Paper - Multiple Regression - Gas met Monthly dummies

*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: Mon, 22 Dec 2008 04:38:40 -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/Dec/22/t1229945959o2pj6i59hicewi0.htm/, Retrieved Mon, 22 Dec 2008 12:39:19 +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/2008/Dec/22/t1229945959o2pj6i59hicewi0.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}, }

Original text written by user:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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127.96 0 127.47 0 126.47 0 125.75 0 125.42 0 125.14 0 125.15 0 125.51 0 125.63 0 126.22 0 126.88 0 127.96 0 128.74 0 129.6 0 131.2 0 132.72 0 134.67 0 135.94 0 136.39 0 136.74 0 137.2 0 137.36 0 138.63 0 141.07 0 143.32 0 147.91 0 152.56 0 151.61 0 156.56 0 157.45 0 158.13 0 159.18 0 159.47 0 159.79 0 161.65 0 162.77 0 163.48 0 166.16 0 163.86 0 162.12 0 149.08 0 145.32 0 141.21 0 134.68 0 133.65 0 139.17 0 138.61 0 144.96 1 157.99 1 167.18 1 174.48 1 182.77 1 190.00 1 189.70 1 188.90 1 198.28 1 201.18 1 204.14 1 221.02 1 221.12 1 220.68 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Gasindex[t] = + 139.980708860760 + 48.9882278481013dumivariable[t] + 0.718215189873432M1[t] -2.11435443037975M2[t] -0.0643544303797487M3[t] + 1.21564556962026M4[t] + 1.36764556962025M5[t] + 0.931645569620248M6[t] + 0.177645569620252M7[t] + 1.09964556962026M8[t] + 1.64764556962025M9[t] + 3.55764556962025M10[t] + 7.57964556962026M11[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) 139.980708860760 8.291106 16.8832 0 0 dumivariable 48.9882278481013 5.507045 8.8956 0 0 M1 0.718215189873432 10.828966 0.0663 0.947396 0.473698 M2 -2.11435443037975 11.357516 -0.1862 0.853101 0.426551 M3 -0.0643544303797487 11.357516 -0.0057 0.995503 0.497751 M4 1.21564556962026 11.357516 0.107 0.915208 0.457604 M5 1.36764556962025 11.357516 0.1204 0.904655 0.452327 M6 0.931645569620248 11.357516 0.082 0.934965 0.467482 M7 0.177645569620252 11.357516 0.0156 0.987585 0.493793 M8 1.09964556962026 11.357516 0.0968 0.923272 0.461636 M9 1.64764556962025 11.357516 0.1451 0.885262 0.442631 M10 3.55764556962025 11.357516 0.3132 0.755454 0.377727 M11 7.57964556962026 11.357516 0.6674 0.507733 0.253866 Multiple Linear Regression - Regression Statistics Multiple R 0.793206893209096 R-squared 0.629177175434427 Adjusted R-squared 0.536471469293034 F-TEST (value) 6.78682253360776 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 6.04391812597527e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 17.8731684436086 Sum Squared Residuals 15333.6072102532 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 127.96 140.698924050633 -12.7389240506328 2 127.47 137.866354430380 -10.3963544303798 3 126.47 139.916354430380 -13.4463544303797 4 125.75 141.196354430380 -15.4463544303798 5 125.42 141.348354430380 -15.9283544303797 6 125.14 140.912354430380 -15.7723544303797 7 125.15 140.158354430380 -15.0083544303797 8 125.51 141.080354430380 -15.5703544303797 9 125.63 141.628354430380 -15.9983544303798 10 126.22 143.538354430380 -17.3183544303797 11 126.88 147.560354430380 -20.6803544303798 12 127.96 139.980708860760 -12.0207088607595 13 128.74 140.698924050633 -11.9589240506329 14 129.6 137.866354430380 -8.26635443037975 15 131.2 139.916354430380 -8.71635443037976 16 132.72 141.196354430380 -8.47635443037975 17 134.67 141.348354430380 -6.67835443037976 18 135.94 140.912354430380 -4.97235443037974 19 136.39 140.158354430380 -3.76835443037976 20 136.74 141.080354430380 -4.34035443037974 21 137.2 141.628354430380 -4.42835443037976 22 137.36 143.538354430380 -6.17835443037973 23 138.63 147.560354430380 -8.93035443037975 24 141.07 139.980708860760 1.0892911392405 25 143.32 140.698924050633 2.62107594936707 26 147.91 137.866354430380 10.0436455696203 27 152.56 139.916354430380 12.6436455696203 28 151.61 141.196354430380 10.4136455696203 29 156.56 141.348354430380 15.2116455696203 30 157.45 140.912354430380 16.5376455696203 31 158.13 140.158354430380 17.9716455696203 32 159.18 141.080354430380 18.0996455696203 33 159.47 141.628354430380 17.8416455696203 34 159.79 143.538354430380 16.2516455696203 35 161.65 147.560354430380 14.0896455696203 36 162.77 139.980708860759 22.7892911392405 37 163.48 140.698924050633 22.7810759493671 38 166.16 137.866354430380 28.2936455696203 39 163.86 139.916354430380 23.9436455696203 40 162.12 141.196354430380 20.9236455696203 41 149.08 141.348354430380 7.73164556962026 42 145.32 140.912354430380 4.40764556962025 43 141.21 140.158354430380 1.05164556962026 44 134.68 141.080354430380 -6.40035443037975 45 133.65 141.628354430380 -7.97835443037974 46 139.17 143.538354430380 -4.36835443037976 47 138.61 147.560354430380 -8.95035443037973 48 144.96 188.968936708861 -44.0089367088608 49 157.99 189.687151898734 -31.6971518987342 50 167.18 186.854582278481 -19.674582278481 51 174.48 188.904582278481 -14.4245822784810 52 182.77 190.184582278481 -7.414582278481 53 190 190.336582278481 -0.336582278481011 54 189.7 189.900582278481 -0.200582278481015 55 188.9 189.146582278481 -0.246582278481004 56 198.28 190.068582278481 8.21141772151898 57 201.18 190.616582278481 10.563417721519 58 204.14 192.526582278481 11.6134177215190 59 221.02 196.548582278481 24.471417721519 60 221.12 188.968936708861 32.1510632911392 61 220.68 189.687151898734 30.9928481012658 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0103125236212692 0.0206250472425385 0.98968747637873 17 0.00717481492501204 0.0143496298500241 0.992825185074988 18 0.00548825405677149 0.0109765081135430 0.994511745943229 19 0.00391101086322017 0.00782202172644035 0.99608898913678 20 0.00262140834611151 0.00524281669222303 0.997378591653889 21 0.00177973166091630 0.00355946332183260 0.998220268339084 22 0.00115582953733045 0.00231165907466090 0.99884417046267 23 0.000855102739922613 0.00171020547984523 0.999144897260077 24 0.000631415882573112 0.00126283176514622 0.999368584117427 25 0.000739798345574926 0.00147959669114985 0.999260201654425 26 0.00128356911098282 0.00256713822196564 0.998716430889017 27 0.00288104959502968 0.00576209919005936 0.99711895040497 28 0.00405748292232896 0.00811496584465792 0.995942517077671 29 0.00693530833733848 0.0138706166746770 0.993064691662662 30 0.0100274723124752 0.0200549446249504 0.989972527687525 31 0.0132140225031355 0.0264280450062710 0.986785977496864 32 0.0161576769410025 0.0323153538820049 0.983842323058998 33 0.0179928656165853 0.0359857312331705 0.982007134383415 34 0.0181107968918279 0.0362215937836558 0.981889203108172 35 0.0173250818284474 0.0346501636568948 0.982674918171553 36 0.0181459658224106 0.0362919316448211 0.98185403417759 37 0.0193979803187337 0.0387959606374675 0.980602019681266 38 0.0342220101885716 0.0684440203771433 0.965777989811428 39 0.0463614485157104 0.0927228970314208 0.95363855148429 40 0.0527061262955551 0.105412252591110 0.947293873704445 41 0.0346824345706170 0.0693648691412341 0.965317565429383 42 0.0208472493029658 0.0416944986059317 0.979152750697034 43 0.0115739208000541 0.0231478416001082 0.988426079199946 44 0.00494239130206985 0.0098847826041397 0.99505760869793 45 0.00177671304085805 0.0035534260817161 0.998223286959142 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 12 0.4 NOK 5% type I error level 26 0.866666666666667 NOK 10% type I error level 29 0.966666666666667 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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