Paper H4 Mannen Multiple Regression (Monthly dummies, No trend)

*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: Tue, 16 Dec 2008 13:57:35 -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/16/t122946113367uz1n369aeiil5.htm/, Retrieved Tue, 16 Dec 2008 21:58:53 +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/16/t122946113367uz1n369aeiil5.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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269645 0 267037 0 258113 0 262813 0 267413 0 267366 0 264777 0 258863 0 254844 0 254868 0 277267 0 285351 0 286602 0 283042 0 276687 0 277915 0 277128 0 277103 0 275037 0 270150 0 267140 0 264993 0 287259 0 291186 0 292300 0 288186 0 281477 0 282656 1 280190 1 280408 1 276836 1 275216 1 274352 1 271311 1 289802 1 290726 1 292300 1 278506 1 269826 1 265861 1 269034 1 264176 1 255198 1 253353 1 246057 1 235372 1 258556 1 260993 1 254663 1 250643 1 243422 1 247105 1 248541 1 245039 1 237080 1 237085 1 225554 1 226839 1 247934 1 248333 1 246969 1 245098 1 246263 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 7 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Mannen[t] = + 283911.545098039 -14322.908496732Dummy[t] -3003.59084967328M1[t] -7998.0908496732M2[t] -14118.7575163399M3[t] -8047.8M4[t] -6856.6M5[t] -8499.4M6[t] -13532.2M7[t] -16384.4M8[t] -21728.4M9[t] -24641.2M10[t] -3154.2M11[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) 283911.545098039 7182.14178 39.5302 0 0 Dummy -14322.908496732 3883.657487 -3.688 0.000557 0.000279 M1 -3003.59084967328 9206.80784 -0.3262 0.745608 0.372804 M2 -7998.0908496732 9206.80784 -0.8687 0.389154 0.194577 M3 -14118.7575163399 9206.80784 -1.5335 0.131453 0.065727 M4 -8047.8 9607.638021 -0.8376 0.406216 0.203108 M5 -6856.6 9607.638021 -0.7137 0.478755 0.239377 M6 -8499.4 9607.638021 -0.8847 0.38058 0.19029 M7 -13532.2 9607.638021 -1.4085 0.165176 0.082588 M8 -16384.4 9607.638021 -1.7054 0.094335 0.047168 M9 -21728.4 9607.638021 -2.2616 0.028105 0.014052 M10 -24641.2 9607.638021 -2.5648 0.013374 0.006687 M11 -3154.2 9607.638021 -0.3283 0.744055 0.372027 Multiple Linear Regression - Regression Statistics Multiple R 0.600803894705908 R-squared 0.360965319893787 Adjusted R-squared 0.207596996668296 F-TEST (value) 2.35358457536942 F-TEST (DF numerator) 12 F-TEST (DF denominator) 50 p-value 0.0173900451783193 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 15191.0095399912 Sum Squared Residuals 11538338542.2052 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 269645 280907.954248366 -11262.9542483664 2 267037 275913.454248366 -8876.454248366 3 258113 269792.787581699 -11679.7875816993 4 262813 275863.745098039 -13050.7450980392 5 267413 277054.945098039 -9641.9450980392 6 267366 275412.145098039 -8046.1450980392 7 264777 270379.345098039 -5602.34509803921 8 258863 267527.145098039 -8664.14509803921 9 254844 262183.145098039 -7339.14509803921 10 254868 259270.345098039 -4402.3450980392 11 277267 280757.345098039 -3490.34509803921 12 285351 283911.545098039 1439.45490196080 13 286602 280907.954248366 5694.04575163408 14 283042 275913.454248366 7128.545751634 15 276687 269792.787581699 6894.21241830066 16 277915 275863.745098039 2051.25490196079 17 277128 277054.945098039 73.0549019607964 18 277103 275412.145098039 1690.85490196079 19 275037 270379.345098039 4657.6549019608 20 270150 267527.145098039 2622.85490196080 21 267140 262183.145098039 4956.85490196079 22 264993 259270.345098039 5722.6549019608 23 287259 280757.345098039 6501.65490196079 24 291186 283911.545098039 7274.4549019608 25 292300 280907.954248366 11392.0457516341 26 288186 275913.454248366 12272.545751634 27 281477 269792.787581699 11684.2124183007 28 282656 261540.836601307 21115.1633986928 29 280190 262732.036601307 17457.9633986928 30 280408 261089.236601307 19318.7633986928 31 276836 256056.436601307 20779.5633986928 32 275216 253204.236601307 22011.7633986928 33 274352 247860.236601307 26491.7633986928 34 271311 244947.436601307 26363.5633986928 35 289802 266434.436601307 23367.5633986928 36 290726 269588.636601307 21137.3633986928 37 292300 266585.045751634 25714.9542483661 38 278506 261590.545751634 16915.454248366 39 269826 255469.879084967 14356.1209150327 40 265861 261540.836601307 4320.1633986928 41 269034 262732.036601307 6301.9633986928 42 264176 261089.236601307 3086.7633986928 43 255198 256056.436601307 -858.436601307196 44 253353 253204.236601307 148.763398692804 45 246057 247860.236601307 -1803.2366013072 46 235372 244947.436601307 -9575.4366013072 47 258556 266434.436601307 -7878.4366013072 48 260993 269588.636601307 -8595.6366013072 49 254663 266585.045751634 -11922.0457516339 50 250643 261590.545751634 -10947.545751634 51 243422 255469.879084967 -12047.8790849673 52 247105 261540.836601307 -14435.8366013072 53 248541 262732.036601307 -14191.0366013072 54 245039 261089.236601307 -16050.2366013072 55 237080 256056.436601307 -18976.4366013072 56 237085 253204.236601307 -16119.2366013072 57 225554 247860.236601307 -22306.2366013072 58 226839 244947.436601307 -18108.4366013072 59 247934 266434.436601307 -18500.4366013072 60 248333 269588.636601307 -21255.6366013072 61 246969 266585.045751634 -19616.0457516339 62 245098 261590.545751634 -16492.545751634 63 246263 255469.879084967 -9206.87908496733 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.39956641352511 0.79913282705022 0.60043358647489 17 0.265261165516803 0.530522331033606 0.734738834483197 18 0.169981534468634 0.339963068937268 0.830018465531366 19 0.106727185256729 0.213454370513458 0.893272814743271 20 0.0686399470797782 0.137279894159556 0.931360052920222 21 0.0450005793142844 0.0900011586285687 0.954999420685716 22 0.0266355198619388 0.0532710397238776 0.973364480138061 23 0.0153359949540722 0.0306719899081444 0.984664005045928 24 0.00749180125353257 0.0149836025070651 0.992508198746467 25 0.00581287062635547 0.0116257412527109 0.994187129373645 26 0.00408336788271488 0.00816673576542976 0.995916632117285 27 0.00299545108719373 0.00599090217438747 0.997004548912806 28 0.00167209076085023 0.00334418152170047 0.99832790923915 29 0.000871674477780847 0.00174334895556169 0.99912832552222 30 0.000486448173315688 0.000972896346631377 0.999513551826684 31 0.000322059392149795 0.000644118784299591 0.99967794060785 32 0.000217803846031181 0.000435607692062363 0.999782196153969 33 0.000249518853467391 0.000499037706934782 0.999750481146533 34 0.000381157204437183 0.000762314408874367 0.999618842795563 35 0.000605513713881362 0.00121102742776272 0.999394486286119 36 0.00143181600355991 0.00286363200711983 0.99856818399644 37 0.00832325293801742 0.0166465058760348 0.991676747061983 38 0.0296999429038946 0.0593998858077891 0.970300057096105 39 0.07329701982962 0.14659403965924 0.92670298017038 40 0.106586109353167 0.213172218706334 0.893413890646833 41 0.156066769792697 0.312133539585394 0.843933230207303 42 0.242077851800494 0.484155703600988 0.757922148199506 43 0.388139213116377 0.776278426232753 0.611860786883623 44 0.491292040531774 0.982584081063547 0.508707959468226 45 0.761543056830975 0.47691388633805 0.238456943169025 46 0.770325001109872 0.459349997780257 0.229674998890128 47 0.771568561858252 0.456862876283497 0.228431438141748 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 11 0.34375 NOK 5% type I error level 15 0.46875 NOK 10% type I error level 18 0.5625 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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