# Cross validation with parametric model clarification

I need a clarification about the Cross validation in parametric model such as a simple linear regression: Are the coefficients of the final model the mean of the coefficients estimated in each round? Only in this case a can see a reduction in variance of the model, infact
$$var(\overline{\beta_i}) = \sigma^2_{\beta_i}/n$$
Different is for non parametric models such as decision trees, which they have hyper parameters, in that case is just model selection. Am I interpreting correctly?