*Unverified author*

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 11:49:28 -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/t1227811878p52ye7ers7ryuti.htm/, Retrieved Thu, 27 Nov 2008 18:51:18 +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/t1227811878p52ye7ers7ryuti.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 «

99,90 0 99,80 0 99,80 0 100,30 0 99,90 0 99,90 0 100,00 0 100,10 0 100,10 0 100,20 0 100,30 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 96,90 1 97,10 1 97,10 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation x[t] = + 99.987186311787 -3.39458174904943d[t] + 0.0113445289395954M1[t] + 0.0156611744824651M2[t] + 0.0482034220532331M3[t] + 0.0607456696239968M4[t] + 0.0132879171947611M5[t] + 0.00583016476552596M6[t] + 0.0183724123362896M7[t] + 0.150914659907055M8[t] + 0.14345690747782M9[t] + 0.155999155048586M10[t] + 0.147457752429236M11[t] + 0.00745775242923516t + 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) 99.987186311787 0.155868 641.4844 0 0 d -3.39458174904943 0.147489 -23.0159 0 0 M1 0.0113445289395954 0.181756 0.0624 0.950496 0.475248 M2 0.0156611744824651 0.190796 0.0821 0.934929 0.467465 M3 0.0482034220532331 0.190508 0.253 0.801351 0.400676 M4 0.0607456696239968 0.190304 0.3192 0.750987 0.375493 M5 0.0132879171947611 0.190186 0.0699 0.944595 0.472298 M6 0.00583016476552596 0.190153 0.0307 0.97567 0.487835 M7 0.0183724123362896 0.190206 0.0966 0.923461 0.46173 M8 0.150914659907055 0.190344 0.7929 0.431848 0.215924 M9 0.14345690747782 0.190567 0.7528 0.455331 0.227666 M10 0.155999155048586 0.190876 0.8173 0.417892 0.208946 M11 0.147457752429236 0.189507 0.7781 0.440402 0.220201 t 0.00745775242923516 0.004034 1.8488 0.070777 0.035389 Multiple Linear Regression - Regression Statistics Multiple R 0.98544365620693 R-squared 0.971099199558481 Adjusted R-squared 0.963105361138487 F-TEST (value) 121.480964279878 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.299568472280454 Sum Squared Residuals 4.21783967046893 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.9 100.005988593156 -0.10598859315585 2 99.8 100.017762991128 -0.217762991128012 3 99.8 100.057762991128 -0.257762991128016 4 100.3 100.077762991128 0.222237008871985 5 99.9 100.037762991128 -0.137762991128005 6 99.9 100.037762991128 -0.137762991128005 7 100 100.057762991128 -0.05776299112801 8 100.1 100.197762991128 -0.0977629911280163 9 100.1 100.197762991128 -0.0977629911280163 10 100.2 100.217762991128 -0.0177629911280094 11 100.3 100.216679340938 0.0833206590621004 12 100.6 100.076679340938 0.523320659062098 13 100 100.095481622307 -0.0954816223067267 14 100.1 100.107256020279 -0.00725602027883717 15 100.2 100.147256020279 0.0527439797211681 16 100 100.167256020279 -0.167256020278834 17 100.1 100.127256020279 -0.0272560202788387 18 100.1 100.127256020279 -0.0272560202788388 19 100.1 100.147256020279 -0.0472560202788376 20 100.5 100.287256020279 0.212743979721167 21 100.5 100.287256020279 0.212743979721168 22 100.5 100.307256020279 0.192743979721166 23 96.3 96.9115906210393 -0.611590621039294 24 96.3 96.7715906210393 -0.471590621039293 25 96.8 96.7903929024081 0.0096070975918763 26 96.8 96.8021673003802 -0.00216730038022850 27 96.9 96.8421673003802 0.0578326996197768 28 96.8 96.8621673003802 -0.0621673003802306 29 96.8 96.8221673003802 -0.02216730038023 30 96.8 96.8221673003802 -0.02216730038023 31 96.8 96.8421673003802 -0.0421673003802289 32 97 96.9821673003802 0.0178326996197734 33 97 96.9821673003802 0.0178326996197734 34 97 97.0021673003802 -0.00216730038022829 35 96.8 97.0010836501901 -0.201083650190116 36 96.9 96.8610836501901 0.0389163498098936 37 97.2 96.879885931559 0.32011406844106 38 97.3 96.891660329531 0.408339670468949 39 97.3 96.931660329531 0.368339670468946 40 97.2 96.951660329531 0.248339670468953 41 97.3 96.911660329531 0.388339670468948 42 97.3 96.911660329531 0.388339670468948 43 97.3 96.931660329531 0.368339670468949 44 97.3 97.071660329531 0.228339670468949 45 97.3 97.071660329531 0.228339670468949 46 97.3 97.091660329531 0.208339670468947 47 98.1 97.090576679341 1.00942332065906 48 96.8 96.950576679341 -0.150576679340937 49 96.8 96.9693789607098 -0.169378960709768 50 96.8 96.9811533586819 -0.181153358681872 51 96.8 97.0211533586819 -0.221153358681876 52 96.8 97.0411533586819 -0.241153358681874 53 96.8 97.0011533586819 -0.201153358681874 54 96.8 97.0011533586819 -0.201153358681874 55 96.8 97.0211533586819 -0.221153358681873 56 96.8 97.1611533586819 -0.361153358681873 57 96.8 97.1611533586819 -0.361153358681873 58 96.8 97.1811533586819 -0.381153358681875 59 96.9 97.1800697084918 -0.280069708491751 60 97.1 97.0400697084918 0.0599302915082384 61 97.1 97.0588719898606 0.0411280101394078 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.261195547590524 0.522391095181048 0.738804452409476 18 0.132563809071366 0.265127618142732 0.867436190928634 19 0.062414563996804 0.124829127993608 0.937585436003196 20 0.0397807526148726 0.0795615052297452 0.960219247385127 21 0.0230252053209093 0.0460504106418185 0.97697479467909 22 0.0100102264010756 0.0200204528021513 0.989989773598924 23 0.0075170795192434 0.0150341590384868 0.992482920480757 24 0.0067443179747332 0.0134886359494664 0.993255682025267 25 0.0795129338152117 0.159025867630423 0.920487066184788 26 0.100989522277920 0.201979044555841 0.89901047772208 27 0.097588287916326 0.195176575832652 0.902411712083674 28 0.0649420996755953 0.129884199351191 0.935057900324405 29 0.0493878623897988 0.0987757247795976 0.950612137610201 30 0.0371466932041682 0.0742933864083364 0.962853306795832 31 0.0272752560296052 0.0545505120592104 0.972724743970395 32 0.0163134707302659 0.0326269414605318 0.983686529269734 33 0.00965088788455913 0.0193017757691183 0.99034911211544 34 0.00573796746948909 0.0114759349389782 0.99426203253051 35 0.0386127394419319 0.0772254788838639 0.961387260558068 36 0.0521442344259848 0.104288468851970 0.947855765574015 37 0.0529309025619563 0.105861805123913 0.947069097438044 38 0.0421010190491774 0.0842020380983548 0.957898980950823 39 0.0270123402752262 0.0540246805504524 0.972987659724774 40 0.0136560852018283 0.0273121704036567 0.986343914798172 41 0.00777446312941898 0.0155489262588380 0.992225536870581 42 0.00397649597364502 0.00795299194729004 0.996023504026355 43 0.00172857512185065 0.0034571502437013 0.99827142487815 44 0.000624322046479607 0.00124864409295921 0.99937567795352 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.107142857142857 NOK 5% type I error level 12 0.428571428571429 NOK 10% type I error level 19 0.678571428571429 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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