Model 3, seizonaliteit + lineair verband

*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, 16 Dec 2009 07:39:07 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/16/t1260974954zkvzrbhx7oxas7x.htm/, Retrieved Wed, 16 Dec 2009 15:49:26 +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/16/t1260974954zkvzrbhx7oxas7x.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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95.1 136 97 133 112.7 126 102.9 120 97.4 114 111.4 116 87.4 153 96.8 162 114.1 161 110.3 149 103.9 139 101.6 135 94.6 130 95.9 127 104.7 122 102.8 117 98.1 112 113.9 113 80.9 149 95.7 157 113.2 157 105.9 147 108.8 137 102.3 132 99 125 100.7 123 115.5 117 100.7 114 109.9 111 114.6 112 85.4 144 100.5 150 114.8 149 116.5 134 112.9 123 102 116 106 117 105.3 111 118.8 105 106.1 102 109.3 95 117.2 93 92.5 124 104.2 130 112.5 124 122.4 115 113.3 106 100 105 110.7 105 112.8 101 109.8 95 117.3 93 109.1 84 115.9 87 96 116 99.8 120 116.8 117 115.7 109 99.4 105 94.3 107 91 109

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation tip[t] = + 122.259777574500 -0.185268531365494wrk[t] -0.416978394569082M1[t] + 2.25199379388721M2[t] + 11.1051832263055M3[t] + 4.06596342772792M4[t] + 1.75915286014624M5[t] + 11.789222012123M6[t] -8.2521158322044M7[t] + 3.93545709541912M8[t] + 18.4126669470263M9[t] + 16.2965674288903M10[t] + 8.1710049734852M11[t] -0.00480062061127904t + 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) 122.259777574500 20.152348 6.0668 0 0 wrk -0.185268531365494 0.137589 -1.3465 0.184589 0.092295 M1 -0.416978394569082 3.000392 -0.139 0.890064 0.445032 M2 2.25199379388721 3.288569 0.6848 0.496837 0.248418 M3 11.1051832263055 3.573807 3.1074 0.003199 0.001599 M4 4.06596342772792 3.793315 1.0719 0.289249 0.144624 M5 1.75915286014624 4.244522 0.4145 0.680428 0.340214 M6 11.789222012123 4.084826 2.8861 0.005874 0.002937 M7 -8.2521158322044 3.703298 -2.2283 0.030681 0.015341 M8 3.93545709541912 4.331012 0.9087 0.368161 0.18408 M9 18.4126669470263 4.191855 4.3925 6.3e-05 3.2e-05 M10 16.2965674288903 3.42099 4.7637 1.9e-05 9e-06 M11 8.1710049734852 3.12615 2.6138 0.011993 0.005996 t -0.00480062061127904 0.106805 -0.0449 0.96434 0.48217 Multiple Linear Regression - Regression Statistics Multiple R 0.878574643479738 R-squared 0.77189340416555 Adjusted R-squared 0.708800090424106 F-TEST (value) 12.2341553865560 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 5.17779152886533e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.91781265256009 Sum Squared Residuals 1136.68942042697 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.1 96.6414782936123 -1.54147829361233 2 97 99.8614554555538 -2.86145545555379 3 112.7 110.006723986919 2.69327601308074 4 102.9 104.074314755923 -1.17431475592336 5 97.4 102.874314755923 -5.47431475592336 6 111.4 112.529046224558 -1.12904622455787 7 87.4 85.6279720990959 1.77202790090412 8 96.8 96.1433276238187 0.656672376181293 9 114.1 110.801005386180 3.29899461381989 10 110.3 110.903327623819 -0.603327623818687 11 103.9 104.625649861457 -0.725649861457294 12 101.6 97.1909183928228 4.40908160717721 13 94.6 97.69548203447 -3.09548203446991 14 95.9 100.915459196411 -5.01545919641138 15 104.7 110.690190665046 -5.9901906650459 16 102.8 104.572512902684 -1.77251290268450 17 98.1 103.187244371319 -5.08724437131901 18 113.9 113.027244371319 0.872755628681004 19 80.9 86.3114387772225 -5.41143877722252 20 95.7 97.0120628333108 -1.31206283331082 21 113.2 111.484472064307 1.71552793569326 22 105.9 111.216257239214 -5.31625723921435 23 108.8 104.938579476853 3.86142052314706 24 102.3 97.689116539584 4.61088346041607 25 99 98.564217243962 0.435782756037974 26 100.7 101.598925874538 -0.898925874538018 27 115.5 111.558925874538 3.94107412546198 28 100.7 105.070711049446 -4.37071104944563 29 109.9 103.314905455349 6.58509454465086 30 114.6 113.154905455349 1.44509454465084 31 85.4 87.1801739867146 -1.78017398671464 32 100.5 98.251335105534 2.24866489446606 33 114.8 112.909012867895 1.89098713210466 34 116.5 113.567140699630 2.93285930036957 35 112.9 107.474731468635 5.4252685313655 36 102 100.595805594096 1.40419440590352 37 106 99.9887580475506 6.01124195244937 38 105.3 103.764540803589 1.53545919641140 39 118.8 113.724540803589 5.07545919641139 40 106.1 107.236325978496 -1.13632597849621 41 109.3 106.221594509862 3.07840549013829 42 117.2 116.617400103958 0.582599896041817 43 92.5 90.8279371666892 1.67206283331082 44 104.2 101.899098285508 2.30090171449153 45 112.5 117.483118704697 -4.98311870469735 46 122.4 117.029635348239 5.37036465176054 47 113.3 110.566689054513 2.73331094548744 48 100 102.576151991782 -2.57615199178157 49 110.7 102.154372976601 8.54562702339879 50 112.8 105.559618669908 7.2403813300918 51 109.8 115.519618669908 -5.7196186699082 52 117.3 108.846135313450 8.4538646865497 53 109.1 108.201940907547 0.898059092453205 54 115.9 117.671403844816 -1.77140384481580 55 96 92.2524779702778 3.74752202972222 56 99.8 103.694176151828 -3.89417615182807 57 116.8 118.722390976920 -1.92239097692046 58 115.7 118.083639089097 -2.38363908909708 59 99.4 110.694350138543 -11.2943501385427 60 94.3 102.148007481715 -7.84800748171523 61 91 101.355691403804 -10.3556914038039 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.199876899867726 0.399753799735451 0.800123100132274 18 0.130445639082920 0.260891278165839 0.86955436091708 19 0.137234687761394 0.274469375522788 0.862765312238606 20 0.0740537618828847 0.148107523765769 0.925946238117115 21 0.0357070679004614 0.0714141358009228 0.964292932099539 22 0.0285746440288704 0.0571492880577407 0.97142535597113 23 0.0357615194275701 0.0715230388551401 0.96423848057243 24 0.019992574007853 0.039985148015706 0.980007425992147 25 0.0378695978911341 0.0757391957822681 0.962130402108866 26 0.0455188325095428 0.0910376650190856 0.954481167490457 27 0.0527138951369769 0.105427790273954 0.947286104863023 28 0.0796322204551651 0.159264440910330 0.920367779544835 29 0.207957461620741 0.415914923241482 0.792042538379259 30 0.147292613097186 0.294585226194371 0.852707386902814 31 0.122348589288778 0.244697178577556 0.877651410711222 32 0.0931361165939759 0.186272233187952 0.906863883406024 33 0.0857413260828835 0.171482652165767 0.914258673917117 34 0.085622768030717 0.171245536061434 0.914377231969283 35 0.126465684373153 0.252931368746307 0.873534315626847 36 0.0980572165774429 0.196114433154886 0.901942783422557 37 0.0863269304846328 0.172653860969266 0.913673069515367 38 0.0726828635427888 0.145365727085578 0.927317136457211 39 0.135393981769129 0.270787963538258 0.864606018230871 40 0.259451818660478 0.518903637320956 0.740548181339522 41 0.188742563371702 0.377485126743405 0.811257436628298 42 0.124688611126330 0.249377222252659 0.87531138887367 43 0.100959105450093 0.201918210900187 0.899040894549907 44 0.088848251001177 0.177696502002354 0.911151748998823 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 6 0.214285714285714 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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