Home » date » 2007 » Nov » 30 » attachments

works paper V

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

Title produced by software: Multiple Regression

Date of computation: Fri, 30 Nov 2007 04:54:56 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u.htm/, Retrieved Fri, 30 Nov 2007 12:44:25 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

106,7 0 110,2 0 125,9 0 100,1 0 106,4 0 114,8 0 81,3 0 87 0 104,2 0 108 0 105 0 94,5 0 92 0 95,9 0 108,8 0 103,4 0 102,1 0 110,1 0 83,2 0 82,7 0 106,8 0 113,7 0 102,5 0 96,6 0 92,1 0 95,6 0 102,3 0 98,6 0 98,2 0 104,5 0 84 0 73,8 0 103,9 0 106 0 97,2 0 102,6 0 89 0 93,8 0 116,7 1 106,8 1 98,5 1 118,7 1 90 1 91,9 1 113,3 1 113,1 1 104,1 1 108,7 1 96,7 1 101 1 116,9 1 105,8 1 99 1 129,4 1 83 1 88,9 1 115,9 1 104,2 1 113,4 1 112,2 1 100,8 1 107,3 1 126,6 1 102,9 1 117,9 1 128,8 1 87,5 1 93,8 1 122,7 1 126,2 1 124,6 1 116,7 1 115,2 1 111,1 1 129,9 1 113,3 1 118,5 1 133,5 1 102,1 1 102,4 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] = + 97.545 + 5.53874999999998`x `[t] -5.30886408730163M1[t] -2.22558531746031M2[t] + 12.8950148809524M3[t] -0.964563492063498M4[t] + 0.304429563492081M5[t] + 14.3591369047619M6[t] -18.4290128968254M7[t] -17.2028769841270M8[t] + 6.26683035714287M9[t] + 6.88344246031746M10[t] + 2.70005456349207M11[t] + 0.116721230158731t + 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) 97.545 3.117271 31.2918 0 0 `x ` 5.53874999999998 2.969448 1.8652 0.066593 0.033297 M1 -5.30886408730163 3.660279 -1.4504 0.151683 0.075842 M2 -2.22558531746031 3.658449 -0.6083 0.545049 0.272525 M3 12.8950148809524 3.677018 3.5069 0.000821 0.00041 M4 -0.964563492063498 3.671017 -0.2628 0.793561 0.39678 M5 0.304429563492081 3.666127 0.083 0.934072 0.467036 M6 14.3591369047619 3.662351 3.9207 0.000213 0.000106 M7 -18.4290128968254 3.659693 -5.0357 4e-06 2e-06 M8 -17.2028769841270 3.658156 -4.7026 1.4e-05 7e-06 M9 6.26683035714287 3.799089 1.6496 0.103785 0.051892 M10 6.88344246031746 3.796386 1.8132 0.074355 0.037177 M11 2.70005456349207 3.794763 0.7115 0.479269 0.239634 t 0.116721230158731 0.064078 1.8215 0.073057 0.036529 Multiple Linear Regression - Regression Statistics Multiple R 0.881461940737189 R-squared 0.776975152968172 Adjusted R-squared 0.733046016431599 F-TEST (value) 17.6870117244694 F-TEST (DF numerator) 13 F-TEST (DF denominator) 66 p-value 1.11022302462516e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.57178533306778 Sum Squared Residuals 2850.43192261904 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.7 92.3528571428574 14.3471428571426 2 110.2 95.5528571428571 14.6471428571429 3 125.9 110.790178571429 15.1098214285714 4 100.1 97.0473214285714 3.05267857142857 5 106.4 98.4330357142857 7.9669642857143 6 114.8 112.604464285714 2.19553571428574 7 81.3 79.9330357142857 1.36696428571428 8 87 81.2758928571428 5.72410714285718 9 104.2 104.862321428571 -0.662321428571399 10 108 105.595654761905 2.40434523809523 11 105 101.528988095238 3.47101190476192 12 94.5 98.9456547619047 -4.44565476190473 13 92 93.7535119047619 -1.75351190476185 14 95.9 96.9535119047619 -1.0535119047619 15 108.8 112.190833333333 -3.39083333333333 16 103.4 98.4479761904762 4.95202380952382 17 102.1 99.8336904761905 2.26630952380952 18 110.1 114.005119047619 -3.90511904761906 19 83.2 81.3336904761905 1.86630952380953 20 82.7 82.6765476190476 0.0234523809523808 21 106.8 106.262976190476 0.537023809523803 22 113.7 106.996309523810 6.70369047619048 23 102.5 102.929642857143 -0.429642857142853 24 96.6 100.346309523810 -3.74630952380952 25 92.1 95.1541666666666 -3.05416666666662 26 95.6 98.3541666666667 -2.75416666666667 27 102.3 113.591488095238 -11.2914880952381 28 98.6 99.848630952381 -1.24863095238096 29 98.2 101.234345238095 -3.03434523809524 30 104.5 115.405773809524 -10.9057738095238 31 84 82.7343452380952 1.26565476190476 32 73.8 84.0772023809524 -10.2772023809524 33 103.9 107.663630952381 -3.76363095238096 34 106 108.396964285714 -2.39696428571429 35 97.2 104.330297619048 -7.13029761904762 36 102.6 101.746964285714 0.85303571428571 37 89 96.5548214285714 -7.55482142857139 38 93.8 99.7548214285714 -5.95482142857143 39 116.7 120.530892857143 -3.83089285714285 40 106.8 106.788035714286 0.0119642857142910 41 98.5 108.17375 -9.67375 42 118.7 122.345178571429 -3.64517857142857 43 90 89.67375 0.326250000000014 44 91.9 91.0166071428571 0.883392857142863 45 113.3 114.603035714286 -1.30303571428572 46 113.1 115.336369047619 -2.23636904761905 47 104.1 111.269702380952 -7.16970238095238 48 108.7 108.686369047619 0.0136309523809659 49 96.7 103.494226190476 -6.79422619047614 50 101 106.694226190476 -5.69422619047618 51 116.9 121.931547619048 -5.03154761904762 52 105.8 108.188690476190 -2.38869047619048 53 99 109.574404761905 -10.5744047619048 54 129.4 123.745833333333 5.65416666666667 55 83 91.0744047619048 -8.07440476190475 56 88.9 92.4172619047619 -3.51726190476191 57 115.9 116.003690476190 -0.103690476190482 58 104.2 116.737023809524 -12.5370238095238 59 113.4 112.670357142857 0.72964285714286 60 112.2 110.087023809524 2.11297619047620 61 100.8 104.894880952381 -4.09488095238091 62 107.3 108.094880952381 -0.794880952380956 63 126.6 123.332202380952 3.2677976190476 64 102.9 109.589345238095 -6.68934523809524 65 117.9 110.975059523810 6.92494047619047 66 128.8 125.146488095238 3.6535119047619 67 87.5 92.4750595238095 -4.97505952380952 68 93.8 93.8179166666667 -0.0179166666666888 69 122.7 117.404345238095 5.29565476190475 70 126.2 118.137678571429 8.06232142857142 71 124.6 114.071011904762 10.5289880952381 72 116.7 111.487678571429 5.21232142857142 73 115.2 106.295535714286 8.90446428571433 74 111.1 109.495535714286 1.60446428571427 75 129.9 124.732857142857 5.16714285714284 76 113.3 110.99 2.30999999999998 77 118.5 112.375714285714 6.1242857142857 78 133.5 126.547142857143 6.95285714285712 79 102.1 93.8757142857143 8.2242857142857 80 102.4 95.2185714285715 7.18142857142855

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/1ml4g1196423691.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/1ml4g1196423691.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/2g9mb1196423691.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/2g9mb1196423691.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/3acz31196423691.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/3acz31196423691.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/4t0h31196423691.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/4t0h31196423691.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/5y6bj1196423691.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/5y6bj1196423691.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/6j9w01196423691.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/6j9w01196423691.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/7go6x1196423691.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/7go6x1196423691.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/8058z1196423691.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/8058z1196423691.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/9m7ut1196423691.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/30/t1196423054sg9e4be8kj5485u/9m7ut1196423691.ps (open in new window)

Parameters:

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