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I have a large set of data points received by experimentation and each point has n ,or let's say 8 in this case, independent variables and one output/dependent variable.

(x1, x2, x3, ...., xn) = y --> some measured output

How would I fit a "curve" through these points or interpolate with the data points? I am not too sure where to start with this. If there area any general formulas or keywords that anyone can pass along to get me started in the right direction, that would be much appreciated.

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If you want to get an exact fit, use Lagrange polynomials. In your case, this will fit a 7th-degree polynomial through your data.

However, I think that's probably not what you want to do. If you want to "learn" how to predict $y$ given the $x_i$s, look into gradient descent algorithms. The Coursera machine learning course has a good introduction.

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  • $\begingroup$ How would I use Lagrange beyond 1 input variable? Is there a general formula for Lagrange for m input variables? $\endgroup$
    – GratefulNoobie
    Commented Jun 12, 2014 at 21:12
  • $\begingroup$ You should only use Lagrange if you want to fit the data exactly... however I doubt that this is what you want (and it's also impossible if you have more than one data point). You should look into linear regression algorithms such as gradient descent. $\endgroup$
    – liangjy
    Commented Jun 12, 2014 at 21:28
  • $\begingroup$ I do want to fit the data points exactly, as these are control points (my mistake for not clarifying sooner). So it is impossible to use Lagrange for more than 1 input variable (ie y = f(x1, x2, xy,..,x8)? Are there other types of interpolation or regression techniques that would allow for 8 independent variables? I am looking into gradient descent. $\endgroup$
    – GratefulNoobie
    Commented Jun 12, 2014 at 21:53

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