Regression splines model a nonlinear relationship by splitting the range of a predictor variable X into K intervals and fitting a separate polynomial on each interval. The pieces are estimated so that the final curve joins smoothly at the knot locations. For example, if X runs from 0 to 100 and knots are placed at 25, 50, and 75, one polynomial is fit on 0-25, another on 25-50, and so on, with the pieces connected at each knot.