*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, 20 Nov 2009 05:58:41 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258722016z1pofjj4yg1fjys.htm/, Retrieved Fri, 20 Nov 2009 14:00:29 +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/2009/Nov/20/t1258722016z1pofjj4yg1fjys.htm/}, year = {2009}, } @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 = {2009}, 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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2.155 22.782 2.172 19.169 2.15 13.807 2.533 29.743 2.058 25.591 2.16 29.096 2.26 26.482 2.498 22.405 2.695 27.044 2.799 17.97 2.947 18.73 2.93 19.684 2.318 19.785 2.54 18.479 2.57 10.698 2.669 31.956 2.45 29.506 2.842 34.506 3.44 27.165 2.678 26.736 2.981 23.691 2.26 18.157 2.844 17.328 2.546 18.205 2.456 20.995 2.295 17.382 2.379 9.367 2.479 31.124 2.057 26.551 2.28 30.651 2.351 25.859 2.276 25.1 2.548 25.778 2.311 20.418 2.201 18.688 2.725 20.424 2.408 24.776 2.139 19.814 1.898 12.738 2.537 31.566 2.069 30.111 2.063 30.019 2.524 31.934 2.437 25.826 2.189 26.835 2.793 20.205 2.074 17.789 2.622 20.52 2.278 22.518 2.144 15.572 2.427 11.509 2.139 25.447 1.828 24.09 2.072 27.786 1.8 26.195 1.758 20.516 2.246 22.759 1.987 19.028 1.868 16.971 2.514 20.036 2.121 22.485

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 geb[t] = + 1.65564518708982 + 0.0511664330027703aut[t] -0.503409077593554M1[t] -0.322898028365517M2[t] + 0.0344064289725780M3[t] -0.71755991817044M4[t] -0.95342693848849M5[t] -0.92829828099687M6[t] -0.589103588357079M7[t] -0.560205585244431M8[t] -0.414334260425892M9[t] -0.205768911117688M10[t] -0.184785737559013M11[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) 1.65564518708982 0.462259 3.5816 0.000795 0.000397 aut 0.0511664330027703 0.022289 2.2956 0.026111 0.013056 M1 -0.503409077593554 0.196486 -2.5621 0.013599 0.0068 M2 -0.322898028365517 0.200708 -1.6088 0.11422 0.05711 M3 0.0344064289725780 0.268073 0.1283 0.89841 0.449205 M4 -0.71755991817044 0.300806 -2.3855 0.021053 0.010527 M5 -0.95342693848849 0.256982 -3.7101 0.000538 0.000269 M6 -0.92829828099687 0.308356 -3.0105 0.00415 0.002075 M7 -0.589103588357079 0.26216 -2.2471 0.029267 0.014633 M8 -0.560205585244431 0.219622 -2.5508 0.013992 0.006996 M9 -0.414334260425892 0.231532 -1.7895 0.079839 0.03992 M10 -0.205768911117688 0.19762 -1.0412 0.302984 0.151492 M11 -0.184785737559013 0.201509 -0.917 0.363723 0.181862 Multiple Linear Regression - Regression Statistics Multiple R 0.525521854351598 R-squared 0.276173219401143 Adjusted R-squared 0.0952165242514282 F-TEST (value) 1.52618403631129 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.147702482386852 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.311704757154909 Sum Squared Residuals 4.66367307038404 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2.155 2.31790978616538 -0.162909786165381 2 2.172 2.31355651295441 -0.141556512954408 3 2.15 2.39650655653165 -0.246506556531648 4 2.533 2.45992848572078 0.0730715142792209 5 2.058 2.01161843557523 0.0463815644247737 6 2.16 2.21608544074156 -0.0560854407415554 7 2.26 2.42153107751210 -0.161531077512105 8 2.498 2.24182353327246 0.256176466727542 9 2.695 2.62505594079085 0.0699440592091503 10 2.799 2.36933707703192 0.429662922968084 11 2.947 2.42920673967270 0.517793260327304 12 2.93 2.66280525431635 0.267194745683649 13 2.318 2.16456398645608 0.153436013543922 14 2.54 2.27825167418250 0.261748325817503 15 2.57 2.23743011632604 0.332569883673965 16 2.669 2.57315980195591 0.0958401980440905 17 2.45 2.21193502078107 0.238064979218928 18 2.842 2.49289584328654 0.349104156713457 19 3.44 2.456477751253 0.983522248747003 20 2.678 2.46342535460746 0.214574645392543 21 2.981 2.45349489093256 0.52750510906744 22 2.26 2.37890520000343 -0.118905200003434 23 2.844 2.35747140060281 0.486528599397188 24 2.546 2.58713009990525 -0.041130099905254 25 2.456 2.22647537038943 0.22952462961057 26 2.295 2.22212209717846 0.0728779028215425 27 2.379 2.16932759399935 0.209672406000652 28 2.479 2.53058932969760 -0.0515893296976046 29 2.057 2.06073821125789 -0.00373821125788589 30 2.28 2.29564924406086 -0.0156492440608636 31 2.351 2.38965438975138 -0.0386543897513792 32 2.276 2.37971707021492 -0.103717070214925 33 2.548 2.56027923660934 -0.0122792366093418 34 2.311 2.49459250502270 -0.183592505022697 35 2.201 2.42705774948658 -0.226057749486580 36 2.725 2.7006684147384 0.0243315852615988 37 2.408 2.41993565357290 -0.0119356535729049 38 2.139 2.34655886224119 -0.207558862241195 39 1.898 2.34180963965169 -0.443809639651687 40 2.537 2.55320489308483 -0.0162048930848292 41 2.069 2.24289071274775 -0.173890712747748 42 2.063 2.26331205840311 -0.200312058403112 43 2.524 2.70049047024321 -0.176490470243209 44 2.437 2.41686390057494 0.0201360994250641 45 2.189 2.61436215629327 -0.42536215629327 46 2.793 2.48369405479311 0.309305945206893 47 2.074 2.38105912621709 -0.307059126217089 48 2.622 2.70558039230667 -0.0835803923066674 49 2.278 2.30440184785265 -0.0264018478526492 50 2.144 2.12951085344344 0.0144891465565571 51 2.427 2.27892609349128 0.148073906508718 52 2.139 2.24011748954088 -0.101117489540877 53 1.828 1.93481761963807 -0.106817619638068 54 2.072 2.14905741350793 -0.0770574135079261 55 1.8 2.40684631124031 -0.60684631124031 56 1.758 2.14517014133022 -0.387170141330225 57 2.246 2.40580777537398 -0.159807775373978 58 1.987 2.42347116314885 -0.436471163148846 59 1.868 2.33920498402082 -0.471204984020823 60 2.514 2.68081583873333 -0.166815838733327 61 2.121 2.30271335556356 -0.181713355563558 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.208666118793157 0.417332237586314 0.791333881206843 17 0.314725067050377 0.629450134100753 0.685274932949623 18 0.391372659398083 0.782745318796166 0.608627340601917 19 0.947108291557684 0.105783416884632 0.0528917084423161 20 0.923030372195544 0.153939255608912 0.0769696278044561 21 0.958129591679992 0.0837408166400153 0.0418704083200077 22 0.95529247764134 0.0894150447173183 0.0447075223586592 23 0.985788049499015 0.0284239010019698 0.0142119505009849 24 0.978090282760748 0.043819434478503 0.0219097172392515 25 0.974607049994555 0.0507859000108897 0.0253929500054448 26 0.959306342502597 0.0813873149948064 0.0406936574974032 27 0.957049088327346 0.085901823345307 0.0429509116726535 28 0.931761096258987 0.136477807482026 0.0682389037410129 29 0.902725036407069 0.194549927185862 0.097274963592931 30 0.863316809117994 0.273366381764012 0.136683190882006 31 0.900999880807041 0.198000238385917 0.0990001191929587 32 0.871677970984543 0.256644058030914 0.128322029015457 33 0.8586322332449 0.2827355335102 0.1413677667551 34 0.82239018247418 0.355219635051639 0.177609817525820 35 0.84904597256987 0.301908054860260 0.150954027430130 36 0.790494322358092 0.419011355283816 0.209505677641908 37 0.707202873781167 0.585594252437667 0.292797126218833 38 0.665675764815987 0.668648470368026 0.334324235184013 39 0.808870804345809 0.382258391308382 0.191129195654191 40 0.722156237632776 0.555687524734448 0.277843762367224 41 0.678088219583429 0.643823560833141 0.321911780416570 42 0.615107014675854 0.769785970648292 0.384892985324146 43 0.497648620252899 0.995297240505798 0.502351379747101 44 0.398525091325621 0.797050182651242 0.601474908674379 45 0.866058898898752 0.267882202202496 0.133941101101248 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 2 0.0666666666666667 NOK 10% type I error level 7 0.233333333333333 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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