# How do you find a linear model?

Jul 4, 2015

For experimental data it may be appropriate to use linear regression.

On the other hand, for precise data you do not need linear regression.

#### Explanation:

If you have a number of experimentally generated data points that are subject to inaccuracies then you can use something like linear regression to generate a linear model that fits the data reasonably well. Many modern calculators have a linear regression capability.

On the other hand, if you are given precise data, you should be able to generate a model that fits the data exactly. For example, given points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ which are supposed to lie on a line, the equation of the line in point-slope form is:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$ where $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

from which we can derive the slope-intercept form:

$y = m x + c$ where $c = {y}_{1} - m {x}_{1}$