Home » date » 2007 » Nov » 20 » attachments

paper (Q3 W6)

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

Title produced by software: Multiple Regression

Date of computation: Tue, 20 Nov 2007 11:22:48 -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/20/t1195582578mtt24c2r8m4alht.htm/, Retrieved Tue, 20 Nov 2007 19:16:18 +0100

User-defined keywords:

paper, q3, W6, multiple regression

Dataseries X:

» Textbox « » Textfile « » CSV «

95.90 96.92 96.06 96.06 96.31 96.59 96.34 96.67 96.49 97.27 96.22 96.38 96.53 96.47 96.50 96.05 96.77 96.76 96.66 96.51 96.58 96.55 96.63 95.97 97.06 97.00 97.73 97.46 98.01 97.90 97.76 98.42 97.49 98.54 97.77 99.00 97.96 98.94 98.23 99.02 98.51 100.07 98.19 98.72 98.37 98.73 98.31 98.04 98.60 99.08 98.97 99.22 99.11 99.57 99.64 100.44 100.03 100.84 99.98 100.75 100.32 100.49 100.44 99.98 100.51 99.96 101.00 99.76 100.88 100.11 100.55 99.79 100.83 100.29 101.51 101.12 102.16 102.65 102.39 102.71 102.54 103.39 102.85 102.80 103.47 102.07 103.57 102.15 103.69 101.21 103.50 101.27 103.47 101.86 103.45 101.65 103.48 101.94 103.93 102.62 103.89 102.71 104.40 103.39 104.79 104.51 104.77 104.09 105.13 104.29 105.26 104.57 104.96 105.39 104.75 105.15 105.01 106.13 105.15 105.46 105.20 106.47 105.77 106.62 105.78 106.52 106.26 108.04 106.13 107.15 106.12 107.32 106.57 107.76 106.44 107.26 106.54 107.89

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 Y[t] = + 89.9393085089868 + 0.0538729697220403X[t] + 0.163315226142462t + 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) 89.9393085089868 5.91696 15.2003 0 0 X 0.0538729697220403 0.062168 0.8666 0.389318 0.194659 t 0.163315226142462 0.01096 14.9004 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.991872264789074 R-squared 0.983810589657807 Adjusted R-squared 0.98332000146562 F-TEST (value) 2005.36948366148 F-TEST (DF numerator) 2 F-TEST (DF denominator) 66 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.450705785203678 Sum Squared Residuals 13.4069565178602 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.9 95.3239919605894 0.576008039410576 2 96.06 95.440976432771 0.619023567229067 3 96.31 95.632844332866 0.677155667133924 4 96.34 95.8004693965863 0.5395306034137 5 96.49 95.996108404562 0.493891595438005 6 96.22 96.1114766876518 0.108523312348163 7 96.53 96.2796404810693 0.25035951893072 8 96.5 96.4203290599285 0.079670940071514 9 96.77 96.6218940945736 0.148105905426399 10 96.66 96.7717410782855 -0.111741078285552 11 96.58 96.9372112232169 -0.357211223216894 12 96.63 97.0692801269206 -0.439280126920575 13 97.06 97.2880845118767 -0.228084511876732 14 97.73 97.4761813040913 0.253818695908669 15 98.01 97.6632006369115 0.34679936308851 16 97.76 97.8545298073094 -0.0945298073094129 17 97.49 98.0243097898185 -0.53430978981853 18 97.77 98.2124065820331 -0.442406582033129 19 97.96 98.3724894299923 -0.412489429992271 20 98.23 98.5401144937125 -0.310114493712486 21 98.51 98.759996338063 -0.249996338063089 22 98.19 98.8505830550808 -0.660583055080804 23 98.37 99.0144370109205 -0.64443701092048 24 98.31 99.1405798879547 -0.830579887954736 25 98.6 99.3599230026081 -0.759923002608128 26 98.97 99.5307804445117 -0.560780444511671 27 99.11 99.7129512100568 -0.602951210056846 28 99.64 99.9231359198575 -0.283135919857482 29 100.03 100.108000333889 -0.07800033388876 30 99.98 100.266466992756 -0.286466992756235 31 100.32 100.415775246771 -0.0957752467709772 32 100.44 100.551615258355 -0.111615258355194 33 100.51 100.713853025103 -0.203853025103208 34 101 100.866393657301 0.133606342698733 35 100.88 101.048564422846 -0.168564422846448 36 100.55 101.194640298678 -0.644640298677855 37 100.83 101.384892009681 -0.554892009681336 38 101.51 101.592921800693 -0.0829218006930849 39 102.16 101.838662670510 0.321337329489723 40 102.39 102.005210274836 0.384789725163943 41 102.54 102.205159120390 0.334840879610499 42 102.85 102.336689294396 0.513310705604029 43 103.47 102.460677252641 1.00932274735866 44 103.57 102.628302316362 0.94169768363843 45 103.69 102.740976950965 0.949023049034691 46 103.5 102.907524555291 0.592475444708908 47 103.47 103.102624833570 0.367375166430441 48 103.45 103.254626736070 0.195373263929612 49 103.48 103.433565123432 0.0464348765677601 50 103.93 103.633513968986 0.296486031014313 51 103.89 103.801677762403 0.0883222375968617 52 104.4 104.001626607957 0.398373392043417 53 104.79 104.225279560188 0.56472043981227 54 104.77 104.365968139047 0.404031860953055 55 105.13 104.540057959134 0.589942040866185 56 105.26 104.718457616798 0.541542383201561 57 104.96 104.925948678113 0.0340513218870146 58 104.75 105.076334391522 -0.326334391522152 59 105.01 105.292445127992 -0.282445127992208 60 105.15 105.419665464421 -0.269665464420902 61 105.2 105.637392389983 -0.437392389982628 62 105.77 105.808788561583 -0.0387885615834027 63 105.78 105.966716490754 -0.186716490753655 64 106.26 106.211918630874 0.0480813691263848 65 106.13 106.327286913963 -0.197286913963471 66 106.12 106.499760544959 -0.37976054495867 67 106.57 106.686779877779 -0.116779877778842 68 106.44 106.823158619060 -0.383158619060279 69 106.54 107.020413816128 -0.480413816127617

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/1yq6e1195582958.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/1yq6e1195582958.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/2rifz1195582958.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/2rifz1195582958.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/3tbm61195582958.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/3tbm61195582958.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/4x1m11195582958.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/4x1m11195582958.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/5pswo1195582958.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/5pswo1195582958.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/6vpai1195582958.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/6vpai1195582958.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/76mg51195582959.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/76mg51195582959.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/81ame1195582959.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/81ame1195582959.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/9ba891195582959.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195582578mtt24c2r8m4alht/9ba891195582959.ps (open in new window)

Parameters:

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')

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