multi regression seizoenaliteit

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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: Thu, 19 Nov 2009 13:04:27 -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/Nov/19/t125866112128m1rk5wdjhclyk.htm/, Retrieved Thu, 19 Nov 2009 21:05:33 +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/Nov/19/t125866112128m1rk5wdjhclyk.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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8.9 6.3 8.2 6.2 7.6 6.1 7.7 6.3 8.1 6.5 8.3 6.6 8.3 6.5 7.9 6.2 7.8 6.2 8 5.9 8.5 6.1 8.6 6.1 8.5 6.1 8 6.1 7.8 6.1 8 6.4 8.2 6.7 8.3 6.9 8.2 7 8.1 7 8 6.8 7.8 6.4 7.8 5.9 7.7 5.5 7.6 5.5 7.6 5.6 7.6 5.8 7.8 5.9 8 6.1 8 6.1 7.9 6 7.7 6 7.4 5.9 6.9 5.5 6.7 5.6 6.5 5.4 6.4 5.2 6.7 5.2 6.8 5.2 6.9 5.5 6.9 5.8 6.7 5.8 6.4 5.5 6.2 5.3 5.9 5.1 6.1 5.2 6.7 5.8 6.8 5.8 6.6 5.5 6.4 5 6.4 4.9 6.7 5.3 7.1 6.1 7.1 6.5 6.9 6.8 6.4 6.6 6 6.4 6 6.4

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 X[t] = + 1.05047871431013 + 1.11395110275261Y[t] + 0.177720977944961M1[t] + 0.0691160882202088M2[t] -0.0708839117797914M3[t] -0.180511198495470M4[t] -0.341533595486408M5[t] -0.477486749871774M6[t] -0.595207727816722M7[t] -0.719254573431356M8[t] -0.803301419045992M9[t] -0.64051119849547M10[t] -0.142092665412891M11[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) 1.05047871431013 1.099323 0.9556 0.344396 0.172198 Y 1.11395110275261 0.184729 6.0302 0 0 M1 0.177720977944961 0.423851 0.4193 0.676991 0.338496 M2 0.0691160882202088 0.424092 0.163 0.871269 0.435634 M3 -0.0708839117797914 0.424092 -0.1671 0.868007 0.434003 M4 -0.180511198495470 0.425137 -0.4246 0.673155 0.336578 M5 -0.341533595486408 0.435416 -0.7844 0.436924 0.218462 M6 -0.477486749871774 0.442058 -1.0801 0.285833 0.142916 M7 -0.595207727816722 0.441022 -1.3496 0.183892 0.091946 M8 -0.719254573431356 0.434584 -1.655 0.104875 0.052438 M9 -0.803301419045992 0.429609 -1.8698 0.06802 0.03401 M10 -0.64051119849547 0.425137 -1.5066 0.138902 0.069451 M11 -0.142092665412891 0.44762 -0.3174 0.752378 0.376189 Multiple Linear Regression - Regression Statistics Multiple R 0.70191490771637 R-squared 0.492684537674481 Adjusted R-squared 0.357400414387675 F-TEST (value) 3.64185039385575 F-TEST (DF numerator) 12 F-TEST (DF denominator) 45 p-value 0.000762777364173739 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.631815781520582 Sum Squared Residuals 17.9636031800309 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.9 8.24609163959646 0.653908360403539 2 8.2 8.02609163959651 0.173908360403488 3 7.6 7.77469652932125 -0.174696529321252 4 7.7 7.8878594631561 -0.187859463156095 5 8.1 7.94962728671568 0.150372713284322 6 8.3 7.92506924260557 0.374930757394427 7 8.3 7.69595315438537 0.604046845614634 8 7.9 7.23772097794495 0.662279022055052 9 7.8 7.15367413233031 0.646325867669687 10 8 6.98227902205505 1.01772097794495 11 8.5 7.70348777568815 0.796512224311849 12 8.6 7.84558044110104 0.754419558898957 13 8.5 8.023301419046 0.476698580953996 14 8 7.91469652932125 0.085303470678748 15 7.8 7.77469652932125 0.0253034706787481 16 8 7.99925457343136 0.000745426568643112 17 8.2 8.1724175072662 0.0275824927337991 18 8.3 8.25925457343136 0.0407454265686433 19 8.2 8.25292870576167 -0.0529287057616704 20 8.1 8.12888186014703 -0.0288818601470353 21 8 7.82204479398188 0.177955206018122 22 7.8 7.53925457343136 0.260745426568643 23 7.8 7.48069755513763 0.319302444862369 24 7.7 7.17720977944948 0.522790220550521 25 7.6 7.35493075739444 0.245069242605561 26 7.6 7.35772097794495 0.242279022055052 27 7.6 7.44051119849547 0.159488801504530 28 7.8 7.44227902205505 0.357720977944947 29 8 7.50404684561463 0.495953154385366 30 8 7.36809369122927 0.63190630877073 31 7.9 7.13897760300906 0.761022396990939 32 7.7 7.01493075739443 0.685069242605574 33 7.4 6.81948880150453 0.580511198495469 34 6.9 6.53669858095401 0.363301419045992 35 6.7 7.14651222431185 -0.446512224311848 36 6.5 7.06581466917422 -0.565814669174218 37 6.4 7.02074542656866 -0.620745426568656 38 6.7 6.9121405368439 -0.212140536843905 39 6.8 6.7721405368439 0.0278594631560951 40 6.9 6.99669858095401 -0.0966985809540086 41 6.9 7.16986151478885 -0.269861514788852 42 6.7 7.03390836040349 -0.333908360403487 43 6.4 6.58200205163276 -0.182002051632756 44 6.2 6.2351649854676 -0.0351649854676001 45 5.9 5.92832791930244 -0.0283279193024429 46 6.1 6.20251325012823 -0.102513250128226 47 6.7 7.36930244486237 -0.66930244486237 48 6.8 7.51139511027526 -0.711395110275261 49 6.6 7.35493075739444 -0.75493075739444 50 6.4 6.68935031629338 -0.289350316293383 51 6.4 6.43795520601812 -0.0379552060181217 52 6.7 6.77390836040349 -0.0739083604034868 53 7.1 7.50404684561463 -0.404046845614634 54 7.1 7.81367413233031 -0.713674132330314 55 6.9 8.03013848521115 -1.13013848521115 56 6.4 7.68330141904599 -1.28330141904599 57 6 7.37646435288084 -1.37646435288083 58 6 7.53925457343136 -1.53925457343136 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.00395058939566930 0.00790117879133861 0.99604941060433 17 0.00245256530853358 0.00490513061706715 0.997547434691466 18 0.00188892963840830 0.00377785927681659 0.998111070361592 19 0.00114964360219061 0.00229928720438122 0.99885035639781 20 0.000265785222803165 0.000531570445606329 0.999734214777197 21 6.8353876962633e-05 0.000136707753925266 0.999931646123037 22 5.60455634651084e-05 0.000112091126930217 0.999943954436535 23 0.000418465177217027 0.000836930354434053 0.999581534822783 24 0.00147760403745991 0.00295520807491983 0.99852239596254 25 0.00485335790294763 0.00970671580589525 0.995146642097052 26 0.00288529163149753 0.00577058326299506 0.997114708368502 27 0.00166111903446521 0.00332223806893043 0.998338880965535 28 0.00134845291100804 0.00269690582201608 0.998651547088992 29 0.00114849919086624 0.00229699838173249 0.998851500809134 30 0.00129107921963813 0.00258215843927626 0.998708920780362 31 0.00282411205872169 0.00564822411744339 0.997175887941278 32 0.0158809336116152 0.0317618672232305 0.984119066388385 33 0.306196138163067 0.612392276326134 0.693803861836933 34 0.934866605282959 0.130266789434082 0.0651333947170411 35 0.978814291795049 0.0423714164099026 0.0211857082049513 36 0.992140001570517 0.0157199968589655 0.00785999842948273 37 0.99307678620953 0.0138464275809389 0.00692321379046943 38 0.989133500309537 0.0217329993809254 0.0108664996904627 39 0.987473532323877 0.0250529353522464 0.0125264676761232 40 0.971538060968684 0.0569238780626326 0.0284619390313163 41 0.938293431689656 0.123413136620689 0.0617065683103445 42 0.913185185636877 0.173629628726246 0.086814814363123 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 16 0.592592592592593 NOK 5% type I error level 22 0.814814814814815 NOK 10% type I error level 23 0.851851851851852 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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