Minimum number of observations in non-linear regression

Question

Are 5 observations enough to verify the following non-linear regression model in the form: $ Y= C K_0^{\alpha_0}K_1^{\alpha_1}K_2^{\alpha_2}$ And in general how many observations do I need for models of this kind?

Answer 1

Are all of those variables unknown? If so, then $5$ won't cut it. Take the logarithm of both sides and convert the problem into a linear regression problem. To solve the resulting set of linear equations, you will need at least $7$ data points.

I just realized: where is your independent variable, $X$?