Paper - Multiple Regression SPAREN 3

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R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 05 Dec 2008 10:06:35 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/05/t1228496884zm08crpl3iqmf90.htm/, Retrieved Fri, 05 Dec 2008 17:08:04 +0000

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/2008/Dec/05/t1228496884zm08crpl3iqmf90.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

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Dataseries X:

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0 0 9 0 1 0 4 0 6 0 21 0 24 0 23 0 22 0 21 0 20 0 16 0 18 0 18 0 24 0 16 0 15 0 24 0 18 0 15 0 4 0 3 0 6 0 5 0 12 0 12 0 12 0 14 0 12 0 17 0 12 0 20 0 21 0 15 0 22 0 19 0 19 0 26 0 25 0 19 0 20 0 30 0 31 0 35 0 33 0 26 0 25 0 17 0 14 0 8 0 12 0 7 0 4 0 10 0 8 0 16 1 14 1 20 1 9 1 10 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Spa[t] = + 11.2673684210526 -7.65263157894737Val[t] -1.21122807017544M1[t] + 0.687017543859648M2[t] + 0.785263157894733M3[t] -2.11649122807018M4[t] -2.81824561403509M5[t] + 6.08M6[t] + 4.17824561403508M7[t] + 8.80701754385965M8[t] + 5.70526315789473M9[t] + 3.80350877192982M10[t] + 3.10175438596491M11[t] + 0.101754385964912t + 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) 11.2673684210526 4.208751 2.6771 0.010258 0.005129 Val -7.65263157894737 4.503635 -1.6992 0.096033 0.048017 M1 -1.21122807017544 5.143066 -0.2355 0.814861 0.40743 M2 0.687017543859648 5.138956 0.1337 0.894232 0.447116 M3 0.785263157894733 5.135757 0.1529 0.879145 0.439572 M4 -2.11649122807018 5.133471 -0.4123 0.68204 0.34102 M5 -2.81824561403509 5.132099 -0.5491 0.585565 0.292782 M6 6.08 5.131642 1.1848 0.24218 0.12109 M7 4.17824561403508 5.132099 0.8141 0.41976 0.20988 M8 8.80701754385965 5.076079 1.735 0.089436 0.044718 M9 5.70526315789473 5.072841 1.1247 0.266564 0.133282 M10 3.80350877192982 5.070527 0.7501 0.457002 0.228501 M11 3.10175438596491 5.069138 0.6119 0.543623 0.271812 t 0.101754385964912 0.068521 1.485 0.14436 0.07218 Multiple Linear Regression - Regression Statistics Multiple R 0.475773157308377 R-squared 0.226360097215181 Adjusted R-squared 0.00772273338468932 F-TEST (value) 1.03532211168937 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.436074132482178 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 8.01427787673871 Sum Squared Residuals 2954.51789473684 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0 10.1578947368421 -10.1578947368421 2 9 12.1578947368421 -3.1578947368421 3 1 12.3578947368421 -11.3578947368421 4 4 9.5578947368421 -5.55789473684211 5 6 8.9578947368421 -2.9578947368421 6 21 17.9578947368421 3.0421052631579 7 24 16.1578947368421 7.8421052631579 8 23 20.8884210526316 2.11157894736842 9 22 17.8884210526316 4.11157894736842 10 21 16.0884210526316 4.91157894736842 11 20 15.4884210526316 4.51157894736842 12 16 12.4884210526316 3.51157894736842 13 18 11.3789473684210 6.62105263157895 14 18 13.3789473684211 4.62105263157895 15 24 13.5789473684210 10.4210526315790 16 16 10.7789473684211 5.22105263157895 17 15 10.1789473684211 4.82105263157895 18 24 19.1789473684211 4.82105263157895 19 18 17.3789473684210 0.62105263157895 20 15 22.1094736842105 -7.10947368421053 21 4 19.1094736842105 -15.1094736842105 22 3 17.3094736842105 -14.3094736842105 23 6 16.7094736842105 -10.7094736842105 24 5 13.7094736842105 -8.70947368421052 25 12 12.6 -0.599999999999996 26 12 14.6 -2.6 27 12 14.8 -2.8 28 14 12 2 29 12 11.4 0.6 30 17 20.4 -3.4 31 12 18.6 -6.6 32 20 23.3305263157895 -3.33052631578947 33 21 20.3305263157895 0.669473684210528 34 15 18.5305263157895 -3.53052631578947 35 22 17.9305263157895 4.06947368421053 36 19 14.9305263157895 4.06947368421052 37 19 13.8210526315789 5.17894736842106 38 26 15.8210526315789 10.1789473684211 39 25 16.0210526315789 8.97894736842106 40 19 13.2210526315789 5.77894736842106 41 20 12.6210526315789 7.37894736842105 42 30 21.6210526315789 8.37894736842105 43 31 19.8210526315790 11.1789473684210 44 35 24.5515789473684 10.4484210526316 45 33 21.5515789473684 11.4484210526316 46 26 19.7515789473684 6.24842105263158 47 25 19.1515789473684 5.84842105263158 48 17 16.1515789473684 0.848421052631577 49 14 15.0421052631579 -1.04210526315789 50 8 17.0421052631579 -9.0421052631579 51 12 17.2421052631579 -5.2421052631579 52 7 14.4421052631579 -7.4421052631579 53 4 13.8421052631579 -9.8421052631579 54 10 22.8421052631579 -12.8421052631579 55 8 21.0421052631579 -13.0421052631579 56 16 18.12 -2.12 57 14 15.12 -1.12000000000000 58 20 13.32 6.68 59 9 12.72 -3.72 60 10 9.72 0.279999999999998 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.195013246227015 0.390026492454030 0.804986753772985 18 0.204478254407841 0.408956508815682 0.795521745592159 19 0.367985809931689 0.735971619863377 0.632014190068311 20 0.456401625401695 0.91280325080339 0.543598374598305 21 0.724394857622372 0.551210284755256 0.275605142377628 22 0.849225938743666 0.301548122512667 0.150774061256334 23 0.877324690971069 0.245350618057862 0.122675309028931 24 0.88197890179719 0.236042196405622 0.118021098202811 25 0.830358329822531 0.339283340354937 0.169641670177469 26 0.769985600743612 0.460028798512776 0.230014399256388 27 0.712616052703575 0.574767894592849 0.287383947296425 28 0.626615735221786 0.746768529556429 0.373384264778214 29 0.53192513142751 0.936149737144981 0.468074868572491 30 0.469793419854151 0.939586839708303 0.530206580145849 31 0.494984004976093 0.989968009952186 0.505015995023907 32 0.518688024839885 0.96262395032023 0.481311975160115 33 0.568356442700037 0.863287114599927 0.431643557299963 34 0.836356723323899 0.327286553352202 0.163643276676101 35 0.891609813817646 0.216780372364707 0.108390186182354 36 0.970885267015579 0.058229465968842 0.029114732984421 37 0.985448371140413 0.0291032577191738 0.0145516288595869 38 0.97287290229022 0.0542541954195583 0.0271270977097791 39 0.95715034285793 0.0856993142841382 0.0428496571420691 40 0.945304530642885 0.10939093871423 0.054695469357115 41 0.908666783763395 0.182666432473209 0.0913332162366046 42 0.824377084041704 0.351245831916593 0.175622915958296 43 0.682156546294123 0.635686907411754 0.317843453705877 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 1 0.037037037037037 OK 10% type I error level 4 0.148148148148148 NOK

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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