WS10MR

*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: Tue, 14 Dec 2010 18:36:16 +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/14/t1292351689jepk51tqbhh5nil.htm/, Retrieved Tue, 14 Dec 2010 19:34:49 +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/14/t1292351689jepk51tqbhh5nil.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:

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Dataseries X:

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2,65 2,89 2,23 2,61 2,55 2,21 2,61 2,47 2,18 2,47 2,24 2,21 2,5 2,26 2,13 2,47 2,33 2,17 2,37 2,3 2,24 2,27 2,28 2,03 2,28 2,26 2,05 2,25 2,23 2,1 2,19 2,31 2,16 2,24 2,24 2,13 2,3 2,07 2,24 2,44 1,98 2,17 2,55 1,93 2,23 2,58 1,96 2,13 2,5 1,99 2,25 2,44 2,01 2,17 2,35 2,11 2,29 2,36 2,26 2,17 2,44 2,39 2,1 2,48 2,63 2,12 2,49 2,73 2,17 2,53 2,87 2,14 2,6 3,01 2,22 2,62 3,18 2,3 2,67 3,24 2,2 2,62 3,06 2,31 2,56 2,94 2,35 2,53 2,85 2,16 2,45 2,84 2,14 2,37 2,73 2,08 2,43 2,42 2,05 2,46 2,14 2,07 2,5 2,03 2,06 2,46 1,98 1,96 2,47 1,9 2,15 2,45 1,88 2,15 2,43 1,87 2,1 2,41 1,83 2,05 2,32 1,82 2,07 2,3 1,83 2,01 2,27 1,83 2,1 2,23 1,82 2,01 2,3 1,84 2,02 2,3 1,87 2,04 2,25 1,87 1,99 2,22 1,87 1,91 2,28 1,84 2,06 2,38 1,81 2,21 2,38 1,78 2,13 2,37 1,79 2,18 2,32 1,79 2,12 2,29 1,8 2,08 2,2 1,82 2,17 2,07 1,94 2,17

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Sinaasappelen[t] = + 1.24111305125144 + 0.163787344724504Citroenen[t] + 0.375998886979869Bananen[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) 1.24111305125144 0.344246 3.6053 0.000689 0.000345 Citroenen 0.163787344724504 0.03753 4.3642 5.9e-05 3e-05 Bananen 0.375998886979869 0.176263 2.1332 0.037559 0.01878 Multiple Linear Regression - Regression Statistics Multiple R 0.667665185920295 R-squared 0.445776800489982 Adjusted R-squared 0.424862717489604 F-TEST (value) 21.3146710989874 F-TEST (DF numerator) 2 F-TEST (DF denominator) 53 p-value 1.61303793544398e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.102702815808202 Sum Squared Residuals 0.559037023871477 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2.65 2.55293599547036 0.0970640045296405 2 2.61 2.48972832052443 0.120271679475567 3 2.61 2.46534536633708 0.144654633662923 4 2.47 2.43895424365984 0.0310457563401635 5 2.5 2.41215007959594 0.0878499204040629 6 2.47 2.43865514920585 0.0313448507941529 7 2.37 2.46006145095270 -0.090061450952703 8 2.27 2.37782593779244 -0.107825937792440 9 2.28 2.38207016863755 -0.102070168637548 10 2.25 2.39595649264481 -0.145956492644806 11 2.19 2.43161941344156 -0.241619413441559 12 2.24 2.40887433270145 -0.168874332701447 13 2.3 2.42239036166607 -0.122390361666067 14 2.44 2.38132957855227 0.0586704214477292 15 2.55 2.39570014453484 0.154299855465162 16 2.58 2.36301387617859 0.216986123821414 17 2.5 2.41304736295791 0.0869526370420947 18 2.44 2.38624319889401 0.0537568011059941 19 2.35 2.44774179980404 -0.0977417998040405 20 2.36 2.42719003507513 -0.067190035075132 21 2.44 2.42216246780073 0.0178375321992732 22 2.48 2.46899140827421 0.0110085917257948 23 2.49 2.50417008709565 -0.0141700870956488 24 2.53 2.51582034874768 0.0141796512523161 25 2.6 2.56883048796750 0.0311695120324963 26 2.62 2.62675424752906 -0.00675424752905896 27 2.67 2.59898159951454 0.0710184004854574 28 2.62 2.61085975503192 0.0091402449680828 29 2.56 2.60624522914417 -0.0462452291441715 30 2.53 2.52006457959279 0.00993542040720883 31 2.45 2.51090672840595 -0.0609067284059483 32 2.37 2.47033018726746 -0.100330187267461 33 2.43 2.40827614379347 0.0217238562065319 34 2.46 2.36993566501020 0.0900643349897955 35 2.5 2.34815906822071 0.151840931779290 36 2.46 2.3023698122865 0.157630187713502 37 2.47 2.36070661323471 0.109293386765287 38 2.45 2.35743086634022 0.0925691336597773 39 2.43 2.33699304854398 0.0930069514560157 40 2.41 2.31164161040601 0.0983583895939894 41 2.32 2.31752371469836 0.00247628530163681 42 2.3 2.29660165492682 0.00339834507318392 43 2.27 2.33044155475500 -0.0604415547550042 44 2.23 2.29496378147957 -0.0649637814795709 45 2.3 2.30199951724386 -0.00199951724385990 46 2.3 2.31443311532519 -0.0144331153251924 47 2.25 2.2956331709762 -0.0456331709761988 48 2.22 2.26555326001781 -0.045553260017809 49 2.28 2.31703947272305 -0.0370394727230547 50 2.38 2.3685256854283 0.0114743145717001 51 2.38 2.33353215412818 0.0464678458718248 52 2.37 2.35396997192441 0.0160300280755864 53 2.32 2.33141003870562 -0.0114100387056216 54 2.29 2.31800795667367 -0.0280079566736717 55 2.2 2.35512360339635 -0.155123603396350 56 2.07 2.37477808476329 -0.304778084763291 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.116340403157543 0.232680806315085 0.883659596842457 7 0.122525034367769 0.245050068735538 0.877474965632231 8 0.461250736037444 0.922501472074887 0.538749263962556 9 0.385629556955933 0.771259113911865 0.614370443044068 10 0.404689325611023 0.809378651222046 0.595310674388977 11 0.795022485136745 0.40995502972651 0.204977514863255 12 0.815844027410272 0.368311945179456 0.184155972589728 13 0.775918334817656 0.448163330364689 0.224081665182344 14 0.851122530181612 0.297754939636776 0.148877469818388 15 0.925407469647426 0.149185060705149 0.0745925303525743 16 0.990395717564307 0.0192085648713865 0.00960428243569323 17 0.98778918730453 0.0244216253909419 0.0122108126954710 18 0.982253038796857 0.0354939224062861 0.0177469612031430 19 0.985563227883052 0.0288735442338957 0.0144367721169478 20 0.97954923085995 0.0409015382801019 0.0204507691400509 21 0.96863318558375 0.0627336288324997 0.0313668144162498 22 0.951877386242202 0.0962452275155955 0.0481226137577977 23 0.9282117173259 0.143576565348201 0.0717882826741004 24 0.896637051865668 0.206725896268663 0.103362948134332 25 0.857448158649904 0.285103682700192 0.142551841350096 26 0.813126373045764 0.373747253908473 0.186873626954236 27 0.781755245595926 0.436489508808149 0.218244754404074 28 0.73230099240676 0.535398015186481 0.267699007593241 29 0.686550126573727 0.626899746852546 0.313449873426273 30 0.622814222441071 0.754371555117857 0.377185777558929 31 0.552355727401126 0.895288545197747 0.447644272598874 32 0.558746532013965 0.88250693597207 0.441253467986035 33 0.528117765657322 0.943764468685357 0.471882234342678 34 0.479674656292547 0.959349312585094 0.520325343707453 35 0.530292034564812 0.939415930870376 0.469707965435188 36 0.679484831121819 0.641030337756362 0.320515168878181 37 0.803495958993771 0.393008082012457 0.196504041006229 38 0.92207054659523 0.155858906809541 0.0779294534047703 39 0.989333462873458 0.0213330742530832 0.0106665371265416 40 0.996333255480342 0.00733348903931571 0.00366674451965786 41 0.992665068376974 0.0146698632460519 0.00733493162302596 42 0.98534184474609 0.0293163105078195 0.0146581552539098 43 0.973585758198045 0.0528284836039097 0.0264142418019548 44 0.976247705723273 0.0475045885534536 0.0237522942767268 45 0.95469316969206 0.0906136606158802 0.0453068303079401 46 0.959851627287966 0.0802967454240682 0.0401483727120341 47 0.934233512017146 0.131532975965709 0.0657664879828545 48 0.886256589370825 0.227486821258351 0.113743410629175 49 0.862444563999364 0.275110872001273 0.137555436000636 50 0.809788899275694 0.380422201448613 0.190211100724306 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0222222222222222 NOK 5% type I error level 10 0.222222222222222 NOK 10% type I error level 15 0.333333333333333 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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