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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 12:47:43 -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/t11950693923a57g5kzl78s3jn.htm/, Retrieved Wed, 14 Nov 2007 20:43:22 +0100

User-defined keywords:

WS6RMPVII

Dataseries X:

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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 1 103.4 1 117.2 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 94.8900503778337 -7.06429471032747X[t] -4.23912178641401M1[t] -2.57966494742313M2[t] + 10.7083633201391M3[t] + 4.12496301627283M4[t] + 3.08441985526367M5[t] + 16.2581624085403M6[t] -19.1446243652793M7[t] -8.31373895485986M8[t] + 10.5525818639799M9[t] + 13.2739434648755M10[t] + 5.96197173243773M11[t] + 0.411971732437728t + 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) 94.8900503778337 2.787481 34.0415 0 0 X -7.06429471032747 2.621794 -2.6945 0.008932 0.004466 M1 -4.23912178641401 3.393268 -1.2493 0.215977 0.107989 M2 -2.57966494742313 3.39268 -0.7604 0.449746 0.224873 M3 10.7083633201391 3.392976 3.156 0.00241 0.001205 M4 4.12496301627283 3.394156 1.2153 0.228576 0.114288 M5 3.08441985526367 3.396219 0.9082 0.367081 0.183541 M6 16.2581624085403 3.399164 4.783 1e-05 5e-06 M7 -19.1446243652793 3.391025 -5.6457 0 0 M8 -8.31373895485986 3.390655 -2.452 0.016862 0.008431 M9 10.5525818639799 3.521784 2.9964 0.003846 0.001923 M10 13.2739434648755 3.519654 3.7714 0.000349 0.000175 M11 5.96197173243773 3.518375 1.6945 0.09488 0.04744 t 0.411971732437728 0.054771 7.5217 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.906693464419773 R-squared 0.822093038421531 Adjusted R-squared 0.78705075811062 F-TEST (value) 23.4600325985512 F-TEST (DF numerator) 13 F-TEST (DF denominator) 66 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.0932663164952 Sum Squared Residuals 2450.44103064651 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 91.0629003238578 6.23709967614223 2 101 93.134328895286 7.86567110471397 3 113.2 106.834328895286 6.36567110471389 4 101 100.662900323857 0.337099676142499 5 105.7 100.034328895286 5.66567110471395 6 113.9 113.620043181000 0.27995681899968 7 86.4 78.6292281396185 7.77077186038148 8 96.5 89.8720852824757 6.6279147175243 9 103.3 109.150377833753 -5.85037783375315 10 114.9 112.283711167086 2.61628883291353 11 105.8 105.383711167086 0.416288832913513 12 94.2 99.8337111670865 -5.63371116708647 13 98.4 96.0065611131102 2.39343888688982 14 99.4 98.0779896845388 1.32201031546120 15 108.8 111.777989684539 -2.9779896845388 16 112.6 105.606561113110 6.99343888688977 17 104.4 104.977989684539 -0.577989684538794 18 112.2 118.563703970253 -6.36370397025309 19 81.1 83.5728889288713 -2.47288892887131 20 97.1 94.8157460717284 2.28425392827156 21 112.6 114.094038623006 -1.49403862300588 22 113.8 117.227371956339 -3.42737195633921 23 107.8 110.327371956339 -2.52737195633921 24 103.2 104.777371956339 -1.57737195633920 25 103.3 100.950221902363 2.34977809763709 26 101.2 103.021650473792 -1.82165047379153 27 107.7 116.721650473792 -9.02165047379152 28 110.4 110.550221902363 -0.150221902362953 29 101.9 109.921650473792 -8.02165047379152 30 115.9 123.507364759506 -7.60736475950581 31 89.9 81.4522550077966 8.44774499220343 32 88.6 92.6951121506537 -4.09511215065371 33 117.2 111.973404701931 5.22659529806886 34 123.9 115.106738035264 8.79326196473552 35 100 108.206738035264 -8.20673803526448 36 103.6 102.656738035264 0.943261964735513 37 94.1 98.8295879812882 -4.72958798128819 38 98.7 100.901016552717 -2.20101655271681 39 119.5 114.601016552717 4.8989834472832 40 112.7 108.429587981288 4.27041201871177 41 104.4 107.801016552717 -3.40101655271681 42 124.7 121.386730838431 3.31326916156891 43 89.1 86.3959157970493 2.70408420295068 44 97 97.6387729399064 -0.63877293990644 45 121.6 116.917065491184 4.68293450881611 46 118.8 120.050398824517 -1.25039882451722 47 114 113.150398824517 0.849601175482788 48 111.5 107.600398824517 3.89960117548279 49 97.2 103.773248770541 -6.57324877054091 50 102.5 105.844677341970 -3.34467734196955 51 113.4 119.544677341970 -6.14467734196953 52 109.8 113.373248770541 -3.57324877054097 53 104.9 112.744677341970 -7.84467734196954 54 126.1 126.330391627684 -0.230391627683832 55 80 91.339576586302 -11.3395765863020 56 96.8 102.582433729159 -5.78243372915917 57 117.2 121.860726280437 -4.66072628043661 58 112.3 124.99405961377 -12.6940596137700 59 117.3 118.09405961377 -0.794059613769945 60 111.1 112.54405961377 -1.44405961376995 61 102.2 108.716909559794 -6.51690955979364 62 104.3 110.788338131222 -6.48833813122228 63 122.9 124.488338131222 -1.58833813122226 64 107.6 118.316909559794 -10.7169095597937 65 121.3 117.688338131222 3.61166186877773 66 131.5 131.274052416937 0.225947583063442 67 89 96.2832373755548 -7.28323737555477 68 104.4 107.526094518412 -3.1260945184119 69 128.9 126.804387069689 2.09561293031066 70 135.9 129.937720403023 5.96227959697733 71 133.3 123.037720403023 10.2622795969773 72 121.3 117.487720403023 3.81227959697732 73 120.5 113.660570349046 6.83942965095362 74 120.4 115.731998920475 4.668001079525 75 137.9 129.431998920475 8.46800107952502 76 126.1 123.260570349046 2.83942965095357 77 133.2 122.631998920475 10.568001079525 78 146.6 136.217713206189 10.3822867938107 79 103.4 101.226898164807 2.17310183519251 80 117.2 112.469755307665 4.73024469233537

Charts produced by software:

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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

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