IsoplotR (version 0.11)

yorkfit: Linear regression of X,Y-variables with correlated errors

Description

Implements the unified regression algorithm of York et al. (2004) which, although based on least squares, yields results that are consistent with maximum likelihood estimates of Ludwig and Titterington (1994)

Usage

yorkfit(x)

Arguments

x

a 5-column matrix with the X-values, the analytical uncertainties of the X-values, the Y-values, the analytical uncertainties of the Y-values, and the correlation coefficients of the X- and Y-values.

Value

a four-element list of vectors containing:

a

the intercept of the straight line fit and its standard error

b

the slope of the fit and its standard error

cov.ab

the covariance of the slope and intercept

mswd

the mean square of the residuals (a.k.a `reduced Chi-square') statistic

References

Ludwig, K. R., and D. M. Titterington. "Calculation of \(^{230}\)Th/U isochrons, ages, and errors." Geochimica et Cosmochimica Acta 58.22 (1994): 5031-5042. York, Derek, et al. "Unified equations for the slope, intercept, and standard errors of the best straight line." American Journal of Physics 72.3 (2004): 367-375.

Examples

   X <- c(1.550,12.395,20.445,20.435,20.610,24.900,
          28.530,50.540,51.595,86.51,106.40,157.35)
   Y <- c(.7268,.7849,.8200,.8156,.8160,.8322,
          .8642,.9584,.9617,1.135,1.230,1.490)
   n <- length(X)
   sX <- X*0.01
   sY <- Y*0.005
   rXY <- rep(0.8,n)
   dat <- cbind(X,sX,Y,sY,rXY)
   fit <- yorkfit(dat)
   covmat <- matrix(0,2,2)
   plot(range(X),fit$a[1]+fit$b[1]*range(X),type='l',ylim=range(Y))
   for (i in 1:n){
       covmat[1,1] <- sX[i]^2
       covmat[2,2] <- sY[i]^2
       covmat[1,2] <- rXY[i]*sX[i]*sY[i]
       covmat[2,1] <- covmat[1,2]
       ell <- ellipse(X[i],Y[i],covmat,alpha=0.05)
       polygon(ell)
   }