Home » date » 2007 » Dec » 16 » attachments

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 14:31:56 -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/t1197839713kyriz4vm5qy2rui.htm/, Retrieved Sun, 16 Dec 2007 22:15:13 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

112.1 0 104.2 0 102.4 0 100.3 0 102.6 0 101.5 0 103.4 0 99.4 0 97.9 0 98 0 90.2 0 87.1 0 91.8 0 94.8 0 91.8 0 89.3 0 91.7 0 86.2 0 82.8 0 82.3 0 79.8 0 79.4 0 85.3 0 87.5 0 88.3 0 88.6 0 94.9 0 94.7 0 92.6 0 91.8 0 96.4 0 96.4 0 107.1 0 111.9 0 107.8 0 109.2 0 115.3 0 119.2 0 107.8 0 106.8 0 104.2 0 94.8 0 97.5 0 98.3 0 100.6 0 94.9 0 93.6 0 98 0 104.3 0 103.9 0 105.3 0 102.6 0 103.3 0 107.9 0 107.8 0 109.8 0 110.6 0 110.8 1 119.3 1 128.1 1 127.6 1 137.9 1 151.4 1 143.6 1 143.4 1 141.9 1 135.2 1 133.1 1 129.6 1 134.1 1 136.8 1 143.5 1 162.5 1 163.1 1 157.2 1 158.8 1 155.4 1 148.5 1 154.2 1 153.3 1 149.4 1 147.9 1 156 1 163 1 159.1 1 159.5 1 157.3 1 156.4 1 156.6 1 162.4 1 166.8 1 162.6 1 168.1 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 Y[t] = + 98.3859649122807 + 49.7918128654971X[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) 98.3859649122807 1.502167 65.496 0 0 X 49.7918128654971 2.414395 20.6229 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.907605168693568 R-squared 0.82374714223928 Adjusted R-squared 0.821810297648502 F-TEST (value) 425.303685263026 F-TEST (DF numerator) 1 F-TEST (DF denominator) 91 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.3411101817907 Sum Squared Residuals 11704.4909941521 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 112.1 98.3859649122807 13.7140350877193 2 104.2 98.3859649122807 5.81403508771929 3 102.4 98.3859649122807 4.0140350877193 4 100.3 98.3859649122807 1.91403508771930 5 102.6 98.3859649122807 4.21403508771929 6 101.5 98.3859649122807 3.1140350877193 7 103.4 98.3859649122807 5.0140350877193 8 99.4 98.3859649122807 1.01403508771930 9 97.9 98.3859649122807 -0.485964912280696 10 98 98.3859649122807 -0.385964912280702 11 90.2 98.3859649122807 -8.1859649122807 12 87.1 98.3859649122807 -11.2859649122807 13 91.8 98.3859649122807 -6.5859649122807 14 94.8 98.3859649122807 -3.58596491228070 15 91.8 98.3859649122807 -6.5859649122807 16 89.3 98.3859649122807 -9.0859649122807 17 91.7 98.3859649122807 -6.6859649122807 18 86.2 98.3859649122807 -12.1859649122807 19 82.8 98.3859649122807 -15.5859649122807 20 82.3 98.3859649122807 -16.0859649122807 21 79.8 98.3859649122807 -18.5859649122807 22 79.4 98.3859649122807 -18.9859649122807 23 85.3 98.3859649122807 -13.0859649122807 24 87.5 98.3859649122807 -10.8859649122807 25 88.3 98.3859649122807 -10.0859649122807 26 88.6 98.3859649122807 -9.7859649122807 27 94.9 98.3859649122807 -3.48596491228070 28 94.7 98.3859649122807 -3.6859649122807 29 92.6 98.3859649122807 -5.78596491228071 30 91.8 98.3859649122807 -6.5859649122807 31 96.4 98.3859649122807 -1.98596491228070 32 96.4 98.3859649122807 -1.98596491228070 33 107.1 98.3859649122807 8.7140350877193 34 111.9 98.3859649122807 13.5140350877193 35 107.8 98.3859649122807 9.4140350877193 36 109.2 98.3859649122807 10.8140350877193 37 115.3 98.3859649122807 16.9140350877193 38 119.2 98.3859649122807 20.8140350877193 39 107.8 98.3859649122807 9.4140350877193 40 106.8 98.3859649122807 8.4140350877193 41 104.2 98.3859649122807 5.8140350877193 42 94.8 98.3859649122807 -3.58596491228070 43 97.5 98.3859649122807 -0.885964912280702 44 98.3 98.3859649122807 -0.0859649122807048 45 100.6 98.3859649122807 2.21403508771929 46 94.9 98.3859649122807 -3.48596491228070 47 93.6 98.3859649122807 -4.78596491228071 48 98 98.3859649122807 -0.385964912280702 49 104.3 98.3859649122807 5.9140350877193 50 103.9 98.3859649122807 5.5140350877193 51 105.3 98.3859649122807 6.9140350877193 52 102.6 98.3859649122807 4.21403508771929 53 103.3 98.3859649122807 4.9140350877193 54 107.9 98.3859649122807 9.5140350877193 55 107.8 98.3859649122807 9.4140350877193 56 109.8 98.3859649122807 11.4140350877193 57 110.6 98.3859649122807 12.2140350877193 58 110.8 148.177777777778 -37.3777777777778 59 119.3 148.177777777778 -28.8777777777778 60 128.1 148.177777777778 -20.0777777777778 61 127.6 148.177777777778 -20.5777777777778 62 137.9 148.177777777778 -10.2777777777778 63 151.4 148.177777777778 3.22222222222223 64 143.6 148.177777777778 -4.57777777777779 65 143.4 148.177777777778 -4.77777777777778 66 141.9 148.177777777778 -6.27777777777778 67 135.2 148.177777777778 -12.9777777777778 68 133.1 148.177777777778 -15.0777777777778 69 129.6 148.177777777778 -18.5777777777778 70 134.1 148.177777777778 -14.0777777777778 71 136.8 148.177777777778 -11.3777777777778 72 143.5 148.177777777778 -4.67777777777778 73 162.5 148.177777777778 14.3222222222222 74 163.1 148.177777777778 14.9222222222222 75 157.2 148.177777777778 9.02222222222221 76 158.8 148.177777777778 10.6222222222222 77 155.4 148.177777777778 7.22222222222223 78 148.5 148.177777777778 0.32222222222222 79 154.2 148.177777777778 6.02222222222221 80 153.3 148.177777777778 5.12222222222223 81 149.4 148.177777777778 1.22222222222223 82 147.9 148.177777777778 -0.277777777777775 83 156 148.177777777778 7.82222222222222 84 163 148.177777777778 14.8222222222222 85 159.1 148.177777777778 10.9222222222222 86 159.5 148.177777777778 11.3222222222222 87 157.3 148.177777777778 9.12222222222223 88 156.4 148.177777777778 8.22222222222223 89 156.6 148.177777777778 8.42222222222222 90 162.4 148.177777777778 14.2222222222222 91 166.8 148.177777777778 18.6222222222222 92 162.6 148.177777777778 14.4222222222222 93 168.1 148.177777777778 19.9222222222222

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/19r2m1197840706.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/19r2m1197840706.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/25lb01197840706.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/25lb01197840706.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/3zdmr1197840706.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/3zdmr1197840706.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/40kay1197840706.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/40kay1197840706.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/50fav1197840706.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/50fav1197840706.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/6445m1197840706.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/6445m1197840706.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/7aa0x1197840706.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/7aa0x1197840706.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/8ciy41197840706.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/8ciy41197840706.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/97rps1197840706.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197839713kyriz4vm5qy2rui/97rps1197840706.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

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