Paper - Multiple Regression - elektriciteit 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 05:08:28 -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/t12299477653o962ix7s6xmxhj.htm/, Retrieved Mon, 22 Dec 2008 13:09:25 +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/t12299477653o962ix7s6xmxhj.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:

» Textbox « » Textfile « » CSV «

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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation elektrictietsindex[t] = + 101.625240688636 + 14.1577792995989dumivariable[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) 101.625240688636 1.046924 97.0703 0 0 dumivariable 14.1577792995989 1.98315 7.139 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.680786174633836 R-squared 0.463469815572571 Adjusted R-squared 0.454376083633123 F-TEST (value) 50.9658541354263 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 1.57324298033501e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.94450613547717 Sum Squared Residuals 2845.34376247512 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.57 101.625240688636 -4.05524068863633 2 97.74 101.625240688636 -3.88524068863638 3 97.92 101.625240688636 -3.70524068863636 4 98.19 101.625240688636 -3.43524068863637 5 98.23 101.625240688636 -3.39524068863636 6 98.41 101.625240688636 -3.21524068863637 7 98.59 101.625240688636 -3.03524068863636 8 98.71 101.625240688636 -2.91524068863637 9 99.14 101.625240688636 -2.48524068863636 10 99.62 101.625240688636 -2.00524068863636 11 100.18 115.783019988235 -15.6030199882353 12 100.66 115.783019988235 -15.1230199882353 13 101.19 115.783019988235 -14.5930199882353 14 101.75 115.783019988235 -14.0330199882353 15 102.2 115.783019988235 -13.5830199882353 16 102.87 115.783019988235 -12.9130199882353 17 98.81 101.625240688636 -2.81524068863636 18 97.6 101.625240688636 -4.02524068863637 19 96.68 101.625240688636 -4.94524068863636 20 95.96 101.625240688636 -5.66524068863637 21 98.89 101.625240688636 -2.73524068863636 22 99.05 101.625240688636 -2.57524068863637 23 99.2 101.625240688636 -2.42524068863636 24 99.11 101.625240688636 -2.51524068863636 25 99.19 101.625240688636 -2.43524068863637 26 99.77 101.625240688636 -1.85524068863637 27 100.6956867 101.625240688636 -0.929553988636368 28 100.7751938 101.625240688636 -0.850046888636367 29 100.5267342 101.625240688636 -1.09850648863636 30 101.013715 101.625240688636 -0.611525688636359 31 100.9242695 101.625240688636 -0.70097118863637 32 101.1031604 101.625240688636 -0.522080288636371 33 103.1107136 101.625240688636 1.48547291136363 34 102.991453 101.625240688636 1.36621231136364 35 102.3057046 101.625240688636 0.680463911363635 36 102.6137945 101.625240688636 0.988553811363634 37 103.6772014 101.625240688636 2.05196071136364 38 104.7207315 101.625240688636 3.09549081136364 39 107.6624925 101.625240688636 6.03725181136363 40 108.8749752 101.625240688636 7.24973451136363 41 108.1196581 101.625240688636 6.49441741136363 42 107.6128006 101.625240688636 5.98755991136364 43 106.4201948 101.625240688636 4.79495411136364 44 105.6052475 101.625240688636 3.98000681136364 45 105.7145697 101.625240688636 4.08932901136363 46 105.4859869 101.625240688636 3.86074621136364 47 105.5654939 101.625240688636 3.94025321136364 48 105.177897 101.625240688636 3.55265631136364 49 106.0922282 101.625240688636 4.46698751136363 50 106.3406877 101.625240688636 4.71544701136364 51 108.4675015 115.783019988235 -7.3155184882353 52 116.8654343 115.783019988235 1.08241431176471 53 121.0793083 115.783019988235 5.2962883117647 54 123.2657523 115.783019988235 7.48273231176471 55 124.1800835 115.783019988235 8.3970635117647 56 125.6012721 115.783019988235 9.81825211176471 57 126.5652952 115.783019988235 10.7822752117647 58 127.1814749 115.783019988235 11.3984549117647 59 128.0361757 115.783019988235 12.2531557117647 60 128.5529716 115.783019988235 12.7699516117647 61 129.6660704 115.783019988235 13.8830504117647 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.000134853703482723 0.000269707406965446 0.999865146296517 6 1.27162010252724e-05 2.54324020505448e-05 0.999987283798975 7 1.62914547312273e-06 3.25829094624545e-06 0.999998370854527 8 2.22381945993298e-07 4.44763891986596e-07 0.999999777618054 9 8.08017111009196e-08 1.61603422201839e-07 0.999999919198289 10 5.71406792301751e-08 1.14281358460350e-07 0.99999994285932 11 7.27987464570286e-09 1.45597492914057e-08 0.999999992720125 12 1.24193601106963e-09 2.48387202213926e-09 0.999999998758064 13 3.94395136326844e-10 7.88790272653688e-10 0.999999999605605 14 3.29268520408547e-10 6.58537040817093e-10 0.999999999670731 15 7.51188568382579e-10 1.50237713676516e-09 0.999999999248811 16 1.21892051548433e-08 2.43784103096865e-08 0.999999987810795 17 2.64226485110396e-09 5.28452970220792e-09 0.999999997357735 18 9.91613280056438e-10 1.98322656011288e-09 0.999999999008387 19 1.93426574390603e-09 3.86853148781206e-09 0.999999998065734 20 1.19664894520854e-08 2.39329789041707e-08 0.99999998803351 21 4.67257444301432e-09 9.34514888602865e-09 0.999999995327426 22 2.0353726910071e-09 4.0707453820142e-09 0.999999997964627 23 9.92346059668885e-10 1.98469211933777e-09 0.999999999007654 24 4.53860328735795e-10 9.0772065747159e-10 0.99999999954614 25 2.25092925755324e-10 4.50185851510648e-10 0.999999999774907 26 1.93866064995587e-10 3.87732129991174e-10 0.999999999806134 27 5.44830191607681e-10 1.08966038321536e-09 0.99999999945517 28 1.17116090732354e-09 2.34232181464708e-09 0.99999999882884 29 1.50034560735732e-09 3.00069121471464e-09 0.999999998499654 30 2.87525546731075e-09 5.7505109346215e-09 0.999999997124745 31 4.30422063919049e-09 8.60844127838097e-09 0.99999999569578 32 6.94220887135134e-09 1.38844177427027e-08 0.999999993057791 33 8.47389232561494e-08 1.69477846512299e-07 0.999999915261077 34 3.76622661594939e-07 7.53245323189878e-07 0.999999623377338 35 6.7892070295815e-07 1.3578414059163e-06 0.999999321079297 36 1.29144369224224e-06 2.58288738448447e-06 0.999998708556308 37 3.91760620710019e-06 7.83521241420038e-06 0.999996082393793 38 1.62328636415824e-05 3.24657272831649e-05 0.999983767136358 39 0.00029853942144895 0.0005970788428979 0.999701460578551 40 0.00298689593484047 0.00597379186968093 0.99701310406516 41 0.00803047595058772 0.0160609519011754 0.991969524049412 42 0.0128437835597603 0.0256875671195205 0.98715621644024 43 0.0131036188438384 0.0262072376876768 0.986896381156162 44 0.0108884546254097 0.0217769092508193 0.98911154537459 45 0.0087418081440308 0.0174836162880616 0.99125819185597 46 0.00649084901714095 0.0129816980342819 0.99350915098286 47 0.00463604447858874 0.00927208895717747 0.995363955521411 48 0.00304489361700262 0.00608978723400523 0.996955106382997 49 0.00209112372352598 0.00418224744705195 0.997908876276474 50 0.00139177324771365 0.0027835464954273 0.998608226752286 51 0.225007093238356 0.450014186476712 0.774992906761644 52 0.7870900850521 0.4258198298958 0.2129099149479 53 0.945603852238264 0.108792295523471 0.0543961477617357 54 0.974145666490764 0.0517086670184716 0.0258543335092358 55 0.984806749991441 0.0303865000171177 0.0151932500085589 56 0.981152145007081 0.0376957099858374 0.0188478549929187 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 40 0.76923076923077 NOK 5% type I error level 48 0.923076923076923 NOK 10% type I error level 49 0.942307692307692 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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