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

Title produced by software: Multiple Regression

Date of computation: Thu, 22 Nov 2007 11:47:56 -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/22/t1195756841elnsl1fl8j6airf.htm/, Retrieved Thu, 22 Nov 2007 19:40:50 +0100

User-defined keywords:

Florence & Inge

Dataseries X:

» Textbox « » Textfile « » CSV «

5,22 0 5,09 0 4,77 0 4,54 0 4,56 0 4,39 0 4,73 0 4,44 0 4,3 0 4,24 0 4,01 0 3,5 0 3,23 0 3,28 1 3,49 1 3,7 1 3,63 1 3,95 1 3,73 1 3,87 1 3,66 1 3,49 1 3,4 1 3,32 1 3,11 1 3,06 1 2,68 1 2,55 1 2,34 1 2,34 1 2,39 1 2,21 1 2,09 1 2,14 1 2,31 1 2,14 1 2,45 1 2,52 1 2,3 1 2,25 1 2,06 1 1,99 1 2,25 1 2,26 1 2,36 1 2,3 1 2,19 1 2,31 1 2,21 1 2,21 1 2,26 1 2,18 1 2,21 1 2,33 1 2,12 1 2,08 1 1,97 1 2,09 1 2,11 1 2,24 1 2,45 1 2,68 1 2,73 1 2,76 1 2,83 1 3,16 1 3,22 1 3,22 1 3,34 1 3,35 1 3,42 1 3,58 1 3,71 1 3,68 1 3,83 1 3,94 1 3,88 1 4,03 1 4,15 1 4,32 1 4,4 1 4,37 1 4,14 1 4,11 1 4,16 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 R1j[t] = + 4.26806722689075 -1.44607843137255Ter[t] + 0.133991596638652M1[t] + 0.188571428571429M2[t] + 0.122857142857143M3[t] + 0.102857142857143M4[t] + 0.0442857142857143M5[t] + 0.141428571428572M6[t] + 0.198571428571429M7[t] + 0.171428571428571M8[t] + 0.131428571428571M9[t] + 0.111428571428571M10[t] + 0.054285714285714M11[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) 4.26806722689075 0.359169 11.8832 0 0 Ter -1.44607843137255 0.23704 -6.1006 0 0 M1 0.133991596638652 0.406354 0.3297 0.742553 0.371276 M2 0.188571428571429 0.41886 0.4502 0.653918 0.326959 M3 0.122857142857143 0.41886 0.2933 0.770126 0.385063 M4 0.102857142857143 0.41886 0.2456 0.806718 0.403359 M5 0.0442857142857143 0.41886 0.1057 0.916091 0.458046 M6 0.141428571428572 0.41886 0.3377 0.736608 0.368304 M7 0.198571428571429 0.41886 0.4741 0.63688 0.31844 M8 0.171428571428571 0.41886 0.4093 0.683553 0.341777 M9 0.131428571428571 0.41886 0.3138 0.754598 0.377299 M10 0.111428571428571 0.41886 0.266 0.790978 0.395489 M11 0.054285714285714 0.41886 0.1296 0.897241 0.448621 Multiple Linear Regression - Regression Statistics Multiple R 0.587825781150622 R-squared 0.345539148985339 Adjusted R-squared 0.236462340482896 F-TEST (value) 3.1678516609477 F-TEST (DF numerator) 12 F-TEST (DF denominator) 72 p-value 0.00114284240787388 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.783614974102538 Sum Squared Residuals 44.2117747899159 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 5.22 4.40205882352943 0.817941176470565 2 5.09 4.45663865546218 0.633361344537818 3 4.77 4.3909243697479 0.379075630252101 4 4.54 4.3709243697479 0.169075630252102 5 4.56 4.31235294117647 0.24764705882353 6 4.39 4.40949579831933 -0.0194957983193267 7 4.73 4.46663865546218 0.263361344537817 8 4.44 4.43949579831933 0.000504201680673236 9 4.3 4.39949579831933 -0.0994957983193274 10 4.24 4.37949579831933 -0.139495798319327 11 4.01 4.32235294117647 -0.312352941176469 12 3.5 4.26806722689075 -0.768067226890755 13 3.23 4.40205882352941 -1.17205882352941 14 3.28 3.01056022408964 0.269439775910363 15 3.49 2.94484593837535 0.54515406162465 16 3.7 2.92484593837535 0.77515406162465 17 3.63 2.86627450980392 0.763725490196078 18 3.95 2.96341736694678 0.986582633053221 19 3.73 3.02056022408964 0.709439775910364 20 3.87 2.99341736694678 0.876582633053221 21 3.66 2.95341736694678 0.706582633053221 22 3.49 2.93341736694678 0.556582633053221 23 3.4 2.87627450980392 0.523725490196078 24 3.32 2.82198879551821 0.498011204481792 25 3.11 2.95598039215686 0.15401960784314 26 3.06 3.01056022408964 0.0494397759103635 27 2.68 2.94484593837535 -0.26484593837535 28 2.55 2.92484593837535 -0.374845938375350 29 2.34 2.86627450980392 -0.526274509803922 30 2.34 2.96341736694678 -0.623417366946779 31 2.39 3.02056022408964 -0.630560224089636 32 2.21 2.99341736694678 -0.783417366946779 33 2.09 2.95341736694678 -0.863417366946779 34 2.14 2.93341736694678 -0.793417366946779 35 2.31 2.87627450980392 -0.566274509803921 36 2.14 2.82198879551821 -0.681988795518207 37 2.45 2.95598039215686 -0.505980392156860 38 2.52 3.01056022408964 -0.490560224089637 39 2.3 2.94484593837535 -0.64484593837535 40 2.25 2.92484593837535 -0.67484593837535 41 2.06 2.86627450980392 -0.806274509803922 42 1.99 2.96341736694678 -0.97341736694678 43 2.25 3.02056022408964 -0.770560224089636 44 2.26 2.99341736694678 -0.733417366946779 45 2.36 2.95341736694678 -0.593417366946779 46 2.3 2.93341736694678 -0.633417366946779 47 2.19 2.87627450980392 -0.686274509803921 48 2.31 2.82198879551821 -0.511988795518207 49 2.21 2.95598039215686 -0.74598039215686 50 2.21 3.01056022408964 -0.800560224089637 51 2.26 2.94484593837535 -0.68484593837535 52 2.18 2.92484593837535 -0.74484593837535 53 2.21 2.86627450980392 -0.656274509803922 54 2.33 2.96341736694678 -0.633417366946779 55 2.12 3.02056022408964 -0.900560224089636 56 2.08 2.99341736694678 -0.913417366946779 57 1.97 2.95341736694678 -0.98341736694678 58 2.09 2.93341736694678 -0.84341736694678 59 2.11 2.87627450980392 -0.766274509803922 60 2.24 2.82198879551821 -0.581988795518207 61 2.45 2.95598039215686 -0.505980392156860 62 2.68 3.01056022408964 -0.330560224089636 63 2.73 2.94484593837535 -0.214845938375350 64 2.76 2.92484593837535 -0.164845938375351 65 2.83 2.86627450980392 -0.0362745098039217 66 3.16 2.96341736694678 0.196582633053221 67 3.22 3.02056022408964 0.199439775910364 68 3.22 2.99341736694678 0.226582633053221 69 3.34 2.95341736694678 0.386582633053221 70 3.35 2.93341736694678 0.416582633053221 71 3.42 2.87627450980392 0.543725490196078 72 3.58 2.82198879551821 0.758011204481793 73 3.71 2.95598039215686 0.75401960784314 74 3.68 3.01056022408964 0.669439775910364 75 3.83 2.94484593837535 0.88515406162465 76 3.94 2.92484593837535 1.01515406162465 77 3.88 2.86627450980392 1.01372549019608 78 4.03 2.96341736694678 1.06658263305322 79 4.15 3.02056022408964 1.12943977591036 80 4.32 2.99341736694678 1.32658263305322 81 4.4 2.95341736694678 1.44658263305322 82 4.37 2.93341736694678 1.43658263305322 83 4.14 2.87627450980392 1.26372549019608 84 4.11 2.82198879551821 1.28801120448179 85 4.16 2.95598039215686 1.20401960784314

Charts produced by software:

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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

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