Multiple Regression met seizoenale dummy

*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, 11 Dec 2008 04:59:09 -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/Dec/11/t1228996821ouozkuzy675hhx2.htm/, Retrieved Thu, 11 Dec 2008 12:00:33 +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/Dec/11/t1228996821ouozkuzy675hhx2.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)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

In samenwerking met Katrien Bourdiaudhy, Stéphanie Claes en Kevin Engels

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

5.014 0 6.153 0 6.441 0 5.584 0 6.427 0 6.062 0 5.589 0 6.216 0 5.809 0 4.989 0 6.706 0 7.174 0 6.122 0 8.075 0 6.292 0 6.337 0 8.576 0 6.077 0 5.931 0 6.288 0 7.167 0 6.054 0 6.468 0 6.401 0 6.927 0 7.914 0 7.728 0 8.699 0 8.522 0 6.481 0 7.502 0 7.778 0 7.424 0 6.941 0 8.574 0 9.169 0 7.701 0 9.035 0 7.158 0 8.195 0 8.124 1 7.073 1 7.017 1 7.390 1 7.776 1 6.197 1 6.889 1 7.087 1 6.485 1 7.654 1 6.501 1 6.313 1 7.826 1 6.589 1 6.729 1 5.684 1 8.105 1 6.391 1 5.901 1 6.758 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 7.31533125 + 0.006171875x[t] -0.866765625M1[t] + 0.449634375000001M2[t] -0.492565624999999M3[t] -0.290965624999999M4[t] + 0.577200000000001M5[t] -0.861399999999998M6[t] -0.764199999999999M7[t] -0.6466M8[t] -0.0615999999999992M9[t] -1.2034M10[t] -0.410199999999999M11[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) 7.31533125 0.425973 17.1732 0 0 x 0.006171875 0.258284 0.0239 0.981037 0.490518 M1 -0.866765625 0.586709 -1.4773 0.146256 0.073128 M2 0.449634375000001 0.586709 0.7664 0.44729 0.223645 M3 -0.492565624999999 0.586709 -0.8395 0.405417 0.202708 M4 -0.290965624999999 0.586709 -0.4959 0.622256 0.311128 M5 0.577200000000001 0.584431 0.9876 0.328392 0.164196 M6 -0.861399999999998 0.584431 -1.4739 0.147172 0.073586 M7 -0.764199999999999 0.584431 -1.3076 0.19737 0.098685 M8 -0.6466 0.584431 -1.1064 0.274195 0.137097 M9 -0.0615999999999992 0.584431 -0.1054 0.916506 0.458253 M10 -1.2034 0.584431 -2.0591 0.04505 0.022525 M11 -0.410199999999999 0.584431 -0.7019 0.486215 0.243108 Multiple Linear Regression - Regression Statistics Multiple R 0.536051580390871 R-squared 0.28735129683955 Adjusted R-squared 0.105398436458159 F-TEST (value) 1.57926232232477 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.13072387664634 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.924065766539892 Sum Squared Residuals 40.133184421875 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 5.014 6.448565625 -1.43456562500001 2 6.153 7.764965625 -1.61196562500000 3 6.441 6.822765625 -0.381765625000001 4 5.584 7.024365625 -1.440365625 5 6.427 7.89253125 -1.46553125 6 6.062 6.45393125 -0.391931250000000 7 5.589 6.55113125 -0.96213125 8 6.216 6.66873125 -0.452731250000001 9 5.809 7.25373125 -1.44473125 10 4.989 6.11193125 -1.12293125000000 11 6.706 6.90513125 -0.199131250000000 12 7.174 7.31533125 -0.141331249999998 13 6.122 6.448565625 -0.326565624999999 14 8.075 7.764965625 0.310034374999999 15 6.292 6.822765625 -0.530765625 16 6.337 7.024365625 -0.687365625 17 8.576 7.89253125 0.68346875 18 6.077 6.45393125 -0.37693125 19 5.931 6.55113125 -0.62013125 20 6.288 6.66873125 -0.380731250000000 21 7.167 7.25373125 -0.0867312500000003 22 6.054 6.11193125 -0.05793125 23 6.468 6.90513125 -0.43713125 24 6.401 7.31533125 -0.91433125 25 6.927 6.448565625 0.478434375000001 26 7.914 7.764965625 0.149034374999999 27 7.728 6.822765625 0.905234375 28 8.699 7.024365625 1.674634375 29 8.522 7.89253125 0.62946875 30 6.481 6.45393125 0.0270687499999994 31 7.502 6.55113125 0.95086875 32 7.778 6.66873125 1.10926875 33 7.424 7.25373125 0.170268750000000 34 6.941 6.11193125 0.82906875 35 8.574 6.90513125 1.66886875 36 9.169 7.31533125 1.85366875 37 7.701 6.448565625 1.252434375 38 9.035 7.764965625 1.270034375 39 7.158 6.822765625 0.335234375000001 40 8.195 7.024365625 1.170634375 41 8.124 7.898703125 0.225296875000000 42 7.073 6.460103125 0.612896875 43 7.017 6.557303125 0.459696875 44 7.39 6.674903125 0.715096875 45 7.776 7.259903125 0.516096875 46 6.197 6.118103125 0.0788968749999997 47 6.889 6.911303125 -0.0223031249999998 48 7.087 7.321503125 -0.234503124999999 49 6.485 6.4547375 0.0302625000000019 50 7.654 7.7711375 -0.117137500000001 51 6.501 6.8289375 -0.327937499999999 52 6.313 7.0305375 -0.717537500 53 7.826 7.898703125 -0.0727031250000006 54 6.589 6.460103125 0.128896875 55 6.729 6.557303125 0.171696875 56 5.684 6.674903125 -0.990903125 57 8.105 7.259903125 0.845096875 58 6.391 6.118103125 0.272896875000000 59 5.901 6.911303125 -1.010303125 60 6.758 7.321503125 -0.563503124999999

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) 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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