Question

What is a line of best fit?

Answer 1

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.