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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: Mon, 24 Nov 2008 02:53:26 -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/Nov/24/t12275205157u38i0lmqtfn1d6.htm/, Retrieved Mon, 24 Nov 2008 09:55:25 +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/Nov/24/t12275205157u38i0lmqtfn1d6.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}, }

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Dataseries X:

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1.1608 0 1.1208 0 1.0883 0 1.0704 0 1.0628 0 1.0378 0 1.0353 0 1.0604 0 1.0501 0 1.0706 0 1.0338 0 1.011 0 1.0137 0 0.9834 0 0.9643 0 0.947 0 0.906 0 0.9492 0 0.9397 0 0.9041 0 0.8721 0 0.8552 0 0.8564 0 0.8973 0 0.9383 0 0.9217 0 0.9095 0 0.892 0 0.8742 0 0.8532 0 0.8607 0 0.9005 0 0.9111 0 0.9059 1 0.8883 1 0.8924 1 0.8833 1 0.87 1 0.8758 1 0.8858 1 0.917 1 0.9554 1 0.9922 1 0.9778 1 0.9808 1 0.9811 1 1.0014 1 1.0183 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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation koers[t] = + 1.09422371794872 + 0.130969230769231dummy[t] + 0.00186591880341965M1[t] -0.0163521367521368M2[t] -0.0240201923076923M3[t] -0.0278632478632479M4[t] -0.0298313034188034M5[t] -0.0140993589743589M6[t] + 0.00080758547008551M7[t] + 0.0113645299145300M8[t] + 0.0110214743589744M9[t] -0.0152138888888889M10[t] -0.0166069444444444M11[t] -0.00683194444444446t + 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) 1.09422371794872 0.038054 28.7547 0 0 dummy 0.130969230769231 0.033295 3.9336 0.000392 0.000196 M1 0.00186591880341965 0.044125 0.0423 0.966517 0.483259 M2 -0.0163521367521368 0.043998 -0.3717 0.712452 0.356226 M3 -0.0240201923076923 0.043898 -0.5472 0.587827 0.293913 M4 -0.0278632478632479 0.043827 -0.6358 0.529189 0.264594 M5 -0.0298313034188034 0.043784 -0.6813 0.500276 0.250138 M6 -0.0140993589743589 0.043769 -0.3221 0.749328 0.374664 M7 0.00080758547008551 0.043784 0.0184 0.985392 0.492696 M8 0.0113645299145300 0.043827 0.2593 0.796962 0.398481 M9 0.0110214743589744 0.043898 0.2511 0.803271 0.401635 M10 -0.0152138888888889 0.043549 -0.3494 0.728981 0.36449 M11 -0.0166069444444444 0.043506 -0.3817 0.705047 0.352523 t -0.00683194444444446 0.001118 -6.1082 1e-06 0 Multiple Linear Regression - Regression Statistics Multiple R 0.74703080051469 R-squared 0.55805501691762 Adjusted R-squared 0.389076052797886 F-TEST (value) 3.3025117642584 F-TEST (DF numerator) 13 F-TEST (DF denominator) 34 p-value 0.00256445494977298 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0615063815681336 Sum Squared Residuals 0.128623189102565 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.1608 1.08925769230769 0.0715423076923101 2 1.1208 1.06420769230769 0.0565923076923076 3 1.0883 1.04970769230769 0.0385923076923075 4 1.0704 1.03903269230769 0.0313673076923075 5 1.0628 1.03023269230769 0.0325673076923075 6 1.0378 1.03913269230769 -0.00133269230769239 7 1.0353 1.04720769230769 -0.0119076923076924 8 1.0604 1.05093269230769 0.00946730769230745 9 1.0501 1.04375769230769 0.0063423076923075 10 1.0706 1.01069038461538 0.0599096153846153 11 1.0338 1.00246538461538 0.0313346153846153 12 1.011 1.01224038461538 -0.00124038461538479 13 1.0137 1.00727435897436 0.00642564102564014 14 0.9834 0.98222435897436 0.00117564102564106 15 0.9643 0.96772435897436 -0.00342435897435896 16 0.947 0.95704935897436 -0.0100493589743590 17 0.906 0.94824935897436 -0.0422493589743590 18 0.9492 0.95714935897436 -0.00794935897435898 19 0.9397 0.96522435897436 -0.025524358974359 20 0.9041 0.96894935897436 -0.064849358974359 21 0.8721 0.96177435897436 -0.089674358974359 22 0.8552 0.928707051282051 -0.0735070512820513 23 0.8564 0.920482051282051 -0.0640820512820513 24 0.8973 0.930257051282051 -0.0329570512820512 25 0.9383 0.925291025641026 0.0130089743589736 26 0.9217 0.900241025641025 0.0214589743589744 27 0.9095 0.885741025641025 0.0237589743589745 28 0.892 0.875066025641026 0.0169339743589745 29 0.8742 0.866266025641026 0.00793397435897452 30 0.8532 0.875166025641026 -0.0219660256410256 31 0.8607 0.883241025641025 -0.0225410256410254 32 0.9005 0.886966025641025 0.0135339743589745 33 0.9111 0.879791025641025 0.0313089743589746 34 0.9059 0.977692948717949 -0.0717929487179487 35 0.8883 0.969467948717949 -0.0811679487179488 36 0.8924 0.979242948717949 -0.0868429487179488 37 0.8833 0.974276923076924 -0.0909769230769239 38 0.87 0.949226923076923 -0.079226923076923 39 0.8758 0.934726923076923 -0.058926923076923 40 0.8858 0.924051923076923 -0.038251923076923 41 0.917 0.915251923076923 0.00174807692307704 42 0.9554 0.924151923076923 0.031248076923077 43 0.9922 0.932226923076923 0.059973076923077 44 0.9778 0.935951923076923 0.041848076923077 45 0.9808 0.928776923076923 0.052023076923077 46 0.9811 0.895709615384615 0.0853903846153847 47 1.0014 0.887484615384615 0.113915384615385 48 1.0183 0.897259615384615 0.121040384615385 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0208919329713117 0.0417838659426233 0.979108067028688 18 0.0587698536065827 0.117539707213165 0.941230146393417 19 0.0606381440050899 0.121276288010180 0.93936185599491 20 0.0516800776201212 0.103360155240242 0.948319922379879 21 0.0642119749791326 0.128423949958265 0.935788025020867 22 0.145104429893832 0.290208859787665 0.854895570106168 23 0.100271375552046 0.200542751104092 0.899728624447954 24 0.0665400738142143 0.133080147628429 0.933459926185786 25 0.137564545795512 0.275129091591024 0.862435454204488 26 0.321508389704407 0.643016779408815 0.678491610295593 27 0.624218982832281 0.751562034335438 0.375781017167719 28 0.874037186275861 0.251925627448277 0.125962813724139 29 0.916899087038637 0.166201825922726 0.0831009129613629 30 0.833083005714168 0.333833988571664 0.166916994285832 31 0.901185349716756 0.197629300566488 0.0988146502832441 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 0.0666666666666667 NOK 10% type I error level 1 0.0666666666666667 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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