Q3 - Consumptieprijsindex met seasonal dummies en lineaire trend

*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: Sat, 15 Nov 2008 14:54:28 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/15/t1226786297jom1zoesj8oua7o.htm/, Retrieved Sat, 15 Nov 2008 21:58:17 +0000

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/2008/Nov/15/t1226786297jom1zoesj8oua7o.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Dataseries X:

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2.2 0 2.3 0 2.1 0 2.8 0 3.1 0 2.9 0 2.6 0 2.7 0 2.3 0 2.3 0 2.1 0 2.2 0 2.9 0 2.6 0 2.7 0 1.8 1 1.3 1 0.9 1 1.3 1 1.3 1 1.3 1 1.3 1 1.1 1 1.4 1 1.2 1 1.7 1 1.8 1 1.5 1 1 1 1.6 1 1.5 1 1.8 1 1.8 1 1.6 1 1.9 1 1.7 1 1.6 1 1.3 1 1.1 1 1.9 0 2.6 0 2.3 0 2.4 0 2.2 0 2 0 2.9 0 2.6 0 2.3 0 2.3 0 2.6 0 3.1 0 2.8 0 2.5 0 2.9 0 3.1 0 3.1 0 3.2 0 2.5 0 2.6 0 2.9 0

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Consumptieprijsindex[t] = + 2.37191489361702 -1.09893617021277Dumivariabele[t] -0.00877068557919695M1[t] + 0.0465721040189127M2[t] + 0.101914893617021M3[t] + 0.09725768321513M4[t] + 0.0326004728132389M5[t] + 0.0479432624113475M6[t] + 0.103286052009456M7[t] + 0.138628841607565M8[t] + 0.0339716312056738M9[t] + 0.0293144208037825M10[t] -0.0353427895981086M11[t] + 0.00465721040189126t + 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) 2.37191489361702 0.190751 12.4346 0 0 Dumivariabele -1.09893617021277 0.093299 -11.7786 0 0 M1 -0.00877068557919695 0.223545 -0.0392 0.968873 0.484437 M2 0.0465721040189127 0.223204 0.2087 0.835641 0.41782 M3 0.101914893617021 0.222895 0.4572 0.649657 0.324828 M4 0.09725768321513 0.222619 0.4369 0.664242 0.332121 M5 0.0326004728132389 0.222374 0.1466 0.884087 0.442043 M6 0.0479432624113475 0.222162 0.2158 0.830095 0.415048 M7 0.103286052009456 0.221982 0.4653 0.643919 0.32196 M8 0.138628841607565 0.221835 0.6249 0.535113 0.267556 M9 0.0339716312056738 0.221721 0.1532 0.878896 0.439448 M10 0.0293144208037825 0.221639 0.1323 0.895354 0.447677 M11 -0.0353427895981086 0.22159 -0.1595 0.873976 0.436988 t 0.00465721040189126 0.002693 1.7292 0.090485 0.045242 Multiple Linear Regression - Regression Statistics Multiple R 0.876092023146262 R-squared 0.76753723302051 Adjusted R-squared 0.701841233656742 F-TEST (value) 11.6831654964336 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.46781253818062e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.350338367781153 Sum Squared Residuals 5.64590070921986 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2.2 2.36780141843972 -0.167801418439719 2 2.3 2.42780141843972 -0.127801418439716 3 2.1 2.48780141843972 -0.387801418439716 4 2.8 2.48780141843972 0.312198581560284 5 3.1 2.42780141843972 0.672198581560284 6 2.9 2.44780141843972 0.452198581560284 7 2.6 2.50780141843972 0.092198581560284 8 2.7 2.54780141843972 0.152198581560284 9 2.3 2.44780141843972 -0.147801418439716 10 2.3 2.44780141843972 -0.147801418439716 11 2.1 2.38780141843972 -0.287801418439716 12 2.2 2.42780141843972 -0.227801418439716 13 2.9 2.42368794326241 0.47631205673759 14 2.6 2.48368794326241 0.116312056737589 15 2.7 2.54368794326241 0.156312056737589 16 1.8 1.44475177304965 0.355248226950355 17 1.3 1.38475177304965 -0.0847517730496454 18 0.9 1.40475177304965 -0.504751773049646 19 1.3 1.46475177304965 -0.164751773049645 20 1.3 1.50475177304965 -0.204751773049645 21 1.3 1.40475177304965 -0.104751773049645 22 1.3 1.40475177304965 -0.104751773049645 23 1.1 1.34475177304965 -0.244751773049645 24 1.4 1.38475177304965 0.0152482269503545 25 1.2 1.38063829787234 -0.18063829787234 26 1.7 1.44063829787234 0.259361702127659 27 1.8 1.50063829787234 0.299361702127659 28 1.5 1.50063829787234 -0.000638297872340376 29 1 1.44063829787234 -0.440638297872341 30 1.6 1.46063829787234 0.139361702127660 31 1.5 1.52063829787234 -0.0206382978723406 32 1.8 1.56063829787234 0.239361702127659 33 1.8 1.46063829787234 0.339361702127659 34 1.6 1.46063829787234 0.139361702127660 35 1.9 1.40063829787234 0.499361702127659 36 1.7 1.44063829787234 0.259361702127660 37 1.6 1.43652482269503 0.163475177304965 38 1.3 1.49652482269504 -0.196524822695036 39 1.1 1.55652482269504 -0.456524822695036 40 1.9 2.6554609929078 -0.755460992907802 41 2.6 2.5954609929078 0.00453900709219863 42 2.3 2.6154609929078 -0.315460992907801 43 2.4 2.6754609929078 -0.275460992907802 44 2.2 2.7154609929078 -0.515460992907801 45 2 2.6154609929078 -0.615460992907801 46 2.9 2.6154609929078 0.284539007092199 47 2.6 2.5554609929078 0.0445390070921986 48 2.3 2.5954609929078 -0.295460992907802 49 2.3 2.59134751773050 -0.291347517730496 50 2.6 2.65134751773050 -0.0513475177304965 51 3.1 2.71134751773050 0.388652482269503 52 2.8 2.71134751773050 0.0886524822695034 53 2.5 2.65134751773050 -0.151347517730497 54 2.9 2.67134751773050 0.228652482269504 55 3.1 2.73134751773050 0.368652482269504 56 3.1 2.77134751773050 0.328652482269503 57 3.2 2.67134751773050 0.528652482269503 58 2.5 2.67134751773050 -0.171347517730496 59 2.6 2.61134751773050 -0.0113475177304964 60 2.9 2.65134751773050 0.248652482269503

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) 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)) 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$resid, main='Residual Normal Q-Q Plot') grid() dev.off() (myerror <- as.ts(mysum$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() 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')

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