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Workshop 6, question 3

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

Title produced by software: Multiple Regression

Date of computation: Thu, 15 Nov 2007 05:23:03 -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/15/t1195129263jk2q90bwoo1k0h4.htm/, Retrieved Thu, 15 Nov 2007 13:21:14 +0100

User-defined keywords:

Workshop 6, question 3, Workshop 6, question 3, multiple lineair regression, seaonality, lineair trend, lineaire trend

Dataseries X:

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108.4 106.7 117 100.6 103.8 101.2 100.8 93.1 110.6 84.2 104 85.8 112.6 91.8 107.3 92.4 98.9 80.3 109.8 79.7 104.9 62.5 102.2 57.1 123.9 100.8 124.9 100.7 112.7 86.2 121.9 83.2 100.6 71.7 104.3 77.5 120.4 89.8 107.5 80.3 102.9 78.7 125.6 93.8 107.5 57.6 108.8 60.6 128.4 91 121.1 85.3 119.5 77.4 128.7 77.3 108.7 68.3 105.5 69.9 119.8 81.7 111.3 75.1 110.6 69.9 120.1 84 97.5 54.3 107.7 60 127.3 89.9 117.2 77 119.8 85.3 116.2 77.6 111 69.2 112.4 75.5 130.6 85.7 109.1 72.2 118.8 79.9 123.9 85.3 101.6 52.2 112.8 61.2 128 82.4 129.6 85.4 125.8 78.2 119.5 70.2 115.7 70.2 113.6 69.3 129.7 77.5 112 66.1 116.8 69 126.3 75.3 112.9 58.2 115.9 59.7

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 Y[t] = + 46.7786688827454 + 0.233342458448343X[t] + 27.3870133153562M1[t] + 23.6664968869897M2[t] + 21.1926872757958M3[t] + 15.9061494946601M4[t] + 10.5863623312492M5[t] + 14.1338469978965M6[t] + 20.7631854802013M7[t] + 16.1087780057079M8[t] + 14.7615821355137M9[t] + 20.4789490881773M10[t] -2.03676361429512M11[t] -0.350138923157501t + 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) 46.7786688827454 15.454616 3.0268 0.004039 0.00202 X 0.233342458448343 0.151851 1.5366 0.13123 0.065615 M1 27.3870133153562 4.133381 6.6258 0 0 M2 23.6664968869897 3.995167 5.9238 0 0 M3 21.1926872757958 3.555255 5.9609 0 0 M4 15.9061494946601 3.603609 4.414 6.1e-05 3e-05 M5 10.5863623312492 3.274076 3.2334 0.002266 0.001133 M6 14.1338469978965 3.26152 4.3335 7.9e-05 3.9e-05 M7 20.7631854802013 3.926855 5.2875 3e-06 2e-06 M8 16.1087780057079 3.260286 4.9409 1.1e-05 5e-06 M9 14.7615821355137 3.257993 4.5309 4.2e-05 2.1e-05 M10 20.4789490881773 3.74252 5.472 2e-06 1e-06 M11 -2.03676361429512 3.319451 -0.6136 0.542512 0.271256 t -0.350138923157501 0.055309 -6.3305 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.934214213782551 R-squared 0.87275619723335 Adjusted R-squared 0.836795992103645 F-TEST (value) 24.2700561380391 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 2.22044604925031e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.14353483274104 Sum Squared Residuals 1216.97372647854 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.7 99.1098657707444 7.59013422925556 2 100.6 97.0459555618762 3.55404443812376 3 101.2 91.1418865760068 10.0581134239932 4 93.1 84.8051824963686 8.29481750363144 5 84.2 81.422012502594 2.77798749740609 6 85.8 83.0792980203246 2.72070197967542 7 91.8 91.3652427221276 0.434757277872374 8 92.4 85.1239812947006 7.27601870529944 9 80.3 81.4665698503827 -1.16656985038274 10 79.7 89.3772306769758 -9.67723067697578 11 62.5 65.368001004949 -2.86800100494898 12 57.1 66.4246010582761 -9.32460105827608 13 100.8 98.5250067988039 2.27499320119612 14 100.7 94.6876939057281 6.01230609427187 15 86.2 89.016967378307 -2.81696737830701 16 83.2 85.5270412917386 -2.32704129173858 17 71.7 74.8869208402205 -3.18692084022045 18 77.5 78.947633679969 -1.44763367996907 19 89.8 88.9836468201347 0.816353179865309 20 80.3 80.9689827085002 -0.668982708500228 21 78.7 78.1982726062861 0.501727393713884 22 93.8 88.8623744425696 4.93762555743037 23 57.6 61.7730243190247 -4.17302431902467 24 60.6 63.7629942061451 -3.16299420614513 25 91 95.3733807839314 -4.37338078393141 26 85.3 89.5993254857344 -4.29932548573443 27 77.4 86.4020290178657 -9.00202901786573 28 77.3 82.9121029312973 -5.61210293129731 29 68.3 72.575327675762 -4.27532767576203 30 69.9 75.025977552217 -5.12597755221707 31 81.7 84.6419742671757 -2.94197426717567 32 75.1 77.6540169727139 -2.55401697271392 33 69.9 75.7933424584484 -5.89334245844834 34 84 83.3773238432137 0.622676156786272 35 54.3 55.2379326566512 -0.937932656651237 36 60 59.3046504239619 0.695349576038052 37 89.9 90.9150370017482 -1.01503700174822 38 77 84.4876228198959 -7.48762281989588 39 85.3 82.2703646775102 3.02963532248977 40 77.6 75.793655122803 1.80634487719698 41 69.2 68.9103482523032 0.289651747696798 42 75.5 72.4343734376206 3.06562656237936 43 85.7 82.9604057405278 2.73959425947224 44 72.2 72.9389964862376 -0.738996486237551 45 79.9 73.5050835398348 6.39491646016525 46 85.3 80.0623581074274 5.23764189257257 47 52.2 51.9929696583994 0.207030341600577 48 61.2 56.2930298841585 4.90697011584152 49 82.4 86.876709644772 -4.47670964477205 50 85.4 83.1794022267653 2.22059777323468 51 78.2 79.4687523503103 -1.26875235031028 52 70.2 72.3620181577925 -2.16201815779253 53 70.2 65.8053907291204 4.39460927087959 54 69.3 68.5127173098686 0.787282690131359 55 77.5 78.5487304500343 -1.04873045003425 56 66.1 69.4140225378478 -3.31402253784776 57 69 68.836731545048 0.163268454951940 58 75.3 76.4207129298134 -1.12071292981344 59 58.2 50.4280723609757 7.77192763902431 60 59.7 52.8147244274584 6.88527557254165

Charts produced by software:

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Parameters:

par1 = 2 ; 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')

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Software written by Ed van Stee & Patrick Wessa

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