Paper - Multiple Regression - elektriciteit 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 05:11:46 -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/t122994799750wrzb1ab8kghgb.htm/, Retrieved Mon, 22 Dec 2008 13:13:26 +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/t122994799750wrzb1ab8kghgb.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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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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation elektrictietsindex[t] = + 101.353243204545 + 14.6742235386364dumivariable[t] -0.0137343840908889M1[t] -2.22380407227273M2[t] -3.83379648M3[t] -1.70781196000000M4[t] + 1.06505220772727M5[t] + 1.29236566772727M6[t] + 1.07082164772728M7[t] + 1.10784808772727M8[t] + 2.39602778772727M9[t] + 2.57769504772728M10[t] -0.165457779999996M11[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) 101.353243204545 3.433573 29.5183 0 0 dumivariable 14.6742235386364 2.168692 6.7664 0 0 M1 -0.0137343840908889 4.500581 -0.0031 0.997578 0.498789 M2 -2.22380407227273 4.718256 -0.4713 0.639548 0.319774 M3 -3.83379648 4.698277 -0.816 0.418531 0.209265 M4 -1.70781196000000 4.698277 -0.3635 0.717829 0.358915 M5 1.06505220772727 4.718256 0.2257 0.82237 0.411185 M6 1.29236566772727 4.718256 0.2739 0.785331 0.392665 M7 1.07082164772728 4.718256 0.227 0.821424 0.410712 M8 1.10784808772727 4.718256 0.2348 0.815362 0.407681 M9 2.39602778772727 4.718256 0.5078 0.613905 0.306952 M10 2.57769504772728 4.718256 0.5463 0.587374 0.293687 M11 -0.165457779999996 4.698277 -0.0352 0.972053 0.486027 Multiple Linear Regression - Regression Statistics Multiple R 0.707474490780227 R-squared 0.500520155104742 Adjusted R-squared 0.375650193880927 F-TEST (value) 4.00833114865487 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.000267584983496993 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.42862879287303 Sum Squared Residuals 2648.85723563050 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.57 101.339508820454 -3.76950882045444 2 97.74 99.1294391322728 -1.38943913227276 3 97.92 97.5194467245454 0.400553275454549 4 98.19 99.6454312445454 -1.45543124454546 5 98.23 102.418295412273 -4.18829541227272 6 98.41 102.645608872273 -4.23560887227273 7 98.59 102.424064852273 -3.83406485227272 8 98.71 102.461091292273 -3.75109129227273 9 99.14 103.749270992273 -4.60927099227272 10 99.62 103.930938252273 -4.31093825227272 11 100.18 115.862008963182 -15.6820089631818 12 100.66 116.027466743182 -15.3674667431818 13 101.19 116.013732359091 -14.8237323590909 14 101.75 113.803662670909 -12.0536626709091 15 102.2 112.193670263182 -9.99367026318181 16 102.87 114.319654783182 -11.4496547831818 17 98.81 102.418295412273 -3.60829541227273 18 97.6 102.645608872273 -5.04560887227273 19 96.68 102.424064852273 -5.74406485227272 20 95.96 102.461091292273 -6.50109129227273 21 98.89 103.749270992273 -4.85927099227272 22 99.05 103.930938252273 -4.88093825227273 23 99.2 101.187785424545 -1.98778542454545 24 99.11 101.353243204545 -2.24324320454545 25 99.19 101.339508820455 -2.14950882045457 26 99.77 99.1294391322727 0.640560867727276 27 100.6956867 97.5194467245455 3.17623997545454 28 100.7751938 99.6454312445454 1.12976255545454 29 100.5267342 102.418295412273 -1.89156121227272 30 101.013715 102.645608872273 -1.63189387227272 31 100.9242695 102.424064852273 -1.49979535227274 32 101.1031604 102.461091292273 -1.35793089227273 33 103.1107136 103.749270992273 -0.638557392272729 34 102.991453 103.930938252273 -0.939485252272721 35 102.3057046 101.187785424545 1.11791917545454 36 102.6137945 101.353243204545 1.26055129545454 37 103.6772014 101.339508820455 2.33769257954544 38 104.7207315 99.1294391322727 5.59129236772728 39 107.6624925 97.5194467245455 10.1430457754545 40 108.8749752 99.6454312445455 9.22954395545454 41 108.1196581 102.418295412273 5.70136268772727 42 107.6128006 102.645608872273 4.96719172772727 43 106.4201948 102.424064852273 3.99612994772727 44 105.6052475 102.461091292273 3.14415620772728 45 105.7145697 103.749270992273 1.96529870772727 46 105.4859869 103.930938252273 1.55504864772727 47 105.5654939 101.187785424545 4.37770847545455 48 105.177897 101.353243204545 3.82465379545455 49 106.0922282 101.339508820455 4.75271937954543 50 106.3406877 99.1294391322727 7.21124856772728 51 108.4675015 112.193670263182 -3.72616876318182 52 116.8654343 114.319654783182 2.54577951681819 53 121.0793083 117.092518950909 3.98678934909090 54 123.2657523 117.319832410909 5.94591988909092 55 124.1800835 117.098288390909 7.0817951090909 56 125.6012721 117.135314830909 8.46595726909092 57 126.5652952 118.423494530909 8.14180066909091 58 127.1814749 118.605161790909 8.57631310909091 59 128.0361757 115.862008963182 12.1741667368182 60 128.5529716 116.027466743182 12.5255048568182 61 129.6660704 116.013732359091 13.6523380409091 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.000416771805278683 0.000833543610557367 0.999583228194721 17 5.55740633752767e-05 0.000111148126750553 0.999944425936625 18 1.36792321537974e-05 2.73584643075948e-05 0.999986320767846 19 3.95291394501148e-05 7.90582789002296e-05 0.99996047086055 20 0.000131159895007100 0.000262319790014200 0.999868840104993 21 2.9286647549791e-05 5.8573295099582e-05 0.99997071335245 22 7.05248664720533e-06 1.41049732944107e-05 0.999992947513353 23 1.47636935649005e-05 2.95273871298011e-05 0.999985236306435 24 8.6436008291465e-06 1.7287201658293e-05 0.99999135639917 25 5.24230628149549e-06 1.04846125629910e-05 0.999994757693718 26 2.97874849890889e-06 5.95749699781778e-06 0.9999970212515 27 2.08104443612206e-06 4.16208887224413e-06 0.999997918955564 28 9.24915554449449e-07 1.84983110889890e-06 0.999999075084446 29 6.8629426476618e-07 1.37258852953236e-06 0.999999313705735 30 1.36986573602832e-06 2.73973147205664e-06 0.999998630134264 31 2.91535187153434e-06 5.83070374306869e-06 0.999997084648129 32 7.89633299694378e-06 1.57926659938876e-05 0.999992103667003 33 1.77083396945187e-05 3.54166793890374e-05 0.999982291660306 34 2.51089268843423e-05 5.02178537686845e-05 0.999974891073116 35 4.35089817103412e-05 8.70179634206825e-05 0.99995649101829 36 6.78666978961213e-05 0.000135733395792243 0.999932133302104 37 0.000209814136259831 0.000419628272519662 0.99979018586374 38 0.000367262738898591 0.000734525477797182 0.999632737261101 39 0.08258984138004 0.16517968276008 0.91741015861996 40 0.598695395865356 0.802609208269287 0.401304604134644 41 0.904078460701588 0.191843078596825 0.0959215392984123 42 0.979696300683228 0.0406073986335448 0.0203036993167724 43 0.995058118788993 0.00988376242201403 0.00494188121100701 44 0.9953704152568 0.0092591694864005 0.00462958474320025 45 0.993785126923816 0.0124297461523685 0.00621487307618425 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 25 0.833333333333333 NOK 5% type I error level 27 0.9 NOK 10% type I error level 27 0.9 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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