MLRM 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: Fri, 10 Dec 2010 14:54:22 +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/10/t129199297557k4i4coj93t6kc.htm/, Retrieved Fri, 10 Dec 2010 15:56:26 +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/10/t129199297557k4i4coj93t6kc.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 «

627 216.234 696 213.586 825 209.465 677 204.045 656 200.237 785 203.666 412 241.476 352 260.307 839 243.324 729 244.460 696 233.575 641 237.217 695 235.243 638 230.354 762 227.184 635 221.678 721 217.142 854 219.452 418 256.446 367 265.845 824 248.624 687 241.114 601 229.245 676 231.805 740 219.277 691 219.313 683 212.610 594 214.771 729 211.142 731 211.457 386 240.048 331 240.636 707 230.580 715 208.795 657 197.922 653 194.596 642 194.581 643 185.686 718 178.106 654 172.608 632 167.302 731 168.053 392 202.300 344 202.388 792 182.516 852 173.476 649 166.444 629 171.297 685 169.701 617 164.182 715 161.914 715 159.612 629 151.001 916 158.114 531 186.530 357 187.069 917 174.330 828 169.362 708 166.827 858 178.037 775 186.413 785 189.226 1006 191.563 789 188.906 734 186.005 906 195.309 532 223.532 387 226.899 991 214.126 841 206.903 892 204.442 782 220.375

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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation werklozen[t] = + 245.835030830493 -0.0600382870744318faillissementen[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) 245.835030830493 14.085548 17.453 0 0 faillissementen -0.0600382870744318 0.020176 -2.9757 0.00401 0.002005 Multiple Linear Regression - Regression Statistics Multiple R 0.335103814391781 R-squared 0.112294566419921 Adjusted R-squared 0.09961306022592 F-TEST (value) 8.8549865214781 F-TEST (DF numerator) 1 F-TEST (DF denominator) 70 p-value 0.00400991597917932 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 26.6107846933963 Sum Squared Residuals 49569.3703398807 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 216.234 208.191024834823 8.0429751651772 2 213.586 204.048383026688 9.53761697331209 3 209.465 196.303443994086 13.1615560059138 4 204.045 205.189110481102 -1.14411048110214 5 200.237 206.449914509665 -6.2129145096652 6 203.666 198.704975477063 4.9610245229365 7 241.476 221.099256555827 20.3767434441734 8 260.307 224.701553780292 35.6054462197076 9 243.324 195.462907975044 47.8610920249558 10 244.46 202.067119553232 42.3928804467683 11 233.575 204.048383026688 29.5266169733121 12 237.217 207.350488815782 29.8665111842183 13 235.243 204.108421313762 31.1345786862376 14 230.354 207.530603677005 22.8233963229950 15 227.184 200.085856079775 27.0981439202246 16 221.678 207.710718538228 13.9672814617717 17 217.142 202.547425849827 14.5945741501729 18 219.452 194.562333668928 24.8896663310723 19 256.446 220.73902683338 35.7069731666201 20 265.845 223.800979474176 42.0440205258240 21 248.624 196.363482281161 52.2605177188393 22 241.114 204.588727610358 36.5252723896422 23 229.245 209.752020298759 19.4929797012411 24 231.805 205.249148768177 26.5558512318234 25 219.277 201.406698395413 17.8703016045871 26 219.313 204.34857446206 14.9644255379399 27 212.61 204.828880758656 7.78111924134447 28 214.771 210.17228830828 4.59871169172002 29 211.142 202.067119553232 9.07488044676832 30 211.457 201.947042979083 9.50995702091718 31 240.048 222.660252019762 17.3877479802382 32 240.636 225.962357808856 14.6736421911445 33 230.58 203.387961868869 27.1920381311308 34 208.795 202.907655572274 5.88734442772627 35 197.922 206.389876222591 -8.46787622259077 36 194.596 206.630029370888 -12.0340293708885 37 194.581 207.290450528707 -12.7094505287073 38 185.686 207.230412241633 -21.5444122416328 39 178.106 202.727540711050 -24.6215407110504 40 172.608 206.569991083814 -33.9619910838141 41 167.302 207.890833399452 -40.5888333994516 42 168.053 201.947042979083 -33.8940429790828 43 202.3 222.300022297315 -20.0000222973152 44 202.388 225.181860076888 -22.7938600768879 45 182.516 198.284707467542 -15.7687074675425 46 173.476 194.682410243077 -21.2064102430766 47 166.444 206.870182519186 -40.4261825191862 48 171.297 208.070948260675 -36.7739482606749 49 169.701 204.708804184507 -35.0078041845067 50 164.182 208.791407705568 -44.6094077055681 51 161.914 202.907655572274 -40.9936555722737 52 159.612 202.907655572274 -43.2956555722737 53 151.001 208.070948260675 -57.0699482606749 54 158.114 190.839959870313 -32.7259598703129 55 186.53 213.954700393969 -27.4247003939692 56 187.069 224.401362344920 -37.3323623449203 57 174.33 190.779921583238 -16.4499215832385 58 169.362 196.123329132863 -26.7613291328629 59 166.827 203.327923581795 -36.5009235817947 60 178.037 194.32218052063 -16.2851805206300 61 186.413 199.305358347808 -12.8923583478078 62 189.226 198.704975477063 -9.4789754770635 63 191.563 185.436514033614 6.12648596638592 64 188.906 198.464822328766 -9.55882232876576 65 186.005 201.766928117860 -15.7619281178595 66 195.309 191.440342741057 3.86865725894275 67 223.532 213.894662106895 9.63733789310527 68 226.899 222.600213732687 4.29878626731265 69 214.126 186.337088339731 27.7889116602695 70 206.903 195.342831400895 11.5601685991047 71 204.442 192.280878760099 12.1611212399007 72 220.375 198.885090338287 21.4899096617132 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0277253781144998 0.0554507562289997 0.9722746218855 6 0.00731909636700973 0.0146381927340195 0.99268090363299 7 0.00926966309585688 0.0185393261917138 0.990730336904143 8 0.00882115297301535 0.0176423059460307 0.991178847026985 9 0.140847130778666 0.281694261557331 0.859152869221334 10 0.180619598530374 0.361239197060748 0.819380401469626 11 0.137167989603916 0.274335979207831 0.862832010396084 12 0.102719037737539 0.205438075475079 0.89728096226246 13 0.0788022181797535 0.157604436359507 0.921197781820246 14 0.0512580990569164 0.102516198113833 0.948741900943084 15 0.0351056620194777 0.0702113240389554 0.964894337980522 16 0.0222616456640492 0.0445232913280983 0.97773835433595 17 0.0136379055779855 0.027275811155971 0.986362094422015 18 0.00875192726151996 0.0175038545230399 0.99124807273848 19 0.0083525537585603 0.0167051075171206 0.99164744624144 20 0.0109079709469802 0.0218159418939603 0.98909202905302 21 0.0399088976264742 0.0798177952529484 0.960091102373526 22 0.0455074022043019 0.0910148044086037 0.954492597795698 23 0.0375431130809493 0.0750862261618987 0.96245688691905 24 0.0342547686976443 0.0685095373952886 0.965745231302356 25 0.0282725365251830 0.0565450730503659 0.971727463474817 26 0.0241874952908469 0.0483749905816938 0.975812504709153 27 0.0227614888867544 0.0455229777735088 0.977238511113246 28 0.0238676769102435 0.0477353538204871 0.976132323089757 29 0.0212168792697132 0.0424337585394264 0.978783120730287 30 0.0188111419999873 0.0376222839999746 0.981188858000013 31 0.0222952443030867 0.0445904886061733 0.977704755696913 32 0.0331324766752752 0.0662649533505504 0.966867523324725 33 0.0527287525821166 0.105457505164233 0.947271247417883 34 0.057253401539161 0.114506803078322 0.942746598460839 35 0.0831996618919438 0.166399323783888 0.916800338108056 36 0.119104190143089 0.238208380286178 0.880895809856911 37 0.155180250483188 0.310360500966376 0.844819749516812 38 0.226578888316661 0.453157776633322 0.773421111683339 39 0.30630664240681 0.61261328481362 0.69369335759319 40 0.446083372868408 0.892166745736815 0.553916627131592 41 0.614511768266738 0.770976463466523 0.385488231733262 42 0.689787681554084 0.620424636891832 0.310212318445916 43 0.692671005096149 0.614657989807702 0.307328994903851 44 0.692665184039353 0.614669631921295 0.307334815960647 45 0.661573534052471 0.676852931895057 0.338426465947529 46 0.647164319128822 0.705671361742357 0.352835680871178 47 0.705091559945829 0.589816880108343 0.294908440054172 48 0.725616889986268 0.548766220027464 0.274383110013732 49 0.738074645608038 0.523850708783924 0.261925354391962 50 0.788670244089595 0.42265951182081 0.211329755910405 51 0.828034144112358 0.343931711775283 0.171965855887642 52 0.87481247424679 0.250375051506421 0.125187525753210 53 0.95858488308777 0.082830233824461 0.0414151169122305 54 0.972927059525113 0.0541458809497744 0.0270729404748872 55 0.964910804165137 0.0701783916697262 0.0350891958348631 56 0.968173518807437 0.0636529623851261 0.0318264811925631 57 0.958395593538905 0.083208812922189 0.0416044064610945 58 0.965934010875446 0.0681319782491072 0.0340659891245536 59 0.9900362514612 0.0199274970776013 0.00996374853880065 60 0.990481252489847 0.0190374950203050 0.00951874751015252 61 0.988889660178166 0.0222206796436684 0.0111103398218342 62 0.985519346791271 0.0289613064174578 0.0144806532087289 63 0.969562793741694 0.0608744125166128 0.0304372062583064 64 0.967464224320403 0.0650715513591937 0.0325357756795968 65 0.993669934675754 0.0126601306484916 0.00633006532424582 66 0.995095231757366 0.00980953648526808 0.00490476824263404 67 0.976931150417696 0.0461376991646077 0.0230688495823038 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0158730158730159 NOK 5% type I error level 21 0.333333333333333 NOK 10% type I error level 37 0.587301587301587 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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