The present invention provides methods for providing mathematical regression analysis. In particular, the method for conducting regression analysis comprises the steps of: selecting a regression model; selecting an initial set of regression parameters; applying the regression model to the initial set of regression parameters to create an initial set of regression values; selecting an improved set of regression values, wherein the improved set of regression values is selected from the set of initial regression values; generating a loss function based on the improved set; applying an iterative optimization method to the loss function and the improved set of regression values to generate a resultant set of regression values; and outputting the resultant set of regression values.