Question

How do you find a linear model?

Answer 1

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 `(x_1, y_1)` and `(x_2, y_2)` which are supposed to lie on a line, the equation of the line in point-slope form is:

`y - y_1 = m(x - x_1)` where `m = (y_2 - y_1) / (x_2 - x_1)`

from which we can derive the slope-intercept form:

`y = mx + c` where `c = y_1 - mx_1`