CURVE FITTING SIMULATIONSTEM PD Grant

Stephanie Sorensen

Monterey High School

http://phet.colorado.edu/sims/curve-fitting/curve-fitting_en.html

Problem Statement

What is the ideal number of data points for each linear, quadratic, cubic, and quartic that you can have and still have a correlation coefficient of 1?

Solution

Linear : 2 points Quadratic : 3 points Cubic : 4 points Quartic : 5 points Essentially one more than the degree of

the regression

Suggestions

Students play around with adding and removing points to see how r2 and equation are affected

If app is set to bet fit quartic, the equation will always show the lowest degree

Extension

How do the deviations assist in finding the best fit?

What are the deviations when r2 = 1? What happens to r2/deviations as more

than the ideal number of data points are added?

What happens to the coefficients A, B, C, D, and E if you add points below the x axis? Or only to the right of the y-axis?

Linear – 2 points

Quadratic – 3 points

Cubic – 4 points

Quartic – 5 points

6 points…