dummy variabele model 4

*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 08:51:10 -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/t126166993010jx7amavscekpe.htm/, Retrieved Thu, 24 Dec 2009 16:52:22 +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/t126166993010jx7amavscekpe.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 8,2 8,7 8,5 0 8,6 8,5 8,3 8,2 8,2 0 8,5 8,6 8,5 8,3 8,1 0 8,2 8,5 8,6 8,5 7,9 0 8,1 8,2 8,5 8,6 8,6 0 7,9 8,1 8,2 8,5 8,7 0 8,6 7,9 8,1 8,2 8,7 0 8,7 8,6 7,9 8,1 8,5 0 8,7 8,7 8,6 7,9 8,4 0 8,5 8,7 8,7 8,6 8,5 0 8,4 8,5 8,7 8,7 8,7 0 8,5 8,4 8,5 8,7 8,7 0 8,7 8,5 8,4 8,5 8,6 0 8,7 8,7 8,5 8,4 8,5 0 8,6 8,7 8,7 8,5 8,3 0 8,5 8,6 8,7 8,7 8 0 8,3 8,5 8,6 8,7 8,2 0 8 8,3 8,5 8,6 8,1 0 8,2 8 8,3 8,5 8,1 0 8,1 8,2 8 8,3 8 0 8,1 8,1 8,2 8 7,9 0 8 8,1 8,1 8,2 7,9 0 7,9 8 8,1 8,1 8 0 7,9 7,9 8 8,1 8 0 8 7,9 7,9 8 7,9 0 8 8 7,9 7,9 8 0 7,9 8 8 7,9 7,7 0 8 7,9 8 8 7,2 0 7,7 8 7,9 8 7,5 0 7,2 7,7 8 7,9 7,3 0 7,5 7,2 7,7 8 7 0 7,3 7,5 7,2 7,7 7 0 7 7,3 7,5 7,2 7 0 7 7 7,3 7,5 7,2 0 7 7 7 7,3 7,3 0 7,2 7 7 7 7,1 0 7,3 7,2 7 7 6,8 0 7,1 7,3 7,2 7 6,4 0 6,8 7,1 7,3 7,2 6,1 0 6,4 6,8 7,1 7,3 6,5 0 6,1 6,4 6,8 7,1 7,7 0 6,5 6,1 6,4 6,8 7,9 0 7,7 6,5 6,1 6,4 7,5 1 7,9 7,7 6,5 6,1 6,9 1 7,5 7,9 7,7 6,5 6,6 1 6,9 7,5 7,9 7,7 6,9 1 6,6 6,9 7,5 7,9 7,7 1 6,9 6,6 6,9 7,5 etc...

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] = + 0.926377432376777 + 0.20862236830311X[t] + 1.51300377809217Y1[t] -0.848950794851456Y2[t] -0.133140187587768Y3[t] + 0.372615536039044Y4[t] -0.240677055650023M1[t] -0.0853905579208965M2[t] -0.0798213024523612M3[t] -0.233163691979213M4[t] -0.135516619773325M5[t] + 0.438080071005953M6[t] -0.500032999637043M7[t] -0.147424418177767M8[t] + 0.0149030110573563M9[t] -0.136869156770028M10[t] -0.0071194533536342M11[t] -0.00493769282430811t + 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) 0.926377432376777 0.647107 1.4316 0.160442 0.080221 X 0.20862236830311 0.095114 2.1934 0.034469 0.017234 Y1 1.51300377809217 0.145007 10.434 0 0 Y2 -0.848950794851456 0.274528 -3.0924 0.00371 0.001855 Y3 -0.133140187587768 0.274445 -0.4851 0.630372 0.315186 Y4 0.372615536039044 0.14781 2.5209 0.016022 0.008011 M1 -0.240677055650023 0.111247 -2.1634 0.036862 0.018431 M2 -0.0853905579208965 0.120872 -0.7065 0.484216 0.242108 M3 -0.0798213024523612 0.121187 -0.6587 0.514083 0.257042 M4 -0.233163691979213 0.115391 -2.0206 0.050406 0.025203 M5 -0.135516619773325 0.115866 -1.1696 0.249445 0.124723 M6 0.438080071005953 0.109585 3.9976 0.000284 0.000142 M7 -0.500032999637043 0.124218 -4.0254 0.000262 0.000131 M8 -0.147424418177767 0.159982 -0.9215 0.3626 0.1813 M9 0.0149030110573563 0.146837 0.1015 0.919692 0.459846 M10 -0.136869156770028 0.120038 -1.1402 0.261333 0.130667 M11 -0.0071194533536342 0.115911 -0.0614 0.951345 0.475673 t -0.00493769282430811 0.003658 -1.3498 0.18506 0.09253 Multiple Linear Regression - Regression Statistics Multiple R 0.979836295763954 R-squared 0.960079166496428 Adjusted R-squared 0.94221984624483 F-TEST (value) 53.7578784058433 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.158771748288892 Sum Squared Residuals 0.957921786079023 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.6 8.64500882573885 -0.0450088257388447 2 8.5 8.57724606270429 -0.0772460627042843 3 8.2 8.3523156841405 -0.152315684140502 4 8.1 7.88623863629586 0.213761363704136 5 7.9 8.13290844868635 -0.232908448686345 6 8.6 8.48654227318045 0.113457726819547 7 8.7 8.67391367129502 0.0260863287049752 8 8.7 8.56798586525684 0.132014134743160 9 8.5 8.47275928366326 0.0272407163367366 10 8.4 8.2609655238617 0.139034476138309 11 8.5 8.44152886921875 0.0584711307812455 12 8.7 8.70653412456 -0.00653412455999671 13 8.7 8.61741596376992 0.0825840362300771 14 8.6 8.54739903734177 0.052600962658231 15 8.5 8.40736373826313 0.0926362617368702 16 8.3 8.2572014647957 0.0427985352042946 17 8 8.14551918680277 -0.145519186802775 18 8.2 8.40611967545525 -0.206119675455255 19 8.1 8.00972138997547 0.0902786100245288 20 8.1 8.00172069089945 0.0982793091005472 21 8 8.10559280846615 -0.105592808466147 22 7.9 7.88541969597182 0.0145803040281778 23 7.9 7.90656485463593 -0.00656485463593173 24 8 8.00695571340918 -0.00695571340918026 25 8 7.88869380789894 0.111306192101061 26 7.9 7.9168859797147 -0.0168859797147071 27 8 7.75290314579094 0.247096854209059 28 7.7 7.86808007433805 -0.168080074338047 29 7.2 7.4353072595656 -0.235307259565607 30 7.5 7.45157403456724 0.0484259654327551 31 7.3 7.46410341183356 -0.164103411833555 32 7 7.20927373937682 -0.209273739376821 33 7 6.85630267703442 0.143697322965576 34 7 7.09269075316744 -0.092690753167435 35 7.2 7.18292171282804 0.0170782871719581 36 7.3 7.37591956816409 -0.0759195681640908 37 7.1 7.11181503852869 -0.0118150385286856 38 6.8 6.84803997081237 -0.0480399708123695 39 6.4 6.62576964744827 -0.225769647448267 40 6.1 6.18086288343713 -0.0808628834371325 41 6.5 6.12467039640016 0.375329603599837 42 7.7 7.49468755827083 0.205312441729166 43 7.9 7.91855685243427 -0.0185568524342709 44 7.5 7.59366917532222 -0.0936691753222164 45 6.9 6.96534523083617 -0.065345230836166 46 6.6 6.66092402699905 -0.0609240269990517 47 6.9 6.96898456331727 -0.0689845633172719 48 7.7 7.61059059386673 0.0894094061332678 49 8 8.1370663640636 -0.137066364063608 50 8 7.91042894942687 0.0895710505731298 51 7.7 7.66164778435716 0.03835221564284 52 7.3 7.30761694113325 -0.00761694113325208 53 7.4 7.16159470854511 0.238405291454889 54 8.1 8.26107645852621 -0.161076458526213 55 8.3 8.23370467446168 0.0662953255383225 56 8.2 8.12735052914467 0.0726494708553302 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.657508608422047 0.684982783155906 0.342491391577953 22 0.495025960157948 0.990051920315897 0.504974039842052 23 0.336593124927146 0.673186249854292 0.663406875072854 24 0.211896594784979 0.423793189569959 0.78810340521502 25 0.170759066963023 0.341518133926046 0.829240933036977 26 0.0981557360692562 0.196311472138512 0.901844263930744 27 0.348587938086083 0.697175876172165 0.651412061913917 28 0.35730491177147 0.71460982354294 0.64269508822853 29 0.460783859741081 0.921567719482161 0.539216140258919 30 0.40192411972055 0.8038482394411 0.59807588027945 31 0.398995728660289 0.797991457320577 0.601004271339711 32 0.349453213245483 0.698906426490966 0.650546786754517 33 0.484682808797050 0.969365617594099 0.515317191202950 34 0.461195560239746 0.922391120479491 0.538804439760254 35 0.686633146375482 0.626733707249036 0.313366853624518 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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