ABSTRACT
Regression analysis builds mathematical models that examine the relationship of a dependent variable to one or more independent variables. These models may be used to predict responses at unobserved and/or future values of the independent variables. In the simple case when both the dependent variable y and the independent variable x are scalar variables, given observations (xi, yi) for i = 1, . . . , n, a regression model relates dependent and independent variables as follows:
yi = f(xi) + ǫi, i = 1, . . . , n, (1.1)
where f is the regression function and ǫi are zero-mean independent random errors with a common variance σ2. The goal of regression analysis is to construct a model for f and estimate it based on noisy data.
