*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Fri, 24 Dec 2010 09:51:58 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/24/t1293184186082vqsd65z3mox8.htm/, Retrieved Fri, 24 Dec 2010 10:49:57 +0100

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/2010/Dec/24/t1293184186082vqsd65z3mox8.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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172.69 104.31 172.98 103.88 172.98 103.88 172.89 103.86 173.38 103.89 173.20 103.98 173.24 103.98 172.86 104.29 172.86 104.29 172.74 104.24 172.28 103.98 171.05 103.54 171.07 103.44 171.07 103.32 171.07 103.30 171.11 103.26 170.72 103.14 170.49 103.11 170.48 102.91 170.48 103.23 170.48 103.23 170.57 103.14 170.39 102.91 170.04 102.42 169.67 102.10 169.57 102.07 169.57 102.06 169.53 101.98 169.24 101.83 169.29 101.75 169.21 101.56 168.58 101.66 168.58 101.65 168.55 101.61 168.46 101.52 167.39 101.31 167.16 101.19 167.16 101.11 167.16 101.10 167.17 101.07 166.52 100.98 166.35 100.93 166.19 100.92 166.19 101.02 166.19 101.01 166.07 100.97 166.64 100.89 166.26 100.62 166.44 100.53 166.27 100.48 166.27 100.48 166.30 100.47 165.97 100.52 164.58 100.49 164.28 100.47 163.93 100.44

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Gemconsprijsblazers[t] = -31.5170225327134 + 1.96368138479357consumptieindexkleding[t] + 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) -31.5170225327134 6.720968 -4.6894 1.9e-05 1e-05 consumptieindexkleding 1.96368138479357 0.065768 29.8579 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.971023618522707 R-squared 0.942886867728931 Adjusted R-squared 0.94182921713132 F-TEST (value) 891.491830910392 F-TEST (DF numerator) 1 F-TEST (DF denominator) 54 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.642161673218539 Sum Squared Residuals 22.268067185745 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 172.69 173.314582715104 -0.62458271510448 2 172.98 172.470199719643 0.509800280357203 3 172.98 172.470199719643 0.509800280357196 4 172.89 172.430926091947 0.459073908053057 5 173.38 172.489836533491 0.890163466509256 6 173.2 172.666567858122 0.533432141877822 7 173.24 172.666567858122 0.573432141877842 8 172.86 173.275309087408 -0.415309087408165 9 172.86 173.275309087408 -0.415309087408165 10 172.74 173.177125018168 -0.437125018168468 11 172.28 172.666567858122 -0.386567858122166 12 171.05 171.802548048813 -0.752548048812989 13 171.07 171.606179910334 -0.536179910333634 14 171.07 171.370538144158 -0.300538144158397 15 171.07 171.331264516463 -0.261264516462533 16 171.11 171.252717261071 -0.142717261070785 17 170.72 171.017075494896 -0.297075494895562 18 170.49 170.958165053352 -0.468165053351743 19 170.48 170.565428776393 -0.0854287763930428 20 170.48 171.193806819527 -0.713806819527 21 170.48 171.193806819527 -0.713806819527 22 170.57 171.017075494896 -0.447075494895568 23 170.39 170.565428776393 -0.175428776393046 24 170.04 169.603224897844 0.436775102155799 25 169.67 168.974846854710 0.695153145289751 26 169.57 168.915936413166 0.654063586833566 27 169.57 168.896299599318 0.673700400681484 28 169.53 168.739205088535 0.790794911464974 29 169.24 168.444652880816 0.795347119184029 30 169.29 168.287558370032 1.00244162996749 31 169.21 167.914458906922 1.29554109307828 32 168.58 168.110827045401 0.469172954598943 33 168.58 168.091190231553 0.48880976844686 34 168.55 168.012642976161 0.537357023838615 35 168.46 167.83591165153 0.624088348470039 36 167.39 167.423538560723 -0.0335385607233452 37 167.16 167.187896794548 -0.0278967945480979 38 167.16 167.030802283765 0.129197716235385 39 167.16 167.011165469917 0.148834530083330 40 167.17 166.952255028373 0.217744971627130 41 166.52 166.775523703741 -0.255523703741447 42 166.35 166.677339634502 -0.327339634501789 43 166.19 166.657702820654 -0.46770282065384 44 166.19 166.854070959133 -0.664070959133187 45 166.19 166.834434145285 -0.644434145285268 46 166.07 166.755886889894 -0.685886889893518 47 166.64 166.59879237911 0.0412076208899576 48 166.26 166.068598405216 0.191401594784218 49 166.44 165.891867080584 0.548132919415653 50 166.27 165.793683011345 0.476316988655339 51 166.27 165.793683011345 0.476316988655339 52 166.3 165.774046197497 0.525953802503285 53 165.97 165.872230266736 0.0977697332635998 54 164.58 165.813319825193 -1.23331982519258 55 164.28 165.774046197497 -1.49404619749672 56 163.93 165.715135755953 -1.78513575595291 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0555280254535018 0.111056050907004 0.944471974546498 6 0.0256417491195943 0.0512834982391887 0.974358250880406 7 0.0126649377231174 0.0253298754462349 0.987335062276883 8 0.00382055576684765 0.0076411115336953 0.996179444233152 9 0.00106029476800363 0.00212058953600726 0.998939705231996 10 0.000338240559150095 0.000676481118300191 0.99966175944085 11 0.00666339201267776 0.0133267840253555 0.993336607987322 12 0.335351702412128 0.670703404824256 0.664648297587872 13 0.382730134741703 0.765460269483407 0.617269865258297 14 0.317763426407296 0.635526852814592 0.682236573592704 15 0.247402972213249 0.494805944426497 0.752597027786751 16 0.180941393196704 0.361882786393409 0.819058606803296 17 0.133521808572217 0.267043617144434 0.866478191427783 18 0.106070812717342 0.212141625434684 0.893929187282658 19 0.073794329862143 0.147588659724286 0.926205670137857 20 0.0838875100998753 0.167775020199751 0.916112489900125 21 0.110463380152671 0.220926760305343 0.889536619847328 22 0.134967324208931 0.269934648417862 0.865032675791069 23 0.175216787810136 0.350433575620273 0.824783212189864 24 0.22445690320819 0.44891380641638 0.77554309679181 25 0.253834977779599 0.507669955559198 0.746165022220401 26 0.23547769277782 0.47095538555564 0.76452230722218 27 0.204917301093638 0.409834602187277 0.795082698906362 28 0.174177365602480 0.348354731204960 0.82582263439752 29 0.138606954712146 0.277213909424292 0.861393045287854 30 0.121832643899561 0.243665287799122 0.87816735610044 31 0.157097810543333 0.314195621086666 0.842902189456667 32 0.117377244897597 0.234754489795195 0.882622755102403 33 0.0852758354652797 0.170551670930559 0.91472416453472 34 0.0618642808526044 0.123728561705209 0.938135719147396 35 0.0497271409344455 0.0994542818688911 0.950272859065554 36 0.0465194933591641 0.0930389867183282 0.953480506640836 37 0.0407365339555444 0.0814730679110888 0.959263466044456 38 0.0320681775451807 0.0641363550903613 0.96793182245482 39 0.0249059357241108 0.0498118714482216 0.97509406427589 40 0.0204113069114104 0.0408226138228209 0.97958869308859 41 0.017670683998665 0.03534136799733 0.982329316001335 42 0.0147000831866726 0.0294001663733452 0.985299916813327 43 0.0124852300359756 0.0249704600719513 0.987514769964024 44 0.0118211542797414 0.0236423085594829 0.988178845720258 45 0.0104141331222867 0.0208282662445735 0.989585866877713 46 0.0127932510071743 0.0255865020143486 0.987206748992826 47 0.014721713128344 0.029443426256688 0.985278286871656 48 0.0198125215394093 0.0396250430788186 0.98018747846059 49 0.00991879744339177 0.0198375948867835 0.990081202556608 50 0.0117479239808080 0.0234958479616159 0.988252076019192 51 0.0228626589996605 0.045725317999321 0.97713734100034 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.0638297872340425 NOK 5% type I error level 18 0.382978723404255 NOK 10% type I error level 23 0.489361702127660 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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