q3

*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: Wed, 19 Nov 2008 07:12:05 -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/19/t1227104086n1dtxo3hyy5oj4e.htm/, Retrieved Wed, 19 Nov 2008 14:14:55 +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/19/t1227104086n1dtxo3hyy5oj4e.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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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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3.4 1 3 1 3.1 1 2.5 0 2.2 0 2.3 0 2.1 0 2.8 0 3.1 1 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 0 1.3 0 0.9 0 1.3 0 1.3 0 1.3 0 1.3 0 1.1 0 1.4 0 1.2 0 1.7 0 1.8 0 1.5 0 1 0 1.6 0 1.5 0 1.8 0 1.8 0 1.6 0 1.9 0 1.7 0 1.6 0 1.3 0 1.1 0 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 1 2.8 0 2.5 0 2.9 0 3.1 1 3.1 1 3.2 1 2.5 0 2.6 0 2.9 0 2.6 0 2.4 0 1.7 0 2 0 2.2 0 1.9 0 1.6 0 1.6 0 1.2 0 1.2 0 1.5 0 1.6 0 1.7 0 1.8 0 1.8 0 1.8 0 1.3 0 1.3 0 1.4 0 1.1 0 1.5 0 2.2 0 2.9 0 3.1 1 3.5 1 3.6 1 4.4 1 4.2 1 5.2 1 5.8 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Consumptieprijsindex[t] = + 1.95696202531645 + 1.70303797468354Dumivariabele[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) 1.95696202531645 0.069957 27.9737 0 0 Dumivariabele 1.70303797468354 0.175126 9.7246 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.711957793377351 R-squared 0.506883899550747 Adjusted R-squared 0.501523941937168 F-TEST (value) 94.568639547935 F-TEST (DF numerator) 1 F-TEST (DF denominator) 92 p-value 8.88178419700125e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.621793259417748 Sum Squared Residuals 35.5696708860760 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.4 3.66000000000001 -0.260000000000011 2 3 3.66 -0.659999999999999 3 3.1 3.66 -0.559999999999999 4 2.5 1.95696202531646 0.543037974683544 5 2.2 1.95696202531646 0.243037974683544 6 2.3 1.95696202531646 0.343037974683544 7 2.1 1.95696202531646 0.143037974683544 8 2.8 1.95696202531646 0.843037974683544 9 3.1 3.66 -0.559999999999999 10 2.9 1.95696202531646 0.943037974683544 11 2.6 1.95696202531646 0.643037974683544 12 2.7 1.95696202531646 0.743037974683544 13 2.3 1.95696202531646 0.343037974683544 14 2.3 1.95696202531646 0.343037974683544 15 2.1 1.95696202531646 0.143037974683544 16 2.2 1.95696202531646 0.243037974683544 17 2.9 1.95696202531646 0.943037974683544 18 2.6 1.95696202531646 0.643037974683544 19 2.7 1.95696202531646 0.743037974683544 20 1.8 1.95696202531646 -0.156962025316456 21 1.3 1.95696202531646 -0.656962025316456 22 0.9 1.95696202531646 -1.05696202531646 23 1.3 1.95696202531646 -0.656962025316456 24 1.3 1.95696202531646 -0.656962025316456 25 1.3 1.95696202531646 -0.656962025316456 26 1.3 1.95696202531646 -0.656962025316456 27 1.1 1.95696202531646 -0.856962025316456 28 1.4 1.95696202531646 -0.556962025316456 29 1.2 1.95696202531646 -0.756962025316456 30 1.7 1.95696202531646 -0.256962025316456 31 1.8 1.95696202531646 -0.156962025316456 32 1.5 1.95696202531646 -0.456962025316456 33 1 1.95696202531646 -0.956962025316456 34 1.6 1.95696202531646 -0.356962025316456 35 1.5 1.95696202531646 -0.456962025316456 36 1.8 1.95696202531646 -0.156962025316456 37 1.8 1.95696202531646 -0.156962025316456 38 1.6 1.95696202531646 -0.356962025316456 39 1.9 1.95696202531646 -0.0569620253164558 40 1.7 1.95696202531646 -0.256962025316456 41 1.6 1.95696202531646 -0.356962025316456 42 1.3 1.95696202531646 -0.656962025316456 43 1.1 1.95696202531646 -0.856962025316456 44 1.9 1.95696202531646 -0.0569620253164558 45 2.6 1.95696202531646 0.643037974683544 46 2.3 1.95696202531646 0.343037974683544 47 2.4 1.95696202531646 0.443037974683544 48 2.2 1.95696202531646 0.243037974683544 49 2 1.95696202531646 0.0430379746835443 50 2.9 1.95696202531646 0.943037974683544 51 2.6 1.95696202531646 0.643037974683544 52 2.3 1.95696202531646 0.343037974683544 53 2.3 1.95696202531646 0.343037974683544 54 2.6 1.95696202531646 0.643037974683544 55 3.1 3.66 -0.559999999999999 56 2.8 1.95696202531646 0.843037974683544 57 2.5 1.95696202531646 0.543037974683544 58 2.9 1.95696202531646 0.943037974683544 59 3.1 3.66 -0.559999999999999 60 3.1 3.66 -0.559999999999999 61 3.2 3.66 -0.459999999999999 62 2.5 1.95696202531646 0.543037974683544 63 2.6 1.95696202531646 0.643037974683544 64 2.9 1.95696202531646 0.943037974683544 65 2.6 1.95696202531646 0.643037974683544 66 2.4 1.95696202531646 0.443037974683544 67 1.7 1.95696202531646 -0.256962025316456 68 2 1.95696202531646 0.0430379746835443 69 2.2 1.95696202531646 0.243037974683544 70 1.9 1.95696202531646 -0.0569620253164558 71 1.6 1.95696202531646 -0.356962025316456 72 1.6 1.95696202531646 -0.356962025316456 73 1.2 1.95696202531646 -0.756962025316456 74 1.2 1.95696202531646 -0.756962025316456 75 1.5 1.95696202531646 -0.456962025316456 76 1.6 1.95696202531646 -0.356962025316456 77 1.7 1.95696202531646 -0.256962025316456 78 1.8 1.95696202531646 -0.156962025316456 79 1.8 1.95696202531646 -0.156962025316456 80 1.8 1.95696202531646 -0.156962025316456 81 1.3 1.95696202531646 -0.656962025316456 82 1.3 1.95696202531646 -0.656962025316456 83 1.4 1.95696202531646 -0.556962025316456 84 1.1 1.95696202531646 -0.856962025316456 85 1.5 1.95696202531646 -0.456962025316456 86 2.2 1.95696202531646 0.243037974683544 87 2.9 1.95696202531646 0.943037974683544 88 3.1 3.66 -0.559999999999999 89 3.5 3.66 -0.159999999999999 90 3.6 3.66 -0.0599999999999992 91 4.4 3.66 0.740000000000001 92 4.2 3.66 0.540000000000001 93 5.2 3.66 1.54 94 5.8 3.66 2.14

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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Software written by Ed van Stee & Patrick Wessa

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