multiple regression

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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: Sat, 18 Dec 2010 21:27:24 +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/18/t1292707543jlviyzf5dezsgof.htm/, Retrieved Sat, 18 Dec 2010 22:25:54 +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/18/t1292707543jlviyzf5dezsgof.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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101,82 107,34 93,63 99,85 101,76 101,68 107,34 93,63 99,91 102,37 101,68 107,34 93,63 99,87 102,38 102,45 107,34 96,13 99,86 102,86 102,45 107,34 96,13 100,10 102,87 102,45 107,34 96,13 100,10 102,92 102,45 107,34 96,13 100,12 102,95 102,45 107,34 96,13 99,95 103,02 102,45 112,60 96,13 99,94 104,08 102,52 112,60 96,13 100,18 104,16 102,52 112,60 96,13 100,31 104,24 102,85 112,60 96,13 100,65 104,33 102,85 112,61 96,13 100,65 104,73 102,85 112,61 96,13 100,69 104,86 103,25 112,61 96,13 101,26 105,03 103,25 112,61 98,73 101,26 105,62 103,25 112,61 98,73 101,38 105,63 103,25 112,61 98,73 101,38 105,63 104,45 112,61 98,73 101,38 105,94 104,45 112,61 98,73 101,44 106,61 104,45 118,65 98,73 101,40 107,69 104,80 118,65 98,73 101,40 107,78 104,80 118,65 98,73 100,58 107,93 105,29 118,65 98,73 100,58 108,48 105,29 114,29 98,73 100,58 108,14 105,29 114,29 98,73 100,59 108,48 105,29 114,29 98,73 100,81 108,48 106,04 114,29 101,67 100,75 108,89 105,94 114,29 101,67 100,75 108,93 105,94 114,29 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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation vrijetijdsbesteding[t] = + 30.5494145341633 + 0.119037724082992bios[t] + 0.352061816366981schouwburg[t] + 0.441421037945499eedagsacttractie[t] -0.197117207935265huurDVD[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) 30.5494145341633 15.039442 2.0313 0.04716 0.02358 bios 0.119037724082992 0.041677 2.8562 0.006074 0.003037 schouwburg 0.352061816366981 0.032113 10.9631 0 0 eedagsacttractie 0.441421037945499 0.047899 9.2156 0 0 huurDVD -0.197117207935265 0.181806 -1.0842 0.283085 0.141542 Multiple Linear Regression - Regression Statistics Multiple R 0.99401619029679 R-squared 0.988068186572143 Adjusted R-squared 0.98718434854045 F-TEST (value) 1117.92902222071 F-TEST (DF numerator) 4 F-TEST (DF denominator) 54 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.64259719517157 Sum Squared Residuals 22.2982823830879 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.76 102.108249539626 -0.348249539625742 2 102.37 102.079757225778 0.290242774221512 3 102.38 102.087641914096 0.292358085904087 4 102.86 103.284824728583 -0.424824728582917 5 102.87 103.237516598678 -0.36751659867845 6 102.92 103.237516598678 -0.317516598678453 7 102.95 103.233574254520 -0.283574254519745 8 103.02 103.267084179869 -0.247084179868747 9 104.08 105.120900506038 -1.04090050603842 10 104.16 105.081925016820 -0.921925016819762 11 104.24 105.056299779788 -0.81629977978818 12 104.33 105.028562378038 -0.698562378037574 13 104.73 105.032082996201 -0.30208299620124 14 104.86 105.024198307884 -0.164198307883835 15 105.03 104.959456588994 0.0705434110060713 16 105.62 106.107151287652 -0.487151287652227 17 105.63 106.0834972227 -0.453497222700007 18 105.63 106.0834972227 -0.453497222700007 19 105.94 106.226342491600 -0.286342491599596 20 106.61 106.214515459123 0.395484540876522 21 107.69 108.348853518297 -0.658853518297459 22 107.78 108.390516721726 -0.610516721726502 23 107.93 108.552152832233 -0.622152832233414 24 108.48 108.610481317034 -0.130481317034084 25 108.14 107.075491797674 1.06450820232595 26 108.48 107.073520625595 1.40647937440531 27 108.48 107.030154839849 1.44984516015107 28 108.89 108.429038016947 0.460961983052936 29 108.93 108.417134244539 0.512865755461242 30 109.21 108.375739630872 0.834260369127633 31 109.47 108.306748608095 1.16325139190498 32 109.8 108.282172755665 1.5178272443354 33 111.73 111.524100217867 0.205899782132949 34 111.85 111.555395355823 0.294604644176539 35 112.12 111.668481193702 0.451518806297707 36 112.15 111.695744760343 0.454255239656895 37 112.17 111.670119523312 0.499880476688474 38 112.67 111.722457751942 0.94754224805805 39 112.8 111.692890170752 1.10710982924834 40 113.44 114.46060007867 -1.02060007866994 41 113.53 114.452715390353 -0.922715390352529 42 114.53 114.506282366190 0.0237176338101247 43 114.51 114.429406655095 0.0805933449048791 44 115.05 114.872342098582 0.177657901417867 45 116.67 116.994867095671 -0.324867095671171 46 117.07 117.118340099714 -0.0483400997136127 47 116.92 117.122282443872 -0.202282443872311 48 117 117.146947523460 -0.146947523459616 49 117.02 117.161232050350 -0.141232050349579 50 117.35 117.193781818254 0.156218181745704 51 117.36 117.448549338825 -0.0885493388252743 52 117.82 118.476581523753 -0.656581523753373 53 117.88 118.494398812400 -0.614398812399727 54 118.24 118.553546462005 -0.31354646200501 55 118.5 118.557898388566 -0.0578983885660175 56 118.8 118.577610109360 0.222389890640454 57 119.76 119.940089338700 -0.180089338699758 58 120.09 119.920377617906 0.169622382093766 59 120.16 120.056362608640 0.103637391359820 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.00189939408454785 0.00379878816909569 0.998100605915452 9 0.000196042168738265 0.00039208433747653 0.999803957831262 10 0.000393444255389006 0.000786888510778012 0.99960655574461 11 9.58428316132757e-05 0.000191685663226551 0.999904157168387 12 0.000721588258076576 0.00144317651615315 0.999278411741923 13 0.00153121607452339 0.00306243214904677 0.998468783925477 14 0.00136197193023516 0.00272394386047033 0.998638028069765 15 0.000464737692344033 0.000929475384688065 0.999535262307656 16 0.000242643102891222 0.000485286205782443 0.999757356897109 17 0.000113401902750261 0.000226803805500523 0.99988659809725 18 5.73520797175512e-05 0.000114704159435102 0.999942647920282 19 3.54653485324525e-05 7.09306970649049e-05 0.999964534651468 20 0.000217585687204713 0.000435171374409425 0.999782414312795 21 0.000239250916308418 0.000478501832616836 0.999760749083692 22 0.000367210756198378 0.000734421512396756 0.999632789243802 23 0.0048240010779645 0.009648002155929 0.995175998922035 24 0.0343076286227614 0.0686152572455229 0.965692371377239 25 0.164654566861623 0.329309133723246 0.835345433138377 26 0.340383743278409 0.680767486556819 0.659616256721591 27 0.394803245782915 0.78960649156583 0.605196754217085 28 0.388690987412482 0.777381974824964 0.611309012587518 29 0.403028080852865 0.80605616170573 0.596971919147135 30 0.385986153091527 0.771972306183054 0.614013846908473 31 0.365734139561010 0.731468279122021 0.63426586043899 32 0.422034780249257 0.844069560498514 0.577965219750743 33 0.426147267041596 0.852294534083192 0.573852732958404 34 0.413366356082934 0.826732712165867 0.586633643917066 35 0.581856248258073 0.836287503483855 0.418143751741927 36 0.649572551277578 0.700854897444844 0.350427448722422 37 0.678857438690081 0.642285122619838 0.321142561309919 38 0.613271631042193 0.773456737915614 0.386728368957807 39 0.545780384578332 0.908439230843336 0.454219615421668 40 0.79483745140399 0.410325097192019 0.205162548596009 41 0.959523557092634 0.0809528858147328 0.0404764429073664 42 0.933247230058293 0.133505539883415 0.0667527699417073 43 0.896440220425651 0.207119559148697 0.103559779574349 44 0.995557907086354 0.00888418582729244 0.00444209291364622 45 0.999691506428725 0.000616987142550151 0.000308493571275076 46 0.999652573748507 0.000694852502985126 0.000347426251492563 47 0.999279704836416 0.00144059032716703 0.000720295163583516 48 0.997416001094168 0.00516799781166453 0.00258399890583227 49 0.990996750188208 0.0180064996235846 0.00900324981179231 50 0.972742466776135 0.0545150664477299 0.0272575332238649 51 0.91755282315295 0.164894353694099 0.0824471768470496 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 21 0.477272727272727 NOK 5% type I error level 22 0.5 NOK 10% type I error level 25 0.568181818181818 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 5 ; 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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