*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, 24 Nov 2009 03:05:24 -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/24/t12590572924dmvm2ysqnxhvzk.htm/, Retrieved Tue, 24 Nov 2009 11:08:24 +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/24/t12590572924dmvm2ysqnxhvzk.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 «

103,52 0 103,5 0 103,52 0 103,53 0 103,53 0 103,53 0 103,52 0 103,54 0 103,59 0 103,59 0 103,59 0 103,59 0 103,63 0 103,74 0 103,7 0 103,72 0 103,81 0 103,8 0 104,22 0 106,91 1 107,06 1 107,17 1 107,25 1 107,28 1 107,24 1 107,23 1 107,34 1 107,34 1 107,3 1 107,24 1 107,3 1 107,32 1 107,28 1 107,33 1 107,33 1 107,33 1 107,28 1 107,28 1 107,29 1 107,29 1 107,23 1 107,24 1 107,24 1 107,2 1 107,23 1 107,2 1 107,21 1 107,24 1 107,21 1 113,89 1 114,05 1 114,05 1 114,05 1 114,05 1 115,12 1 115,68 1 116,05 1 116,18 1 116,35 1 116,44 1 117 1 117,61 1 118,17 1 118,33 1 118,33 1 118,42 1 118,5 1 118,67 1 119,09 1 119,14 1 119,23 1 119,33 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 103.708251028807 + 7.79209876543207X[t] -1.25631687242790M1[t] -0.0279835390946507M2[t] + 0.108683127572014M3[t] + 0.140349794238680M4[t] + 0.138683127572013M5[t] + 0.143683127572011M6[t] + 0.413683127572011M7[t] -0.314999999999997M8[t] -0.151666666666663M9[t] -0.0999999999999963M10[t] -0.0416666666666662M11[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) 103.708251028807 2.171404 47.7609 0 0 X 7.79209876543207 1.265432 6.1577 0 0 M1 -1.25631687242790 2.692659 -0.4666 0.642525 0.321263 M2 -0.0279835390946507 2.692659 -0.0104 0.991743 0.495872 M3 0.108683127572014 2.692659 0.0404 0.96794 0.48397 M4 0.140349794238680 2.692659 0.0521 0.958607 0.479303 M5 0.138683127572013 2.692659 0.0515 0.959098 0.479549 M6 0.143683127572011 2.692659 0.0534 0.957625 0.478812 M7 0.413683127572011 2.692659 0.1536 0.878423 0.439211 M8 -0.314999999999997 2.684387 -0.1173 0.906985 0.453493 M9 -0.151666666666663 2.684387 -0.0565 0.955135 0.477567 M10 -0.0999999999999963 2.684387 -0.0373 0.970409 0.485205 M11 -0.0416666666666662 2.684387 -0.0155 0.987668 0.493834 Multiple Linear Regression - Regression Statistics Multiple R 0.633977059741042 R-squared 0.401926912277897 Adjusted R-squared 0.280284928334419 F-TEST (value) 3.30417919247892 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 0.00106190316840671 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.64949479158511 Sum Squared Residuals 1275.45030720165 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.52 102.451934156378 1.06806584362184 2 103.5 103.680267489712 -0.180267489711939 3 103.52 103.816934156379 -0.296934156378628 4 103.53 103.848600823045 -0.318600823045288 5 103.53 103.846934156379 -0.316934156378624 6 103.53 103.851934156379 -0.321934156378616 7 103.52 104.121934156379 -0.601934156378624 8 103.54 103.393251028807 0.146748971193395 9 103.59 103.55658436214 0.0334156378600592 10 103.59 103.608251028807 -0.0182510288066077 11 103.59 103.66658436214 -0.0765843621399387 12 103.59 103.708251028807 -0.118251028806605 13 103.63 102.451934156379 1.17806584362129 14 103.74 103.680267489712 0.0597325102880376 15 103.7 103.816934156379 -0.116934156378618 16 103.72 103.848600823045 -0.128600823045290 17 103.81 103.846934156379 -0.0369341563786187 18 103.8 103.851934156379 -0.0519341563786220 19 104.22 104.121934156379 0.0980658436213797 20 106.91 111.185349794239 -4.27534979423868 21 107.06 111.348683127572 -4.28868312757201 22 107.17 111.400349794239 -4.23034979423868 23 107.25 111.458683127572 -4.20868312757201 24 107.28 111.500349794239 -4.22034979423868 25 107.24 110.244032921811 -3.00403292181079 26 107.23 111.472366255144 -4.24236625514402 27 107.34 111.609032921811 -4.26903292181069 28 107.34 111.640699588477 -4.30069958847735 29 107.3 111.639032921811 -4.33903292181069 30 107.24 111.644032921811 -4.40403292181069 31 107.3 111.914032921811 -4.61403292181069 32 107.32 111.185349794239 -3.86534979423869 33 107.28 111.348683127572 -4.06868312757201 34 107.33 111.400349794239 -4.07034979423868 35 107.33 111.458683127572 -4.12868312757201 36 107.33 111.500349794239 -4.17034979423868 37 107.28 110.244032921811 -2.96403292181078 38 107.28 111.472366255144 -4.19236625514402 39 107.29 111.609032921811 -4.31903292181069 40 107.29 111.640699588477 -4.35069958847735 41 107.23 111.639032921811 -4.40903292181069 42 107.24 111.644032921811 -4.40403292181069 43 107.24 111.914032921811 -4.67403292181069 44 107.2 111.185349794239 -3.98534979423868 45 107.23 111.348683127572 -4.11868312757201 46 107.2 111.400349794239 -4.20034979423868 47 107.21 111.458683127572 -4.24868312757202 48 107.24 111.500349794239 -4.26034979423868 49 107.21 110.244032921811 -3.03403292181079 50 113.89 111.472366255144 2.41763374485597 51 114.05 111.609032921811 2.44096707818931 52 114.05 111.640699588477 2.40930041152264 53 114.05 111.639032921811 2.41096707818931 54 114.05 111.644032921811 2.40596707818931 55 115.12 111.914032921811 3.20596707818931 56 115.68 111.185349794239 4.49465020576133 57 116.05 111.348683127572 4.70131687242798 58 116.18 111.400349794239 4.77965020576133 59 116.35 111.458683127572 4.89131687242798 60 116.44 111.500349794239 4.93965020576132 61 117 110.244032921811 6.75596707818922 62 117.61 111.472366255144 6.13763374485597 63 118.17 111.609032921811 6.56096707818931 64 118.33 111.640699588477 6.68930041152264 65 118.33 111.639032921811 6.69096707818931 66 118.42 111.644032921811 6.77596707818931 67 118.5 111.914032921811 6.58596707818931 68 118.67 111.185349794239 7.48465020576132 69 119.09 111.348683127572 7.74131687242799 70 119.14 111.400349794239 7.73965020576132 71 119.23 111.458683127572 7.771316872428 72 119.33 111.500349794239 7.82965020576132 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 3.05761553116227e-05 6.11523106232454e-05 0.999969423844688 17 1.67616289768937e-06 3.35232579537874e-06 0.999998323837102 18 8.65071151287355e-08 1.73014230257471e-07 0.999999913492885 19 4.42190766381789e-08 8.84381532763578e-08 0.999999955780923 20 1.86561742461450e-09 3.73123484922901e-09 0.999999998134383 21 7.64247020955035e-11 1.52849404191007e-10 0.999999999923575 22 3.20560846422532e-12 6.41121692845065e-12 0.999999999996794 23 1.38580969181783e-13 2.77161938363566e-13 0.999999999999861 24 5.80915115406661e-15 1.16183023081332e-14 0.999999999999994 25 2.0791217265765e-16 4.158243453153e-16 1 26 7.24435287739447e-18 1.44887057547889e-17 1 27 2.98616000440021e-19 5.97232000880043e-19 1 28 1.13290598184980e-20 2.26581196369959e-20 1 29 3.78662500913844e-22 7.57325001827689e-22 1 30 1.28099039044866e-23 2.56198078089732e-23 1 31 6.44130023183776e-25 1.28826004636755e-24 1 32 6.58627463579632e-26 1.31725492715926e-25 1 33 3.28257033663368e-27 6.56514067326736e-27 1 34 1.63406811258701e-28 3.26813622517401e-28 1 35 7.45162305307745e-30 1.49032461061549e-29 1 36 3.39437538610767e-31 6.78875077221533e-31 1 37 1.12001750893996e-32 2.24003501787992e-32 1 38 5.89001857616625e-34 1.17800371523325e-33 1 39 3.52863098029060e-35 7.05726196058119e-35 1 40 2.37896549793899e-36 4.75793099587798e-36 1 41 2.0455254055737e-37 4.0910508111474e-37 1 42 1.94376099665675e-38 3.88752199331351e-38 1 43 5.48634687005665e-39 1.09726937401133e-38 1 44 1.44965644724045e-39 2.89931289448091e-39 1 45 7.67810623754994e-40 1.53562124750999e-39 1 46 1.06083314804767e-39 2.12166629609535e-39 1 47 7.66757483720664e-39 1.53351496744133e-38 1 48 1.27426931324897e-36 2.54853862649794e-36 1 49 4.81602224676094e-34 9.63204449352188e-34 1 50 4.11740315149802e-06 8.23480630299603e-06 0.999995882596848 51 0.00252444260048059 0.00504888520096118 0.99747555739952 52 0.0328437147600731 0.0656874295201463 0.967156285239927 53 0.120597706973997 0.241195413947995 0.879402293026003 54 0.264549251456340 0.529098502912681 0.73545074854366 55 0.369243025913480 0.738486051826961 0.63075697408652 56 0.425177000433599 0.850354000867198 0.574822999566401 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 36 0.878048780487805 NOK 5% type I error level 36 0.878048780487805 NOK 10% type I error level 37 0.902439024390244 NOK

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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