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Paper bouwen model

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 18 Nov 2007 09:05:02 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge.htm/, Retrieved Sun, 18 Nov 2007 16:59:35 +0100

User-defined keywords:

paper, wim, dhondt, model

Dataseries X:

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0 115.4 0 106.9 0 107.1 0 99.3 0 99.2 0 108.3 0 105.6 0 99.5 0 107.4 0 93.1 0 88.1 0 110.7 0 113.1 0 99.6 0 93.6 0 98.6 0 99.6 0 114.3 1 107.8 1 101.2 1 112.5 1 100.5 1 93.9 1 116.2 1 112 1 106.4 1 95.7 1 96 1 95.8 1 103 1 102.2 1 98.4 1 111.4 1 86.6 1 91.3 1 107.9 1 101.8 1 104.4 1 93.4 1 100.1 1 98.5 1 112.9 1 101.4 1 107.1 1 110.8 1 90.3 1 95.5 1 111.4 1 113 1 107.5 1 95.9 1 106.3 1 105.2 1 117.2 1 106.9 1 108.2 1 110 1 96.1 1 100.6

Text written by user:

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 compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation B [t] = + 110.608581349206 -1.81894841269841A[t] -0.378570601851804M1[t] -6.55542493386244M2[t] -14.4522792658730M3[t] -11.6091335978836M4[t] -12.0859879298942M5[t] -0.682842261904766M6[t] -6.75590691137567M7[t] -8.73276124338625M8[t] -1.26961557539683M9[t] -18.4464699074074M10[t] -17.963324239418M11[t] + 0.0768543320105817t + 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) 110.608581349206 2.393717 46.2079 0 0 A -1.81894841269841 2.063509 -0.8815 0.382741 0.19137 M1 -0.378570601851804 2.904091 -0.1304 0.896864 0.448432 M2 -6.55542493386244 2.904031 -2.2574 0.028886 0.014443 M3 -14.4522792658730 2.905029 -4.9749 1e-05 5e-06 M4 -11.6091335978836 2.907084 -3.9934 0.000238 0.000119 M5 -12.0859879298942 2.910194 -4.153 0.000144 7.2e-05 M6 -0.682842261904766 2.914355 -0.2343 0.815812 0.407906 M7 -6.75590691137567 2.898667 -2.3307 0.02431 0.012155 M8 -8.73276124338625 2.898687 -3.0127 0.00424 0.00212 M9 -1.26961557539683 2.899767 -0.4378 0.663601 0.331801 M10 -18.4464699074074 2.901905 -6.3567 0 0 M11 -17.963324239418 2.9051 -6.1834 0 0 t 0.0768543320105817 0.055432 1.3865 0.172437 0.086218 Multiple Linear Regression - Regression Statistics Multiple R 0.862898988561897 R-squared 0.744594664461145 Adjusted R-squared 0.670810900861031 F-TEST (value) 10.0915787990516 F-TEST (DF numerator) 13 F-TEST (DF denominator) 45 p-value 1.94781590856508e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.31989105790929 Sum Squared Residuals 839.76564384921 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 115.4 110.306865079365 5.09313492063515 2 106.9 104.206865079365 2.69313492063491 3 107.1 96.386865079365 10.7131349206349 4 99.3 99.306865079365 -0.00686507936508507 5 99.2 98.906865079365 0.293134920634920 6 108.3 110.386865079365 -2.08686507936509 7 105.6 104.390654761905 1.20934523809522 8 99.5 102.490654761905 -2.99065476190477 9 107.4 110.030654761905 -2.63065476190477 10 93.1 92.9306547619048 0.169345238095228 11 88.1 93.4906547619048 -5.39065476190477 12 110.7 111.530833333333 -0.830833333333343 13 113.1 111.229117063492 1.87088293650787 14 99.6 105.129117063492 -5.52911706349207 15 93.6 97.309117063492 -3.70911706349208 16 98.6 100.229117063492 -1.62911706349207 17 99.6 99.829117063492 -0.229117063492073 18 114.3 111.309117063492 2.99088293650793 19 107.8 103.493958333333 4.30604166666666 20 101.2 101.593958333333 -0.393958333333335 21 112.5 109.133958333333 3.36604166666666 22 100.5 92.0339583333333 8.46604166666667 23 93.9 92.5939583333333 1.30604166666667 24 116.2 110.634136904762 5.56586309523809 25 112 110.332420634921 1.66757936507931 26 106.4 104.232420634921 2.16757936507937 27 95.7 96.4124206349206 -0.712420634920633 28 96 99.3324206349206 -3.33242063492063 29 95.8 98.9324206349206 -3.13242063492064 30 103 110.412420634921 -7.41242063492064 31 102.2 104.416210317460 -2.21621031746032 32 98.4 102.516210317460 -4.11621031746031 33 111.4 110.056210317460 1.34378968253969 34 86.6 92.9562103174603 -6.35621031746032 35 91.3 93.5162103174603 -2.21621031746032 36 107.9 111.556388888889 -3.65638888888888 37 101.8 111.254672619048 -9.45467261904767 38 104.4 105.154672619048 -0.75467261904761 39 93.4 97.3346726190476 -3.93467261904761 40 100.1 100.254672619048 -0.154672619047616 41 98.5 99.8546726190476 -1.35467261904762 42 112.9 111.334672619048 1.56532738095239 43 101.4 105.338462301587 -3.93846230158729 44 107.1 103.438462301587 3.6615376984127 45 110.8 110.978462301587 -0.178462301587302 46 90.3 93.8784623015873 -3.57846230158730 47 95.5 94.4384623015873 1.06153769841270 48 111.4 112.478640873016 -1.07864087301586 49 113 112.176924603175 0.823075396825353 50 107.5 106.076924603175 1.42307539682540 51 95.9 98.2569246031746 -2.35692460317459 52 106.3 101.176924603175 5.12307539682541 53 105.2 100.776924603175 4.42307539682541 54 117.2 112.256924603175 4.94307539682541 55 106.9 106.260714285714 0.639285714285728 56 108.2 104.360714285714 3.83928571428572 57 110 111.900714285714 -1.90071428571428 58 96.1 94.8007142857143 1.29928571428572 59 100.6 95.3607142857143 5.23928571428572

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/1yl3w1195401892.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/1yl3w1195401892.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/20xxq1195401892.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/20xxq1195401892.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/38eqa1195401892.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/38eqa1195401892.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/4rgxe1195401892.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/4rgxe1195401892.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/5dg3e1195401892.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/5dg3e1195401892.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/6s7jn1195401892.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/6s7jn1195401892.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/7zxgg1195401892.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/7zxgg1195401892.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/86f2r1195401892.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/86f2r1195401892.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/9jd831195401893.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t1195401575rkcxgfio9ctlhge/9jd831195401893.ps (open in new window)

Parameters:

par1 = 2 ; 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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