# Finding the equation to a non-linear set of points

by Joshk80k
Tags: equation, nonlinear, points
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,339 A "linear regression" line or "least squares line" is a line that does NOT go through all the points but comes "closest" in the sense of the average distance from each point to the line being smallest. You could, as zachach suggests, use a piecewise linear function- although you might need 3, not two pieces- a line from (12. 270) to (14, 300), a line from (14, 300) to (16, 330), and a line from (16, 330) to (18. 380). It is also true that there exists a unique n-1 or less degree polynomial through any given n points. Here you have four points so there exist a unique cubic (or less) polynomial whose graph passes through those four points. Write the polynomial as $y= ax^3+ bx+ c+ d$ and put in the given x and y values to get four linear equations to solve for a, b, c, and d.