q3 Seatbelt law met lineaire trend

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Mon, 24 Nov 2008 09:49:56 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80.htm/, Retrieved Mon, 24 Nov 2008 16:51:45 +0000

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

7.8 0 7.6 0 7.5 0 7.6 0 7.5 0 7.3 0 7.6 0 7.5 0 7.6 0 7.9 0 7.9 0 8.1 0 8.2 0 8.0 0 7.5 0 6.8 0 6.5 0 6.6 0 7.6 0 8.0 0 8.0 0 7.7 0 7.5 0 7.6 0 7.7 0 7.9 0 7.8 0 7.5 0 7.5 0 7.1 0 7.5 0 7.5 0 7.6 0 7.7 0 7.7 1 7.9 1 8.1 1 8.2 1 8.2 1 8.1 1 7.9 1 7.3 1 6.9 1 6.6 1 6.7 1 6.9 1 7.0 1 7.1 1 7.2 1 7.1 1 6.9 1 7.0 1 6.8 1 6.4 1 6.7 1 6.7 1 6.4 1 6.3 1 6.2 1 6.5 1 6.8 1 6.8 1 6.5 1 6.3 1 5.9 1 5.9 1 6.4 1 6.4 1

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 computational 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] = + 8.08970588235294 + 0.347310924369748x[t] -0.0291596638655462t + 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) 8.08970588235294 0.124154 65.1585 0 0 x 0.347310924369748 0.218234 1.5915 0.116357 0.058179 t -0.0291596638655462 0.005559 -5.2452 2e-06 1e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.699797922898922 R-squared 0.489717132893646 Adjusted R-squared 0.474016121598066 F-TEST (value) 31.1901649947543 F-TEST (DF numerator) 2 F-TEST (DF denominator) 65 p-value 3.1904878738942e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.449754008754155 Sum Squared Residuals 13.1481134453781 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.8 8.06054621848739 -0.260546218487385 2 7.6 8.03138655462185 -0.431386554621849 3 7.5 8.0022268907563 -0.502226890756304 4 7.6 7.97306722689076 -0.373067226890757 5 7.5 7.94390756302521 -0.443907563025210 6 7.3 7.91474789915966 -0.614747899159664 7 7.6 7.88558823529412 -0.285588235294118 8 7.5 7.85642857142857 -0.356428571428572 9 7.6 7.82726890756303 -0.227268907563026 10 7.9 7.79810924369748 0.101890756302521 11 7.9 7.76894957983193 0.131050420168067 12 8.1 7.73978991596639 0.360210084033613 13 8.2 7.71063025210084 0.489369747899159 14 8 7.6814705882353 0.318529411764706 15 7.5 7.65231092436975 -0.152310924369748 16 6.8 7.6231512605042 -0.823151260504202 17 6.5 7.59399159663866 -1.09399159663866 18 6.6 7.56483193277311 -0.96483193277311 19 7.6 7.53567226890756 0.0643277310924364 20 8 7.50651260504202 0.493487394957983 21 8 7.47735294117647 0.522647058823529 22 7.7 7.44819327731092 0.251806722689076 23 7.5 7.41903361344538 0.0809663865546217 24 7.6 7.38987394957983 0.210126050420168 25 7.7 7.36071428571429 0.339285714285714 26 7.9 7.33155462184874 0.56844537815126 27 7.8 7.3023949579832 0.497605042016806 28 7.5 7.27323529411765 0.226764705882353 29 7.5 7.2440756302521 0.255924369747899 30 7.1 7.21491596638655 -0.114915966386555 31 7.5 7.18575630252101 0.314243697478992 32 7.5 7.15659663865546 0.343403361344538 33 7.6 7.12743697478992 0.472563025210084 34 7.7 7.09827731092437 0.60172268907563 35 7.7 7.41642857142857 0.283571428571429 36 7.9 7.38726890756303 0.512731092436975 37 8.1 7.35810924369748 0.74189075630252 38 8.2 7.32894957983193 0.871050420168066 39 8.2 7.29978991596639 0.900210084033613 40 8.1 7.27063025210084 0.829369747899159 41 7.9 7.2414705882353 0.658529411764706 42 7.3 7.21231092436975 0.0876890756302518 43 6.9 7.1831512605042 -0.283151260504201 44 6.6 7.15399159663866 -0.553991596638656 45 6.7 7.12483193277311 -0.424831932773109 46 6.9 7.09567226890756 -0.195672268907563 47 7 7.06651260504202 -0.0665126050420169 48 7.1 7.03735294117647 0.062647058823529 49 7.2 7.00819327731092 0.191806722689076 50 7.1 6.97903361344538 0.120966386554621 51 6.9 6.94987394957983 -0.0498739495798316 52 7 6.92071428571429 0.0792857142857143 53 6.8 6.89155462184874 -0.0915546218487396 54 6.4 6.8623949579832 -0.462394957983193 55 6.7 6.83323529411765 -0.133235294117647 56 6.7 6.8040756302521 -0.104075630252101 57 6.4 6.77491596638655 -0.374915966386554 58 6.3 6.74575630252101 -0.445756302521008 59 6.2 6.71659663865546 -0.516596638655462 60 6.5 6.68743697478992 -0.187436974789916 61 6.8 6.65827731092437 0.141722689075630 62 6.8 6.62911764705882 0.170882352941176 63 6.5 6.59995798319328 -0.0999579831932773 64 6.3 6.57079831932773 -0.270798319327731 65 5.9 6.54163865546218 -0.641638655462184 66 5.9 6.51247899159664 -0.612478991596638 67 6.4 6.48331932773109 -0.083319327731092 68 6.4 6.45415966386555 -0.0541596638655458

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/1hmq21227545391.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/1hmq21227545391.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/2izo31227545391.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/2izo31227545391.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/3vsq21227545391.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/3vsq21227545391.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/453to1227545391.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/453to1227545391.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/55qg01227545391.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/55qg01227545391.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/6dqp81227545391.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/6dqp81227545391.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/7tchl1227545391.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/7tchl1227545391.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/8ovbl1227545391.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/8ovbl1227545391.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/9qhfd1227545391.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t1227545496er7iyraoewddq80/9qhfd1227545391.ps (open in new window)

Parameters (Session):

par1 = 0 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 0 ; 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