Paper - Multiple Regression - Elektriciteit Met 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 05:06:36 -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/t1229947657drb2twnu5lc35rk.htm/, Retrieved Mon, 22 Dec 2008 13:07:46 +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/t1229947657drb2twnu5lc35rk.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)

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Dataseries X:

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97.57 0 97.74 0 97.92 0 98.19 0 98.23 0 98.41 0 98.59 0 98.71 0 99.14 0 99.62 0 100.18 1 100.66 1 101.19 1 101.75 1 102.2 1 102.87 1 98.81 0 97.6 0 96.68 0 95.96 0 98.89 0 99.05 0 99.2 0 99.11 0 99.19 0 99.77 0 100.6956867 0 100.7751938 0 100.5267342 0 101.013715 0 100.9242695 0 101.1031604 0 103.1107136 0 102.991453 0 102.3057046 0 102.6137945 0 103.6772014 0 104.7207315 0 107.6624925 0 108.8749752 0 108.1196581 0 107.6128006 0 106.4201948 0 105.6052475 0 105.7145697 0 105.4859869 0 105.5654939 0 105.177897 0 106.0922282 0 106.3406877 0 108.4675015 1 116.8654343 1 121.0793083 1 123.2657523 1 124.1800835 1 125.6012721 1 126.5652952 1 127.1814749 1 128.0361757 1 128.5529716 1 129.6660704 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation elektrictietsindex[t] = + 90.8627766197539 + 9.71251637015386dumivariable[t] + 1.38814478414702M1[t] + 0.249173786304261M2[t] -0.715009116953851M3[t] + 1.06444347381880M4[t] + 2.49843427862222M5[t] + 2.37921580939487M6[t] + 1.81113986016752M7[t] + 1.50163437094017M8[t] + 2.44328214171282M9[t] + 2.27841747248547M10[t] + 0.181074149227351M11[t] + 0.34653192922735t + 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) 90.8627766197539 2.056076 44.1923 0 0 dumivariable 9.71251637015386 1.236734 7.8534 0 0 M1 1.38814478414702 2.395845 0.5794 0.565089 0.282544 M2 0.249173786304261 2.518124 0.099 0.921597 0.460799 M3 -0.715009116953851 2.5134 -0.2845 0.777293 0.388647 M4 1.06444347381880 2.510092 0.4241 0.673453 0.336726 M5 2.49843427862222 2.511552 0.9948 0.324939 0.162469 M6 2.37921580939487 2.510136 0.9478 0.348057 0.174029 M7 1.81113986016752 2.50911 0.7218 0.473978 0.236989 M8 1.50163437094017 2.508472 0.5986 0.552297 0.276149 M9 2.44328214171282 2.508224 0.9741 0.33499 0.167495 M10 2.27841747248547 2.508366 0.9083 0.368339 0.18417 M11 0.181074149227351 2.497795 0.0725 0.942517 0.471258 t 0.34653192922735 0.031264 11.0839 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.928325847275186 R-squared 0.861788878719192 Adjusted R-squared 0.823560270705351 F-TEST (value) 22.5430357916036 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 6.66133814775094e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.94905205124836 Sum Squared Residuals 732.965568863038 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.57 92.5974533331281 4.97254666687189 2 97.74 91.8050142645128 5.93498573548716 3 97.92 91.187363290482 6.73263670951795 4 98.19 93.313347810482 4.87665218951795 5 98.23 95.0938705445128 3.13612945548718 6 98.41 95.3211840045128 3.08881599548717 7 98.59 95.0996399845128 3.49036001548718 8 98.71 95.1366664245128 3.57333357548717 9 99.14 96.4248461245128 2.71515387548718 10 99.62 96.6065133845128 3.01348661548718 11 100.18 104.568218360636 -4.3882183606359 12 100.66 104.733676140636 -4.07367614063592 13 101.19 106.468352854010 -5.27835285401028 14 101.75 105.675913785395 -3.92591378539486 15 102.2 105.058262811364 -2.85826281136411 16 102.87 107.184247331364 -4.3142473313641 17 98.81 99.252253695241 -0.442253695241026 18 97.6 99.479567155241 -1.87956715524103 19 96.68 99.258023135241 -2.57802313524102 20 95.96 99.295049575241 -3.33504957524103 21 98.89 100.583229275241 -1.69322927524103 22 99.05 100.764896535241 -1.71489653524103 23 99.2 99.0140851412103 0.185914858789742 24 99.11 99.1795429212103 -0.0695429212102604 25 99.19 100.914219634585 -1.72421963458464 26 99.77 100.121780565969 -0.351780565969229 27 100.6956867 99.5041295919385 1.19155710806153 28 100.7751938 101.630114111938 -0.854920311938464 29 100.5267342 103.410636845969 -2.88390264596922 30 101.013715 103.637950305969 -2.62423530596923 31 100.9242695 103.416406285969 -2.49213678596924 32 101.1031604 103.453432725969 -2.35027232596924 33 103.1107136 104.741612425969 -1.63089882596923 34 102.991453 104.923279685969 -1.93182668596923 35 102.3057046 103.172468291938 -0.866763691938469 36 102.6137945 103.337926071938 -0.724131571938466 37 103.6772014 105.072602785313 -1.39540138531283 38 104.7207315 104.280163716697 0.44056778330257 39 107.6624925 103.662512742667 3.99997975733333 40 108.8749752 105.788497262667 3.08647793733333 41 108.1196581 107.569019996697 0.550638103302563 42 107.6128006 107.796333456697 -0.183532856697434 43 106.4201948 107.574789436697 -1.15459463669743 44 105.6052475 107.611815876697 -2.00656837669743 45 105.7145697 108.899995576697 -3.18542587669743 46 105.4859869 109.081662836697 -3.59567593669744 47 105.5654939 107.330851442667 -1.76535754266666 48 105.177897 107.496309222667 -2.31841222266666 49 106.0922282 109.230985936041 -3.13875773604104 50 106.3406877 108.438546867426 -2.09785916742563 51 108.4675015 117.533412263549 -9.06591076354872 52 116.8654343 119.659396783549 -2.79396248354871 53 121.0793083 121.439919517579 -0.36061121757949 54 123.2657523 121.667232977579 1.59851932242052 55 124.1800835 121.445688957579 2.73439454242051 56 125.6012721 121.482715397579 4.11855670242052 57 126.5652952 122.770895097579 3.79440010242051 58 127.1814749 122.952562357579 4.22891254242052 59 128.0361757 121.201750963549 6.83442473645128 60 128.5529716 121.367208743549 7.1857628564513 61 129.6660704 123.101885456923 6.56418494307691 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00140585050800878 0.00281170101601756 0.998594149491991 18 0.000749324002815359 0.00149864800563072 0.999250675997185 19 0.000711881260266661 0.00142376252053332 0.999288118739733 20 0.000670370303346628 0.00134074060669326 0.999329629696653 21 0.000187448398558828 0.000374896797117656 0.99981255160144 22 3.90922133188768e-05 7.81844266377536e-05 0.99996090778668 23 0.000478638218293698 0.000957276436587396 0.999521361781706 24 0.000234507469143422 0.000469014938286843 0.999765492530857 25 8.2089176518151e-05 0.000164178353036302 0.999917910823482 26 2.73488971768266e-05 5.46977943536533e-05 0.999972651102823 27 1.79419466235211e-05 3.58838932470421e-05 0.999982058053376 28 5.55088738900961e-06 1.11017747780192e-05 0.99999444911261 29 1.83927676296787e-06 3.67855352593574e-06 0.999998160723237 30 1.17564147811592e-06 2.35128295623184e-06 0.999998824358522 31 7.67908653421392e-07 1.53581730684278e-06 0.999999232091347 32 6.21804287717982e-07 1.24360857543596e-06 0.999999378195712 33 5.08026280877746e-07 1.01605256175549e-06 0.999999491973719 34 2.33774347655197e-07 4.67548695310394e-07 0.999999766225652 35 1.26082563710130e-07 2.52165127420259e-07 0.999999873917436 36 6.20148206975187e-08 1.24029641395037e-07 0.99999993798518 37 4.28475254370735e-08 8.5695050874147e-08 0.999999957152475 38 3.06524279088880e-08 6.13048558177761e-08 0.999999969347572 39 0.000172108200203505 0.000344216400407011 0.999827891799796 40 0.0354870256232863 0.0709740512465725 0.964512974376714 41 0.276729776952452 0.553459553904904 0.723270223047548 42 0.631253277469313 0.737493445061374 0.368746722530687 43 0.84989902846493 0.300201943070140 0.150100971535070 44 0.868992909776545 0.26201418044691 0.131007090223455 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 23 0.821428571428571 NOK 5% type I error level 23 0.821428571428571 NOK 10% type I error level 24 0.857142857142857 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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