*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, 15 Dec 2009 09:03:21 -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/Dec/15/t1260893096d3pie7p4gpag3nq.htm/, Retrieved Tue, 15 Dec 2009 17:05:08 +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/Dec/15/t1260893096d3pie7p4gpag3nq.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:

» Textbox « » Textfile « » CSV «

594 0 595 0 591 0 589 0 584 0 573 0 567 0 569 0 621 0 629 0 628 0 612 0 595 0 597 0 593 0 590 0 580 0 574 0 573 0 573 0 620 0 626 0 620 0 588 0 566 0 557 0 561 0 549 0 532 0 526 0 511 0 499 0 555 0 565 0 542 0 527 0 510 0 514 0 517 0 508 0 493 0 490 0 469 0 478 0 528 0 534 0 518 1 506 1 502 1 516 1 528 1 533 1 536 1 537 1 524 1 536 1 587 1 597 1 581 1 564 1 558 1

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation WlhBe[t] = + 561.130434782609 -19.5971014492753X[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) 561.130434782609 5.940473 94.4589 0 0 X -19.5971014492753 11.979545 -1.6359 0.107189 0.053594 Multiple Linear Regression - Regression Statistics Multiple R 0.208301807925622 R-squared 0.0433896431850828 Adjusted R-squared 0.027175908323813 F-TEST (value) 2.67610415221041 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.107188900753538 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 40.2902500559395 Sum Squared Residuals 95774.9507246376 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 594 561.13043478261 32.8695652173903 2 595 561.130434782609 33.8695652173913 3 591 561.130434782609 29.8695652173913 4 589 561.130434782609 27.8695652173913 5 584 561.130434782609 22.8695652173913 6 573 561.130434782609 11.8695652173913 7 567 561.130434782609 5.86956521739133 8 569 561.130434782609 7.86956521739133 9 621 561.130434782609 59.8695652173913 10 629 561.130434782609 67.8695652173913 11 628 561.130434782609 66.8695652173913 12 612 561.130434782609 50.8695652173913 13 595 561.130434782609 33.8695652173913 14 597 561.130434782609 35.8695652173913 15 593 561.130434782609 31.8695652173913 16 590 561.130434782609 28.8695652173913 17 580 561.130434782609 18.8695652173913 18 574 561.130434782609 12.8695652173913 19 573 561.130434782609 11.8695652173913 20 573 561.130434782609 11.8695652173913 21 620 561.130434782609 58.8695652173913 22 626 561.130434782609 64.8695652173913 23 620 561.130434782609 58.8695652173913 24 588 561.130434782609 26.8695652173913 25 566 561.130434782609 4.86956521739133 26 557 561.130434782609 -4.13043478260867 27 561 561.130434782609 -0.130434782608669 28 549 561.130434782609 -12.1304347826087 29 532 561.130434782609 -29.1304347826087 30 526 561.130434782609 -35.1304347826087 31 511 561.130434782609 -50.1304347826087 32 499 561.130434782609 -62.1304347826087 33 555 561.130434782609 -6.13043478260867 34 565 561.130434782609 3.86956521739133 35 542 561.130434782609 -19.1304347826087 36 527 561.130434782609 -34.1304347826087 37 510 561.130434782609 -51.1304347826087 38 514 561.130434782609 -47.1304347826087 39 517 561.130434782609 -44.1304347826087 40 508 561.130434782609 -53.1304347826087 41 493 561.130434782609 -68.1304347826087 42 490 561.130434782609 -71.1304347826087 43 469 561.130434782609 -92.1304347826087 44 478 561.130434782609 -83.1304347826087 45 528 561.130434782609 -33.1304347826087 46 534 561.130434782609 -27.1304347826087 47 518 541.533333333333 -23.5333333333333 48 506 541.533333333333 -35.5333333333333 49 502 541.533333333333 -39.5333333333333 50 516 541.533333333333 -25.5333333333333 51 528 541.533333333333 -13.5333333333333 52 533 541.533333333333 -8.53333333333333 53 536 541.533333333333 -5.53333333333333 54 537 541.533333333333 -4.53333333333333 55 524 541.533333333333 -17.5333333333333 56 536 541.533333333333 -5.53333333333333 57 587 541.533333333333 45.4666666666667 58 597 541.533333333333 55.4666666666667 59 581 541.533333333333 39.4666666666667 60 564 541.533333333333 22.4666666666667 61 558 541.533333333333 16.4666666666667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.00261322856879795 0.0052264571375959 0.997386771431202 6 0.00465648662350058 0.00931297324700116 0.9953435133765 7 0.00503631155278504 0.0100726231055701 0.994963688447215 8 0.00261849390261454 0.00523698780522908 0.997381506097385 9 0.0125133806838428 0.0250267613676856 0.987486619316157 10 0.0338397480249393 0.0676794960498786 0.96616025197506 11 0.0516819942852665 0.103363988570533 0.948318005714734 12 0.0397127424782849 0.0794254849565697 0.960287257521715 13 0.0236962632025064 0.0473925264050128 0.976303736797494 14 0.0142303132376573 0.0284606264753146 0.985769686762343 15 0.00840317174794535 0.0168063434958907 0.991596828252055 16 0.00499087113184195 0.0099817422636839 0.995009128868158 17 0.00335873887049745 0.00671747774099489 0.996641261129503 18 0.00260879919573684 0.00521759839147369 0.997391200804263 19 0.00202834842183563 0.00405669684367125 0.997971651578164 20 0.00154021218864134 0.00308042437728267 0.998459787811359 21 0.00349493784847173 0.00698987569694346 0.996505062151528 22 0.0131925579960557 0.0263851159921113 0.986807442003944 23 0.0398103130002391 0.0796206260004781 0.96018968699976 24 0.0501546387243473 0.100309277448695 0.949845361275653 25 0.0692793591597516 0.138558718319503 0.930720640840248 26 0.104694933681323 0.209389867362646 0.895305066318677 27 0.142487199623736 0.284974399247471 0.857512800376264 28 0.207489135264876 0.414978270529752 0.792510864735124 29 0.330855802228780 0.661711604457561 0.66914419777122 30 0.458700274998114 0.917400549996227 0.541299725001886 31 0.623535070294531 0.752929859410939 0.376464929705469 32 0.778667677508568 0.442664644982864 0.221332322491432 33 0.793887881880216 0.412224236239569 0.206112118119784 34 0.848330433254147 0.303339133491705 0.151669566745853 35 0.8660453977319 0.267909204536202 0.133954602268101 36 0.876877979067981 0.246244041864038 0.123122020932019 37 0.891521273989051 0.216957452021898 0.108478726010949 38 0.894731426896045 0.210537146207910 0.105268573103955 39 0.892895555799093 0.214208888401814 0.107104444200907 40 0.890548024291618 0.218903951416764 0.109451975708382 41 0.896858439401009 0.206283121197982 0.103141560598991 42 0.900320094724097 0.199359810551807 0.0996799052759034 43 0.941244950224709 0.117510099550583 0.0587550497752915 44 0.965491714896675 0.0690165702066502 0.0345082851033251 45 0.94654561412747 0.106908771745059 0.0534543858725296 46 0.91741319985991 0.165173600280182 0.0825868001400908 47 0.891588462536243 0.216823074927513 0.108411537463757 48 0.891308205439402 0.217383589121196 0.108691794560598 49 0.914927998479665 0.170144003040670 0.0850720015203351 50 0.91357307030424 0.17285385939152 0.08642692969576 51 0.89075459350939 0.218490812981221 0.109245406490610 52 0.855084364628297 0.289831270743406 0.144915635371703 53 0.806992273425882 0.386015453148236 0.193007726574118 54 0.752528924764954 0.494942150470092 0.247471075235046 55 0.817706330464946 0.364587339070107 0.182293669535054 56 0.881314429288549 0.237371141422902 0.118685570711451 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 9 0.173076923076923 NOK 5% type I error level 15 0.288461538461538 NOK 10% type I error level 19 0.365384615384615 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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