MRLM 1

*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, 21 Dec 2010 14:16:43 +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/21/t12929423266l5f3fwdwtk7tv9.htm/, Retrieved Tue, 21 Dec 2010 15:38:58 +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/21/t12929423266l5f3fwdwtk7tv9.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:

» Textbox « » Textfile « » CSV «

216.234 627 1,59 213.586 696 1,26 209.465 825 1,13 204.045 677 1,92 200.237 656 2,61 203.666 785 2,26 241.476 412 2,41 260.307 352 2,26 243.324 839 2,03 244.460 729 2,86 233.575 696 2,55 237.217 641 2,27 235.243 695 2,26 230.354 638 2,57 227.184 762 3,07 221.678 635 2,76 217.142 721 2,51 219.452 854 2,87 256.446 418 3,14 265.845 367 3,11 248.624 824 3,16 241.114 687 2,47 229.245 601 2,57 231.805 676 2,89 219.277 740 2,63 219.313 691 2,38 212.610 683 1,69 214.771 594 1,96 211.142 729 2,19 211.457 731 1,87 240.048 386 1,6 240.636 331 1,63 230.580 707 1,22 208.795 715 1,21 197.922 657 1,49 194.596 653 1,64 194.581 642 1,66 185.686 643 1,77 178.106 718 1,82 172.608 654 1,78 167.302 632 1,28 168.053 731 1,29 202.300 392 1,37 202.388 344 1,12 182.516 792 1,51 173.476 852 2,24 166.444 649 2,94 171.297 629 3,09 169.701 685 3,46 164.182 617 3,64 161.914 715 4,39 159.612 715 4,15 151.001 629 5,21 158.114 916 5,8 186.530 531 5,91 187.069 357 5,39 174.330 917 5,46 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 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation werklozen[t] = + 260.190949372379 -0.0647261802161827faillissementen[t] -5.17543693747146inflatie[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) 260.190949372379 14.565274 17.8638 0 0 faillissementen -0.0647261802161827 0.019443 -3.329 0.001401 0.000701 inflatie -5.17543693747146 1.955416 -2.6467 0.010061 0.00503 Multiple Linear Regression - Regression Statistics Multiple R 0.440580564404765 R-squared 0.194111233731221 Adjusted R-squared 0.170752139056764 F-TEST (value) 8.30987829093725 F-TEST (DF numerator) 2 F-TEST (DF denominator) 69 p-value 0.000584105125278511 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 25.5379050338095 Sum Squared Residuals 45000.7369525952 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 216.234 211.378689646251 4.85531035374853 2 213.586 208.620477400701 4.96552259929858 3 209.465 200.943606954685 8.52139304531492 4 204.045 206.434486446078 -2.38948644607773 5 200.237 204.222684743762 -3.98568474376226 6 203.666 197.684410423990 5.9815895760103 7 241.476 221.050960104005 20.4250398959949 8 260.307 225.710846457597 34.5961535424032 9 243.324 195.379547187934 47.9444528120658 10 244.46 198.203814353613 46.256185646387 11 233.575 201.944163751363 31.6308362486368 12 237.217 206.953226005745 30.2637739942547 13 235.243 203.509766643446 31.7332333565539 14 230.354 205.594773465152 24.7592265348476 15 227.184 194.98100864961 32.20299135039 16 221.678 204.805618987681 16.8723810123186 17 217.142 200.533026723458 16.6089732765425 18 219.452 190.061287457215 29.3907125427845 19 256.446 216.884534058354 39.5614659416462 20 265.845 220.340832357503 45.5041676424967 21 248.624 190.502196151834 58.1218038481657 22 241.114 202.940734328307 38.1732656716934 23 229.245 207.989642133151 21.2553578668488 24 231.805 201.479038796947 30.3259612030534 25 219.277 198.682176866853 20.5948231331465 26 219.313 203.147618931814 16.1653810681857 27 212.61 207.236479860399 5.37352013960095 28 214.771 211.599741926522 3.17125807347796 29 211.142 201.671357101719 9.47064289828107 30 211.457 203.198044561277 8.25895543872257 31 240.048 226.925944708978 13.1220552910222 32 240.636 230.330621512744 10.3053784872563 33 230.58 208.115506895822 22.4644931041778 34 208.795 207.649451823468 1.14554817653248 35 197.922 209.954447933514 -12.0324479335141 36 194.596 209.437037113758 -14.8410371137581 37 194.581 210.045516357387 -15.4645163573867 38 185.686 209.411492114049 -23.7254921140486 39 178.106 204.298256750961 -26.1922567509614 40 172.608 208.647749762296 -36.0397497622959 41 167.302 212.659444195788 -45.3574441957877 42 168.053 206.199797985011 -38.1467979850109 43 202.3 227.727938123299 -25.4279381232991 44 202.388 232.128654008044 -29.7406540080437 45 182.516 201.11290486558 -18.5969048655800 46 173.476 193.451265088255 -19.9752650882549 47 166.444 202.96787381591 -36.5238738159100 48 171.297 203.486081879613 -32.1890818796129 49 169.701 197.946504120642 -28.2455041206422 50 164.182 201.416305726598 -37.2343057265978 51 161.914 191.191562362308 -29.2775623623083 52 159.612 192.433667227301 -32.8216672273014 53 151.001 192.514155572173 -41.5131555721734 54 158.114 170.884234057021 -12.7702340570208 55 186.53 195.234515377129 -8.70451537712928 56 187.069 209.188097942230 -22.1190979422302 57 174.33 172.579156435545 1.75084356445511 58 169.362 182.169609808514 -12.8076098085141 59 166.827 198.113941795661 -31.2869417956609 60 178.037 191.044487601344 -13.0074876013439 61 186.413 198.021146009903 -11.6081460099032 62 189.226 199.392304613355 -10.1663046133553 63 191.563 191.867641173666 -0.304641173666517 64 188.906 206.016731019328 -17.1107310193276 65 186.005 214.596844760565 -28.5918447605649 66 195.309 207.242010727736 -11.9330107277357 67 223.532 234.451355552321 -10.9193555523215 68 226.899 239.178758439944 -12.2797584399436 69 214.126 202.206074733733 11.9199252662674 70 206.903 210.776405639916 -3.87340563991628 71 204.442 203.076249052040 1.36575094795980 72 220.375 208.229462839581 12.1455371604188 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.00325369624869355 0.0065073924973871 0.996746303751306 7 0.0137481324458649 0.0274962648917297 0.986251867554135 8 0.0111509305669108 0.0223018611338217 0.988849069433089 9 0.257676226792407 0.515352453584813 0.742323773207593 10 0.275593703160754 0.551187406321508 0.724406296839246 11 0.204315695631644 0.408631391263288 0.795684304368356 12 0.154047824299269 0.308095648598538 0.84595217570073 13 0.117680837736671 0.235361675473343 0.882319162263329 14 0.0801155240057484 0.160231048011497 0.919884475994252 15 0.0572688514530596 0.114537702906119 0.94273114854694 16 0.0429592085540721 0.0859184171081442 0.957040791445928 17 0.0293998520479186 0.0587997040958371 0.970600147952081 18 0.0206058323370341 0.0412116646740683 0.979394167662966 19 0.0190521906267498 0.0381043812534996 0.98094780937325 20 0.0262611045563526 0.0525222091127052 0.973738895443647 21 0.0756527178230765 0.151305435646153 0.924347282176924 22 0.106129795661670 0.212259591323339 0.89387020433833 23 0.107171421935832 0.214342843871664 0.892828578064168 24 0.136049111696921 0.272098223393841 0.86395088830308 25 0.153536578435954 0.307073156871908 0.846463421564046 26 0.165644960813179 0.331289921626358 0.834355039186821 27 0.145418874739932 0.290837749479863 0.854581125260068 28 0.142803409089066 0.285606818178131 0.857196590910934 29 0.149417038918777 0.298834077837554 0.850582961081223 30 0.143494503577131 0.286989007154262 0.856505496422869 31 0.194704804030739 0.389409608061478 0.80529519596926 32 0.302388217816774 0.604776435633547 0.697611782183226 33 0.584001699538829 0.831996600922343 0.415998300461171 34 0.583205934087724 0.833588131824551 0.416794065912276 35 0.608639798526438 0.782720402947124 0.391360201473562 36 0.65437516997295 0.6912496600541 0.34562483002705 37 0.68709659940503 0.62580680118994 0.31290340059497 38 0.770151693070886 0.459696613858228 0.229848306929114 39 0.843838185838769 0.312323628322463 0.156161814161231 40 0.929701774842412 0.140596450315177 0.0702982251575883 41 0.97796973822381 0.0440605235523805 0.0220302617761902 42 0.990352410050646 0.019295179898709 0.0096475899493545 43 0.986223659642437 0.0275526807151256 0.0137763403575628 44 0.979161160945542 0.0416776781089166 0.0208388390544583 45 0.971201247251869 0.0575975054962626 0.0287987527481313 46 0.975049067129044 0.0499018657419121 0.0249509328709560 47 0.995480865061829 0.0090382698763412 0.0045191349381706 48 0.998273831607256 0.00345233678548850 0.00172616839274425 49 0.99903043928084 0.00193912143832009 0.000969560719160047 50 0.999634709269494 0.000730581461012705 0.000365290730506353 51 0.999711600494062 0.000576799011876593 0.000288399505938297 52 0.999797120318146 0.000405759363708043 0.000202879681854021 53 0.999946964183646 0.000106071632708622 5.30358163543111e-05 54 0.9998701422355 0.000259715528999780 0.000129857764499890 55 0.99977792615319 0.000444147693619349 0.000222073846809675 56 0.999520256099086 0.000959487801828603 0.000479743900914302 57 0.999442957191327 0.00111408561734540 0.000557042808672701 58 0.99880213838255 0.00239572323489946 0.00119786161744973 59 0.998312531159327 0.00337493768134507 0.00168746884067253 60 0.995791342711289 0.00841731457742244 0.00420865728871122 61 0.989623311195012 0.0207533776099768 0.0103766888049884 62 0.975747703192946 0.0485045936141088 0.0242522968070544 63 0.946319485926928 0.107361028146145 0.0536805140730723 64 0.91813432650606 0.163731346987880 0.0818656734939401 65 0.97683852048091 0.0463229590381793 0.0231614795190897 66 0.97512934613346 0.0497413077330779 0.0248706538665390 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 15 0.245901639344262 NOK 5% type I error level 28 0.459016393442623 NOK 10% type I error level 32 0.524590163934426 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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