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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 08:41:05 -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/t1195141099w8q13uwafpv7oro.htm/, Retrieved Thu, 15 Nov 2007 16:38:32 +0100

User-defined keywords:

Workshop 6, question 3, eigen model, lineair, seasonality, war iraq, oorlog irak

Dataseries X:

» Textbox « » Textfile « » CSV «

108.4 106.7 0 117 100.6 0 103.8 101.2 0 100.8 93.1 0 110.6 84.2 0 104 85.8 0 112.6 91.8 1 107.3 92.4 1 98.9 80.3 1 109.8 79.7 1 104.9 62.5 1 102.2 57.1 1 123.9 100.8 1 124.9 100.7 1 112.7 86.2 1 121.9 83.2 1 100.6 71.7 1 104.3 77.5 1 120.4 89.8 1 107.5 80.3 1 102.9 78.7 1 125.6 93.8 1 107.5 57.6 1 108.8 60.6 1 128.4 91 1 121.1 85.3 1 119.5 77.4 1 128.7 77.3 1 108.7 68.3 1 105.5 69.9 1 119.8 81.7 1 111.3 75.1 1 110.6 69.9 1 120.1 84 1 97.5 54.3 1 107.7 60 1 127.3 89.9 1 117.2 77 1 119.8 85.3 1 116.2 77.6 1 111 69.2 1 112.4 75.5 1 130.6 85.7 1 109.1 72.2 1 118.8 79.9 1 123.9 85.3 1 101.6 52.2 1 112.8 61.2 1 128 82.4 1 129.6 85.4 1 125.8 78.2 1 119.5 70.2 1 115.7 70.2 1 113.6 69.3 1 129.7 77.5 1 112 66.1 1 116.8 69 1 126.3 75.3 1 112.9 58.2 1 115.9 59.7 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] = + 40.9669725515544 + 0.362886468119393X[t] -10.2431896256701Z[t] + 24.1331561763916M1[t] + 20.5212629928483M2[t] + 18.7260702690305M3[t] + 13.2450227500879M4[t] + 8.92253073784375M5[t] + 12.5941839304749M6[t] + 19.3210338289674M7[t] + 16.3220050747697M8[t] + 14.9020708358594M9[t] + 19.0724885897504M10[t] -1.38884984263954M11[t] -0.298127595988762t + 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) 40.9669725515544 13.192171 3.1054 0.003284 0.001642 X 0.362886468119393 0.132368 2.7415 0.008743 0.004372 Z -10.2431896256701 2.36306 -4.3347 8.1e-05 4.1e-05 M1 24.1331561763916 3.589385 6.7235 0 0 M2 20.5212629928483 3.46937 5.915 0 0 M3 18.7260702690305 3.072236 6.0953 0 0 M4 13.2450227500879 3.121111 4.2437 0.000108 5.4e-05 M5 8.92253073784375 2.806674 3.179 0.002673 0.001337 M6 12.5941839304749 2.792324 4.5103 4.6e-05 2.3e-05 M7 19.3210338289674 3.351191 5.7654 1e-06 0 M8 16.3220050747697 2.76903 5.8945 0 0 M9 14.9020708358594 2.766836 5.386 3e-06 1e-06 M10 19.0724885897504 3.194621 5.9702 0 0 M11 -1.38884984263954 2.822796 -0.492 0.625102 0.312551 t -0.298127595988762 0.048477 -6.1499 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.954063310173485 R-squared 0.910236799819187 Adjusted R-squared 0.882310470874045 F-TEST (value) 32.5942160749894 F-TEST (DF numerator) 14 F-TEST (DF denominator) 45 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.3678245805265 Sum Squared Residuals 858.505120481318 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.7 104.138894276099 2.56110572390075 2 100.6 103.349697122394 -2.74969712239422 3 101.2 96.4662754234116 4.7337245765884 4 93.1 89.5984409041221 3.50155909587789 5 84.2 88.5341086834592 -4.33410868345921 6 85.8 89.5125835905136 -3.7125835905136 7 91.8 88.818939893174 2.98106010682603 8 92.4 83.5984852619548 8.80151473804521 9 80.3 78.8321770948528 1.46782290514721 10 79.7 86.6599297552564 -6.95992975525638 11 62.5 64.1223200330927 -1.62232003309268 12 57.1 64.2332488158211 -7.13324881582111 13 100.8 95.9429137544147 4.85708624558527 14 100.7 92.3957794430021 8.30422055699788 15 86.2 85.875244212139 0.324755787861091 16 83.2 83.434624603906 -0.234624603905994 17 71.7 71.08452322473 0.615476775269983 18 77.5 75.8007287534141 1.69927124658586 19 89.8 88.07192319264 1.72807680735990 20 80.3 80.0935314037135 0.206468596286468 21 78.7 76.7061918154652 1.99380818453478 22 93.8 88.8160047996776 4.98399520032236 23 57.6 61.488293698338 -3.88829369833796 24 60.6 63.050768353544 -2.45076835354396 25 91 93.9983717090869 -2.99837170908686 26 85.3 87.4392797122833 -2.1392797122833 27 77.4 84.7653410434857 -7.36534104348565 28 77.3 82.3247214352527 -5.02472143525272 29 68.3 70.446372464632 -2.14637246463196 30 69.9 72.6586613632923 -2.75866136329226 31 81.7 84.2766601599033 -2.57666015990331 32 75.1 77.894968830702 -2.79496883070208 33 69.9 75.9228864681194 -6.02288646811939 34 84 83.2425980731558 0.757401926844173 35 54.3 54.2818978652789 0.0181021347211149 36 60 59.0740620867475 0.925937913252518 37 89.9 90.0216654422904 -0.121665442290369 38 77 82.4464913347525 -5.44649133475252 39 85.3 81.2966758320563 4.00332416794368 40 77.6 74.2111094318952 3.38889056810483 41 69.2 67.7034801894414 1.49651981055859 42 75.5 71.585046841451 3.91495315854907 43 85.7 84.6183028637276 1.08169713627240 44 72.2 73.5190874489743 -1.31908744897426 45 79.9 75.3210243548333 4.57897564516673 46 85.3 81.0440355001444 4.25596449985562 47 52.2 52.1922012327032 0.00779876729676343 48 61.2 57.3472519222912 3.85274807770877 49 82.4 86.6981548181088 -4.2981548181088 50 85.4 83.3687523875678 2.03124761243216 51 78.2 79.8964634889075 -1.69646348890752 52 70.2 71.831103624824 -1.63110362482401 53 70.2 65.8315154377374 4.36848456226259 54 69.3 68.442979451329 0.85702054867094 55 77.5 80.714173890555 -3.21417389055501 56 66.1 70.9939270546553 -4.89392705465535 57 69 71.0177202667293 -2.01772026672934 58 75.3 78.3374318717658 -3.03743187176577 59 58.2 52.7152871705872 5.48471282941276 60 59.7 54.8946688215962 4.80533117840379

Charts produced by software:

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Parameters:

par1 = 2 ; 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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Software written by Ed van Stee & Patrick Wessa

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