Three rational functions are provided in GenStat, each of which is a ratio of polynomials.
Linear-by-linear
Y = a + b / (1 + d*X)
This produces a rectangular hyperbola.
Quadratic-by-linear
Y = a + b/(1 + d*X) + c*X
This produces a hyperbola with non-horizontal asymptote.
Quadratic-by-quadratic
Y = a + (b + c*X)/(1 + d*X + e*X*X)
This is a cubic curve with asymmetric maximum, falling to an asymptote.
See Also