Home » date » 2007 » Nov » 20 » attachments

paper (Q3 W6)

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

Title produced by software: Multiple Regression

Date of computation: Tue, 20 Nov 2007 10:56:04 -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/Nov/20/t1195580955h7j3ou4hojersml.htm/, Retrieved Tue, 20 Nov 2007 18:49:26 +0100

User-defined keywords:

paper, Q3, multiple regression

Dataseries X:

» Textbox « » Textfile « » CSV «

95,90 96,92 96,06 96,06 96,31 96,59 96,34 96,67 96,49 97,27 96,22 96,38 96,53 96,47 96,50 96,05 96,77 96,76 96,66 96,51 96,58 96,55 96,63 95,97 97,06 97,00 97,73 97,46 98,01 97,90 97,76 98,42 97,49 98,54 97,77 99,00 97,96 98,94 98,23 99,02 98,51 100,07 98,19 98,72 98,37 98,73 98,31 98,04 98,60 99,08 98,97 99,22 99,11 99,57 99,64 100,44 100,03 100,84 99,98 100,75 100,32 100,49 100,44 99,98 100,51 99,96 101,00 99,76 100,88 100,11 100,55 99,79 100,83 100,29 101,51 101,12 102,16 102,65 102,39 102,71 102,54 103,39 102,85 102,80 103,47 102,07 103,57 102,15 103,69 101,21 103,50 101,27 103,47 101,86 103,45 101,65 103,48 101,94 103,93 102,62 103,89 102,71 104,40 103,39 104,79 104,51 104,77 104,09 105,13 104,29 105,26 104,57 104,96 105,39 104,75 105,15 105,01 106,13 105,15 105,46 105,20 106,47 105,77 106,62 105,78 106,52 106,26 108,04 106,13 107,15 106,12 107,32 106,57 107,76 106,44 107,26 106,54 107,89

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 X[t] = + 116.963217020579 -0.242322317806448Y[t] + 1.00872149293644M1[t] + 1.14669854609754M2[t] + 1.45965244398060M3[t] + 1.93063256790926M4[t] + 2.08395036348201M5[t] + 1.65449785574894M6[t] + 1.48036439887373M7[t] + 1.12146370946024M8[t] + 1.30579398428416M9[t] + 0.525442112192919M10[t] + 0.717140915762134M11[t] + 0.212478733778654t + 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) 116.963217020579 22.404579 5.2205 3e-06 1e-06 Y -0.242322317806448 0.236762 -1.0235 0.310559 0.155279 M1 1.00872149293644 0.478432 2.1084 0.039567 0.019783 M2 1.14669854609754 0.491784 2.3317 0.023406 0.011703 M3 1.45965244398060 0.494312 2.9529 0.004623 0.002311 M4 1.93063256790926 0.49995 3.8617 0.000299 0.000149 M5 2.08395036348201 0.495706 4.204 9.7e-05 4.9e-05 M6 1.65449785574894 0.48764 3.3929 0.001288 0.000644 M7 1.48036439887373 0.500981 2.9549 0.004597 0.002298 M8 1.12146370946024 0.494314 2.2687 0.02723 0.013615 M9 1.30579398428416 0.489399 2.6682 0.010002 0.005001 M10 0.525442112192919 0.502891 1.0448 0.300666 0.150333 M11 0.717140915762134 0.498718 1.438 0.156108 0.078054 t 0.212478733778654 0.041074 5.173 3e-06 2e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.979912611016258 R-squared 0.9602287252287 Adjusted R-squared 0.95082824210094 F-TEST (value) 102.146742053388 F-TEST (DF numerator) 13 F-TEST (DF denominator) 55 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.784336695927402 Sum Squared Residuals 33.8351228918073 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 96.92 94.9457069696555 1.97429303034454 2 96.06 95.2573911857464 0.802608814253595 3 96.59 95.7222432379565 0.867756762043497 4 96.67 96.3984324261296 0.271567573870375 5 97.27 96.72788060781 0.542119392189937 6 96.38 96.5763338596634 -0.196333859663392 7 96.47 96.5395592180468 -0.0695592180468275 8 96.05 96.4004069319462 -0.350406931946186 9 96.76 96.731788914741 0.028211085258984 10 96.51 96.1905712313871 0.319428768612863 11 96.55 96.6141345541595 -0.0641345541595285 12 95.97 96.0973562562857 -0.127356256285724 13 97 97.214357886344 -0.214357886344048 14 97.46 97.4024577203535 0.0575422796465193 15 97.9 97.8600401030294 0.0399598969706189 16 98.42 98.6040795401883 -0.184079540188308 17 98.54 99.0353030953475 -0.495303095347447 18 99 98.7504790724072 0.249520927592767 19 98.94 98.7427831089275 0.197216891072549 20 99.02 98.5309341274849 0.489065872515128 21 100.07 98.8598928871016 1.21010711289835 22 98.72 98.3695628904871 0.35043710951288 23 98.73 98.7301224106298 -0.000122410629820019 24 98.04 98.2399995677147 -0.199999567714725 25 99.08 99.390926322266 -0.310926322265963 26 99.22 99.6517228516173 -0.431722851617322 27 99.57 100.143230358786 -0.573230358786143 28 100.44 100.698258388056 -0.258258388056033 29 100.84 100.969549213463 -0.129549213462911 30 100.75 100.764691555399 -0.0146915553988233 31 100.49 100.720647244248 -0.230647244248079 32 99.98 100.545146610476 -0.565146610476458 33 99.96 100.924993056833 -0.964993056832593 34 99.76 100.238381982795 -0.478381982794836 35 100.11 100.671638198279 -0.561638198279485 36 99.79 100.246942381172 -0.456942381172125 37 100.29 101.400292358901 -1.11029235890142 38 101.12 101.585968969733 -0.465968969732779 39 102.65 101.953892094820 0.696107905179692 40 102.71 102.581616819432 0.128383180567852 41 103.39 102.911065001113 0.478934998887429 42 102.8 102.618971308638 0.181028691361835 43 102.07 102.507076748502 -0.437076748501611 44 102.15 102.336422561086 -0.186422561086118 45 101.21 102.704152891552 -1.49415289155193 46 101.27 102.182320993623 -0.912320993622567 47 101.86 102.593768200505 -0.733768200504626 48 101.65 102.093952464877 -0.443952464877267 49 101.94 103.307883022058 -1.36788302205818 50 102.62 103.549293765985 -0.929293765985017 51 102.71 104.084419290359 -1.37441929035901 52 103.39 104.644293765985 -1.25429376598502 53 104.51 104.915584591392 -0.405584591391901 54 104.09 104.703457263794 -0.61345726379362 55 104.29 104.654566506287 -0.364566506286737 56 104.57 104.476642649337 0.093357350662928 57 105.39 104.946148353282 0.443851646718420 58 105.15 104.429162901708 0.72083709829166 59 106.13 104.770336636427 1.35966336357346 60 105.46 104.231749329950 1.22825067004984 61 106.47 105.440833440775 1.02916655922507 62 106.62 105.653165506565 0.966834493435003 63 106.52 106.176174915049 0.343825084951341 64 108.04 106.743319060209 1.29668093979114 65 107.15 107.140617490875 0.0093825091248946 66 107.32 106.926066940099 0.393933059901234 67 107.76 106.855367173989 0.904632826010706 68 107.26 106.740447119669 0.519552880330705 69 107.89 107.113023896491 0.77697610350877

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/1jpfu1195581360.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/1jpfu1195581360.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/2uxto1195581360.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/2uxto1195581360.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/3g92c1195581360.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/3g92c1195581360.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/4nkpc1195581360.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/4nkpc1195581360.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/56w9o1195581360.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/56w9o1195581360.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/66im71195581360.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/66im71195581360.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/7jxnv1195581360.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/7jxnv1195581360.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/82aw81195581360.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/82aw81195581360.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/9ew5h1195581360.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/20/t1195580955h7j3ou4hojersml/9ew5h1195581360.ps (open in new window)

Parameters:

par1 = 2 ; 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