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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: Wed, 12 Dec 2007 13:04:52 -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/12/t1197489011k4o4o1prb18n84d.htm/, Retrieved Wed, 12 Dec 2007 20:50:21 +0100

User-defined keywords:

s0650062

Dataseries X:

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1.3 0 1.2 0 1.6 0 1.7 0 1.5 0 0.9 0 1.5 0 1.4 0 1.6 0 1.7 0 1.4 0 1.8 0 1.7 0 1.4 0 1.2 0 1.0 0 1.7 0 2.4 0 2.0 0 2.1 0 2.0 0 1.8 0 2.7 0 2.3 0 1.9 0 2.0 0 2.3 0 2.8 0 2.4 0 2.3 0 2.7 0 2.7 0 2.9 0 3.0 0 2.2 0 2.3 0 2.8 0 2.8 0 2.8 0 2.2 0 2.6 0 2.8 0 2.5 0 2.4 0 2.3 0 1.9 0 1.7 0 2.0 0 2.1 0 1.7 0 1.8 0 1.8 0 1.8 0 1.3 0 1.3 0 1.3 0 1.2 0 1.4 0 2.2 0 2.9 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] = + 1.85434782608696 + 0.554347826086957x[t] -0.0990579710144927M1[t] -0.247246376811593M2[t] -0.135434782608695M3[t] -0.183623188405796M4[t] -0.091811594202898M5[t] -0.159999999999999M6[t] -0.108188405797101M7[t] -0.136376811594202M8[t] -0.124565217391304M9[t] -0.172753623188405M10[t] -0.100942028985506M11[t] + 0.00818840579710145t + 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) 1.85434782608696 0.323788 5.727 1e-06 0 x 0.554347826086957 0.670306 0.827 0.412502 0.206251 M1 -0.0990579710144927 0.394375 -0.2512 0.802796 0.401398 M2 -0.247246376811593 0.394138 -0.6273 0.533558 0.266779 M3 -0.135434782608695 0.393953 -0.3438 0.732575 0.366288 M4 -0.183623188405796 0.393821 -0.4663 0.64323 0.321615 M5 -0.091811594202898 0.393742 -0.2332 0.816658 0.408329 M6 -0.159999999999999 0.393715 -0.4064 0.686344 0.343172 M7 -0.108188405797101 0.393742 -0.2748 0.784723 0.392362 M8 -0.136376811594202 0.393821 -0.3463 0.730703 0.365351 M9 -0.124565217391304 0.393953 -0.3162 0.753286 0.376643 M10 -0.172753623188405 0.394138 -0.4383 0.663215 0.331607 M11 -0.100942028985506 0.394375 -0.256 0.799127 0.399564 t 0.00818840579710145 0.004561 1.7954 0.079166 0.039583 Multiple Linear Regression - Regression Statistics Multiple R 0.350389114316179 R-squared 0.122772531431276 Adjusted R-squared -0.125139579251189 F-TEST (value) 0.495226034312328 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.915973912243563 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.586916262709505 Sum Squared Residuals 15.8456521739130 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.3 1.76347826086957 -0.463478260869569 2 1.2 1.62347826086957 -0.423478260869565 3 1.6 1.74347826086957 -0.143478260869565 4 1.7 1.70347826086957 -0.00347826086956534 5 1.5 1.80347826086957 -0.303478260869566 6 0.9 1.74347826086957 -0.843478260869565 7 1.5 1.80347826086956 -0.303478260869565 8 1.4 1.78347826086956 -0.383478260869565 9 1.6 1.80347826086957 -0.203478260869565 10 1.7 1.76347826086956 -0.063478260869565 11 1.4 1.84347826086957 -0.443478260869565 12 1.8 1.95260869565217 -0.152608695652173 13 1.7 1.86173913043478 -0.161739130434782 14 1.4 1.72173913043478 -0.321739130434783 15 1.2 1.84173913043478 -0.641739130434783 16 1 1.80173913043478 -0.801739130434783 17 1.7 1.90173913043478 -0.201739130434782 18 2.4 1.84173913043478 0.558260869565217 19 2 1.90173913043478 0.0982608695652175 20 2.1 1.88173913043478 0.218260869565218 21 2 1.90173913043478 0.0982608695652175 22 1.8 1.86173913043478 -0.0617391304347827 23 2.7 1.94173913043478 0.758260869565217 24 2.3 2.05086956521739 0.249130434782609 25 1.9 1.96 -0.0599999999999992 26 2 1.82 0.180000000000000 27 2.3 1.94 0.36 28 2.8 1.9 0.9 29 2.4 2 0.4 30 2.3 1.94 0.36 31 2.7 2 0.7 32 2.7 1.98 0.72 33 2.9 2 0.9 34 3 1.96 1.04 35 2.2 2.04 0.16 36 2.3 2.14913043478261 0.150869565217392 37 2.8 2.05826086956522 0.741739130434783 38 2.8 1.91826086956522 0.881739130434783 39 2.8 2.03826086956522 0.761739130434782 40 2.2 1.99826086956522 0.201739130434783 41 2.6 2.09826086956522 0.501739130434782 42 2.8 2.03826086956522 0.761739130434782 43 2.5 2.09826086956522 0.401739130434783 44 2.4 2.07826086956522 0.321739130434782 45 2.3 2.09826086956522 0.201739130434783 46 1.9 2.05826086956522 -0.158260869565218 47 1.7 2.13826086956522 -0.438260869565218 48 2 2.24739130434783 -0.247391304347825 49 2.1 2.15652173913043 -0.0565217391304339 50 1.7 2.01652173913044 -0.316521739130435 51 1.8 2.13652173913043 -0.336521739130435 52 1.8 2.09652173913044 -0.296521739130435 53 1.8 2.19652173913043 -0.396521739130435 54 1.3 2.13652173913044 -0.836521739130435 55 1.3 2.19652173913044 -0.896521739130435 56 1.3 2.17652173913044 -0.876521739130435 57 1.2 2.19652173913044 -0.996521739130435 58 1.4 2.15652173913044 -0.756521739130435 59 2.2 2.23652173913043 -0.0365217391304347 60 2.9 2.9 -6.2450045135165e-17

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')

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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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