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

Title produced by software: Multiple Regression

Date of computation: Sun, 16 Dec 2007 10:17:30 -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/Dec/16/t11978244562qaj8k0cslyb23j.htm/, Retrieved Sun, 16 Dec 2007 18:00:56 +0100

User-defined keywords:

Dataseries X:

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102.7 0 103.2 0 105.6 0 103.9 0 107.2 0 100.7 0 92.1 0 90.3 0 93.4 0 98.5 0 100.8 0 102.3 0 104.7 0 101.1 0 101.4 0 99.5 0 98.4 0 96.3 0 100.7 0 101.2 0 100.3 0 97.8 0 97.4 0 98.6 0 99.7 0 99 0 98.1 0 97 0 98.5 0 103.8 0 114.4 0 124.5 0 134.2 0 131.8 0 125.6 0 119.9 0 114.9 0 115.5 0 112.5 0 111.4 0 115.3 0 110.8 0 103.7 0 111.1 0 113 0 111.2 0 117.6 0 121.7 0 127.3 0 129.8 0 137.1 0 141.4 0 137.4 0 130.7 0 117.2 0 110.8 0 111.4 0 108.2 0 108.8 0 110.2 0 109.5 0 109.5 0 116 0 111.2 0 112.1 0 114 0 119.1 0 114.1 0 115.1 0 115.4 0 110.8 0 116 0 119.2 0 126.5 0 127.8 0 131.3 0 140.3 0 137.3 0 143 0 134.5 0 139.9 1 159.3 1 170.4 1 175 1 175.8 1 180.9 1 180.3 1 169.6 1 172.3 1 184.8 1 177.7 1 184.6 1 211.4 1

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 Graan[t] = + 96.395975503011 + 44.6480074863631ToenemendeVraag[t] + 0.396488259184912t + 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) 96.395975503011 2.348861 41.0395 0 0 ToenemendeVraag 44.6480074863631 3.898376 11.453 0 0 t 0.396488259184912 0.050356 7.8737 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.916384589760264 R-squared 0.839760716350087 Adjusted R-squared 0.83619984338009 F-TEST (value) 235.830012310309 F-TEST (DF numerator) 2 F-TEST (DF denominator) 90 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.4228175455078 Sum Squared Residuals 9777.16130282514 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 102.7 96.792463762196 5.90753623780406 2 103.2 97.188952021381 6.01104797861905 3 105.6 97.5854402805658 8.0145597194342 4 103.9 97.9819285397507 5.9180714602493 5 107.2 98.3784167989356 8.82158320106438 6 100.7 98.7749050581205 1.92509494187947 7 92.1 99.1713933173054 -7.07139331730545 8 90.3 99.5678815764904 -9.26788157649036 9 93.4 99.9643698356753 -6.56436983567526 10 98.5 100.360858094860 -1.86085809486018 11 100.8 100.757346354045 0.0426536459549009 12 102.3 101.15383461323 1.14616538676999 13 104.7 101.550322872415 3.14967712758509 14 101.1 101.946811131600 -0.846811131599838 15 101.4 102.343299390785 -0.943299390784739 16 99.5 102.739787649970 -3.23978764996966 17 98.4 103.136275909155 -4.73627590915456 18 96.3 103.532764168339 -7.23276416833948 19 100.7 103.929252427524 -3.22925242752439 20 101.2 104.325740686709 -3.1257406867093 21 100.3 104.722228945894 -4.42222894589422 22 97.8 105.118717205079 -7.31871720507913 23 97.4 105.515205464264 -8.11520546426404 24 98.6 105.911693723449 -7.31169372344896 25 99.7 106.308181982634 -6.60818198263386 26 99 106.704670241819 -7.70467024181878 27 98.1 107.101158501004 -9.0011585010037 28 97 107.497646760189 -10.4976467601886 29 98.5 107.894135019374 -9.39413501937351 30 103.8 108.290623278558 -4.49062327855843 31 114.4 108.687111537743 5.71288846225667 32 124.5 109.083599796928 15.4164002030718 33 134.2 109.480088056113 24.7199119438868 34 131.8 109.876576315298 21.9234236847019 35 125.6 110.273064574483 15.326935425517 36 119.9 110.669552833668 9.2304471663321 37 114.9 111.066041092853 3.8339589071472 38 115.5 111.462529352038 4.03747064796228 39 112.5 111.859017611223 0.640982388777369 40 111.4 112.255505870408 -0.855505870407537 41 115.3 112.651994129592 2.64800587040754 42 110.8 113.048482388777 -2.24848238877737 43 103.7 113.444970647962 -9.74497064796228 44 111.1 113.841458907147 -2.74145890714720 45 113 114.237947166332 -1.23794716633210 46 111.2 114.634435425517 -3.43443542551701 47 117.6 115.030923684702 2.56907631529807 48 121.7 115.427411943887 6.27258805611316 49 127.3 115.823900203072 11.4760997969282 50 129.8 116.220388462257 13.5796115377433 51 137.1 116.616876721442 20.4831232785584 52 141.4 117.013364980626 24.3866350193735 53 137.4 117.409853239811 19.9901467601886 54 130.7 117.806341498996 12.8936585010037 55 117.2 118.202829758181 -1.00282975818122 56 110.8 118.599318017366 -7.79931801736614 57 111.4 118.995806276551 -7.59580627655104 58 108.2 119.392294535736 -11.1922945357360 59 108.8 119.788782794921 -10.9887827949209 60 110.2 120.185271054106 -9.98527105410578 61 109.5 120.581759313291 -11.0817593132907 62 109.5 120.978247572476 -11.4782475724756 63 116 121.374735831661 -5.37473583166052 64 111.2 121.771224090845 -10.5712240908454 65 112.1 122.167712350030 -10.0677123500304 66 114 122.564200609215 -8.56420060921526 67 119.1 122.960688868400 -3.86068886840017 68 114.1 123.357177127585 -9.25717712758509 69 115.1 123.75366538677 -8.65366538677 70 115.4 124.150153645955 -8.7501536459549 71 110.8 124.546641905140 -13.7466419051398 72 116 124.943130164325 -8.94313016432473 73 119.2 125.339618423510 -6.13961842350964 74 126.5 125.736106682695 0.763893317305446 75 127.8 126.132594941879 1.66740505812053 76 131.3 126.529083201064 4.77091679893563 77 140.3 126.925571460249 13.3744285397507 78 137.3 127.322059719434 9.9779402805658 79 143 127.718547978619 15.2814520213809 80 134.5 128.115036237804 6.38496376219598 81 139.9 173.159531983352 -33.2595319833521 82 159.3 173.556020242537 -14.2560202425370 83 170.4 173.952508501722 -3.55250850172189 84 175 174.348996760907 0.651003239093191 85 175.8 174.745485020092 1.05451497990829 86 180.9 175.141973279277 5.75802672072337 87 180.3 175.538461538462 4.76153846153847 88 169.6 175.934949797646 -6.33494979764646 89 172.3 176.331438056831 -4.03143805683136 90 184.8 176.727926316016 8.07207368398374 91 177.7 177.124414575201 0.575585424798795 92 184.6 177.520902834386 7.0790971656139 93 211.4 177.917391093571 33.482608906429

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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