Question
The “not-a-knot” condition on these functions requires continuity of the third derivative at the second and next-to-last points. For 10 points each:
[10m] Name these piecewise polynomial functions. Control points are used to adjust the shape of their “B” type.
ANSWER: splines [accept cubic splines or B-splines]
[10e] Splines are preferred over summing together polynomial basis functions for this task of approximating a function from a set of discrete data points.
ANSWER: interpolation [or interpolating a function or interpolate a function]
[10h] Unlike regression splines or natural splines, these splines do not require selecting knots, since they treat every unique value in the input as a knot. These splines control for overfitting by using a sum of squared errors loss function that is penalized by the integral of the squared second derivative of the spline.
ANSWER: smoothing splines [reject “smooth splines”]
Data
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total |
|---|---|---|---|---|---|
| Chicago A | Florida A | 10 | 10 | 0 | 20 |
| Chicago C | Toronto A | 10 | 10 | 0 | 20 |
| Claremont A | Penn A | 10 | 10 | 0 | 20 |
| Columbia A | Cornell B | 10 | 10 | 0 | 20 |
| Columbia B | Vanderbilt A | 10 | 10 | 0 | 20 |
| Cornell A | Yale A | 10 | 10 | 0 | 20 |
| Duke A | WUSTL A | 0 | 10 | 0 | 10 |
| Georgia Tech A | Chicago B | 10 | 10 | 0 | 20 |
| Imperial A | Rutgers B | 10 | 10 | 0 | 20 |
| Indiana A | Harvard A | 0 | 10 | 0 | 10 |
| Maryland A | Stanford A | 0 | 10 | 0 | 10 |
| McGill A | Iowa State A | 10 | 10 | 0 | 20 |
| Michigan A | Johns Hopkins A | 0 | 10 | 0 | 10 |
| Minnesota A | Northwestern A | 10 | 10 | 0 | 20 |
| North Carolina A | MIT A | 10 | 10 | 0 | 20 |
| Ohio State A | Brown A | 0 | 10 | 0 | 10 |
| Purdue A | Florida B | 0 | 10 | 0 | 10 |
| Rutgers A | South Carolina A | 0 | 10 | 0 | 10 |
| UC Berkeley A | Texas A | 10 | 10 | 0 | 20 |
| UC Berkeley B | Minnesota B | 10 | 10 | 0 | 20 |
| Virginia A | Illinois A | 0 | 10 | 0 | 10 |
| WUSTL B | Georgia Tech B | 0 | 0 | 0 | 0 |
| Yale B | Penn State A | 0 | 10 | 0 | 10 |