dummy variabele model 2

*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: Thu, 24 Dec 2009 08:44:40 -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/24/t1261669536kyphqoi0c56lz0s.htm/, Retrieved Thu, 24 Dec 2009 16:45:48 +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/24/t1261669536kyphqoi0c56lz0s.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:

» Textbox « » Textfile « » CSV «

8,7 0 8,2 0 8,3 0 8,5 0 8,6 0 8,5 0 8,2 0 8,1 0 7,9 0 8,6 0 8,7 0 8,7 0 8,5 0 8,4 0 8,5 0 8,7 0 8,7 0 8,6 0 8,5 0 8,3 0 8 0 8,2 0 8,1 0 8,1 0 8 0 7,9 0 7,9 0 8 0 8 0 7,9 0 8 0 7,7 0 7,2 0 7,5 0 7,3 0 7 0 7 0 7 0 7,2 0 7,3 0 7,1 0 6,8 0 6,4 0 6,1 0 6,5 0 7,7 0 7,9 0 7,5 1 6,9 1 6,6 1 6,9 1 7,7 1 8 1 8 1 7,7 1 7,3 1 7,4 1 8,1 1 8,3 1 8,2 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 8.0288 -0.321999999999999X[t] -0.144400000000006M1[t] -0.344399999999999M2[t] -0.204399999999999M3[t] + 0.0756000000000006M4[t] + 0.115600000000000M5[t] -0.00439999999999969M6[t] -0.204399999999999M7[t] -0.464399999999999M8[t] -0.564399999999999M9[t] + 0.0556000000000004M10[t] + 0.0956000000000006M11[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) 8.0288 0.316634 25.3567 0 0 X -0.321999999999999 0.215442 -1.4946 0.141703 0.070851 M1 -0.144400000000006 0.433033 -0.3335 0.740269 0.370134 M2 -0.344399999999999 0.433033 -0.7953 0.430425 0.215213 M3 -0.204399999999999 0.433033 -0.472 0.639097 0.319549 M4 0.0756000000000006 0.433033 0.1746 0.862158 0.431079 M5 0.115600000000000 0.433033 0.267 0.790672 0.395336 M6 -0.00439999999999969 0.433033 -0.0102 0.991936 0.495968 M7 -0.204399999999999 0.433033 -0.472 0.639097 0.319549 M8 -0.464399999999999 0.433033 -1.0724 0.289 0.1445 M9 -0.564399999999999 0.433033 -1.3034 0.198799 0.099399 M10 0.0556000000000004 0.433033 0.1284 0.898383 0.449191 M11 0.0956000000000006 0.433033 0.2208 0.826229 0.413115 Multiple Linear Regression - Regression Statistics Multiple R 0.387829572007958 R-squared 0.150411776923876 Adjusted R-squared -0.066504365138113 F-TEST (value) 0.693409791885807 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.749314651603673 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.68128726718289 Sum Squared Residuals 21.8151599999999 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.7 7.88440000000003 0.815599999999974 2 8.2 7.6844 0.5156 3 8.3 7.8244 0.4756 4 8.5 8.1044 0.395600000000000 5 8.6 8.1444 0.4556 6 8.5 8.0244 0.4756 7 8.2 7.8244 0.375599999999999 8 8.1 7.5644 0.5356 9 7.9 7.4644 0.435600000000000 10 8.6 8.0844 0.5156 11 8.7 8.1244 0.575599999999999 12 8.7 8.0288 0.6712 13 8.5 7.8844 0.615600000000007 14 8.4 7.6844 0.7156 15 8.5 7.8244 0.6756 16 8.7 8.1044 0.5956 17 8.7 8.1444 0.5556 18 8.6 8.0244 0.5756 19 8.5 7.8244 0.6756 20 8.3 7.5644 0.7356 21 8 7.4644 0.5356 22 8.2 8.0844 0.115600000000000 23 8.1 8.1244 -0.0244000000000003 24 8.1 8.0288 0.0712000000000006 25 8 7.8844 0.115600000000007 26 7.9 7.6844 0.2156 27 7.9 7.8244 0.0756000000000002 28 8 8.1044 -0.1044 29 8 8.1444 -0.144400000000000 30 7.9 8.0244 -0.124399999999999 31 8 7.8244 0.175600 32 7.7 7.5644 0.135600000000000 33 7.2 7.4644 -0.2644 34 7.5 8.0844 -0.5844 35 7.3 8.1244 -0.8244 36 7 8.0288 -1.02880000000000 37 7 7.8844 -0.884399999999993 38 7 7.6844 -0.6844 39 7.2 7.8244 -0.6244 40 7.3 8.1044 -0.8044 41 7.1 8.1444 -1.0444 42 6.8 8.0244 -1.2244 43 6.4 7.8244 -1.4244 44 6.1 7.5644 -1.4644 45 6.5 7.4644 -0.9644 46 7.7 8.0844 -0.384399999999999 47 7.9 8.1244 -0.224400000000000 48 7.5 7.7068 -0.2068 49 6.9 7.5624 -0.662399999999994 50 6.6 7.3624 -0.762400000000001 51 6.9 7.5024 -0.6024 52 7.7 7.7824 -0.0824000000000005 53 8 7.8224 0.177600000000000 54 8 7.7024 0.297599999999999 55 7.7 7.5024 0.197600000000000 56 7.3 7.2424 0.0575999999999991 57 7.4 7.1424 0.257600000000000 58 8.1 7.7624 0.337599999999999 59 8.3 7.8024 0.4976 60 8.2 7.7068 0.493199999999999 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0205188468201001 0.0410376936402003 0.9794811531799 17 0.00506218856671496 0.0101243771334299 0.994937811433285 18 0.00126809325832566 0.00253618651665131 0.998731906741674 19 0.00093863250915197 0.00187726501830394 0.999061367490848 20 0.000469061050603817 0.000938122101207633 0.999530938949396 21 0.000159323662258763 0.000318647324517526 0.99984067633774 22 0.000204972915216014 0.000409945830432028 0.999795027084784 23 0.000654781371272177 0.00130956274254435 0.999345218628728 24 0.00128952582531370 0.00257905165062740 0.998710474174686 25 0.00397528651671241 0.00795057303342481 0.996024713483288 26 0.00606487492833997 0.0121297498566799 0.99393512507166 27 0.0103667916900097 0.0207335833800194 0.98963320830999 28 0.0166221092224031 0.0332442184448062 0.983377890777597 29 0.0264923071931726 0.0529846143863452 0.973507692806827 30 0.0403781466080727 0.0807562932161453 0.959621853391927 31 0.0721659139091055 0.144331827818211 0.927834086090894 32 0.20048093260975 0.4009618652195 0.79951906739025 33 0.273126119506474 0.546252239012948 0.726873880493526 34 0.321979242662475 0.64395848532495 0.678020757337525 35 0.456223258794996 0.912446517589991 0.543776741205004 36 0.59077750527719 0.81844498944562 0.40922249472281 37 0.727002806262114 0.545994387475772 0.272997193737886 38 0.868874993714035 0.262250012571931 0.131125006285965 39 0.960635504714138 0.0787289905717236 0.0393644952858618 40 0.95913537561909 0.0817292487618181 0.0408646243809090 41 0.93703328422819 0.125933431543620 0.0629667157718102 42 0.91818946902091 0.163621061958181 0.0818105309790905 43 0.913902749679675 0.17219450064065 0.086097250320325 44 0.902089225675967 0.195821548648067 0.0979107743240333 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 8 0.275862068965517 NOK 5% type I error level 13 0.448275862068966 NOK 10% type I error level 17 0.586206896551724 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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