*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, 20 Nov 2009 08:02:23 -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/20/t1258729488t2ui4xyxnb0z3if.htm/, Retrieved Fri, 20 Nov 2009 16:05:00 +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/20/t1258729488t2ui4xyxnb0z3if.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 «

20366 0 22782 0 19169 0 13807 0 29743 0 25591 0 29096 0 26482 0 22405 0 27044 0 17970 0 18730 0 19684 0 19785 0 18479 0 10698 0 31956 0 29506 0 34506 0 27165 0 26736 0 23691 0 18157 0 17328 0 18205 0 20995 0 17382 0 9367 0 31124 0 26551 0 30651 0 25859 0 25100 0 25778 0 20418 0 18688 0 20424 0 24776 0 19814 0 12738 0 31566 0 30111 0 30019 0 31934 1 25826 1 26835 1 20205 1 17789 1 20520 1 22518 1 15572 1 11509 1 25447 1 24090 1 27786 1 26195 1 20516 1 22759 1 19028 1 16971 1 20036 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 Y[t] = + 18279.6417582418 -946.104395604395X[t] + 1908.22637362637M1[t] + 4080.77912087912M2[t] -7.22087912088476M3[t] -6466.62087912088M4[t] + 11876.7791208791M5[t] + 9079.37912087912M6[t] + 12321.1791208791M7[t] + 9625.8M8[t] + 6215.4M9[t] + 7320.2M10[t] + 1254.40000000000M11[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) 18279.6417582418 906.255645 20.1705 0 0 X -946.104395604395 563.482576 -1.679 0.099645 0.049823 M1 1908.22637362637 1189.112908 1.6047 0.11511 0.057555 M2 4080.77912087912 1246.473047 3.2739 0.001972 0.000986 M3 -7.22087912088476 1246.473047 -0.0058 0.995402 0.497701 M4 -6466.62087912088 1246.473047 -5.1879 4e-06 2e-06 M5 11876.7791208791 1246.473047 9.5283 0 0 M6 9079.37912087912 1246.473047 7.2841 0 0 M7 12321.1791208791 1246.473047 9.8848 0 0 M8 9625.8 1241.368017 7.7542 0 0 M9 6215.4 1241.368017 5.0069 8e-06 4e-06 M10 7320.2 1241.368017 5.8969 0 0 M11 1254.40000000000 1241.368017 1.0105 0.317324 0.158662 Multiple Linear Regression - Regression Statistics Multiple R 0.951725983616065 R-squared 0.905782347889966 Adjusted R-squared 0.882227934862457 F-TEST (value) 38.4548894014946 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1962.77517338917 Sum Squared Residuals 184919346.301099 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 20366 20187.8681318682 178.131868131848 2 22782 22360.4208791209 421.579120879116 3 19169 18272.4208791209 896.579120879119 4 13807 11813.0208791209 1993.97912087913 5 29743 30156.4208791209 -413.420879120878 6 25591 27359.0208791209 -1768.02087912088 7 29096 30600.8208791209 -1504.82087912089 8 26482 27905.4417582418 -1423.44175824175 9 22405 24495.0417582418 -2090.04175824175 10 27044 25599.8417582418 1444.15824175824 11 17970 19534.0417582418 -1564.04175824175 12 18730 18279.6417582418 450.358241758241 13 19684 20187.8681318681 -503.868131868128 14 19785 22360.4208791209 -2575.42087912088 15 18479 18272.4208791209 206.579120879122 16 10698 11813.0208791209 -1115.02087912088 17 31956 30156.4208791209 1799.57912087912 18 29506 27359.0208791209 2146.97912087912 19 34506 30600.8208791209 3905.17912087912 20 27165 27905.4417582418 -740.441758241761 21 26736 24495.0417582418 2240.95824175824 22 23691 25599.8417582418 -1908.84175824176 23 18157 19534.0417582418 -1377.04175824176 24 17328 18279.6417582418 -951.641758241757 25 18205 20187.8681318681 -1982.86813186813 26 20995 22360.4208791209 -1365.42087912088 27 17382 18272.4208791209 -890.420879120877 28 9367 11813.0208791209 -2446.02087912088 29 31124 30156.4208791209 967.579120879122 30 26551 27359.0208791209 -808.02087912088 31 30651 30600.8208791209 50.1791208791221 32 25859 27905.4417582418 -2046.44175824176 33 25100 24495.0417582418 604.95824175824 34 25778 25599.8417582418 178.158241758242 35 20418 19534.0417582418 883.95824175824 36 18688 18279.6417582418 408.358241758243 37 20424 20187.8681318681 236.131868131871 38 24776 22360.4208791209 2415.57912087912 39 19814 18272.4208791209 1541.57912087912 40 12738 11813.0208791209 924.979120879121 41 31566 30156.4208791209 1409.57912087912 42 30111 27359.0208791209 2751.97912087912 43 30019 30600.8208791209 -581.820879120878 44 31934 26959.3373626374 4974.66263736264 45 25826 23548.9373626374 2277.06263736263 46 26835 24653.7373626374 2181.26263736264 47 20205 18587.9373626374 1617.06263736263 48 17789 17333.5373626374 455.462637362638 49 20520 19241.7637362637 1278.23626373627 50 22518 21414.3164835165 1103.68351648352 51 15572 17326.3164835165 -1754.31648351648 52 11509 10866.9164835165 642.083516483515 53 25447 29210.3164835165 -3763.31648351649 54 24090 26412.9164835165 -2322.91648351648 55 27786 29654.7164835165 -1868.71648351648 56 26195 26959.3373626374 -764.337362637366 57 20516 23548.9373626374 -3032.93736263737 58 22759 24653.7373626374 -1894.73736263736 59 19028 18587.9373626374 440.062637362636 60 16971 17333.5373626374 -362.537362637362 61 20036 19241.7637362637 794.236263736267 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.444646728861701 0.889293457723403 0.555353271138299 17 0.373734125999532 0.747468251999064 0.626265874000468 18 0.473765815152593 0.947531630305186 0.526234184847407 19 0.729445454765014 0.541109090469971 0.270554545234986 20 0.629623140223638 0.740753719552724 0.370376859776362 21 0.692604734125284 0.614790531749432 0.307395265874716 22 0.68811130452436 0.623777390951279 0.311888695475640 23 0.615387884392322 0.769224231215356 0.384612115607678 24 0.533973162300977 0.932053675398046 0.466026837699023 25 0.512736578420784 0.974526843158432 0.487263421579216 26 0.473233939862382 0.946467879724765 0.526766060137618 27 0.40095321850008 0.80190643700016 0.59904678149992 28 0.45731230031979 0.91462460063958 0.54268769968021 29 0.380376314153221 0.760752628306443 0.619623685846779 30 0.31068454542381 0.62136909084762 0.68931545457619 31 0.242797239427937 0.485594478855874 0.757202760572063 32 0.344424389811744 0.688848779623487 0.655575610188256 33 0.262124225735962 0.524248451471925 0.737875774264038 34 0.201962132053665 0.40392426410733 0.798037867946335 35 0.186802908789842 0.373605817579684 0.813197091210158 36 0.141507782374813 0.283015564749626 0.858492217625187 37 0.146402066498895 0.292804132997789 0.853597933501105 38 0.159153131255997 0.318306262511993 0.840846868744003 39 0.110716339025206 0.221432678050412 0.889283660974794 40 0.102797706666297 0.205595413332594 0.897202293333703 41 0.0684697624078916 0.136939524815783 0.931530237592108 42 0.0683108443845984 0.136621688769197 0.931689155615402 43 0.0381611037632188 0.0763222075264377 0.961838896236781 44 0.108675702773237 0.217351405546474 0.891324297226763 45 0.380341107985626 0.760682215971251 0.619658892014374 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 1 0.0333333333333333 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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