*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 08:10:36 -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/t1258729892ktduf3uzd6f3r0u.htm/, Retrieved Fri, 20 Nov 2009 16:11:44 +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/t1258729892ktduf3uzd6f3r0u.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:

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100.6 71.7 104.3 77.5 120.4 89.8 107.5 80.3 102.9 78.7 125.6 93.8 107.5 57.6 108.8 60.6 128.4 91 121.1 85.3 119.5 77.4 128.7 77.3 108.7 68.3 105.5 69.9 119.8 81.7 111.3 75.1 110.6 69.9 120.1 84 97.5 54.3 107.7 60 127.3 89.9 117.2 77 119.8 85.3 116.2 77.6 111 69.2 112.4 75.5 130.6 85.7 109.1 72.2 118.8 79.9 123.9 85.3 101.6 52.2 112.8 61.2 128 82.4 129.6 85.4 125.8 78.2 119.5 70.2 115.7 70.2 113.6 69.3 129.7 77.5 112 66.1 116.8 69 127 79.2 112.1 56.2 114.2 63.3 121.1 77.8 131.6 92 125 78.1 120.4 65.1 117.7 71.1 117.5 70.9 120.6 72 127.5 81.9 112.3 70.6 124.5 72.5 115.2 65.1 104.7 54.9 130.9 80 129.2 77.4 113.5 59.6 125.6 57.4 107.6 50.8

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 71.5670283035868 + 0.600308352328144X[t] -9.06114044400578M1[t] -10.8421961581726M2[t] -2.76076096387848M3[t] -10.0107189858019M4[t] -10.5541324307141M5[t] -4.46488841486347M6[t] -6.61278423001557M7[t] -5.74956059221821M8[t] -3.03290485901032M9[t] -4.19653415055227M10[t] -4.83803581103003M11[t] + 0.243875973404465t + 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) 71.5670283035868 7.870786 9.0927 0 0 X 0.600308352328144 0.099595 6.0275 0 0 M1 -9.06114044400578 2.371891 -3.8202 0.00039 0.000195 M2 -10.8421961581726 2.463892 -4.4004 6.2e-05 3.1e-05 M3 -2.76076096387848 2.655728 -1.0395 0.303868 0.151934 M4 -10.0107189858019 2.48833 -4.0231 0.000207 0.000104 M5 -10.5541324307141 2.467976 -4.2764 9.2e-05 4.6e-05 M6 -4.46488841486347 2.739256 -1.63 0.109794 0.054897 M7 -6.61278423001557 2.788529 -2.3714 0.021869 0.010935 M8 -5.74956059221821 2.652871 -2.1673 0.035312 0.017656 M9 -3.03290485901032 2.821722 -1.0748 0.287933 0.143966 M10 -4.19653415055227 2.79126 -1.5035 0.139412 0.069706 M11 -4.83803581103003 2.516816 -1.9223 0.060643 0.030322 t 0.243875973404465 0.034301 7.1099 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.920674569568137 R-squared 0.847641663049474 Adjusted R-squared 0.805499995382308 F-TEST (value) 20.1140987049710 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 6.4392935428259e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.86504183797615 Sum Squared Residuals 702.111775237386 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100.6 105.791872694913 -5.19187269491314 2 104.3 107.736481397654 -3.43648139765421 3 120.4 123.445585298989 -3.04558529898893 4 107.5 110.736573903353 -3.23657390335264 5 102.9 109.476543068120 -6.57654306811981 6 125.6 124.87431917753 0.725680822470073 7 107.5 101.239136981503 6.26086301849652 8 108.8 104.147161649690 4.65283835031027 9 128.4 125.357067267078 3.04293273292234 10 121.1 121.015556340670 0.0844436593302421 11 119.5 115.875494670204 3.62450532979587 12 128.7 120.897375619406 7.80262438059418 13 108.7 106.677335977851 2.02266402214880 14 105.5 106.100649600814 -0.600649600813876 15 119.8 121.509599325985 -1.70959932598456 16 111.3 110.541482152100 0.758517847900137 17 110.6 107.120341248486 3.47965875151426 18 120.1 121.917809005568 -1.81780900556770 19 97.5 102.184631099674 -4.68463109967418 20 107.7 106.713488319146 0.986511680853573 21 127.3 127.623239760370 -0.32323976037029 22 117.2 118.959508697200 -1.75950869719973 23 119.8 123.54444233445 -3.74444233445004 24 116.2 124.003979805958 -7.80397980595782 25 111 110.144125175800 0.855874824199886 26 112.4 112.388888054705 0.0111119452949567 27 130.6 126.837344416151 3.76265558384929 28 109.1 111.727099611202 -2.62709961120183 29 118.8 116.049936452621 2.75006354737925 30 123.9 125.624721544448 -1.72472154444785 31 101.6 103.850495240639 -2.25049524063866 32 112.8 110.360370022794 2.43962997720622 33 128 126.047438798763 1.95256120123722 34 129.6 126.928610537610 2.67138946239027 35 125.8 122.208764713774 3.5912352862262 36 119.5 122.488209679583 -2.98820967958314 37 115.7 113.670945208982 2.02905479101817 38 113.6 111.593487951124 2.00651204887586 39 129.7 124.841327607913 4.85867239208649 40 112 110.991730342854 1.00826965714629 41 116.8 112.433087093098 4.36691290690245 42 127 124.889352276100 2.11064772390024 43 112.1 109.178240330805 2.92175966919518 44 114.2 114.547529243536 -0.347529243536449 45 121.1 126.212532058907 -5.1125320589069 46 131.6 133.817157343829 -2.21715734382905 47 125 125.075245559395 -0.0752455593945539 48 120.4 122.353148763563 -1.95314876356317 49 117.7 117.137734406931 0.56226559306927 50 117.5 115.480492995703 2.01950700429726 51 120.6 124.466143350962 -3.86614335096229 52 127.5 123.403113990492 4.09688600950804 53 112.3 116.320092137676 -4.02009213767615 54 124.5 123.793797996355 0.706202003645235 55 115.2 117.447496347379 -2.24749634737886 56 104.7 112.431450764834 -7.73145076483362 57 130.9 130.459722114882 0.440277885117625 58 129.2 127.979167080692 1.22083291930827 59 113.5 116.896052722177 -3.39605272217747 60 125.6 120.65728613149 4.94271386850995 61 107.6 107.877986535523 -0.277986535522993 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.414562559892497 0.829125119784994 0.585437440107503 18 0.454269134784751 0.908538269569503 0.545730865215249 19 0.901532072909545 0.19693585418091 0.098467927090455 20 0.842386842828769 0.315226314342462 0.157613157171231 21 0.7576346690069 0.4847306619862 0.2423653309931 22 0.70284903355407 0.594301932891859 0.297150966445929 23 0.622875241709268 0.754249516581463 0.377124758290732 24 0.865658583752903 0.268682832494194 0.134341416247097 25 0.882252598741211 0.235494802517577 0.117747401258789 26 0.883838407086867 0.232323185826266 0.116161592913133 27 0.891717537944631 0.216564924110738 0.108282462055369 28 0.886272315261258 0.227455369477483 0.113727684738742 29 0.868689170953814 0.262621658092372 0.131310829046186 30 0.8468175722001 0.306364855599801 0.153182427799900 31 0.826431500219575 0.347136999560850 0.173568499780425 32 0.78708971155895 0.425820576882099 0.212910288441049 33 0.718131555735192 0.563736888529615 0.281868444264808 34 0.655192336545511 0.689615326908977 0.344807663454488 35 0.611196007896644 0.777607984206711 0.388803992103356 36 0.62391610125777 0.75216779748446 0.37608389874223 37 0.525485954565934 0.949028090868131 0.474514045434066 38 0.426463430303853 0.852926860607706 0.573536569696147 39 0.468711198053277 0.937422396106554 0.531288801946723 40 0.412408606673024 0.824817213346047 0.587591393326976 41 0.44692004366887 0.89384008733774 0.55307995633113 42 0.321349696463359 0.642699392926717 0.678650303536641 43 0.382502017587302 0.765004035174605 0.617497982412698 44 0.80918144799484 0.38163710401032 0.19081855200516 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 0 0 OK

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

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