Kernel regression is an elegant method of extending generalized linear regression to infinite-dimensional subspaces by leveraging the tools developed for linear regression. In generalized linear regression, the exogenous variables are linear. By including higher powers and non-linear combinations of exogenous variables, we can take one step toward generalization. This enhancement enables us to improve the accuracy of the fitted model. As an example, let us try to fit a logistic regression model (from the class of generalized linear models) to data shown in Figure 4.1. Logistic regression would attempt to fit a model shown in Equation 4-1. However, it only involves linear exogenous variables. If one augments the space of exogenous variables by adding \(\frac {x^2}{a^2} + \frac {y^2}{b^2}\) , one can use logistic regression to classify the points. This modified equation is shown in Equation 4-2.