[surroundingbox]

The general case require some work and conditions. But to give a hint, the case of only one parameter is an application of the mean value theorem (1). Suppose a model (y = f(p,x) ) with only one parameter p0 and an exact point (x0,y0) (that is y0=f(p0,x)) and a data point (x0,y1) such that y1-y0=error in the data. And that there is a value p1 of the parameter such that f(p1,x0) = y1, then y1 - y0 = f(p1,x0) - f(p0,x0) = f'(sigma) . (p1-p0), so that p1-p0 = (y1-y0)/f'(sigma) that is (error in the parameter) = (error in the data)/(derivative with respect to the parameter) where sigma is between p0 and p1. The general case is a generalization of this idea using the mean value inequality.

(1) https://en.wikipedia.org/wiki/Mean_value_theorem