Home » date » 2007 » Nov » 17 » attachments

mult regr

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

Title produced by software: Multiple Regression

Date of computation: Sat, 17 Nov 2007 11:22:13 -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/17/t119532370472pnpgf3d75vzp8.htm/, Retrieved Sat, 17 Nov 2007 19:21:53 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

95,90 96,92 95,86 96,06 96,06 96,02 96,31 96,59 96,34 96,34 96,67 96,84 96,49 97,27 96,73 96,22 96,38 96,34 96,53 96,47 96,60 96,50 96,05 96,64 96,77 96,76 97,20 96,66 96,51 97,50 96,58 96,55 96,99 96,63 95,97 97,08 97,06 97,00 97,55 97,73 97,46 98,42 98,01 97,90 98,78 97,76 98,42 97,49 97,49 98,54 96,99 97,77 99,00 97,16 97,96 98,94 97,29 98,23 99,02 97,80 98,51 100,07 98,12 98,19 98,72 98,03 98,37 98,73 98,11 98,31 98,04 98,07 98,60 99,08 98,21 98,97 99,22 98,48 99,11 99,57 98,83 99,64 100,44 99,20 100,03 100,84 99,88 99,98 100,75 99,71 100,32 100,49 100,03 100,44 99,98 100,60 100,51 99,96 100,85 101,00 99,76 101,96 100,88 100,11 101,40 100,55 99,79 100,81 100,83 100,29 100,66 101,51 101,12 101,55 102,16 102,65 102,23 102,39 102,71 102,90 102,54 103,39 102,68 102,85 102,80 103,41 103,47 102,07 104,62 103,57 102,15 104,93 103,69 101,21 105,88 103,50 101,27 105,18 103,47 101,86 104,54 103,45 101,65 104,58 103,48 101,94 104,34 103,93 102,62 104,66 103,89 102,71 104,73 104,40 103,39 105,44 104,79 104,51 105,72 104,77 104,09 105,68 105,13 104,29 105,90 105,26 104,57 105,97 104,96 105,39 105,21 104,75 105,15 104,75 105,01 106,13 104,89 105,15 105,46 105,26 105,20 106,47 104,84 105,77 106,62 105,47 105,78 106,52 105,40 106,26 108,04 105,73 106,13 107,15 105,72 106,12 107,32 105,63 106,57 107,76 105,97 106,44 107,26 105,92 106,54 107,89 106,32

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 x[t] = + 0.80040639255172 + 0.379659939126742y[t] + 0.611032021039155z[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) 0.80040639255172 0.653634 1.2245 0.225098 0.112549 y 0.379659939126742 0.015551 24.4133 0 0 z 0.611032021039155 0.015164 40.2942 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.998619183453074 R-squared 0.997240273560485 Adjusted R-squared 0.99715664548656 F-TEST (value) 11924.7069406202 F-TEST (DF numerator) 2 F-TEST (DF denominator) 66 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.186084686163247 Sum Squared Residuals 2.28541568801528 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.9 96.1705772295294 -0.270577229529418 2 96.06 95.9418348052463 0.118165194753693 3 96.31 96.338584819716 -0.0285848197160194 4 96.34 96.6744736253657 -0.334473625365734 5 96.49 96.8350560665275 -0.345056066527479 6 96.22 96.2588562324994 -0.0388562324994034 7 96.53 96.451893952491 0.0781060475090164 8 96.5 96.3168780588993 0.183121941100678 9 96.77 96.9286145474612 -0.158614547461245 10 96.66 97.0170091689913 -0.357009168991304 11 96.58 96.7205692358264 -0.140569235826396 12 96.63 96.5553593530264 0.074640646973585 13 97.06 97.2335941402154 -0.173594140215355 14 97.73 97.9398355705177 -0.209835570517721 15 98.01 98.3268574713076 -0.316857471307586 16 97.76 97.736049332513 0.0239506674870234 17 97.49 97.4760925146886 0.0139074853113800 18 97.77 97.7546115302636 0.0153884697364248 19 97.96 97.811266096651 0.148733903348932 20 98.23 98.1532652225112 0.0767347774888395 21 98.51 98.7474384053268 -0.237438405326772 22 98.19 98.1799046056122 0.0100953943878467 23 98.37 98.2325837666865 0.137416233313453 24 98.31 97.9461771278475 0.363822872152472 25 98.6 98.4265679474848 0.173432052515173 26 98.97 98.6446989846431 0.325301015356855 27 99.11 98.9914411707012 0.118558829298797 28 99.64 99.547827165526 0.0921728344740407 29 100.03 100.115192915483 -0.085192915483279 30 99.98 99.9771480773852 0.00285192261478946 31 100.32 100.073966739945 0.246033260055199 32 100.44 100.228628422982 0.211371577017525 33 100.51 100.373793229460 0.136206770540282 34 101 100.976106784988 0.0238932150121592 35 100.88 100.766809831900 0.113190168099716 36 100.55 100.284809758967 0.265190241033377 37 100.83 100.382984925374 0.447015074625884 38 101.51 101.241921173574 0.268078826425846 39 102.16 102.238302654745 -0.0783026547447078 40 102.39 102.670473705189 -0.280473705188539 41 102.54 102.794215419166 -0.254215419166107 42 102.85 103.01626943044 -0.166269430439917 43 103.47 103.478466420335 -0.00846642033477176 44 103.57 103.698259141987 -0.128259141987061 45 103.69 103.921859219195 -0.231859219195105 46 103.5 103.516916400815 -0.0169164008153062 47 103.47 103.349855271435 0.120144728564973 48 103.45 103.29456796506 0.155432034940029 49 103.48 103.258021662357 0.221978337642672 50 103.93 103.711720667696 0.218279332303962 51 103.89 103.788662303690 0.101337696309808 52 104.4 104.480663797234 -0.0806637972341706 53 104.79 105.076971894947 -0.286971894947087 54 104.77 104.893073439672 -0.123073439672304 55 105.13 105.103432472126 0.0265675278737328 56 105.26 105.252509496554 0.00749050344552279 57 104.96 105.099446310649 -0.139446310648659 58 104.75 104.727253195580 0.0227468044197707 59 105.01 105.18486441887 -0.174864418869910 60 105.15 105.156574107439 -0.00657410743948088 61 105.2 105.283397197121 -0.083397197121049 62 105.77 105.725296361245 0.0447036387552654 63 105.78 105.644558125859 0.135441874140684 64 106.26 106.423281800275 -0.163281800274884 65 106.13 106.079274134242 0.0507258657583022 66 106.12 106.088823442000 0.0311765580002959 67 106.57 106.463624702369 0.106375297631199 68 106.44 106.243243131753 0.19675686824653 69 106.54 106.726841701819 -0.186841701818964

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/1jkqf1195323728.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/1jkqf1195323728.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/2jo8y1195323728.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/2jo8y1195323728.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/3f41a1195323728.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/3f41a1195323728.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/4pi5b1195323728.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/4pi5b1195323728.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/5t0dz1195323728.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/5t0dz1195323728.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/61ljk1195323728.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/61ljk1195323728.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/7aamy1195323728.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/7aamy1195323728.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/8l3el1195323728.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/8l3el1195323728.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/9hbtj1195323728.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/17/t119532370472pnpgf3d75vzp8/9hbtj1195323728.ps (open in new window)

Parameters:

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')

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