Home » date » 2007 » Dec » 16 » attachments

Paper regressiemodel prod & met seizoenaal

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 04:39:44 -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/t1197804376mn25q2w4n2kyrtx.htm/, Retrieved Sun, 16 Dec 2007 12:26:16 +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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 95.6788888888889 + 12.8027777777778X[t] + 18.7M1[t] + 20.14M2[t] + 13.68M3[t] + 9.34M4[t] + 2.66M5[t] + 4.62M6[t] + 19.48M7[t] + 12.52M8[t] + 12.34M9[t] + 28.16M10[t] -10.52M11[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) 95.6788888888889 3.311537 28.8926 0 0 X 12.8027777777778 1.899297 6.7408 0 0 M1 18.7 4.558312 4.1024 0.000161 8.1e-05 M2 20.14 4.558312 4.4183 5.8e-05 2.9e-05 M3 13.68 4.558312 3.0011 0.004296 0.002148 M4 9.34 4.558312 2.049 0.046068 0.023034 M5 2.66 4.558312 0.5835 0.562314 0.281157 M6 4.62 4.558312 1.0135 0.315995 0.157998 M7 19.48 4.558312 4.2735 9.3e-05 4.7e-05 M8 12.52 4.558312 2.7466 0.008508 0.004254 M9 12.34 4.558312 2.7071 0.009431 0.004716 M10 28.16 4.558312 6.1777 0 0 M11 -10.52 4.558312 -2.3079 0.025456 0.012728 Multiple Linear Regression - Regression Statistics Multiple R 0.88079480244979 R-squared 0.775799484022564 Adjusted R-squared 0.718556799092155 F-TEST (value) 13.5528143895716 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 1.77285963687268e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.20732471523432 Sum Squared Residuals 2441.43988888889 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 112.6 114.378888888889 -1.77888888888897 2 113.8 115.818888888889 -2.01888888888889 3 107.8 109.358888888889 -1.55888888888889 4 103.2 105.018888888889 -1.81888888888888 5 103.3 98.338888888889 4.9611111111111 6 101.2 100.298888888889 0.901111111111115 7 107.7 115.158888888889 -7.45888888888889 8 110.4 108.198888888889 2.20111111111112 9 101.9 108.018888888889 -6.11888888888888 10 115.9 123.838888888889 -7.93888888888888 11 89.9 85.1588888888889 4.74111111111111 12 88.6 95.6788888888889 -7.0788888888889 13 117.2 114.378888888889 2.82111111111113 14 123.9 115.818888888889 8.08111111111111 15 100 109.358888888889 -9.35888888888889 16 103.6 105.018888888889 -1.41888888888889 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 -3.61888888888888 22 124.7 123.838888888889 0.861111111111119 23 89.1 85.1588888888889 3.94111111111111 24 97 95.6788888888889 1.32111111111111 25 121.6 114.378888888889 7.22111111111113 26 118.8 115.818888888889 2.98111111111111 27 114 109.358888888889 4.64111111111111 28 111.5 105.018888888889 6.48111111111111 29 97.2 98.3388888888889 -1.13888888888889 30 102.5 100.298888888889 2.20111111111111 31 113.4 115.158888888889 -1.75888888888888 32 109.8 108.198888888889 1.60111111111111 33 104.9 108.018888888889 -3.11888888888889 34 126.1 123.838888888889 2.26111111111111 35 80 85.1588888888889 -5.15888888888889 36 96.8 95.6788888888889 1.12111111111111 37 117.2 127.181666666667 -9.98166666666664 38 112.3 128.621666666667 -16.3216666666667 39 117.3 122.161666666667 -4.86166666666667 40 111.1 117.821666666667 -6.72166666666667 41 102.2 111.141666666667 -8.94166666666666 42 104.3 113.101666666667 -8.80166666666667 43 122.9 127.961666666667 -5.06166666666667 44 107.6 121.001666666667 -13.4016666666667 45 121.3 120.821666666667 0.478333333333326 46 131.5 136.641666666667 -5.14166666666667 47 89 97.9616666666667 -8.96166666666666 48 104.4 108.481666666667 -4.08166666666666 49 128.9 127.181666666667 1.71833333333336 50 135.9 128.621666666667 7.27833333333334 51 133.3 122.161666666667 11.1383333333333 52 121.3 117.821666666667 3.47833333333333 53 120.5 111.141666666667 9.35833333333334 54 120.4 113.101666666667 7.29833333333334 55 137.9 127.961666666667 9.93833333333333 56 126.1 121.001666666667 5.09833333333333 57 133.2 120.821666666667 12.3783333333333 58 146.6 136.641666666667 9.95833333333332 59 103.4 97.9616666666667 5.43833333333334 60 117.2 108.481666666667 8.71833333333334

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/14yy31197805175.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/14yy31197805175.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/2ranq1197805175.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/2ranq1197805175.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/3km2z1197805175.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/3km2z1197805175.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/4icho1197805175.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/4icho1197805175.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/537jb1197805175.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/537jb1197805175.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/6wmy31197805175.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/6wmy31197805175.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/75w0y1197805175.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/75w0y1197805175.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/8hil71197805175.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/8hil71197805175.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/9neu31197805175.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/16/t1197804376mn25q2w4n2kyrtx/9neu31197805175.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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