paper multiple regression met trend+ seasonal 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: Wed, 30 Dec 2009 09:37:41 -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/30/t12621911221vo89p0x6tmzkyc.htm/, Retrieved Wed, 30 Dec 2009 17:38:54 +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/30/t12621911221vo89p0x6tmzkyc.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}, }

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Dataseries X:

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4223.4 401 4627.3 394 5175.3 372 4550.7 334 4639.3 320 5498.7 334 5031.0 400 4033.3 427 4643.5 423 4873.2 395 4608.7 373 4733.5 377 3955.6 391 4590.9 398 5127.5 393 5257.3 375 5416.9 371 5813.3 364 5261.9 400 4669.2 406 5855.8 407 5274.6 397 5516.7 389 5819.5 394 5156.0 399 5377.3 401 6386.8 396 5144.0 392 6138.5 384 5567.8 370 5822.6 380 5145.5 376 5706.6 378 6078.5 376 6074.5 373 5577.6 374 5727.5 379 6067.0 376 7069.9 371 5490.0 375 5948.3 360 6177.5 338 6890.1 352 5756.2 344 6528.8 330 6792.0 334 6657.4 333 5753.7 343 5750.9 350 5968.4 341 5871.7 320 7004.9 302 6363.4 287 6694.7 304 7101.6 370 5364.0 385 6958.6 365 6503.3 333 5316.0 313 5312.7 330 4478.0 367

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 Werkloosheid[t] = + 402.296605635782 -0.000281740366301887Export[t] + 12.2479148725478M1[t] + 8.04473827591623M2[t] -2.35386429189957M3[t] -16.2446090803411M4[t] -26.3525719887406M5[t] -27.6500485207064M6[t] + 11.8023026228968M7[t] + 19.7450661823929M8[t] + 14.0436527713366M9[t] + 1.46631411513886M10[t] -8.37732368405701M11[t] -1.03233630798111t + 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) 402.296605635782 31.805243 12.6488 0 0 Export -0.000281740366301887 0.006777 -0.0416 0.967015 0.483508 M1 12.2479148725478 14.160889 0.8649 0.391481 0.19574 M2 8.04473827591623 14.635625 0.5497 0.58515 0.292575 M3 -2.35386429189957 15.442257 -0.1524 0.8795 0.43975 M4 -16.2446090803411 14.677951 -1.1067 0.274041 0.13702 M5 -26.3525719887406 14.879461 -1.7711 0.083033 0.041517 M6 -27.6500485207064 15.256046 -1.8124 0.076315 0.038158 M7 11.8023026228968 15.333147 0.7697 0.445315 0.222657 M8 19.7450661823929 14.663258 1.3466 0.184578 0.092289 M9 14.0436527713366 15.031505 0.9343 0.354934 0.177467 M10 1.46631411513886 14.91632 0.0983 0.92211 0.461055 M11 -8.37732368405701 14.562618 -0.5753 0.567858 0.283929 t -1.03233630798111 0.265501 -3.8883 0.000316 0.000158 Multiple Linear Regression - Regression Statistics Multiple R 0.757394894570616 R-squared 0.573647026321634 Adjusted R-squared 0.455719608070171 F-TEST (value) 4.86440757227819 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 2.72288071523352e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 22.8968501011770 Sum Squared Residuals 24640.4899941212 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 401 412.32228193731 -11.3222819373099 2 394 406.972974098748 -12.9729740987476 3 372 395.387641502217 -23.3876415022173 4 334 380.640535438587 -46.6405354385868 5 320 369.475274025752 -49.4752740257518 6 334 366.903333515005 -32.9033335150051 7 400 405.455118319947 -5.45511831994658 8 427 412.646637934921 14.3533620650791 9 423 405.740970244366 17.2590297556339 10 395 392.066579518048 2.93342048195222 11 373 381.265125737758 -8.26512573775767 12 377 388.574951916119 -11.5749519161191 13 391 400.009696311632 -9.009696311632 14 398 394.595193752308 3.40480624769224 15 393 383.013072995953 9.98692700404674 16 375 368.053421999985 6.94657800001536 17 371 356.868157021142 14.1318429788578 18 364 354.426662299993 9.57333770000674 19 400 393.002028773594 6.99797122640577 20 406 400.079443540216 5.92055645978371 21 407 393.011380702525 13.9886192974749 22 397 379.565453239241 17.4345467607591 23 389 368.621269789382 20.3787302106177 24 394 375.880946182542 18.1190538174581 25 399 387.28345948015 11.7165405198501 26 401 381.985597432475 19.0144025675254 27 396 370.270241656896 25.729758343104 28 392 355.697307487713 36.3026925122867 29 384 344.276817477045 39.7231825229545 30 370 342.107793864147 27.8922061358529 31 380 380.456021254435 -0.456021254435470 32 376 387.557214907973 -11.5572149079734 33 378 380.665380669404 -2.66538066940401 34 376 366.950926462998 9.04907353700247 35 373 356.076079317286 16.9239206827142 36 374 363.561063481377 10.4389365186229 37 379 374.734409165035 4.2655908349649 38 376 369.403245406063 6.59675459393705 39 371 357.689749116902 13.3102508830981 40 375 343.2117896252 31.7882103748004 41 360 331.942368798943 28.0576312010572 42 338 329.547981067040 8.45201893296043 43 352 367.767227717635 -15.7672277176349 44 344 374.997120370500 -30.9971203704996 45 330 368.045698044457 -38.0456980444573 46 334 354.361869015868 -20.3618690158678 47 333 343.523817161995 -10.5238171619951 48 343 351.123413307098 -8.12341330709804 49 350 362.339780744690 -12.3397807446904 50 341 357.042989310407 -16.0429893104070 51 320 345.639294728032 -25.6392947280315 52 302 330.396945448516 -28.3969454485156 53 287 319.437382677118 -32.4373826771176 54 304 317.014229253815 -13.0142292538149 55 370 355.319603934389 14.6803960656112 56 385 362.71958324639 22.2804167536101 57 365 355.536570339247 9.46342966075253 58 333 342.055171763846 -9.05517176384593 59 313 331.513707993579 -18.5137079935792 60 330 338.859625112864 -8.85962511286389 61 367 350.310372361183 16.6896276388172 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0551487505532761 0.110297501106552 0.944851249446724 18 0.0174735385647804 0.0349470771295608 0.98252646143522 19 0.0386114333343126 0.0772228666686252 0.961388566665687 20 0.413973951537776 0.827947903075551 0.586026048462224 21 0.537793291631677 0.924413416736646 0.462206708368323 22 0.425768943352035 0.85153788670407 0.574231056647965 23 0.315064701286897 0.630129402573794 0.684935298713103 24 0.222106440758586 0.444212881517171 0.777893559241414 25 0.170201798652701 0.340403597305402 0.829798201347299 26 0.115038719672443 0.230077439344887 0.884961280327557 27 0.0761837712162595 0.152367542432519 0.92381622878374 28 0.0721165099217812 0.144233019843562 0.927883490078219 29 0.078560786396099 0.157121572792198 0.9214392136039 30 0.0500830077104435 0.100166015420887 0.949916992289557 31 0.0807243804694465 0.161448760938893 0.919275619530553 32 0.192050222444525 0.384100444889051 0.807949777555475 33 0.244215712394809 0.488431424789618 0.755784287605191 34 0.202721794058848 0.405443588117697 0.797278205941152 35 0.160028535124598 0.320057070249196 0.839971464875402 36 0.114484504644782 0.228969009289563 0.885515495355218 37 0.0820586557301155 0.164117311460231 0.917941344269884 38 0.062460689060049 0.124921378120098 0.937539310939951 39 0.098310601894288 0.196621203788576 0.901689398105712 40 0.0921590016477914 0.184318003295583 0.907840998352209 41 0.332438396113481 0.664876792226962 0.667561603886519 42 0.625822655704349 0.748354688591303 0.374177344295651 43 0.522839768532824 0.954320462934352 0.477160231467176 44 0.642535187818652 0.714929624362696 0.357464812181348 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 1 0.0357142857142857 OK 10% type I error level 2 0.0714285714285714 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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