Multiple regression met dummy 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: Thu, 11 Dec 2008 05:01:46 -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/t1228996963nn6ro2z8iu0ihqc.htm/, Retrieved Thu, 11 Dec 2008 12:02:51 +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/t1228996963nn6ro2z8iu0ihqc.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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 5.95530625 -1.693859375x[t] -0.583427083333335M1[t] + 0.676305208333333M2[t] -0.322562500000001M3[t] -0.177630208333334M4[t] + 0.973873958333332M5[t] -0.52139375M6[t] -0.480861458333333M7[t] -0.419929166666668M8[t] + 0.108403124999999M9[t] -1.09006458333333M10[t] -0.353532291666667M11[t] + 0.0566677083333334t + 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) 5.95530625 0.383389 15.5333 0 0 x -1.693859375 0.332025 -5.1016 6e-06 3e-06 M1 -0.583427083333335 0.437784 -1.3327 0.1892 0.0946 M2 0.676305208333333 0.436944 1.5478 0.128522 0.064261 M3 -0.322562500000001 0.436289 -0.7393 0.463462 0.231731 M4 -0.177630208333334 0.435821 -0.4076 0.685476 0.342738 M5 0.973873958333332 0.438343 2.2217 0.031263 0.015631 M6 -0.52139375 0.437131 -1.1928 0.239078 0.119539 M7 -0.480861458333333 0.436102 -1.1026 0.275921 0.137961 M8 -0.419929166666668 0.435259 -0.9648 0.339699 0.16985 M9 0.108403124999999 0.434601 0.2494 0.804138 0.402069 M10 -1.09006458333333 0.434131 -2.5109 0.015619 0.00781 M11 -0.353532291666667 0.433849 -0.8149 0.419344 0.209672 t 0.0566677083333334 0.009037 6.2709 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.784728342047574 R-squared 0.615798570812734 Adjusted R-squared 0.50721990604242 F-TEST (value) 5.67145094402648 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 4.93350161678840e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.685827085819758 Sum Squared Residuals 21.636504415625 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 5.014 5.428546875 -0.414546875000003 2 6.153 6.744946875 -0.591946874999999 3 6.441 5.802746875 0.638253125 4 5.584 6.004346875 -0.420346875 5 6.427 7.21251875 -0.785518750000001 6 6.062 5.77391875 0.288081250000001 7 5.589 5.87111875 -0.282118749999999 8 6.216 5.98871875 0.22728125 9 5.809 6.57371875 -0.76471875 10 4.989 5.43191875 -0.442918749999999 11 6.706 6.22511875 0.48088125 12 7.174 6.63531875 0.538681250000001 13 6.122 6.108559375 0.0134406250000012 14 8.075 7.424959375 0.650040624999998 15 6.292 6.482759375 -0.190759375000000 16 6.337 6.684359375 -0.347359375 17 8.576 7.89253125 0.68346875 18 6.077 6.45393125 -0.376931250000000 19 5.931 6.55113125 -0.62013125 20 6.288 6.66873125 -0.380731249999999 21 7.167 7.25373125 -0.0867312500000002 22 6.054 6.11193125 -0.0579312499999998 23 6.468 6.90513125 -0.43713125 24 6.401 7.31533125 -0.91433125 25 6.927 6.788571875 0.138428125000001 26 7.914 8.104971875 -0.190971875000000 27 7.728 7.162771875 0.565228125 28 8.699 7.364371875 1.334628125 29 8.522 8.57254375 -0.0505437499999997 30 6.481 7.13394375 -0.65294375 31 7.502 7.23114375 0.270856249999999 32 7.778 7.34874375 0.429256249999999 33 7.424 7.93374375 -0.50974375 34 6.941 6.79194375 0.149056249999999 35 8.574 7.58514375 0.98885625 36 9.169 7.99534375 1.17365625 37 7.701 7.468584375 0.232415625000001 38 9.035 8.784984375 0.250015625000001 39 7.158 7.842784375 -0.684784375 40 8.195 8.044384375 0.150615625 41 8.124 7.558696875 0.565303125000001 42 7.073 6.120096875 0.952903125 43 7.017 6.217296875 0.799703125 44 7.39 6.334896875 1.055103125 45 7.776 6.919896875 0.856103125 46 6.197 5.778096875 0.418903125 47 6.889 6.571296875 0.317703125 48 7.087 6.981496875 0.105503124999999 49 6.485 6.4547375 0.0302625000000014 50 7.654 7.7711375 -0.117137500000000 51 6.501 6.8289375 -0.327937499999999 52 6.313 7.0305375 -0.7175375 53 7.826 8.238709375 -0.412709375000001 54 6.589 6.800109375 -0.211109375 55 6.729 6.897309375 -0.168309375000000 56 5.684 7.014909375 -1.330909375 57 8.105 7.599909375 0.505090625000001 58 6.391 6.458109375 -0.0671093750000004 59 5.901 7.251309375 -1.350309375 60 6.758 7.661509375 -0.903509375

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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