In math, what is a "curve of best fit"?

Question

Can someone explain what type of graph this is? Why is used? How is it used? My textbook doesn't really mention it and it's going to be on the test.

Thank you.

Answer 1

A 'curve of best fit' is a curve that 'approximates' a set of sampled data points in a way that minimizes (in some way) some parameter that measures the 'goodnes of fit' of the curve. In the case of a straight line, it's usually the square root of the sums of the squares of the distance from the line to each of the sampled data points. When this number is minimum, the line 'fits' the data in the least squares sense.

When dealing with higher-order data sets, sometimes you want to try and get a best fit to some other type of curve. A parabola, an exponential, a logarithm etc.

HTH

Doug

Answer 2

well lets say you are given a plot of points that look like they are taking the shape of a curve....
curve of best fit is pretty much the equation of a curve that best fits a given number of points. there is a method of calculating the curve based on the given points but i forgot :(

its slightly different than linear interpolation or line of best fit in that it doesnt take the form y=mx+b .....rather x^2, x^3, and so on - curve equations....