Model II regression should be used when the two variables in the regression equation are random and subject to error, i.e. not controlled by the researcher. Model I regression using ordinary least squares underestimates the slope of the linear relationship between the variables when they both contain error. According to Sokal and Rohlf (1995), the subject of Model II regression is one on which research and controversy are continuing and definitive recommendations are difficult to make.

RMAREGRESS is a Model II procedure. Ranged major axis regression is only described in Legendre and Legendre (1998:511-512). The slope estimator has several desirable properties when the variables x and y are not expressed in the same units or when the error variances on the two axes differ. The slope estimator scales proportionally to the units of the two variables: the position of the regression line in the
scatter of points remains the same irrespective of any linear change of scale of the variables. The estimator is sensitive to the covariance of the variables. The procedure should not be used in the presence of outliers because they cause important changes to the estimates of the ranges of the variables.

Ranged major axis regression is major axis regression (MAREGRESS) computed from ranged data.

[B,BINT,L,ANG,R] = RMAREGRESS(X,Y,ALPHA) returns the vector B of regression coefficients in the linear Model II, a matrix BINT of the given confidence intervals for B, the L eigenvalues of the axes, the angle in degrees of the confidence bounds, and R the minimum and maximum x and y ratio-scales.

RMAREGRESS treats NaNs in X or Y as missing values, and removes them.

Syntax: [b,bint,l,ang,r] = rmaregress(x,y,s,alpha)