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Tijdreeks 1 Outliers?

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

Title produced by software: Multiple Regression

Date of computation: Fri, 07 Dec 2007 04:41:33 -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/Dec/07/t1197026934aeohpvkw9wt135c.htm/, Retrieved Fri, 07 Dec 2007 12:29:04 +0100

User-defined keywords:

Dataseries X:

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1,1608 0 1,1208 0 1,0883 0 1,0704 0 1,0628 0 1,0378 0 1,0353 0 1,0604 0 1,0501 0 1,0706 0 1,0338 0 1,0110 0 1,0137 0 0,9834 0 0,9643 0 0,9470 0 0,9060 0 0,9492 0 0,9397 0 0,9041 0 0,8721 0 0,8552 0 0,8564 0 0,8973 0 0,9383 0 0,9217 0 0,9095 0 0,8920 0 0,8742 0 0,8532 0 0,8607 0 0,9005 0 0,9111 1 0,9059 1 0,8883 1 0,8924 1 0,8833 1 0,8700 1 0,8758 1 0,8858 1 0,9170 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

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] = + 0.978875 + 0.0468416666666669x[t] + 0.0122844444444448M1[t] -0.00480611111111124M2[t] -0.0157966666666668M3[t] -0.0235872222222223M4[t] -0.0160177777777779M5[t] -0.00734833333333342M6[t] -0.00677888888888897M7[t] -0.00852944444444454M8[t] -0.0220483333333335M9[t] -0.012978888888889M10[t] -0.0194294444444445M11[t] + 7.05555555555448e-05t + 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) 0.978875 0.060727 16.1193 0 0 x 0.0468416666666669 0.058435 0.8016 0.426901 0.21345 M1 0.0122844444444448 0.070868 0.1733 0.863143 0.431572 M2 -0.00480611111111124 0.070687 -0.068 0.946087 0.473044 M3 -0.0157966666666668 0.070546 -0.2239 0.823812 0.411906 M4 -0.0235872222222223 0.070445 -0.3348 0.739275 0.369638 M5 -0.0160177777777779 0.070385 -0.2276 0.820986 0.410493 M6 -0.00734833333333342 0.070365 -0.1044 0.91728 0.45864 M7 -0.00677888888888897 0.070385 -0.0963 0.923691 0.461846 M8 -0.00852944444444454 0.070445 -0.1211 0.904156 0.452078 M9 -0.0220483333333335 0.070304 -0.3136 0.755231 0.377616 M10 -0.012978888888889 0.070203 -0.1849 0.854138 0.427069 M11 -0.0194294444444445 0.070142 -0.277 0.783019 0.39151 t 7.05555555555448e-05 0.001687 0.0418 0.966818 0.483409 Multiple Linear Regression - Regression Statistics Multiple R 0.257737388983056 R-squared 0.0664285616798032 Adjusted R-squared -0.197406844801991 F-TEST (value) 0.251780314725829 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.995250764916281 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.110871822749110 Sum Squared Residuals 0.565457809666667 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.1608 0.991229999999998 0.169570000000002 2 1.1208 0.97421 0.146590000000000 3 1.0883 0.96329 0.12501 4 1.0704 0.95557 0.11483 5 1.0628 0.96321 0.0995899999999999 6 1.0378 0.97195 0.0658499999999999 7 1.0353 0.97259 0.0627099999999999 8 1.0604 0.97091 0.0894899999999999 9 1.0501 0.957461666666667 0.0926383333333332 10 1.0706 0.966601666666667 0.103998333333333 11 1.0338 0.960221666666667 0.0735783333333333 12 1.011 0.979721666666667 0.0312783333333331 13 1.0137 0.992076666666667 0.0216233333333328 14 0.9834 0.975056666666667 0.0083433333333333 15 0.9643 0.964136666666667 0.000163333333333293 16 0.947 0.956416666666667 -0.00941666666666674 17 0.906 0.964056666666667 -0.0580566666666666 18 0.9492 0.972796666666667 -0.0235966666666667 19 0.9397 0.973436666666667 -0.0337366666666667 20 0.9041 0.971756666666667 -0.0676566666666667 21 0.8721 0.958308333333333 -0.0862083333333333 22 0.8552 0.967448333333333 -0.112248333333333 23 0.8564 0.961068333333333 -0.104668333333333 24 0.8973 0.980568333333333 -0.0832683333333334 25 0.9383 0.992923333333334 -0.0546233333333338 26 0.9217 0.975903333333333 -0.0542033333333333 27 0.9095 0.964983333333333 -0.0554833333333333 28 0.892 0.957263333333333 -0.0652633333333332 29 0.8742 0.964903333333333 -0.0907033333333332 30 0.8532 0.973643333333333 -0.120443333333333 31 0.8607 0.974283333333333 -0.113583333333333 32 0.9005 0.972603333333333 -0.0721033333333332 33 0.9111 1.00599666666667 -0.0948966666666668 34 0.9059 1.01513666666667 -0.109236666666667 35 0.8883 1.00875666666667 -0.120456666666667 36 0.8924 1.02825666666667 -0.135856666666667 37 0.8833 1.04061166666667 -0.157311666666667 38 0.87 1.02359166666667 -0.153591666666667 39 0.8758 1.01267166666667 -0.136871666666667 40 0.8858 1.00495166666667 -0.119151666666667 41 0.917 1.01259166666667 -0.0955916666666666 42 0.9554 1.02133166666667 -0.0659316666666667 43 0.9922 1.02197166666667 -0.0297716666666667 44 0.9778 1.02029166666667 -0.0424916666666666 45 0.9808 1.00684333333333 -0.0260433333333333 46 0.9811 1.01598333333333 -0.0348833333333333 47 1.0014 1.00960333333333 -0.00820333333333322 48 1.0183 1.02910333333333 -0.0108033333333334 49 1.0622 1.04145833333333 0.0207416666666663 50 1.0773 1.02443833333333 0.0528616666666666 51 1.0807 1.01351833333333 0.0671816666666667 52 1.0848 1.00579833333333 0.0790016666666668 53 1.1582 1.01343833333333 0.144761666666667 54 1.1663 1.02217833333333 0.144121666666667 55 1.1372 1.02281833333333 0.114381666666667 56 1.1139 1.02113833333333 0.0927616666666667 57 1.1222 1.00769 0.114510000000000 58 1.1692 1.01683 0.15237 59 1.1702 1.01045 0.15975 60 1.2286 1.02995 0.19865

Charts produced by software:

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Parameters:

par1 = 1 ; 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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