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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: Thu, 27 Nov 2008 11:58:16 -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/27/t12278123956xtg7kre9evp0jz.htm/, Retrieved Thu, 27 Nov 2008 18:59:56 +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/27/t12278123956xtg7kre9evp0jz.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)

Feedback Forum:

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

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

100.30 0 100.60 0 100.00 0 100.10 0 100.20 0 100.00 0 100.10 0 100.10 0 100.10 0 100.50 0 100.50 0 100.50 0 96.30 1 96.30 1 96.80 1 96.80 1 96.90 1 96.80 1 96.80 1 96.80 1 96.80 1 97.00 1 97.00 1 97.00 1 96.80 1 96.90 1 97.20 1 97.30 1 97.30 1 97.20 1 97.30 1 97.30 1 97.30 1 97.30 1 97.30 1 97.30 1 98.10 1 96.80 1 96.80 1 96.80 1 96.80 1 96.80 1 96.80 1 96.80 1 96.80 1 96.80 1 96.80 1 96.80 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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation x[t] = + 100.297916666667 -3.41944444444446d[t] + 0.0361111111111511M1[t] -0.194444444444445M2[t] -0.15M3[t] -0.105555555555558M4[t] -0.0611111111111095M5[t] -0.166666666666666M6[t] -0.122222222222225M7[t] -0.127777777777780M8[t] -0.133333333333336M9[t] + 0.0111111111111109M10[t] + 0.00555555555555547M11[t] + 0.00555555555555548t + 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) 100.297916666667 0.198013 506.5206 0 0 d -3.41944444444446 0.175364 -19.4992 0 0 M1 0.0361111111111511 0.243373 0.1484 0.882921 0.441461 M2 -0.194444444444445 0.241987 -0.8035 0.427249 0.213625 M3 -0.15 0.240726 -0.6231 0.537367 0.268683 M4 -0.105555555555558 0.239592 -0.4406 0.662318 0.331159 M5 -0.0611111111111095 0.238588 -0.2561 0.799388 0.399694 M6 -0.166666666666666 0.237713 -0.7011 0.487996 0.243998 M7 -0.122222222222225 0.236971 -0.5158 0.609354 0.304677 M8 -0.127777777777780 0.236362 -0.5406 0.592306 0.296153 M9 -0.133333333333336 0.235887 -0.5652 0.57562 0.28781 M10 0.0111111111111109 0.235547 0.0472 0.962653 0.481326 M11 0.00555555555555547 0.235343 0.0236 0.981305 0.490652 t 0.00555555555555548 0.00566 0.9816 0.333243 0.166621 Multiple Linear Regression - Regression Statistics Multiple R 0.981263802119858 R-squared 0.96287864935072 Adjusted R-squared 0.948685191749525 F-TEST (value) 67.8396114890038 F-TEST (DF numerator) 13 F-TEST (DF denominator) 34 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.332729232004140 Sum Squared Residuals 3.76409722222221 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100.3 100.339583333333 -0.0395833333332142 2 100.6 100.114583333333 0.485416666666652 3 100 100.164583333333 -0.164583333333343 4 100.1 100.214583333333 -0.114583333333346 5 100.2 100.264583333333 -0.0645833333333415 6 100 100.164583333333 -0.164583333333343 7 100.1 100.214583333333 -0.114583333333346 8 100.1 100.214583333333 -0.114583333333346 9 100.1 100.214583333333 -0.114583333333346 10 100.5 100.364583333333 0.135416666666658 11 100.5 100.364583333333 0.135416666666658 12 100.5 100.364583333333 0.135416666666658 13 96.3 96.9868055555556 -0.686805555555595 14 96.3 96.7618055555556 -0.461805555555554 15 96.8 96.8118055555556 -0.0118055555555551 16 96.8 96.8618055555555 -0.0618055555555523 17 96.9 96.9118055555556 -0.0118055555555480 18 96.8 96.8118055555556 -0.0118055555555551 19 96.8 96.8618055555555 -0.0618055555555523 20 96.8 96.8618055555555 -0.0618055555555523 21 96.8 96.8618055555555 -0.0618055555555523 22 97 97.0118055555556 -0.0118055555555516 23 97 97.0118055555556 -0.0118055555555517 24 97 97.0118055555556 -0.0118055555555516 25 96.8 97.0534722222223 -0.253472222222261 26 96.9 96.8284722222222 0.0715277777777883 27 97.2 96.8784722222222 0.321527777777785 28 97.3 96.9284722222222 0.371527777777782 29 97.3 96.9784722222222 0.321527777777778 30 97.2 96.8784722222222 0.321527777777785 31 97.3 96.9284722222222 0.371527777777782 32 97.3 96.9284722222222 0.371527777777782 33 97.3 96.9284722222222 0.371527777777782 34 97.3 97.0784722222222 0.22152777777778 35 97.3 97.0784722222222 0.22152777777778 36 97.3 97.0784722222222 0.22152777777778 37 98.1 97.120138888889 0.97986111111107 38 96.8 96.8951388888889 -0.095138888888886 39 96.8 96.9451388888889 -0.145138888888887 40 96.8 96.9951388888889 -0.195138888888884 41 96.8 97.0451388888889 -0.245138888888888 42 96.8 96.9451388888889 -0.145138888888887 43 96.8 96.9951388888889 -0.195138888888884 44 96.8 96.9951388888889 -0.195138888888884 45 96.8 96.9951388888889 -0.195138888888884 46 96.8 97.1451388888889 -0.345138888888886 47 96.8 97.1451388888889 -0.345138888888886 48 96.8 97.1451388888889 -0.345138888888886 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.696340849191334 0.607318301617332 0.303659150808666 18 0.604557946263308 0.790884107473384 0.395442053736692 19 0.488730849848715 0.97746169969743 0.511269150151285 20 0.385294080835093 0.770588161670187 0.614705919164907 21 0.302958581320406 0.605917162640812 0.697041418679594 22 0.208007442039671 0.416014884079342 0.791992557960329 23 0.140729631755651 0.281459263511303 0.859270368244349 24 0.0993196783824367 0.198639356764873 0.900680321617563 25 0.996581364162082 0.00683727167583626 0.00341863583791813 26 0.999997075970544 5.8480589121988e-06 2.9240294560994e-06 27 0.99999766313758 4.67372483799206e-06 2.33686241899603e-06 28 0.999981584150046 3.68316999080638e-05 1.84158499540319e-05 29 0.999847061509798 0.000305876980403075 0.000152938490201538 30 1 5.26779043697933e-53 2.63389521848966e-53 31 1 2.42326766016825e-41 1.21163383008413e-41 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.466666666666667 NOK 5% type I error level 7 0.466666666666667 NOK 10% type I error level 7 0.466666666666667 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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