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multiple regression: 2 Irak incl seiz

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

Title produced by software: Multiple Regression

Date of computation: Sat, 17 Nov 2007 08:07:38 -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/17/t1195311739gp3gf3ybeak2zmo.htm/, Retrieved Sat, 17 Nov 2007 16:02:28 +0100

User-defined keywords:

s0650921

Dataseries X:

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99.9 0 98.2 0 104.5 0 100.8 0 101.5 0 103.9 0 99.6 0 98.4 0 112.7 0 118.4 0 108.1 0 105.4 0 114.6 0 106.9 0 115.9 1 109.8 1 101.8 1 114.2 2 110.8 2 108.4 2 127.5 2 128.6 2 116.6 2 127.4 2 105 2 108.3 2 125 2 111.6 2 106.5 2 130.3 2 115 2 116.1 2 134 2 126.5 2 125.8 2 136.4 2 114.9 2 110.9 2 125.5 2 116.8 2 116.8 2 125.5 2 104.2 2 115.1 2 132.8 2 123.3 2 124.8 2 122 2 117.4 2 117.9 2 137.4 2 114.6 2 124.7 2 129.6 2 109.4 2 120.9 2 134.9 2 136.3 2 133.2 2 127.2 2

Text written by user:

met maandseizonaliteit

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] = + 111.713076923077 + 7.47932692307695x[t] -10.3282692307694M1[t] -12.2482692307693M2[t] -0.524134615384614M3[t] -11.4641346153846M4[t] -11.9241346153846M5[t] -2.98000000000001M6[t] -15.8800000000000M7[t] -11.9M8[t] + 4.69999999999999M9[t] + 2.93999999999999M10[t] -1.98000000000001M11[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) 111.713076923077 3.026443 36.9123 0 0 x 7.47932692307695 0.917525 8.1516 0 0 M1 -10.3282692307694 3.760734 -2.7463 0.008514 0.004257 M2 -12.2482692307693 3.760734 -3.2569 0.002094 0.001047 M3 -0.524134615384614 3.747279 -0.1399 0.88936 0.44468 M4 -11.4641346153846 3.747279 -3.0593 0.003658 0.001829 M5 -11.9241346153846 3.747279 -3.1821 0.002592 0.001296 M6 -2.98000000000001 3.742783 -0.7962 0.42992 0.21496 M7 -15.8800000000000 3.742783 -4.2428 0.000103 5.1e-05 M8 -11.9 3.742783 -3.1795 0.002611 0.001306 M9 4.69999999999999 3.742783 1.2557 0.215414 0.107707 M10 2.93999999999999 3.742783 0.7855 0.436096 0.218048 M11 -1.98000000000001 3.742783 -0.529 0.599283 0.299641 Multiple Linear Regression - Regression Statistics Multiple R 0.877616207306407 R-squared 0.770210207326883 Adjusted R-squared 0.711540473027364 F-TEST (value) 13.1278966322708 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 3.05591107974124e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.91786013143165 Sum Squared Residuals 1645.99022115385 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.9 101.384807692308 -1.48480769230812 2 98.2 99.4648076923077 -1.26480769230774 3 104.5 111.188942307692 -6.68894230769227 4 100.8 100.248942307692 0.55105769230774 5 101.5 99.7889423076923 1.71105769230773 6 103.9 108.733076923077 -4.83307692307689 7 99.6 95.833076923077 3.76692307692307 8 98.4 99.8130769230769 -1.41307692307689 9 112.7 116.413076923077 -3.7130769230769 10 118.4 114.653076923077 3.7469230769231 11 108.1 109.733076923077 -1.63307692307690 12 105.4 111.713076923077 -6.3130769230769 13 114.6 101.384807692308 13.2151923076924 14 106.9 99.4648076923077 7.43519230769235 15 115.9 118.668269230769 -2.76826923076923 16 109.8 107.728269230769 2.07173076923077 17 101.8 107.268269230769 -5.46826923076923 18 114.2 123.691730769231 -9.49173076923078 19 110.8 110.791730769231 0.00826923076922678 20 108.4 114.771730769231 -6.37173076923078 21 127.5 131.371730769231 -3.87173076923078 22 128.6 129.611730769231 -1.01173076923078 23 116.6 124.691730769231 -8.09173076923078 24 127.4 126.671730769231 0.728269230769223 25 105 116.343461538461 -11.3434615384614 26 108.3 114.423461538462 -6.12346153846154 27 125 126.147596153846 -1.14759615384617 28 111.6 115.207596153846 -3.60759615384617 29 106.5 114.747596153846 -8.24759615384617 30 130.3 123.691730769231 6.60826923076923 31 115 110.791730769231 4.20826923076923 32 116.1 114.771730769231 1.32826923076922 33 134 131.371730769231 2.62826923076922 34 126.5 129.611730769231 -3.11173076923077 35 125.8 124.691730769231 1.10826923076923 36 136.4 126.671730769231 9.72826923076922 37 114.9 116.343461538461 -1.44346153846144 38 110.9 114.423461538462 -3.52346153846153 39 125.5 126.147596153846 -0.647596153846172 40 116.8 115.207596153846 1.59240384615383 41 116.8 114.747596153846 2.05240384615383 42 125.5 123.691730769231 1.80826923076922 43 104.2 110.791730769231 -6.59173076923076 44 115.1 114.771730769231 0.328269230769217 45 132.8 131.371730769231 1.42826923076923 46 123.3 129.611730769231 -6.31173076923078 47 124.8 124.691730769231 0.108269230769227 48 122 126.671730769231 -4.67173076923079 49 117.4 116.343461538461 1.05653846153857 50 117.9 114.423461538462 3.47653846153847 51 137.4 126.147596153846 11.2524038461538 52 114.6 115.207596153846 -0.607596153846170 53 124.7 114.747596153846 9.95240384615384 54 129.6 123.691730769231 5.90826923076921 55 109.4 110.791730769231 -1.39173076923076 56 120.9 114.771730769231 6.12826923076923 57 134.9 131.371730769231 3.52826923076923 58 136.3 129.611730769231 6.68826923076923 59 133.2 124.691730769231 8.50826923076922 60 127.2 126.671730769231 0.52826923076922

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Include Monthly 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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