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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 15:29:24 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t1227824995ecapjt64xvjptwe.htm/, Retrieved Thu, 27 Nov 2008 22:30:05 +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/t1227824995ecapjt64xvjptwe.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 «

123,9 0 124,9 0 112,7 0 121,9 0 100,6 0 104,3 0 120,4 0 107,5 0 102,9 0 125,6 0 107,5 0 108,8 0 128,4 0 121,1 0 119,5 0 128,7 0 108,7 0 105,5 0 119,8 0 111,3 0 110,6 0 120,1 0 97,5 0 107,7 0 127,3 0 117,2 0 119,8 0 116,2 0 111 0 112,4 0 130,6 0 109,1 0 118,8 0 123,9 0 101,6 0 112,8 0 128 0 129,6 0 125,8 0 119,5 0 115,7 0 113,6 0 129,7 0 112 0 116,8 0 127 1 112,1 1 114,2 1 121,1 1 131,6 1 125 1 120,4 1 117,7 1 117,5 1 120,6 1 127,5 1 112,3 1 124,5 1 115,2 1 105,4 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 Consumptieindex[t] = + 104.086878306878 -0.638624338624347Dummy[t] + 17.6498941798941M1[t] + 16.6246560846561M2[t] + 12.139417989418M3[t] + 12.7541798941799M4[t] + 1.98894179894179M5[t] + 1.7437037037037M6[t] + 15.1384656084656M7[t] + 4.23322751322751M8[t] + 2.86798941798940M9[t] + 14.7704761904762M10[t] -2.83476190476191M11[t] + 0.165238095238096t + 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) 104.086878306878 2.633884 39.5184 0 0 Dummy -0.638624338624347 2.246184 -0.2843 0.777445 0.388722 M1 17.6498941798941 3.114935 5.6662 1e-06 0 M2 16.6246560846561 3.110376 5.3449 3e-06 1e-06 M3 12.139417989418 3.106826 3.9073 0.000304 0.000152 M4 12.7541798941799 3.104288 4.1086 0.000162 8.1e-05 M5 1.98894179894179 3.102763 0.641 0.524689 0.262344 M6 1.7437037037037 3.102255 0.5621 0.576793 0.288396 M7 15.1384656084656 3.102763 4.879 1.3e-05 7e-06 M8 4.23322751322751 3.104288 1.3637 0.179308 0.089654 M9 2.86798941798940 3.106826 0.9231 0.360759 0.180379 M10 14.7704761904762 3.090034 4.78 1.8e-05 9e-06 M11 -2.83476190476191 3.088503 -0.9178 0.363488 0.181744 t 0.165238095238096 0.056155 2.9426 0.005085 0.002543 Multiple Linear Regression - Regression Statistics Multiple R 0.860622563195654 R-squared 0.740671196281457 Adjusted R-squared 0.66738262131752 F-TEST (value) 10.1062300180612 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.5097584293855e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.88254403512026 Sum Squared Residuals 1096.60486772487 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 123.9 121.902010582011 1.99798941798925 2 124.9 121.042010582011 3.85798941798943 3 112.7 116.722010582011 -4.02201058201055 4 121.9 117.502010582011 4.39798941798944 5 100.6 106.902010582011 -6.3020105820106 6 104.3 106.822010582011 -2.52201058201058 7 120.4 120.382010582011 0.0179894179894405 8 107.5 109.642010582011 -2.14201058201057 9 102.9 108.442010582011 -5.54201058201058 10 125.6 120.509735449735 5.09026455026455 11 107.5 103.069735449735 4.43026455026456 12 108.8 106.069735449735 2.73026455026455 13 128.4 123.884867724868 4.51513227513233 14 121.1 123.024867724868 -1.92486772486772 15 119.5 118.704867724868 0.795132275132277 16 128.7 119.484867724868 9.21513227513227 17 108.7 108.884867724868 -0.184867724867715 18 105.5 108.804867724868 -3.30486772486772 19 119.8 122.364867724868 -2.56486772486772 20 111.3 111.624867724868 -0.324867724867722 21 110.6 110.424867724868 0.175132275132281 22 120.1 122.492592592593 -2.39259259259259 23 97.5 105.052592592593 -7.55259259259259 24 107.7 108.052592592593 -0.352592592592593 25 127.3 125.867724867725 1.43227513227517 26 117.2 125.007724867725 -7.80772486772487 27 119.8 120.687724867725 -0.887724867724875 28 116.2 121.467724867725 -5.26772486772487 29 111 110.867724867725 0.132275132275134 30 112.4 110.787724867725 1.61227513227514 31 130.6 124.347724867725 6.25227513227513 32 109.1 113.607724867725 -4.50772486772487 33 118.8 112.407724867725 6.39227513227513 34 123.9 124.475449735450 -0.575449735449732 35 101.6 107.035449735450 -5.43544973544975 36 112.8 110.035449735450 2.76455026455025 37 128 127.850582010582 0.149417989418024 38 129.6 126.990582010582 2.60941798941798 39 125.8 122.670582010582 3.12941798941798 40 119.5 123.450582010582 -3.95058201058202 41 115.7 112.850582010582 2.84941798941799 42 113.6 112.770582010582 0.829417989417978 43 129.7 126.330582010582 3.36941798941797 44 112 115.590582010582 -3.59058201058202 45 116.8 114.390582010582 2.40941798941799 46 127 125.819682539683 1.18031746031746 47 112.1 108.379682539683 3.72031746031746 48 114.2 111.379682539683 2.82031746031746 49 121.1 129.194814814815 -8.09481481481478 50 131.6 128.334814814815 3.26518518518518 51 125 124.014814814815 0.98518518518518 52 120.4 124.794814814815 -4.39481481481481 53 117.7 114.194814814815 3.50518518518519 54 117.5 114.114814814815 3.38518518518518 55 120.6 127.674814814815 -7.07481481481482 56 127.5 116.934814814815 10.5651851851852 57 112.3 115.734814814815 -3.43481481481481 58 124.5 127.802539682540 -3.30253968253969 59 115.2 110.362539682540 4.83746031746032 60 105.4 113.362539682540 -7.96253968253969 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.429297244636762 0.858594489273523 0.570702755363238 18 0.299003809521609 0.598007619043217 0.700996190478391 19 0.226602971920378 0.453205943840755 0.773397028079622 20 0.129194062044644 0.258388124089289 0.870805937955356 21 0.0936843297875747 0.187368659575149 0.906315670212425 22 0.156684814731713 0.313369629463425 0.843315185268287 23 0.373626111366593 0.747252222733185 0.626373888633407 24 0.281908374043036 0.563816748086073 0.718091625956964 25 0.213415450012391 0.426830900024783 0.786584549987609 26 0.312177726952651 0.624355453905301 0.68782227304735 27 0.250067640149742 0.500135280299484 0.749932359850258 28 0.320802451864492 0.641604903728984 0.679197548135508 29 0.309329343597055 0.61865868719411 0.690670656402945 30 0.287759020918872 0.575518041837744 0.712240979081128 31 0.332644612496077 0.665289224992154 0.667355387503923 32 0.384901973284336 0.769803946568673 0.615098026715664 33 0.413883664441752 0.827767328883504 0.586116335558248 34 0.319350377352250 0.638700754704499 0.68064962264775 35 0.480044246979297 0.960088493958593 0.519955753020703 36 0.383587235658304 0.767174471316608 0.616412764341696 37 0.37007754695779 0.74015509391558 0.62992245304221 38 0.29305415014155 0.5861083002831 0.70694584985845 39 0.220635709356417 0.441271418712833 0.779364290643583 40 0.164813090980795 0.32962618196159 0.835186909019205 41 0.107465982960651 0.214931965921301 0.89253401703935 42 0.0608914231004689 0.121782846200938 0.939108576899531 43 0.0979466985641583 0.195893397128317 0.902053301435842 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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