blok 11 Q3 eigen datareeks verwerking

*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, 27 Nov 2008 06:04:37 -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/27/t1227791732rn6h668h5rc7f0j.htm/, Retrieved Thu, 27 Nov 2008 13:15:41 +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/27/t1227791732rn6h668h5rc7f0j.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}, }

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Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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13 0 8 0 7 0 3 0 3 0 4 0 4 0 0 0 -4 0 -14 1 -18 1 -8 1 -1 1 1 1 2 1 0 1 1 1 0 1 -1 1 -3 1 -3 1 -3 1 -4 1 -8 1 -9 1 -13 1 -18 1 -11 1 -9 1 -10 1 -13 1 -11 1 -5 1 -15 1 -6 1 -6 1 -3 1 -1 1 -3 1 -4 1 -6 1 0 1 -4 1 -2 1 -2 1 -6 1 -7 1 -6 1 -6 1 -3 1 -2 1 -5 1 -11 1 -11 1 -11 1 -10 1 -14 1 -8 1 -9 1 -5 1 -1 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 4 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 3.32137931034485 -8.79827586206899D[t] + 3.8109674329502M1[t] + 2.92837164750959M2[t] + 1.75956896551725M3[t] + 1.19076628352491M4[t] + 0.221963601532572M5[t] + 1.25316091954024M6[t] -0.315641762452104M7[t] -0.484444444444441M8[t] -0.853247126436776M9[t] -2.66239463601532M10[t] -2.23119731800765M11[t] -0.0311973180076629t + 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) 3.32137931034485 2.995121 1.1089 0.273103 0.136551 D -8.79827586206899 2.405891 -3.657 0.000643 0.000322 M1 3.8109674329502 3.123444 1.2201 0.228507 0.114254 M2 2.92837164750959 3.272931 0.8947 0.375494 0.187747 M3 1.75956896551725 3.270588 0.538 0.593117 0.296559 M4 1.19076628352491 3.268941 0.3643 0.717293 0.358646 M5 0.221963601532572 3.267991 0.0679 0.946137 0.473069 M6 1.25316091954024 3.267738 0.3835 0.703082 0.351541 M7 -0.315641762452104 3.268183 -0.0966 0.92347 0.461735 M8 -0.484444444444441 3.269326 -0.1482 0.882836 0.441418 M9 -0.853247126436776 3.271166 -0.2608 0.795356 0.397678 M10 -2.66239463601532 3.24678 -0.82 0.416349 0.208175 M11 -2.23119731800765 3.245726 -0.6874 0.495193 0.247596 t -0.0311973180076629 0.047754 -0.6533 0.51675 0.258375 Multiple Linear Regression - Regression Statistics Multiple R 0.680458196061591 R-squared 0.463023356587394 Adjusted R-squared 0.31449790202646 F-TEST (value) 3.1174680323731 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0.00210479876690073 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.13138840663048 Sum Squared Residuals 1237.56390804598 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 7.10114942528733 5.89885057471267 2 8 6.18735632183905 1.81264367816095 3 7 4.98735632183909 2.01264367816091 4 3 4.38735632183909 -1.38735632183909 5 3 3.38735632183908 -0.387356321839084 6 4 4.38735632183908 -0.387356321839079 7 4 2.78735632183908 1.21264367816092 8 0 2.58735632183908 -2.58735632183908 9 -4 2.18735632183908 -6.18735632183908 10 -14 -8.45126436781609 -5.54873563218391 11 -18 -8.05126436781609 -9.94873563218391 12 -8 -5.85126436781609 -2.14873563218391 13 -1 -2.07149425287356 1.07149425287356 14 1 -2.98528735632182 3.98528735632182 15 2 -4.18528735632184 6.18528735632184 16 0 -4.78528735632184 4.78528735632184 17 1 -5.78528735632184 6.78528735632184 18 0 -4.78528735632184 4.78528735632184 19 -1 -6.38528735632184 5.38528735632184 20 -3 -6.58528735632184 3.58528735632184 21 -3 -6.98528735632184 3.98528735632184 22 -3 -8.82563218390804 5.82563218390804 23 -4 -8.42563218390804 4.42563218390804 24 -8 -6.22563218390805 -1.77436781609195 25 -9 -2.44586206896551 -6.55413793103449 26 -13 -3.35965517241379 -9.64034482758621 27 -18 -4.55965517241379 -13.4403448275862 28 -11 -5.1596551724138 -5.8403448275862 29 -9 -6.15965517241379 -2.84034482758621 30 -10 -5.15965517241379 -4.84034482758621 31 -13 -6.7596551724138 -6.24034482758621 32 -11 -6.9596551724138 -4.0403448275862 33 -5 -7.3596551724138 2.35965517241379 34 -15 -9.2 -5.8 35 -6 -8.8 2.80000000000000 36 -6 -6.6 0.600000000000005 37 -3 -2.82022988505747 -0.179770114942532 38 -1 -3.73402298850574 2.73402298850574 39 -3 -4.93402298850575 1.93402298850575 40 -4 -5.53402298850575 1.53402298850575 41 -6 -6.53402298850575 0.534022988505747 42 0 -5.53402298850575 5.53402298850575 43 -4 -7.13402298850575 3.13402298850575 44 -2 -7.33402298850575 5.33402298850575 45 -2 -7.73402298850575 5.73402298850575 46 -6 -9.57436781609195 3.57436781609195 47 -7 -9.17436781609195 2.17436781609195 48 -6 -6.97436781609196 0.97436781609196 49 -6 -3.19459770114942 -2.80540229885058 50 -3 -4.10839080459769 1.10839080459769 51 -2 -5.3083908045977 3.30839080459770 52 -5 -5.9083908045977 0.908390804597704 53 -11 -6.9083908045977 -4.0916091954023 54 -11 -5.9083908045977 -5.0916091954023 55 -11 -7.5083908045977 -3.49160919540230 56 -10 -7.7083908045977 -2.29160919540230 57 -14 -8.1083908045977 -5.8916091954023 58 -8 -9.9487356321839 1.94873563218391 59 -9 -9.5487356321839 0.548735632183907 60 -5 -7.34873563218392 2.34873563218392 61 -1 -3.56896551724138 2.56896551724138

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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Software written by Ed van Stee & Patrick Wessa

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