Home » date » 2007 » Nov » 25 » attachments

paper

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

Title produced by software: Multiple Regression

Date of computation: Sun, 25 Nov 2007 10:34:14 -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/25/t1196011507df7jhyewou4y2tn.htm/, Retrieved Sun, 25 Nov 2007 18:25:17 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

8,7 0 8,5 0 8,2 0 8,3 0 8 0 8,1 0 8,7 0 9,3 0 8,9 0 8,8 0 8,4 0 8,4 0 7,3 0 7,2 0 7 0 7 0 6,9 0 6,9 0 7,1 0 7,5 0 7,4 0 8,9 0 8,3 1 8,3 1 9 1 8,9 1 8,8 1 7,8 1 7,8 1 7,8 1 9,2 1 9,3 1 9,2 1 8,6 1 8,5 1 8,5 1 9 1 9 1 8,8 1 8 1 7,9 1 8,1 1 9,3 1 9,4 1 9,4 1 9,3 1 9 1 9,1 1 9,7 1 9,7 1 9,6 1 8,3 1 8,2 1 8,4 1 10,6 1 10,9 1 10,9 1 9,6 1 9,3 1 9,3 1 9,6 1 9,5 1 9,5 1 9 1 8,9 1 9 1 10,1 1 10,2 1 10,2 1 9,5 1 9,3 1 9,3 1 9,4 1 9,3 1 9,1 1 9 1 8,9 1 9 1 9,8 1 10 1 9,8 1 9,4 1 9 1 8,9 1 9,3 1 9,1 1 8,8 1 8,9 1 8,7 1 8,6 1 9,1 1 9,3 1 8,9 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation WLHvrouwen[t] = + 7.78274496865721 + 0.820381062355658x[t] + 0.295018489497414M1[t] + 0.187880100076984M2[t] + 0.00574171065655037M3[t] -0.438896678763882M4[t] -0.571035068184316M5[t] -0.503173457604751M6[t] + 0.489688152974816M7[t] + 0.732549763554384M8[t] + 0.575411374133950M9[t] + 0.460045502034533M10[t] + 0.0071383894204342M11[t] + 0.0071383894204333t + 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) 7.78274496865721 0.242362 32.112 0 0 x 0.820381062355658 0.20357 4.03 0.000128 6.4e-05 M1 0.295018489497414 0.288862 1.0213 0.310224 0.155112 M2 0.187880100076984 0.288881 0.6504 0.517339 0.258669 M3 0.00574171065655037 0.288936 0.0199 0.984196 0.492098 M4 -0.438896678763882 0.289026 -1.5185 0.132871 0.066436 M5 -0.571035068184316 0.289152 -1.9749 0.051778 0.025889 M6 -0.503173457604751 0.289314 -1.7392 0.085896 0.042948 M7 0.489688152974816 0.289512 1.6914 0.094697 0.047349 M8 0.732549763554384 0.289746 2.5283 0.013456 0.006728 M9 0.575411374133950 0.290015 1.9841 0.05072 0.02536 M10 0.460045502034533 0.298973 1.5388 0.127861 0.063931 M11 0.0071383894204342 0.29797 0.024 0.980948 0.490474 t 0.0071383894204333 0.00322 2.2171 0.029494 0.014747 Multiple Linear Regression - Regression Statistics Multiple R 0.788645798693523 R-squared 0.621962195796944 Adjusted R-squared 0.559753443206568 F-TEST (value) 9.99798533001226 F-TEST (DF numerator) 13 F-TEST (DF denominator) 79 p-value 5.30164800949251e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.557417664560849 Sum Squared Residuals 24.5464417683932 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.7 8.08490184757508 0.615098152424921 2 8.5 7.98490184757505 0.515098152424946 3 8.2 7.80990184757506 0.390098152424942 4 8.3 7.37240184757506 0.927598152424945 5 8 7.24740184757506 0.752598152424943 6 8.1 7.32240184757506 0.777598152424941 7 8.7 8.32240184757506 0.37759815242494 8 9.3 8.57240184757505 0.727598152424946 9 8.9 8.42240184757506 0.477598152424943 10 8.8 8.31417436489607 0.485825635103928 11 8.4 7.86840564170241 0.531594358297592 12 8.4 7.8684056417024 0.531594358297594 13 7.3 8.17056252062025 -0.870562520620254 14 7.2 8.07056252062026 -0.870562520620258 15 7 7.89556252062026 -0.895562520620256 16 7 7.45806252062026 -0.458062520620257 17 6.9 7.33306252062026 -0.433062520620256 18 6.9 7.40806252062026 -0.508062520620256 19 7.1 8.40806252062026 -1.30806252062026 20 7.5 8.65806252062026 -1.15806252062026 21 7.4 8.50806252062026 -1.10806252062026 22 8.9 8.39983503794127 0.500164962058728 23 8.3 8.77444737710327 -0.474447377103266 24 8.3 8.77444737710326 -0.474447377103265 25 9 9.07660425602111 -0.0766042560211122 26 8.9 8.97660425602112 -0.0766042560211162 27 8.8 8.80160425602111 -0.00160425602111462 28 7.8 8.36410425602112 -0.564104256021116 29 7.8 8.23910425602111 -0.439104256021115 30 7.8 8.31410425602112 -0.514104256021115 31 9.2 9.31410425602111 -0.114104256021115 32 9.3 9.56410425602112 -0.264104256021115 33 9.2 9.41410425602112 -0.214104256021116 34 8.6 9.30587677334213 -0.705876773342132 35 8.5 8.86010805014847 -0.360108050148466 36 8.5 8.86010805014847 -0.360108050148465 37 9 9.16226492906631 -0.162264929066312 38 9 9.06226492906632 -0.0622649290663162 39 8.8 8.88726492906632 -0.0872649290663143 40 8 8.44976492906632 -0.449764929066315 41 7.9 8.32476492906632 -0.424764929066314 42 8.1 8.39976492906631 -0.299764929066315 43 9.3 9.39976492906631 -0.0997649290663137 44 9.4 9.64976492906631 -0.249764929066315 45 9.4 9.49976492906631 -0.0997649290663147 46 9.3 9.39153744638733 -0.0915374463873306 47 9 8.94576872319367 0.0542312768063343 48 9.1 8.94576872319366 0.154231276806335 49 9.7 9.24792560211151 0.452074397888488 50 9.7 9.14792560211152 0.552074397888483 51 9.6 8.97292560211151 0.627074397888485 52 8.3 8.53542560211151 -0.235425602111514 53 8.2 8.41042560211151 -0.210425602111515 54 8.4 8.48542560211151 -0.0854256021115142 55 10.6 9.48542560211151 1.11457439788849 56 10.9 9.73542560211152 1.16457439788848 57 10.9 9.58542560211152 1.31457439788849 58 9.6 9.47719811943253 0.122801880567469 59 9.3 9.03142939623886 0.268570603761135 60 9.3 9.03142939623886 0.268570603761137 61 9.6 9.33358627515671 0.266413724843288 62 9.5 9.23358627515672 0.266413724843284 63 9.5 9.05858627515672 0.441413724843285 64 9 8.62108627515672 0.378913724843285 65 8.9 8.49608627515671 0.403913724843286 66 9 8.57108627515671 0.428913724843286 67 10.1 9.57108627515671 0.528913724843286 68 10.2 9.82108627515671 0.378913724843284 69 10.2 9.67108627515671 0.528913724843285 70 9.5 9.56285879247773 -0.0628587924777308 71 9.3 9.11709006928407 0.182909930715936 72 9.3 9.11709006928406 0.182909930715937 73 9.4 9.4192469482019 -0.0192469482019105 74 9.3 9.31924694820191 -0.0192469482019145 75 9.1 9.14424694820191 -0.0442469482019143 76 9 8.70674694820191 0.293253051798086 77 8.9 8.58174694820191 0.318253051798087 78 9 8.65674694820191 0.343253051798086 79 9.8 9.65674694820191 0.143253051798087 80 10 9.90674694820192 0.0932530517980854 81 9.8 9.75674694820191 0.0432530517980865 82 9.4 9.64851946552293 -0.24851946552293 83 9 9.20275074232926 -0.202750742329265 84 8.9 9.20275074232926 -0.302750742329263 85 9.3 9.50490762124711 -0.20490762124711 86 9.1 9.40490762124712 -0.304907621247115 87 8.8 9.22990762124711 -0.429907621247113 88 8.9 8.79240762124711 0.107592378752886 89 8.7 8.66740762124711 0.0325923787528858 90 8.6 8.74240762124711 -0.142407621247114 91 9.1 9.74240762124711 -0.642407621247113 92 9.3 9.99240762124711 -0.692407621247114 93 8.9 9.84240762124711 -0.942407621247114

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/12wfh1196012049.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/12wfh1196012049.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/2066y1196012049.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/2066y1196012049.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/3ql9f1196012049.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/3ql9f1196012049.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/4irkw1196012049.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/4irkw1196012049.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/5a84w1196012049.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/5a84w1196012049.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/67qgj1196012049.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/67qgj1196012049.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/7sv1u1196012049.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/7sv1u1196012049.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/8a8jl1196012049.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/8a8jl1196012049.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/93c4r1196012049.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/25/t1196011507df7jhyewou4y2tn/93c4r1196012049.ps (open in new window)

Parameters:

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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by