Finding the best water line: the least squares method in action
Unreviewed Activity submitted in preparation for the NNN Writing
with Numbers Workshop In this project, students are introduced
to several different ways of measuring the goodness of fit of a
line representing a perforated pipe or straight hose used to
water several bushes. They use the least squares method to
compare different possible "water lines", and are guided in the
use of the derivative to make the sum of squared errors as small
as possible. Consider various ways of measuring the total error
of a line used to fit data points on a scatterplot. Master the
use of the least squares method to determine which of several
proposed lines fits the data best. Estimate the best line and
find the resulting sum of squared errors. For students with
calculus background, use calculus to optimize the choice of
line. Context for Use I use this in Calculus I as a project done
over 2 to 3 weeks, after they have learned how to take the
derivative of a polynomi