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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 05:12:26 -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/t1195128473moi3o2h9jjdcw06.htm/, Retrieved Thu, 15 Nov 2007 13:07:54 +0100

User-defined keywords:

Workshop 6, question 3, multiple lineair regression, pure

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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 18.3994219532531 + 0.521216112951609X[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) 18.3994219532531 19.909292 0.9242 0.359231 0.179615 X 0.521216112951609 0.173441 3.0051 0.003917 0.001958 Multiple Linear Regression - Regression Statistics Multiple R 0.36705234008517 R-squared 0.134727420361999 Adjusted R-squared 0.11980892760962 F-TEST (value) 9.03090027915266 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.00391666502419119 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.9449615201539 Sum Squared Residuals 8275.56213164159 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.7 74.8992485972076 31.8007514027924 2 100.6 79.3817071685914 21.2182928314086 3 101.2 72.5016544776301 28.6983455223699 4 93.1 70.9380061387753 22.1619938612247 5 84.2 76.045924045701 8.15407595429894 6 85.8 72.6058977002205 13.1941022997796 7 91.8 77.0883562716043 14.7116437283957 8 92.4 74.3259108729607 18.0740891270393 9 80.3 69.9476955241672 10.3523044758328 10 79.7 75.6289511553398 4.07104884466023 11 62.5 73.0749922018769 -10.5749922018769 12 57.1 71.6677086969076 -14.5677086969075 13 100.8 82.9780983479575 17.8219016520425 14 100.7 83.499314460909 17.2006855390909 15 86.2 77.1404778828994 9.05952211710056 16 83.2 81.9356661220542 1.26433387794575 17 71.7 70.833762916185 0.866237083815031 18 77.5 72.762262534106 4.73773746589407 19 89.8 81.1538419526268 8.64615804737316 20 80.3 74.4301540955511 5.86984590444892 21 78.7 72.0325599759737 6.66744002402632 22 93.8 83.8641657399752 9.9358342600248 23 57.6 74.4301540955511 -16.8301540955511 24 60.6 75.1077350423882 -14.5077350423882 25 91 85.3235708562397 5.67642914376029 26 85.3 81.518693231693 3.78130676830704 27 77.4 80.6847474509704 -3.28474745097038 28 77.3 85.4799356901252 -8.17993569012518 29 68.3 75.055613431093 -6.75561343109301 30 69.9 73.3877218696479 -3.48772186964785 31 81.7 80.8411122848559 0.858887715144137 32 75.1 76.4107753247672 -1.31077532476719 33 69.9 76.045924045701 -6.14592404570106 34 84 80.9974771187413 3.00252288125865 35 54.3 69.217992966035 -14.917992966035 36 60 74.5343973181414 -14.5343973181414 37 89.9 84.750233131993 5.14976686800707 38 77 79.4859503911817 -2.48595039118168 39 85.3 80.8411122848559 4.45888771514413 40 77.6 78.9647342782301 -1.36473427823008 41 69.2 76.2544104908817 -7.0544104908817 42 75.5 76.984113049014 -1.48411304901396 43 85.7 86.4702463047332 -0.770246304733238 44 72.2 75.2640998762736 -3.06409987627365 45 79.9 80.3198961719043 -0.41989617190425 46 85.3 82.9780983479575 2.32190165204253 47 52.2 71.3549790291366 -19.1549790291366 48 61.2 77.1925994941946 -15.9925994941946 49 82.4 85.115084411059 -2.71508441105905 50 85.4 85.9490301917816 -0.549030191781625 51 78.2 83.9684089625655 -5.76840896256552 52 70.2 80.6847474509704 -10.4847474509704 53 70.2 78.7041262217543 -8.50412622175427 54 69.3 77.6095723845559 -8.3095723845559 55 77.5 86.0011518030768 -8.50115180307679 56 66.1 76.7756266038333 -10.6756266038333 57 69 79.277463946001 -10.2774639460010 58 75.3 84.2290170190413 -8.92901701904132 59 58.2 77.2447211054898 -19.0447211054898 60 59.7 78.8083694443446 -19.1083694443446

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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