How do you find two curves that enclose a set of data points?

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I'd assume you'd use least squares here to first get the best fit line for the data, but I need to specifically minimize the vertical distance between the two curves. Originally, I was thinking I'd find the least squares solution and then compute an upper bound/lower bound summation integral to get two functions that bound the data, but now I'm not so sure about that, and whether it's a right approach or not, since I can't guarantee that the vertical distance between the two curves is at minimum really. Any suggestions?