Find a quadratic model for a set of values?

Question

We went over this in class but I didn't get it?

 

Can someone help?

 

Answer 1

Sure, Zack, I might be able to help.

Quadratic equations usually come in the form of y= a*x² + b*x + c, right?  So the plan is to come up with an equation for which the graph of that equation comes as close as possible to all of the given values.  This is computationally tricky, so instead of doing it directly, most people either use a computer or a short-cut.

 

The short cut I use to solve this problem is actually kind of simple.  Take the square root of all the given "y" values first, and leave the "x" values as they are.  Then, do a linear regression on those square roots to get a line.  This gives you the line that is closest to all the square roots of the given values.  That means that √y=(the results of your linear regression) and therefore that y=(your line)² .  Square a line, and you get a parabola.  Square the line that goes through the square roots of your target values, and you get the quadratic that goes through your targets.  The catch is, if any of your values are negative, you end up in imaginary number land for your square roots.  That complicates things.  But for the positive numbers case, this method should work pretty well.