dummy variabele model 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 08:47:29 -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/t1261669701o3t1u6mj3iyfhi9.htm/, Retrieved Thu, 24 Dec 2009 16:48:33 +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/Dec/24/t1261669701o3t1u6mj3iyfhi9.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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8,7 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 8.9974956521739 + 0.888869565217389X[t] -0.346211594202904M1[t] -0.505849275362318M2[t] -0.325486956521738M3[t] -0.00512463768115932M4[t] + 0.0752376811594204M5[t] -0.00440000000000004M6[t] -0.164037681159420M7[t] -0.383675362318840M8[t] -0.443313043478261M9[t] + 0.217049275362319M10[t] + 0.297411594202898M11[t] -0.0403623188405796t + 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) 8.9974956521739 0.227349 39.5756 0 0 X 0.888869565217389 0.194356 4.5734 3.6e-05 1.8e-05 M1 -0.346211594202904 0.271424 -1.2755 0.208523 0.104262 M2 -0.505849275362318 0.271062 -1.8662 0.068399 0.0342 M3 -0.325486956521738 0.270779 -1.202 0.2355 0.11775 M4 -0.00512463768115932 0.270577 -0.0189 0.984971 0.492486 M5 0.0752376811594204 0.270456 0.2782 0.782115 0.391057 M6 -0.00440000000000004 0.270416 -0.0163 0.987088 0.493544 M7 -0.164037681159420 0.270456 -0.6065 0.54715 0.273575 M8 -0.383675362318840 0.270577 -1.418 0.162933 0.081467 M9 -0.443313043478261 0.270779 -1.6372 0.108418 0.054209 M10 0.217049275362319 0.271062 0.8007 0.4274 0.2137 M11 0.297411594202898 0.271424 1.0957 0.278895 0.139447 t -0.0403623188405796 0.004675 -8.6328 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.822035461648252 R-squared 0.675742300207254 Adjusted R-squared 0.584104254613652 F-TEST (value) 7.37403657869405 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.60430240536691e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.425442813902998 Sum Squared Residuals 8.32607304347826 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.7 8.61092173913046 0.08907826086954 2 8.2 8.41092173913043 -0.210921739130433 3 8.3 8.55092173913043 -0.250921739130433 4 8.5 8.83092173913043 -0.330921739130433 5 8.6 8.87092173913043 -0.270921739130434 6 8.5 8.75092173913043 -0.250921739130433 7 8.2 8.55092173913043 -0.350921739130434 8 8.1 8.29092173913043 -0.190921739130433 9 7.9 8.19092173913043 -0.290921739130433 10 8.6 8.81092173913043 -0.210921739130433 11 8.7 8.85092173913043 -0.150921739130434 12 8.7 8.51314782608696 0.186852173913044 13 8.5 8.12657391304347 0.373426086956529 14 8.4 7.92657391304348 0.473426086956522 15 8.5 8.06657391304348 0.433426086956522 16 8.7 8.34657391304348 0.353426086956522 17 8.7 8.38657391304348 0.313426086956522 18 8.6 8.26657391304348 0.333426086956522 19 8.5 8.06657391304348 0.433426086956522 20 8.3 7.80657391304348 0.493426086956523 21 8 7.70657391304348 0.293426086956522 22 8.2 8.32657391304348 -0.126573913043478 23 8.1 8.36657391304348 -0.266573913043478 24 8.1 8.0288 0.0712000000000003 25 8 7.64222608695652 0.357773913043484 26 7.9 7.44222608695652 0.457773913043478 27 7.9 7.58222608695652 0.317773913043478 28 8 7.86222608695652 0.137773913043478 29 8 7.90222608695652 0.0977739130434783 30 7.9 7.78222608695652 0.117773913043479 31 8 7.58222608695652 0.417773913043478 32 7.7 7.32222608695652 0.377773913043478 33 7.2 7.22222608695652 -0.0222260869565221 34 7.5 7.84222608695652 -0.342226086956522 35 7.3 7.88222608695652 -0.582226086956522 36 7 7.54445217391304 -0.544452173913044 37 7 7.15787826086956 -0.15787826086956 38 7 6.95787826086957 0.0421217391304335 39 7.2 7.09787826086957 0.102121739130433 40 7.3 7.37787826086957 -0.0778782608695662 41 7.1 7.41787826086957 -0.317878260869566 42 6.8 7.29787826086957 -0.497878260869567 43 6.4 7.09787826086957 -0.697878260869566 44 6.1 6.83787826086957 -0.737878260869567 45 6.5 6.73787826086957 -0.237878260869567 46 7.7 7.35787826086957 0.342121739130434 47 7.9 7.39787826086957 0.502121739130434 48 7.5 7.94897391304348 -0.448973913043478 49 6.9 7.5624 -0.662399999999994 50 6.6 7.3624 -0.762400000000001 51 6.9 7.5024 -0.602400000000001 52 7.7 7.7824 -0.0824 53 8 7.8224 0.177600000000000 54 8 7.7024 0.297599999999999 55 7.7 7.5024 0.197600000000000 56 7.3 7.2424 0.0575999999999992 57 7.4 7.1424 0.257600000000000 58 8.1 7.7624 0.337599999999999 59 8.3 7.8024 0.4976 60 8.2 7.46462608695652 0.735373913043477 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0360839340510355 0.072167868102071 0.963916065948965 18 0.0086425812989875 0.017285162597975 0.991357418701013 19 0.00342402840015307 0.00684805680030613 0.996575971599847 20 0.000881132533890571 0.00176226506778114 0.99911886746611 21 0.000190340236380468 0.000380680472760937 0.99980965976362 22 0.00132982009044388 0.00265964018088775 0.998670179909556 23 0.00660552700157844 0.0132110540031569 0.993394472998422 24 0.00999920614943096 0.0199984122988619 0.99000079385057 25 0.0143034375921006 0.0286068751842012 0.9856965624079 26 0.0113283552367510 0.0226567104735020 0.98867164476325 27 0.00898079936669755 0.0179615987333951 0.991019200633303 28 0.00671281792372933 0.0134256358474587 0.99328718207627 29 0.00502261478170388 0.0100452295634078 0.994977385218296 30 0.00367036026733956 0.00734072053467911 0.99632963973266 31 0.00433826090676763 0.00867652181353526 0.995661739093232 32 0.0160384184668854 0.0320768369337709 0.983961581533115 33 0.0327120127628913 0.0654240255257825 0.967287987237109 34 0.0396457622211885 0.079291524442377 0.960354237778811 35 0.0509954932103726 0.101990986420745 0.949004506789627 36 0.090322561266544 0.180645122533088 0.909677438733456 37 0.133944862273623 0.267889724547245 0.866055137726377 38 0.282677084124084 0.565354168248169 0.717322915875916 39 0.638588905342135 0.722822189315729 0.361411094657865 40 0.64985691315727 0.70028617368546 0.35014308684273 41 0.540776842775894 0.918446314448211 0.459223157224106 42 0.50550491786733 0.98899016426534 0.49449508213267 43 0.598565107353217 0.802869785293566 0.401434892646783 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.222222222222222 NOK 5% type I error level 15 0.555555555555556 NOK 10% type I error level 18 0.666666666666667 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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