The following equation: y = a*x**b where y is a nonlinear function of x. By taking logs, the equation can be expressed as: ln(y) = ln(a) + bln(x). I would like to run a quantile regression instead of least squares. In Python, Scipy.optimize.curve_fit can handle exponential model functions (since a is nonlinear) but the method doesn't allow for quantile regression. Questions:
- Is it a correct assumption that least squares cannot be used, i.e. because the intercept is nonlinear?
- If yes, how to fit using quantile regression?