Paper. Multi Regressie met Montly Dummies

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 12 Dec 2009 11:19:05 -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/12/t12606420062mugfaz1jkqn4eh.htm/, Retrieved Sat, 12 Dec 2009 19:20:18 +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/12/t12606420062mugfaz1jkqn4eh.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:

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Dataseries X:

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593530 3922 18004 707169 610763 3759 17537 703434 612613 4138 20366 701017 611324 4634 22782 696968 594167 3996 19169 688558 595454 4308 13807 679237 590865 4143 29743 677362 589379 4429 25591 676693 584428 5219 29096 670009 573100 4929 26482 667209 567456 5761 22405 662976 569028 5592 27044 660194 620735 4163 17970 652270 628884 4962 18730 648024 628232 5208 19684 629295 612117 4755 19785 624961 595404 4491 18479 617306 597141 5732 10698 607691 593408 5731 31956 596219 590072 5040 29506 591130 579799 6102 34506 584528 574205 4904 27165 576798 572775 5369 26736 575683 572942 5578 23691 574369 619567 4619 18157 566815 625809 4731 17328 573074 619916 5011 18205 567739 587625 5299 20995 571942 565742 4146 17382 570274 557274 4625 9367 568800 560576 4736 31124 558115 548854 4219 26551 550591 531673 5116 30651 548872 525919 4205 25859 547009 511038 4121 25100 545946 498662 5103 25778 539702 555362 4300 20418 542427 564591 4578 18688 542968 541657 3809 20424 536640 527070 5526 etc...

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 Werkzoekend[t] = + 209400.287969295 + 34.5996594276739Bouw[t] -4.21531532225463Auto[t] + 0.428751010829713Krediet[t] + 50230.3882566328M1[t] + 52158.6967352739M2[t] + 49001.5473624691M3[t] + 32176.4747719479M4[t] + 21960.4676447585M5[t] -17646.9872676785M6[t] + 70509.793065085M7[t] + 54730.6017553894M8[t] + 41849.4634677005M9[t] + 38938.8730270538M10[t] + 8305.34542181486M11[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) 209400.287969295 50245.948141 4.1675 0.000134 6.7e-05 Bouw 34.5996594276739 4.942389 7.0006 0 0 Auto -4.21531532225463 1.573651 -2.6787 0.010217 0.005109 Krediet 0.428751010829713 0.045606 9.4013 0 0 M1 50230.3882566328 14831.822937 3.3867 0.001458 0.000729 M2 52158.6967352739 16153.822204 3.2289 0.002295 0.001148 M3 49001.5473624691 14633.167771 3.3487 0.001628 0.000814 M4 32176.4747719479 13187.896006 2.4398 0.018607 0.009303 M5 21960.4676447585 16094.576952 1.3645 0.17906 0.08953 M6 -17646.9872676785 24072.077946 -0.7331 0.467223 0.233612 M7 70509.793065085 15421.784964 4.5721 3.6e-05 1.8e-05 M8 54730.6017553894 13482.87988 4.0593 0.000189 9.5e-05 M9 41849.4634677005 14981.511368 2.7934 0.007577 0.003788 M10 38938.8730270538 13462.095109 2.8925 0.005821 0.00291 M11 8305.34542181486 12603.550445 0.659 0.513201 0.256601 Multiple Linear Regression - Regression Statistics Multiple R 0.914421890058059 R-squared 0.836167393017353 Adjusted R-squared 0.786305295240026 F-TEST (value) 16.7695991602978 F-TEST (DF numerator) 14 F-TEST (DF denominator) 46 p-value 1.45661260830821e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 19632.4366647768 Sum Squared Residuals 17729898192.2376 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 593530 622637.427016828 -29107.4270168276 2 610763 619293.158238804 -8530.15823880356 3 612613 616287.861549253 -3674.86154925329 4 611324 604704.005373442 6619.99462655826 5 594167 584037.553789624 10129.4462103755 6 595454 573831.325204607 21622.6747953927 7 590865 588299.988611049 2565.01138895091 8 589379 599631.454689424 -10252.4546894243 9 584428 596443.59538871 -12015.5953887096 10 573100 593317.435136088 -20217.4351360879 11 567456 606841.761714664 -39385.7617146636 12 569028 571941.440757504 -2913.44075750436 13 620735 607581.263916315 13153.7360836850 14 628884 632130.583840771 -3246.5838407711 15 628232 625433.462187913 2798.53781208656 16 612117 590650.790148172 21466.2098518277 17 595404 573523.58575504 21880.4142449599 18 597141 605531.235745682 -8390.23574568201 19 593408 599125.61170229 -5717.61170229043 20 590072 567583.664373484 22488.3356265165 21 579799 567540.173613213 12258.8263867865 22 574205 550809.575645171 23395.424354829 23 572775 537595.202569972 35179.7974300275 24 572942 548793.442296577 24148.5577034234 25 619567 585931.527019620 33635.4729803804 26 625809 597913.046333092 27895.9536669076 27 619916 598459.583419643 21456.4165803575 28 587625 581640.523493718 5984.47650628174 29 565742 546045.886619663 19696.1133803371 30 557274 556165.441890990 1108.55810901047 31 560576 551868.964403215 8707.03559678461 32 548854 534252.4635326 14601.5364674001 33 531673 534387.403942674 -2714.40394267437 34 525919 519357.551654485 6561.44834551483 35 511038 488561.314662401 22476.6853375991 36 498662 508697.729698452 -10035.7296984524 37 555362 554907.028066459 454.971933541107 38 564591 573978.491670353 -9387.49167035267 39 541657 534183.280401702 7473.71959829783 40 527070 557140.091496697 -30070.0914966966 41 509846 526770.43292249 -16924.43292249 42 514258 501378.838880535 12879.1611194645 43 516922 528429.240432233 -11507.2404322333 44 507561 533149.785396111 -25588.7853961110 45 492622 503843.390907396 -11221.3909073963 46 490243 499197.453193739 -8954.45319373926 47 469357 477460.251457931 -8103.25145793148 48 477580 484859.118209351 -7279.1182093508 49 528379 533004.325558074 -4625.32555807404 50 533590 540321.71991698 -6731.71991698028 51 517945 545998.812441489 -28053.8124414886 52 506174 510174.589487971 -4000.58948797108 53 501866 536647.540913183 -34781.5409131825 54 516141 543361.158278186 -27220.1582781856 55 528222 522269.194851212 5952.80514878816 56 532638 533886.632008381 -1248.63200838119 57 536322 522629.436148006 13692.5638519938 58 536535 537319.984370517 -784.984370516744 59 523597 533764.469595032 -10167.4695950316 60 536214 540134.269038116 -3920.26903811579 61 586570 600081.428422705 -13511.4284227048 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.0817711613951422 0.163542322790284 0.918228838604858 19 0.0917454015935123 0.183490803187025 0.908254598406488 20 0.0633702450794417 0.126740490158883 0.936629754920558 21 0.0343175640135565 0.068635128027113 0.965682435986444 22 0.0148272779477321 0.0296545558954643 0.985172722052268 23 0.00807449433868457 0.0161489886773691 0.991925505661315 24 0.00367425671240134 0.00734851342480268 0.9963257432876 25 0.00249307230379243 0.00498614460758486 0.997506927696208 26 0.00156640502875234 0.00313281005750468 0.998433594971248 27 0.00160441056250040 0.00320882112500081 0.9983955894375 28 0.0251434788764243 0.0502869577528487 0.974856521123576 29 0.183566415808004 0.367132831616007 0.816433584191996 30 0.325891201245336 0.651782402490672 0.674108798754664 31 0.456554866607715 0.91310973321543 0.543445133392285 32 0.639641961218244 0.720716077563511 0.360358038781756 33 0.713145785291525 0.573708429416951 0.286854214708475 34 0.729152300445538 0.541695399108925 0.270847699554462 35 0.899997431310376 0.200005137379249 0.100002568689624 36 0.943571206852178 0.112857586295644 0.0564287931478219 37 0.97542751957891 0.0491449608421814 0.0245724804210907 38 0.984710736830297 0.030578526339407 0.0152892631697035 39 0.986980537243881 0.026038925512238 0.013019462756119 40 0.995596105729697 0.00880778854060663 0.00440389427030332 41 0.99230413576598 0.0153917284680387 0.00769586423401936 42 0.980229973729025 0.0395400525419498 0.0197700262709749 43 0.955617589817132 0.0887648203657354 0.0443824101828677 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.192307692307692 NOK 5% type I error level 12 0.461538461538462 NOK 10% type I error level 15 0.576923076923077 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 = 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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