M3

*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: Thu, 19 Nov 2009 09:06:21 -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/t12586472434jzxsfi7r88v08q.htm/, Retrieved Thu, 19 Nov 2009 17:14:15 +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/t12586472434jzxsfi7r88v08q.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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21 2472,81 19 2407,6 25 2454,62 21 2448,05 23 2497,84 23 2645,64 19 2756,76 18 2849,27 19 2921,44 19 2981,85 22 3080,58 23 3106,22 20 3119,31 14 3061,26 14 3097,31 14 3161,69 15 3257,16 11 3277,01 17 3295,32 16 3363,99 20 3494,17 24 3667,03 23 3813,06 20 3917,96 21 3895,51 19 3801,06 23 3570,12 23 3701,61 23 3862,27 23 3970,1 27 4138,52 26 4199,75 17 4290,89 24 4443,91 26 4502,64 24 4356,98 27 4591,27 27 4696,96 26 4621,4 24 4562,84 23 4202,52 23 4296,49 24 4435,23 17 4105,18 21 4116,68 19 3844,49 22 3720,98 22 3674,4 18 3857,62 16 3801,06 14 3504,37 12 3032,6 14 3047,03 16 2962,34 8 2197,82 3 2014,45 0 1862,83 5 1905,41 1 1810,99 1 1670,07 3 1864,44

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 Consvertr[t] = + 2.73170303613635 + 0.00637395336616299Aand[t] -0.190088819280827t + 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) 2.73170303613635 1.89563 1.4411 0.154947 0.077474 Aand 0.00637395336616299 0.000513 12.4272 0 0 t -0.190088819280827 0.023593 -8.0571 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.885297448485684 R-squared 0.783751572295263 Adjusted R-squared 0.776294729960617 F-TEST (value) 105.105021284114 F-TEST (DF numerator) 2 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.24057281102741 Sum Squared Residuals 609.076104327064 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 21 18.3031898402370 2.69681015976295 2 19 17.6974555219487 1.30254447805129 3 25 17.8070699899449 7.19293001005515 4 21 17.5751042970483 3.42489570295165 5 23 17.7023746158688 5.29762538413122 6 23 18.4543561041068 4.54564389589316 7 19 18.9725409828740 0.0274590171259583 8 18 19.3721065894970 -1.37210658949695 9 19 19.6420259846521 -0.642025984652107 10 19 19.8369876882212 -0.836987688221185 11 22 20.2761992847816 1.72380071521837 12 23 20.2495386298092 2.75046137019078 13 20 20.1428848600915 -0.142884860091468 14 14 19.5827880479049 -5.58278804790488 15 14 19.6224802474742 -5.62248024747423 16 14 19.8427465459070 -5.84274654590697 17 15 20.2611790544937 -5.26117905449373 18 11 20.1976132095312 -9.19761320953123 19 17 20.1242314763849 -3.12423147638485 20 16 20.3718420347584 -4.37184203475844 21 20 21.0115144646847 -1.01151446468471 22 24 21.9232272242788 2.07677277572118 23 23 22.6639268150588 0.336073184941232 24 20 23.1424657038884 -3.14246570388844 25 21 22.8092816315373 -1.80928163153725 26 19 22.0171729168223 -3.01717291682233 27 23 20.3550833071598 2.64491669284018 28 23 21.0031056159958 1.99689438400423 29 23 21.8370561445227 1.16294385547731 30 23 22.3342707167152 0.665729283284787 31 27 23.2176831233636 3.78231687663644 32 26 23.4178714686929 2.58212853130711 33 17 23.8087047592042 -6.80870475920416 34 24 24.5939582840136 -0.59395828401359 35 26 24.7782117459275 1.22178825407248 36 24 23.6596928793314 0.340307120668616 37 27 24.9629575942089 2.03704240579111 38 27 25.4465319061978 1.55346809380217 39 26 24.7748271705697 1.22517282943028 40 24 24.2114796421664 -0.211479642166392 41 23 21.7247279459897 1.27527205401028 42 23 22.1335995245272 0.866400475472777 43 24 22.8278329952678 1.17216700473215 44 17 20.5340208674849 -3.53402086748493 45 21 20.417232511915 0.582767488085021 46 19 18.4922173258982 0.507782674101756 47 22 17.5148815263626 4.48511847363737 48 22 17.0278939592859 4.97210604071407 49 18 18.0056408757535 -0.00564087575348349 50 16 17.4550412540825 -1.45504125408248 51 14 15.3738642105948 -1.37386421059475 52 12 12.1767354117592 -0.176735411759213 53 14 12.0786227395521 1.92137726044788 54 16 11.3487238096909 4.65127619030905 55 8 6.2856201629112 1.71437983708881 56 3 4.92673951487706 -1.92673951487706 57 0 3.7702318862186 -3.7702318862186 58 5 3.85154600126899 1.14845399873101 59 1 3.05962850515506 -2.05962850515506 60 1 1.97132217751454 -0.97132217751454 61 3 3.02013867401481 -0.0201386740148131 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.455478779237516 0.910957558475032 0.544521220762484 7 0.485626431096738 0.971252862193476 0.514373568903262 8 0.376440063913408 0.752880127826817 0.623559936086592 9 0.260417119201056 0.520834238402112 0.739582880798944 10 0.172178570066617 0.344357140133233 0.827821429933383 11 0.261369691646148 0.522739383292297 0.738630308353852 12 0.352007986835993 0.704015973671987 0.647992013164007 13 0.304159081663245 0.608318163326489 0.695840918336756 14 0.602717203396292 0.794565593207415 0.397282796603708 15 0.598289554334765 0.80342089133047 0.401710445665235 16 0.545967573630398 0.908064852739204 0.454032426369602 17 0.471408999663114 0.942817999326227 0.528591000336886 18 0.632602004193664 0.734795991612673 0.367397995806336 19 0.685136866718399 0.629726266563202 0.314863133281601 20 0.698301953253656 0.603396093492688 0.301698046746344 21 0.801192185109193 0.397615629781615 0.198807814890808 22 0.921052894488658 0.157894211022684 0.078947105511342 23 0.908503523840487 0.182992952319025 0.0914964761595126 24 0.895495881875126 0.209008236249749 0.104504118124874 25 0.873649204765375 0.252701590469249 0.126350795234625 26 0.885701021524903 0.228597956950193 0.114298978475097 27 0.971516162104481 0.056967675791037 0.0284838378955185 28 0.977563819397473 0.0448723612050531 0.0224361806025265 29 0.974638828956385 0.05072234208723 0.025361171043615 30 0.967582366928053 0.0648352661438942 0.0324176330719471 31 0.985440264451248 0.0291194710975044 0.0145597355487522 32 0.991591896095851 0.0168162078082976 0.00840810390414882 33 0.998372075927885 0.00325584814423085 0.00162792407211542 34 0.997272591163706 0.00545481767258742 0.00272740883629371 35 0.995728428550184 0.00854314289963143 0.00427157144981571 36 0.99277301680974 0.0144539663805196 0.00722698319025982 37 0.989905739239504 0.0201885215209911 0.0100942607604956 38 0.984250360517767 0.0314992789644654 0.0157496394822327 39 0.975177446943094 0.0496451061138111 0.0248225530569055 40 0.96192766540098 0.0761446691980401 0.0380723345990200 41 0.944462660513401 0.111074678973197 0.0555373394865986 42 0.916074101135524 0.167851797728953 0.0839258988644763 43 0.877241732235747 0.245516535528505 0.122758267764253 44 0.92941649839219 0.141167003215620 0.0705835016078101 45 0.902750341422409 0.194499317155181 0.0972496585775907 46 0.873284877907532 0.253430244184935 0.126715122092468 47 0.861789177484656 0.276421645030688 0.138210822515344 48 0.915773151041255 0.16845369791749 0.084226848958745 49 0.867817576579756 0.264364846840488 0.132182423420244 50 0.87240259624574 0.255194807508519 0.127597403754260 51 0.935311958043336 0.129376083913329 0.0646880419566645 52 0.936752597451172 0.126494805097656 0.0632474025488278 53 0.932016055514294 0.135967888971411 0.0679839444857057 54 0.89378906063738 0.212421878725240 0.106210939362620 55 0.832875439212906 0.334249121574188 0.167124560787094 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.06 NOK 5% type I error level 10 0.2 NOK 10% type I error level 14 0.28 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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