Paper H4 Mannen Multiple Regression (No seasonal, 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 13:42:07 -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/t12294606910fojzx044nwf03r.htm/, Retrieved Tue, 16 Dec 2008 21:51:31 +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/t12294606910fojzx044nwf03r.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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Mannen[t] = + 273502.296296296 -14577.3796296296Dummy[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) 273502.296296296 2995.373533 91.3082 0 0 Dummy -14577.3796296296 3962.506727 -3.6788 0.000498 0.000249 Multiple Linear Regression - Regression Statistics Multiple R 0.426120960192175 R-squared 0.181579072715101 Adjusted R-squared 0.168162336202234 F-TEST (value) 13.5337734732258 F-TEST (DF numerator) 1 F-TEST (DF denominator) 61 p-value 0.000497507392827723 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 15564.4174428114 Sum Squared Residuals 14777316510.3796 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 269645 273502.296296297 -3857.29629629676 2 267037 273502.296296296 -6465.29629629628 3 258113 273502.296296296 -15389.2962962963 4 262813 273502.296296296 -10689.2962962963 5 267413 273502.296296296 -6089.29629629628 6 267366 273502.296296296 -6136.29629629628 7 264777 273502.296296296 -8725.29629629628 8 258863 273502.296296296 -14639.2962962963 9 254844 273502.296296296 -18658.2962962963 10 254868 273502.296296296 -18634.2962962963 11 277267 273502.296296296 3764.70370370372 12 285351 273502.296296296 11848.7037037037 13 286602 273502.296296296 13099.7037037037 14 283042 273502.296296296 9539.70370370372 15 276687 273502.296296296 3184.70370370372 16 277915 273502.296296296 4412.70370370372 17 277128 273502.296296296 3625.70370370372 18 277103 273502.296296296 3600.70370370372 19 275037 273502.296296296 1534.70370370372 20 270150 273502.296296296 -3352.29629629628 21 267140 273502.296296296 -6362.29629629628 22 264993 273502.296296296 -8509.29629629628 23 287259 273502.296296296 13756.7037037037 24 291186 273502.296296296 17683.7037037037 25 292300 273502.296296296 18797.7037037037 26 288186 273502.296296296 14683.7037037037 27 281477 273502.296296296 7974.70370370372 28 282656 258924.916666667 23731.0833333333 29 280190 258924.916666667 21265.0833333333 30 280408 258924.916666667 21483.0833333333 31 276836 258924.916666667 17911.0833333333 32 275216 258924.916666667 16291.0833333333 33 274352 258924.916666667 15427.0833333333 34 271311 258924.916666667 12386.0833333333 35 289802 258924.916666667 30877.0833333333 36 290726 258924.916666667 31801.0833333333 37 292300 258924.916666667 33375.0833333333 38 278506 258924.916666667 19581.0833333333 39 269826 258924.916666667 10901.0833333333 40 265861 258924.916666667 6936.08333333333 41 269034 258924.916666667 10109.0833333333 42 264176 258924.916666667 5251.08333333333 43 255198 258924.916666667 -3726.91666666667 44 253353 258924.916666667 -5571.91666666667 45 246057 258924.916666667 -12867.9166666667 46 235372 258924.916666667 -23552.9166666667 47 258556 258924.916666667 -368.916666666667 48 260993 258924.916666667 2068.08333333333 49 254663 258924.916666667 -4261.91666666667 50 250643 258924.916666667 -8281.91666666667 51 243422 258924.916666667 -15502.9166666667 52 247105 258924.916666667 -11819.9166666667 53 248541 258924.916666667 -10383.9166666667 54 245039 258924.916666667 -13885.9166666667 55 237080 258924.916666667 -21844.9166666667 56 237085 258924.916666667 -21839.9166666667 57 225554 258924.916666667 -33370.9166666667 58 226839 258924.916666667 -32085.9166666667 59 247934 258924.916666667 -10990.9166666667 60 248333 258924.916666667 -10591.9166666667 61 246969 258924.916666667 -11955.9166666667 62 245098 258924.916666667 -13826.9166666667 63 246263 258924.916666667 -12661.9166666667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0459234375474238 0.0918468750948475 0.954076562452576 6 0.0134880939563151 0.0269761879126301 0.986511906043685 7 0.00338657715907624 0.00677315431815247 0.996613422840924 8 0.00214407335897841 0.00428814671795682 0.997855926641022 9 0.00311974747987324 0.00623949495974648 0.996880252520127 10 0.00297904942876872 0.00595809885753743 0.997020950571231 11 0.00788571018579346 0.0157714203715869 0.992114289814207 12 0.0373454756015955 0.074690951203191 0.962654524398404 13 0.0765950260221371 0.153190052044274 0.923404973977863 14 0.0822179025725723 0.164435805145145 0.917782097427428 15 0.0590978251737607 0.118195650347521 0.94090217482624 16 0.0430132347604459 0.0860264695208919 0.956986765239554 17 0.0293695803480882 0.0587391606961764 0.970630419651912 18 0.0194009580887999 0.0388019161775999 0.9805990419112 19 0.0117161568249372 0.0234323136498743 0.988283843175063 20 0.00675220199757975 0.0135044039951595 0.99324779800242 21 0.00421071499770931 0.00842142999541863 0.99578928500229 22 0.00307561848783921 0.00615123697567841 0.99692438151216 23 0.00408473676745112 0.00816947353490223 0.995915263232549 24 0.00680644144728614 0.0136128828945723 0.993193558552714 25 0.0102785577440498 0.0205571154880996 0.98972144225595 26 0.00995789835520041 0.0199157967104008 0.9900421016448 27 0.00664598547248897 0.0132919709449779 0.993354014527511 28 0.00542188218777766 0.0108437643755553 0.994578117812222 29 0.00430737649781857 0.00861475299563714 0.995692623502181 30 0.00357328551197892 0.00714657102395783 0.996426714488021 31 0.00283338318539935 0.0056667663707987 0.9971666168146 32 0.00223146939864900 0.00446293879729799 0.99776853060135 33 0.00176500426772352 0.00353000853544703 0.998234995732276 34 0.00137767985762710 0.00275535971525421 0.998622320142373 35 0.00400313765411199 0.00800627530822397 0.995996862345888 36 0.0156969062040021 0.0313938124080043 0.984303093795998 37 0.0946275042470452 0.189255008494090 0.905372495752955 38 0.186277257112944 0.372554514225888 0.813722742887056 39 0.270521108329521 0.541042216659041 0.72947889167048 40 0.359444195205112 0.718888390410225 0.640555804794888 41 0.521637497215584 0.956725005568832 0.478362502784416 42 0.656655237020949 0.686689525958102 0.343344762979051 43 0.720802002107029 0.558395995785942 0.279197997892971 44 0.760418225341274 0.479163549317453 0.239581774658726 45 0.791101633504361 0.417796732991278 0.208898366495639 46 0.878368836815623 0.243262326368755 0.121631163184377 47 0.897254498821749 0.205491002356503 0.102745501178251 48 0.941319341295646 0.117361317408708 0.0586806587043542 49 0.95053371546127 0.0989325690774605 0.0494662845387303 50 0.947031397177078 0.105937205645844 0.0529686028229219 51 0.92911154010792 0.141776919784159 0.0708884598920797 52 0.9071531328337 0.185693734332601 0.0928468671663005 53 0.885696037806983 0.228607924386033 0.114303962193017 54 0.841637144072972 0.316725711854057 0.158362855927028 55 0.786002541406128 0.427994917187745 0.213997458593872 56 0.707359730685285 0.58528053862943 0.292640269314715 57 0.828964171976758 0.342071656046484 0.171035828023242 58 0.998798520621807 0.00240295875638605 0.00120147937819303 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 15 0.277777777777778 NOK 5% type I error level 26 0.481481481481481 NOK 10% type I error level 31 0.574074074074074 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 = Do not include Seasonal 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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