# Derivation of Line of Best Fit

**1. The problem statement, all variables and given/known data**

Consider a set of data points: (x1, y1), (x2,y2). One seeks to find the best coefficients A and B such that the sum of squared vertical distances of the data f(x) = Ax + B is minimized. Let D = ∑[y

_{i}– f(x

_{i}]

^{2}. By requiring the derivatives of D respect to both A and B each to vanish, find expressions for the values of A and B in terms of the data points. Why are these derivatives made to vanish?

**2. Relevant equations**

Line of best fit is a linear equation: f(x) = Ax + B

D must be a minimum

**3. The attempt at a solution**

I am totally lost by this question. I do not understand how to differentiate D with respect to these parameters (maybe implicit differentiation?)

http://ift.tt/1ktQz8a

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