I have collected data for a parametric function and id like to explain a bit of the methodology first.
If I launch a ball, the things I need to take into account are elevation change between me and the target, the x and y magnitude of the wind, how far left or right I am aimed, and how far I throw the ball.
I can know the wind, elevation, and distance to the target, but I can’t know how hard/where to hit it. My only data point for those are how far I DID hit it, and then the ball is usually a little off target.
How can I find an equation that will allow me to solve for a set of values for how left/right I should aim and how hard I should hit it given the x and y of the wind, elevation change, and distance to target?
To derive an equation for aiming and hitting the ball based on wind, elevation, and target distance, you could use regression analysis. Create a dataset with input variables (wind components, elevation change, distance to target) and corresponding output variables (how far you hit it and the deviation from the target). Then, apply regression techniques like linear regression or machine learning algorithms to find relationships and coefficients. This will help you establish an equation that estimates how left/right to aim and how hard to hit the ball based on the given parameters.