20 1 0.892672192692598 0.107327807307402 21 5 4.99168906472336 0.00831093527663622 22 5 4.93757135792106 0.0624286420789421 23 2 2.22517811108134 -0.225178111081343 24 1 1.7577442288818 -0.757744228881802 25 1 1.62202065571838 -0.622020655718378 26 1 0.712038548998443 0.287961451001557 27 3 3.54617328311211 -0.546173283112106 28 4 4.23734012552544 -0.23734012552544 29 5 4.92860326590098 0.071396734099022 30 1 0.707659737725898 0.292340262274102 31 4 3.40790626014173 0.592093739858272 32 4 3.8908632019268 0.109136798073202 33 1 0.904452845480769 0.095547154519231 34 1 1.03855914984522 -0.03855914984522 35 1 1.557899823044 -0.557899823043996 36 3 2.21877300712377 0.78122699287623 37 3 2.88478294134035 0.11521705865965 38 3 2.8851518768664 0.114848123133595 39 1 1.565652892695 -0.565652892695 40 1 1.56656683744538 -0.566566837445378 41 5 5.01108203224868 -0.0110820322486828 42 2 1.91294875118881 0.0870512488111864 43 4 3.93420030348804 0.0657996965119633 44 2 1.56544302982516 0.434556970174844 45 4 3.91561258947383 0.084387410526173 46 5 4.9286022166008 0.0713977833992019 47 2 1.7138220266662 0.286177973333795 48 3 2.22513453394093 0.774865466059068 49 1 0.909803054422399 0.0901969455776014 50 2 2.2755132315655 -0.275513231565498 51 2 1.91395575160755 0.0860442483924511 52 3 2.57463728932944 0.425362710670564 53 5 4.73707492738858 0.262925072611418 54 5 4.94008557583977 0.0599144241602345 55 2 1.71175041897305 0.288249581026945 56 2 2.21222220054232 -0.212222200542322 57 2 1.56528470775553 0.434715292244468 58 3 2.22806889848158 0.771931101518417 59 2 2.57093342857586 -0.570933428575865 60 4 3.58391718030808 0.41608281969192 61 1 1.56548422362213 -0.565484223622135 62 1 2.02585565436812 -1.02585565436812 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.395848099934039 0.791696199868077 0.604151900065961 13 0.30018743695253 0.60037487390506 0.69981256304747 14 0.252055487514735 0.504110975029471 0.747944512485265 15 0.150261942324308 0.300523884648617 0.849738057675692 16 0.0868705511517335 0.173741102303467 0.913129448848267 17 0.151941785428544 0.303883570857087 0.848058214571456 18 0.100900081691462 0.201800163382923 0.899099918308539 19 0.191325381497917 0.382650762995834 0.808674618502083 20 0.135206833297493 0.270413666594986 0.864793166702507 21 0.0863771283343526 0.172754256668705 0.913622871665647 22 0.0590502119817367 0.118100423963473 0.940949788018263 23 0.0360142578807865 0.072028515761573 0.963985742119214 24 0.114393837373718 0.228787674747436 0.885606162626282 25 0.151501629088509 0.303003258177017 0.848498370911491 26 0.136803173324547 0.273606346649093 0.863196826675453 27 0.174069806651124 0.348139613302249 0.825930193348876 28 0.135083367970207 0.270166735940415 0.864916632029793 29 0.10278385869338 0.20556771738676 0.89721614130662 30 0.0882647675655606 0.176529535131121 0.91173523243444 31 0.121967695462096 0.243935390924192 0.878032304537904 32 0.0921773175097955 0.184354635019591 0.907822682490204 33 0.0658731499788223 0.131746299957645 0.934126850021178 34 0.0429199905320568 0.0858399810641136 0.957080009467943 35 0.0646802389467788 0.129360477893558 0.935319761053221 36 0.143233657448197 0.286467314896395 0.856766342551803 37 0.10216283425388 0.204325668507761 0.89783716574612 38 0.0695364348514551 0.13907286970291 0.930463565148545 39 0.0852282305413933 0.170456461082787 0.914771769458607 40 0.118125044053256 0.236250088106511 0.881874955946744 41 0.084846208813476 0.169692417626952 0.915153791186524 42 0.0555439297401748 0.11108785948035 0.944456070259825 43 0.034002074040047 0.068004148080094 0.965997925959953 44 0.0308749098500609 0.0617498197001218 0.96912509014994 45 0.0187365927608298 0.0374731855216596 0.98126340723917 46 0.0161423205082935 0.0322846410165871 0.983857679491706 47 0.0152584003822682 0.0305168007645364 0.984741599617732 48 0.0522565931433494 0.104513186286699 0.94774340685665 49 0.0281737822563611 0.0563475645127222 0.971826217743639 50 0.0202833145274041 0.0405666290548082 0.979716685472596 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 4 0.102564102564103 NOK 10% type I error level 9 0.230769230769231 NOK

Charts produced by software:

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Parameters (Session):

par1 = 9 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 9 ; 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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