# Interpolation vs Regression

• Jun 6th 2011, 11:06 PM
JoernE
Interpolation vs Regression
Hi,
Can someone please explain the difference between interpolation and regression?

I've read conflicting comments through the multiple webpages I've read.

Is it true that linear and nonlinear regression is a "line of best fit" using a linear function and a polynomial respectively, whereas interpolation must "go through" the data points?

Thanks for any explanation you can provide.
• Jun 6th 2011, 11:11 PM
Prove It
Regression is the process of finding the line of best fit. Interpolation is the process of using the line of best fit to estimate the value of one variable from the value of another, provided that the value you are using is within the range of your data. If it's outside the range, then you would be using Extrapolation.
• Jun 7th 2011, 12:51 AM
CaptainBlack
Quote:

Originally Posted by JoernE
Hi,
Can someone please explain the difference between interpolation and regression?

I've read conflicting comments through the multiple webpages I've read.

Is it true that linear and nonlinear regression is a "line of best fit" using a linear function and a polynomial respectively, whereas interpolation must "go through" the data points?

Thanks for any explanation you can provide.

Regression is the process of finding a curve/function/line of best fit (minimising some function measuring the error between the regression prediction of a data value and the observed data value). A regression fit does not generally pass through the data points.

Interpolation is finding an approximation to the value of a function defined by its values on a discrete set at a point not necessarily in the set on which the function values are known. Typically an interpolation scheme will give the tabulated function values for the points at which the function is tabulated. Also interpolation is usually confined to points in some sense between the tabulated points.

CB