Nonlinear Regression

Suppose we were required to fit a regression line to a set of data that might have a curvilinear relationship.  How do we do this? First, let us discuss the concept of RSS, or residual sum of squares.


As in linear regression, a curve which best approximates a given set of data would minimize the difference between our data and the curve.  We call this quantity we are attempting to minimize the RSS, or residual sum of squares.  The RSS is the sum of the squared vertical distances between the observed data and the predicted data of the curve (we square the distance to avoid negative values).  This variable should come as close to zero as possible.


yi = observed data

f(p1,p2,x) = predicted data of the model curve

Two new values are utilized in this equation, p1 and p2. These values are the Parameter Values used to create the regression curve.