lineair regression wlh 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: Fri, 25 Dec 2009 12:23:01 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/25/t1261769057t02mhochm2u0nra.htm/, Retrieved Fri, 25 Dec 2009 20:24:29 +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/2009/Dec/25/t1261769057t02mhochm2u0nra.htm/}, year = {2009}, } @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 = {2009}, 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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612613 1 611324 1 594167 1 595454 1 590865 1 589379 1 584428 1 573100 1 567456 1 569028 1 620735 1 628884 1 628232 1 612117 1 595404 1 597141 1 593408 1 590072 1 579799 1 574205 1 572775 1 572942 1 619567 1 625809 1 619916 1 587625 0 565742 0 557274 0 560576 0 548854 0 531673 0 525919 0 511038 0 498662 0 555362 0 564591 0 541657 0 527070 0 509846 0 514258 0 516922 0 507561 0 492622 0 490243 0 469357 0 477580 0 528379 0 533590 0 517945 0 506174 0 501866 0 516141 0 528222 0 532638 0 536322 0 536535 0 523597 0 536214 0 586570 0 596594 0

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 wlh[t] = + 563417.716666666 + 66189.7083333334dummies[t] -19058.9416666668M1[t] -21031.6M2[t] -36488.6M3[t] -33840M4[t] -31895M5[t] -36192.7999999999M6[t] -44924.800M7[t] -49893.2M8[t] -61049M9[t] -59008.4M10[t] -7771.00000000001M11[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) 563417.716666666 9475.26483 59.4619 0 0 dummies 66189.7083333334 5434.437087 12.1797 0 0 M1 -19058.9416666668 13087.857632 -1.4562 0.151977 0.075989 M2 -21031.6 13042.649008 -1.6125 0.113543 0.056772 M3 -36488.6 13042.649008 -2.7976 0.007439 0.003719 M4 -33840 13042.649008 -2.5946 0.012593 0.006296 M5 -31895 13042.649008 -2.4454 0.018268 0.009134 M6 -36192.7999999999 13042.649008 -2.775 0.007898 0.003949 M7 -44924.800 13042.649008 -3.4445 0.001214 0.000607 M8 -49893.2 13042.649008 -3.8254 0.000384 0.000192 M9 -61049 13042.649008 -4.6807 2.5e-05 1.2e-05 M10 -59008.4 13042.649008 -4.5243 4.1e-05 2.1e-05 M11 -7771.00000000001 13042.649008 -0.5958 0.554158 0.277079 Multiple Linear Regression - Regression Statistics Multiple R 0.900460169939781 R-squared 0.81082851764798 Adjusted R-squared 0.762529415770868 F-TEST (value) 16.7876520708602 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 4.03233002543857e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 20622.2387931578 Sum Squared Residuals 19988006443.575 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 612613 610548.483333334 2064.51666666624 2 611324 608575.825 2748.17500000006 3 594167 593118.825 1048.17500000001 4 595454 595767.425 -313.424999999998 5 590865 597712.425 -6847.42499999995 6 589379 593414.625 -4035.62499999997 7 584428 584682.625 -254.624999999969 8 573100 579714.225 -6614.22500000013 9 567456 568558.425 -1102.42499999992 10 569028 570599.025 -1571.02499999999 11 620735 621836.425 -1101.42499999998 12 628884 629607.425 -723.424999999985 13 628232 610548.483333333 17683.5166666668 14 612117 608575.825 3541.17499999999 15 595404 593118.825 2285.17500000000 16 597141 595767.425 1373.57500000001 17 593408 597712.425 -4304.42499999999 18 590072 593414.625 -3342.62499999999 19 579799 584682.625 -4883.62499999999 20 574205 579714.225 -5509.22499999997 21 572775 568558.425 4216.57499999999 22 572942 570599.025 2342.97500000000 23 619567 621836.425 -2269.42499999999 24 625809 629607.425 -3798.425 25 619916 610548.483333333 9367.51666666678 26 587625 542386.116666667 45238.8833333333 27 565742 526929.116666667 38812.8833333333 28 557274 529577.716666667 27696.2833333333 29 560576 531522.716666667 29053.2833333333 30 548854 527224.916666667 21629.0833333333 31 531673 518492.916666667 13180.0833333333 32 525919 513524.516666667 12394.4833333334 33 511038 502368.716666667 8669.28333333331 34 498662 504409.316666667 -5747.31666666666 35 555362 555646.716666667 -284.716666666661 36 564591 563417.716666667 1173.28333333332 37 541657 544358.775 -2701.77499999989 38 527070 542386.116666667 -15316.1166666667 39 509846 526929.116666667 -17083.1166666667 40 514258 529577.716666667 -15319.7166666667 41 516922 531522.716666667 -14600.7166666667 42 507561 527224.916666667 -19663.9166666667 43 492622 518492.916666667 -25870.9166666667 44 490243 513524.516666667 -23281.5166666666 45 469357 502368.716666667 -33011.7166666667 46 477580 504409.316666667 -26829.3166666667 47 528379 555646.716666667 -27267.7166666667 48 533590 563417.716666667 -29827.7166666667 49 517945 544358.775 -26413.7749999999 50 506174 542386.116666667 -36212.1166666667 51 501866 526929.116666667 -25063.1166666667 52 516141 529577.716666667 -13436.7166666667 53 528222 531522.716666667 -3300.71666666667 54 532638 527224.916666667 5413.08333333332 55 536322 518492.916666667 17829.0833333333 56 536535 513524.516666667 23010.4833333334 57 523597 502368.716666667 21228.2833333333 58 536214 504409.316666667 31804.6833333333 59 586570 555646.716666667 30923.2833333333 60 596594 563417.716666667 33176.2833333333 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0227304127906566 0.0454608255813133 0.977269587209343 17 0.00487437808852431 0.00974875617704862 0.995125621911476 18 0.000902988296663778 0.00180597659332756 0.999097011703336 19 0.000191527358410654 0.000383054716821307 0.99980847264159 20 3.1542348726219e-05 6.3084697452438e-05 0.999968457651274 21 6.77596979377441e-06 1.35519395875488e-05 0.999993224030206 22 1.20391617748891e-06 2.40783235497782e-06 0.999998796083823 23 1.71334042010777e-07 3.42668084021554e-07 0.999999828665958 24 2.80357057529287e-08 5.60714115058575e-08 0.999999971964294 25 3.47959885367815e-09 6.95919770735629e-09 0.999999996520401 26 1.41771300556696e-09 2.83542601113392e-09 0.999999998582287 27 7.49514847491946e-10 1.49902969498389e-09 0.999999999250485 28 2.10807284421578e-09 4.21614568843156e-09 0.999999997891927 29 6.04637803077696e-10 1.20927560615539e-09 0.999999999395362 30 6.56667615591793e-10 1.31333523118359e-09 0.999999999343332 31 5.57742982365768e-09 1.11548596473154e-08 0.99999999442257 32 4.5712252363196e-09 9.1424504726392e-09 0.999999995428775 33 3.67048921210336e-08 7.34097842420673e-08 0.999999963295108 34 1.22457756438428e-06 2.44915512876856e-06 0.999998775422436 35 1.49831742040249e-06 2.99663484080497e-06 0.99999850168258 36 9.965403572335e-07 1.993080714467e-06 0.999999003459643 37 5.57019575459058e-06 1.11403915091812e-05 0.999994429804245 38 7.65320063196666e-05 0.000153064012639333 0.99992346799368 39 0.000211910546041816 0.000423821092083633 0.999788089453958 40 0.000218190187619457 0.000436380375238914 0.99978180981238 41 0.000151892067994757 0.000303784135989513 0.999848107932005 42 0.000133674371599451 0.000267348743198903 0.9998663256284 43 0.000208762582946504 0.000417525165893008 0.999791237417053 44 0.000257246618288865 0.00051449323657773 0.999742753381711 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 28 0.96551724137931 NOK 5% type I error level 29 1 NOK 10% type I error level 29 1 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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