dummy variabele model 4 zonder yt-3

*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 09:15:17 -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/t1261671418g2p5fk6caj0ecim.htm/, Retrieved Thu, 24 Dec 2009 17:17:10 +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/t1261671418g2p5fk6caj0ecim.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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8.6 0 8.5 8.3 8.7 8.5 0 8.6 8.5 8.2 8.2 0 8.5 8.6 8.3 8.1 0 8.2 8.5 8.5 7.9 0 8.1 8.2 8.6 8.6 0 7.9 8.1 8.5 8.7 0 8.6 7.9 8.2 8.7 0 8.7 8.6 8.1 8.5 0 8.7 8.7 7.9 8.4 0 8.5 8.7 8.6 8.5 0 8.4 8.5 8.7 8.7 0 8.5 8.4 8.7 8.7 0 8.7 8.5 8.5 8.6 0 8.7 8.7 8.4 8.5 0 8.6 8.7 8.5 8.3 0 8.5 8.6 8.7 8 0 8.3 8.5 8.7 8.2 0 8 8.3 8.6 8.1 0 8.2 8 8.5 8.1 0 8.1 8.2 8.3 8 0 8.1 8.1 8 7.9 0 8 8.1 8.2 7.9 0 7.9 8 8.1 8 0 7.9 7.9 8.1 8 0 8 7.9 8 7.9 0 8 8 7.9 8 0 7.9 8 7.9 7.7 0 8 7.9 8 7.2 0 7.7 8 8 7.5 0 7.2 7.7 7.9 7.3 0 7.5 7.2 8 7 0 7.3 7.5 7.7 7 0 7 7.3 7.2 7 0 7 7 7.5 7.2 0 7 7 7.3 7.3 0 7.2 7 7 7.1 0 7.3 7.2 7 6.8 0 7.1 7.3 7 6.4 0 6.8 7.1 7.2 6.1 0 6.4 6.8 7.3 6.5 0 6.1 6.4 7.1 7.7 0 6.5 6.1 6.8 7.9 0 7.7 6.5 6.4 7.5 1 7.9 7.7 6.1 6.9 1 7.5 7.9 6.5 6.6 1 6.9 7.5 7.7 6.9 1 6.6 6.9 7.9 7.7 1 6.9 6.6 7.5 8 1 7.7 6.9 6.9 8 1 8 7.7 6.6 7.7 1 8 8 6.9 7.3 1 7.7 8 7.7 7.4 1 7.3 7.7 8 8.1 1 7.4 7.3 8 8.3 1 8.1 7.4 7.7 8.2 1 8.3 8.1 7.3

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] = + 0.933206362031773 + 0.203416557420044X[t] + 1.55831064545628Y1[t] -0.96569014876742Y2[t] + 0.310028322021338Y4[t] -0.229525744446432M1[t] -0.0745053665131565M2[t] -0.0873305504983145M3[t] -0.233405271732744M4[t] -0.128829768856069M5[t] + 0.438079153344970M6[t] -0.517682899618016M7[t] -0.0964094832665481M8[t] -0.0127744572064306M9[t] -0.13721343353349M10[t] -0.00475098863174447M11[t] -0.00495389769238005t + 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) 0.933206362031773 0.64058 1.4568 0.153172 0.076586 X 0.203416557420044 0.093576 2.1738 0.035852 0.017926 Y1 1.55831064545628 0.109835 14.1878 0 0 Y2 -0.96569014876742 0.130832 -7.3811 0 0 Y4 0.310028322021338 0.071426 4.3406 9.8e-05 4.9e-05 M1 -0.229525744446432 0.107774 -2.1297 0.039564 0.019782 M2 -0.0745053665131565 0.117601 -0.6335 0.530078 0.265039 M3 -0.0873305504983145 0.11901 -0.7338 0.467454 0.233727 M4 -0.233405271732744 0.114254 -2.0429 0.047865 0.023933 M5 -0.128829768856069 0.113909 -1.131 0.264969 0.132484 M6 0.438079153344970 0.108506 4.0374 0.000245 0.000122 M7 -0.517682899618016 0.117601 -4.402 8.1e-05 4e-05 M8 -0.0964094832665481 0.119378 -0.8076 0.424219 0.21211 M9 -0.0127744572064306 0.133967 -0.0954 0.924521 0.46226 M10 -0.13721343353349 0.118853 -1.1545 0.255331 0.127665 M11 -0.00475098863174447 0.114667 -0.0414 0.967162 0.483581 t -0.00495389769238005 0.003622 -1.3678 0.179211 0.089605 Multiple Linear Regression - Regression Statistics Multiple R 0.979710122102373 R-squared 0.959831923349847 Adjusted R-squared 0.943352712416451 F-TEST (value) 58.2450171448862 F-TEST (DF numerator) 16 F-TEST (DF denominator) 39 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.157207564722478 Sum Squared Residuals 0.963854517832907 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.6 8.62638537308738 -0.0263853730873752 2 8.5 8.58413072710974 -0.0841307271097387 3 8.2 8.34495439821197 -0.144954398211967 4 8.1 7.88500726492928 0.214992735070718 5 7.9 8.1495076824003 -0.249507682400309 6 8.6 8.46536676049232 0.134633239507679 7 8.7 8.69559779480343 0.00440220519656844 8 8.7 8.56076244166882 0.139237558331181 9 8.5 8.48086889075555 0.0191311092444536 10 8.4 8.25683371305979 0.143166286940211 11 8.5 8.45265205767915 0.0473479423208551 12 8.7 8.70484922804088 -0.00484922804087848 13 8.7 8.62345703571231 0.0765429642876882 14 8.6 8.54938265399759 0.0506173460024102 15 8.5 8.40677533997656 0.0932246600234418 16 8.3 8.25849033578513 0.0415096642148698 17 8 8.14301882675491 -0.143018826754913 18 8.2 8.39961585517804 -0.199615855178037 19 8.1 8.00926624604202 0.0907337539579807 20 8.1 8.01461100599773 0.085388994002271 21 8 8.0968526526358 -0.0968526526358063 22 7.9 7.873634378475 0.0263656215249933 23 7.9 7.91087804381335 -0.0108780438133530 24 8 8.00724414962946 -0.00724414962945946 25 8 7.89759273983414 0.102407260165859 26 7.9 7.92008737299616 -0.0200873729961606 27 8 7.746477226773 0.253522773227004 28 7.7 7.87885151947069 -0.178851519470689 29 7.2 7.41441091614136 -0.214410916141359 30 7.5 7.45591483034997 0.0440851696500283 31 7.3 7.47653997991733 -0.176539979917333 32 7 7.19848182824854 -0.198481828248537 33 7 6.84779363172221 0.152206368277793 34 7 7.1011162989394 -0.101116298939395 35 7.2 7.16661918174449 0.0333808182555072 36 7.3 7.38506990516871 -0.0850699051687119 37 7.1 7.11328329782204 -0.0132832978220429 38 6.8 6.85511863409494 -0.0551186340949409 39 6.4 6.62499005293827 -0.224990052938272 40 6.1 6.17134705266131 -0.0713470526613127 41 6.5 6.12774585931142 0.372254140688577 42 7.7 7.50972369002642 0.190276309973583 43 7.9 7.90869312560308 -0.0086931256030812 44 7.5 7.58825465564616 -0.0882546556461627 45 6.9 6.97448482488644 -0.0744848248864398 46 6.6 6.66841560952581 -0.0684156095258094 47 6.9 6.96985071676301 -0.0698507167630093 48 7.7 7.60283671716095 0.0971632828390504 49 8 8.13928155354413 -0.139281553544129 50 8 7.89128061180157 0.10871938819843 51 7.7 7.6768029821002 0.0231970178997923 52 7.3 7.30630382715359 -0.00630382715358653 53 7.4 7.165316715392 0.234683284608004 54 8.1 8.26937886395325 -0.169378863953252 55 8.3 8.20990285363414 0.090097146365865 56 8.2 8.13789006843875 0.0621099315612478 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.711837282107374 0.576325435785251 0.288162717892626 21 0.55582336766044 0.888353264679121 0.444176632339561 22 0.407012329802466 0.814024659604933 0.592987670197534 23 0.270946079716402 0.541892159432805 0.729053920283598 24 0.167948561281238 0.335897122562477 0.832051438718762 25 0.134516310249866 0.269032620499731 0.865483689750134 26 0.0768095057356391 0.153619011471278 0.923190494264361 27 0.339672590094511 0.679345180189021 0.66032740990549 28 0.358037651477736 0.716075302955472 0.641962348522264 29 0.425221685984339 0.850443371968677 0.574778314015661 30 0.407944949897866 0.815889899795732 0.592055050102134 31 0.366491055880529 0.732982111761058 0.633508944119471 32 0.330516912971677 0.661033825943354 0.669483087028323 33 0.513533918903337 0.972932162193326 0.486466081096663 34 0.4533858656908 0.9067717313816 0.5466141343092 35 0.793166520565068 0.413666958869865 0.206833479434933 36 0.643159750442999 0.713680499114002 0.356840249557001 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 0 0 OK 10% type I error level 0 0 OK

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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