What is a line of best fit?

1 Answer
George C.
Dec 19, 2017

A line of best fit is a particular linear function chosen to fit some data points.

Explanation:

A line of best fit is a particular linear function chosen to model a set of data points.

For example, given points (1, 2), (2, 4), (3, 5), (4, 7) we might want to find a line which approximates the relation between the x and y coordinates of the points, something like:

graph{(y-4.5-1.5(x-2.5))((x-1)^2+(y-2)^2-0.01)((x-2)^2+(y-4)^2-0.01)((x-3)^2+(y-5)^2-0.01)((x-4)^2+(y-7)^2-0.01) = 0 [-9.66, 10.34, -1.44, 8.56]}

Here, due to the symmetry of the points, I chose to make the line run through (5/2, 9/2) and have slope 3/2.

So the linear function can be written:

f(x) = 3/2(x-5/2)+9/2

or:

f(x) = 3/2x+3/4

More generally you might seek to minimise the sum of the squares of the distances of the points from the line, or the squares of their y offsets. The process of finding such a line of best fit is called linear regression.

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