What is a line of best fit?

1 Answer
Dec 19, 2017

Answer:

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.