For the last week my students have been working on using experimental results and statistical tests as evidence to either accept or refute someone else s or their own claims.

They are trying to show evidence of the Law of Conservation of Mechanical Energy.

The only measured values in the entire experiment are position and time.

Our motion sensors are giving us very clean data that fit to quadratic fit with a R^2 value = 1.

Using any of the numerical methods for taking the derivative of data set leads to results that get very "wobbly" as time goes on.

However when we replace the discrete values with the continuous function returned by regression, and then use basic calculus to take the derivative we are able to get clean functions for velocity, acceleration, potential & Kinetic energy.

They are also able to clearly see that there is a loss do to air resistance, and actually solve the differential equation and measure the work done by this force.

In short as long as we give evidence that our experimental model achieved via regression is correct (R^2 values & Residuals Analysis all point very strongly to this) can we move out of the discrete domain and into the continuous domain where calculus works better and the data is far far cleaner for the students to see?

I've showed my students findings to a few other teachers and they say the kids should try and publish, but I would hate for them to be embarrassed do to us using regression and calculus if it is wrong to do so.

Any guidance would be appreciated.