Home » date » 2007 » Dec » 16 » attachments

Paper regr.model prod & met Lin.trend

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 05:22:44 -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/t1197806833bl7jo23pgv24s5x.htm/, Retrieved Sun, 16 Dec 2007 13:07:23 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

112,6 0 113,8 0 107,8 0 103,2 0 103,3 0 101,2 0 107,7 0 110,4 0 101,9 0 115,9 0 89,9 0 88,6 0 117,2 0 123,9 0 100 0 103,6 0 94,1 0 98,7 0 119,5 0 112,7 0 104,4 0 124,7 0 89,1 0 97 0 121,6 0 118,8 0 114 0 111,5 0 97,2 0 102,5 0 113,4 0 109,8 0 104,9 0 126,1 0 80 0 96,8 0 117,2 1 112,3 1 117,3 1 111,1 1 102,2 1 104,3 1 122,9 1 107,6 1 121,3 1 131,5 1 89 1 104,4 1 128,9 1 135,9 1 133,3 1 121,3 1 120,5 1 120,4 1 137,9 1 126,1 1 133,2 1 146,6 1 103,4 1 117,2 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 Y[t] = + 86.8722222222222 + 1.79444444444443X[t] + 22.7363888888889M1[t] + 23.8094444444445M2[t] + 16.9825000000000M3[t] + 12.2755555555556M4[t] + 5.22861111111112M5[t] + 6.82166666666668M6[t] + 21.3147222222222M7[t] + 13.9877777777778M8[t] + 13.4408333333333M9[t] + 28.8938888888889M10[t] -10.1530555555555M11[t] + 0.366944444444445t + 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) 86.8722222222222 3.73172 23.2794 0 0 X 1.79444444444443 3.351184 0.5355 0.594907 0.297454 M1 22.7363888888889 4.159835 5.4657 2e-06 1e-06 M2 23.8094444444445 4.136145 5.7564 1e-06 0 M3 16.9825000000000 4.114593 4.1274 0.000153 7.6e-05 M4 12.2755555555556 4.095214 2.9975 0.004378 0.002189 M5 5.22861111111112 4.078039 1.2821 0.206218 0.103109 M6 6.82166666666668 4.063094 1.6789 0.099946 0.049973 M7 21.3147222222222 4.050406 5.2624 4e-06 2e-06 M8 13.9877777777778 4.039995 3.4623 0.001168 0.000584 M9 13.4408333333333 4.031879 3.3336 0.0017 0.00085 M10 28.8938888888889 4.026072 7.1767 0 0 M11 -10.1530555555555 4.022584 -2.524 0.015118 0.007559 t 0.366944444444445 0.09674 3.7931 0.000433 0.000216 Multiple Linear Regression - Regression Statistics Multiple R 0.910612939435822 R-squared 0.829215925467949 Adjusted R-squared 0.780950860926282 F-TEST (value) 17.1804582329336 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.82520665248376e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.35842398362641 Sum Squared Residuals 1859.75955555556 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 112.6 109.975555555556 2.62444444444444 2 113.8 111.415555555556 2.38444444444447 3 107.8 104.955555555556 2.84444444444446 4 103.2 100.615555555556 2.58444444444441 5 103.3 93.9355555555556 9.36444444444444 6 101.2 95.8955555555556 5.30444444444443 7 107.7 110.755555555556 -3.05555555555555 8 110.4 103.795555555556 6.60444444444446 9 101.9 103.615555555556 -1.71555555555555 10 115.9 119.435555555556 -3.53555555555555 11 89.9 80.7555555555556 9.14444444444444 12 88.6 91.2755555555556 -2.67555555555557 13 117.2 114.378888888889 2.82111111111111 14 123.9 115.818888888889 8.0811111111111 15 100 109.358888888889 -9.3588888888889 16 103.6 105.018888888889 -1.41888888888888 17 94.1 98.3388888888889 -4.23888888888889 18 98.7 100.298888888889 -1.59888888888889 19 119.5 115.158888888889 4.34111111111111 20 112.7 108.198888888889 4.50111111111112 21 104.4 108.018888888889 -3.61888888888889 22 124.7 123.838888888889 0.861111111111118 23 89.1 85.1588888888889 3.9411111111111 24 97 95.6788888888889 1.32111111111112 25 121.6 118.782222222222 2.81777777777777 26 118.8 120.222222222222 -1.42222222222223 27 114 113.762222222222 0.237777777777767 28 111.5 109.422222222222 2.07777777777779 29 97.2 102.742222222222 -5.54222222222222 30 102.5 104.702222222222 -2.20222222222222 31 113.4 119.562222222222 -6.16222222222222 32 109.8 112.602222222222 -2.80222222222222 33 104.9 112.422222222222 -7.52222222222222 34 126.1 128.242222222222 -2.14222222222222 35 80 89.5622222222222 -9.56222222222222 36 96.8 100.082222222222 -3.28222222222222 37 117.2 124.98 -7.78 38 112.3 126.42 -14.12 39 117.3 119.96 -2.66000000000001 40 111.1 115.62 -4.51999999999999 41 102.2 108.94 -6.74 42 104.3 110.9 -6.60000000000001 43 122.9 125.76 -2.86 44 107.6 118.8 -11.2 45 121.3 118.62 2.67999999999999 46 131.5 134.44 -2.94000000000000 47 89 95.76 -6.76 48 104.4 106.28 -1.87999999999999 49 128.9 129.383333333333 -0.483333333333325 50 135.9 130.823333333333 5.07666666666666 51 133.3 124.363333333333 8.93666666666667 52 121.3 120.023333333333 1.27666666666667 53 120.5 113.343333333333 7.15666666666667 54 120.4 115.303333333333 5.09666666666667 55 137.9 130.163333333333 7.73666666666667 56 126.1 123.203333333333 2.89666666666666 57 133.2 123.023333333333 10.1766666666666 58 146.6 138.843333333333 7.75666666666666 59 103.4 100.163333333333 3.23666666666667 60 117.2 110.683333333333 6.51666666666668

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/1adod1197807759.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/1adod1197807759.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/2gl9e1197807759.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/2gl9e1197807759.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/3way41197807759.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/3way41197807759.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/48kte1197807759.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/48kte1197807759.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/57de71197807759.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/57de71197807759.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/6ax2p1197807759.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/6ax2p1197807759.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/7zwdy1197807759.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/7zwdy1197807759.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/8t69n1197807759.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/8t69n1197807759.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/9o8yo1197807759.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197806833bl7jo23pgv24s5x/9o8yo1197807759.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

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