The basic principle behind parametric price estimating is that you can use basic properties of the item you are going to buy (size, power, temperature, etc) and find some regression curve that relates to price. A simple example might be the price of a tank P=(V/V0)^.65 where P is price, V is the volume of the tank you want to buy, and V0 is a basis volume given for this equation. The .65 is the constant found to best match this regression, and is often just given to you in text books.
My question is, how did they get to .65? I am trying to develop my own parametric equations using data I have collected myself. However I can't figure out which constants to use or how to come up with best regression curves. I know there must be a method for doing this.
The easiest way is to put your data into Excel and ask it to perform the regression. Plot the data on an XY chart and add trendline. There is a menu for various kinds of curves to use. Pick the one that works best for you.
The basic idea is to have your fitting function depend on some parameters. You have a bunch of data points, $V_i, P_i$ and your function may be $P=cV^k$. You want to find the values of $c,k$ that make the best fit. The error is usually taken as the sum of the squares of the error at each point, so you have $$error=\sum_i(P_i-cV_i^k)^2$$. Now you take the partial derivative of the error with respect to each of $c$ and $k$, set it to zero, and solve. Finding the proper functional form can be an art. If the function is linear in the parameters you can do a simple linear equation solution, so people would often fit this as $\log P= k \log V + \log c$. Any numerical analysis text will have an extensive discussion.