Browsing by Author "Lähteenmäki, Mervi"

The main objective of regularization is to minimize the prediction error in a multiple regression model by reducing the variance of the estimator via shrinkage of the parameter norm. In regularization, the loss function of the model is minimized subject to an extra condition that penalizes the size of the parameter, which condition depends on the applied method. Regularization may produce unambiguous and consistent estimates also for high-dimensional data sets in which the amount of independent variables exceeds the sample size, or for data sets including highly correlated predictors. L1-regularization, also known as the Lasso (Least Absolute Shrinkage and Selection Operator), is one of the most popular methods in linear regression. Lasso is well-known for its property to perform the variable selection and estimation simultaneously. In addition, Lasso is computationally efficient as it is a convex optimization algorithm, which makes it also applicable for high-dimensional data sets. In the thesis, we focus on the theory of regularized linear regression, after which we form a prediction model for the sales of a specific consumer product by using collected data and applying the Lasso, Elastic net and OLS post-Lasso methods. We compare the results to those obtained by best subset selection using a stepwise algorithm. In our study, the regularized models result in more accurate predictions than the model obtained by stepwise algorithm, in terms of test data prediction error. All regularized algorithms selected the same subset of variables, the models differing only in that OLS post-Lasso coefficients were systematically larger in absolute size than the Lasso and Elastic Net coefficients, resulting in the smallest prediction error for OLS post-Lasso. Lasso and Elastic Net generated an equal and to some extent underfitted model.