Home » date » 2007 » Nov » 14 » attachments

WS6 - Regression - Metal production - Verhofstadt II

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

Title produced by software: Multiple Regression

Date of computation: Wed, 14 Nov 2007 13:28:26 -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/14/t1195071848fsvi267qwgcloi3.htm/, Retrieved Wed, 14 Nov 2007 21:24:18 +0100

User-defined keywords:

WS6RMPV

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 1 88,6 1 117,2 1 123,9 1 100 1 103,6 1 94,1 1 98,7 1 119,5 1 112,7 1 104,4 1 124,7 1 89,1 1 97 1 121,6 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 1 120,5 1 120,4 1 137,9 1 126,1 1 133,2 1 146,6 0 103,4 0 117,2 0

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 95.6270870655679 -6.5084378359011X[t] -4.31804112424862M1[t] -2.63221266770174M2[t] + 10.6821872174165M3[t] + 4.12515853110623M4[t] + 3.11098698765305M5[t] + 15.3813243247855M6[t] -20.0744989563961M7[t] -9.21724192842071M8[t] + 10.4734670113119M9[t] + 13.2212002297635M10[t] + 5.93560011488173M11[t] + 0.385600114881735t + 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) 95.6270870655679 2.705772 35.3419 0 0 X -6.5084378359011 1.923382 -3.3839 0.001207 0.000603 M1 -4.31804112424862 3.30037 -1.3084 0.195293 0.097646 M2 -2.63221266770174 3.299704 -0.7977 0.427899 0.213949 M3 10.6821872174165 3.299543 3.2375 0.001888 0.000944 M4 4.12515853110623 3.299886 1.2501 0.215681 0.10784 M5 3.11098698765305 3.300733 0.9425 0.349367 0.174683 M6 15.3813243247855 3.328652 4.6209 1.8e-05 9e-06 M7 -20.0744989563961 3.303939 -6.0759 0 0 M8 -9.21724192842071 3.306295 -2.7878 0.006925 0.003463 M9 10.4734670113119 3.423646 3.0592 0.003206 0.001603 M10 13.2212002297635 3.422431 3.8631 0.000258 0.000129 M11 5.93560011488173 3.421701 1.7347 0.087463 0.043732 t 0.385600114881735 0.040797 9.4516 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.911986029816551 R-squared 0.831718518580555 Adjusted R-squared 0.798572166179755 F-TEST (value) 25.0923090578282 F-TEST (DF numerator) 13 F-TEST (DF denominator) 66 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.92613924965973 Sum Squared Residuals 2317.86234281960 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 91.6946460562013 5.60535394379869 2 101 93.7660746276296 7.23392537237036 3 113.2 107.466074627630 5.73392537237038 4 101 101.294646056201 -0.294646056201046 5 105.7 100.666074627630 5.0339253723704 6 113.9 113.322012079644 0.577987920356247 7 86.4 78.2517889133439 8.14821108665613 8 96.5 89.494646056201 7.00535394379895 9 103.3 109.570955110815 -6.2709551108154 10 114.9 112.704288444149 2.19571155585129 11 105.8 105.804288444149 -0.00428844414869245 12 94.2 100.254288444149 -6.05428844414871 13 98.4 96.3218474347818 2.07815256521820 14 99.4 98.3932760062104 1.00672399378957 15 108.8 112.093276006210 -3.29327600621043 16 112.6 105.921847434782 6.67815256521813 17 104.4 105.293276006210 -0.89327600621043 18 112.2 117.949213458225 -5.74921345822455 19 81.1 82.8789902919247 -1.77899029192473 20 97.1 94.1218474347819 2.97815256521814 21 112.6 114.198156489396 -1.59815648939619 22 113.8 117.331489822730 -3.53148982272952 23 107.8 110.431489822730 -2.63148982272953 24 103.2 104.881489822730 -1.68148982272952 25 103.3 100.949048813363 2.35095118663737 26 101.2 103.020477384791 -1.82047738479124 27 107.7 116.720477384791 -9.02047738479125 28 110.4 110.549048813363 -0.149048813362669 29 101.9 109.920477384791 -8.02047738479125 30 115.9 122.576414836805 -6.67641483680536 31 89.9 80.9977538346044 8.90224616539558 32 88.6 92.2406109774616 -3.64061097746157 33 117.2 112.316920032076 4.88307996792412 34 123.9 115.450253365409 8.44974663459079 35 100 108.550253365409 -8.55025336540922 36 103.6 103.000253365409 0.599746634590766 37 94.1 99.0678123560423 -4.96781235604234 38 98.7 101.139240927471 -2.43924092747095 39 119.5 114.839240927471 4.66075907252905 40 112.7 108.667812356042 4.03218764395762 41 104.4 108.039240927471 -3.63924092747095 42 124.7 120.695178379485 4.00482162051493 43 89.1 85.6249552131852 3.47504478681475 44 97 96.8678123560424 0.132187643957619 45 121.6 116.944121410657 4.6558785893433 46 118.8 120.07745474399 -1.27745474399004 47 114 113.17745474399 0.82254525600996 48 111.5 107.62745474399 3.87254525600996 49 97.2 103.695013734623 -6.49501373462315 50 102.5 105.766442306052 -3.26644230605176 51 113.4 119.466442306052 -6.06644230605176 52 109.8 113.295013734623 -3.4950137346232 53 104.9 112.666442306052 -7.76644230605176 54 126.1 125.322379758066 0.7776202419341 55 80 90.252156591766 -10.2521565917661 56 96.8 101.495013734623 -4.6950137346232 57 117.2 121.571322789238 -4.37132278923751 58 112.3 124.704656122571 -12.4046561225709 59 117.3 117.804656122571 -0.50465612257086 60 111.1 112.254656122571 -1.15465612257086 61 102.2 108.322215113204 -6.12221511320397 62 104.3 110.393643684633 -6.09364368463258 63 122.9 124.093643684633 -1.19364368463258 64 107.6 117.922215113204 -10.322215113204 65 121.3 117.293643684633 4.00635631536741 66 131.5 129.949581136647 1.55041886335329 67 89 94.8793579703469 -5.87935797034688 68 104.4 106.122215113204 -1.72221511320401 69 128.9 126.198524167818 2.70147583218168 70 135.9 129.331857501152 6.56814249884834 71 133.3 122.431857501152 10.8681424988483 72 121.3 116.881857501152 4.41814249884832 73 120.5 112.949416491785 7.55058350821522 74 120.4 115.020845063213 5.37915493678661 75 137.9 128.720845063213 9.17915493678661 76 126.1 122.549416491785 3.55058350821516 77 133.2 121.920845063213 11.2791549367866 78 146.6 141.085220351129 5.51477964887135 79 103.4 106.014997184829 -2.6149971848288 80 117.2 117.257854327686 -0.0578543276859312

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/1p2hw1195072094.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/1p2hw1195072094.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/2je061195072094.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/2je061195072094.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/3c0f11195072094.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/3c0f11195072094.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/4imye1195072095.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/4imye1195072095.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/55xc61195072095.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/55xc61195072095.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/6pss31195072095.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/6pss31195072095.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/7i12r1195072095.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/7i12r1195072095.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/8cr4m1195072095.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/8cr4m1195072095.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/9reyf1195072095.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/14/t1195071848fsvi267qwgcloi3/9reyf1195072095.ps (open in new window)

Parameters:

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