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Multiple regressiondollar-euroinvoering (seizoenaliteit)

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

Title produced by software: Multiple Regression

Date of computation: Thu, 29 Nov 2007 02:32:47 -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/29/t1196328154rjenn95o82e1run.htm/, Retrieved Thu, 29 Nov 2007 10:22:44 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0.9383 0 0.9217 0 0.9095 0 0.892 0 0.8742 0 0.8532 0 0.8607 0 0.9005 0 0.9111 0 0.9059 0 0.8883 0 0.8924 0 0.8833 1 0.87 1 0.8758 1 0.8858 1 0.917 1 0.9554 1 0.9922 1 0.9778 1 0.9808 1 0.9811 1 1.0014 1 1.0183 1 1.0622 1 1.0773 1 1.0807 1 1.0848 1 1.1582 1 1.1663 1 1.1372 1 1.1139 1 1.1222 1 1.1692 1 1.1702 1 1.2286 1 1.2613 1 1.2646 1 1.2262 1 1.1985 1 1.2007 1 1.2138 1 1.2266 1 1.2176 1 1.2218 1 1.249 1 1.2991 1 1.3408 1 1.3119 1 1.3014 1 1.3201 1 1.2938 1 1.2694 1 1.2165 1 1.2037 1 1.2292 1 1.2256 1 1.2015 1 1.1786 1 1.1856 1 1.2103 1 1.1938 1 1.202 1 1.2271 1 1.277 1 1.265 1 1.2684 1 1.2811 1 1.2727 1 1.2611 1 1.2881 1 1.3213 1

Text written by user:

paper

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 Dollar[t] = + 0.940945833333333 + 0.268265000000001Euroinvoering[t] -0.0532833333333328M1[t] -0.0597000000000001M2[t] -0.0621166666666666M3[t] -0.0675M4[t] -0.0484166666666665M5[t] -0.0527999999999999M6[t] -0.0496999999999999M7[t] -0.0444833333333332M8[t] -0.0421333333333332M9[t] -0.0365333333333332M10[t] -0.0268833333333332M11[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) 0.940945833333333 0.06181 15.2231 0 0 Euroinvoering 0.268265000000001 0.040226 6.669 0 0 M1 -0.0532833333333328 0.073442 -0.7255 0.471002 0.235501 M2 -0.0597000000000001 0.073442 -0.8129 0.419549 0.209775 M3 -0.0621166666666666 0.073442 -0.8458 0.401084 0.200542 M4 -0.0675 0.073442 -0.9191 0.361787 0.180894 M5 -0.0484166666666665 0.073442 -0.6593 0.512298 0.256149 M6 -0.0527999999999999 0.073442 -0.7189 0.475017 0.237509 M7 -0.0496999999999999 0.073442 -0.6767 0.501223 0.250612 M8 -0.0444833333333332 0.073442 -0.6057 0.54704 0.27352 M9 -0.0421333333333332 0.073442 -0.5737 0.568353 0.284176 M10 -0.0365333333333332 0.073442 -0.4974 0.620723 0.310361 M11 -0.0268833333333332 0.073442 -0.3661 0.715637 0.357818 Multiple Linear Regression - Regression Statistics Multiple R 0.661136045016303 R-squared 0.437100870019799 Adjusted R-squared 0.322612911379758 F-TEST (value) 3.81787635321613 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 0.000260448057095686 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.127204699977350 Sum Squared Residuals 0.954681106083333 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.9383 0.887662499999998 0.0506375000000016 2 0.9217 0.881245833333334 0.0404541666666655 3 0.9095 0.878829166666667 0.0306708333333333 4 0.892 0.873445833333333 0.0185541666666665 5 0.8742 0.892529166666667 -0.0183291666666666 6 0.8532 0.888145833333333 -0.0349458333333332 7 0.8607 0.891245833333333 -0.0305458333333333 8 0.9005 0.8964625 0.00403750000000003 9 0.9111 0.8988125 0.0122875000000001 10 0.9059 0.9044125 0.00148750000000003 11 0.8883 0.9140625 -0.0257625 12 0.8924 0.940945833333333 -0.0485458333333333 13 0.8833 1.1559275 -0.2726275 14 0.87 1.14951083333333 -0.279510833333333 15 0.8758 1.14709416666667 -0.271294166666667 16 0.8858 1.14171083333333 -0.255910833333333 17 0.917 1.16079416666667 -0.243794166666667 18 0.9554 1.15641083333333 -0.201010833333333 19 0.9922 1.15951083333333 -0.167310833333333 20 0.9778 1.1647275 -0.1869275 21 0.9808 1.1670775 -0.1862775 22 0.9811 1.1726775 -0.1915775 23 1.0014 1.1823275 -0.1809275 24 1.0183 1.20921083333333 -0.190910833333333 25 1.0622 1.1559275 -0.0937275000000003 26 1.0773 1.14951083333333 -0.0722108333333331 27 1.0807 1.14709416666667 -0.0663941666666667 28 1.0848 1.14171083333333 -0.0569108333333333 29 1.1582 1.16079416666667 -0.00259416666666679 30 1.1663 1.15641083333333 0.0098891666666666 31 1.1372 1.15951083333333 -0.0223108333333333 32 1.1139 1.1647275 -0.0508275000000001 33 1.1222 1.1670775 -0.0448774999999999 34 1.1692 1.1726775 -0.00347750000000003 35 1.1702 1.1823275 -0.0121275000000001 36 1.2286 1.20921083333333 0.0193891666666666 37 1.2613 1.1559275 0.105372500000000 38 1.2646 1.14951083333333 0.115089166666667 39 1.2262 1.14709416666667 0.0791058333333333 40 1.1985 1.14171083333333 0.0567891666666666 41 1.2007 1.16079416666667 0.0399058333333334 42 1.2138 1.15641083333333 0.0573891666666667 43 1.2266 1.15951083333333 0.0670891666666666 44 1.2176 1.1647275 0.0528725000000001 45 1.2218 1.1670775 0.0547225 46 1.249 1.1726775 0.0763225 47 1.2991 1.1823275 0.1167725 48 1.3408 1.20921083333333 0.131589166666667 49 1.3119 1.1559275 0.155972500000000 50 1.3014 1.14951083333333 0.151889166666667 51 1.3201 1.14709416666667 0.173005833333333 52 1.2938 1.14171083333333 0.152089166666667 53 1.2694 1.16079416666667 0.108605833333333 54 1.2165 1.15641083333333 0.0600891666666666 55 1.2037 1.15951083333333 0.0441891666666667 56 1.2292 1.1647275 0.0644725000000001 57 1.2256 1.1670775 0.0585225 58 1.2015 1.1726775 0.0288225000000000 59 1.1786 1.1823275 -0.00372749999999989 60 1.1856 1.20921083333333 -0.0236108333333334 61 1.2103 1.1559275 0.0543724999999996 62 1.1938 1.14951083333333 0.0442891666666669 63 1.202 1.14709416666667 0.0549058333333333 64 1.2271 1.14171083333333 0.0853891666666668 65 1.277 1.16079416666667 0.116205833333333 66 1.265 1.15641083333333 0.108589166666667 67 1.2684 1.15951083333333 0.108889166666667 68 1.2811 1.1647275 0.1163725 69 1.2727 1.1670775 0.1056225 70 1.2611 1.1726775 0.0884225 71 1.2881 1.1823275 0.1057725 72 1.3213 1.20921083333333 0.112089166666667

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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