Case Q3

*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 14:03:03 -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/t12275606529wl9qw6znjzv44e.htm/, Retrieved Mon, 24 Nov 2008 21:04:12 +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/t12275606529wl9qw6znjzv44e.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 «

97.3 0 101 0 113.2 0 101 0 105.7 0 113.9 0 86.4 0 96.5 0 103.3 0 114.9 0 105.8 0 94.2 0 98.4 0 99.4 0 108.8 0 112.6 0 104.4 0 112.2 0 81.1 0 97.1 0 112.6 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 1 118.8 1 114 1 111.5 1 97.2 1 102.5 1 113.4 1 109.8 1 104.9 1 126.1 1 80 1 96.8 1 117.2 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

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 104.281818181818 + 8.47175324675324x[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) 104.281818181818 1.702152 61.2647 0 0 x 8.47175324675324 2.729516 3.1038 0.002756 0.001378 Multiple Linear Regression - Regression Statistics Multiple R 0.347808537442269 R-squared 0.12097077871773 Adjusted R-squared 0.108413218413698 F-TEST (value) 9.63330263115554 F-TEST (DF numerator) 1 F-TEST (DF denominator) 70 p-value 0.00275644600004932 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.2908022601222 Sum Squared Residuals 8923.7550974026 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 104.281818181818 -6.98181818181792 2 101 104.281818181818 -3.28181818181819 3 113.2 104.281818181818 8.91818181818181 4 101 104.281818181818 -3.28181818181819 5 105.7 104.281818181818 1.41818181818181 6 113.9 104.281818181818 9.61818181818182 7 86.4 104.281818181818 -17.8818181818182 8 96.5 104.281818181818 -7.78181818181819 9 103.3 104.281818181818 -0.981818181818192 10 114.9 104.281818181818 10.6181818181818 11 105.8 104.281818181818 1.51818181818181 12 94.2 104.281818181818 -10.0818181818182 13 98.4 104.281818181818 -5.88181818181818 14 99.4 104.281818181818 -4.88181818181818 15 108.8 104.281818181818 4.51818181818181 16 112.6 104.281818181818 8.3181818181818 17 104.4 104.281818181818 0.118181818181816 18 112.2 104.281818181818 7.91818181818181 19 81.1 104.281818181818 -23.1818181818182 20 97.1 104.281818181818 -7.1818181818182 21 112.6 104.281818181818 8.3181818181818 22 113.8 104.281818181818 9.5181818181818 23 107.8 104.281818181818 3.51818181818181 24 103.2 104.281818181818 -1.08181818181819 25 103.3 104.281818181818 -0.981818181818192 26 101.2 104.281818181818 -3.08181818181819 27 107.7 104.281818181818 3.41818181818181 28 110.4 104.281818181818 6.11818181818182 29 101.9 104.281818181818 -2.38181818181818 30 115.9 104.281818181818 11.6181818181818 31 89.9 104.281818181818 -14.3818181818182 32 88.6 104.281818181818 -15.6818181818182 33 117.2 104.281818181818 12.9181818181818 34 123.9 104.281818181818 19.6181818181818 35 100 104.281818181818 -4.28181818181819 36 103.6 104.281818181818 -0.681818181818195 37 94.1 104.281818181818 -10.1818181818182 38 98.7 104.281818181818 -5.58181818181819 39 119.5 104.281818181818 15.2181818181818 40 112.7 104.281818181818 8.41818181818181 41 104.4 104.281818181818 0.118181818181816 42 124.7 104.281818181818 20.4181818181818 43 89.1 104.281818181818 -15.1818181818182 44 97 104.281818181818 -7.28181818181819 45 121.6 112.753571428571 8.84642857142857 46 118.8 112.753571428571 6.04642857142857 47 114 112.753571428571 1.24642857142857 48 111.5 112.753571428571 -1.25357142857143 49 97.2 112.753571428571 -15.5535714285714 50 102.5 112.753571428571 -10.2535714285714 51 113.4 112.753571428571 0.646428571428577 52 109.8 112.753571428571 -2.95357142857143 53 104.9 112.753571428571 -7.85357142857142 54 126.1 112.753571428571 13.3464285714286 55 80 112.753571428571 -32.7535714285714 56 96.8 112.753571428571 -15.9535714285714 57 117.2 112.753571428571 4.44642857142857 58 112.3 112.753571428571 -0.453571428571431 59 117.3 112.753571428571 4.54642857142857 60 111.1 112.753571428571 -1.65357142857143 61 102.2 112.753571428571 -10.5535714285714 62 104.3 112.753571428571 -8.45357142857143 63 122.9 112.753571428571 10.1464285714286 64 107.6 112.753571428571 -5.15357142857143 65 121.3 112.753571428571 8.54642857142857 66 131.5 112.753571428571 18.7464285714286 67 89 112.753571428571 -23.7535714285714 68 104.4 112.753571428571 -8.35357142857142 69 128.9 112.753571428571 16.1464285714286 70 135.9 112.753571428571 23.1464285714286 71 133.3 112.753571428571 20.5464285714286 72 121.3 112.753571428571 8.54642857142857

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/1usc91227560575.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/1usc91227560575.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/2kpgc1227560575.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/2kpgc1227560575.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/3y53t1227560575.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/3y53t1227560575.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/40x8q1227560575.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/40x8q1227560575.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/5w9ke1227560575.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/5w9ke1227560575.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/6forb1227560575.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/6forb1227560575.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/756cq1227560575.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/756cq1227560575.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/8ansn1227560575.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/8ansn1227560575.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/9bt0p1227560575.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/24/t12275606529wl9qw6znjzv44e/9bt0p1227560575.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