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I want to take data sets and come up with equations to predict, outside the usual of what they teach in statistics classes. In statistics, they have multiple regression which takes multiple independent variables (X and more) to predict a dependent variable (Y) on multidimensional scatterplots. However, I want to see if I can tweak it to make it more precise, perhaps adding Calculus and others to an equation.

Since I don't have a degree in Math, but rather minor in Statistics, I'm not as mathematical savy. So I was thinking if I could find a free computer program that helps you "visualize" how a wide variety mathematical equations/concepts work, then look at data sets/scatterplots, maybe I can brainstorm various formats for new equations, and then work out the details from there? Are there any free computer programs that one can download, which help you visualize 3D concepts in math, possibly allowing you to use your mouse to maneuver the image around? If not 3D visualizing, perhaps anything else that allows you to concept-ualize the many concepts within Trigonometry, Calculus, Polynomials, Geometry, and much much more, so that I can look at a scatterplot and get ideas? Anything that can give me insight?

Any help would be greatly appreciated!