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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: Fri, 21 Dec 2007 06:17:25 -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/Dec/21/t11982419536u95u7m67p9de24.htm/, Retrieved Fri, 21 Dec 2007 13:59:24 +0100

User-defined keywords:

Dataseries X:

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8.1 8.3 8.2 8.1 7.7 7.6 7.7 8.2 8.4 8.4 8.6 8.4 8.5 8.7 8.7 8.6 7.4 7.3 7.4 9 9.2 9.2 8.5 8.3 8.3 8.6 8.6 8.5 8.1 8.1 8 8.6 8.7 8.7 8.6 8.4 8.4 8.7 8.7 8.5 8.3 8.3 8.3 8.1 8.2 8.1 8.1 7.9 7.7 8.1 8 7.7 7.8 7.6 7.4 7.7 7.8 7.5 7.2 7

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 Werkl[t] = + 8.33999999999999 + 0.0961111111111028M1[t] + 0.385555555555556M2[t] + 0.355000000000001M3[t] + 0.204444444444446M4[t] -0.20611111111111M5[t] -0.276666666666666M6[t] -0.287222222222221M7[t] + 0.282222222222223M8[t] + 0.431666666666667M9[t] + 0.361111111111111M10[t] + 0.190555555555556M11[t] -0.00944444444444437t + 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) 8.33999999999999 0.222574 37.4708 0 0 M1 0.0961111111111028 0.270773 0.355 0.724215 0.362107 M2 0.385555555555556 0.270369 1.426 0.160467 0.080233 M3 0.355000000000001 0.270002 1.3148 0.194955 0.097478 M4 0.204444444444446 0.269674 0.7581 0.452165 0.226083 M5 -0.20611111111111 0.269384 -0.7651 0.448025 0.224012 M6 -0.276666666666666 0.269132 -1.028 0.309213 0.154607 M7 -0.287222222222221 0.268919 -1.0681 0.290948 0.145474 M8 0.282222222222223 0.268744 1.0502 0.299019 0.149509 M9 0.431666666666667 0.268609 1.607 0.114742 0.057371 M10 0.361111111111111 0.268512 1.3449 0.185124 0.092562 M11 0.190555555555556 0.268453 0.7098 0.481318 0.240659 t -0.00944444444444437 0.003229 -2.9251 0.005287 0.002643 Multiple Linear Regression - Regression Statistics Multiple R 0.625069560512103 R-squared 0.390711955478794 Adjusted R-squared 0.235149050494656 F-TEST (value) 2.51160104986875 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.0121966782731734 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.424431200516211 Sum Squared Residuals 8.4666666666667 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.1 8.4266666666667 -0.326666666666703 2 8.3 8.70666666666667 -0.406666666666664 3 8.2 8.66666666666666 -0.466666666666665 4 8.1 8.50666666666666 -0.406666666666664 5 7.7 8.08666666666667 -0.386666666666666 6 7.6 8.00666666666667 -0.406666666666666 7 7.7 7.98666666666667 -0.286666666666665 8 8.2 8.54666666666667 -0.346666666666665 9 8.4 8.68666666666667 -0.286666666666665 10 8.4 8.60666666666666 -0.206666666666664 11 8.6 8.42666666666666 0.173333333333335 12 8.4 8.22666666666666 0.173333333333336 13 8.5 8.31333333333332 0.186666666666677 14 8.7 8.59333333333333 0.106666666666667 15 8.7 8.55333333333333 0.146666666666667 16 8.6 8.39333333333333 0.206666666666667 17 7.4 7.97333333333333 -0.573333333333332 18 7.3 7.89333333333333 -0.593333333333333 19 7.4 7.87333333333333 -0.473333333333332 20 9 8.43333333333333 0.566666666666668 21 9.2 8.57333333333333 0.626666666666667 22 9.2 8.49333333333333 0.706666666666667 23 8.5 8.31333333333333 0.186666666666668 24 8.3 8.11333333333333 0.186666666666669 25 8.3 8.19999999999999 0.100000000000010 26 8.6 8.48 0.120000000000000 27 8.6 8.44 0.160000000000000 28 8.5 8.28 0.22 29 8.1 7.86 0.240000000000000 30 8.1 7.78 0.32 31 8 7.76 0.24 32 8.6 8.32 0.28 33 8.7 8.46 0.24 34 8.7 8.38 0.320000000000000 35 8.6 8.2 0.4 36 8.4 8 0.400000000000001 37 8.4 8.08666666666666 0.313333333333342 38 8.7 8.36666666666667 0.333333333333332 39 8.7 8.32666666666667 0.373333333333332 40 8.5 8.16666666666667 0.333333333333332 41 8.3 7.74666666666667 0.553333333333333 42 8.3 7.66666666666667 0.633333333333333 43 8.3 7.64666666666667 0.653333333333333 44 8.1 8.20666666666667 -0.106666666666668 45 8.2 8.34666666666667 -0.146666666666668 46 8.1 8.26666666666667 -0.166666666666668 47 8.1 8.08666666666667 0.0133333333333323 48 7.9 7.88666666666667 0.0133333333333331 49 7.7 7.97333333333333 -0.273333333333325 50 8.1 8.25333333333334 -0.153333333333335 51 8 8.21333333333333 -0.213333333333335 52 7.7 8.05333333333333 -0.353333333333335 53 7.8 7.63333333333333 0.166666666666665 54 7.6 7.55333333333334 0.0466666666666645 55 7.4 7.53333333333333 -0.133333333333335 56 7.7 8.09333333333334 -0.393333333333335 57 7.8 8.23333333333333 -0.433333333333335 58 7.5 8.15333333333333 -0.653333333333335 59 7.2 7.97333333333334 -0.773333333333335 60 7 7.77333333333334 -0.773333333333335

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

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')

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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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