Paper - Multiple Regression - Gas zonder trend & 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 04:39:51 -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/t1229946030kqtyolq01i26sgz.htm/, Retrieved Mon, 22 Dec 2008 12:40:39 +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/t1229946030kqtyolq01i26sgz.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:

IsPrivate?

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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Gasindex[t] = + 141.352340425532 + 48.8190881458967dumivariable[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) 141.352340425532 2.375027 59.5161 0 0 dumivariable 48.8190881458967 4.957576 9.8474 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.788494656230365 R-squared 0.621723822903841 Adjusted R-squared 0.615312362275093 F-TEST (value) 96.9706996430866 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 4.56301663120939e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 16.2823628266916 Sum Squared Residuals 15641.8050139818 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 127.96 141.352340425532 -13.3923404255321 2 127.47 141.352340425532 -13.8823404255319 3 126.47 141.352340425532 -14.8823404255319 4 125.75 141.352340425532 -15.6023404255319 5 125.42 141.352340425532 -15.9323404255319 6 125.14 141.352340425532 -16.2123404255319 7 125.15 141.352340425532 -16.2023404255319 8 125.51 141.352340425532 -15.8423404255319 9 125.63 141.352340425532 -15.7223404255319 10 126.22 141.352340425532 -15.1323404255319 11 126.88 141.352340425532 -14.4723404255319 12 127.96 141.352340425532 -13.3923404255319 13 128.74 141.352340425532 -12.6123404255319 14 129.6 141.352340425532 -11.7523404255319 15 131.2 141.352340425532 -10.1523404255319 16 132.72 141.352340425532 -8.63234042553191 17 134.67 141.352340425532 -6.68234042553193 18 135.94 141.352340425532 -5.41234042553191 19 136.39 141.352340425532 -4.96234042553193 20 136.74 141.352340425532 -4.6123404255319 21 137.2 141.352340425532 -4.15234042553192 22 137.36 141.352340425532 -3.9923404255319 23 138.63 141.352340425532 -2.72234042553192 24 141.07 141.352340425532 -0.282340425531919 25 143.32 141.352340425532 1.96765957446808 26 147.91 141.352340425532 6.55765957446808 27 152.56 141.352340425532 11.2076595744681 28 151.61 141.352340425532 10.2576595744681 29 156.56 141.352340425532 15.2076595744681 30 157.45 141.352340425532 16.0976595744681 31 158.13 141.352340425532 16.7776595744681 32 159.18 141.352340425532 17.8276595744681 33 159.47 141.352340425532 18.1176595744681 34 159.79 141.352340425532 18.4376595744681 35 161.65 141.352340425532 20.2976595744681 36 162.77 141.352340425532 21.4176595744681 37 163.48 141.352340425532 22.1276595744681 38 166.16 141.352340425532 24.8076595744681 39 163.86 141.352340425532 22.5076595744681 40 162.12 141.352340425532 20.7676595744681 41 149.08 141.352340425532 7.7276595744681 42 145.32 141.352340425532 3.96765957446808 43 141.21 141.352340425532 -0.142340425531905 44 134.68 141.352340425532 -6.6723404255319 45 133.65 141.352340425532 -7.7023404255319 46 139.17 141.352340425532 -2.18234042553193 47 138.61 141.352340425532 -2.7423404255319 48 144.96 190.171428571429 -45.2114285714286 49 157.99 190.171428571429 -32.1814285714286 50 167.18 190.171428571429 -22.9914285714286 51 174.48 190.171428571429 -15.6914285714286 52 182.77 190.171428571429 -7.40142857142857 53 190 190.171428571429 -0.171428571428578 54 189.7 190.171428571429 -0.471428571428589 55 188.9 190.171428571429 -1.27142857142857 56 198.28 190.171428571429 8.10857142857142 57 201.18 190.171428571429 11.0085714285714 58 204.14 190.171428571429 13.9685714285714 59 221.02 190.171428571429 30.8485714285714 60 221.12 190.171428571429 30.9485714285714 61 220.68 190.171428571429 30.5085714285714 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.000633439867576986 0.00126687973515397 0.999366560132423 6 7.7989392811013e-05 0.000155978785622026 0.99992201060719 7 8.49415475879794e-06 1.69883095175959e-05 0.999991505845241 8 7.09225414044868e-07 1.41845082808974e-06 0.999999290774586 9 5.40684809529012e-08 1.08136961905802e-07 0.999999945931519 10 3.71344945754857e-09 7.42689891509713e-09 0.99999999628655 11 3.30086568201878e-10 6.60173136403756e-10 0.999999999669913 12 9.04713500101705e-11 1.80942700020341e-10 0.999999999909529 13 5.19194777938022e-11 1.03838955587604e-10 0.99999999994808 14 5.25512872219194e-11 1.05102574443839e-10 0.999999999947449 15 1.66760571437730e-10 3.33521142875459e-10 0.99999999983324 16 7.30407998279186e-10 1.46081599655837e-09 0.999999999269592 17 4.57726219520558e-09 9.15452439041115e-09 0.999999995422738 18 1.92277051622740e-08 3.84554103245479e-08 0.999999980772295 19 4.38221185396608e-08 8.76442370793217e-08 0.999999956177881 20 7.08894382343276e-08 1.41778876468655e-07 0.999999929110562 21 9.79848737138093e-08 1.95969747427619e-07 0.999999902015126 22 1.12935065956926e-07 2.25870131913852e-07 0.999999887064934 23 1.55557459565689e-07 3.11114919131378e-07 0.99999984444254 24 3.39504515366946e-07 6.79009030733892e-07 0.999999660495485 25 9.64933313924195e-07 1.92986662784839e-06 0.999999035066686 26 5.86504932720041e-06 1.17300986544008e-05 0.999994134950673 27 5.03457933450006e-05 0.000100691586690001 0.999949654206655 28 0.000149181001291081 0.000298362002582161 0.99985081899871 29 0.000629589690435504 0.00125917938087101 0.999370410309564 30 0.00171669003312533 0.00343338006625067 0.998283309966875 31 0.00350076615186224 0.00700153230372449 0.996499233848138 32 0.0061332602939096 0.0122665205878192 0.99386673970609 33 0.00909390182596374 0.0181878036519275 0.990906098174036 34 0.0120744234931027 0.0241488469862054 0.987925576506897 35 0.0165476239945617 0.0330952479891234 0.983452376005438 36 0.0223672790374593 0.0447345580749186 0.97763272096254 37 0.0295757243815842 0.0591514487631685 0.970424275618416 38 0.0446281608489648 0.0892563216979297 0.955371839151035 39 0.0570631421655638 0.114126284331128 0.942936857834436 40 0.0681101533448781 0.136220306689756 0.931889846655122 41 0.0507159156674761 0.101431831334952 0.949284084332524 42 0.0347522103788658 0.0695044207577316 0.965247789621134 43 0.022202122727358 0.044404245454716 0.977797877272642 44 0.0140016136174852 0.0280032272349703 0.985998386382515 45 0.00869991102824577 0.0173998220564915 0.991300088971754 46 0.00485771646026722 0.00971543292053444 0.995142283539733 47 0.00258711347959355 0.0051742269591871 0.997412886520406 48 0.0178626062983751 0.0357252125967503 0.982137393701625 49 0.0623245888461069 0.124649177692214 0.937675411153893 50 0.145609885404135 0.291219770808269 0.854390114595865 51 0.258269538153086 0.516539076306172 0.741730461846914 52 0.338616260768344 0.677232521536687 0.661383739231656 53 0.358025027796001 0.716050055592003 0.641974972203998 54 0.403453651725555 0.80690730345111 0.596546348274445 55 0.554237352098733 0.891525295802534 0.445762647901267 56 0.576518170774828 0.846963658450343 0.423481829225172 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 29 0.557692307692308 NOK 5% type I error level 38 0.730769230769231 NOK 10% type I error level 41 0.788461538461538 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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